UNSATURATED SOILS: ADVANCES IN GEO-ENGINEERING
PROCEEDINGS OF THE FIRST EUROPEAN CONFERENCE ON UNSATURATED SOILS, E-UNSAT 2008, DURHAM, UNITED KINGDOM, JULY 2–4 2008
Unsaturated Soils: Advances in Geo-Engineering
Editors
D.G. Toll & C.E. Augarde School of Engineering, Durham University, Durham, UK
D. Gallipoli & S.J. Wheeler Department of Civil Engineering, University of Glasgow, Glasgow, UK
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Table of Contents
Preface
XIII
Organisation
XV
Keynotes Unsaturated soil mechanics in earth and rockfill dam engineering E.E. Alonso & N.M. Pinyol
3
Recent developments in the techniques of controlling and measuring suction in unsaturated soils P. Delage, E. Romero & A. Tarantino
33
Developments in modelling the generalised behaviour of unsaturated soils A. Gens, L. do N. Guimarães, M. Sánchez & D. Sheng
53
A thermo-hydro-mechanical stress-strain framework for modelling the performance of clay barriers in deep geological repositories for radioactive waste L. Laloui, B. François, M. Nuth, H. Peron & A. Koliji
63
Advances in testing techniques A novel suction-controlled true triaxial apparatus for unsaturated soils L.R. Hoyos, A. Laikram & A.J. Puppala
83
A simple shear apparatus for testing unsaturated soils S. Tombolato, A. Tarantino & L. Mongiovì
89
A device for simultaneous measurement of acoustic and hydraulic properties in unsaturated soils L.A. George, M.M. Dewoolkar & C. Wei
97
A modified triaxial apparatus to reduce testing time: Equipment and preliminary results J.C. Rojas, C. Mancuso & F. Vinale
103
A large physical model to simulate flowslides in pyroclastic soils L. Pagano, M.C. Zingariello & F. Vinale
111
Climatic chamber to model soil-atmosphere interaction in the centrifuge J. Tristancho & B. Caicedo
117
Experimental determination of unsaturated hydraulic conductivity in compacted silt J.J. Mu˜noz, V. De Gennaro & E. Delaure
123
Testing for coefficient of permeability of a sandy soil in the residual state zone N. Ebrahimi-Birang, D.G. Fredlund & L. Samarasekera
129
Preparation of unsaturated soils by oedometric compression B. Caicedo, J.C. Ulloa & C. Murillo
135
V
Influence of sample height on the soil water characteristic curve C.N. Khoury & G.A. Miller Observations of unsaturated soils by Environmental Scanning Electron Microscopy in dynamic mode S.D.N. Lourenço, D.G. Toll, C.E. Augarde, D. Gallipoli, A. Congreve, T. Smart & F.D. Evans
141
145
Recent advances in ESEM analysis of partially saturated geomaterials C. Sorgi, V. De Gennaro, H.D. Nguyen & P. Delalain
151
Study of desiccation crack evolution using image analysis S. Costa, J. Kodikara & N.I. Thusyanthan
159
Theoretical analysis of the effect of temperature, cable length and double-impedance probe head on TDR water content measurement A. Tarantino & A. Pozzato
165
Effect of dry density on the relationship between water content and TDR-measured apparent dielectric permittivity in compacted clay A. Pozzato, A. Tarantino, J. McCartney & J. Zornberg
173
Spatial Time Domain Reflectometry (Spatial TDR) – Principles, limitations and accuracy R. Becker, A. Scheuermann, S. Schlaeger, C. Huebner & N. Wagner
181
Spatial Time Domain Reflectometry (Spatial TDR) – On the use in geohydraulics and geotechnics A. Scheuermann, A. Bieberstein, Th. Triantafyllidis, C. Huebner, R. Becker, S. Schlaeger & N. Wagner
189
Water content dynamics in unsaturated soils – Results of experimental investigations in laboratory and in situ A. Scheuermann
197
A new high capacity tensiometer: First results J.C. Rojas, L. Pagano, M.C. Zingariello, C. Mancuso, G. Giordano & G. Passeggio
205
Evaluation of suction measurement by the tensiometer and the axis translation technique S.D.N. Lourenço, D.G. Toll, C.E. Augarde, D. Gallipoli, F.D. Evans & G.M. Medero
213
A system for field measurement of suction using high capacity tensiometers J. Mendes, D.G. Toll, C.E. Augarde & D. Gallipoli
219
Engineering behaviour Water retention behaviour and hydraulic properties Water retention properties of Boom clay: A comparison between different experimental techniques T.T. Le, P. Delage, Y.J. Cui, A.M. Tang, A. Lima, E. Romero, A. Gens & X.L. Li
229
Determination of soil suction state surface in pure and composite clays by filter paper method M. Biglari, A. Shafiee & I. Ashayeri
235
Soil water retention curves for remolded expansive soils K.C. Chao, J.D. Nelson, D.D. Overton & J.M. Cumbers
243
Hydromechanical couplings in confined MX80 bentonite during hydration D. Marcial, P. Delage & Y.J. Cui
249
VI
Effect of temperature on the water retention capacity of FEBEX and MX-80 bentonites M.V. Villar & R. Gómez-Espina Soil-water characteristic curves and void ratio changes relative to suction for soils from Greece M.E. Bardanis & M.J. Kavvadas
257
263
Prediction of soil-water retention properties of a lime stabilised compacted silt M. Cecconi & G. Russo
271
Time dependency of the water retention properties of a lime stabilised compacted soil D.V. Tedesco & G. Russo
277
Retention and compressibility properties of a partially saturated mine chalk H.D. Nguyen, V. De Gennaro, P. Delage & C. Sorgi
283
Effect of grain size distribution on water retention behaviour of well graded coarse material C. Hoffmann & A. Tarantino
291
Water retention functions of sand mixtures E. Imre, I. Laufer, K. Rajkai, A. Scheuermann, T. Firgi & G. Telekes
299
Permeability of a heavily compacted bentonite-sand mixture as sealing and buffer element for nuclear waste repository S.S. Agus & T. Schanz
305
Volumetric behaviour Volumetric behaviour of compacted London Clay during wetting and loading R. Monroy, L. Zdravkovic & A. Ridley Stress path dependence of hydromechanical behaviour of compacted scaly clay in wetting and drying suction controlled oedometer tests at constant vertical net stress C. Air`o Farulla
315
321
Long-term behaviour of lime-treated expansive soil submitted to cyclic wetting and drying O. Cuisinier & D. Deneele
327
Hydro-mechanical properties of compacted sand-bentonite in a semi-arid climate H. Bilsel & A. Iravanian
335
Grain size effects on rockfill constitutive behaviour A. Ramon, E.E. Alonso & E.E. Romero
341
The influence of suction on stiffness, viscosity and collapse of some volcanic ashy soils E. Bilotta, V. Foresta & G. Migliaro
349
Role of critical volumetric water content and net overburden pressure on swelling or collapse behavior of compacted soils I. Ashayeri, A. Shafiee & M. Biglari
355
The changes in stress regime during wetting of unsaturated compacted clays when laterally confined J.L. Brown & V. Sivakumar
361
Compression-induced suction change in a compacted expansive clay A.M. Tang, Y.J. Cui & N. Barnel
369
Theoretical modelling of the compaction curve N. Kurucuk, J. Kodikara & D.G. Fredlund
375
VII
Prediction of the residual void ratio of clayey soils after drying based on their initial state, physical properties and structure M.E. Bardanis & M.J. Kavvadas
381
An evaluation of soil suction measurements using the filter paper method and their use in volume change prediction J.M. Cumbers, J.D. Nelson, K.C. Chao & D.D. Overton
389
Validation of a swelling potential index for expansive soils J.L. Zheng, R. Zhang & H.P. Yang
397
Shear behaviour Effect of moisture content on tensile strength and fracture toughness of a silty soil M.R. Lakshmikantha, P.C. Prat, J. Tapia & A. Ledesma
405
Tensile strength of some compacted fine-grained soils A.J. Lutenegger & A. Rubin
411
Unsaturated characteristics of rammed earth P.A. Jaquin, C.E. Augarde & L. Legrand
417
Experimental study of the influence of suction on the residual friction angle of clays V. Merchán, J. Vaunat, E. Romero & T. Meca
423
Ultimate shear strength of unsaturated soils T.B. Hamid
429
Critical State conditions for an unsaturated artificially bonded soil D.G. Toll, Z. Ali Rahman & D. Gallipoli
435
Determination of the shear strength behavior of an unsaturated soil in the high suction range using the vapor pressure technique T. Nishimura, H. Toyota, S.K. Vanapalli & W.T. Oh
441
Effect of suction on compressibility and shear behaviour of unsaturated silty soil A.R. Estabragh & A.A. Javadi
449
Mechanical behaviour of an unsaturated clayey sand A. Mirzaii, S.S. Yasrebi & B. Gatmiri
453
Shear strength of unsaturated soil and its influence on slope stability O. Tomboy, V. Whenham, M. De Vos, R. Charlier, J. Maertens & J.-C. Verbrugge
459
Behaviour of a silt used in flood embankment construction in Indonesia G. McCloskey, M. Sanchez, M. Dyer & M. Kenny
465
Strength and yielding of unsaturated compacted silt from Beijing – Kowloon railway embankment J.K. Liu & L.Y. Peng
471
Estimation of the shear strength of lean clay based on empirical equations and a laboratory experiment on slope failure J.V. Vasquez & L.M. Salinas
475
Effects of drying and wetting cycles on unsaturated shear strength E.Y.M. Tse & C.W.W. Ng
481
Degradation of compacted marls due to suction changes R. Cardoso & E.E. Alonso
487
VIII
Multiaxial behavior of partially saturated sand at high stresses N. Massoudi, H.-Y. Ko & S. Sture
495
A simple method for the prediction of modulus of elasticity for unsaturated sandy soils S.K. Vanapalli, W.T. Oh & A.J. Puppala
503
Suction effects on the pre-failure behaviour of a compacted clayey soil J.A. Pineda, E.E. Romero & J.E. Colmenares
511
Influence of hydraulic paths on the low-strain shear modulus of a stiff clay J.A. Pineda, A. Lima & E. Romero
519
Drying and wetting effects on shear wave velocity of an unsaturated soil J. Xu, C.W.W. Ng & S.Y. Yung
525
Effects of unsaturated soil state on the local seismic response of soil deposits F. D’Onza, A. d’Onofrio & C. Mancuso
531
Constitutive modelling Thermo-plasticity in unsaturated soils, a constitutive approach B. François & L. Laloui
539
A thermomechanical framework for modeling the response of unsaturated soils S. Samat, J. Vaunat & A. Gens
547
Discussion on meta-stable equilibrium in unsaturated soils E.J. Murray, B.J. Murray & V. Sivakumar
553
Advanced hydro-mechanical coupling for unified constitutive modelling of unsaturated soils M. Nuth & L. Laloui
559
Generalised elasto-plastic stress-strain relations of a fully coupled hydro-mechanical model M. Lloret, M. Sanchez, M. Karstunen & S. Wheeler
567
Effect of degree of saturation on mechanical behaviour of unsaturated soils A.R. Estabragh & A.A. Javadi
575
An improved constitutive model for unsaturated and saturated soils K. Georgiadis, D.M. Potts & L. Zdravkovic
581
Modifying the Barcelona Basic Model to account for residual void ratio and subsequent decrease of shear strength relative to suction M.E. Bardanis & M.J. Kavvadas
589
A cap model for partially saturated soils R. Kohler, M. Hofmann & G. Hofstetter
597
Boundary surfaces and yield loci in unsaturated compacted clay A. Tarantino & S. Tombolato
603
Application to a compacted soil of a Cam Clay model extended to unsaturated conditions F. Casini, R. Vassallo, C. Mancuso & A. Desideri
609
Mixed isotropic-rotational hardening to model the deformational response of unsaturated compacted soils C. Jommi & E. Romero An anisotropic elasto-plastic model for unsaturated soils K. Stropeit, S.J. Wheeler & Y.J. Cui
IX
617 625
An elasto-viscoplastic model for chalk including suction effects F. Collin, V. De Gennaro, P. Delage & G. Priol
633
New basis for constitutive modelling of unsaturated aggregated soil with structure degradation A. Koliji, L. Vulliet & L. Laloui
641
A damage model for unsaturated natural loess submitted to cyclic loading J.M. Pereira, A.N. Ta, Y.J. Cui, J.P. Karam & H.Y. Chai
647
Desiccation shrinkage of unconstrained soil in the saturated phase L.B. Hu, T. Hueckel, H. Peron & L. Laloui
653
Modelling of the collapsible behaviour of unsaturated soils in hypoplasticity D. Mašín & N. Khalili
659
Swelling pressure in compacted bentonite: Laboratory tests and modelling M. Sanchez, M.V. Villar, R. Gómez-Espina, A. Lloret & A. Gens
667
Modelling water retention characteristic of unsaturated soils Y. Wang, G. Wu, S.M. Grove & M.G. Anderson
675
Temperature effect on hydric behaviour for unsaturated deformable soils S. Salager, M.S. El Youssoufi & C. Saix
683
A study of applied pressure on the Soil Water Characteristic Curve J. Zhou
689
Outline of the modelling of the excavated damaged zone in geological barriers C. Arson & B. Gatmiri
695
Numerical modelling Stress path dependency and non-convexity of unsaturated soil models D.C. Sheng, D. Pedroso & A.J. Abbo
705
Implicit integration of an extended Cam-clay model for unsaturated soils R. Tamagnini & V. De Gennaro
713
Parametric investigations on a three-invariant implicit integration algorithm for unsaturated soils L.R. Hoyos & P. Arduino A multi-cell extension to the Barcelona Basic Model W.T. Solowski, R.S. Crouch & D. Gallipoli
721 727
A numerical simulation of triaxial tests of unsaturated soil at constant water and air content by using an elasto-viscoplastic model F. Oka, H. Feng, S. Kimoto, T. Kodaka & H. Suzuki
735
Stress condition of an unsaturated pendular state granular soil C. Medina & M. Zeghal
743
A numerical investigation of steady-state unsaturated conductivity tests G. Steger, S. Semprich, M.P.H. Moncada, T.M.P. de Campos & E. Vargas Jr.
747
Numerical modelling of hydraulic hysteresis in unsaturated soils A.A. Javadi & A.S.I. Elkassas
755
The drift shadow phenomenon in an unsaturated fractured environment Claudia Cherubini, T.A. Ghezzehei & G.W. Su
761
X
Identification of hydraulic parameters for unsaturated soils using particle swarm optimization Y. Zhang, C.E. Augarde & D. Gallipoli
765
A precipitation boundary condition for finite element analysis P.G. Smith, D.M. Potts & T.I. Addenbrooke
773
On boundary condition in tunnels under partial saturation P. Gerard, R. Charlier & F. Collin
779
Numerical modelling of tree root-water-uptake in a multiphase medium S. Hemmati & B. Gatmiri
785
Numerical modelling of the soil surface moisture changes due to soil-atmosphere interaction S. Hemmati, B. Azari & B. Gatmiri
791
Identification of coupled hydro-mechanical model parameters with application to engineering barrier systems T. Schanz, M. Datcheva & M. Zimmerer
797
Surface flux boundary simplifications for flow through clay under landscaped conditions H.B. Dye, S.L. Houston & W.N. Houston
805
Preliminary analysis of tree-induced suctions on slope stability N. Ali & S.W. Rees
811
Numerical predictions of seasonal pore water pressure fluctuations using FLAC tp flow O.C. Davies, M. Rouainia & S. Glendinning
817
Infiltration analysis in unsaturated soil slopes J.F. Xue & K. Gavin
823
Prediction of changes in pore-water pressure response due to rainfall events M. Karthikeyan, D.G. Toll & K.K. Phoon
829
Modelling unsaturated soil slopes subjected to wetting and drying cycles Y.D. Zhou, C.Y. Cheuk, L.G. Tham & E.C.Y. To
835
Numerical analysis of piezocone penetrometer testing in partially saturated marine sediments A. Haghighi, B. Gatmiri, V. De Gennaro & N. Sultan
841
Experimental and numerical studies of the hydromechanical behaviour of a natural unsaturated swelling soil H. Nowamooz, M. Mrad, A. Abdallah & F. Masrouri
847
Numerical modelling of shallow foundations on swelling clay soil using the swelling equilibrium limit G.A. Siemens & J.A. Blatz
855
Meshfree modelling of two-dimensional contaminant transport through unsaturated porous media R. Praveen Kumar, G.R. Dodagoudar & B.N. Rao
861
Numerical modeling of hydraulic behavior of bioreactor landfills M.V. Khire & M. Mukherjee
867
Finite element modelling of contaminant transport in unsaturated soil A.A. Javadi & M.M. Al-Najjar
873
XI
Case studies Gulfs between theory and practice in unsaturated soil mechanics G.E. Blight
883
The repeatability of soil water balances at the same site from year to year G.E. Blight
889
Near-surface movement of water in unsaturated soil during evapotranspiration G.E. Blight
895
Studies of rainfall-induced landslides in Thailand and Singapore A. Jotisankasa, B. Kulsawan, D.G. Toll & H. Rahardjo
901
Field investigation on triggering mechanisms of fast landslides in unsaturated pyroclastic soils A. Evangelista, M.V. Nicotera, R. Papa & G. Urciuoli
909
Mechanical properties of unsaturated pyroclastic soils affected by fast landslide phenomena R. Papa, A. Evangelista, M.V. Nicotera & G. Urciuoli
917
Stability of a tailings dam considering the hydro-mechanical behaviour of tailings and climate factors M.T. Zandarín, L. Oldecop & R.R. Pacheco
925
A simplified model for the evaluation of the degree of saturation in slope stability analysis of shallow soils L. Montrasio & R. Valentino
933
Predicting the variation of stability with time for a slope in Switzerland A. Thielen & S.M. Springman
941
In situ field experiment to apply variable high water levels to a river levee P.A. Mayor, S.M. Springman & P. Teysseire
947
A new treatment for preventing landslides in expansive soil slopes H.P. Yang, Y.X. He & J.L. Zheng
953
Flow processes in the unsaturated Chalk of the Hallue Basin (France) N. Amraoui, H. Machard de Gramont, C. Robelin, A. Wuilleumier, M.L. Noyer & M.J. Feret
959
Loading-collapse tests for investigating compressibility and potential collapsibility of embankment coarse well graded material C. Hoffmann & A. Tarantino
967
An example of the impact of loess soils on foundations and earthworks in Kazakhstan S. Walthall & W.P. Duffy
973
Negative skin friction for cast-in-place piles in thick collapsible loess Z.H. Chen, X.F. Huang, B. Qin, X.W. Fang & J.F. Guo
979
Author index
987
XII
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Preface
This volume of proceedings of the First European Conference on Unsaturated Soils is the first publication to focus on European research developments in geo-engineering applications of unsaturated soils. The resurgence of interest in unsaturated soil research within Europe in recent years has lead to major advances. We are fortunate to have the latest developments reported here, in the 136 papers from leading international researchers and practitioners. The volume contains 90 papers from 15 countries within Europe with a further 46 contributions from 15 other countries. It hence represents European advances in geo-engineering together with an international state-of-the-art perspective on unsaturated soils in 2008. The volume addresses five areas: Advances in testing techniques, Engineering behaviour, Constitutive modelling, Numerical modelling and Case histories. The areas of application include slope stability, foundations, dams, contaminated land, landfill and nuclear waste repositories. It therefore provides a comprehensive collection that we believe geo-engineers will come to treat as essential reference material. Keynote papers from four international leading researchers are contained in the volume. We are grateful for the participation of Professors Eduardo Alonso, Pierre Delage, Antonio Gens and Lyesse Laloui. There is no doubt that these keynote papers will be seen as landmark contributions in unsaturated soil research. The motivation for organising this First European Conference on Unsaturated Soils grew from the MUSE project (Mechanics of Unsaturated Soils for Engineering: http://muse.dur.ac.uk) funded by the European Community. The editors (from Durham and Glasgow Universities) would like to thank our MUSE colleagues from Ecole Nationale des Ponts et Chaussées in France; Universitat Politécnica de Catalunya in Spain; Università degli Studi di Trento and Università degli Studi di Napoli Federico II in Italy for their support, both for this conference and our joint research activities. We would also like to acknowledge the vital role played by the Technical Advisory Committee members who have contributed to the very thorough reviews that have ensured the high technical quality of the papers accepted for inclusion in these Proceedings. We also thank the International Society of Soil Mechanics and Geotechnical Engineering, and in particular Technical Committee 6 on Unsaturated Soils, for their support of the conference. Particular thanks are due to Professor Pedro Seco e Pinto (President of ISSMGE), Professor Neil Taylor (General Secretary ISSMGE), Professor Eduardo Alonso (Chair of TC6) and Professor Gerald Miller (Secretary TC6). We hope that this first conference, and this volume of proceedings, will form the foundation and the impetus for a future series of European Conferences on Unsaturated Soils. We look forward to many such successful conferences and research collaborations in the future. David Toll & Charles Augarde (Durham University) Domenico Gallipoli & Simon Wheeler (University of Glasgow)
XIII
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Organisation
Organizing Committee C.E. Augarde (Durham University) R.S. Crouch (Durham University) D. Gallipoli (University of Glasgow) D.G. Toll (Durham University) S.J. Wheeler (University of Glasgow) Technical Advisory Committee E.E. Alonso (Spain) G.E. Blight (South Africa) J.B. Burland (United Kingdom) Y.J. Cui (France) T.M.P. de Campos (Brazil) R. Charlier (Belgium) P. Delage (France) D.G. Fredlund (Canada) A. Gens (Spain) S.L. Houston (United States of America) D. Karube (Japan) N. Khalili (Australia) L. Laloui (Switzerland) C. Mancuso (Italy) J. McDougall (United Kingdom) G.M. Medero (United Kingdom) C.W.W. Ng (Hong Kong) H. Rahardjo (Singapore) A. Ridley (United Kingdom) M. Sanchez (United Kingdom) T. Schanz (Germany) V. Sivakumar (United Kingdom) A. Tarantino (Italy) H. Thomas (United Kingdom)
XV
Keynotes
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Unsaturated soil mechanics in earth and rockfill dam engineering E.E. Alonso & N.M. Pinyol Universitat Politècnica de Catalunya, Barcelona, Spain
ABSTRACT: The paper examines a few relevant aspects of the design and performance of earth and rockfill dams. It covers the behaviour of compacted soil and rockfill, the generation of pore pressures and deformations during construction, the seepage phenomena during the operation of the dam, the important case of drawdown and a case history of a dam failure at the end of impoundment. It is argued that unsaturated soil mechanics offers today theories, experimental procedures and computational tools which provide a definite advantage over classical design methods. It offers also a new insight into field observations.
1
of the project. Typically, the upstream and downstream slopes should exhibit adequate safety factors at the end of construction, during reservoir impoundment and during the operational phase, including drawdown and long-term steady state conditions as a limiting case. In addition, other failure possibilities should be examined. They include the phenomena of hydraulic fracture and internal erosion. Other aspects are also of concern, such as the deformation of the structure during the construction and operational stages. In virtually all the mentioned topics, concepts developed in unsaturated soil mechanics in the last few decades may be used to gain an improved understanding of relevant phenomena. The paper starts with a review of some key ideas of compaction. The purpose is to add a different fundamental perspective to the powerful and well established concepts of soil compaction. Compacted soils and rockfill are often combined in earth dam design. They exhibit qualitatively similar behaviour against water action. However, basic principles of deformation are substantially different. Both types of materials will be dealt with in this paper. The issue of pore pressure generation during construction, which requires the solution of undrained and consolidation phenomena in unsaturated soils will be developed through some examples. Impoundment introduces two topics: the expected deformation of the dam in the course of partial or total wetting and the stability conditions of upstream and downstream slopes. Consistent answers for both problems require the solution of coupled flow-deformation phenomena under unsaturated (or saturated) conditions. Drawdown conditions will then be described. Some simplified recommendations for design will be reviewed and discussed. A case history of a dam failure during first impoundment will be finally discussed.
INTRODUCTION
Earth and rockfill dams are made of compacted soil and rockfill and, therefore, it is natural to consider their design, construction and performance from the perspective of unsaturated soil mechanics. However, earth and rockfill dams have been designed and built successfully all over the world, centuries before soil mechanics and unsaturated soil mechanics were developed. Accumulated experience and traditional design rules are certainly sufficient to achieve safe designs in practice. Dams are not currently being built in significant numbers in well-developed countries, but new projects are being commissioned in areas of Africa, South America and Asia. Therefore, the interest in these structures should be maintained. There are two additional aspects, which make the subject extremely interesting for a soils engineer, in general, and for specialists in unsaturated soils, in particular. The first aspect is the current trend to use any kind of soil or rock in the design of dams because of sustainability constraints. It is no longer feasible to select ‘‘the best’’ emplacement or to import ‘‘good’’ materials. The second point is that the behaviour of soils and rocks outcropping in tropical areas are not understood as well as more ‘‘regular’’ sedimentary and alluvial formations, often found in temperate climates of the northern hemisphere. Facing these challenges, unsaturated soil mechanics offers today a sufficient degree of development to provide theories and models of compacted soil behaviour, specialised testing and computational tools, which could improve today’s state of the art on earth dam and rockfill engineering. This paper is a contribution in this direction. Earth and rockfill dam design is, first of all, an exercise in ensuring the stability of the structure under a set of conditions expected to occur during the life
3
process. However, it is not easy to distinguish between the effect of the structure and the effect of initial conditions established during compaction. This section initially focuses in some aspects of soil compaction and in the interpretation of soil behaviour within a context of an elasto-plastic framework for unsaturated soils. The BBM model (Alonso et al, 1990) has been chosen as a reference model. Emphasis is placed in the dependence of initial conditions and constitutive parameters with the compaction procedure. The effect of the initial condition induced by compaction on the subsequent mechanical behaviour of a core dam is presented. The construction of San Salvador Dam, an earth and rockfill dam designed to be built in Huesca (Spain), has been modelled under different assumptions of compaction conditions in terms of density and water content. The mechanical response and pore pressure generation during construction will be discussed.
The examples and cases presented are taken from the recent involvement of the authors in a number of dam projects. Material parameters are real in the sense that they have been approximated from actual published on unpublished laboratory tests and field instrumentation results. Extensive use has been made of the coupled flow-deformation computer program CODE_BRIGHT described in Olivella et al. (1996) and DIT-UPC (2002). 2
COMPACTED SOILS
The design of earth dams and the analysis of their behaviour require knowing the response of the compacted fill materials under stress and humidity changes. The behaviour of fill materials depends on the compaction procedure. During compaction, permanent strains are induced which modify the original properties of the soil and its microstructure. The conceptual bases of compaction of fine-grained materials were established in 1933 by Proctor who defined the compaction state by two variables: dry density (γd ) and water content (w). For a given compaction procedure and compaction energy, the soil density reached at the end of compaction depends on the water content of the soil. An optimum or maximum dry density can exist at certain water content, lower than the water content at saturation. In practice, the compacted soil behaviour is characterized by the pair of variables (γd , w) and their significant influence on the subsequent mechanical behaviour of the soil is widely accepted. For instance, it is known that core dams compacted on the wet side of optimum are more deformable and more impervious. Therefore, the risk of cracking and hydraulic fracture is reduced. However, high initial water content may induce the development of high pore water pressures during construction, which increases the risk of instability. Dry of optimum compaction leads to more rigid cores which are prone to collapse upon saturation if the density achieved in not high enough. Deformation may crack these rigid cores and make them more susceptible to hydraulic fracture. Microscopic observations and porosimetry show that the compaction procedure also induces substantial differences in the soil fabric. In particular, several authors have reported the relevant effect of the compaction water content on the microstructure of fine-grained soils (Lambe, 1958; Seed & Chan, 1959; Barden & Sides, 1970; Delage et al, 1996; Simms & Yanful, 2001). Compacted samples on the dry side exhibit a double-structure fabric due to the aggregation of clay particles whereas dispersed fabrics are observed in samples compacted wet of optimum. Differences in the mechanical behaviour of a soil due to compaction conditions are often attributed to these microstructural differences acquired during the
2.1
Basic properties of compacted materials
The dry density (γd ) of a soil induced by compaction depends on the water content (w), the compaction procedure (dynamic and static) and the compaction energy. Figures 1 and 2 show the static compaction curves for different compaction stresses of a low plasticity silty clay from Barcelona (wL = 30.5%, PI = 11.8%, % < 2 μm = 16.1%) and a high plasticity soil—Boom clay—(wL = 56%, PI = 27%, % <2 μm = 49.7%). Contours of equal degree of saturation and equal suction, obtained after compaction by interpolating measurements from transistor psychrometers, are also plotted. As expected, suction increases as water content decreases. At high water contents, contours of equal suction follow the degree of saturation contours, whereas, as water content decreases, suction is controlled by the humidity with negligible influence of the dry density. This behaviour was explained by Romero (1999), who pointed out that in fine grained soils, high values of suction are mainly controlled by the intra-aggregates voids. Since density changes of a soil are basically associated with the volume of macropores, probably empty at relatively high suctions, the effect of density on suction, for relatively dry states, is negligible. The shape of the compaction curve generally depends on the compaction procedure. Honda et al. (2003) presented the relationship between dry density and water content of a soil (wL = 33.5%; PI = 13.2) compacted dynamically and statically (Fig. 3). The dynamic compaction curve has a clear maximum density unlike the curve obtained by static compaction. A similar result may be observed in Figure 2 for Boom clay. However this feature was not observed in the case of the low plasticity silty clay from Barcelona where a clear peak was obtained for all static compaction
4
Figure 3. Dynamic and static compaction curves of a soil (wL = 33.5%; PI = 13.2) (Honda et al., 2003). Figure 1. Static compaction curves of Barcelona silty clay and contours of equal suction (Suriol et al. 1998).
2.2 Microstructure of compacted materials Differences in microstructure become evident when samples compacted on the dry side are compared with sample compacted on wet side at the same density. Several authors have investigated the fabric of compacted soils for different compaction conditions by scanning electron microscopy and mercury intrusion porosimetry (MIP): Barden & Sides (1970), Collins (1983) and Suriol et al (1998) and Suriol & Lloret (2007), for clays, Delage et al. (1996) for silt and Simms & Yanful (2001) for clayey till, among others. Consider, in Figure 4, the two compaction states (Dry and Wet) of the Barcelona silty clay at approximately the same dry density. Samples were compacted statically applying a compaction stress of 0.6 MPa. The pore size distribution of the two states was determined by MIP. Differences in pore size distribution induced by the compaction water content are clear in Figure 5: compacting on the dry side induces a significant proportion of bigger pores (5 to 100 μm) which are absent in the samples compacted on the wet side. Consider now the application of a drying (or wetting) path to a sample initially compacted on the wet (or dry) side (states DW and WD in Fig. 6 and 7). The implied suction change is expected to induce deformations and therefore a change in soil microstructure. This is indeed the case, but the main question here is to what extent the final state (density, water content) explains the microstructure. Figure 5 indicates that the origin of the specimen is maintained to some extent. In fact, the comparison of the DD and WD states indicates that direct compaction on the dry side implies a larger proportion of larger pores than compacting on the wet side and later bringing the sample, by means of controlled drying, to the same target
Figure 2. Static compaction curves of Boom clay and contours of equal degree of saturation and equal suction (Romero, 1999).
stresses. Well defined dry and wet branches could be identified in this case. The value of suction reached for a given degree of saturation depends on the material properties. This fact can be observed if Figures 1 and 2 are compared. Equal values of degree of saturation correspond to different suction values depending on the clay nature. For a given compaction water content, the higher the fine’s content and the soil plasticity the higher the suction. Data in this regard was also given by Marinho & Chandler (1993) who measured suction in samples of varying plasticity, compacted at different water contents.
5
0.6
DD 0.5
WD
0.4 0.3 0.2 0.1 0 1.E+00
Figure 4. Moisture and dry density of samples of Barcelona silty clay. DD: samples compacted on the dry side; WW: samples compacted on the wet side; DW (WD): samples taken to the dry (wet) side, after compacting on the wet (dry) side. Compaction stress: 0.6 MPa. (Suriol et al, 1998).
1.E+02 1.E+04 Tamaño de poro (nm)
1.E+06
Figure 6. Pore size distributions of compacted Barcelona silty clay. DD: Sample compacted on dry side; WD: Sample compacted on wet side and subsequently dried (Suriol & Lloret, 2007). 0.6
0.6 0.5
DW
0.5
WW
WW
DD Δe/Δlog D
0.4
0.4 0.3
0.3 0.2
0.2 0.1
0.1 0 1.E+00
0 1.E+00
1.E+02 1.E+04 Void Size (nm)
1.E+02 1.E+04 Void size (nm)
1.E+06
1.E+06
Figure 7. Pore size distributions of compacted Barcelona silty clay. DW: Sample compacted on dry side and subsequently wetted; and WW: Sample compacted on wet side (Suriol & Lloret, 2007).
Figure 5. Pore size distributions of compacted Barcelona silty clay compacted on the dry (DD) or wet (WW) side (Suriol & Lloret, 2007).
a result of clay expansion. In all cases, the distribution of micropores has remained essentially unaffected because microporosity depends on the mineralogy and the grain size distribution of the fine fraction of the soil which remain unchanged during compaction and suction-paths. The preceding experiments were performed on unloaded specimens. Loading them will modify the observed trends in a quantitative manner. It is concluded that compaction on the wet or dry side, for the same dry density, leads to changes in pore size
state: (γd , w) of specimen DD. In a similar manner (Fig. 7), wetting the specimen DD towards DW maintains a larger proportion of larger pores than the specimen initially compacted on the wet side. It is also interesting to check that drying develops large pores in an initially wet specimen (compare pore size distributions of WD and WW specimens in Fig. 6 and 7). A comparison of states DW and DD (Fig. 6 and 7) suggests that wetting leads to a reduction of the proportion of bigger pores, surely as
6
distribution. In addition, the application of suction paths (drying or wetting) after compaction induces a continuous and significant modification of the microstructure of compacted clayey soils. Fabric modifications induced by suction increase have also been presented by Cuisinier and Laloui (2004). In the next section, the volumetric response of these samples, in one dimensional wetting tests, is described. Not only has the compaction water content had a relevant effect on the fabric of compacted soils. Seed & Chan (1959), based on indirect evidence (stress-strain curves) pointed out the effect of shear straining during compaction. They proposed that static compaction, which involves comparatively smaller shear straining than dynamic compaction, induce the aggregation of clay particles even for compaction on the wet side. The static and dynamic compaction curves given in Figure 3 reflect also these effects. 2.3
Some aspects of hydraulic and mechanical behaviour
The water retention curve (WRC) is a basic hydraulic property in the characterization of the soil from the perspective of unsaturated soil mechanics. It depends on the mineralogy and the pore structure of the soil. For a given soil density, variations on compaction conditions may induce relevant differences in the microstructure and in the pore size distribution. Therefore, different retention curves will be found. The effect of the microstructure of compacted Boom clay on the WRC was published in Romero et al (1999). There are alternative procedures to determine the WRC. Consider the technique used by Barrera (2002). Specimens are compacted at a fixed dry density, and varying water contents. If suction is measured in these samples, a relationship between degree of saturation and suction is immediately established. If the target dry density is changed, and the procedure is repeated a new WRC may be determined. Figure 8 shows the final result for the Barcelona low plasticity silty clay. For a given degree of saturation, increasing the soil density leads to increasing suction. Differences tend to reduce as the soil becomes wetter, but the effect of density (which essentially reflects the soil macropores) is clearly marked. Marinho & Stuermer (2000) provided also some experimental data about the effect of compaction conditions on the WRC. In particular, they examined the effect of the compaction energy and compaction water content on the drying branch of the WRC for a residual soil of Gneiss (LL = 48%, PL = 29% and % < 2 μm = 45%). The experimental work involved obtaining the WRC of a high number of samples compacted at different water content under three different compaction energies (Standard Proctor,
Figure 8. Retention curves for different constant densities of Barcelona low plasticity silty clay (Barrera, 2002).
Modified Proctor and a non-standard low energy). As a representative example, Figure 9 shows the WRC for samples compacted at Modified Proctor energy. Initial conditions of samples after compaction are also shown in the same figure. The technique here was different if compared with the procedure reported by Barrera (2002): once compacted at a given density and water content, specimens were equilibrated (by drying) to a different water content. The equilibrium suction could then be related with the attained humidity. In this way, the WRC associated with a particular compaction ‘‘point’’ (MP1, MP2, MP3 etc. in Fig. 9) was determined. The measured WRCs are also indicated in Figure 9. Samples MP2 and MP4, which were compacted at the same dry density (or void ratio), but at different compaction water content presented a different WRC. During the drying process samples compacted near the optimum water content or below it (MP2) always presented smaller suction than samples compacted at wet of optimum (MP4). For low degrees of saturation curves tend to be similar, irrespective of the original compaction state (in contrast with the results presented in Fig. 8). It is concluded that the WRC of a given soil is not a unique relationship (irrespective of hysteresis effects) even for a given density. The differences reported here are attributed to differences in microstructure built into the specimen by the compaction procedure. In addition, there are alternative procedures to determine the WRC. For instance, direct compaction to the target
7
Figure 9. Water retention curves of a low plasticity soil obtained by drying of compacted samples at different conditions. (a), (b) and (c): Initial state. (d): Measured WRC (Marinho & Stuermer, 2000).
of optimum water content involves lower collapse (or higher swelling if the attained density is high enough). The microstructure described before gives a good explanation for the volumetric response during wetting. The proportion of large pores is associated with the volumetric instability by compression and collapse. Suction controlled tests on the described samples of Barcelona silty clay (Fig. 1) corroborate the soil fabric effect on the volumetric behaviour of the soil during wetting. Samples WD and DD, which have a common initial state (defined it terms of dry density, water content and suction) but they were compacted at different water contents, were loaded in a suction-controlled oedometer cell and they were later saturated. (Suction controlled loading is necessary if the effect of loading and final wetting is to be isolated). Since they have the
density value at different water contents or compaction to a given state followed by suitable application of a stress-suction path. Most likely these alternate procedures lead to a different microstructure. In fact, microstructure changes during stress-suction paths. An example is presented by Simms & Yanful (2001) who analysed the porosimetry of compacted clayey till samples. Significant changes in the shape of pore size distribution before, during and after the WRC test were obtained. This microstructural differences lead to differences in mechanical and hydraulic behaviour. Regarding the mechanical behaviour, in general terms, compacted samples on the dry side exhibit higher stiffness and lower shrinkage during drying than compacted samples on the wet side, at the same dry density (Seed & Chan, 1959; Sivakumar & Wheeler, 2000a, b). Compaction on the wet side
8
relevant question is whether the compaction procedure only modifies initial conditions or, alternatively, every combination of compaction method, compaction water content and achieved density effectively lead to different soils which have to be modelled with different constitutive parameters. As discussed previously, compaction is characterized in practice by the achieved dry density (γd ) and the compaction water content (w). Undoubtedly, these compaction conditions will determine the initial conditions. Initial conditions (in the context of BBM) are determined by the initial stress state, which will be a state of negligible stress immediately after compaction, before any subsequent load due to construction, the initial value of suction and initial position of the yield surface. The rest of the effects of the compaction procedure on the mechanical response of the soil that can not be explained by initial conditions must be attributed to the constitutive parameters. The influence of the initial suction and the initial position of the yield curve on the subsequent behaviour during isotropic loading and wetting in the context of BBM is described in Sivakumar & Wheeler (2000a and b). Suction induced by compaction will be essentially determined by the water content and, to a lesser extent, by the dry density achieved as shown in the previous section. Numerical calculations with BBM require the independent determination of the WRC. The position of the yield surface after compaction is closely related to the dry density achieved. The initial yield stress can be interpreted as the maximum stress of compaction experienced by the soil. Honda et al (2003) reported that the yield stress measured in suction-controlled oedometer tests of samples previously compacted at two different static loads and at different water contents almost coincide with the compaction pressure. At given water content, soils compacted with higher compaction effort will reach higher dry densities and will yield at higher stress. In BBM, the position of yield surface is uniquely defined with the yield stress at saturated conditions (p∗0 ). Then, for a given soil, p∗0 is determined by the dry density and it is essentially independent of compaction water content (Alonso et al, 1987; Gens, 1995; Wheeler, 2000a). The compaction effort required to achieve a given dry density depends on the soil properties, namely its plasticity and grain size distribution. In order to know the preconsolidation stress of a compacted soil, it is interesting to describe its value by the attained dry density. In order to do so, a review has been made of published compression data of compacted specimens of a variety of soil types. In all cases, except for some results from Honda et al (2003) and Balmaceda (1991) results, samples were compacted statically. For each type of soil, tests were performed on specimens compacted at different dry densities. The preconsolidation yield stress was derived from
Figure 10. Volumetric deformation measured at the final phase of saturation at different vertical stresses. Samples WD and DD of Barcelona red silty clay (from Suriol et al 1998).
same initial state, the different mechanical behaviour exhibited by the samples is attributed exclusively to the fabric produced during compaction. Differences attributed to initial conditions have been eliminated in these tests. The volumetric deformation measured during the final phase of saturation for the samples DD and WD is presented in Figure 10. They exhibit a similar behaviour, in qualitative terms. At low vertical confining stress (σv = 0.2 MPa) a small swelling is measured. Collapse then increases with increasing stress. A maximum value was found for σv = 2 MPa. At higher vertical stresses, the magnitude of the collapse reduces progressively. It is clear that the sample compacted on the wet side was able to develop collapse because of the drying episode after wet compaction. It can also be observed that the samples compacted on the dry side (DD) exhibit higher collapse than specimens WD. 2.4
Behaviour of compacted materials from the perspective of an elastoplastic framework for unsaturated soils (BBM)
Modelling dam behaviour during construction and operation is an important consideration in design. Existing constitutive models for unsaturated soils offer the possibility of a consistent analysis of dam performance. A fundamental initial step is the proper characterization of compacted soils. In this section, the behaviour of compacted materials is interpreted in the context of an elasto-plastic critical state model for unsaturated soils: the Barcelona Basic Model (BBM) (Alonso et al, 1990). Compacted soil properties will be defined through material parameters. In this way, different soils should be characterized by different constitutive parameters. It is widely accepted that variations in mineralogy and in grain size distribution involve fundamentally different materials and, therefore, they should be characterized by different constitutive parameters. But the
9
suction and β controls the rate of increase of stiffness with suction). It is then expected that r and β will depend on the type of soil but also on compaction conditions. Collapse susceptibility of a soil increases when the LC curve exhibits a rapid increase in yield stress with suction. Therefore, in view of the previous discussion, soils compacted dry of optimum should have an LC displaced towards the right, if compared with soils compacted wet of optimum, at the same dry density. This is shown in Figure 12, which was built using compressibility and collapse data of compacted Barcelona silty clay. The figure may also be interpreted in the sense that compaction dry of optimum leads to a larger elastic domain. Note also that the compressibility coefficient λ(0) for saturated conditions is higher for wet of optimum compaction. Modelling this material with BBM implies that specimens located at different point in the (w, γd ) compaction plane would require different sets of constitutive parameters. In other words, variations in compaction procedure lead to different soils. However, the simplest approach: a unique set of material parameters defining the type of soil (plasticity, grain size distribution etc.) and an initial state characterized by a pair (s0 , p∗0 ), exclusively determined by the initial compaction variables (w, γd ) may be enough to reproduce with sufficient engineering approximation the behaviour of a soil in the compaction plane. In fact, a unique set of parameters was enough to model by BBM the volumetric behaviour along loading—collapse paths of a compacted residual soil of low plasticity (wL = 23.9–30.1%, wP = 21.4–28.8%) reported by Booth (1975). Similar conclusion was obtained in the simulation of results reported by Balmaceda (1991) who tested a non plastic
oedometer, isotropic compression tests or considering the maximum stress applied to the compacted sample. The results are given in Figure 11. The derived value of p∗0 is plotted against the initial dry density of the specimen. The results follow a definite pattern. The saturated yield stress increases exponentially with the attained dry density. On the other hand, for a given dry density, the more plastic the soil, the higher p∗0 . Figure 11 may be useful, in the absence of experiments, to approximate the p∗0 associated with a given dry density. The simplest approach to describe the compaction state in terms of the parameters of an elastoplastic constitutive model such as BBM is therefore to substitute the pair (γd , w) by the stress pair (p∗0 , s). However, the discussion on microstructure and its consequences in terms of mechanical behaviour (only volume change has been examined here) suggests that material parameters are also controlled by the compaction state. In particular, the shape of the LC curve is a piece of information key to interpret the effect of suction on the mechanical response of the compacted soil. In BBM the shape of the LC curve is given by parameters r and β (r establishes a minimum value of the compressibility coefficient for high values of 2.2 2 1.8
wL=56%, IP=27%
Yield stress (p0*) (MPa)
1.6 1.4 1.2 1 0.8 0.6 wL=43%, IP=13.4%
0.4
wL=33.5%, IP=13.2%
wL=28% IP=8% wL=30.5% IP=11.8%
0.2
NP
0 1
1.2
1.4 1.6 1.8 Dry density (g/cm3)
2
High plasticity Boom Clay (Romero, 1999) Medium plasticity soil (Honda et al, 2003) Medium-low plasticity soil (Honda et al, 2003) Low plasticity silty clay from Barcelona (Barrera, 2002) Non plastic silty sand (Balmaceda,1991) Measured value of San Salvador silty clay Estimated curve of San Salvador silty clay
Figure 12. Yield surface (LC) for samples of compacted silty clay from Barcelona at dry side (D) and wet side (D) to the optimum value of water content.
Figure 11. Relationship between the isotropic yield stress at saturated conditions and dry density of several soil types.
10
Dam construction (expected to last one year long) and operation stages (reservoir impoundment and drawdown) were modelled by means of CODE_BRIGHT during the design stage. Dam materials were modelled through BBM. Constitutive parameters of the fill materials and foundation soil used in the analysis are collected in Table 1. These parameters were derived from conventional laboratory test (triaxial, oedometer and permeability tests). The effect of compaction conditions in the clay core of the dam during constructions has been analysed. Dam construction has been simulated considering four different compaction states of the core material (a silty clay having wL = 28%, IP = 8%). Figure 14 shows the compaction curve of this material and the compaction states considered in terms of γ d and w (Cases 1, 2, 3 and 4). The influence of varying compaction conditions has been attributed only to the initial conditions
silty sand and Lawton et al (1989, 1991) who tested compacted samples of slightly expansive clayey sands (wL = 34%, wP = 15%). Sivakumar and Wheeler (2000a and b) also concluded that most of the collapse potential of a compacted soil prepared by mixing dry speswhite kaolin powder and water, at low water content, could be attributed solely to the value of suction after compaction.
3
EFFECT OF COMPACTION CONDITIONS IN THE BEHAVIOUR OF A DAM CORE DURING CONSTRUCTION
San Salvador dam will be built in the near future in the Province of Huesca (Spain). It is a 54 meters high earthdam (a central section is indicated in Fig. 13).
3
2
3
4
1
Figure 13. Central section of San Salvador Dam; 1: Claystone with sandstone layers; 2: Clay core; 3: Clay and silty gravels; 4: Rockfill. Table 1.
Constitutive parameters of fill materials. San Salvador dam. Value
Parameter
Symbol
Core
Shells
Found.
Unit
Elastic modulus Poisson’s ratio Plastic virgin compressibility for saturated conditions Parameter that establishes the minimum value of the compressibility coefficient for high values of suction Parameter that controls the rate of increase in stiffness with suction Reference stress Slope of critical state strength line Saturated permeability Retention curve (Van Genuchten parameters)
E ν
40 0.3
100 0.3
120 0.3
MPa –
λ(0) − κ
0.022
0.018
–
–
r
0.65
0.8
–
–
β pc M ksat p0 λ Sw max Sw min
6 0.01 1.1 2.10e−9 0.5 0.24 1.0 0.001
6.5 0.01 1.72 1.567e−5 0.05 0.4 1.0 0.05
– – – 1.0e−10 0.5 0.24 1.0 0.001
MPa−1 MPa – m/s MPa− – – –
11
(s0 , p∗0 ) (Tab. 2). Initial suction has been determined with the estimated water retention curve, indicated in Figure 15. In order to estimate the value of the saturated yield stress (p∗0 ) for the different compaction conditions, data given in Figure 14 was used. An oedometer test performed on a saturated specimen, previously compacted at a dry density of 1.8 g/cc provided the yield stress shown in Figure 14. Then a trend for higher and lower densities was approximated following the patterns observed in the figure for other materials. A curve in the (γd , p∗0 ) plane for the core material of San Salvador dam was established and the value of p∗0 for the four cases could be estimated. Pore water pressure distributions at the end of dam construction are plotted in Figure 16. Figure 17 shows the calculated evolution of pore pressure for a point located in the lower part of the core. The higher the initial water content, the higher the expected pore water pressure generated during construction. In Cases 2 and 4 (clay core compacted at wet side of optimum) positive pore water pressures develop during construction. However if the clay core is compacted at the dry side (Cases 1 and 3), pore water pressures remain negative. In Cases 2 and 4 the soil is almost saturated and a similar response in terms of pore pressure generation should be expected. Figures 16 and 17
illustrate this comment. The soil compacted in 4 has, however, a higher density than the soil in 2. Therefore its elastic domain will be larger than the domain for point 2. During dam construction the soil 2 will tend to accumulate more (plastic) deformations and therefore positive pore water pressures will also be larger than for compaction conditions in 4. This is also shown in Figures 16 and 17 although the effect is small because differences in p∗0 are also small. The effect on the initial conditions can also be observed in vertical displacements (plotted for each case in Figure 18). Higher displacements are expected for Cases 2 and 4 because at low values of suction the material is more deformable. 1000
100
Suction (MPa)
10
1
0.1
0.01
0.001 0
0.2
0.4
0.6
0.8
1
Degree of saturation
Figure 14. Compaction curve of silty clay used in the clay core of San Salvador Dam. Tested samples from a trial embankment. Table 2.
Figure 15. Water retention curve for the silty clay of San Salvador dam core.
Initial conditions for the clay core of San Salvador dam. Value
Parameter
Symbol
Case 1
Case 2
Case 3
Case 4
Unit
Dry density Compaction water content Degree of saturation Initial suction Initial yield mean net stress for saturated conditions
γd w Sr s0
17.4 0.1 0.49 5.0
17.4 0.204 0.99 0.045
17.8 0.13 0.67 1.4
17.8 0.186 0.96 0.11
KN/m3 – – MPa
0.071
0.1
0.1
p∗0
0.071
12
MPa
Note also that the evolution of settlements is also controlled by the dissipation of pore pressures. When positive pressures develop and the dissipation is slow because of the low core permeability, settlements are delayed. This behaviour is observed in Case 2, during the first stage of construction. Later, the higher deformability of wetter materials (Cases 2 and 4) lead to higher settlements.
(a) Case 1
(b) Case 2
4
COMPACTED ROCKFILL
Rockfill offers a significant and reliable strength and it is a favourite solution to stabilize clay cores. Strength envelopes are nonlinear (Fig. 19) and depend on suction. Suction dependence is more marked in materials prone to particle breakage such as schist and shales (Fig. 19a). Hard, tough lithologies, with isotropic properties such as the sound limestone in Figure 19b exhibit a limited sensitively to water content changes. Rockfill properties (strength, deformation, long term creep, collapse phenomena) are strongly linked to particle breakage. Particle breakage, in turn, depends
(c) Case 3
(d) Case 4
Figure 16. Pore water pressure distribution at the end of construction of San Salvador dam.
(a) Figure 17. Pore pressure evolution during construction of the point indicated in the figure.
(b) Figure 19. Strength envelopes determined in suction controlled triaxial tests on gravel of: (a) Pancrudo slate. (b) Hard limestone.
Figure 18. Calculated vertical displacements, during construction, of the point indicated in the figure.
13
Table 3. A comparison between unsaturated rockfill and unsaturated soil.
Table 4. (RM).
Unsaturated rockfill
Unsaturated soil
Parameter
Description
Collapse is associated with particle breakage and a subsequent rearrangement of structure Particle toughness is a fundamental property
Collapse is associated with particle rearrangement
E ν λi − κ λd0
Particle strength does not affect the overall behaviour The effect of suction is to ‘‘prestress’’ soil structure
αs
There is no equivalent parameter
ks
Elastic modulus Poisson’s ratio Plastic virgin instantaneous compressibility Virgin clastic compressibility for saturated conditions Parameter to describe the rate of change of plastic compressibility with total suction Slope of critical state strength envelope for dry conditions Parameter that controls the increase in cohesion with suction Parameter that controls the increase in cohesion with suction Threshold yield mean stress for the onset of plastic phenomena Parameter that defines the non-associativeness of plastic potential
Mdry Msat
py α
Matric suction (s) controls water induced effects There is no equivalent concept
0,00
0,20
0,40
0,60
0,80
1,00
0,00 Test 2 0,50
Yield stress of the saturated soil is conveniently chosen as the hardening parameter Elastoplastic strains are linearly related to log (confining stress)
Vertical strain [%]
The effect of suction is to control particle breakage velocity A threshold toughness to initiate fracture propagation is included in the model through a parameter, σy . For σ < σy no time delayed deformations exist (no collapse) Total suction (ψ) controls water induced effects Time delayed deformations (and hence collapse) is inhibited for very dry states Yield stress for the very dry state is conveniently chosen as a hardening parameter Elastoplastic strains (instantaneous and delayed) are linearly related to confining stress for the relevant range of stresses in practice
Constitutive parameters of the Rockfill Model
Test 3
1,00
1,50
2,00
2,50
Vertical stress [MPa]
Figure 20. Large diameter oedometer tests on crushed Pancrudo slate.
on the stress concentrations at particle-to-particle contacts and on the prevailing relative humidity (RH) at each particular contact (which will presumable be in equilibrium at a larger scale). In a series of publications (Oldecop and Alonso, 2001, 2004; Chávez and Alonso, 2003) a phenomenological elastoplastic constitutive framework has been described. The resulting model has similarities with elastoplastic models conceived for ‘‘regular’’ unsaturated soils and, in particular, with BBM (Alonso et al, 1990). However there are significant differences, which have been summarized in Table 3. The rockfill elastoplastic model developed in Oldecop and Alonso (2001) and Alonso et al (2005) is characterized by a few parameters described in Table 4. One significant feature of compacted rockfill is the apparent lack of elastic domain after compaction.
This is shown in the stress-strain curves determined in large diameter (30 cm) oedometers with RH control (Fig. 20). Loading-unloading cycles performed at low stress levels results immediately in significant plastic deformations. The implication is that a loaded rockfill after compaction is always prone to collapse deformation if wetted. Again, the intensity of collapse depends on the susceptibility of the rockfill particle to break under stress and RH changes. A side effect of particle breakage phenomena is the significant creep behaviour observed in laboratory experiments and in real structures. This is illustrated in Figure 21 which shows several records of long term
14
0.0
0
5
Time [years] 15 20
10
Crest settlement [% of height over foundation]
0.2 Mackintosh (75)
25
0.00
0
assessment of dams for full reservoir height (or partially filled), an appropriate conservative assumption involves the consideration of steady state conditions because pore pressure reaches maximum values. However, the actual distribution of pore pressures in shoulders and cores is difficult to determine by means of a classical ‘‘saturated’’ analysis. The case described below illustrate this comment. In order to estimate actual pore pressure distributions in the dam, unsaturated analysis and the characterization of the materials in the context of unsaturated conditions (relative permeability and water retention curve) are necessary. In the 1960s saturated flow was adopted in the analysis of pore pressure distribution for the steady state condition. This analysis required finding explicitly the position of the free surface (pw = 0), imposing zero normal flow through the free surface, and then the steady state flow equation for saturated media (Laplace equation) together with Darcy’s Law were solved in the saturated domain. This methodology assumes that no flow takes place through the unsaturated zone. The analysis of transient seepage in unsaturated/saturated media was developed at the end of the 1970s. The flow equation for partially saturated conditions could be solved in the entire domain. More recently, coupled models for unsaturated conditions have been introduced (Naylor et al, 1997; Alonso et al, 1988, 1993, 2005; Khogo, 2002). Consider again the design of San Salvador dam (Fig. 13). The set of material properties are given in Table 1. The analysis has been carried out by means of the programme CODE_BRIGHT. The saturated permeability and WRC of the different materials involved are indicated in the table. A cubic law describes the relative permeability:
30
5
10
Time [years] 15 20
25
30
0.02 0.4 Exchequer (150)
0.04 0.06
0.6 El Infiernillo (146) 0.8
0.08
Murchison (94)
Alicurá (130)
Chocón (90)
0.10 Dix River (84)
1.0
Nanthala (80)
0.12
Cethana (110) Alto Anchicaya (140) Foz do Areia (160)
0.14
1.2 CRFD/dumped rockfill 1.4
Beliche (54)
CRFD/compacted rockfill Central core/rockfill shells
Rivera de 1.6 Gata (60)
Central core/gravel shells
Figure 21. Crest settlements of several types of rockfill dams built in the 20th century (Oldecop and Alonso, 2007).
settlements of rockfill dams built in the 20th century. Concrete faced rockfill dams (CFRD) as well as zoned embankments are represented. Well compacted gravely materials exhibit a very limited creep which is expressed in terms of the variation of the ratio of settlement with respect to dam height with time. Two modern dams (Beliche and Rivera de Gata) built in Portugal and Spain respectively, exhibit remarkably fast creeping rates. The reason, again, is the high sensitivity of the rockfill used (schist and grauwackes in the case of Beliche and shales and phyllites in the case of Rivera de Gata) to degrade as a consequence of particle breakage. A portion of the apparent creep observed in Figure 21 is in fact due to collapse deformations induced by atmospheric action on the downstream shell of the dams. This point will be addressed later.
5
krel =
Sw max − Sw Sw max − Sw min
3 (1)
where Sw is the degree of saturation and the remaining Sw values are parameters. Dam construction (360 days), followed by reservoir impounding (300 days) and flow through the dam during 340 additional days, at maximum reservoir level were simulated. At the end of this period flow conditions were close to the stationary state. Some calculated results are given in Figures 22 to 25. They illustrate the behaviour of the dam and the flow-mechanical interaction. Figure 22 shows the transition from the unsaturated to the saturated state of two representative points in the lower third part of the dam. The initial negative pressure (−0.5 MPa) corresponds to the assumed suction at the end of layer placement. The accumulation of upper layers leads to a progressive saturation of the soil because of the increasing weight. Wetting of the dam materials during
FLOW AND DEFORMATION
Dam operations lead to reservoir level fluctuations during their lifetime. It leads to transient conditions. Steady state conditions may not be reached in several years or in the entire lifetime of the dam. Piezometers readings indicate that in impervious clay cores of zoned dams the time to reach the saturation after construction may take many years (more than 20 to 30). LeBihan and Leroueil (2000) calculated that for typical central core earth and rockfill dams full saturation will take a few years for a core with a value of saturated permeability of 10−6 m/s, several decades for 10−7 m/s and centuries for 10−8 m/s. However, it is an accepted practice to consider the steady state conditions at the design stage. In the safety
15
0.4
0.6 B
Deviatoric stress (MPa)
Liquid pressure Vertical displacement
0.2
A
0.4 B 0.3 A 0.2 0.1
0 0
200
400
600
800
1000
1200 0
Time (days)
0
0.1
(a)
0.2 0.3 Net mean stress, p (MPa)
0.4
0.5
0.6
-0.2 0.5 B
Suction (MPa)
Pore pressure (MPa); Vertical displacement (m)
Final construction Final impoundment After 340 days at maximum reservoir level
0.5
-0.4
0.4 0.3
Final construction Final impoundment After 340 days at maximum reservoir level
0.2
A B
0.1
-0.6 0 0
A
(b)
0.1
0.2 0.3 Net mean stress, p (MPa)
0.4
0.5
Figure 23. Stress paths of points A and B. (a) Deviatoric plane; (b) Net mean stress-suction plane.
-0.8
Figure 22. San Salvador dam. Calculated evolution of pore pressures and settlements of two points of the upstream shoulder and the core respectively.
impoundment increase their unit weight. This effect, the hydrostatic stress against the upstream slope, and the collapse associated with the decrease in suction is reflected in the progressive settlement of point B, located in the upstream shell. Collapse intensifies in the final stages of suction reduction. When the soil around B becomes saturated effective stresses decrease and a small elastic expansion is calculated. Point A, in the core, receives later the changes in suction, if compared with point B. A significant collapse is calculated. A negligible elastic rebound is calculated when the water pressure becomes positive. These comments may be also followed in the stress paths plotted in Figure 23 in a net stress-suction space. The stress reversal associated with the development of positive pore water pressures is now well illustrated. The position of the infiltration front at the end of the calculation period is given in Figure 24. The deformed shape of the dam is also plotted in the figure. Symmetry is lost because of the higher collapse of the upstream shoulder. In this case no rain effects (which
Figure 24. San Salvador dam. Contours of positive pore water pressure and dam deformation at the end of the calculation period.
would contribute to the collapse of the downstream shoulder) are considered. The strong stress interactions between core and shoulders are indicated in Figure 25. Dam construction results in a fairly symmetric vertical stress distribution around the core axis. The lower overall elastoplastic stiffness of the core creates a silo effect and stresses show a marked discontinuity at the transitions. When water percolation wets the upstream core, differential collapse deformations are reflected in some shearing of the shell, which provides a ‘‘kink’’ in the calculated settlements. The silo effect is enhanced at the shellcore transitions because of the larger collapse potential
16
Sherard et al. (1963) in their book on earth and earth-rock dams describe several upstream slope failures attributed to rapid drawdown conditions. Interestingly, in most of the reported failures the drawdown did not reach the maximum water depth but approximately half of it (from maximum reservoir elevation to approximately mid-dam level). Drawdown rates in those cases were not exceptional at all (10 to 15 cm/day). A Report on Deterioration of Dams and Reservoirs (ICOLD, 1980) reviews causes of deterioration and failures of embankment dams. Thirty-three cases of upstream slips were collected and a third of them were attributed to an excessively rapid drawdown of the reservoir. A significant case was San Luis dam, in California (ICOLD, 1980). San Luis dam is one of the largest earthfill dams in the world (100 m high; 5500 m long; 70 million m3 of compacted embankment). An upstream slide developed in 1981 after 14 years of successful operation of the dam because of a drawdown, which was more intense than all the previous ones. In this case, the average drawdown rate was around 0.3 m/day and the change in reservoir level reached 55 m. Von Thun (1985) described this case. The stability of riverbanks under drawdown conditions is also of concern and Desai (1971, 1972, 1977) in a series of papers describe experimental and theoretical studies performed at the Waterways Experiment Station to investigate the stability conditions of the Mississippi earth banks. Consider, in qualitative terms, the nature of the drawdown problem in connection with Figure 26a, b. The position of the water level MO (height H ) provides the initial conditions of the slope CBO. Pore water pressures in the slope are positive below a zero pressure line (pw = 0). Above this line, pore
Vertical stress (MPa)
-1 Final construction
-0.8
Final impoundment After 340 days at maximum reservoir level
-0.6 -0.4 -0.2 0
(a)
0
20
40
60
0
20
40
60
80 100 Distance (m)
120
140
160
180
0.4
Pore Pressure (MPa)
0.3 0.2 0.1 0 -0.1
80 100 Distance (m)
120
140
160
180
-0.2 -0.3 -0.4
(b)
Figure 25. (a) San Salvador dam. Vertical stresses against the horizontal plane indicated at three times of the life of the dam. (b) Pore pressures in the horizontal reference plane.
of the core when wetted. Figure 25b provides information on the pore pressure evolution on the reference plane. It helps to follow the changes in stresses plotted in the same figure. This example shows the capabilities of current computational methods to analyze and interpret the behaviour of earthdams. Note also that the transition from unsaturated to saturated states is well managed in CODE_BRIGHT.
HD
6 6.1
RAPID DRAWDOWN Introduction
The drawdown condition is a classical scenario in slope stability, which arises when totally or partially submerged slopes experience a reduction of the external water level. Rapid drawdown conditions have been extensively analysed in the field of dam engineering because reservoir water levels fluctuate widely due to operational reasons. Drawdown rates of 0.1 m/day are common. Drawdown rates of 0.5 m/day are quite significant. One meter/day and higher rates are rather exceptional. However, reverse pumping storage schemes may lead to such fast water level changes in reservoir levels.
HD = HD
w
Figure 26. The drawdown scenario: (a) Hydrostatic stresses acting against the exposed slope surface. (b) Change in applied stresses on the exposed boundaries induced by a drawdown HD .
17
, the bulk moduwhere n is the soil porosity; Kskel lus of the soil skeleton, and Kw , the bulk modulus of water. Kw is close to Kw = 2100 MPa and, therefore, in practically all cases involving compacted materials in dam engineering, Kskel Kw and B = 1. Even ∼ for an exceptionally stiff soil material (Kskel = Kw ) the value of B is close to 1. This is a well-known result but it is often read, in connection with drawdown analysis, that in cases of rigid materials the (stress) uncoupled flow analysis is sufficiently accurate, implying that no stress-related changes in pore pressures are generated. It is clear that this is never the case in practice. Two wide classes of procedures have been developed to analyze drawdown. The first class highlights the effect of changing boundary stresses in order to calculate the pore water pressures immediately after a (sudden) drawdown. The second class of procedures uses pure Darcy-type flow, and they are said to be valid for rigid (!) and pervious materials. It is also common, at present, to find flow-based stress uncoupled analysis in practical applications and, therefore, a distinction of the results likely to be found in case of stress coupled or uncoupled (pure flow) analysis is useful for discussion. Figure 27 shows in qualitative terms the expected evolution of pore pressures in a representative point (P2 ) of the slope, plotted in Figure 26, during a drawdown which takes place in a time interval, tDD . Points such as P1, in the upper part of the slope will experience a small change in stresses. During drawdown they will likely become unsaturated. Away from the upstream slope (point P3 in Figure 26) stress effects associated with the slope geometry disappear and pore pressures will follow the changing levels of the reservoir. However, the behaviour of Point P2 , close to the slope toe, is strongly controlled by the stress state induced by drawdown. The resulting pore pressures during the drawdown process will be affected by the
water pressures are negative and suction is defined as s = −pw . A drawdown of intensity HD takes the free water to a new level M N O during a time interval tDD . This change in level implies: – A change in total stress conditions against the slope. Initial hydrostatic stresses (OAB against the slope surface; M N B C against the horizontal lower surface) change to O A B and M N B C. The stress difference is plotted in Figure 26b. The slope OB is subjected to a stress relaxation of constant intensity ( σ = HD γw ) in the lower part (BO ) and a linearly varying stress distribution in its upper part (O O). The bottom horizontal surface CB experiences a uniform decrease of stress of intensity, HD γw . – A change in hydraulic boundary conditions. In its new state, water pressures against the slope are given by the hydrostatic distribution O’ A’ B on the slope face and by the uniform water pressure value pw = (H-H D )γw on the horizontal lower surface. The change in hydrostatic pressures against the slope surface is also a change in total stress which will modify the state of stress inside the slope. This stress change will induce, in general, a change in pore pressure. The sign and intensity of these pore pressure depend on the constitutive (stress-strain) behaviour of the soil skeleton. An elastic soil skeleton will result in a change of pore pressure equal to the change in mean (octahedral) stress. If dilatancy (of positive or negative sign) is present, due to shear effects, additional pore water pressures will be generated. The resulting pore pressures will not be in equilibrium with the new boundary conditions and a transient regime will develop. If soil permeability is high pore pressures will dissipate fast, perhaps concurrently with the modification of boundary conditions. This situation will constitute a ‘‘drained’’ reaction of the slope. In fact, velocity of drawdown and permeability should be considered jointly in order to decide if the slope reacts in a drained or undrained manner. In practice, however, drawdown rates vary between narrow limits and the soil permeability becomes the dominant parameter. Skempton (1954) and Henkel (1960) provided expressions for the development of pore pressures (pw ) under undrained conditions before modern constitutive equations were born. The B coefficient of the well known Henkel expression is given by: ⎞
⎛ B=⎝
1 1+
K n Kskel w
⎠
Figure 27. Change in pore water pressures in Point P2 for coupled or uncoupled analysis and pervious or impervious fill.
(2)
18
rate of water level lowering, the ‘‘map’’ of initial pore pressures, (which, in turn, depend on the stress field), and by the source terms associated with the volume change experienced by the soil skeleton—controlled by soil stiffness- and any possible change in saturation conditions. Figure 27 indicates that the uncoupled analysis (which makes the assumption of rigid soil) leads, in the case of an impervious soil, to the prediction of the highest pore pressures inside the slope. If the soil is definitely pervious no difference between coupled or uncoupled hypothesis will be found. Most cases in practice will remain in an intermediate zone, which will require a coupled analysis for a reasonable pore pressure prediction. A reference to the usual expression of time to reach a given degree of consolidation, U , in one-dimensional consolidation problems, provides a clue on the effect of soil stiffness:
t=
L2 T (U ) γw kEm
(3)
where L is a reference length associated with the geometry of the consolidation domain; T is the time factor; k, the soil permeability, Em , the confined stiffness modulus, and γw , the water specific unit weight. Soft materials (Em low) will react with high consolidation times, all the remaining factors being maintained. Figure 28b indicates this effect. Permeability and stiffness control the rate of pore pressure dissipation in this case, in the manner indicated. However, if more advanced soil models are introduced, the simple trends given in Figure 28 may change. The changing boundary condition and the soil permeability essentially control the transient behaviour of the uncoupled model (Fig. 28a). Note that a comparison of Figures 28a and 28b does not provide clear indication of the relative position of the pressure dissipation curves. Therefore, it is difficult to define ‘‘a priori’’ the degree of conservatism associated with either one of the two approaches. Of course, it is expected that the fully coupled approach should provide answers close to actual field conditions.
Figure 28. Change in pore water pressures in point P2 for (a) uncoupled analysis or (b) coupled analysis.
derived first his well-known expression in terms of ¯ soil parameters A and B ( or B).In his wording: The ‘‘overall’’ coefficient B¯ is a useful parameter, especially in stability calculations involving rapid drawdown, and it can be measured directly in the laboratory for the relevant values of stress-changes in a particular problem. Only the change in major principal stress is required to use Skempton’s B¯ parameter. Bishop (1954) followed this recommendation and assumed that the major principal stress in any point within the slope is the vertical stress. He proposed also that the change in weight, statically computed in a column of soil and water above a reference point, would provide σ1 . Finally he suggested B¯ = 1 as an appropriate value in practice. Bishop’s approach has been criticized because it may lead to unacceptable large negative pore water pressures under the dam (Baker et al., 1993). Morgenstern (1963) accepted Bishop’s proposal based on a correspondence between Bishop’s method and pore pressures measured in two dams subjected to rapid drawdown (Alcova and Glen Shira dams). It is not clear that results of Glen Shira dam follow Bishop’s recommendation, however. Morgenstern
6.2 Brief historical perspective The literature describes two approaches to predict the pore water pressure regime after drawdown: The undrained analysis and the flow methods. The aim of the undrained approach is the determination of pore water pressures immediately after drawdown in impervious soils. Skempton (1954)
19
drawdown conditions may be found in Cedergren (1967). Finite difference approximations and, later, finite element techniques were used in the 60’s and 70’s to calculate the flow regime under drawdown conditions. The major problem was to predict the location of the phreatic surface during drawdown. When Dupuit-type of assumptions -horizontal flow- are made (Brahma & Harr, 1962; Stephenson 1978) the location of the zero-pressure surface comes automatically from the analysis. When solving the Laplace equation by finite elements (Desai, 1972, 1977), some re-meshing procedures were devised. An additional example of a determination of the free surface is given in Cividini & Gioda (1984). In parallel, the liquid water flow equation for unsaturated porous media was being solved by means of finite difference or finite element approximations (Rubin, 1968; Richards & Chan, 1969; Freeze, 1971; Cooley, 1971; Neumann, 1973; Akai et al., 1979; Hromadka & Guymon, 1980, among others). These developments made it obsolete the involved numerical techniques required to approximate the free surface through the saturated flow equation. Berilgen (2007) published recently a contribution to the drawdown problem. The author used two commercial programs for transient/flow and deformation analysis respectively. He reported a sensitivity analysis involving a simple slope geometry. Safety factors are calculated by a (c , ϕ ) reduction method built into the mechanical finite element program. The author emphasized that the undrained rapid drawdown case and the fully drained case (high permeability) are rough approximations for other intermediate situations likely to be found in practice. Pauls et al. (1999) reports a case history. A stressuncoupled finite element program was used to analyse the pore pressure evolution in a river bank as a result of a flooding situation. Consistently, predicted pore pressures remained well above the measured piezometric data. One possible explanation, not given in the original paper, is the uncoupled nature of the computational code used. In fact, no riverbank failures were observed in this case despite the calculated safety factors, lower than one.
published plots providing safety factors after drawdown in terms of drawdown ratio (HD /H in Fig. 26) for different values of slope angle, effective cohesion and effective friction. The dam geometry was simple: a homogeneous triangular dam on an impervious base. Much later, Lane & Griffiths (2000) solved a similar case in term of geometry, but failure conditions were calculated by means of a (c , ϕ ) reduction procedure built into a finite element program, which uses a MohrCoulomb failure criterion. They do not solve any flow equation in their program and it is not clear how they could derive the pore water pressures induced by total stress unloading. Lowe & Karafiath (1980) and Baker et al. (1993) performed undrained analyses to calculate the safety factors of slopes under rapid drawdown conditions. The analysis is applicable to relatively impervious soils and it does not require a determination of pore pressures after drawdown (which is required for a drained analysis of the type performed by Morgenstern). Instead, the idea is to find the distribution of undrained strengths for the particular stress state just before drawdown. However, the emphasis in this paper lies on the determination of pore pressures after drawdown so that general effective stress analysis could be performed. Flow methods probably started with the contribution of Casagrande (1937), who developed a procedure to find the time required to reach a certain ‘‘proportion of drainage’’ of the upstream shell of dams having an impervious clay core. By assuming a straight saturation line, he was able to derive some analytical expressions. Later Reinius (1954) demonstrated the use of flow nets to solve slow drawdown problems. This contribution was based on earlier work published in Sweden. The key idea is that: [... ] the flow net at slow drawdown is determined by dividing the time in intervals and assuming the reservoir water level to be stationary and equal to the average value during the interval. He also computed, based on the Swedish friction circle method of analysis, safety factors during drawdown and plotted them in terms of a coefficient (k/nv), which integrates the soil permeability (k), the porosity (n) and the rate of drawdown, v. He also explained, in the following terms, the pore water pressure generation due to rapid drawdown: When the reservoir is lowered rapidly the total stresses decrease. If the soil does not contain air bubbles and the water content remains unchanged, the effective stresses in the soil also remains unchanged provided that the compressibility of the water is neglected. Hence the neutral stresses must decrease. A similar statement may be found in Terzaghi and Peck (1948). Examples of flow net construction for
6.3 Drawdown in a single slope Consider the case sketched in Figure 26. A fully submerged simple slope will experience a drawdown condition when the water level acting against the slope surface is lowered. The actual geometry of the slope analyzed is given in Figure 29. The figure indicates the position of three singular points used in the discussion: A point at midslope (PA ), a point at the slope toe (PB ) and a point away from the slope (PC ) which is representative of ‘‘bottom of the sea’’ conditions. Three
20
The initial state of pore pressure will be hydrostatic (Fig. 31). Consider first the case of a total and rapid drawdown. If the analysis is performed uncoupled, no change in pore pressures inside the slope will be calculated immediately after drawdown. This is the case plotted in Figure 32, which was obtained with program Code_Bright when only the flow calculation was activated. Note that Figures 31 and 32 provide essentially the same distribution of water pressures. A realistic condition concerning the drawdown rate (v = 0.5 m/day) will be imposed in the cases presented here. During drawdown boundary conditions of the upstream slope will follow a ‘‘seepage face condition’’: the boundary is assumed impervious unless the calculated water pressure at the boundary becomes positive. In this case water flows out of the slope following a ‘‘spring’’ type of condition. Three elastic moduli spanning the range 100–10000 MPa are considered. They cover the majority of situations in practice for compacted upstream shells of dams (especially for small to medium shear strains). The saturated permeability considered is a low value in order to highlight the differences between coupled and uncoupled analysis. Of course, these differences decrease as the soil becomes more pervious. Consider first the case of the ‘‘bottom of the sea’’ conditions (Fig. 33). All the coupled analyses lead essentially to the same response. This is because variations in the instantaneous response are erased by the simultaneous dissipation of pressures. For the stiffer materials considered (E = 1000, 10000 MPa), water pressures remain slightly above the values found in common cases soils. However, the pure flow analysis is far from the correct answer. Similar results were obtained for the three reference points. Only the case of the mid slope point is plotted in Figure 34. It may be argued that the pure flow analysis is a conservative approach if viewed in terms of slope safety against failure. However, this is a result which depends on the particular case considered and cannot
50 m PA PC
PB
Profile 3
Profile 2
100 m
Profile 1
Figure 29. Geometry of the slope. Labels indicate the position of three singular points mentioned in the discussion.
1000
1.E-08 1.E-09
Permeability (m/s)
Suction (MPa)
100
10
1
0.1
0.01
1.E-10 1.E-11 1.E-12 1.E-13 1.E-14 1.E-15
0.001 0
0.2
0.4
0.6
0.8
Degree of saturation
1
0
0.2
0.4
0.6
0.8
1
Degree of saturation
Figure 30. Retention curve and relative permeability function for the analysis of a simple slope.
Figure 31. Initial pore water pressure distribution before drawdown.
Figure 32. Pore water pressure distribution after immediate drawdown in an uncoupled analysis.
0.7
Pore water pressure (MPa)
0.6
auxiliary vertical profiles will assist in the analysis of results. An elastic constitutive law will characterize the soil. Concerning the hydraulic description, Figure 31 indicates the water retention curve and the relative permeability law adopted in calculations. The retention curve (Fig. 30) has been defined by means of a Van Genuchten model and the relative permeability varies with the degree of saturation following a cubic law (krel = ksat Sr3 ). A constant saturated permeability ksat = 10−10 m/s was also used in all calculations.
Uncoupled 0.5
0.4
Coupled; E=10000 MPa and E=1000 MPa 0.3
0.2
Coupled; E=100 MPa 0.1 0
100
200
300
400
500
600
700
800
900
1000
Time (days)
Figure 33. Pore water pressure evolution after progressive drawdown in point PC (see Fig. 30).
21
Table 5. Drawdown of a zoned earthdam. Constitutive parameters.
0.5 0.45 Uncoupled
Pore water pressure (MPa)
0.4
Definition of parameter
0.35
Units
ROCKFILL HYDRAULIC BEHAVIOUR Saturated permeability k m/s Retention curve parameters MPa (Van Genuchten) p0 λ – Maximum degree of saturation Sw max – Minimum degree of – saturation Sw min
0.25 0.2 Coupled; E =100 MPa
0.15 0.1 0.05 0 0
100
200
300
400
500
600
700
800
900
1000
Time (days)
Figure 34. Pore water pressure evolution after progressive drawdown in the point PA (see Fig. 29).
be generalized. It is also interesting to realize that the unrealistic uncoupled analysis leads to a lower pore pressure prediction in the long term. This is a result of the implicit assumption of infinite skeleton stiffness of the uncoupled calculation, which leads to faster dissipation rates than the coupled approach. 6.4
Symbol
Value
Coupled; E =10000 MPa and E=1000 MPa
0.3
In order to illustrate the behaviour of a dam during drawdown, of a zoned dam with a central core, stabilized by means of two rockfill shells, has been simulated. Once steady state conditions are reached, at maximum reservoir elevation, a drawdown at a constant rate of 0.5 m/day was simulated. Table 5 indicates the constitutive parameters selected for the rockfill shells and the clay core. Linear elastic materials were assumed in this case because drawdown is, in general, a case of mechanical unloading (see, however, Pinyol et al, 2008). The values of saturated permeability are indicated in Table 5. A cubic law describes the relative permeability. A sensitivity analysis against a variation of the value of p0 (0.2 or 0.007 MPa), of the shell material, was performed. The shell saturated permeability was 10−6 m/s. The second parameter of the retention curve, λ, was kept constant at the value given in Table 5. This drawdown case is discussed in detail in (Pinyol et al. 2008). Initial conditions result from the steady state situation reached at maximum reservoir level. Calculated pore pressures, at the end of drawdown, are plotted in Figure 35. Only positive pore pressure values are indicated in the figures to make them clearer. For the same permeability, the higher is p0 , the lower is the pore pressure calculated . The amount of drained water is similar in both cases. For p0 = 0.007 MPa the relatively small zone that becomes unsaturated during the drawdown has low values of degree of saturation. Whereas, for p0 = 0.2 MPa, the shell material is practically saturated above the phreatic line (suction
0.007, 0.2 0.33 1 0
ELASTIC BEHAVIOUR Elastic modulus Poisson’s ratio
E ν
MPa –
100 0.3
INITIAL STATE Initial degree of saturation Initial mean yield stress Initial porosity
Sw0 p∗o n
– MPa –
0.8 0.02 0.3
CLAY CORE HYDRAULIC BEHAVIOUR Saturated permeability k m/s Retention curve parameters (Van Genuchten) p0 MPa λ – Maximum degree of saturation Sw max – Minimum degree of – saturation Sw min
Drawdown in a simple zoned earthdam
10−6
10−8 0.05, 2 0.33 1 0
ELASTIC BEHAVIOUR Elastic modulus Poisson’s ratio
E ν
MPa –
50 0.3
INITIAL STATE Initial degree of saturation Initial mean yield stress Initial porosity
Sw0 p∗o n
– MPa –
0.8 0.02 0.3
(a)
(b)
Figure 35. Pore pressure distribution after total drawdown: (a) p0 = 0.2 MPa and (b) p0 = 0.007 MPa (Pinyol et al. 2008).
higher than 0). If positive pore pressure values are considered in stability calculation, higher p0 may leads to higher safety factors against slope failure than the case of a lower air entry value.
22
Table 6.
Parameters for the drawdown analysis of San Salvador dam.
Parameter
Symbol
Unit
Foundation
Upstream shell
Core
Young modulus Coefficient of volumetric compressibility Saturated permeability Retention curve (Van Genuchten)
E
MPa
150
100
30
mw ksat P0 λ Sr max Sr min
MPa−1 m/s MPa – – –
4.95 × 10−3 1 × 10−9 0.5 0.24 1 0.01
7.42 × 10−3 1.8 × 10−9 0.05 0.4 1 0.075
2.47 × 10−2 2.81 × 10−10 0.5 0.24 1 0.01
Water Pressure (kPa)
500
(a)
Start drawdown
400 300 200
Drawdown completed
100 0 0
100
200 300 Time (days) Coupled Mod.
400
500
Uncoupled Mod.
Figure 37. San Salvador dam. Evolution of pore pressures in a point distant from the dam toe, during drawdown and subsequent times. (b)
Figure 36. Pore water pressure contours. The represented interval is 100 kPa. (a) Uncoupled analysis. (b) Flowdeformation coupled analysis.
Water Pressure (kPa)
6.5
800
Drawdown analysis of San Salvador dam
Some relevant results of the drawdown analysis performed on San Salvador earthdam, (Fig. 16), which has recently been designed, are now discussed. Parameters for the analysis are given in Table 6. They were determined from tests performed at the design stage of the dam. Figure 36 shows a comparison of calculated pore water pressures alter drawdown for the coupled and uncoupled cases. The analyzed drawdown corresponds to the design specifications: reservoir level decreases 24 m in 60 days. Calculated pore pressures in the upstream shell, core and foundation under the hypothesis of uncoupled analysis are significantly higher than in the coupled case. This is clear also in Figures 37–39 which provide the evolution of pore water pressures in three representative points of the dam: two in the foundation and a third one in the shell, close to the core. Figure 37 indicates that non-coupled analyses are unable to reproduce an elementary result:
Start drawdown
700 600 500
Drawdown completed
400 300 0
400
800 1200 Time (days) Coupled Mod.
1600
2000
Uncoupled Mod.
Figure 38. San Salvador dam. Evolution of pore pressures in a point within the foundation, Ander the upstream shell during drawdown and subsequent times.
pore pressures under the bottom of the reservoir should follow, in an essentially instantaneous manner, the variations of reservoir water level. The uncoupled analysis results in pore pressures higher than the level in the reservoir. A similar result is observed in a profile directly affected by the dam (below the upstream toe; see Fig. 40). Three cases are represented: initial profile, profile immediately after drawdown and long term. In
23
Water Pressure (kPa)
800
Start drawdown
700 600 500
Drawdown completed
400 300 0
400
800 1200 Time (days) Coupled Mod.
1600
2000
Uncoupled Mod.
Figure 39. San Salvador dam. Evolution of pore pressures in a point within the upstream shell, close to the core, during drawdown and subsequent times. x = 227 m x = 180 m x=4m
Uncoupled model x=180
Coupled model x=180 m 100
80 Height (m)
80 Height (m)
Figure 41. Beliche dam. Settlement record of surface marker J54.
100
60 40
60 40 20
20 0
0
0 Initial state
250 500 750 Water Pressure (kPa) Drawdown completed
1000
Long term
0
250
500
750
1000
Water Pressure (kPa) Initial state
Drawdown completed
Long term
Figure 40. San Salvador dam. Vertical profiles at the toe of the dam. Comparison of coupled and uncoupled analyses.
the correct coupled analysis pore pressures after drawdown are higher than the hydrostatic long term values. This is due to the presence of the dam and the particular stress distribution associated with changes in total stresses against the boundary of the dam and the foundation soil. Pure flow analysis results in abnormally high pore water pressures.
7
Figure 42. Martín Gonzalo dam. Strain records of extensometers located at several depths and accumulated rainfall (Justo, 1991).
LONG TERM EFFECTS heavy rains. Then ‘‘jumps’’ are properly interpreted as collapse settlement of the rockfill material as it becomes wet. In fact, the jump is associated to a situation in which the rockfill becomes wetter that in the previous dam history. Such trends have been observed in several dams. Another example is shown in Figure 42. It describes the vertical strain measured at different elevations of Martin Gonzalo rockfill dam. The figure shows also the accumulated rainfall. Strain rates increase in times of rapid accumulation of rain. This is true during the first three years of dam operation. Later, the strain
Going back to the records of dam settlements in Figure 21, a more detailed examination of settlement during the first years of dam operation reveals also some interesting features of the delayed deformation of rockfill materials. Figure 41 shows the settlements of a surface marker (J54) located on the downstream edge of the dam crest, directly above the inner rockfill shell of the dam. Also included in the Figure is the record of rainfall intensity (in mm/month). The settlement records shows that finite ‘‘jumps’’ occurred at the time of
24
Vertical displacements (m) .
0.2
B
Base Case
-0.2 -0.4 -0.6 -0.8 -1
(a)
0
100 ,
90
,
,
0.4
0.2
0.6
0.8
1.0
1.2
360
720 1080 1440 1800 2160 2520 2880 3240 3600 Time (d)
(a) 0 Base Case
70
Waterm pressure (MPa)
.
80
Water suction [MPa]
J54
0
1
60
3
50 40 30
2
-0.2 -0.4 -0.6 -0.8 -1 -1.2
20
0
4
10 0 0
0,2
,
y
0,4
0,6
0,8
360
720 1080 1440 1800 2160 2520 2880 3240 3600 Time (d)
(b) 1
1,2
Figure 44. (a) Evolution of vertical displacements of surface marker J54. Comparison of measured and calculated values when the rockfill permeability of shells is increased ten times with respect to the base case. Also indicated (b) is the calculated evolution of water pressure (suction) in a reference point within the inner downstream rockfill.
1,4
Vertical stress [MPa]
(b)
Figure 43. (a) Sketch of a deforming dam because of shell collapse (Soriano, 1993). (b) Interpretation of deformations of point B (1–2: first wetting; 2–3: first drying; 3–4: second wetting).
current yield line towards zero suction state. Only rainfall intensities exceeding previous rainfall events will have the chance of deforming the dam (Path 3–4 in Fig. 43b). Eventually, if a rainfall event is capable of taking the entire downstream shell to 100% relative humidity the full collapse potential of the rockfill would be developed. Beyond this time no additional water-induced settlements would be expected. For a given weather regime, the most significant property which would control the necessary time span to develop the entire collapse potential of the dam downstream shell is the shell permeability. Of course, the upstream shell is affected by reservoir level changes in a direct manner and saturation (and the associated collapse) would be typically a consequence of the first impounding. In the downstream shell, the resulting Relative Humidity at a given point for a given rainfall intensity will be smaller, the higher the rockfill permeability, K. This is shown in Figure 44 in connection will Beliche dam. The history of calculated pressure in a point of the downstream shell is given Figure 44b. When Kincreases suction remains higher and collapse strains are reduced. The calculate settlements are now smaller than the values found for the ‘‘base case’’ which corresponds to lower permeability
records exhibit a slow accumulation of deformations but they are no longer associated with rainfall events. It is concluded that long term settlements of rockfill shells have two origins: a water content or suction related mechanism and a true creep effect which is not much dependent of water action. The first effect may easily be explained by current elastoplastic models of rockfill (or unsaturated soil behaviour). Figure 43a shows the deformation of a dam due to the collapse of the upstream shell. Consider now point B within the downstream shell of a dam. Compaction and subsequent construction of the entire dam will result in a given state of stress (Point 1 in a simplified vertical stress-suction space). Most likely, loading of Point B during construction will follow a yielding path and therefore Point B will end up in a yield line (the LC yield curve passing through Point B in Fig. 43b). Rainfall will induce a suction reduction (path 1–2). Irreversible compressible deformation will take place. Drying during subsequent stages (path 2–3) will only result in negligible shrinkage. Once in Point 2 and given the current LC yield surface at that moment, the only possibility for additional significant volumetric compression of Point B will be to drag again the
25
0,01 0
0,1
1
10
100
1000 10000 0.2MPa 0.4MPa 0.6MPa 0.8MPa 1.0MPa 1.2MPa 1.4MPa 1.6MPa 1.8MPa 2.0MPa
1 2 3 4 5
2.4MPa 6
2.8MPa
7 0,01 -1 0
0,1
1
10
100
1000 10000
0.2MPa
Figure 46. Time-dependent compressibility index, λt , measured in oedometer tests performed on compacted gravel of a quartzitic slate (after Oldecop & Alonso, 2002).
1 0.4MPa 2 3 4 5
0.6MPa 0.8MPa 1.0MPa
6 7 8
1.2MPa 1.4MPa
9
1.6MPa
10
1.8MPa
11 12 2.6 MPa 13
2.8MPa
14
Figure 45. Tests on Pancrudo slate gravel Strain-time records. (Oldecop, 2000). Figure 47. Correlation between the time-dependent compressibility index and the compressibility index for the tested rockfill.
Figure 44a. The practical consequences of this discussion is than pervious shells maintain a higher collapse potential than more impervious ones. However, the risk of transforming the collapse potential into settlements is low in this case because it would require rainfall events of low probability of occurrence. Pure creep effects are always present and this is also shown in Figure 41. The results of suction controlled oedometer tests on a crushed slate are shown in Figure 45. Two sets of time records for two Relative Humidities (50% to 100%) clearly show the effect of
RH and applied stress. Note also that the scale of time is logarithmic. A long term compressibility is defined as λt = dε/d (ln t). This index, for times in excess of 100 minutes, is plotted in Figure 46 for several suction controlled tests. The figure indicates that the rate of deformation ε˙ = dε/dt is proportional to1/t, p and logarithm of suction. In fact, given a value of time, confining stress (σv ) and suction, the long term strain rate is defined. These
26
experimental findings led to propose the following phenomenological relationship for ε˙ in the case of volumetric creep. ε˙ vc =
μp s + patm 1 − β c ln t patm
creek, but progressively decreased in height in the rest of the dyke perimeter. In fact, the ground topography was used to reduce the length of the artificial dam and, in some parts of the perimeter, the dam was not necessary. Figure 48 shows the dam cross section at the position of the original creek draining the area later occupied by the pond. On first impoundment, when the water level reached 15 m over foundation, a section of the dam, located directly above the position of the creek, failed causing a violent flood. Figure 49 shows the failed section. The development of the failure was not observed. When the photograph in Figure 49 was taken, the reservoir was essentially empty. Field observations (Fig. 50) indicated that the fill could have a significant collapse potential and, probably, a susceptibility to internal erosion. Troughs and sinkholes were observed in the downstream slope of the dam a few years after the collapse. The compacted soils (they are observed in the background of Fig. 50, where the almost vertical slope of the failed section remained stable a few years after the dam failure) were rather heterogeneous. Low plasticity sandy clays and high plasticity clays were compacted within short distances. There are also indications that the achieved field densities were lower than the Optimum Normal Proctor values. Wetting under load tests performed on some specimens indicated a high collapse potential. In two tests performed, collapse deformations reached values of 3.8% (for a vertical load of 85 kPa) and 8.3% (for a vertical load of 245 kPa). These two vertical loads are well within the range of vertical stresses expected within the maximum cross section given in Figure 48. Existing trees along the creek were felled during construction works. However, stumps were left ‘‘in situ’’. A few years after the failure stumps grew green again and gave rise to new trees in their ancient locations. This is an indication of the imperfect cleaning operations of the creek, which implies that any rain water falling into the pond area during construction was eventually drained out through the creek bed. This situation could only change in the final stage of the works, when the HDPE membrane covered the pond and the upstream slopes of the dam.
(4)
where μ and β c are model parameters. The following values were identified for the compacted Pancrudo shale: μ = 0.0012 MPa−1 and β c = 0.083. No experimental information is available for shear creep. In the analysis of Beliche dam (Alonso et al, 2005) an equation similar to (3) was suggested for deviatoric creep. Under triaxial conditions it was the proposed to substitute p by qand to maintain the β c coefficient. However the μ coefficient was substituted by η = 0.3 μ. The calculations reproduced in Figure 44 were performed with a generalized constitutive model for rockfill behaviour in which deformations had tree origins: elastic, plastic and creep. The model was able to reproduce in a satisfactory manner the recorded short and long term behaviour (10 years) of Beliche dam. Finally, in a recent work (Oldecop and Alonso, 2007) it was shown that the creep coefficient λt could be simply related with the stress-based compressibility coefficient λ. This is shown in the Figure 47 which shows the measured correlation between the two compressibility indices. The correlation depends on the current suction (λt /λ decreases as suction increases) but λt /λ for rockfill is similar to values reported in the literature for granular soils. Further discussion of this topic is given in Oldecop and Alonso (2007 a, b).
8
DAM FAILURE DURING IMPOUNDMENT: A CASE OF FILL COLLAPSE
An homogeneous dam covered by an impervious membrane was built in an arid environment to create an artificial pond. The pond occupied a small watershed area which was drained by a small creek. The dam had a maximum height of 20 m at the location of the
Figure 48.
Representative cross section of the dam.
27
connecting the upstream and downstream slopes of the dam.
Figure 49.
Downstream view of failed dam.
Figure 50.
Field indications of collapse potential of fill.
Additional field observations indicated that the polyethylene membrane penetrated into the upstream slope, adopting tunnel-like shapes, forced by the water hydrostatic force. These symptoms are also interpreted as an indication of the collapse potential of the fill. Voids were also observed in the lateral nearly vertical cuts into the fill left by the failure. It is believed that the membrane broke when forced by the water pressure into a collapsing soil, located upstream immediately above the creek elevation. Once the membrane was broken, the water under pressure found a preferential path of interconnected voids and cracks, which extended from upstream to downstream, above the creek location, creating a ‘‘tunnel’’ inside the fill, which increased in size and eventually collapsed, leaving a breach of approximately rectangular shape in cross section (Figure 49). Simulating of the entire process is a major challenge, but the preceding explanation could be supported by some analysis even if it only covers some partial aspects. Consider in Figure 51a a central vertical section through the dam longitudinal axis. A simplified geometry to analyse the collapse effects induced by creek wetting is shown in Figure 51b. The creek position becomes a point where wetting is simulated by imposing the condition of zero suction. The remaining fill maintains the expected suction after compaction and layer-by-layer construction. A simple two-dimensional model (in plane strain) was solved with the help of CODE_BRIGHT. The behaviour of the compacted fill was simulated by means of BBM (Alonso et al., 1990). Model
In view of the preceding description, a possible explanation for the failure could be described as follows: – Insufficient compaction of the fill, probably dry of optimum, builds a collapse potential into the fill. This collapse potential develops when a given point within the fill experiences an increase in confining stress over the initial (saturated) yield stress and, also, an increase in water content. – The fill located immediately above the creek holds the most critical situation: the dam reaches here the maximum height and the seeping waters through the creek bed could easily lead to a capillary rise affecting a certain thickness above the original ground level. Therefore, the fill volume having the highest collapse potential is viewed as an elongated mass of compacted soil lying directly above the creek. A collapse of this volume will tend to create voids and cracks, which could lead to a preferential path
Figure 51. (a) Longitudinal central plane and position of creek. (b) Two-dimensional representation.
28
parameters were approximated from some available laboratory data. In particular, collapse tests provided important information to approximate most of BBM parameters. A simulated collapse test under a vertical stress of 200 kPa is shown in Figure 52. The model in this case predicts a collapse of 5.5% for a full wetting. Starting at an initial suction of 3 MPa, these collapse strains are believed to approximate actual ‘‘in situ’’ conditions. BBM parameters selected to perform the calculations are summarized in Table 7. The model dimensions are 100 m (horizontal dimension) by 20 m (vertical dimension). It was ‘‘built’’ in 500 days, assuming an initial porosity n = 0.5 and initial suction s = 3 MPa. Boundaries were considered impervious during this phase. Then the suction in the lower centred point was brought to zero. Vertical stresses around this wetting point began to change at a rate controlled by
Figure 52. Model.
Figure 53. Evolution of vertical stresses against a plane located 2 m above the base during wetting of the central lower point (creek).
the assumed soil permeability. Results are shown in Figure 53. Arching effects are clear in the figure. Points above the creek position experience a reduction in stress, compensated by an increase away from the wetting point. The final result of collapse and unloading phenomena is a decrease in porosity, indicating a trend towards the development of open voids (this is the case if the reduction in porosity concentrates on preferential planes, namely the planes between compaction layers). This demonstration exercise was not developed in more detail because its aim was to support, in a qualitative way, a proposed mechanism for dam collapse. The dam failure highlights the risks associated with differential collapse inside an embankment structure. This differential collapse may be triggered by differential wetting processes (this is the case discussed here) or by other situations (differential stiffness, for instance). Of course, the original and fundamental risk is associated with the inherent high collapse potential of an insufficiently compacted soil, especially if compacted on the dry side.
Collapse test simulated with the adopted BBM
Table 7. Set of model parameters used in the simulation of collapse conditions of the fill.
9
BBM model κ Elastic compressibility λ(o) Saturated virgin compressibility r Parameter defining LC curve β Parameter defining LC curve pc Reference stress ν Poisson’s ratio M Critical state slope Hydraulic parameters K Saturated intrinsic permeability (isotropic) po Parameter of V. Genuchten model λ Shape of V. Genuchten model λr Power for relative permeability (Kr = Sλr r )
0.008 0.1 0.5 12 MPa−1 0.02 MPa 0.3 1
SUMMARY AND CONCLUSIONS
Compacted soils are first reviewed in the paper. An effort is made to relate the basic compaction variables (γ d , w) with constitutive parameters needed to perform comprehensive analysis of earthdam structures. The discussion was centered on the hypothesis and parameters of the Barcelona Basic Model. It is shown that a first reasonable approximation is to substitute the pair (γ d , w) by the pair of stress variable (saturated isotropic yield stress, p∗0 , suction, s). A relationship between yield stress, p∗0 , dry density and soil plasticity has tentatively been provided on the basis of a number of experimental results. However, the paper also
10−12 m2 0.24 MPa 0.5 3
29
ACKNOWLEDGEMENTS
highlights the relevant effect of microstructure to properly define the mechanical and hydraulic properties of compacted soils. The effect of compaction conditions on the behaviour of a zoned dam during construction is then discussed. A sensitivity analysis of a recently designed dam (San Salvador) was performed using the computer code CODE_BRIGHT, for coupled thermohydro-mechanical analysis of unsaturated/saturated soils. Pore pressure generation during construction and its relationship with compaction conditions was discussed. The selection of constitutive parameters in this case has benefited from some results given in the first chapter of the paper. The behaviour of rockfill and, in particular, its dependence on the ambient Relative Humidity (RH) is described. Particle breakage due to subcritical crack propagation (which is controlled by stress and RH) explains the compressibility, collapse and long term deformation of rockfill. Dam behaviour during reservoir impoundment and subsequent operation is then considered through The analysis of San Salvador dam. This dam is expected to be built within the next few years. The analysis shows the capabilities of current computational methods to capture the interaction between the development of flow and the stress and deformation changes of the structure. A historical review of published approaches to deal with rapid drawdown conditions has been made. The relevance of hydro-mechanical coupling effects is presented through some examples which include the performance of San Salvador dam under the design drawdown specifications. Long term deformation of earth and rockfill dams is the final topic. Long trerm effects are associated with two mechanisms: the collapse of dam shells induced by weather-induced changes in RH and the intrinsic creep phenomena, which, in the case of rockfill, is attributed to particle breakage. A few real cases, the results of laboratory tests and the analysis of Beliche dam illustrate the nature of long term deformations of dams. In a final chapter, the failure of a homogeneous earth dam, with an upstream impervious membrane, is described and analyzed. The suggested explanation for the accident is that the collapse of the insufficiently compacted fill was able to create preferential flowpaths connecting the upstream and downstream slopes. The case warns against the risks of poor compaction conditions but it also highlights the possibility of modern computational procedures, based on unsaturated soil mechanics, to assist in the design of dams. In fact, alternative scenarios concerning the soil type, compaction state and initial and boundary conditions can be examined at a limited effort.
The authors wish to acknowledge the contribution of Prof. S. Olivella, Prof. L. Oldecop and Eng. E. Ortega and C. Delorme to the preparation of this paper
REFERENCES Akai, K., Y. Ohnishi, Murakami, T. and Horita, M. 1979. Coupled stress flow analysis in saturated/unsaturated medium by finite element method. Proc. Third Int. Conf. Num. Meth. Geomech., 1: 241–249, Aachen. Alonso, E.E., Gens, A. and Hight, D.W. 1987. Special problems soils. General report. Procedding 9th European Conference on Soil Mechanics and Foundation Engineering, Dublin 3, 1087–1146 Alonso, E.E., Gens. A. and Josa. A. 1990. A constitutive model for partially saturated soil. Géotechnique, 40 (3), 405–430 Alonso, E.E. , Olivella, S. and Pinyol, N.M. 2005. A review of Beliche Dam. Géotechnique, 55, No. 4, 267–283 Baker, R, S. Rydman and M. Talesnick 1993. Slope stability analysis for undrained loading conditions. Int. Jnl. Num. and Anal. Methods Geomech. 17, 14–43. Balmaceda, A. 1991. Suelos compactados. Un estudio teórico and experimental. PhD Thesis, E.T.S. de Ingenieros de Caminos, Canales & Puertos de Barcelona. Barden, L. and G.R. Sides 1970. Engineering behaviour and structure of compacted clay. Inl. of SMFD. Proc. ASCE, 96 (SM4). 1171–1200. Barrera, M. 2002. Estudio experimental del comportamiento hidro-mecánico de suelos colapsables. PhD Thesis, E.T.S. de Ingenieros de Caminos, Canales & Puertos de Barcelona. (http://www. tdcat. cesca. es/TDCat0604102–0955249) Booth, A.R. 1975. The factors influencing collapse settlement in compacted soils. Proc. 6th Regional Conf. for Africa on Soil Mech. and Foundn. Eng. Durban, 1, 57–63. Brahma, S.P. and M.E. Harr 1962. Transient development of the free surface in a homogeneous earth dam. Géotechnique, 12, 283–302. Casagrande, A. 1937. Seepage through dams. Contributions to soil mechanics, 1925–1940. Boston Society of Civil Engineers. Cedergren, H.R. 1967. Seepage, drainage and flow nets, edited by Wiley, New York. Chávez, C and Alonso, EE. 2003. A constitutive model for crushed granular aggregates which includes suction effects. Soils and Foundations, 43 (4): 215–228. Cividini, A. and Gioda, G. 1984. Approximate F.E. analysis of seepage with a free surface. International Journal for Numerical and Analytical Methods in Geomechanics, 8, 6, 549–566. Collins, k. 1983. Scanning Electron Microscopy of Engineering soils. Geoderma. Vol. 30, pp 243–252. Cooley, R.L. 1971. A finite difference method for unsteady flor in variable saturated porous media: Application to a single pumping well. Water Res. Res., 7 (6), 1607–1625.
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Delage, P, Audiguier, M, Cui, Y.-J. and Howat, M.D. 1996. Micro-structure of a compacted silt. Canadian Geotechnical Journal, 33, 150–158 Desai, C.S. and Shernan, Jr., W.C. 1971. Unconfined transient seepage in sloping banks. Jnl. of the Soil Mech. and Found. Div., ASCE, N◦ SM2: 357–373. Desai, C.S. 1972. Seepage analysis of earth banks under drawdown. Jnl. of the Soil Mech. and Found. Div., ASCE, N◦ SM11: 1143–1162. Desai, C.S. 1977. Drawdown analysis of slopes by numerical method. Jnl. of the Soil Mech. and Found. Div., ASCE, N◦ GT7: 667–676. DIT-UPC 2002. CODE_BRIGHT. A 3-D program for thermo-hydro-mechanical analysis in geological media. USER’S GUIDE. Centro Internacional de Métodos Numéricos en Ingeniería (CIMNE), Barcelona. Freeze, R.S. 1971. Three dimensional transient saturatedunsaturated flow in a groundwater basin. Water Res. Res., 7 (2): 347–366. Honda, M., Seguchi, H., Kim, E., Hawai, K., Iizuka, A., and Karube, D. 2003. A study of the relation between volume change characteristics of compacted soil and the condition of compaction. Proceedings of the 2nd Asian Conference on Unsaturated Soils. April, Osaka, Japan, pp 177–180 Hromadka, T.V. and Guymon, G.L. 1980. Some effects of linearizing the unsaturated soil moisture transfer diffusivity model. Water Res. Res. 16 (4), 643–650. ICOLD 1980. Deterioration of dams and reservoirs. Examples and their analysis. ICOLD, Paris. Balkema, Rotterdam. Justo, J.L. 1991. Collapse: Its importance, fundamentals and modelling. In Advances in Rockfill Structures (ed. Maranha das Neves, E.), Kluwer Academic Publishers, Netherlands, 97–152. Lambe, T.W. 1958. The structure of compacted clay. Jnl. of the Soil Mech. and Foundn. Div. ASCE, 84 (SM2), 1–34. Lane, P.A. and Griffiths, D.V. 2000. Assessment of stability of slopes under drawdown conditions. Jnl. Geotech. and Geoenv. Engng. 126 (5): 443–450. Lawrence Von Thun, J. 1985. San Luis dam upstream slide. Proc. 11th Int. Conf. on Soil Mech. and Found. Engng. San Francisco. Vol. 5: 2593–2598. Lawton, E.C., R.J. Fragaszy and Hardcastle, J.H. 1989. Collapse of compacted clayey sand. Jnl. Geotech. Engng. ASCE. 115, 9: 1252–1267. Lawton, E.C., R.J. Fragaszy and Hardcastle, J.H. 1991. Stress ratio effects on collapse of compacted clayey sand. Jnl. Geotech. Engng. ASCE. 115, 5: 714–730. LeBihan, J.P. and Leroueil, S. 2000. Transient water flow through unsaturated soils—implications for earth dams. Proceddings 52nd Canadian Geotechnical Conference. Regina (Canada), pp 559–566. Lowe, J. and Karafiath, L. 1980. Effect of anisotropic consolidation on the undrained shear strength of compacted clays. Proc. Research Conf. on Shear Strength of Cohesive Soils. Boulder: 237–258. Marinho, F.A.M. and Chandler, R.J. 1993. Aspects of the behaviour of clays on drying. Unsaturated Soils. ASCE Geotechnical Special Publication number 39. Edited by Houston, S.L. and Wray, W.K. pp 77–90 Morgenstern 1963. Stability charts for earth slopes during rapid drawdown. Géotechnique 13 (2), 121–131.
Neumann, S.P. 1973. Saturated-unsaturated seepage by finite elements. Jnl. Hydraul. Div., ASCE, 99, HY12: 2233–2250. Oldecop, L. and Alonso, E.E. 2001. A model for rockfill compressibility. Géotechnique 51(1), 127–139 Oldecop, L. and Alonso, E.E. 2002. Fundamentals of rockfill time-dependent behaviour. Proc. 3rd International Conference on Unsaturated Soils. Recife (Brazil) 2: 793–798. Oldecop, L.A. and Alonso, E. 2004. Testing rockfill under relative humidity control. Geotechnical Testing Journal, 27(4): 269–278. Oldecop L.A., Alonso, E.E. 2007a. Theoretical investigation of the time-dependent behaviour of rockfill. Géotechnique, 57, No. 3, 289–301. Oldecop L.A., Alonso, E.E. 2007b. Discussion: Theoretical investigation of the time-dependent behaviour of rockfill. Géotechnique, 57, No. 9, 779–781 Olivella, S., Gens, A., Carrera, J., Alonso, E. 1996. Numerical formulation for a simulato (CODE-BRIGHT) for the coupled analysis of saline media. Engineering Computations, 13 (7): 87–112. Pauls, G.J., Karlsauer, E. Christiansen, E.A. and Wigder, R.A. 1999. A transient analysis of slope stability following drawdown after flooding of highly plastic clay. Can. Geotech. Jnl., 36, 1151–1171. Pinyol, N.M., Alonso, E.E. and Olivella, S. 2008. Rapid drawdown in slopes and embankment. Water Resources Research. In print. Reinius, E. 1954. The stability of the slopes of earth dams. Géotechnique, 5: 181–189. Richards, B.G. & Chan, C.Y. 1969. Prediction of pore pressures in earthdams. Proc. 7th Int. Conf. S.M.F.E., 2: 355–362. Mexico Romero, E., Gens, A. & Lloret, A. 1999. Water permeability, water retention and microstructure of unsaturated compaced Boom clay. Engineering Geology, 54, 117–127 Rubin, J. 1968. Theoretical analysis of two-dimensional transient flow of water in unsaturated and partly saturated soils. Soil Sci. Soc. Am. Proc. 32 (5), 607–615. Seed, H.B. and Chan, C.K. 1959. Structure and strength characteristics of compacted clays. Jnl. of the SMFD, ASCE, 85 (SM1). 87–128. Sherard, J.L., Woodward, R.J. Gizienski, S.F. and Clevenger W.A. 1963. Earth and earth-rock dams, edited by John Wiley and Sons, New York. Simms, P.H. and Yanful, E.K. 2001. Measurement and estimation of pore shrinkage and pore distribution in a clayey till during soil-water characteristic curve test. Canadian Geotechnical Journal, 38: 741–754. Soriano, A. 1993. Comportamiento de las presas de materiales sueltos & su auscultación. Memorias del Simposio sobre geotecnia de presas de materiales sueltos. Sociedad Española de Mecánica del Suelo & Cimentaciones, pp 389–409. Sivakumar, V. and Wheeler, S.J. 2000a. Influence of compaction procedure on the mechanical behaviour of an unsaturated compacted clay. Part1: Wetting and isotropic compression. Géotechnique 50, No.4, 359–368
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Sivakumar, V. and Wheeler, S.J. 2000b. Influence of compaction procedure on the mechanical behaviour of an unsaturated compacted clay. Part1: Shearing and constitutive modelling. Géotechnique, 50, No.4, 359–368 Stephenson, D. 1978. Drawdown in embankments. Géotechnique, 28 (4): 273–280. Suriol, J and Lloret, A 2007. Cambios en la estructura de suelos compactados frente a humedecimiento & secado. Ingeniería Civil, 147, pp 67–76.
Suriol, J., Gens, A. and Alonso, E.E. 1998. Behaviour of compacted soils in suction-controlled oedometer. 2nd International Conference on Unsaturated Soils. Pekin (China). Ed. International Academic Publishers. pp 438–443. Terzaghi, K. and Peck, R.B. 1948. Soil mechanics in engineering practice. Edited by Wiley, New York.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Recent developments in the techniques of controlling and measuring suction in unsaturated soils P. Delage Ecole des Ponts, CERMES (Université Paris-Est, UR Navier), France
E. Romero Universitat Politècnica de Catalunya, Barcelona, Spain
A. Tarantino Universita degli Studi di Trento, Italy
ABSTRACT: The difficulty of measuring and controlling suction in unsaturated soils is one of the reasons why the development of the mechanics of unsaturated soils has not been as advanced as that of saturated soils. However, significant developments have been carried out in the last decade in this regard. In this paper, a review of some developments carried out in the techniques of controlling suction by using the axis translation, the osmotic method and the vapour control technique is presented. The paper also deals with some recent developments in the direct measurement of suction by using high capacity tensiometers and in the measurement of high suction by using high range psychrometers. The recent progresses made in these techniques have been significant and will certainly help further experimental investigation of the hydromechanical behaviour of unsaturated soils.
1
2
INTRODUCTION
The coupled effects of changes in suction and stress on the response of unsaturated soils is a fundamental aspect to consider when dealing with unsaturated soils. The difficulty of measuring and controlling suction is one of the reasons why the development of the mechanics of unsaturated soils has not been as advanced as that of saturated soils in which water pressure is positive. In relation with the significant increase in research efforts carried out during the last two decades in the mechanics of unsaturated soils, various techniques of measuring and controlling suction have been adopted and/or further developed. These techniques have been described in detail in various papers (including Ridley and Wray 1996, Agus and Schanz 2005, Rahardjo and Leong 2006). Recently, significant advances have been performed in the field of controlling and measuring suction. This paper deals with some recent achievements gained in the use of the three techniques of controlling suction, i.e. the axis-translation technique, the osmotic technique and the vapour control technique. Two techniques of measuring suction are also considered, i.e. high capacity tensiometers and high range psychrometers.
2.1
TECHNIQUES OF CONTROLLING SUCTION Axis translation technique
2.1.1 Introduction The axis translation technique is the most commonly used technique of controlling suction. Early developments of this technique started with the pressure plate outflow technique (Richards 1941, Gardner 1956). The axis translation technique is associated with the matrix suction component, in which water potential is controlled by means of liquid phase transfer through a saturated interface—usually a saturated high airentry value (HAEV) ceramic disk or a cellulose acetate membrane—which is permeable to dissolved salts. The procedure involves the translation of the reference pore air pressure, through an artificial increase of the atmospheric pressure in which the soil is immersed. Consequently, the negative pore water pressure increases by an equal amount if incompressibility of soil particles and water is assumed—i.e., if the curvature of the menisci is not greatly affected. The translation of the pore water pressure into the positive range allows its measurement (Hilf 1956), and consequently, its control if water pressure is regulated through a saturated interface in contact with the sample.
33
This technique has been experimentally evaluated with soils having a continuous air phase and a degree of saturation varying between 0.76 and 0.95 by Fredlund and Morgenstern (1977) and by Tarantino et al. (2000) for degrees of saturation between 0.56 and 0.77. The axis translation technique has been criticised concerning the following aspects: i) it is not representative of field conditions where air pressure is under atmospheric conditions; ii) there are some doubts in how the air pressurisation process affects the water pressure when water is held by adsorption mechanisms; and finally iii) its application at nearly saturated states in the absence of a continuous gaseous phase is not straightforward. Nevertheless, the axis translation technique has proved to provide reasonable results and a good continuity between vapour equilibrium results at elevated suctions and nearly saturated states. An example can be found in Figure 1, in which the overall picture of water retention results under constant volume conditions obtained by combining different techniques (high-range transistor psychrometers and vapour control technique) jointly with axis translation, shows an adequate overlapping. The major experimental difficulties concerning the application of the axis translation are associated with: i) the accumulation of diffused air beneath the HAEV ceramic disk, ii) the control of the relative humidity of the air chamber to minimise evaporation or condensation effects on the sample, iii) the application of the air pressurisation process at elevated degrees of saturation, and iv) the estimation of the equalisation time.
continuity between the pore water and the water in the control system. In addition, the accumulation of air can lead to water volume change errors in drained tests and to pore-water pressure measurement errors in undrained tests. Consequently, an auxiliary device is required to flush periodically air bubbles accumulated below the HAEV ceramic. The following expression describes the rate of accumulation of dissolved air beneath the ceramic disk, which is based on the gradient of air concentration being the driving mechanism (Fredlund and Rahardjo 1993, Romero 1999): dVd n A D h(ua − uw ) = dt (uw + uatm )tc
(1)
where n, A and tc , represent the porosity, the crosssectional area and the disk thickness, respectively. h, is the volumetric coefficient of solubility of dissolved air in water (h = 0.018 at 22◦ C). D, is the diffusion coefficient through the saturated interface. uatm , represents the absolute atmospheric pressure; ua and uw refer to air and water gauge pressures respectively. The quantification of air diffusion has been recently carried out by Romero (2001a), De Gennaro et al. (2002), Airò Farulla and Ferrari (2005) and Padilla et al. (2006). Lawrence et al. (2005) presented a pressure pulse technique for measuring the diffused air volume by using pressure/volume controllers. Figure 2 presents values of the coefficient of diffusion of air through a saturated ceramic disk with an air-entry value higher than 1 MPa as a function of the applied matrix suction. Typical values are included between 3 × 10−11 and 2 × 10−10 m2 /s (for suctions
2.1.2 Air diffusion Air diffusion through the saturated porous network of the interface can induce the progressive loss of
additional data (Hoffmann 2005) wetting axis translation wetting vapor transfer drying SMI psychrometer
1000
Suction (MPa)
100 drying
10 wetting
1 0.1
vapor transfer axis translation
0.01 0.00
0.10
0.20 Water content
0.30
0.40
Figure 2. Diffusion coefficients for air through saturated ceramic disks as a function of the applied matrix suction (Airò Farulla and Ferrari 2005).
Figure 1. Water retention curves obtained by combining axis translation with other techniques (Hoffmann et al. 2005).
34
<0.7 MPa) with lower values than that of air diffusion in water (around 2.2 × 10−9 m2 /s at 20◦ C). Factors such as the tortuosity of the paths and a possible breakdown of Henry’s law in curved air-water interfaces can be associated with this reduction (Barden and Sides 1967). The figure shows how this coefficient tends to increase as suction increases over 0.7 MPa and how it gets closer to the air-entry value of the ceramic (the value at which the gas convection transport is initiated). As deduced from Equation (1), increasing the water pressure is an efficient way to reduce air diffusion rates for a given geometry of the interface element and for a specified matrix suction. The conventional technique of the pressure plate apparatus, in which the pressure of water is maintained under atmospheric conditions, is the less efficient configuration to control the diffusion of air.
dries the clay surface, and b) a liquid flux through the ceramic disk that regulates the imposed matrix suction. A series of 1-D numerical analysis was carried out by Romero (1999) to simulate evaporative fluxes and matrix suction changes during a wetting path. A maximum volumetric evaporative flux of 9.4 × 10−7 (mm3/s)/mm2 was computed when an initial relative humidity of 0.5 was imposed in the air chamber. With measured volumetric evaporative fluxes lower than this value, no important consequences are expected and relatively uniform matrix suction distribution is expected throughout the sample height (Romero 1999, 2001a, b). 2.1.4 Air pressurisation at elevated degrees of saturation The application of air pressure at elevated degrees of saturation (involving occluded air bubbles) can induce irreversible arrangements in the soil skeleton due to pore fluid compression and to the fact that air pressure acts as a total stress when the continuity of air is not ensured. Bocking and Fredlund (1980) studied the effect of occluded air when using the axis translation technique. As a consequence, if nearly saturated states are expected to be reached during the hydraulic paths, it is preferable to increase the air pressure when the continuity of air is ensured (degrees of saturation < 0.85) and then to maintain the continuous air phase at constant pressure. After this initial stage it is possible to attain nearly saturated states, since the air pathways have already been created. This can be observed in Figure 1, in which the drying path followed a wetting path that attained very low matrix suctions. Nevertheless, if air pressure is required to be increased at high saturation values, it is preferable to change it at very slow rates to allow the system to create air pathways and to diffuse air through the liquid (Di Mariano 2000, Romero 2001a).
2.1.3 Evaporation and condensation effects Vapour transfers between the soil and the surrounding air can be controlled by maintaining an adequate relative humidity in the air chamber (around 95%). Evaporative fluxes are originated by the difference in vapour pressure between the soil surface and the air chamber. Volumetric evaporative fluxes can be detected in the water volume change device as a nonstop inflow into the soil under steady-state conditions. Condensation of vapour in the internal walls of the pressure chamber due to temperature variations has also been reported by Oliveira and Marinho (2006). Measured volumetric evaporative fluxes at different porosities are presented in Figure 3 for a compacted clay specimen placed inside an air chamber at an initial relative humidity of 0.50 (Romero 1999). As shown in the figure, two different water fluxes are involved in the process: a) an evaporative flux that
Volumetric evaporative flux ((mm 3 /s)/mm 2 )
1.0E-00 6
Computed evaporative flux at 22˚C and constant h r =50%
2.1.5 Time to reach suction equalisation An important difficulty faced when using the axis translation technique is the estimation of the required time to reach suction equalisation. Water volume measurements are usually affected by the relative humidity of the air chamber and the diffusion of air. Although these phenomena can be minimised as previously suggested, the estimation of the equalisation time in oedometer and triaxial cells has been conventionally determined based on overall soil volume change measurements that are independently determined. Oliveira and Marinho (2006) studied the equilibration time in the pressure plate and recommended around three days for increments from 50 kPa to 100 kPa for gneissic soils. From the analytical solution proposed by Kunze and Kirkham (1962), that considers the ceramic disk
air chamber
8.0E-007
evaporative flux soil 6.0E-007
ceramic disc
liquid flux
water pressure system 4.0E-007
2.0E-007
(u a -u w)
≤ 0.06 MPa
0.0E+000 0 .3 5
0 .4 0
0 .4 5
Porosity, n
Figure 3. 1999).
Measured volumetric evaporative fluxes (Romero
35
membrane (permeable to water) while an aqueous solution containing large sized soluble polyethylene glycol molecules (PEG) is circulated behind the membrane. The PEG molecules cannot go through the membrane, resulting in an osmotic suction applied to the sample through the membrane. Being the membrane permeable to the salts dissolved in the water, the osmotic technique controls the matrix suction, like the axis translation technique. The value of the imposed suction depends on the concentration of the solution, the higher the concentration, the higher the suction. The suction/concentration relation will be discussed later in some details. Semi-permeable membranes are characterised by there molecular Weight Cut Off (MWCO) that is linked to the size of the PEG molecules that they can retain (MWCO 12 000–14 000 membranes are used with PEG 20 000, MWCO 6 000 with PEG 3 500, MWCO 4 000 with PEG 2 000 and MWCO 1 500 with PEG 1 000). Note that the smaller the MWCO, the higher the membrane permeability. Semi-permeable membranes are most often made up of cellulose acetate, but interesting results using more resistant polyether sulfonated membranes have been published by Slatter et al. (2000) and Monroy et al. (2007). Semi-permeable membranes are obviously thinner than the ceramic disks used in the axis translation technique, but, as shown in Delage and Cui (2008a), they have comparable impedances I (I = e/k, being e and k the thickness and water permeability respectively). On a Spectrapor 12 000–14 000 membrane, Suraj de Silva (1987) obtained e = 50 μm and k = 10−12 m/s, giving I = 5 × 107 s, compared to an impedance value of 7.5 × 10−7 s given by Fredlund and Rahardjo (1993) for a 6 mm thick 1 500 kPa air entry value ceramic disk. The osmotic technique was used to control the osmotic pressure of culture solutions in biology by Lagerwerff et al. (1961) and the water matrix potential in soil science by Painter (1966), Zur (1966) and Waldron and Manbeian (1970). Peck and Rabbidge (1969) designed an osmotic tensiometer for measuring the osmotic suction applied as a function of the PEG concentration. The first application to geotechnical engineering was by Kassiff and Ben Shalom (1971) with subsequent work carried out on a hollow cylinder triaxial apparatus by Komornik et al. (1980) and on a standard triaxial apparatus by Delage et al. (1987). The Kassiff and Ben Shalom’s device (Figure 4), was further improved by Delage et al. (1992) with the introduction of a closed circuit comprising a 1 litre bottle in which the solution was circulated by a peristaltic pump (being the bottle placed in a temperature controlled bath to allow water exchange measurements by using a capillary tube). The close circuit was adopted by Dineen and Burland (1995) with the bottle being permanently weighted by an electronic
impedance and the soil permeability to determine the time evolution of the water volume change in a soil with a rigid matrix, it is possible to estimate an equalisation time t95 for which 95% of the water outflow or inflow has occurred (note that for simplicity only one term of the Fourier series has been kept): 2 α L2 t95 ≈ − 2 ln 1 (a + csc2 α1 ) ; 40 α1 D π (2) aα1 = cot α1 with 0 < α1 ≤ ; 2 kw δs D= nγw δSr where L is the soil height, D the capillary diffusivity that is assumed constant and dependent on the water permeability kw and on the soil water capacity, δs/δSr (being s the matrix suction, Sr the degree of saturation respectively), n the porosity and γw the unit weight of water; a the ratio of impedance of the ceramic disk with respect to the impedance of the soil a = kw tc /(Lkd ) (being tc the ceramic disk thickness and kd its water permeability respectively) and α1 the solution of the equation in the indicated range. For low disk impedance, a ≈ 0 and α1 ≈ π/2, the minimum equalisation time can be approximately estimated as: t95 ≈ 1.129
L2 D
(3)
For a clayey soil with L = 20 mm, n = 0.48, kw = 5 × 10−12 m/s and δs/δSr ≈ 2.8 MPa in the suction range 0.1 MPa < s < 0.5 MPa and with disk properties characterised by tc = 7 mm and kd = 10−10 m/s, then a ≈ 0.018, α1 ≈ 1.543, D ≈ 3.0 × 10−9 m2 /s and t95 ≈ 2615 min. If no ceramic disk impedance is considered, then t95 ≈ 2500 min. It is important to remark that this estimation is based on the hypothesis of a constant soil volume, which is not exactly the case with a clayey soil. Nevertheless, it gives an approximate estimation of the minimum time required to reach suction equalisation. As a conclusion, provided its specific problems are adequately considered, the axis translation method has proven to be an efficient and reliable technique of controlling suction. It remains widely used to determine the water retention and transfer properties and the mechanical behaviour features of unsaturated soils, following the first adaptation to triaxial testing by Bishop and Daniel (1961). 2.2 Osmotic technique 2.2.1 Introduction In the osmotic technique (see Delage and Cui 2008a) the sample is placed in contact with a semi-permeable
36
Figure 4. (1971).
A technological advantage of the osmotic technique is that there is no need to apply any air pressure (resulting in no air diffusion problems). High level of suctions can easily be applied by using high concentration PEG solutions. It has been showed that the higher limit of the technique could be extended up to around 10 MPa (Delage et al. 1998) and an osmotically suction controlled oedometer compression test at a suction of 8.5 MPa has been presented by Cuisinier and Masrouri (2005a). This extension to high suction is obviously easier than when using the axis translation technique (Escario and Juca 1989). In the triaxial apparatus, the application of high suctions is facilitated by the fact that there is no need to impose high values of confining stress to maintain constant the net total mean stress σ − ua at the elevated air pressures needed to impose high suctions. The highest suctions applied in triaxial testing (1500 kPa) were by using the osmotic technique (Cui and Delage 1996). In clays, with air entry values frequently higher than 1 MPa, this advantage is significant to ensure significant sample desaturation. In the oedometer, the application of the osmotic technique is easy since no air-tight device is necessary to apply the air-pressure on the sample, resulting in less friction effects between the piston and the ring. The adaptation of the osmotic technique to the oedometer only consists in replacing a porous stone (most often the bottom one) by a semipermeable membrane clamped between the oedometer base and the ring. In the triaxial apparatus, the adaptation is less straightforward, as compared to that of the axis-translation technique, more often used. The main drawback of the osmotic technique is the sensitivity to bacteria attacks of the cellulose acetate membranes that have been most commonly used up to now. When a semi-permeable membrane fails, the PEG solution can infiltrate the sample and suction is no longer controlled. The problem seems to be more serious when applying high suctions along wetting paths (suction decrease), as observed by Marcial (2003). In this regard, note that a concern recently evidenced by Delage and Cui (2008b) is related to the possible presence of PEG molecules of dimensions smaller than that defined by the molecular weight given by the manufacturer. The presence of these small molecules was demonstrated by developing a novel filtration system applied to PEG 6 000, filtrated by using a MWCO 3 500 cellulose acetate membrane. When using cellulose acetate membranes, this effect can be corrected by adding few drops of penicillin in the solution. In such conditions (Kassiff and Ben Shalom 1971), the life duration of the membrane appears to be longer than 10 days. More recently, Slatter et al. (2000) suggested the alternative use of polyether sulfonated semi-permeable membranes. By using these membranes, Monroy et al. (2007) carried out tests as long as 146 days. This option seems to
The osmotic oedometer of Kassif and Ben Shalom
Figure 5. Comparison of the osmotic technique with various other suction control techniques (after Fleureau et al. 1993).
balance to monitor the water exchanges. Tarantino and Mongiovi (2000) and Monroy et al. (2007) also used this device. Figure 5 shows a comparison carried out on a kaolinite slurry submitted to changes in suction over a wide range by using various suction control techniques, with a reasonable agreement observed between the various techniques. Ng et al. (2007) drew similar conclusions based on results from shear testing. 2.2.2 Advantages and drawbacks Compared to the axis translation technique, the osmotic technique presents the advantage of exactly reproducing the real conditions of water suction, with no artificial air pressure applied to the sample. This advantage is believed to be significant in the range of high degrees of saturation when air continuity is no longer ensured with the apparition of occluded air bubbles and possible artefacts created by the air pressure application (see discussion above).
37
be an excellent way to enhance the reliability of the osmotic method.
observed some difference when comparing calibration points along a wetting path (suction decrease) compared to that along a drying path (suction increase) with smaller suction obtained during the subsequent drying path. Actually, a similar membrane effect had also been observed from the data of Waldron and Manbeian (1970) who developed a null type osmometer in which the osmotic pressure was compensated by an air pressure applied to the solution for suctions included between 16 and 2480 kPa. As a conclusion, it seems that the use of more resistant membranes together with the completion of specific calibrations based on the couple membrane/PEG used will give good reliability to the osmotic technique. The advantages of the technique should probably help for better experimental investigation and understanding of the transition zone at high degrees of saturation (Sr < 0.85), where the air continuity no longer stands and where samples get closer to saturation. The technique seems also particularly suitable to study the behaviour of unsaturated plastic soils with AEV higher than 1 MPa.
2.2.3 Calibration of the method Initially, the calibration curves giving the total suction as a function of the solution concentration of various PEGs were investigated by measuring the relative humidity above solutions of PEG by using psychrometers (Lagerwerff et al. 1961, Zur 1966). The data from various authors gathered by Williams and Shaykewich (1969) indeed showed no significant difference between points obtained with PEG 6 000 and with PEG 20 000, the calibration curve being independent on the molecular mass of the PEG used. Based on this calibration, reasonable comparison with the axis translation techniques have been obtained by Zur (1966) and Waldron and Manbeian (1970) on various soils. This is confirmed by the data of Figure 5. Further calibrations were carried out by Dineen and Burland (1995) who used the high range tensiometer (up to 1500 kPa) developed by Ridley and Burland (1993). They made direct suction measurements on a sample kept under a suction controlled by the osmotic technique in a oedometer and they also measured directly the suction by placing the probe in contact, through a kaolinite thin layer, with the semi-permeable membrane behind which the solution was circulated. The same approach was adopted by Tarantino and Mongiovi (2000) and, more recently, by Monroy et al. (2007). The effect of the pair membrane/PEG used on the calibration has been observed by these authors on various membranes and PEGs, as seen in Figure 6. In accordance with Slatter et al. (2000), Monroy et al. (2007) observed that, for a given concentration, the highest suctions were obtained by using the polyether sulfonated membrane with PEG 35 000 with suction values close to that of Williams and Shaykewich (1969). Monroy et al. (2007) also
2.3 Vapour control technique Vapour equilibrium technique is implemented by controlling the relative humidity of a closed system. Soil water potential is controlled by means of the migration of water molecules through the vapour phase from a reference system of known potential to the soil pores, until equilibrium is achieved. The thermodynamic relation between total suction of soil moisture and the relative humidity of the reference system is given by the psychrometric law (Fredlund and Rahardjo 1993). The relative humidity of the reference system can be controlled by varying the chemical potential of different types of aqueous solutions (Delage et al. 1998, Tang and Cui 2005). Oedometer cells installed inside a chamber with relative humidity control were used by Esteban (1990), Bernier et al. (1997) and Villar (1999) and Cuisinier and Masrouri (2005b). The main drawback of this experimental setup is that the time to reach moisture equalisation is extremely long due to the fact that vapour transfer depends on diffusion (several weeks are required for each suction step in the case of highdensity clays as observed in Figure 7). In order to speed up the process, vapour transfer—through the sample or along the boundaries of the sample—can be forced by a convection circuit driven by an air pump (Yahia-Aissa 1999, Blatz and Graham 2000, Pintado 2002, Lloret et al. 2003, Oldecop and Alonso 2004, Dueck 2004, Alonso et al. 2005). The mass rate transfer of vapour by convection (assuming isothermal conditions and constant dry air pressure uda ) can be expressed in terms of mixing ratio (mass of vapour per unit mass of dry air) or relative
1600 Dineen and Burland (1997) (PEG 20 000)
suction (kPa) Pa)
1200
Tarantino and Mongiovi T o (2000) (Spectrum 14 000, PEG 20 000) r
800 Tarantino and Mongiovi (2000) (Viskase14 000, PEG 20 000)
400
Monroy et al. (2007) (PEF 15 000, PEG 35 000)
0
50
100
150 200
250 300
350
400
450
500
concentration (g PEG/L water)
Figure 6. Dependency of the calibration curve of the osmotic technique with respect to the membrane and PEG used (after Delage and Cui 2008a).
38
expressed as ρv = Mmw uv0 hr /(RT ), where uv0 is the saturated vapour pressure at absolute temperature T , Mmw is the molecular mass of water, R is the gas constant, and hr the relative humidity. Based on the same assumption and that dry air is also an ideal gas, the following expression is obtained x = Mmw uv /(Mmda uda ) = 0.622 uv /uda , in which Mmda is the molecular mass of dry air mixture, uda the dry air pressure and uv the vapour pressure. One of the difficulties in using the vapour equilibrium technique is associated with maintaining thermal equilibrium between the reference system (vessel with aqueous solution) and the sample. Assuming that the vapour pressure set by the reference saline solution is also present in the sample, the following correction is proposed, in which hr is the relative humidity and uv0 the saturation vapour pressure at temperature T
humidity differences between two points in the circuit (in and out) as (Oldecop and Alonso 2004, Dueck 2007). Figure 7 shows the evolution of vertical strains (expansive deformations are positive) of compacted bentonite subjected to a reduction (from 150 MPa to 4 MPa) in suction under oedometer conditions (vertical net stress of 10 kPa), using both relative humidity controlled chamber (pure diffusion of vapour) and forced flow of humid air on both ends of the sample. As observed, the forced flow speeds up the process of suction change. The mass rate transfer of vapour by convection (assuming isothermal conditions and constant dry air pressure uda ) can be expressed in terms of vapour density or mixing ratio differences between the reference vessel with aqueous solution (superscript r) and the soil (superscript s) (a: Oldecop and Alonso 2004, b: Jotisankasa et al. 2007) a) Mdry b) Mdry
hrsample = hrreference
qMmw dw = q(ρvr − ρvs ) = uv0 (hrr − hsr ) dt RT dw = qda (xr − xs ) = qda x0 (hrr − hsr ) (4) dt
25
Volumetric strain (%)
20
forced convection along boundaries 15
10
5
pure diffusion 0 1000 Time (min)
(5)
A possible way to minimise this thermal effect is achieved by disconnecting the reference system that regulates the relative humidity, and allow the equalisation of vapour in the remaining circuit and the soil. This way, the mass of water being transferred from or to the soil is drastically reduced (there is no contribution in water transfer between the vessel and the soil). An equivalent testing procedure was used by Oldecop and Alonso (2004) to overcome the long equalisation periods of the conventional vapour equilibrium technique. Another problem that comes up when using the forced convection system is associated with air pressure differences created along the circuit. This fact makes that the intended relative humidity applied by the reference vessel cannot be assigned to the remaining circuit and the soil. Dueck (2004) studied the influence of air pressure changes in a forced convection circuit of vapour and their consequences on the applied relative humidity. Figure 8 shows the experimental setup and the evolution of differential air pressures between two points of the circuit (before and after the filter stones). The consequences on the evolution of the relative humidity at the same two points of the circuit are shown in Figure 9. An expression to account for the effects of air pressure variations on the relative humidity can be proposed based on the assumption that the mixing ratio x = 0.622 uv /uda (mass of vapour per unit mass of dry air) set by the reference saline solution is also set in the sample under isothermal conditions
where Mdry is the soil dry mass, w the gravimetric water content, q the volumetric air flow rate, ρv the vapour density in air (water mass per unit volume of air), qda the flow rate of dry air mass, and x the mixing ratio (mass of water vapour per unit mass of dry air; x0 represents the saturated mixing ratio). Assuming vapour an ideal gas, the vapour density can be
100
uv0 (Treference ) uv0 (Tsample )
10000
x0 reference x0 sample uda sample = hrreference uda reference
hrsample = hrreference
Figure 7. Evolution of volumetric strain on compacted bentonite using humid air flow along the boundaries of the sample (forced convection) or controlling the air relative humidity inside a closed chamber (pure diffusion) (Pintado 2002).
hrsample
39
(6)
tensiometer and comprises a water reservoir, a high airentry interface and a pressure gauge. Figure 10 shows the second prototype developed by Ridley & Burland (1995) which will be referred to as ‘IC tensiometer’. This tensiometer includes an integral strain-gauged diaphragm in contrast to the first prototype (Ridley & Burland 1993) obtained by fitting a porous ceramic disk to a commercial pressure transducer. Key elements of the IC tensiometer were the very thin water reservoir (less than 4 mm3 ) and the use of a sufficiently thick high air-entry value ceramic disk (Ridley 1993). Provided adequate de-airing processes and pressurisation were carried out, the IC tensiometer could move the maximum sustainable suction up to 1800 kPa, a value significantly higher than 70–80 kPa typical of standard tensiometers. The IC tensiometer was particularly welcome by the geotechnical community since suction was difficult to measure accurately in the range 0–1500 kPa using other techniques such as the psychrometer. As shown in Table 1, the concept of the IC tensiometer had significant success and many similar devices have been developed since that time with some specific technological improvements, as discussed in Tarantino (2004), Mahler and Diene (2007), and Marinho et al. (2008). Design and use of high capacity tensiometers have been satisfactorily documented. This measurement technique now appears to be reasonably affordable to develop and to use in the laboratory.
Figure 8. a) Experimental setup to study air pressure and relative humidity changes along a forced convection circuit. b) Time evolution of differential air pressures (at 80 min the air is forced through the filter stones) (Dueck 2004).
3.1.1 Water under tension and cavitation Cavitation of water typically occurring at negative gauge pressures close to −70/ − 80 kPa has long been explained by the inability of water to sustain tensile stresses. This supposition is incorrect as water can indeed sustain high tensile stresses as earlier recognised by Berthelot (1850) and confirmed by several experiments carried out by using metal and glass Berthelot-type systems (see Marinho and Chandler 1995). Using a Berthelot-type device, relatively long measurements could be carried out by Henderson & Speedy (1980) who reported a tension of 10 MPa sustained for over a week. Zheng et al. (1991) were able
Figure 9. Time evolution of measured and calculated relative humidity at two points of the forced convection circuit (at 80 min the air is forced through the filter stones) (Dueck 2004).
in which hr = x/x0 is the relative humidity, x0 = 0.622 uv0 /uda the saturated mixing ratio (uv0 is the saturated vapour pressure), and uda the dry air pressure.
3 3.1
TECHNIQUES OF MEASURING SUCTION High capacity tensiometers
In terms of suction measurement, significant progress has been made with the development of the highcapacity tensiometer (HCT) by Ridley & Burland (1993). The HCT is similar in conception to a standard
Figure 10. The Imperial College suction probe (Ridley and Burland 1995).
40
to measure a tensile stress of 140 MPa in a single crystal of water, a value believed to be very close to the maximal tension that water can sustain. The state of water under tension is thermodynamically metastable (De Benedetti 1996) in the sense that a gas phase will rapidly separate in the liquid if tiny amounts of gas (cavitation nuclei) are pre-existent in the liquid. Marinho and Chandler (1995) reviewed the sources of impurities in the water which include i) solid particles that contain gas micro-bubbles trapped in crevices, ii) gas trapped in tiny crevices in the walls of the water container, iii) air bubbles stabilized by ionic phenomena and iv) bubbles covered by surface active substances. Note that in high range tensiometers, case i) also applies to the pores of the ceramic porous stone. Since it is virtually impossible to completely remove air from the water reservoir and the porous ceramic filter, heterogeneous cavitation will inevitably occur in the HCTs. The main challenge in tensiometer measurement is then to delay cavitation by minimising the number of potential cavitation nuclei present in the tensiometer. This has essentially been achieved by adopting special design features and by implementing specific procedures for saturating the porous ceramic disk (initial saturation and subsequent re-saturation).
Table 1. High-capacity tensiometers developed by various authors including the pressure transducers used. Authors
Pressure transducer
Ridley & Burland (1993) König et al. (1994) Ridley & Burland (1995) Guan & Fredlund (1997) Meilani et al. (2002) Tarantino & Mongiovi (2002) Take and Bolton (2002, 2003) Toker et al. (2004) Mahler et al. (2002) Chiu et al. (2005) Lourenco et al. (2006, 2007)
Entran EPX (3.5 MPa) Druck PDCR 81 (1.5 MPa) Home-made (4 MPa) Brand not given (1.5 MPa) Druck PDCR 81 (1.5 MPa)
Oliveira and Marinho (2007) He et al. (2006) Mahler & Diene (2007) Cui et al. (2008)
Home-made (4 MPa) Druck PDCR 81 (1.5 MPa) and Entran EPB (0.7 MPa) Data Instr. Inc. AB-HP 200 Ashcroft K8 Druck PDCR 81 (1.5 MPa) Ceramic transducer by Wykeham Farrance (0.8 MPa) Entran EPX (3.5 MPa) Entran EPX (3.5 MPa) Entran EPX (1.5 MPa) Entran EPXO (0.5 MPa) Ashcroft (0.5–1.5 MPa) Home-made
1997, He et al. 2006), araldite (Meilani et al. 2002, Take & Bolton 2003, Lourenço et al. 2006) or copper gasket (Toker et al. 2004). In general, the best performance in terms of maximum sustainable tension and measurement duration appear to be achieved by the integral strain-gauged diaphragms. On the other end, concerns arise about the use of O-rings to seal the water reservoir. The change in design from the 1993 to the 1995 IC tensiometer was also aimed at eliminating O-rings and elastomers which are sources of nucleation sites (Take 2003). Toker et al. (2004) also found that cavitation occurred at very low tensions when sealing the water reservoir using rubber O-rings and that significant improvement could be obtained by replacing the O-ring with araldite or copper gasket. The tensiometer presented by Guan & Fredlund (1997) which included an O-ring to seal the water reservoir also exhibited relative poor performance. Despite the high pre-pressurisation pressure (12 MPa), the maximum sustained tension (1.25 MPa) was significantly lower than the nominal AEV of the ceramic disk (1.5 MPa). As shown in the next section, this is not the case of integral strain-gauged diaphragms and araldite-assembled tensiometers where maximum sustained tension can significantly exceed the nominal AEV of the ceramic disk.
3.1.2 Design The very small water reservoir designed by Ridley and Burland (1993, 1995) was assumed to decrease the number of cavitation germs in free water and hence the probability of cavitation occurrence. In this regard, Ridley and Burland (1999) mentioned that the change in design from the 1993 to the 1995 IC tensiometer was aimed at reducing as far as possible the size of the water reservoir. According to their experience, this reduction (with a water reservoir thickness close to 0.1 mm as shown in Figure 10) appeared to allow suction measurements with no cavitation along a longer period of time, with less random breakdowns of the measurements (Guan and Fredlund 1997 give a water reservoir thickness between 0.1 and 0.5 mm). Reducing the thickness of the water reservoir is believed to be an important feature necessary to develop high capacity tensiometers that has been followed in all the prototypes described in Table 1. In general, the reservoir volume is of the order of 5–10 mm3 with thickness as low as 0.1 mm. Two types of design have been presented in the literature, integral strain-gauged tensiometers (Ridley & Burland 1995, Tarantino & Mongiovì 2002, Cui et al. 2008) and tensiometers obtained by fitting a high AEV ceramic disk to a commercial transducer. The latter can be further divided in three classes, depending on whether the water reservoir was sealed by means of O-Ring (Ridley & Burland 1993, Guan & Fredlund
3.1.3 Initial saturation Ridley and Burland (1999) emphasized the importance of careful initial saturation of the porous stone by
41
de-aired water under vacuum, prior to pressurisation. They observed that a subsequent pressurisation at 4 MPa for at least 24 h could provide satisfactory suction measurements. Adopting these precautions, they concluded that the maximum sustainable suction was only depending on the air entry value of the ceramic filter, most often equal to 1500 kPa in existing devices. This observation is nicely illustrated by the results presented in Figure 11 (Ridley and Burland 1999) that shows the maximum suction obtained with various ceramic porous stones with air entry values (AEV) of 100, 500 and 1500 kPa respectively. It is interesting to note that the combination of an initial saturation under vacuum and a prepressurisation pressure about 2.7 times the AEV of the ceramic disk could produce maximum sustained tensions significantly higher than the nominal AEVs of the porous ceramic disks (164/100 kPa, 740/500 kPa and 1800/1500 kPa respectively). The importance of the initial saturation under vacuum has also been discussed by Take & Bolton (2003). Three procedures for initial saturation of the ceramic disk were investigated i) saturation at atmospheric pressure; ii) evacuation in presence of water followed by saturation under vacuum; iii) evacuation in absence of water followed by saturation under vacuum. In case i), the tensiometer could not sustain any tension even after four pre-pressurisation cycle of 1000 kPa. In case ii), once subjecting the tensiometer to a pre-pressurisation cycle of 1000 kPa, a maximum sustainable tension of 460 kPa could be attained (greater that the nominal 300 kPa AEV of the ceramic disk). In this case, vacuum in presence of water was somehow limited by the vapour pressure of water (2.3 kPa at 20◦ C). Finally, in case iii), an absolute pressure of 0.05 kPa could be attained when applying vacuum in absence of water and the maximum sustainable tension, once subjecting the tensiometer to a pre-pressurisation cycle of 1000 kPa, could be increased to 530 kPa. A procedure similar to case iii) was devised by Tarantino & Mongiovì (2002) with the exception of the porous ceramic initially dried using silica gel instead of oven-drying at 60◦ C.
Figure 11. Maximum suction response obtained with various ceramic porous stones (Ridley and Burland 1999).
about −0.1 MPa were also used by Take & Bolton (2003). On the other hand, Ridley & Burland (1995) observed that, provided initial saturation was carried out under vacuum, pre-pressurisation at a constant pressure of 4 MPa (2.7 times the nominal AEV) for a period of 24 h was sufficient to measure water tensions higher than the ceramic disk nominal AEV. The application of a constant pre-pressurisation pressure over a period of time was also adopted by Tarantino & Mongiovì (2002), Meilani et al. (2002), Chiu et al. (2005), Lourenço et al. (2006), He et al. (2006) and Cui et al. (2008).
3.1.4 Pre-pressurisation An issue that has long been debated is the procedure to be used to re-saturate the porous ceramic disk. Guan and Fredlund (1998) observed that the cavitation tension was essentially depending on the number of pre-pressurisation cycles and to a less extent on the pre-pressurisation pressure and duration. In particular, they found that 6 pressures cycles from −0.1 to 12 MPa produced the maximum sustainable tension. Cycles including the application of a positive pressure followed by a negative gauge pressure of
42
water
Table 2. Effect of the pre-pressurisation pressure on the maximum sustained tension (in bold sustained tension greater than the ceramic disk nominal AEV).
Authors Ridley & Burland (1993) Ridley & Burland (1995)
Max Ceramic pressure AEV positive (MPa) (MPa)
1.5 0.1 0.5 1.5 Guan and Fredlund (1997) 1.5 Meilani et al. (2002) 0.5 Tarantino & Mongiovi (2002) 1.5 MPa Take & Bolton (2003) 0.3 Mahler et al. (2002) Chiu et al. (2005) 0.5 Lourenco et al. (2006) 1.5 He et al. (2006) 0.5 Mahler and Diene (2007) 0.5 1.5
solid air
Max tension water (MPa)
6 4 4 4 12 0.8 4 MPa 1
1.37 0.164 0.74 1.8 1.25 0.495 2.06 0.53
0.7 1 2 0.6 0.6
0.47 1.23 0.55 0.8 1.4
There is no experimental evidence showing that that one procedure is preferable to the other. On the other hand, little attention has been given so far to the pre-pressurisation pressure in relation to the AEV of the ceramic disk. Table 2 shows the pre-pressurisation pressure adopted by different authors together with the AEV of the ceramic disk and the maximum sustained tension. It can be observed that pre-pressurisation pressures greater than 2.7 times the nominal AEV of the ceramic disk can produce maximum tensions greater than the ceramic AEV (Ridley & Burland 1995, Tarantino & Mongiovì 2002, Take & Bolton 2003, He et al. 2006). The only exception is given by the tensiometers developed by Ridley & Burland (1993) and Guan & Fredlund (1997) which, however, were sealed using O-rings. On the other hand, pre-pressurisation pressures in the range 0.67–1.6 AEV appear to produce relative poor performance (Meilani et al. 2002, Chiu et al. 2005, Lourenço et al. 2006), in the sense that the maximum sustained tension was lower than the ceramic disk AEV. The only exception appears to be given by the tensiometers by Mahler & Diene (2007) which, however, showed unusual response upon cavitation as water pressure appear to return to zero instead of −100 kPa gauge pressure as in all other tensiometers presented in the literature. Another experimental procedure that can be adopted to improve both maximum sustainable tension and measurement duration consists in subjecting the tensiometers to repeated cycles of cavitation (induced by placing the probe in contact with a dry sample for instance) and subsequent pressurisation. Experimental evidence of the beneficial effect of
a)
b)
c)
d)
Figure 12. Possible cavitation mechanism inside the tensiometer: a) pre-pressurisation; b) measurement; c) cavitation; d) air diffusion (Tarantino and Mongiovi (2001).
this procedure is provided by Tarantino & Mongiovì (2001) using IC tensiometer, Tarantino & Mongiovì (2002) using Trento tensiometer, Toker (2002) using MIT 6.1 tensiometer, and Take & Bolton (2003) using the tensiometer developed at the University of Cambridge. The application of repeated cycles of cavitation and pre-pressurisation appeared to not improve the response of the tensiometer presented by Chiu et al. (2005) and Lourenço et al. (2006). However, these authors applied relatively low prepressurisation pressures (see Table 2) which may explain the non-beneficial effect of this procedure. Tarantino & Mongiovì (2001) assumed that repeated cycles of cavitation and re-saturation can reduce number and size of cavitation nuclei in the porous ceramic disk. Air in small nuclei would be driven together by cavitation in larger cavities that are subsequently more easily forced into solution by pressurisation. This phenomenon is illustrated in Figure 12 and would suggest that cavitation occurs inside the
43
porous stone rather that in the water reservoir. Experimental evidence supporting this assumption is provided by Tarantino & Mongiovì (2001) and Tarantino (2004). Evidence is also given by Guan and Fredlund (1997) who observed that the inner face of the ceramic disk became relatively soft after repeated cavitations and it was possible to peel the surface with a slight fingernail scratch. This degradation is likely to be related to the occurrence of cavitation localised in this area. 3.1.5 Evaluation of tensiometer performance The quality of the suction measurements provided by the various tensiometers developed so far has been investigated by various means by the different authors. Most often, the tensiometer calibration has been conducted by extrapolating calibration established with positive water pressures to negative pressures. In a first attempt, Ridley and Burland (1993) performed suction measurements on a saturated clay sample put under a given isotropic effective stress situation and subsequently unloaded in undrained conditions, considering that a suction equal to the effective stress would develop (hence implicitly assuming sample isotropy and ‘‘perfect sampling’’, see Doran et al. 2000). Guan and Fredlund (1997) measured the suction of samples put at controlled suctions by using the axis translation method. They also compared the tensiometer measured suctions with filter paper measurements, as done also by Marinho and Chandler (1994) in an attempt to investigate possible osmotic effects. Tarantino and Mongiovi (2001) stated that the comparison between direct and indirect methods was probably not the best approach, and they successfully compared the measurements given by two IC tensiometers put in contact with the same sample, concluding on the satisfactory quality of the measurement. They also observed an excellent agreement between the measurements given by a Trento tensiometer and a IC tensiometer placed in contact with a dry kaolinite sample, before cavitation (Tarantino and Mongiovi 2002). Such a good agreement between two different systems is certainly a good indicator of the quality of the measurement. Note that in this experiment, the IC tensiometer was able to reach a suction value as high as 2900 kPa before cavitating.
Figure 13. Effect of compacted sample microstructure on suction measurements (Oliveira and Marinho (2008).
with higher water contents resulting in longer equilibration rates. Boso et al. (2004) also showed that preparing the paste at the liquid limit may significantly increase the equilibration time. They suggested that the water content of the paste should be kept as low as possible. However contact may not establish if the paste water content is excessively low and optimal water content should therefore be chosen by trial and error. Oliveira and Marinho (2008) also showed that equilibration time also depends on the permeability of the soil. Figure 13 shows suction measurements on samples of low plasticity soil (IP = 13) compacted on the dry side, wet side and at Proctor optimum. The results show that similar levels of suction (between 400 and 500 kPa) are attained after different periods of time due to changes in the microstructure. The changes in permeability of compacted samples with the compaction state has been known for long time since the work of Lambe (1958) who observed a decrease of two orders of magnitude when passing from the dry side of optimum to optimum water content, followed by a constant value along the saturation line. This is compatible with the trend observed in Figure 13 in which similar response are observed at
3.1.6 Time to reach equilibrium All authors agree that the contact between the soil and the probe needs particular attention, a good contact being ensured by placing a soil paste between the probe and the sample. However, the water content of the paste may affect the time necessary to reach equilibrium. Oliveira and Marinho (2008) used soil pastes at various water contents and recommended to choose the water content between the plastic and liquid limits,
44
resulted from the stress release due to sample extraction (block sampling). In the range where measured pressures remain negative (vertical stress smaller than 800 kPa), the figure shows that each loading step results in a peak in the response of the tensiometer, with apparently positive pressures monitored just before going back to a suction state. These peaks, not always equal to the stress increment applied, are interpreted as a local consolidation process of a thin soil layer in contact with the bottom of the cell where the tensiometer was placed. This instantaneous positive response is apparently very quickly compensated by suction subsequent homogenisation within the soil mass. Note that the transition between negative and positive pressures is well captured once a load of 800 kPa is reached, with subsequent stabilisation of the pressure measurements at zero. During unloading, a suction state seems reached again when the load is smaller than 400 kPa. As seen in Figure 15, Tarantino & De Col (2008) could investigate suction changes occurring during the compaction process in clay samples at various water contents. The figure clearly shows the simultaneous decrease in suction and increase in degree of saturation that occurred during compaction. Also
optimum and on the wet side of optimum, as compared to longer equilibration times on the dry side. This is related to the aggregate microstructure observed on the dry side (Ahmed et al. 1974, Delage et al. 1996, Romero et al. 1999), as compared to the matrix microstructure on the wet side. Obviously, the measurement of suction is corresponding to a very tiny water movement that is sufficient to extract some water from the porous stone. This transfer rate is dependent on the microstructure, with slower rates in the aggregate macrostructure, in which inter-aggregates pores are known to be dry and in which water is moving through the inter-aggregates contacts and, probably, inside the inter-aggregates smaller pores. 3.1.7 Use in geotechnical testing Tensiometers have been extensively used in mechanical testing including null tests (Tarantino et al. 2000), oedometer tests (Dineen & Burlan 1995, Dineen et al., 1999, Tarantino & Mongiovì 2000, Delage et al. 2007, Tarantino & De Col 2008), direct shear tests (Caruso & Tarantino 2004, Tarantino & Tombolato 2005), and triaxial tests (Cunningham et al. 2003, Oliveira & Marinho 2003). The use of the tensiometer makes it possible to investigate unsaturated soil behaviour under more realistic atmospheric conditions. Tests have been carried out under suction-controlled conditions by coupling the tensiometer with either the osmotic technique (Dineen & Burland 1995, Dineen et al. 1999, Tarantino & Mongiovì 2000) or air circulation (Cunningham et al. 2003). Tests have also been carried out at constant water content with suction changes monitored by the tensiometer (Tarantino & Tombolato 2005, Delage et al. 2007, Tarantino & De Col 2008). It is interesting to observe that suction equalisation in constant water tests is generally fast (1–2 h) which significantly reduces the overall test duration. This point is of importance especially if a comparison is made with the long-lasting tests based on the axis-translation technique. The advantage of using the tensiometer is that quasisaturate states (occluded air-phase) and the transition from unsaturated to saturated states can be successfully examined in contrast to the axis-translation technique which is problematic to use at very high degrees of saturation. For example, Tarantino & Mongiovì (2000) could perform constant suction one-dimensional compression on a sample having an initial degree of saturation equal to 0.95. As seen in Figure 14, Delage et al. (2007) could monitor the changes in suction or water pressure occurring during a step loading oedometer compression test carried out on a saturated intact Boom clay sample (a stiff clay from Belgium) using dry porous stones. The initial suction state of the saturated sample
Vertical stress (kPa)
1600 (a) 1200 Unloading
Loading 800 400 50 kP a
Vertical displacement (mm)
0
0 (b) 1 2 3
Swelling
Compression
4
(c ) 400 0
0
-400
400 Unloading
Loading -800
800 0
100
200
300
400
Suction (kPa)
Water pressure (kPa)
800
500
Time (h)
Figure 14. Monitoring suction changes during oedometer step loading compression (After Delage et al. 2007).
45
1
Region
I
Degree of saturation, S r
0.8
0.6
w=0.311 0.4
w=0.299 w=0.275 w=0.259 w=0.254
w=0.236 w=0.215
0.2 0
200
400 600 800 Matric suction, s : kPa
1000
1200
Figure 15. Degree of saturation-suction paths at different compaction water contents. Dotted lines join ‘‘postcompaction’’ suctions (Tarantino and De Col 2008).
apparent are the hysteresis obtained during stress cycles and the significant suction increase due to vertical stress release. The profile of the post-compaction suctions at given water content, once stress is released, shows some increase in suction with increasing the degree of saturation. This trend is different from some observations by Li (1995), Gens et al. (1995) and Romero et al. (1999) who measured constant values of suction on samples of equal water content compacted at various densities, at least on the dry side of the compaction curve. When implementing the HCTs in mechanical testing, an important aspect is that water tension has to be sustained for a time long enough to carry out the test. Tarantino & Mongiovì (2000) and Cunningham et al. (2003) showed that water tensions of the order of 800 kPa could be sustained for more than two weeks without cavitation occurring in the tensiometer. Interestingly, water tensions were simultaneously measured using two tensiometers which showed excellent agreement with each other. The results and considerations presented in this section devoted to the direct measurement of suction by high capacity tensiometers clearly show the quality of the measurements obtained with this device provided adequate preliminary preparation procedures are carried out. Further use of HCTs in laboratory testing of unsaturated soils will definitely complete in a sound fashion our understanding of the behaviour of unsaturated soils.
Figure 16. In-situ measurement of soil suction at shallow depth (Cui et al. 2008).
changes is certainly an important aspect in which progress is needed in the mechanics of unsaturated soils, with obvious applications in many fields in which soil atmosphere exchanges are playing a key role. The behaviour and stability of geotechnical structures like embankments or earth-dams, cover liners of surface waste disposals and the investigation of slope stability problems are some typical examples. In spite of some attempts (Ridley et al. 1996), it seems that experimental in-situ suction profiles determined by using high capacity tensiometers are scarce. In this regard, a recent paper by Cui et al. (2008) shows a device allowing to measure suction changes in a low range (20–160 kPa) at small depths (25 cm and 45 cm) along a period of three weeks. The system (Figure 16) also allows simple replacement of the tensiometer to carry out, when necessary, a new
3.1.8 In-situ suction measurements The measurement of in-situ suction profiles and of suction changes with respect to time and climatic
46
Table 3. Specifications of two high-range psychrometers (Cardoso et al. 2007). Equipment
SMI Psychrometer
Suction range
1 to 70 MPa (∗ )
Output reading
Voltage, suction (logger) < ± 0.05 pF ±0.01 pF (repeatability)
Accuracy
Figure 17. 2008).
Measuring time Calibration
Suction changes and rainfall data (Cui et al.
Sample geometry
resaturation of the probe in the laboratory after the occurrence of cavitation due to progressive air diffusion in the porous stone. The authors are aware that the period of three weeks measurements should probably be reduced when measuring higher in-situ suctions. The data of Figure 17 show that rainfall events generally cause slight changes in suction, with a more pronounced reaction at 45 cm on 11 June. Due to progressive air diffusion in the ceramic disk, it is not sure that direct measurements of in-situ suction by using HCT be the more reliable technique to be used for long term monitoring, as compared to indirect techniques (see for instance Whalley et al. 2007). 3.2
Usually 1 hour Multiple point calibration. Bi-linear Ø = 15 mm, h = 12 mm
Chilled-mirror dew-point WP4 1 to 60 MPa (max. 300 MPa) Suction and temperature ±0.1 MPa from 1 to 10 MPa and ±1% from 10 to 60 MPa 3 to10 minutes Single point calibration Sample cup: Ø = 37 mm, h = 7 mm
The transistor psychrometer probe consists of two bulbs, which act as ‘wet’ and ‘dry’ thermometers that are placed inside a sealed and thermally insulated chamber in equilibrium with soil sample. A drop of distilled water with specified dimensions is used in the ‘wet’ thermometer. The psychrometer measures indirectly the relative humidity by the difference in temperature between the ‘dry’ and the ‘wet’ bulbs (evaporation from the ‘wet’ bulb lowers its temperature). The standard equilibration period is one hour. The extended range calibration for standard conditions (standard drop size and equilibration period) is bi-linear, as shown by Cardoso et al. (2007). On the other hand, the chilled-mirror dew-point psychrometer measures the temperature at which condensation first appears (dew-point temperature). A soil sample in equilibrium with the surrounding air is placed in a housing chamber containing a mirror and a photoelectric detector of condensation on the mirror. The temperature of the mirror is precisely controlled by a thermoelectric (Peltier) cooler. The relative humidity is computed from the difference between the dew-point temperature and the temperature of the soil sample, which is measured with an infrared thermometer. The measuring time is around 5 minutes (WP4 psychrometer, Decagon Devices, Inc.) Table 3 presents the comparison of both equipment (SMI and WP4) concerning suction range, output, accuracy, measurement time and calibration. Figure 18 shows multi-stage drying results of a clayey silt obtained with SMI psychrometers within this extended range (Boso et al. 2003). The figure also includes results obtained with high-range tensiometer readings. The ‘dynamic’ determination in the figure was monitored continuously by placing the sample along with the tensiometer on a balance. The ‘static’
High-range psychrometers
In recent years, a great effort has been dedicated to extend the working range of psychrometers. Improved versions of widely used thermocouple psychrometers (Peltier-type: Spanner 1951; wet-loop: Richards and Ogata 1958; double-junction: Meeuwig 1972, Campbell 1979; screen-caged: Brown and Johnston 1976, Brown and Collins 1980) displayed a range between 0.3 MPa and 8 MPa, although above 4 MPa the repeatability of the outputs was not very good (Ridley and Wray 1996). Two alternatives, with different working principles, have been developed in the 90 s and 2000 s that allow extending this range: a) transistor psychrometers (Soil Mechanics Instrumentation SMI type: Dimos 1991, Woodburn et al. 1993, Truong and Holden 1995) with an upper limit of 15 MPa, and b) chilled-mirror dew-point psychrometers (Gee et al. 1992, Loiseau 2001, Brye 2003, Leong et al. 2003, Tang and Cui 2005, Thakur and Singh 2005, Agus and Schanz 2005) with an upper limit of 60 MPa and involving a reduced time of reading. Woodburn and Lucas (1995) and Mata et al. (2002) extended the range of transistor psychrometers to 70 MPa, disconnecting the probes from the standard logger and reading the outputs using a millivoltmeter.
47
SMI
1000 transistor psychrometer tensiometer (staticcurve) tensiometer (dynamiccurve)
Matric suction (MPa)
100
HRb HR0=40% HRSOIL
10
HRb> HR0 (fast process) HRSOIL> HR0
1
HR1
HReq SMI
HRSOIL HR1> HRSOIL HR1> HR0
HR1> HRSeq SMI > HRSOIL
WP4 HR0=40%
HReq WP4
0.1 HRSOIL HRSOIL> HR0
0.01 0.00
0.05
0.10 0.15 Water content
0.20
HRSOIL > HRSeq WP4 > HR0
0.25
Figure 20. Equalisation process in the measurement chamber of SMI and WP4 psychrometers. HRb : relative humidity near the wet bulb; HRSOIL : relative humidity of the soil pores; HR0 : initial relative humidity of the soil chamber; HR1 : intermediate relative humidity; HReq : final equilibrated relative humidity. The scheme is for HRSOIL > HR0 (Cardoso et al. 2007).
Figure 18. Comparison between SMI psychrometer data (total suction minus osmotic component) and high-range tensiometer readings. Drying paths on a clayey silt (Boso et al. 2003).
100
Total suction (MPa)
SMI -Drying WP4-Drying Curve SMI (drying) Curve WP4 (drying)
readings of both psychrometers were observed—systematically larger values were detected with WP4 psychrometer—, which increased with total suction of the soil. Cardoso et al. (2007) put forward a possible explanation to account for these discrepancies between SMI and WP4 readings. These authors suggested that the hydraulic paths undergone by the soil during the measurement period inside each equipment chamber were quite different. As observed in Figure 20, the sample in the SMI chamber experiences some wetting due to the relatively fast evaporation of the drop of the wet thermometer, which increases the relative humidity of the chamber to HR1 > HR0 as shown schematically in the figure. The sample at a lower relative humidity HRsoil undergoes some wetting before reaching the equalisation state at HReq SMI , which is the state finally measured by the SMI psychrometer. During the determination of a main drying curve, SMI readings will follow a scanning wetting path, which will end below the main drying curve. On the contrary, the soil inside the WP4 chamber will undergo some drying before reaching HReq WP4 , and it will follow the same intended main drying path during the measuring period. As a consequence, the total suctions measured and the final water contents are slightly different.
10
1
0 0
5
10
15
20
25
water content (%)
Figure 19. Comparison between SMI and WP4 psychrometer data. Drying paths on a compacted destructured argillite (Cardoso et al. 2007).
determination was achieved by constant water content measurements. To compare matrix suction results, a constant osmotic suction of 0.3 MPa was subtracted from total suctions measured by the psychrometer. A relatively good overlapping in the range from 1 MPa to nearly 3 MPa and between the different techniques is observed in the figure. Cardoso et al. (2007) studied the performance of SMI and WP4 psychrometers by evaluating the drying branch of the retention curve of a compacted destructured argillite. As observed in Figure 19, the retention curves display a quite good agreement in the low total suction range from 1 to 7 MPa. However, in the highsuction range (7 to 70 MPa) differences between the
4
CONCLUSION
Some recent developments concerning the three techniques used for controlling suction in unsaturated soils
48
(axis-translation, osmotic and vapour control techniques) and concerning two techniques of measuring suction (high capacity tensiometers and high range psychrometers) have been commented and discussed. The advantages, drawbacks and complementarities of these techniques have been discussed and some recommendations aimed at facilitating their use have been given, based on the experience gained by the authors, their co-workers and data available in the literature. As a general conclusion, it can be stated that the recent significant progresses made in the field of controlling and measuring suction provided further insight into the behaviour of unsaturated soils. The potentialities of these techniques are high and they should keep helping the experimental investigations necessary to better understand the hidden remaining aspects of the hydromechanical behaviour of unsaturated soils.
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ACKNOWLEDGEMENTS The authors acknowledge the fruitful collaboration and discussions with the many colleagues involved in the works conducted: C. Airò Farulla, M. Boso, R. Cardoso, A. Caruso, Y.J. Cui, E. De Col, V. De Gennaro, E. De Laure, A. Di Mariano, A. Dueck, A. Ferrari, Ch. Hoffmann, M. Howat, T.T. Le, A. Lima, A. Lloret, C. Loiseau, A.T. Mantho, D. Marcial, F. Marinho, L. Mongiovi, L. Oldecop, X. Pintado, G. Priol, G.P.R. Suraj de Silva, A. Take, A.M. Tang, A. Thielen, S. Tombolato, T. Vicol, M. Yahia-Aissa. The authors also wish to acknowledge the support of the European Commission via the ‘‘Marie Curie’’ Research Training Network contract number MRTNCT-2004–506861.
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De Benedetti, P.G. 1996. Metastable liquids. Princeton University Press. Delage, P., Suraj De Silva, G.P.R. et De Laure, E. 1987. Un nouvel appareil triaxial pour les sols non saturés. 9e Eur. Conf. Soil Mechanics Found. Eng. 1, 26–28, Dublin. Delage, P., Suraj De Silva, G.P.R. and Vicol, T. 1992. Suction controlled testing of non saturated soils with an osmotic consolidometer. Proc. 7th Int. Conf. Expansive Soils, 206–211, Dallas. Delage, P., Howat, M.D. and Cui, Y.J. 1998. The relationship between suction and swelling properties in a heavily compacted unsaturated clay. Engineering Geology, 50: 31–48. Delage, P., Le, T.-T., Tang, A.-M., Cui, Y.-J. and Li, X.-L. 2007. Suction effects in deep Boom Clay block samples. Géotechnique 57 (2): 239–244, 239. Delage, P. and Cui, Y.J. 2008a. An evaluation of the osmotic method of controlling suction. Geomechanics and Geoengineering: An International Journal, vol. 3 (1), 1–11. Delage P. and Cui Y.J. 2008b. A novel filtration system for polyethylene glycol solutions used in the osmotic method of controlling suction. Canadian Geotechnical Journal, in press. De Gennaro, V., Cui, Y.J., Delage, P. and De Laure, E. 2002. On the use of high air entry value porous stones for suction control and related problems. Proc. 3rd Int. Conf. on Unsaturated Soils, Recife, Brasil, J.F.T. Jucá, T.M.P. de Campos and F.A.M. Marinho (eds). A.A. Balkema, 1: 435–440. Di Mariano, A. 2000. Le argille a scaglie e il ruolo della suzione sulla loro deformabilità. Ph.D. Thesis, Università di Palermo e di Catania. Dimos, A. 1991. Measurement of soil suction using transistor psychrometer. Internal Report IR/91–3, Special Research Section, Materials Tech. Dept., Vic Roads. Dineen, K. and Burland, J.B. 1995. A new approach to osmotically controlled oedometer testing. In E.E. Alonso and P. Delage (eds), Proc. 1st Int. Conf. on Unsaturated Soils, Paris, 2: 459–465. Balkema. Dineen, K., Colmenares, J.E. Ridley, A.M. abd Burland, J.B. 1999. Suction and volume changes of a bentonite-enriched sand. Geotechnical Engineering 137 (4): 197–201. Doran, I.G. Sivakumar, V. Graham, J. and Johnson, A. (2000). Estimation of in-situ stresses using anisotropic elasticity and suction measurements. Géotechnique 50 (2), 189–196. Dueck, A. 2004. Hydro-mechanical properties of a water unsaturated sodium bentonite. Laboratory study and theoretical interpretation. Ph.D. Thesis, Lund University, Sweden. Dueck, A. 2007. Results from suction controlled laboratory tests on unsaturated bentonite—Verification of a model. Proc. 2nd Int. Conf. Mechanics of Unsaturated Soils, Weimar, T. Schanz (ed.). Springer Proceedings in Physics, 112. Springer-Verlag, Berlin: 329–335. Escario, V. and Juca, F. 1989. Strength and deformation of partly saturated soils. Proc. 12th Int. Conf. Soil Mech. and Found. Eng. 1, 43–46. Rio de Janeiro, Balkema. Esteban, F. 1990. Caracterización experimental de la expansividad de una roca evaporítica. Ph.D. Thesis, Universidad de Cantabria. Spain (in Spanish).
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EXPERUS, Trento, A. Tarantino, E. Romero and Y.J. Cui (eds). A.A. Balkema, Leiden: 9–13. Leong, E.C., Tripathy, S. and Rahardjo, H. 2003. Total suction measurement of unsaturated soils with a device using the chilled-mirror dew-point technique. Géotechnique, 53 (2): 173–182. Li, Z.M. 1995. Compressibility and collapsibility of compacted unsaturated loessial soils. Proc. 1st Int. Conf on Unsaturated Soils UNSAT’ 95 1, 139–144, Paris, Balkema, Rotterdam. Lloret, A., Villar, M.V., Sánchez, M., Gens, A., Pintado, X. and Alonso, E.E. 2003. Mechanical behaviour of heavily compacted bentonite under high suction changes. Géotechnique, 53 (1): 27–40. Loiseau, C. 2001. Transferts d’eau et couplages hydromécaniques dans les barrières ouvragées. Ph.D. Thesis, École Nationale des Ponts et Chaussées, Paris. Lourenço, S.D.N., Gallipoli, D., Toll, D.G. and Evans, F.D. 2006. Development of a commercial tensiometer for triaxial testing of unsaturated soils, Geotechnical Special Publication No. 147, ASCE, Reston, Vol. 2: 1875–1886. Mahler, C.F. and Diene, A.A. 2007. Teniometer development for high suction analysis in laboratory lysimeters. In Experimental Unsaturated Soil Mechanics, T. Schanz (ed.), pp. 103–115. Mahler, C.F., Pacheco, A.C. and Souza, H.G. 2002. Development of an automatic tensiometer in laboratory using a Mini-Lysimeter. Proc. 3rd Int. Conf. on Unsaturated Soils, Recife, Juca, de Campos and Marinho (eds) (3), 1021–1027, Recife, Brazil. Marcial, D. 2003. Interactions eau-argile dans les montmorillonites et comportement des barrières ouvragées. Ph.D. thesis, Ecole Nationale des Ponts et Chaussées, Paris. Marinho, F.A.M., Take, A. and Tarantino, A. 2008. Tensiometeric and axis translation techniques for suction measurement. Geotechnical and Geological Engineering, accepted for publication. Marinho, F.A.M. and Chandler, R.J. 1995. Cavitation and the direct measurement of soil suction, in Unsaturated Soils, Proc. 1st Int. Conf. Unsaturated Soils. Vol. 2 Paris, E.E. Alonso and P. Delage (eds), Balkema, Rotterdam, 623–630. Meeuwig, R.O. 1972. A low-cost thermocouple psychrometer recording system. Proc. Symp. Thermocouple Psychrometers. Psychrometry in Water Relations Res. R.W. Brown and B.P. Van Haveren (eds). Utah Agricultural Experiment Station, Utah State Univ., Logan. Monroy, R., Ridley, A. Dineen, K. and Zdrakovic, L. 2007. The suitability of osmotic technique for the long term testing of partly saturated soils. Geotech. Testing J. (30) 3, 220–226. Ng, C.W.W., Cui, Y., Chen, R. and Delage, P. 2007. The axis-translation and osmotic techniques in shear testing of unsaturated soils: a comparison. Soils and Foundations. Vol. 47, No. 4, 675–684. Oldecop, L. and Alonso, E.E. 2004. Testing rockfill under relative humidity control. Geotechnical Testing Journal, 27 (3): 1–10. Oliveira, O.M. and Marinho, F.A.M. 2003. Unsaturated Shear Strength Behaviour of a Compacted Residual Soil. Proc. 2nd Asia Conference on Unsaturated Soils, Osaka, 1:237–242.
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Geological and Geotechnical Engineering 19 (3): 189–210. Tarantino, S. and Mongiovi, L. 2002. Design and construction of a tensiometer for direct measurement of matrix suction. Proc. 3rd Int. Conf. on Unsaturated Soils, Recife, Juca, de Campos and Marinho (eds) (1): 319–324, Balkema. Tarantino, A. and Tombolato, S. 2005. Coupling of hydraulic and mechanical behaviour in unsaturated compacted clay. Géotechnique, 55 (4): 307–317. Tarantino, A. and De Col, E. 2008. Compaction behaviour of clay. Géotechnique, 58 (3): 199–213. Thakur, V.K.S. and Singh, D.N. 2005. Swelling and suction in clay minerals. Proc. Int. Symposium on Advanced Experimental Unsaturated Soil Mechanics EXPERUS 2005, Trento. A. Tarantino, E. Romero and Y.J. Cui (eds). A.A. Balkema Publishers, Leiden: 27–31. Toker, N.K. 2002. Improvements and reliability of MIT tensiometers and studies on soil moisture characteristic curves. MSc Dissertation, Massachusetts Institute of Technology, Boston, US. Toker, N, Germaine, J, Sjoblom, K, Culligan, P. 2004. A new technique for rapid measurement of continuous soil moisture characteristic curves, Géotechnique 54 (3): 179–186. Truong, H.V.P. and Holden, J.C. 1995. Soil suction measurement with transistor psychrometer. Proc. 1st Int. Conf. on Unsaturated Soils, Paris. Unsaturated Soils. E.E. Alonso and P. Delage (eds). A.A. Balkema/Presses des Ponts et Chaussées, Paris, 2: 659–665. Villar, M.V. 1999. Investigation of the behaviour of the bentonite by means of suction-controlled oedometer tests. Engineering Geology, 54: 67–73. Waldron, L.J. and Manbeian, T. 1970. Soil moisture characteristics by osmosis with polyethylene glycol: a simple system with osmotic pressure data and some results. Soil Science 110 (6): 401–404. Whalley, W.R. Clark, L.J. Take, W.A. Bird, N.R.A., Leech, P.K. Cope, R.E. Watts, C.W. 2007. A porous-matrix sensor to measure the matric potential of soil water in the field. European Journal of Soil Science 58 (1): 18–25. Williams, J. and Shaykewich, C.F. 1969. An evaluation of polyethylene glycol PEG 6000 and PEG 20000 in the osmotic control of soil water matrix potential. Can. J. Soil Science 102 (6), pp. 394–398. Woodburn, J.A., Holden, J. and Peter, P. 1993. The transistor psychrometer: a new instrument for measuring soil suction. Unsaturated Soils Geotechnical Special Publications N◦ 39. S.L. Houston and W.K. Wray (eds). ASCE, Dallas: 91–102. Woodburn, J.A. and Lucas, B. 1995. New approaches to the laboratory and field measurement of soil suction. Proc. 1st Int. Conf. on Unsaturated Soils, Paris, E.E. Alonso and P. Delage (eds). A.A. Balkema/Presses des Ponts et Chaussées, Paris, 2: 667–671. Yahia-Aissa, M. 1999. Comportement hydromécanique d’une argile gonflante fortement compactée. Ph.D. Thesis, Ecole Nationale des Ponts et Chaussées, France. Zheng, Q, Durben, D.J., Wolf, G.H. and Angell, C.A. 1991. Liquids at large negative pressures: water at the homogeneous nucleation limit. Science, 254 (5033) (Nov. 8, 1991): 829–832. Zur, B. 1966. Osmotic control the matrix soil water potential. Soil Science 102: 394–398.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Developments in modelling the generalised behaviour of unsaturated soils A. Gens Universitat Politècnica de Catalunya, Barcelona, Spain
L. do N. Guimarães Universidade Federal de Pernambuco, Recife, Brazil
M. Sánchez University of Strathclyde, Glasgow, UK
D. Sheng The University of Newcastle, NSW, Australia
ABSTRACT: A number of developments for the description of the generalised behaviour of unsaturated soils are presented. They can be considered as extensions of the conventional elastoplastic models developed in recent years to simulate the stress-strain behaviour of this type of soils. The following topics are addressed: the consideration of coupled hydraulic models in a thermodynamical framework, the introduction of structural components in the modelling of expansive soil behaviour and the incorporation of temperature and chemical effects.
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and, very recently, in Nuth & Laloui (2008) in a rather comprehensive manner. A welcome clarification of this perennial unsaturated soil discussion was provided in Houlsby (1997) by means of the extension, under reasonably general conditions, of the work input for saturated soils to the case of unsaturated soils. This topic is however outside the scope of this paper. The present contribution will introduce, albeit briefly, a number of developments that attempt to extend the modelling of unsaturated soils to deal with more generalised behaviour. The following themes will be considered: i) the modelling of hydraulic behaviour and its thermodynamic consistency, ii) the incorporation of structural considerations in model formulation, and iii) the consideration of thermal and chemical effects. Inevitably, special attention will be given to developments associated with the work of the authors. The implementation of the constitutive models into numerical tools for analysis require also especial attention but this issue is not addressed herein and has been treated elsewhere (e.g. Sheng et al. 2003a, b, Borja 2004, Sanchez et al. 2008, Sheng et al. 2008).
INTRODUCTION
Constitutive modelling of unsaturated soils has progressively incorporated a number of features that are deemed to be necessary to achieve a satisfactory reproduction of their mechanical behaviour. Among them, the following can be mentioned: a central role of matric suction in the description of behaviour, the use of more then one stress variable in the formulation, the recognition that collapse behaviour (i.e. the compression of the soil upon wetting) is irreversible and the increase of shear strength with suction. Another important characteristic is the requirement that a model for unsaturated soils should be compatible with existing models for saturated materials. Based on those considerations, a number of elastoplastic models have been developed in the last few decades to describe, using a variety of approaches, the mechanical behaviour of unsaturated soils (e.g. Alonso et al. 1990, Josa et al. 1992, Kohgo et al. 1993, Modaressi & Abou-Bekr 1994, Wheeler & Sivakumar 1995, Cui et al. 1996, Bolzon et al. 1996, Alonso et al. 1999, Khalili & Loret 2001, Loret & Khalili 2002, Gallipoli et al. 2003a, Russell & Khalili 2006). All those models deal with stress-strain relations. A variety of stress variables have been adopted in the formulation of those models; this issue has been summarized and discussed in a number of publications (e.g. Gens 1995, Jardine et al. 2004, Gens et al. 2006)
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HYDROMECHANICAL MODELS FOR UNSATURATED SOILS
One crucial shortcoming of many constitutive models for unsaturated soils (especially the early
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formulations) is that they either do not take into account the hydraulic behaviour of unsaturated soils or they consider it in a manner that is uncoupled from the mechanical stress-strain law. Thus, in the BBM model (Alonso et al. 1990), hydraulic behaviour was simply defined in terms of a state surface. Probably, this issue of the hydraulic component of the constitutive model was first properly addressed by Wheeler (1996) and Dangla et al. (1997) and the first full attempt to couple hydraulic behaviour with a mechanical model for unsaturated soil was presented in Vaunat et al. (2000). In recent years quite a number of constitutive developments have addressed explicitly this question (e.g. Wheeler et al. 2003, Gallipoli et al. 2003b, Sun et al. 2007). As strongly suggested by Houlsby’s (1997) work input equation (neglecting the work dissipated by the flow of fluids), ˙ ≡ ua n(1 − Sr )ρ˙a /ρa − (ua − uw ) n S˙ r W
+ σij − (Sr uw + (1 − Sr )ua ) δij ε˙ ij
a)
b)
Figure 1. a) Hysteretic hydraulic behaviour under constant void ratio. b) SI, SD and LC yield surfaces in three-dimensional space (Sheng et al., 2004).
(1)
the incorporation of an hydraulic component of the model in a coupled manner provides the opportunity of casting the resulting constitutive law in the thermodynamic framework proposed by Collins & Houlsby (1997). In the above expression, σij is the total stress, Sr is degree of saturation, ua the air pressure, uw the water pressure. ρa is the air density, n the porosity and εij the strains. The model proposed in Sheng et al. (2004) has provided an excellent opportunity for such an exercise. The model is defined in terms of Bishop’s stress: (σij )c = σij −ua δij +Sr (ua −uw )δij and matric suction, s(=ua − uw ). The subscript c implies that Bishop’s stress is the constitutive stress. Please note, that in Bishop’s expression the original variable χ (Sr ) has been replaced by Sr . The hysteretic water retention model is presented in Figure 1a; it is composed of a wetting and a drying curve with scanning curves spanning the two. No dependency on void ratio is introduced. The two main water retention curves correspond to the SI and SD yield surfaces that together with the LC yield curve constitute the mechanical part of the model (Figure 1b). In this particular model, the yield surfaces are not coupled but move independently of each other. Accepting the hypotheses that led to Houlsby’s expression for the rate of work input (1) and neglecting the air compressibility term, the plastic component of the work input rate is dW p = (σc )T dεp + nsdSrp
For uncoupled materials, where the elastic modulus is independent of the plastic strains, the plastic work increment can be decomposed into two components (Collins & Hilder, 2002): dW p = dψ2 + dφ
(3)
where ψ2 is the part of the Helmholtz free energy that depends on plastic strains only and dφ is the dissipation increment. The basic thermodynamical requirements on any constitutive model are that i) the dissipation dφ is strictly positive for any non-zero plastic strain, and ii) that the free energy dψ2 yields zero when integrated over a closed loop of plastic strain. In terms of triaxial stress states, the plastic work increment can be expressed as dW p = pc dεvp + qdεγp + nsdSrp
(4)
where pc is the mean constitutive stress, i.e. the mean Bishop’s stress in this case. The last term of the equation is only relevant to yielding in the SI or SD yield surfaces, as the movep ment of the LC yield surface does not contribute to Sr . Therefore, dW p = pc dεvp + qdεγp + (nsI dSrp or nsD dSrp )
(2)
where σc is the constitutive (Bishop) stress and the superscript p denotes plastic.
(5)
In (5), the third term will appear when either the SI or the SD yield curves are engaged. Since both sI
54
3
and sD are known function of the plastic increment of p the degree of saturation and n is independent of dSr , the last two terms of the equation above are integrable and give zero when integrated around a closed loop p of Sr . Therefore, these two terms belong to the free energy dψ2 . To find the first two terms in (4), it is assumed that plastic volumetric and plastic deviator strains are caused only by yielding at the LC yield surface. This is a strong restriction on the role of the SI and SD surfaces. Then: 1 pc dεvp + (nsI dSrp or nsD dSrp ) 2 ⎞ ⎛ p 2 p 2 M2 ) + (dε ) (dε γ v 1 ⎟ ⎜ ζ + ⎝ pc ⎠ p 2 p 2 2 M2 (dεv ) + ζ (dεγ )
The behaviour of expansive clays has always presented challenging aspects concerning their constitutive modelling. Although expansive clays have always been one of the main areas of interest in unsaturated soil mechanics, in recent years this interest has been enhanced because they are widely used as one of the main components of waste-isolation barriers. One of the characteristic features of the behaviour of expansive clays is the irreversible and stress path-dependent behaviour exhibited during wetting. An example is offered in Figure 2 where it can be seen that the volume change of an expansive clay varies strongly depending on the stress path followed. Irreversibility and strain accumulation is also a feature of expansive clay behaviour when drying/wetting cycles are applied (Figure 3). This type of behaviour is difficult to model with conventional elastoplastic models where predicted behaviour inside the yield locus is elastic and, therefore, computed strains will be small and, often, largely reversible. Because the source of expansive clay behaviour lies in the physicochemical phenomena occurring in the vicinity of the clay particle, there is some merit in trying to incorporate explicitly this microstructural level in the model (Gens & Alonso, 1992). The formulation developed contains now two structural levels: a microstructure where the interactions at particle level occur and a macrostructure that accounts for the overall fabric arrangement of the material comprising aggregates and the larger pores. In some cases, for instance in compacted swelling clays, the two structural levels are readily distinguished. See for example Figure 4 where the pore volume distributions for a compacted bentonite at two
dW p =
(6)
where M and ζ are model parameters. The terms of the first brackets are all integrable and give zero in a closed loop. Therefore they are the contribution of the plastic strain work from the free energy and hence correspond to dψ2 . The term in the second set of brackets is not integrable because it involves the plastic shear strain. This term thus corresponds to the dissipation function dφ. dψ2 =
1 pc dεvp + (nsI dSrp or nsD dSrp ) 2 2
p
v
ζ
(7)
p
(dεv )2 + Mζ (dεγ )2 1 ≥0 dφ = pc 2 p p 2 (dε )2 + M (dε )2
INCORPORATION OF STRUCTURAL EFFECTS
(8)
γ
The dissipation function (8) is obviously strictly positive whenever the plastic strains are non zero, as required. It can also be shown that the dissipation function above is a homogeneous function of degree 1 in the plastic strain increments. Equations (7) and (8) indicate that the plastic yielding at the suction-increase and suction-decrease yield surfaces does not contribute to the plastic dissipation, but only to the plastic work. This means that all plastic work associated with a plastic increment of degree of saturation is stored and can be recovered during a reversed plastic increment of saturation. This plastic work is very much the same as the ‘locked-in elastic energy’ due to the shift or back stress (Collins & Hilder, 2002). Ideally, analogous analyses should be attempted concerning other constitutive models. Tellingly, Tamagnini & Pastor (2005) and Santagiuliana & Schrefler (2006) have also examined their particular models in terms of a similar thermodynamic framework.
Figure 2. Volume increase of an expansive clay under different generalised stress paths (Brackley, 1975). NMC denotes Natural Moisture Content.
55
to define carefully the type of suction to be used. Whereas in the macrostructure the matric suction (s) is the relevant one, total suction (i.e. matric plus osmotic suction) has to be used when dealing with the microstructure. The inclusion of the macrostructural level in the analysis allows the consideration of phenomena that affect the skeleton of the material, for instance deformations due to loading and collapse. Figure 5a shows the BBM yield surface (Alonso et al., 1990), defined as:
8 Swelling (%)
3
Dry Density:1.65 Mg/m Vertical Stress: 0.0007 MPa 6
4
2
Shrinkage (%)
0
FLC = 3J 2 −
g(θ) g(−30◦ )
2 M 2 ( p + Ps )( p0 − p) = 0 (9)
-2
where M is the slope of the critical state, po is the apparent unsaturated isotropic pre-consolidation pressure, g(θ) is a function of Lode’s angle and ps considers the dependence of shear strength on suction. The trace of the yield function on the isotropic p-s plane is called LC (Loading-Collapse) yield curve, because it represents the locus of activation of irreversible deformations due to loading increments or collapse.
-4 0
5
10 15 20 Time (days)
25
30
Figure 3. Evolution of shrinkage and swelling in a cyclic suction test (Day, 1994).
Incremental Pore Volume (ml/g)
0.2 Dry density 1.8 Mg/m3
0.16
Intra-aggregate
1.5 Mg/m 3
Inter-aggregate
0.12
0.08
0.04
0 1
10
100
1000
10000
100000
Pore diameter (nm)
Figure 4. Distributions of incremental pore volume for two statically compacted specimens of FEBEX bentonite (modified from Lloret et al., 2003).
different dry densities are plotted. The two structural levels can be easily observed. However, even in more matrix-dominated fabrics, it is still possible to distinguish the behaviour related to the hydration processes close to the particle from the behaviour associated with the overall structural rearrangements of mechanical origin. The model has been developed in terms of net stresses (i.e. the excess of total stress over air pressure) and suction. In this case, however, it is necessary
Figure 5. a) BBM yield surface. b) Microstructural load directions on the p-s plane
56
has a number of advantages (Gens et al., 2006) both for the formulation of the model and for its implementation in numerical codes (Sanchez et al., 2008). An additional advantage of keeping track of two structural levels and, hence, two pore structures, is that important parameters such as permeability can be related to the macrostructural pore sizes since the contribution of the microstructural pores to overall water flow is negligible. This possibility has proved very valuable in the analysis of hydration of engineered barriers for radioactive waste disposal (Sanchez & Gens, 2005). Also, time dependent behaviour arises in a natural way if transient hydraulic non-equilibrium between macrostructure and microstructure is considered, a very plausible scenario. Finally, the incorporation of a microstructural level provides a suitable platform to introduce the effects of new variables as described in the following section.
The position of the LC curve is given by the preconsolidation yield stress of the saturated state, p∗o (hardening variable), according to: p˙ ∗0 = p∗0
(1 + e) p ε˙ (λ(0) − κ) v
(10) p
where e is the void index, ε˙ v is the volumetric plastic strain, κ is the elastic compression index for changes in p and λ(0) is the stiffness parameter for changes in p for virgin states of the soil in saturated conditions. For the microstructural level, it is assumed that the strains arising from basic physicochemical phenomena may be considered elastic and volumetric (Gens & Alonso, 1992). The increment of microstructural strains is then expressed as: ε˙ v1 =
pˆ˙ p˙ s˙ = +χ K1 K1 K1
(11) 4
where pˆ (= p + χ s) is the microstructural effective stress, the subscript 1 refers to the microstructural level, the subscript v refers to the volumetric component of the strains and K1 is the microstructural bulk modulus. The Neutral Line (NL) (Figure 5b) corresponds to a constant pˆ locus and no microstructural deformation occurs when the stress path moves on the NL. The NL divides the p-s plane into two parts, defining two main generalized stress paths, which are identified as: MC (microstructural contraction) and MS (microstructural swelling). In spite that reversible behaviour is assumed for microstructural strains, irreversible behaviour may arise form the effects of those strains on the macrostructure (Gens & Alonso 1992). An assumption of model is that the irreversible deformations of the macrostructure are proportional to the microstructural strains according to interaction functions f . The plastic macrostructural strains are evaluated by the following expression: p
p
ε˙ v2 = ε˙ vLC + f ε˙ v1
TEMPERATURE AND CHEMICAL EFFECTS
4.1 Temperature effects One of the potentially important roles of compacted swelling clays lies in providing the basic material for engineered barriers in high level radioactive waste storage schemes. High level radioactive waste is strongly heat emitting. In this context, thermal effects on behaviour and, more specifically, the variation of swelling capacity with temperature is a significant issue. Figure 6 shows the observed variation of swelling pressure with temperature for a bentonite compacted at dry densities of 1.6 and 1.5 Mg/m3 (Sánchez et al., 2007). It can be noted that swelling pressure decreases with temperature although, even at temperatures as high as 80◦ C, the pressure values are still large. In the model outlined in the previous section, the expansion of the microstructure depends on the microstructural effective stress through a microstructural bulk modulus, K1 (eq. 11). A straightforward extension to the model is to include a dependence of K1 on temperature. The expression used is follows:
(12)
p
where εvLC is the plastic strains induced by the yielding of the macrostructure (BBM ). A first mathematical expression of this conceptual model was presented in Alonso et al. (1999) but, recently, a more convenient formulation based on generalised plasticity concepts has been developed (Sanchez et al., 2005) while keeping the same basic features and assumptions. The generalised stressstrain relationships are derived within a framework of multi-dissipative materials that provides a consistent and formal approach when several sources of energy dissipation exist. The generalised plasticity framework
K1 =
e−αm pˆ βm
(13)
where αm and βm are model parameters. The extension suggested here is to include a dependence of the parameter βm on temperature. The following expression is proposed: βm =
57
βm eτ T /Tref
(14)
where T is the temperature difference, that is the actual temperature minus Tref , a reference temperature, and τ is a new parameter that may be obtained from experiments. It should be noted that, in this version of the model, only the microstructural level is affected by temperature. This is acceptable because the fabric of the compacted bentonite is quite dense and no irreversible strains in the macrostructure due to temperature changes are expected. If the fabric was more open, independent plastic temperature effects must be introduced in the description of the macrostructural behaviour. Figure 7 shows how the change of temperature affects the microstructural bulk modulus according to the suggested law. An increase in the microstructural stiffness with temperature is predicted. This means lower expansions when tests are conducted at higher temperature. As Figure 6 shows, the adopted expression (14) yields a satisfactory variation of swelling pressure with temperature.
4.2 Chemical effects Expansive clays contain significant amounts of active minerals. Therefore, their behaviour is generally susceptible to variations in the chemical environment. Two major effects can be identified: changes in osmotic suction and the effects of cation exchange. Both must be considered in a proper chemomechanical constitutive model. Again, the effects of chemical variables are taken into account through an adequate modification of the microstructural model. As before, an exponential law is adopted to define the elastic volumetric microstructural strain as a function of microstructural effective stresses: dεme = βm e−αm pˆ d pˆ
(15)
where αm and βm are material parameters. To incorporate the influence of geochemical variables on the behaviour of the microstructure, it is postulated that the material parameter αm is constant and that βm depends on the exchangeable cation concentrations as: βmi xi (16) βm =
Swelling pressure (MPa)
i Error bars obtained from values of tests performed at laboratory
6
3
temperature (1.6Mg/m )
4
Dry density (Mg/m3) 1.6 1.5 Test Test Model Model
where xi is the equivalent fraction of the exchangeable cation i, defined as: xi =
2
Error bars obtained from values of tests performed at laboratory
20
30
40 50 60 Temperature (ºC)
70
(17)
where CEC is the cation exchange capacity of the clay. Since xi are defined as equivalent fractions, they are subjected to the following restrictions:
3
temperature (1.5 Mg/m )
0
concentration of exchangeable cation CEC
80
Figure 6. Swelling pressure as a function of temperature for FEBEX bentonite compacted to different nominal dry densities. Experimental and modelling data (Sanchez et al., 2007).
xi = 1;
0 ≤ xi ≤ 1
(18)
i
The βmi values are parameters that control microstructure stiffness and are established for each one of the exchangeable cations. If a rough analogy is established with the diffuse double layer theory, the values of βmi are related to the hydrated radii of the cations and their valences. Finally, the microstructural volumetric strain is given by: dεme = dem = βm e−αm pˆ d pˆ −
1 −αm pˆ e dβm αm
(19)
From (19), it can be noted that cation exchange not only affects the stiffness of the microstructure but it also contributes independently to the microstructural volumetric strains. If all βmi are constant and the same for all cations (βmi = βm ), then dβm is always zero and (19) becomes
Figure 7. Changes in micro-structural stiffness with temperature.
58
(15). In this case, the influence of exchangeable cations disappears and the only geochemical variable that affects microstructural behaviour is the osmotic suction (so ). It is convenient to define a new variable: ψ = pˆ −
1 1 ln βm = p + χ sm − ln βm αm αm
A numerical simulation has been performed in which the soil was subjected to the same sequence of mechanical and chemical actions. A 1-D mesh composed of 100 elements was used for the analysis performed with the computer code CODE_BRIGHT enhanced with a chemical module. The following parameters were used: intrinsic permeability, taken as constant and equal to 5 × 10−19 m2 , the coefficient of molecular diffusion is 7.6 × 10−10 m2 /s, and the CEC is 80 meq/100 g of solid. No mechanical dispersion is considered. Arguably, the most interesting result of the experiment is the observation of positive pore pressures measured at the bottom of the sample (Figure 9). It can be noted that the same response is obtained in the computations (Figure 10). The pore pressure generation corresponds to the undrained response of the soil due to the tendency towards compression induced by the saline solution. It can be stated that pore pressures are generated because the diffusion of salts inside the sample is faster than the ability of the pore pressures to dissipate. Naturally this phenomenon depends on the relative values of intrinsic permeability and the coefficient of molecular diffusion. This a clear example of interaction between geochemical parameters and hydromechanical behaviour, successfully reproduced by the model.
(20)
that will be called the ‘‘chemically modified effective stress’’ for the microstructure, reflecting the fact that the microstructural volumetric strain depends on changes of ψ only: dεme = dem = e−αm ψ d.
(21)
Therefore, a cation exchange process that causes an increase in βm (for instance the replacement of Ca2+ by Na+ in the exchange sites of the clay) will result in a reduction of ψc and an expansion of the double layer. In fact, any reduction of p, sm or ψc will cause a double layer expansion. Therefore a reduction of ψ will be associated with microstructural wetting. Conversely, when the net effect of changes in microstructural variables p, sm , and ψc is an increase of ψ, there will be shrinkage of the double layer and it will be associated with microstructural drying. An example of application demonstrating the interaction between cation exchange and hydromechanical effects is now presented. It concerns a laboratory test carried out in the oedometer cell depicted in Figure 8 (Santamarina & Fam, 1995). In the test, the sample can only drain from the top whereas pore pressure is measured at the bottom. First the sample is subjected to a load of 100 kPa. Once consolidation is finished, the specimen is placed in contact with a KCl saline solution of 4.0 M concentration through the upper surface of the sample. The material tested is a sodium bentonite with a cation exchange capacity (CEC) between 80 and 85 meq/100 g of solid. The samples were prepared from slurry with an initial void ratio of 4.6.
Figure 9. Observed variation of the pore pressure at the bottom of a bentonite oedometer sample exposed to a 4.0 M solution of KCl. (Santamarina & Fam, 1995).
pore pressure (MPa)
0.05
0.04
0.03
0.02
0.01
0.00 0
1000
2000
3000
4000
5000
6000
7000
8000
time (min)
Figure 10. Computed variation of the pore pressure at the bottom of a bentonite oedometer sample exposed to a 4.0 M solution of KCl.
Figure 8. Schematic layout of the oedometer test with changes of chemical variables (Santamarina & Fam, 1995).
59
5
CONCLUDING REMARKS
Day, R.W. 1994. Swell-shrink behaviour of compacted clay. Journal of Geotechnical Engineering, ASCE; 120(3): 618–623. Gallipoli, D., Gens, A., Sharma, R. & Vaunat, J. 2003a. An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour. Géotechnique 53: 123–135. Gallipoli, D., Wheeler, S.J. & Karstunnen, M. 2003b. Modelling the variation of degree of saturation in a deformable unsaturated soil. Géotechnique 53: 105–112. Gens, A. 1995. Constitutive modelling: Application to compacted soil. Unsaturated Soils. Balkema, Rotterdam. 3: 1179–1200. Gens, A. & Alonso, E.E. 1992. A framework for the behaviour of unsaturated expansive clays. Canadian Geotechnical Journal 29: 1013–1032. Gens, A., Sanchez, M. & Sheng, D. 2006, On constitutive modelling of unsaturated soils. Acta Geotechnica 1(3): 137–147. Houlsby, G.T. 1997. The work input to an unsaturated granular material. Géotechnique 47: 193–196. Jardine, R.J., Gens, A., Hight, D.W. & Coop, M.R. 2004. Developments in understanding soil behaviour. Advances on Geotechnical Engineering. The Skempton Conference Thomas Telford: London, 103–206. Josa, A., Balmaceda, A., Gens, A. & Alonso, E.E. 1992. An elasto-plastic model for partially saturated soil exhibiting a maximum of collapse. 3rd. Int. Conf. Computational Plasticity, Barcelona 1: 815–826. Khalili, N. & Loret, B. 2001. An elasto-plastic model for non-isothermal analysis of flow and deformation in unsaturated porous media: formulation. Int. J. of Solids and Structures 38: 8305–8330. Kohgo, Y., Nakano, M. & Miyazaki, T. 1993. Theoretical aspects of constitutive modelling for unsaturated soils. Soils and Foundations 33 (4): 681–687. Lloret, A., Villar, M.V., Sanchez, M., Gens, A., Pintado, X. & Alonso, E.E. 2003. Mechanical behaviour of heavily compacted bentonite under high suction changes. Géotechnique 53: 27–40. Loret, B. & Khalili, N. 2002. An effective stress elasticplastic model for unsaturated porous media. Mechanics of Materials 34: 97–116. Modaressi, A. & Abou-Bekr, N. 1994. A unified approach to model the behaviour of saturated and unsaturated soils. 8th Int. Conf. Computer Meth. and Advances in Geomech. Balkema, Rotterdam: 1507–1513. Nuth, M. & Laloui, L. 2007. Effective Stress Concept in Unsaturated Soils: Clarification and Validation of a Unified Framework, International Journal of Numerical and Analytical Methods in Geomechanics, DOI: 10.1002/nag.645. Russell, A.R. & Khalili, N. 2006. A unified bounding surface plasticity model for unsaturated soils. Int. Journal for Numer. Anal. Meth. in Geomech 30: 181–212. Sánchez, M. & Gens, A. 2005. Final Report on Thermohydro-mechanical modelling. Deliverable D19-3, Febex II Project, EC Contract FIKW-CT-2000-00016. Sánchez, M., Gens, A., Guimarães, L. do N. & Olivella, S. 2005. A double structure generalized plasticity model for expansive materials. Int. Journal for Numer. Anal. Meth. in Geomech 29: 751–787.
The paper has presented a number of developments related to the constitutive modelling of unsaturated soils under increasingly generalised conditions. In the first part, coupled hydromechanical models have been examined. By making suitable choices in the formulation of the constitutive model, it has been possible to prove its consistency with respect to a thermodynamical framework. Subsequently, the behaviour of expansive clays has been described using a double structure approach that takes explicitly into account the microstructure of the material and the interaction between the two structural levels, albeit in an approximate form. It has been shown that such an approach provides a very convenient platform to extend the constitutive mode to account for more general soil behaviour that includes both temperature and chemical effects. ACKNOWLEDGMENTS The contribution of the Spanish Ministry of Education and Science through research grant BIA2005-05801 is gratefully acknowledged. REFERENCES Alonso, E.E., Gens, A. & Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique 40: 405–430. Alonso, E.E., Vaunat, J. & Gens, A. 1999. Modelling the mechanical behaviour of expansive clays. Engineering Geology 54: 173–183. Bolzon, G., Schrefler, B.A. & Zienkiewicz, O.C. 1996. Elasto-plastic soil constitutive laws generalised to partially saturated states. Géotechnique 46: 279–289. Borja, R.I. 2004. Cam Clay plasticity, Part V: A mathematical framework for three-phase deformation and strain localization analysis of partially saturated porous media. Computer Methods in Applied Mechanics and Engineering 193: 5301–5338. Brackley, I.J. 1975. Swell under load. Proceedings, 6th Regional Conference for Africa on Soil Mechanics and Foundation Engineering, Durban, 1: 65–70. Collins, I.F. & Hilder, T. 2002. A theoretical framework for constructing elastic/plastic constitutive models of triaxial tests. Int. J. Numer. Anal. Meth. Geomech. 26: 1313–1347. Collins, I.F. & Houlsby, G.T. 1997. Application of thermomechanical principles to the modelling of geotechnical materials. Proc. R. Soc. London A 453: 1975–2001. Cui, Y.J., Delage, P. & Sultan, N. 1995. An elasto-plastic model for compacted soils. Unsaturated soils. Balkema, Rotterdam, 2: 703–709. Dangla, O.L., Malinsky, L. & Coussy, O. 1997. Plasticity and imbibition-drainage curves for unsaturated soils.: A unified approach. 6th Int. Conf. Num. Models in Geomechanics, Montreal, Balkema, Rotterdam, 141–146.
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Sánchez, M., Gens, A., Guimarães, L. do N. & Olivella, S. 2008. Implementation algorithm of a generalised plasticity model for swelling clays. Computers and Geotechnics (submitted). Sánchez, M., Villar, M.V., Gens, A., Olivella, S. & Guimarães L. do N. 2007. Modelling the effect of temperature on unsaturated swelling clays. Numerical Models in Geomechanics NUMOG X. Pande & Pietruszcak (eds), Taylor & Francis, London: 57–62. Santagiuliana, R. & Schrefler, B.A. 2006. Enhancing the Bolzon-Schrefler-Zienkiewicz constitutive model for partially saturated soil. Transport in Porous Media 65(1): 1–30. Santamarina, J.C. & Fam, M. 1995. Changes in dielectric permittivity and shear wave velocity during concentration diffusion. Canadian Geotechnical Journal 32: 647–659. Sheng, D., Fredlund, D.G. & Gens, A. 2008. ‘A new modelling approach for unsaturated soils using independent stress variables. Canadian Geotechnical Journal 45(4), (in press). Sheng, D., Gens, A., Fredlund, D. & Sloan, S.W. 2008. Unsaturated soils: from constitutive modelling to numerical algorithms. Computers and Geotechnics (submitted). Sheng, D., Sloan, S.W., Gens, A. & Smith, D.W. 2003a. Finite element formulation and algorithms for unsaturated soils. Part I: Theory. Int. J. for Numer. and Anal. Meth. in Geomech. 27: 745–765. Sheng, D., Smith, D.W., Sloan, S.W. & Gens, A. 2003b. Finite element formulation and algorithms for unsaturated soils.
Part II: Verification and application. Int. J. for Numer. and Anal. Meth. in Geomech. 27: 767–790. Sheng, D., Sloan, S.W. & Gens, A. 2004. A constitutive model for unsaturated soils: thermomechanical and computational aspects. Computational Mechanics 33: 453–465. Sun, D.A., Sheng, D. & Sloan, S.W. 2007. Elastoplastic modelling of hydraulic and stress-strain behaviour of unsaturated soil. Mechanics of Materials 39(3): 212–221. Tamagnini, R. 2004. An extended Cam-clay model for unsaturated soils with hydraulic hysteresis. Géotechnique 54: 223–228. Tamagnini, R. & Pastor, M. 2005. A thermodynamically based model for unsaturated soil: a new framework for generalized plasticity. C. Mancuso & A. Tarantino (eds), A.A. Balkema. Leiden: 121–134. Vaunat, J., Romero, E. & Jommi, C. 2000. An elastoplastic hydro-mechanical model for unsaturated soils. Experimental Evidence and Theoretical Approaches in Unsaturated Soils, Balkema, Rotterdam: 121–138. Wheeler, S.J. 1996. Inclusion of specific water volume within an elastoplastic model for unsaturated soil. Canadian Geotech. J. 33: 42–57. Wheeler, S.J., Sharma, R.S. & Buisson, M.S.R. 2003. Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils. Géotechnique 53: 41–54. Wheeler, S.J. & Sivakumar, V. 1995. An elasto-plastic critical state framework for unsaturated soils. Géotechnique 45: 35–53.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A thermo-hydro-mechanical stress-strain framework for modelling the performance of clay barriers in deep geological repositories for radioactive waste L. Laloui, B. François, M. Nuth, H. Peron & A. Koliji Soil Mechanics Laboratory, Ecole Polytechnique Fédérale de Lausanne, EPFL, Switzerland
ABSTRACT: Assessing the performance of deep geological repositories for heat-generating radioactive waste requires reliable predictions of the Thermo-Hydro-Mechanical (THM) behaviour of the clay barriers (the buffer material as well as the host rock/clay). This represents an important element of the waste isolation system. In order to provide reasonable assurance that clay barriers will ensure nuclear waste isolation, it is essential to understand their behaviour under a variety of environmental conditions. The phenomena involved are complex, and adequately understanding the constitutive behaviour of clays and modelling their evolution is challenging. The stress-strain material behaviours that need to be understood and modelled include drying and wetting in nonisothermal conditions and heating-cooling in non-saturated conditions. Other aspects should be considered, such as drying induced cracks and the role of the material structure and its multi-porosity. The difficulty of some of these tasks is increased by the fact that some effects are coupled. The fundamental behaviours of clayey materials under the considered THM conditions are first identified and highlighted for deep repository experiments. We then propose a mechanical stress-strain constitutive framework to model the behaviour of clay barriers. This includes aspects such as the thermo-plastic behaviour of saturated and unsaturated materials. In the third part, we show that the proposed framework allows us to experimentally explain observed behaviours and to predict the THM behaviour of clay barriers.
1
migration into the buffer material. We therefore do not consider chemical effects. To increase the performance of the engineered barrier system (EBS), the multibarrier concept in the near-field of the waste was developed. This multiprotection generally consists of a solid waste form (e.g., vitrified high-level radioactive waste (HLW) or spent fuel), an overpack (or container) and materials placed between the overpack and the surrounding rock (backfill or buffer materials). Therefore, in many proposals for deep geological repositories (Chapman and Mc Kinley, 1987), the argillaceous materials constitute either the main barrier or an important element of the multi-barrier system. They can be either the host material1 or engineered parts of the repository (buffer materials such as compacted swelling clays, most probably bentonite). Figure 1 schematically illustrates a possible concept of the barrier system.
INTRODUCTION
In all nuclear power generating countries, spent nuclear fuel and long-lived radioactive waste management is an important environmental issue. Disposal in deep clay geological formations is a promising option to dispose of these wastes. A safety case for a geological repository for highlevel and/or long-lived radioactive waste aims at conveying reasoned and complementary arguments to illustrate and instill confidence in the performances of the disposal system. This need requires that, both in repository design and in performance assessment, all analyses and predictions about the behaviour of isolation barriers be based on robust science (Gera et al., 1996). This implies a good understanding of the fundamental behaviour of the argillaceous materials and their modelling based on the best available knowledge. In this context, predicting the short-term (up to a few years) response of clay barriers in a repository for heat-generating radioactive waste is an important task. In this paper, we suppose that during this time period, the mechanical properties of the clayey materials remain unchanged and that the efficiency of vitrification and the container prevent radionuclide
1 To maintain a general context, we use the phrase ‘‘host material’’ rather than host rock/clay.
63
capacity. Several experimental results on the THM behaviour of bentonite materials that could be used in radioactive waste storage sites have been reported in the literature in the last decade. Four well-known and widely-studied bentonites are briefly presented below. The Febex bentonite extracted from the Cortijo de Archidona deposit (Almeria, Spain) is a material that has been selected in the ENRESA R& D plans as the most suitable material for backfilling and sealing the HLW repository and was tested over the last 10 years within the framework of the Febex project (ENRESA, 2000; Lloret et al., 2004; Villar, 2002, Villar et al., 2006). This clay is made of approximately 90% montmorillonite, giving it high swelling capacities upon wetting. Its liquid and plastic limits are 100% and 50%, respectively. The FoCa Clay is a sedimentary clay from the Paris Basin. This clay is supplied by the SFBD French Company. Manufacturing consists of disaggregation and gentle grinding, drying at about 60◦ C and sieving. The maximum grain size is 4 mm. The clay is largely made of an interstratified clay (50% calcium beidellite and 50% kaolinite) (Imbert et al., 2005; Olchitzky, 2002). Bentonite Kunigel V1 is a domestic bentonite produced in Japan by Kunimine Industries. More than 90% of its grains are smaller than 74 μm. The properties and behavioural features of this bentonite have already largely been investigated under the supervision of the Japan Nuclear Cycle Development Institute (JNC, 1999; Komine and Ogata, 1994). The two main constituents are montmorillonite (48%) and quartz (34%). Its liquid and plastic limits are 416 and 21%, respectively. MX-80, considered by many as the reference buffer material, is produced in the United States by the ‘‘American Colloid’’ society. The grain sizes are distributed between 10 μm and 1 mm (Tang, 2005). It is
Figure 1. The engineered barrier system: (1) steel canisters; (2) nuclear waste; (3) host material; (4) buffer material (from www.grimsel.com/febex/febex_intro_1.htm).
Clay barriers provide waste isolation mainly by restricting the contact between the groundwater and waste containers and by limiting the migration of most radionuclides released from the waste (aftercontainer failure). These two functions result from the low permeability and high retention capability of clays. Therefore, the buffer material must have several specific properties in order to ensure efficient containment with high safety for the long term. These characteristics are related to sufficient mechanical properties under isothermal, non-isothermal, saturated, and unsaturated conditions, to liquid, air and thermal conductivities, to the nuclide filtration abilities and to manufacturability of the buffer material. Such required properties are summarized in Table 1. The use of bentonite as a buffer material is the most usual solution in several national concepts. Bentonite is a clay mainly composed of smectite, which gives swelling properties due to its high water absorption Table 1.
The function of the buffer material in parallel with its required properties (JNC, 1999).
Function
Requirement
Property
Restriction of radionuclide migration
Restriction of groundwater movement
Low hydraulic conductivity (low permeability) High sorption coefficients Colloid filtration function Capability of chemical buffering
Technical feasibility of manufacturing/installation No significant impact on the engineered barriers for a specified period
Sorption of dissolved nuclides Prevention of colloid migration Buffering of changes in groundwater chemistry Possibility of filling gaps created during installation Manufacturable and placement properties Mechanical support of the overpack to ensure stability To inhibit thermal alteration of vitrified waste and buffer Stress buffering properties
64
Self-sealing ability Compaction properties Strength to support the overpack in a stable position High thermal conductivity Plasticity
made of 75% montmorillonite and 15% quartz. Its liquid limit is approximately 450% while its plastic limit is around 50%. After manufacturing of the bentonite powder, all of these materials are partially wetted to reach the desired water content, and eventually mixed with additive soil (sand or graphite) in different proportions to adjust the desired properties. They are subsequently compacted with a well-defined energy. This compaction induces particular properties in the bentonite (e.g., a double structure, expansive tendency under wetting). The purposes of this keynote paper are to identify the fundamental mechanical behaviours of argillaceous materials in the context of deep repository experiments and to analyse them in a comprehensive THM stress-strain constitutive framework, named ACMEG (Advanced Constitutive Modelling for Environmental Geomechanics). Among possible failure scenarios, observed drying cracks in the material will be discussed in this framework.
2
near-field, which can be defined as the zone altered by the presence of the radioactive waste (including the buffer materials and a portion of the host material adjacent to the waste location), is subjected to complex mechanical, hydric, and thermal solicitations with a great inter-dependence (THM couplings). In this paper, we limit our analysis to processes where THM coupling is predominant. With the ‘‘intact state’’ of the host massif as the initial state with a generally anisotropic stress state, the first step is excavation. This process induces a stress redistribution due to opening, causing tension, compression and shear and leading to an Excavation Disturbed Zone (EDZ) in the host material around the excavation (Davies and Bernier, 2003). This stage is not considered in this paper. After excavation and before HLW emplacement, the galleries are ventilated. During this stage, the excavated area plays a drainage role and a consolidation process occurs in the surrounding host material. In addition, a negative pore water pressure (suction) is acting on the field material; a strong suction gradient can develop between the gallery surface and the surrounding host material. In this situation, drainage and drying in the vicinity of the ventilated excavation are likely to be associated with radial cracking in the galleries. After placing the canister and filling the gap between it and the host material with buffer material (i.e. blocks of compacted clay, initially unsaturated), the main action that affects the EBS is heating from the canister (Figure 3) and hydration from the surrounding host material. This stage can be subdivided into several expected phases:
THERMO-HYDRO-MECHANICAL PROCESSES
Figure 2 illustrates a possible layout of a deep geological repository. In the first year following the construction of the underground disposal, the
– In the very early closure stage, the thermal flux from the vitrified waste into the buffer material occurs in unsaturated conditions at a constant water content
Figure 3. Time-dependent temperature evolution at various positions within the buffer material (bentonite) and surrounding rock/clay for canisters containing four spent fuel assemblies. The bentonite is assumed to have a thermal conductivity of 0.4 W m−1 K−1 and a heat capacity of 1.2 MJ m−3 K −1 . The initial ambient temperature is 38◦ C. Canisters have a heat output of 1490 W at the time of waste emplacement in the repository (Nagra, 2002b).
Figure 2. Possible layout for a deep geological repository for Spent Fuel, High Level Waste, and Intermediate Level Waste (SF/HLW/ILW) in Opalinus Clay (Nagra, 2002a).
65
(i.e. constant suction). The impact of the thermal load generated by the waste is particularly important as it will significantly affect the temperature and the stress far (more than 50 m) from the repository in the host material (Timodaz, 2007); – During early closure, the resaturation process induced by the water flux from the surrounding rock/clay mass occurs in a media in which temperature progressively increases. The buffer material is
subjected to wetting (suction decrease) and thermal swelling (and/or eventual collapse); – The THM processes progress and the buffer material reaches a saturated state while the temperature is still increasing (Figure 3); – In a later closure stage, the high temperature induces a desaturation process of the buffer material, which tends to shrink with a risk of desiccation crack occurrence. This phase is generally seen as the most critical stage for the integrity of the engineered barrier. In Figure 4 we show an example of cracks in the inner wall of the bentonite buffer annulus in which the heat-generating waste is enveloped (Graham et al., 1997). Those cracks were identified after decommissioning a large-scale test of EBS performance conducted over 2.5 years; – Finally, in the very late closure stage, when the maximum of thermal power has been emitted by the vitrified waste, temperature around the repository is slowly falling and the buffer material is re-saturated (wetting process). The thermal and hydraulic gradients are largely lower than previously and progressively vanish. When the temperature has totally decreased, irreversible thermal strains predominate. In terms of theoretical and constitutive studies of the processes encountered, the succession of different phases above clearly shows the necessity of using high-performance modelling tools to best approach the complex phenomena and interactions. Table 2 summarizes the THM processes and the modelling aspects required to treat the problems.
Figure 4. Image of cracks of inside wall of buffer annulus after removal of heater (Graham et al., 1997).
Table 2.
THM processes occurring in the life of underground nuclear waste disposal.
Stage
Processes
Modelling
Excavation
Stress redistribution EDZ formation
Ventilation of the excavation
Consolidation process in the host material; Swelling and eventual desaturation of the host material Thermal diffusion in an unsaturated medium; Hydraulic diffusion in an isothermal medium Thermal and hydraulic swelling and/or collapse of the buffer material Coupled thermal and hydraulic diffusion in a deformable media; Thermal and hydraulic swelling and/or collapse of the buffer material Desaturation of the buffer material due to thermal effects Shrinkage and risk of desiccation cracks in the buffer material Temperature decrease and wetting of the buffer material; Lower thermal and hydraulic gradient; Irreversible thermal strains
Elasto-plastic (EP) model for saturated and isothermal conditions—(EDZ aspect not considered here) Hydro-mechanical coupling in unsaturated conditions considering desiccation crack occurrence Thermo-hydraulic (TH) diffusive law coupled with an isothermal and a non-isothermal (T) EP mechanical model for unsaturated conditions TH diffusive law coupled with a THM-EP mechanical model for unsaturated conditions TH diffusive law coupled with a THM-EP mechanical model for unsaturated soil considering desiccation crack occurrence TH diffusive law coupled with a THM-EP mechanical model for unsaturated conditions considering wetting paths
Very early closure stage Early closure stage Late closure stage Very late closure stage
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3
confining stresses (similar to paths followed in underground nuclear storage) induces mainly irreversible compression strains for low over-consolidation states and reversible dilatation strains for highly overconsolidated states. For instance, Figure 5 shows the evolution of the apparent preconsolidation pressure with temperature for Boom clay (the material involved in the multi-barrier concept in the Belgian underground laboratory of nuclear waste disposal), while Figure 6 shows its mechanical response under a heating-cooling cycle at different over-consolidated states.
THM STRESS-STRAIN BEHAVIOURS OF ARGILLACEOUS MATERIALS UNDER ENVIRONMENTAL LOADINGS
Natural host materials are different in terms of mineralogical compositions and consolidation histories of buffer materials. However, natural clays exhibit THM behaviours similar to those of buffer materials. Both of these could be modelled in the following theoretical framework. All constitutive processes considered are rate independent. Very few results are available in the literature on the role of the skeleton intrinsic viscosity in THM environmental loading conditions. However, readers interested in thermo-viscoplasticity modelling of clays may refer to the paper by Modaressi and Laloui (1997). The common features of the behaviour of argillaceous materials under environmental loadings such as suction or temperature variations are their high strain irreversibility (plasticity) and the important effects of pore fluids on mechanical behaviour. The predominant THM stress-strain behaviour can be mainly characterised by the following four processes:
3.2 Hydromechanical unsaturated isothermal behaviour of clayey materials Partial saturation is also observed to significantly affect the stress-strain response of bentonite and host materials. Like most fine-grained soils, such materials
– Non-linearity and irreversibility of the strains. – Modification of the internal state through isotropic hardening. – The interaction between pore fluids and the solid skeleton through ‘‘generalized’’ effective stress. – Modification of the elastic yield limit under environmental loadings: it shrinks with increasing temperature in saturated conditions and dilates with increasing suction at ambient temperature. Such processes are expressed by a dependence of the apparent preconsolidation stress. In its geological meaning, the preconsolidation pressure is unique and constant. However, the stress yield limit that separates ‘‘elastic’’ pre-yield from ‘‘plastic’’ post-yield behaviour in isotropic or oedometric conditions varies with environmental loads (suction/temperature) and is to be considered a rheological parameter. It is evaluated as the stress value at the intersection of two linear parts of the compression curves (mean/vertical effective stress versus void ratio). It should have a specific appellation; the term apparent preconsolidation pressure, pc , is used in this paper. In this section, we present general trends of the stress-strain behaviour of clayey materials. 3.1
Thermo-mechanical behaviour of saturated clayey materials
Several results from the literature show a decrease in the apparent preconsolidation pressure with increasing temperature T (Laloui and Cekerevac, 2003). Moreover, a heating-cooling cycle under constant effective
Figure 5. Evolution of the preconsolidation pressure with temperature, Boom clay (experimental results: Sultan, 1997).
67
case where the mechanical external or total stress is fixed, suction changes cause straining of the material. Figure 8a shows that the complete drying-wetting cycle of fine-grained materials is not a reversible process from the viewpoint of deformation. In parallel, Figure 8b draws the soil water retention curve corresponding to such a suction cycle, highlighting a clear capillary hysteresis in the degree of saturation versus suction relationship. Focussing in particular on the wetting process, that is decreasing suction under a given stress state, it is understood from Figure 9 that the lower the applied stress, the higher the wetting induced swelling. Indeed, the volumetric response can be interpreted as a fully reversible heave under a low applied stress (e.g., 100 kPa), whereas plastic 0.1 (a) 0 Volumetric strain v
Figure 6. Heating-cooling cycle under constant effective confining stresses at different overconsolidation ratios, Boom clay (experimental results: Baldi et al., 1991).
100
-0.1 Drying
-0.2 -0.3
Matric suction s (MPa)
80
Wetting
-0.4 60
-0.5 100
40
104 106 Matric suction s (Pa)
108
1 (b) 20
1
10
100
Degree of saturation S (-) r
0.8 1000
Apparent preconsolidation pressure p' (MPa) c
Figure 7. Evolution of the apparent preconsolidation pressure with suction for FEBEX Bentonite (after Lloret et al., 2004).
show a non-linear dependency of the apparent preconsolidation pressure on suction (Figure 7). This feature, attributed to capillary effects, signifies that the domain of elastic behaviour is larger for drier materials. In addition, the material compressibility and elastic rigidity are noted to depend on the level of saturation. The volumetric response to a direct suction loading, that is a drying or wetting cycle, is also of interest. In the
drying
0.6 wetting 0.4
0.2
0 1
100 104 Matric suction s (Pa)
106
Figure 8. Drying wetting cycle of an overconsolidated white clay under zero mechanical stress: (a) Volumetric response, (b) Saturation states—Soil Water Retention Curve (after Fleureau et al., 1993).
68
σ = 14000 kPa
0.32
v
Volumetric strain ε (-)
v
σ = 5100 kPa v
σ = 100 kPa
0.24
v
0.16
0.08
Initial point
0
Wetting 10
5
10
7
10
9
Matric suction s (Pa) Figure 9. Wetting of bentonite samples under different levels of vertical stress σv (after Lloret et al., 2004). Figure 10. Thermal effect on the retention curve of FEBEX Bentonite (after Lloret et al., 2004).
compression episodes are added when the vertical stress reaches 14 MPa. The large irreversible compressions upon wetting are commonly called wetting collapse. 3.3
Thermo-mechanical behaviour of unsaturated clayey soils
The main thermal effect on the retention behaviour of fine-grained soils concerns the diminishing retention capacity with temperature increase, mainly because the interfacial tension between the water and gas phases decreases under heating (Romero et al., 2001). Figure 10 depicts such experimental evidence on FEBEX bentonite, while Tang and Cui (2005) and Romero et al. (2001) underlined the same trends for MX80 bentonite and compacted Boom Clay, respectively. This thermal effect indirectly influences the mechanical response of the host materials by changing the suction value at a given degree of saturation. It is also observed that the temperature influences the mechanical response of fine-grained soils along drying-wetting paths (swelling and/or collapse), mainly because of the thermal effect on the physicochemical interactions between clay particles. Romero et al. (2003) observed that the swelling potential of compacted Boom Clay increases with temperature, while Villar and Lloret (2004) observed a lower swelling capacity of FEBEX bentonite at 80◦ C than at ambient temperature. The coupled temperature and suction effects on the apparent preconsolidation pressure were investigated by Salager et al. (2008) along mechanical compression paths for a sandy silt. In agreement with Figures 5 and 7, this study proved that a temperature increase tends to decrease the
Figure 11. Combined effect of temperature and suction on the evolution of the apparent preconsolidation pressure of a sandy silt (Salager et al., 2008): (a) Increase with suction, (b) decrease with temperature. The normalized preconsolidation pressure is the preconsolidation pressure measured at a given temperature T and suction s over the established preconsolidation pressure at ambient and saturated conditions (T0 and s = 0). se is the air-entry suction.
isotropic yield limit, while a suction increase enhances this limit. It was observed that logarithmic functions fit well with the evolution of the apparent preconsolidation pressure pc with temperature and suction. Indeed, the decrease (or increase, respectively) with temperature (or suction, respectively) of pc appears fast for low values of the two variables and becomes asymptotic for higher values (Figure 11). In addition, an additional coupled effect of temperature and suction on this limit was observed, probably due to the thermal influence on physico-chemical properties of clay particles and the capillary meniscus.
69
3.4
Double structure effect
One of the key issues that should be precisely understood for such THM phenomena is soil structure effects. The term soil structure in general corresponds to the combination of soil fabric, namely arrangement of particles, and interparticle bonding (Mitchell, 1993). These two components of soil structure characterize the compacted materials that are used as buffer materials. Meanwhile, changes in soil structure can influence, through a coupled process, the host material behaviour in the phenomenon under study. In general, materials involved in such problems have complex structures. Unlike homogenous soils, these materials exhibit a wide and often bi- or multi-modal pore size distribution. There are two extremes in conceptualizing the structure of these materials: aggregation and macro void formation. The first explains structure changes in clay during compaction stages. For compacted materials, the pores can be divided into two main groups of macro and micro pores; therefore, they can be addressed by the concept of double porosity. However, this requires a rigorous consideration of soil structure and double porosity effects in a strain-stress constitutive approach. Soil structure may influence many soil characteristics, including compressibility (Lambe, 1958), hydraulic conductivity (Tamari, 1984) and the soilwater retention curves (Brustaert, 1968) of both compacted and natural soils. Based on experimental results, mainly from mercury intrusion porosimetry (MIP), it has been shown that compacted bentonite has an aggregated structure. Figure 12 presents the pore size distribution of the FEBEX bentonite obtained by MIP tests (Lloret et al., 2003). As can be seen in the figure, these materials have a bi-modal pore size distribution corresponding to two dominant classes of inter-aggregate and intra-aggregate pores.
Figure 13. Modification of soil fabric due to suction increase (after Cuisinier and Laloui, 2004).
Moreover, pore size distribution of the material might be strongly influenced by environmental loading. Figure 13 shows the MIP results of a natural aggregated soil at different suction levels (Cuisinier and Laloui, 2004). These results represent the strong evolution of macro and micro porosity due to suction variations. We can therefore conclude that in such materials, so-called double structure soils, deformation is a combined phenomenon at both the macro and micro scales. A direct consequence of such a structure is collapse upon wetting that can be ascribed to the collapse and disintegration of aggregates due to wetting (Gens and Alonso, 1992; Lloret et al., 2003). Moreover, the strength of structural units has an important influence on the compressibility and mechanical behaviour of the material. In other words, the yield limit depends not only on the stress state and stress history, but also strongly on the soil structure. Common experimental evidence for the latter point is the extension of preconsolidation pressure in natural structured soils compared to reconstituted soil of the same mineralogy (Callisto and Rampello, 2004; Liu and Carter, 1999). It is noteworthy that in these materials, hardening (or softening) of material depends also on the degradation of structures that might happen due to different environmental loadings.
4
ACMEG—A THM STRESS-STRAIN CONSTITUTIVE FRAMEWORK TO MODEL THE BEHAVIOUR OF CLAY BARRIERS
4.1 Generalised effective stress in host materials Defining an adequate stress framework is an essential prerequisite to constitutive stress-strain modelling of host materials submitted to THM loadings. According to the effective stress principle, first stated by Terzaghi (1936), a multiphase porous medium can
Figure 12. Distribution of incremental pore volume for two compacted samples of FEBEX bentonite at different dry densities. Mercury Intrusion Porosimeter test (Lloret et al., 2003).
70
This section presents the main layout of the model with its temperature and suction extension. A more complete description can be found in François and Laloui (2008a). In an elasto-plastic framework, the total strain dε is generated by non-linear thermo-elasticity, inducing reversible strain dε e , coupled with a multi-dissipative thermo-plasticity, producing irrecoverable strain dεp . Due to the strain history dependence, the formulation is given in terms of infinitesimal increments. Reference is made here to strains and stresses in the small deformation domain. The elastic part of the deformation is expressed as:
be converted into a mechanically equivalent, singlephase, single-stress state continuum. Consequently, the constitutive equations for mechanical behaviour directly link the change in strain to a variation in a single stress averaged over a volume comprehending several constituents, each of which is likely to react internally to a global external load. Under full saturation in water, the intergranular stress in bentonite is a combination of total stress and pore water pressure, the formulation being likely to include physico-chemical interactions whenever justified (Verwey and Overbeek, 1948; Hueckel and Pellegrini, 1992). A possible generalisation to partial saturation in water is the generalised effective stress inherited from Bishop’s proposal (1959): σij
= (σij − pa δij ) + Sr (pa − pw )δij
1 −1 dεije = Eijkl dσkl − βs dT δij 3
(1)
(3)
where σij is the exterior stress, δij the Kronecker delta, pa the pore air pressure, pw the pore water pressure, and Sr (= volume of water / volume of voids) the degree of saturation. The direct dependence of the mechanical stress variable (1) on suction (s = pa − pw ) and degree of saturation is noteworthy. The main implications of the use of advanced stress variables have been investigated by Nuth and Laloui (2007). While the stress variable (1) is the unique stress entering the mechanical stress-strain relationships, later expressed by equations (4) and (5), thermodynamic (Hutter et al., 1999) and energetic (Houlsby, 1997) considerations call for a supplementary set of variables to describe the retention behaviour in parallel. The complete stress and work conjugate strain framework is then formulated as: σij εij (2) and Sr s
where compression is taken as positive. Eijkl is the mechanical elastic tensor and βs the volumetric thermal expansion coefficient of the solid skeleton. Elastic strain may be induced by total stress, suction, saturation degree variation (first term of Equation 3), or by temperature change (second term of Equation 3). Eijkl is composed of the non-linear hypo-elastic modulus. Using the concept of multi-mechanism plasticity (Mandel, 1965), the total irreversible strain increment p dεij is induced by two coupled dissipative processes: an isotropic and a deviatoric plastic mechanism. These p,iso p,dev produce plastic strain increments dεij and dεij , respectively. The yield limits of each mechanism, restricting the elastic domain in the generalised effective stress space, take the following expressions (Figure 14):
where εij is the mechanical strain variable. The sets of variables (σij , εij ) and (s, Sr ) enter the mechanical model and the retention model, respectively, developed hereafter. Coping with the particular behavioural features of unsaturated fine-grained materials reviewed in Section 3.2 raises the need for constant interaction between the two models.
(5)
4.2
fiso = p − pc riso = 0 dp fdev = q − Mp 1 − bLog rdev = 0 pc
(4)
where q is the deviatoric stress and p the mean generalized effective stress. b is a material parameter and d the distance (in the logarithmic plane) between the
Introduction to the ACMEG constitutive framework
Mathematical formulation The basic concept of the ACMEG model family is to introduce all the environmental effects mentioned above (S—partially saturated state, T—temperature, 2S—double structure effect and DC—desiccation cracks) in an elasto-plastic framework where each environmental loading can cause reversible and irreversible changes in the material state.
Figure 14. Suction (a) and temperature (b) effects on the THM yield limits.
71
apparent preconsolidation pressure, pc , and the critical pressure, pcr . M is the slope of the critical state line in the (q − p ) plane and may depend on temperature. riso and rdev are the degrees of plastification of the isotropic and deviatoric mechanisms, respectively. According to bounding surface theory (Dafalias & Herrmann, 1980), this enables progressive evolution of the isotropic and deviatoric yield limits (Hujeux, 1979). The apparent preconsolidation pressure pc is shared by both yield limits, coupling the two mechanisms. Moreover, this parameter is the main hardening varip able and depends on volumetric plastic strain εv (in the sense of the Cam-Clay model family according to Roscoe & Burland (1968)), on temperature and on suction (Figure 14): ⎧ p ⎪ ⎨pc0 exp{βεv }{1 − γT log[T /T0 ]} pc = pc0 exp{βεvp }{1 − γT log[T /T0 ]} ⎪ ⎩ {1 + γs log[s/se ]}
Figure 15.
if s ≤ se
hydraulic limits, fdry and fwet , on drying and wetting paths, respectively:
if s ≥ se (6)
where pc0 is the initial preconsolidation pressure (at the initial temperature and under saturated conditions) and β the plastic compressibility modulus. γT and γs are material parameters. The flow rule of the isotropic mechanism is associated, while the deviatoric one is not; these are assumed to take the following forms, respectively:
fdry = s − sd = 0 fwet = sd shys − s = 0
p,dev dεij
=
λiso 3
=
p λdev
1 Mp
q 1 ∂q δij +α M − ∂σij p 3
(9) (10)
(7)
where sd is the drying yield limit and shys is a material parameter considering the size of retention hysteresis. If the initial state is saturated, the initial hydraulic drying limit sd0 is equal to air-entry suction se and increases when suction overtakes se as follows:
(8)
sd = sd0 exp(−βh Sr )
p
p,iso
dεii
The retention model in the ACMEG framework.
(11)
where βh is the slope of the desaturation curve in the Sr − ln s plane (Figure 15). Finally, because the air-entry suction of the materials depends on temperature and dry density, sd0 is a function of temperature and volumetric plastic strain (François and Laloui, 2008b):
where α is a material parameter. The plastic multip p pliers, λiso and λdev , are determined using Prager’s consistency equation for multidissipative plasticity (Prager, 1958; Rizzi et al., 1996). As presented earlier, the generalised effective stress concept requires evaluating the degree of saturation to fully describe the behaviour of the unsaturated soil. Therefore, the retention behaviour (the degree of the saturation/suction relationship) of materials must be modelled. This retention model considers that the desaturation process is also seen as a yielding phenomenon. As long as the soil is drying, suction increases and the degree of saturation, Sr , tends to decrease, mainly when the air entry suction, se , is reached. se is therefore considered as a hydraulic limit separating fully and partially saturated states. Under re-wetting, a hysteretic retention phenomenon occurs, represented by a second limit (Figure 15). Then, a sorption-desorption cycle activates two successive
sd = sd0 exp(−βh Sr ){1 − θT log[T /T0 ] −θe log[1 − εvp ]}
(12)
where θT and θe are material parameters describing the logarithmic evolution of the air-entry suction with respect to temperature and volumetric plastic strain, respectively. Because this retention response is governed by yielding mechanisms, the processes must be controlled by evolution laws that agree with the consistency equations, in addition to the yield functions
72
origins): (i) intrinsic strain hardening, which describes the evolution of the preconsolidation pressure of saturated reconstituted soil, p∗ c0 , according to a plastic strain hardening rule similar to the Cam-clay model, (ii) primary suction effects as in reconstituted soils, (iii) pure soil structure effects and (vi) secondary suction effects in aggregated soils. The primary effects of suction on the increase of effective preconsolidation pressure are of the same nature in reconstituted and aggregated soils and are taken into account by ψ s . These effects are linked to capillary effects and depend on the geometry of the pores and the air entry value of the pore system. Similar to reconstituted soils, a reversible function is proposed to quantify the evolution of apparent preconsolidation pressure due to primary suction effects:
(François and Laloui, 2008b). Within this framework, the current degree of saturation is given by: Sr = Sr0 + Srdry + Srwet
(13) dry
where Sr0 is the initial degree of saturation. Sr and Srwet are the variations of saturation degree induced by the drying and wetting mechanisms, respectively. For very high suctions, the hydraulic conditions reach a residual state defined by the residual degree of saturation Sr,res . In this state, no more variation of the degree of saturation is possible, even if the suction increases (Figure 15). Soil structure considerations In the ACMEG constitutive framework, the influence of soil structure on the stress-strain behaviour is taken into account by making the apparent preconsolidation pressure depend not only on stress state and stress history, but also on the soil structure and suction. For this purpose, as a first requirement, a state parameter named degree of soil structure R is introduced to describe and quantify soil structure effects. This parameter is defined here as the ratio of current macro void to its initial value in the intact state. The degree of soil structure is a scaling parameter that represents the openness of the structure. Obviously, any degradation of structure due to hydro-mechanical loadings changes this parameter. Onthebasisofpore-scaleexperimentalobservations, the evolution of the degree of soil structure has been found to be reasonably reproduced by a decreasing exponentialfunctionofplasticstrain(Kolijietal., 2008): R = exp(−ωεD )
⎧ if 0 < s < s1e ⎨1; 1 s ψ = 1 + γs log(sse ); if s1e ≤ s < sref ⎩ 1 + γs log(s se ) ; if s ≥ sref
in which s1e and se are the air entry suction values of micropores and reconstituted soil, respectively, and γs and γs are two dependent material parameters. The soil structure effects and secondary suction effects on soil structure are taken into account by ψ st , a function of degree of soil structure, which controls the extension of yield limits with respect to the reconstituted reference state. At constant suction, the following evolution rule has been derived for this variable (Koliji et al., 2008): ψ st = exp[R ln ψist ]
(14)
∗
(17)
where the subscript i designates the initial value. In the presence of suction variation, however, secondary effects of suction on soil structure should be considered in ψ st . The following relation is proposed to account for additional effects of suction: s + pat nst st ψ st = ψref , ψist = 1 (18) sref + pat
where R is the degree of soil structure, ε D is a combination of volumetric and deviatoric plastic strains, and ω is the parameter controlling the rate of structure degradation. The expression of the degree of soil structure given by Equation 14 provides an experimentally based relation that establishes the link between the pore-scale structure of the soil and the macroscopic behaviour of the material. Combining the effects of suction and soil structure, a general expression of the apparent preconsolidation pressure in unsaturated structured soils reads: pc = ψ st ψ s p c0
(16)
st in which ψref is the value at the reference suction sref and the exponent nst is a material parameter. The atmospheric pressure pat in the denominator is added to avoid infinite values when the saturated state (zero suction) is the reference state. Double effects of suction on the apparent preconsolidation pressure in structured soils are illustrated in Figure 16. In this figure, the abscissa is the ratio of apparent preconsolidation pressure to saturated preconsolidation pressure in the reconstituted state (pc /p∗ c0 ). The increase of apparent preconsolidation pressure due to the intrinsic suction effect ( ψ1 ) is represented by curve a. Multiplying this curve by a
(15)
where p ∗c0 is the reference effective preconsolidation pressure in saturated reconstituted soil, and ψ st and ψ s are two functions that incorporate the effects of soil structure and suction, respectively. Equation 15 considers four sources for the evolution of the apparent preconsolidation pressure (hardening
73
Griffith’s theory (Griffith, 1924) assumes that defects are present in the material that induce large stress concentrations and lower the overall strength of the material with respect to its theoretical value. Criteria based on this theory actually reflect the failure behaviour of unsaturated (or cemented) soils when the minor net stress is tensile (Bishop and Garga, 1969; Bagge, 1985; Baker, 1981). Based on available uniaxial traction test data on clayey soils performed at various known suctions and degrees of saturation (Farrell et al., 1969; Rodriguez et al., 2007; Peron, 2008), one can establish a dependence of tensile strength on suction. An exponential law of the following form is chosen (Peron, 2008): k1 s σt = σtsat + k2 1 − exp − k2
Figure 16. Combined effects of suction and soil structure on the apparent isotropic preconsolidation pressure.
(20)
σtsat g is the tensile strength in the saturated state (s = 0), namely the saturated tensile strength. Unless the soil is cemented, the value of σtsat should not greatly differ from zero. k2 and k1 are material parameters accounting for the increase in tensile strength as suction increases. k2 has the dimension of stress, and k1 is dimensionless. The evolution of the criterion (denoted fcut ) with respect to the normalized yield surfaces fiso and fdev is sketched in Figure 17. Within the ACMEG framework, desiccation cracking is therefore the consequence of a threefold process: (1) increase of suction and effective stress, (2) constraint in the resulting shrinkage process, and (3) coupling of tensile strength with suction. During a
st ψref
reference soil structure function gives the curve b, which represents the increase in apparent preconsolidation pressure due to intrinsic suction ( ψ1 ) and pure soil structure effects ( ψ2 ) without considering suction-hardening of soil structure. The final evolution of apparent preconsolidation pressure with suction in structured soils is represented by curve c. The grey area between curves b and c ( ψ3 ) corresponds to the effects of suction on soil structure. This effect is a hardening effect for suctions beyond sref and a softening effect for suctions below it. Desiccation cracks Desiccation cracks (actually cracks that occur during drying shrinkage) are likely to form if shrinkage deformations are constrained and/or tensile stresses are generated in soil reaching its tensile strength (Corte and Higashi, 1960). Typically, these constraints can arise from (i) a frictional or other traction or displacement boundary condition or (ii) any eigen-stress concentrations within the soil sample. Intrinsic factors, such as soil texture (existence of large particles, Towner 1988) and soil structure (solid network formed by soil particles, Scherer 1997) may be the origin of constrained shrinkage in some situations. Therefore, in order to capture the possibility of desiccation crack occurrence (essentially mode I fracturing), a tensile failure criterion is integrated into the ACMEG framework. Such a criterion actually stems from Griffith’s tensile failure criterion. It is assumed that a crack is likely to appear in the medium on a drying path as soon as the minor principal stress σ3 becomes equal to this overall strength, namely the tensile strength σt : σ3 = σt
Figure 17. Tensile criteria considered in the ACMEG framework.
(19)
74
initial state, simplifying their comparison. In addition, the whole history of equalization to a given level of suction and subsequent oedometric compression at a constant level of suction is retraced (Figure 19a). Simulation of wetting or drying processes from an initial suction of 138 MPa predicts a satisfactory volumetric response (Figure 19b). The magnitude of strain is observed to vary depending on the net stress applied during equalization, as shown by the comparison of wetting tests 5 and 1, under a vertical net stress of 0.1 and 5.1 MPa, respectively. Even though the global swelling trend is observed upon wetting for all tests, a punctual decrease in εv is attributed to (i) mechanical compression prior to or during equalization and (ii) seamless plastic episodes due to the initiation of minor wetting collapse. Subsequent oedometric compression tests (Figure 19c) at constant suctions from 0 (test 5) to 500 MPa (test 1) are also remarkably well predicted with the proposed framework, as a consequence of the reliability of the isotropic yield limit formulation (Equation 6). Underground confinement brings particular boundary conditions for the bentonite layers, so that their overall volume is often totally constrained. Under the effect of moisturisation, the constraint leads to inner stresses, the latter quantified by the means of swelling pressure tests. On the basis of advances brought by using the generalised effective stress, ACMEG makes it straightforward to simulate the constrained conditions and predict the generated stresses. The superposition of innovative numerical simulations (predictions for tests SP1 and SP4) with experimental points in Figure 20 shows a satisfying qualification of the stress increase trends. A close estimate of the maximum swelling pressure is then available from numerical results, even though the quantification could still be refined (Nuth and Laloui, 2007). The simulated results are also strongly dependent on the soil water retention curve shape (Equations 9 to 13).
Figure 18. Interception of stress path with tensile failure criterion during constrained shrinkage in the radial direction.
constrained desiccation phase, prescribed strains make the stress path deviate from the isotropic path normally followed during unconstrained desiccation. The stress path then tends to come closer to the tensile failure criterion. In turn, the tensile failure criterion tends to move towards higher minor effective stresses, due to its dependence on suction (this could be seen as an expression of brittleness affecting the soil as suction increases). This behaviour can be illustrated using the parameter X r , defined as ‘‘degree of shrinkage restraint,’’ and equal to the ratio of hindered strains to shrinkage strains resulting from unconstrained shrinkage. Figure 18 shows different evolutions of the minor stress during drying depending on the value of X r (from 0, unconstrained shrinkage, no crack is possible, to 1, all strains are hindered in two of the three principal directions). The trace of a possible tensile failure criterion in the s − σ3 plane, given by Equation 19, is also sketched.
5 5.1
5.2 Modelling the effect of temperature on the hydro-mechanical response of host materials In confining barriers, saturation and desaturation processes often occur in a medium affected by nuclear waste heat emission. Under such non-isothermal conditions, several couplings between capillary and temperature effects must be considered in order to understand and to predict the THM response of clay simultaneously submitted to stress, moisture and temperature changes. Figure 21 presents the retention behaviour of compacted Boom clay at two temperatures as predicted by ACMEG and as compared with experimental observations (Romero et al., 2003). This example shows the temperature effect on the retention curve. In particular, the air-entry suction is reduced with increasing temperature. Moreover, during these
MODELLING PERFORMANCES OF THE ACMEG FRAMEWORK Modelling the unsaturated behaviour of host materials
The applicability of the ACMEG framework to waste confining material is illustrated with the modelling of the complex experimental stress-strain response in unsaturated FEBEX bentonite (Lloret et al., 2004). These experimental data were preferred because most published stress paths actually start from the same
75
1000
Test 1
10
SP2 EXP SP3 EXP
Test 2
Test 3 7
10
Test 4 106
SP4 EXP
100
SP1 MOD SP2 MOD SP3 MOD SP4 MOD
10 Wetting
Initial point
8
SP1 EXP
(b)
(a)
Matric suction s (MPa)
Matric suction s (Pa)
109
1
105 104
Final point
Test 5 106 Vertical stress
108
-2
0.16
2
4
6
8 v
Experiment
12
Numerical simulation T=22˚C T=80˚C
0.08
10
(MPa)
Figure 20. Comparison of experimental swelling pressure tests on Febex bentonite and their numerical simulation using ACMEG.
Exp. test 1 ACMEG-s test 1 Exp. test 3 ACMEG-s test 3 Exp. test 5 ACMEG-s test 5
0.24
0
Vertical net stress (b)
0.32 Volumetric strain v (-)
0.1
v (Pa)
T=22˚C T=80˚C
1.1
Initial point
1
0 105
107 Matric suction s (Pa)
0.4
109
Exp. 1 Mod. 1 Exp. 2 Mod. 2 Exp. 3 Mod. 3 Exp. 4 Mod. 4 Exp. 5 Mod. 5
(c) Volumetric strain v (-)
Degree of Saturation [-]
Wetting
0.3 0.2 0.1
0.9 0.8 0.7 0.6 0.5 0.4 0.01
0.1
1
Suction [MPa]
0 -0.1 4 10
Figure 21. Comparison between experimental retention curve on compacted Boom Clay at two temperatures (22 and 80◦ C) and their numerical simulation using ACMEG model.
105 106 107 Vertical net stress v (Pa)
108
wetting-drying cycles, the porosity of the compacted Boom Clay is strongly modified by suction changes. Figure 22 shows drastic collapse upon wetting. The collapse intensity is affected not only by the external stress level, but also by the temperature condition. The evolution of these volumetric responses with suction
Figure 19. Simulations of hydro-mechanical paths in oedometric conditions; (a) stress paths, (b) volumetric response with suction changes and (c) volumetric response with respect to vertical net stress.
76
Experiment
Experiment
Numerical simulation v,net v,net v,net
= 0.085MPa
v,net
= 0.3MPa
v,net
= 1.2MPa
v,net
= 0.085MPa
Numerical simulation T= 22˚C T= 80˚C
= 0.3MPa = 1.2MPa
T= 22˚C T= 80˚C
0
s= 0.06 MPa
0.05
-0.02
Volumetric strain [-]
Volumetric strain [-]
0
-0.05
-0.1
-0.04
-0.06
-0.08 -0.15
T=22˚C -0.2 0.01
0.1
(a)
-0.1 0.1
1
Experiment
Numerical simulation = 0.085MPa v,net v,net v,net
Figure 23. Comparison between experimental oedometric compression tests on compacted Boom Clay at a suction of 60 kPa and two different temperatures (22 and 80◦ C) and their numerical simulation using ACMEG model.
= 0.085MPa v,net
= 0.3MPa
v,net
= 1.2MPa
v,net
1
Vertical net stress [MPa]
Suction [MPa]
= 0.3MPa = 1.2MPa
0.05
Volumetric strain [-]
0
-0.05
-0.1
-0.15
Figure 24. Simulation of ACMEG for oedometric compression of unsaturated aggregated silty clay at a constant suction of 500 kPa.
-0.2
T=80˚C -0.25 0.01
(b)
0.1
the interconnection between temperature, suction, and stress states. Only a unified approach can consider in a relevant manner the THM response of this kind of material.
1
Suction [MPa]
Figure 22. Volumetric strain observed for drying-wetting cycles of compacted Boom Clay under oedometric conditions. Comparison between experimental results and numerical simulations using ACMEG. a) 22◦ C and b) 80◦ C.
5.3 Modelling the behaviour of unsaturated structured material Figure 24 shows results of the model simulation for a sample of unsaturated aggregated silt during oedometric compression at a constant suction of 500 kPa. The model was found to reasonably reproduce the experimental results. Thanks to a modified equation for water properties, the model can also address increasing saturation, even at a constant suction.
is well reproduced by the ACMEG model. In addition, a temperature increase modifies the yield point along compression paths, resulting in a translation of the normally consolidated line towards lower generalized effective stress (Figure 23). All of these examples clearly indicate the necessity to consider
77
Figure 26. Experimental values of uniaxial tensile strength from Rodriguez et al. (2007) and evolution law of tensile strength with ACMEG.
Figure 25. Crack pattern obtained after drying under atmosphere with controlled relative humidity, after Rodriguez et al. (2007).
5.4
Modelling of desiccation tests
Rodriguez et al. (2007) reported an experimental and numerical study of desiccation of low plasticity silt. The experimental programme consisted mainly of desiccation tests under ambient air or controlled atmosphere. Disk-shaped slabs of the soil in a slurry state were placed on plates, grooved to create radial restraint at the base. Only water loss and vertical shrinkage were recorded during the test. For tests under controlled atmospheric conditions (simulated later), slabs were 1.6 cm tall and relative humidity was controlled with a saline solution, corresponding to a total suction of about 38 MPa. Cracking was observed, leading to the formation of the patterns shown in Figure 25. The experimental degrees of saturation at cracking were between 0.98 and 0.86; suction values extrapolated from the water retention curve were between 10 and 40 kPa. Such a drying situation is in some ways similar to that which prevails for instance during air drying of gallery walls drilled in the host clay of nuclear waste repositories. The constraint in this situation stems from the deeper intact (i.e. not dried) host material. Radial cracking is a direct consequence in the galleries. Mechanical tests were also performed: traction tests, unconfined compression tests and one determination of the water retention curve in an oedometer apparatus. For the present simulation, parameters β sat , and Kref were calibrated on the basis of a water retention curve test in oedometric conditions. The value of the
Figure 27. Simulation of nickel mining waste constrained desiccation tests, predicted evolution of minor effective stress with respect to suction.
friction angle was fixed at 25◦ prior to calibration, representative of low plasticity silts. Poisson’s ratio was fixed at 0.25. The values of d, b and α were also fixed beforehand. Parameters for suction tensile strength evolutions were calibrated from tensile strength test results. The parameter σtsat was considered fixed and equal to the experimental value given by Rodriguez et al. (2007). k1 and k2 were calibrated with experimental results (see Figure 26). On the basis of the parameters determined above, desiccation tests were simulated under a controlled atmosphere. For the simulation, the suction field was considered homogeneous within the sample. This is in
78
accordance with the authors’ claim based on boundary value problem calculations. Furthermore, strains were assumed totally constrained in the radial (horizontal) direction. Such a condition should prevail at the slab base (and was adopted by the authors themselves). Results of the simulation are presented in Figure 27. The predicted suction at cracking was 19 kPa (degree of saturation 0.98), very close to the experimental results. In this sense, the model can predict desiccation crack occurrence.
6
Corte, A. & Higashi, A. 1960. Experimental Research on Desiccation Cracks in Soil. Research report 66, U.S. Army Snow and Ice and Permafrost Research Establishment. Dafalias, Y. & Herrmann, L. 1980. A bounding surface soil plasticity model. International Symposium on soils under Cyclic and Transient Loading, Swansea, 335–345. Davies, C. & Bernier, F. 2003. Impact of the Excavation Disturbed or Damaged Zone (EDZ) on the Performance of Radioactive Waste Geological Repositories. Proceedings of a European Commission CLUSTER—Conference and Workshop, Luxembourg. ENRESA. 2000. Febex Project: Full-scale engineered barriers experiment for a deep geological repository for high level radioactive waste in crystalline host rock. Publicación técnica 1/2000. Farrell, D.A., Geacen, E.L. & Larson, W.E. 1967. The effect of water content on axial strain in a loam soil under tension and compression. Soil Science Society of America Proceedings, 31 (4), 445–450. Fleureau, J.M., Kheirbeksaoud, S., Soemitro, R. & Taibi, S. 1993. Behavior of clayey soils on drying wetting Paths. Canadian Geotechnical Journal, 30 (2), 287–296. François, B. & Laloui, L. 2008a. Thermo-plasticity in unsaturated soils, a constitutive approach. E-UNSAT 08. This conference. François, B. & Laloui, L. 2008b. ACMEG-TS: A constitutive model for unsaturated soils under non-isothermal conditions. International Journal for Numerical and Analytical Methods in Geomechanics, Submitted. Gens, A. & Alonso, E.E. 1992. A framework for the behaviour of unsaturated expansive clays. Canadian Geotechnical Journal, 29, 1013–1032. Gera, F., Hueckel, T. & Peano, A. 1996. Critical issues in modelling the long-term hydro-thermo-mechanical performance of natural clay barriers. Engineering Geology, 41, 17–33. Graham, J., Chandler, N.A., Dixon, D.A., Roach, P.J., To, T. & Wan, A.W.L. 1997. The Buffer/Container Experiment: results, synthesis, issues. Atomic Energy of Canada Limited Report, AECL-11746, COG-97–46-I. Chalk River, ON, Canada. Griffith, A.A. 1924. Theory of rupture. In Proceedings of the First International Conference on Applied Mechanics, Delft, Holland, 55–63. Houlsby, G.T. 1997. The work input to an unsaturated granular material. Géotechnique, 47 (1), 193–196. Hueckel, T. & Pellegrini, R. 1992. Effective stress and water pressure in saturated clays during heating-cooling cycles. Canadian Geotechnical Journal, 29, 1095–1102. Hujeux, J.C. 1979. Calcul numérique de problèmes de consolidation élastoplastique. PhD Thesis, Ecole Centrale de Paris. Hutter, K., Laloui, L. & Vulliet, L. 1999. Thermodynamically based mixture models of saturated and unsaturated soils. Mechanics of cohesive-frictional materials, 4, 295–338. Imbert, C., Olchitzky, E., Lassabatère, T., Danglas, P. & Courtois, A. 2005. Evaluation of a thermal criterion for an engineered barrier system. Engineering Geology, 81, 269–283. JNC. 1999. Project to Establish the Scientific and Technical Basis for HLW Disposal in Japan. Technical report support report 2.
CONCLUSIONS
We present a THM stress-strain framework for modelling the performance of clay barriers in deep geological repositories for radioactive waste. This study aims to contribute to the performance assessment of deep geological repositories for heat-generating radioactive waste. The model framework is built on the conceptual understanding of the behaviour of soils submitted to loads representing the planned in-situ scenarios. The ACMEG framework considers the main mechanisms related to the thermo-plastic behaviour of saturated and unsaturated materials. It is extended to include soil structure aspects and induced desiccation cracks. The performances of the model are illustrated through comparisons with experimental results.
REFERENCES Baldi, G., Hueckel, T., Peano, A. & Pellegrini, R. 1991. Developments in modelling of thermo-hydro-mechanical behaviour of Boom clay and clay-based buffer materials (Vol 1 and 2). EUR 13365/1 and 13365/2, Luxembourg. Bagge, G. 1985. Tension cracks in saturated clays cuttings. In Proceedings of the Eleventh International Conference on Soil Mechanics and Foundations Engineering, San Francisco, vol. 2, 393–395. Baker, R. 1981. Tensile strength, tension cracks and stability of slopes. Soils and Foundations, 21 (2), 1–7. Bishop, A.W. 1959. The principle of effective stress. Tecnisk Ukeblad, 39, 859–863. Bishop, A.W. & Garga, V.K. 1969. Drained tension tests on London Clay. Géotechnique, 19, 309–313. Brustaert, W. 1968. The permeability of a porous medium determined from certain probability laws for pore-size distribution. Water Resources Research, 4, 425–434. Callisto, L. & Rampello, S. 2004. An interpretation of structural degradation for three natural clays. Canadian Geotechnical Journal, 41, 392–407. Chapman, N.A. & McKinley, I.G. 1987. The geological disposal of nuclear waste, John Wiley and Sons. Cuisinier, O. & Laloui, L., 2004. Fabric evolution during hydromechanical loading of a compacted silt. International Journal for Numerical and Analytical Methods in Geomechanics, 28 (6), 483–499.
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Koliji, A., Vulliet, L. & Laloui, L. 2008. New basis for the constitutive modelling of aggregated soils, Acta Geotechnica, (in press). Komine, H. & Ogata, N. 1994 Experimental study on swelling characteristics of compacted bentonite. Canadian Geotechnical Journal, 31 (2), 478–490. Laloui, L. & Cekerevac, C. 2003. Thermo-plasticity of clays: An isotropic yield mechanism. Computer and Geotechnics, 30, 649–660. Lambe, T.W. 1958. The engineering behaviour of compacted clays. Journal of the Soil Mechanics and Foundation Division ASCE, 84, 1–35. Liu, M.D. & Carter, J.P. 1999. Virgin compression of structured soils. Géotechnique, 49 (1), 43–57. Lloret, A., Romero, E. & Villar, M. 2004. FEBEX II Project: Final report on thermo-hydro-mechanical laboratory tests. publicación técnica 10/2004, ENRESA. Lloret, A., Villar, M.V., Sanchez, M., Pintado, X. & Alonso, E.E. 2003. Mechanical behaviour of heavily compacted bentonite under high suction changes. Géotechnique, 53 (1), 27–40. Mandel, W. 1965. Généralisation de la théorie de Koiter. International Journal of Solids and Structures, 1, 273–295. Mitchell, J.K. 1993. Fundamentals in soils behaviour, 2nd edition, John Wiley & Sons, New York. Modaressi, H. & Laloui, L. 1997. A thermo-mechanical constitutive model for clays. International journal for numerical and analytical methods in Geomechanics, 21, 313–335. Nagra 2002a. Project Opalinus Clay: Safety Report. Nagra Technischer Bericht NTB 02–05, 360p. Nagra 2002b. Calculations of the Temperature Evolution of a Repository for Spent Fuel, vitrified high-Level Waste and Intermediate Level Waste in Opalinus Clay. Nagra Technischer Bericht NTB 01–04. Nuth, M. & Laloui, L. 2007. Effective stress concept in unsaturated soils: Clarification and validation of a unified framework. International Journal for Numerical and Analytical Methods in Geomechanics. DOI 10.1002/nag.645. Olchitzky, E. 2002. Couplage hydro-mécanique et perméabilité d’une argile gonflante non saturée sous sollicitations hydriques et thermiques. PhD Thesis. Ecole nationale des ponts et chaussées, Paris. Peron, H. 2008. Desiccation Cracking of Soils. PhD Thesis, Ecole Polytechnique Fédérale de Lausanne, Switzerland. Prager, W. 1958. Non-isothermal plastic deformation. Koninkklijk-Nederland Akademie Van Wetenschappen Te Amsterdam—Proc. of the section of sciences-B, 61, 176–182. Rizzi, E., Maier, G. & Willam, K. 1996. On failure indicators in multi-dissipative materials. International Journal of Solids and Structures, 33 (20–22), 3187–3214. Rodriguez, R., Sanchez, M., Ledesma, A. & Lloret, A. 2007. Experimental and numerical analysis of desiccation of a mining waste. Canadian Geotechnical Journal, 44, 644–658. Romero, E., Gens, A. & Lloret, A. 2001. Temperature effects on the hydraulic behaviour of an unsaturated clay. Geotechnical and Geological Engineering, 19, 311–332.
Romero, E., Gens, A. & Lloret, A. 2003. Suction effects on a compacted clay under non-isothermal conditions. Géotechnique, 53 (1), 65–81. Roscoe, K.H. & Burland, J.B. 1968. On the generalized stress—strain behaviour of ‘‘wet’’ clay. In Engineering Plasticity. Cambridge University Press, Cambridge, England, 535–609. Salager, S., François, B., El Youssoufi, M.S., Laloui, L. & Saix, C. 2008. Experimental investigations of temperature and suction effects on compressibility and preconsolidation pressure of a sandy silt. Soils and Foundations. (Accepted for publication). Scherer, G.W. 1997. Stress from re-immersion of partially dried gel. Journal of Non-Crystalline Solids, 212, 268–280. Sultan, N. 1997. Etude du comportement thermo-mécanique de l’argile de Boom: Expériences et modélisation. PhD Thesis, Ecole nationale des ponts et chaussée, Paris. Tamari, S. 1984. Relations between pore-space and hydraulic properties in compacted beds of silty-loam aggregates. Soil Technology, 7, 57–73. Tang, A. 2005. Effet de la temperature sur le comportement des barrières de confinement. PhD Thesis, Ecole National des Ponts et Chaussée, Paris. Tang, A. & Cui, Y. 2005. Controlling suction by the vapour equilibrium technique at different temperatures and its application in determining the water retention properties of MX80 clay. Canadian Geotechnical Journal, 42 (1), 287–296. TIMODAZ 2007. Thermal impact on the damaged zone around a radioactive waste disposal in clay host rocks. Deliverable 2. State of the art on THMC. Terzaghi, K. 1936. The shearing resistance of saturated soils and the angle between the planes of shear. International Conference on Soil Mechanics and Foundation Engineering, Harvard University Press, 54–56. Towner, G.D. 1988. The influence of sand- and silt-size particles on the cracking during drying of small claydominated aggregates. Journal of Soil Science, 39, 347–356. Verwey, E. & Overbeek, J. 1948. Theory of stability of lyophobic colloids—The interaction of soil particles having an electric double layer, Elsevier Publishing Company, Inc. Villar, M. 2002. Thermo-hydro-mechanical characterisation of a bentonite from Cabo de Gata: A study applied to the use of bentonite as sealing material in high level radioactive waste repositories. publicación técnica 04/2002, ENRESA. Villar, M. & Lloret, A. 2004. Influence of temperature on the hydro-mechanical behaviour of a compacted bentonite. Applied Clay Science, 26, 337–350. Villar, M.V., Perez del Villar, L., Martin, P., Pelayo, M., Fernandez, A., Garralon, A., Cuevas, J., Leguey, S., Caballero, E., Huertas, F., Jimenez de Cisneros, C., Linares, J., Reyes, E., Delgado, A., Fernandez-Soler, J. & Astudillo, J. 2006. The study of spanish clays for their use as sealing materials in nuclear waste repositories: 20 years of progress. Journal of Iberian Geology 32 (1), 15–36.
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Advances in testing techniques
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A novel suction-controlled true triaxial apparatus for unsaturated soils L.R. Hoyos, A. Laikram & A.J. Puppala The University of Texas at Arlington, Texas, USA
ABSTRACT: This paper describes a novel servo-controlled true triaxial testing apparatus that has been developed to test 7.5-cm (3-in) side, cubical specimens of unsaturated soil under controlled-suction states for a wide range of stress paths that are not achievable in a conventional cylindrical apparatus. The equipment is a mixedboundary type of device, with the specimen seated on top of a high-air-entry disk and between five flexible (latex) membranes on the remaining sides of the cube. The new cell is an upgraded, more elaborate version of the one previously reported by Hoyos (1998), featuring two independent pore-air and pore-water pressure control systems via a PCP-5000-UNSAT pressure panel. Matric suction states in the specimens are induced during testing via the axis-translation technique. The technique is implemented by utilizing the s = ua testing concept (uw = 0). The paper outlines the full development of the new cell, including details of its main components and the step-by-step assembling process. Results from a short series of constant-suction Triaxial Compression (TC) and Triaxial Extension (TE) tests are presented. The operational true triaxial apparatus will play a fundamental role in the complete characterization of unsaturated soil behavior under multiaxial stress paths that are likely to be experienced in the field.
1
as critical a role in unsaturated soil response under multiaxial stress states (Fig. 1). The present work has been largely motivated by the lack of experimental evidence of this kind. It is in the above context that a true triaxial (cubical) test cell, capable of inducing in the test specimens a wide range of simple-to-complex multiaxial stress paths under controlled-suction states, plays a fundamental role in a thorough stress-strain-strength characterization of this type of materials. This paper describes a novel servo-controlled true triaxial apparatus that has been developed to test 7.5-cm (3-in) per side, cubical specimens of unsaturated soil
BACKGROUND AND IMPORTANCE
Over the last few decades, the description of the stressstrain-strength behavior of unsaturated soils has been closely linked with efforts to isolate the relevant stress fields governing the soil’s mechanical response. The adoption of matric suction, s = (ua − uw ), and the excess of total stress over air pressure, (σ − ua ), as the relevant stress state variables, have allowed the modeling of various key features of unsaturated soil behavior via suction-controlled oedometer, triaxial, and direct shear testing (Alonso et al., 1990; Wheeler and Sivakumar, 1992; Fredlund and Rahardjo, 1993). The majority of these devices, however, allow for the application of loads along limited paths and modes of deformation, such as one-dimensional, hydrostatic or axisymmetric loading. In nature, pavement subgrades and shallow foundation soils well above the ground-water table are subject to three-dimensional stress gradients due to changes in the stress state variables (σij − ua δij ) and (ua − uw )δij , as depicted schematically in Figure 1. Therefore, accurate predictions of the stress-strain response of geosystems involving unsaturated soils require that all the constitutive relations be valid for all major stress paths likely to be experienced in the field. Moreover, matric suction has been shown to play a paramount role in unsaturated soil response under one-dimensional, isotropic and axisymmetric loading conditions. Hence, suction is also expected to play
Foundation load
Traffic load
Pavement Pavement (
1
– ua)
(ua – uw)
(
1
– ua)
(ua – uw)
(ua – uw) ( 2 – ua) (
3
– ua) (ua – uw)
(ua – uw) ( 2 – ua) (
3
– ua) (ua – uw)
Figure 1. Unsaturated soil systems subject to multiaxial stress states.
83
considerably enhanced performance, which includes: (1) More testing accuracy and reliability, (2) More flexibility of operation and breadth of application, (3) More refined data acquisition and process control systems, and (4) Increased amount and quality of testing variables monitored during a typical suction-controlled testing. In general, true triaxial devices can be classified into three major categories: rigid-boundary, flexibleboundary and mixed-boundary cells (Sture, 1979; Arthur, 1988). The apparatus presented in this paper is a mixed-boundary type of cell, with the specimen seating on top of a HAE ceramic disk and between five flexible membranes on the remaining sides of the cube. The cell consists mainly of a stainless steel frame featuring six pressure cavities to accommodate one top and four lateral flexible latex membranes, and a cubical base aluminum piece at the bottom to house a 5-bar ceramic disk and four symmetrically spaced coarse porous stones, as shown in Figures 2–5.
under controlled-suction states for a wide range of stress paths that are not achievable in a conventional cylindrical apparatus. The equipment can be defined as a mixed-boundary type of device, with the specimen seating on top of a high-air-entry (HAE) disk and between five flexible (latex) membranes on the remaining sides of the cube. The new cubical cell is an upgraded, more elaborate version of the one implemented by Hoyos (1998), featuring two independent pore-air pressure (ua ) and pore-water pressure (uw ) control systems by using a PCP-5000-UNSAT pressure control panel. Suction states in the cubical specimens during suction-controlled testing are induced via axis-translation technique. The following sections describe details of the design, main components, and assembling process of the developed apparatus. Preliminary results from a short series of suction-controlled triaxial compression (TC) and triaxial extension (TE) tests are also presented. 2
PREVIOUS WORK
Hoyos (1998) reported a first attempt to test unsaturated soils under suction-controlled multiaxial loading. In order to achieve this goal, a then 30-year-old cubical apparatus was modified to test 10-cm (4-in) side, cubical specimens of silty sand under suctioncontrolled conditions. The original development of the apparatus was presented by Atkinson (1972) for multiaxial testing of rock materials. Pore-water pressure (uw ) was applied to the bottom of the specimen through a 5-bar HAE ceramic disk. Pore-air pressure (ua ) was applied to the top and four lateral faces of the specimen via an air-pressurized manifold. Test results are reported in Hoyos (1998) and Hoyos and Macari (2001). This previous device, however, presented some equipment and testing related limitations that can be summarized as follows: (1) The steel frame is highly corrosive, which resulted in occasional clogging of the 5-bar ceramic; (2) Hydraulic oil is used to pressurize latex membranes in contact with soil, with oil temperatures ranging from 28◦ C to 38◦ C; (3) Latex membranes had low durability when exposed to hydraulic oil for extended time periods; (4) Porewater temperature cannot be controlled, retarding equalization of pore fluids; and finally, (5) The device allows only for stress-controlled testing. 3
Figure 2. Cubical base aluminum piece with porous stones and grooved compartment for housing a 5-bar ceramic disk.
A NOVEL TRUE TRIAXIAL APPARATUS
3.1 General design and assembling The true triaxial apparatus described herein is aimed at overcoming all of the above limitations, yielding a
Figure 3. Sealing of previously saturated, 5-bar ceramic disk onto cubical base aluminum piece.
84
Figure 6. Photograph of entire cubical test layout, including external pressure application/control system (left) and PCP5000-UNSAT pressure control panel (right).
Figure 4. Close view of cubical base aluminum piece fitted onto bottom assembly.
(a) Figure 5. Plan view of cubical base aluminum piece fitted onto bottom assembly.
Sample preparation and saturation of the ceramic disks are described in sections 3.2 and 3.3. After setting of the compacted specimen into the inner cavity of the frame, the remaining five walls are assembled to the frame. Three LVDTs per face (top and four lateral) are used to monitor soil deformations while de-aired water is used to pressurize the specimen via latex membranes. The external pressure is transmitted to the water-filled latex membranes via pressure inlet/outlet connections on the walls. Figure 6 shows a photograph of the entire test layout, including the servo-controlled external pressure application system (on the left) and the assembled cubical cell interacting with the PCP-5000-UNSAT pressure control panel (on the right). Pore-air pressure (ua ) is supplied at the bottom of the specimen via a full set of air-pressurized manifolds with nylon tubing from the PCP-5000-UNSAT pressure control panel. Pore-water pressure (uw ) can be applied and controlled at the bottom of the specimen through the 5-bar ceramic disk. Water pressure is
(b) Figure 7. Suction-controlled mechanism: (a) cubical cell interacting with PCP-5000-UNSAT panel; and (b) pore-air pressure, pore-water pressure, and flushing control systems.
also supplied via nylon tubing from the PCP-5000UNSAT pressure panel. As shown in Figure 2, a grooved compartment uniformly distributes the water
85
lateral wall assemblies are then set into place. A typical 7.5-cm (3-in) side, cubical specimen is then prepared in-place using a combined pluviation-tamping compaction process, as shown in Figure 10. The specimen is prepared in approximately eight pluviated layers, with each layer compacted at a target moisture content 4% greater than standard Proctor
underneath the 5-bar disk. In this work, however, the axis-translation technique is implemented by utilizing the s = ua testing concept (uw = 0). The panel also features a flushing mechanism at the bottom assembly, as shown in Figure 7. All suctioncontrolled tests are entirely computer-driven via a data acquisition/process control system (DA/PCS). The core of the cubical cell (Fig. 6) was manufactured and check-out tested at the University of Colorado, Boulder. The PCP-5000-UNSAT pressure control panel from Geotechnical Consulting and Testing Systems (GCTS), Tempe, Arizona, was then adapted to the cubical cell at the geotechnical research laboratories of the University of Texas at Arlington to control pore-air (ua ) and pore-water (uw ) pressures. The panel has been successfully utilized in cylindrical cells, featuring both pressure/volume control cell pressure, pore/back pressure, pore-air pressure with 2 MPa (300 psi) pressure range, and 300 cc (18 in3 ) volume capacity. It also includes a full set of hydraulic servo valves, an electro-hydraulic pump, pressure transducers with 0.1 kPa (0.02 psi) resolution, and specific water volume (vw = 1 + eSr ) change transducer with 0.01 cc resolution. 3.2
Figure 8. Bottom plate of custom-made chamber housing three 5-bar disks prior to saturation.
Saturation of HAE ceramic disks
A procedure similar to that suggested by Bishop and Henkel (1962) and Fredlund (1973), to ensure proper saturation of a HAE disk, was adapted to the working conditions of the 5-bar disks in the modified test cell (Figs. 2 and 3). The same approach was successfully used by Hoyos (1998). A custom-made saturation chamber, made of high burst-resistance acrylic and capable of housing up to three HAE ceramics at the same time, was designed and utilized for saturation of the 5-bar ceramics used in this work, as shown in Figure 8. After the 5-bar ceramics are fully sealed and set into place, the inner cavity of the assembled saturation chamber is filled with distilled, de-aired water to a height of about 25 mm (1 in) above the disks. The water is poured into the cavity using a pipette to minimize the generation of air bubbles. Once the cavity is partially filled with water and the top plate of the chamber is set into place, the water film is subjected to an air pressure of 600 kPa (87 psi), as shown in Figure 9. The water is then allowed to flow through the disks under this constant pressure until air in the disks dissolves in the grooved, previously saturated compartments underneath them. 3.3
Figure 9.
Saturation process of 5-bar ceramic disks.
Preparation of cubical test specimens
Poorly graded silty sand (SM) was used for suctioncontrolled testing in this research work. After saturation of the 5-bar disk, the bottom and the four
Figure 10. In-place, combined pluviation and tamping compaction process.
86
optimum. Tamping corresponds to a compactive effort considerably less than that of standard Proctor compaction. The intention is to reproduce specimens with low preconsolidation stress values, so that, subsequently, it is relatively feasible to reconsolidate the soil to a virgin state. A custom-made, 0.25 mm (0.01-in) thick, stainless steel shaft introduced into the cubical cavity of the frame facilitates the pluviation-tamping compaction process for each layer (Fig. 10). Upon completion of the soil compaction process, the shaft is gently removed and the top assembly of the cell, as well as the remaining components and connections for external stress and suction state applications, are set into place (Fig. 6). 4
Figures 12 and 13 present the deviator stress versus principal strain response of silty sand from suctioncontrolled TC tests. In these figures, suction is shown to exert an important influence on the shear resistance of silty sand, with a considerable increase for s = 200 kPa. During TC testing, the major principal stress σ1 is increased while the intermediate σ2 and minor σ3 principal stresses reduce, such that the net (σ1 – ua)
TE (b = 1, θ = 60o)
σ2 – σ3 σ1 – σ3
θ s = 50, 100, or 200 kPa
A
The suitability of the axis-translation technique in the newly developed apparatus was first validated experimentally by conducting two drained (constant-suction) tests, each involving isotropic loading followed by axisymmetric shearing, on two identically prepared specimens of silty sand. Both tests were performed at the same constant suction s = 200 kPa and loading rate of 10 kPa/hr. The first specimen, however, was subjected to a suction state s = ua = 200 kPa(uw = 0), while the second specimen was subjected to ua = 300 kPa and uw = 100 kPa(s = 200 kPa). Test results showed no significant difference in soil response under both test conditions, hence validating the technique (Hoyos et al., 2005). In this work, four identically prepared specimens of silty sand (SM soil: 80% sand and 20% silt) were subject to a multi-stage testing scheme in which suction was kept constant at 50 or 200 kPa. A soil specimen was first brought under isotropic stress state and subsequently imposed a constant-suction, monotonic triaxial compression (TC) or triaxial extension (TE) shearing until it was apparent that the deviator stress had reached a peak value. At this point, the specimen was brought back to the initial hydrostatic condition and a new octahedral stress applied via ramped consolidation. The same TC or TE stress path was then carried out. The suctioncontrolled test scheme is depicted schematically on a deviatoric plane in Figure 11. In this work, the net octahedral stress σoct and deviator stress q are both defined in terms of total principal stresses σ1 , σ2 , and σ3 as follows: σ1 + σ 2 + σ 3 − ua 3
b=
σoct = 50, 100, or 200 kPa
SUCTION-CONTROLLED TESTING
σoct =
TC (b = 0, θ = 0o)
SS (b = 0.5, θ = 30o)
(σ2 – ua)
Figure 11.
(σ3 – ua)
Suction-controlled true triaxial testing scheme.
60
Deviator stress, q (psi)
50 40 s = 200 kPa 30 s = 50 kPa 20 10 0 -15
-10
-5
0
5
10
15
Principal strain (%)
Figure 12. 100 kPa.
Silty sand response from TC tests at σoct =
60 s = 200 kPa
Deviator stress, q (psi)
50 s = 50 kPa
40 30 20 10 0
(1)
-15
-10
-5
0
5
10
15
Principal strain (%)
1 q = √ (σ1 − σ2 )2 + (σ2 − σ3 )2 + (σ1 − σ3 )2 (2) 2
Figure 13. 200 kPa.
87
Silty sand response from TC tests at σoct =
oped apparatus is suitable for testing soils under suction-controlled conditions using the axis-translation technique. On-going testing involves a wide range of stress paths that are not achievable in a conventional cylindrical apparatus, including simple shear (SS) in a deviatoric stress plane (π -plane). The operational true triaxial apparatus will continue to play a fundamental role in the complete characterization of unsaturated soil behavior under multiaxial stress paths that are likely to be experienced in the field.
60
Deviator stress, q (psi)
50 40 30 s = 200 kPa 20 s = 50 kPa 10 0 -15
-10
-5
0
5
10
ACKNOWLEDGMENTS
15
Principal strain (%)
Figure 14. 100 kPa.
This on-going research effort has been supported by the U.S. National Science Foundation (NSF), Award # 0216545. This support is gratefully acknowledged.
Silty sand response from TE tests at σoct =
60
REFERENCES
Deviator stress, q (psi)
50 s = 200 kPa
Alonso, E.E., Gens, A., and Josa, A. 1990. A constitutive model for par-tially saturated soils. Géotechnique, 40(3), 405–430. Arthur, J.R.F. 1988. Cubical devices: versatility and constraints. Advanced Triaxial Testing of Soil And Rock, STP 977, ASTM, Philadelphia, PA, 743–765. Atkinson, R.H. 1972. A cubical test cell for multiaxial testing of materials. Ph. D. Dissertation, University of Colorado at Boulder, Boulder, CO. Bishop, A.W., and Henkel, D.J. 1962. The measurement of soil properties in the triaxial test. 2nd ed., London, England: Edward Arnold, 227 pp. Fredlund, D.G. 1973. Volume change behavior of unsaturated soils. Ph. D. Dissertation, University of Alberta, Edmonton, Alta., Canada. Fredlund, D.G., and Rahardjo, H. 1993. Soil mechanics for unsaturated soils. John Wiley and Sons, Inc., NY. Hoyos, L.R. 1998. Experimental and computational modeling of unsaturated soil behavior under true triaxial stress states. Ph. D. Dissertation, Georgia Institute of Technology, Atlanta, GA, 352 p. Hoyos, L.R., and Macari, E.J. 2001. Development of a stress/suction-controlled true triaxial testing device for unsaturated soils. Geotechnical Testing Journal, ASTM, 24(1), pp. 5–13. Hoyos, L.R., Laikram, A., and Puppala, A.J. 2005. A novel true triaxial apparatus for testing unsaturated soils under suction-controlled multi-axial stress states. CDRom Proc., 16th International Conf. on Soil Mechanics and Geotechnical Engineering, September 12–16, 2005, Osaka, Japan, pp. 387–390. Sture, S. 1979. Development of multiaxial cubical test device with pore-water pressure monitoring facilities. Rep. VPIE-79.18, Dept. Civil Eng., Virginia Poly. Inst. & State U., Blacksburg, VA. Wheeler, S.J., and Sivakumar, V. 1992. Development and application of a critical state model for unsaturated soils. Predictive Soil Mech., eds: G.T. Houlsby & A.N. Schofield, 709–728, London.
40 s = 50 kPa
30 20 10 0 -15
-10
-5
0
5
10
15
Principal strain (%)
Figure 15. 200 kPa.
Silty sand response from TE tests at σoct =
octahedral stress σoct remains constant. Therefore, the corresponding minor and intermediate principal strains were found to be expansive (−) whereas the major principal strain was compressive (+). Figures 14 and 15 present the deviator stress versus principal strain response of silty sand from suctioncontrolled TE tests. In these figures, suction is also shown to have an important effect on the shear resistance of silty sand, with a slight increase for s = 200 kPa. During TE testing, the major σ1 and intermediate σ2 principal stresses are equally increased while the minor principal stress σ3 is decreased. Consequently, the major and intermediate principal strains were found to be compressive (+) while the minor principal strain was expansive (−). 5
CONCLUDING REMARKS
Preliminary suction-controlled testing on silty sand, as described herein, has shown that the newly devel-
88
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A simple shear apparatus for testing unsaturated soils S. Tombolato, A. Tarantino & L. Mongiovì Dipartimento di Ingegneria Meccanica e Strutturale, Università degli Studi di Trento, Italy
ABSTRACT: The paper presents a simple shear apparatus developed to investigate shear strength of unsaturated soils. The apparatus is designed to impose a simple shear-constant volume-constant degree of saturation mode of deformation. Total vertical and shear forces are simultaneously measured by 5 pairs of biaxial load cells at the bottom surface of the sample whereas negative pore-water pressure can be measured at the top surface of the sample by 5 pairs of tensiometers. A series of tests was performed on rubber and kaolin specimens to set up the apparatus and to adjust the experimental procedure in order to achieve a uniform distribution of vertical and shear forces along the sample. Preliminary results on both saturated and unsaturated compacted kaolin samples are presented.
1
INTRODUCTION
Shear strength of unsaturated soils controls stability of artificial and natural slopes above the phreatic surface and is of major interest in unsaturated soil mechanics. A simple shear apparatus has been developed at the University of Trento to investigate shear strength of unsaturated soils. The apparatus was designed to shear the sample under constant volume and water content and, hence, under constant degree of saturation. Suction is measured at the top surface of the sample by 5 pairs of Trento high-capacity tensiometers (Tarantino & Mongiovì 2002). Total vertical and shear forces are simultaneously measured by 5 pairs of biaxial load cells at the bottom surface of the sample. The paper presents a series of preliminary tests performed on rubber and kaolin specimens to set up the apparatus and to adjust the experimental procedure in order to achieve a uniform distribution of vertical and shear forces along the sample. First results on saturated and unsaturated compacted kaolin samples are then presented to validate the apparatus. 2 2.1
Figure 1.
Ideal boundary conditions for simple shear tests.
constant degree of saturation. The only degree of freedom is then the shear strain γzy . To ensure constant volume, the specimen is laterally confined by stacked steel plates and vertically confined by the loading cap which is locked in place during shearing (Figure 2). To ensure εx = εy = εz = 0, the confinement system must be designed to be adequately stiff. The deformation of the confinement system could then be assumed to be acceptable when resulting in negligible error in the measurement of total stress. To this end, the interaction between the specimen and the confinement system was numerically analysed and its different components were designed to produce an error in the measurement of total stress lower than 5% (Tombolato 2007). To produce uniform shear strains, the specimen was bonded to the loading cap and the cell base using epoxy resin. In addition, a very low height to length ratio was adopted. The specimen is 300 mm long, 60 mm wide and 10 mm high. This was expected to minimize the in-homogeneity of stresses resulting from the non-ideal boundary conditions at
SIMPLE SHEAR APPARATUS Design criteria
The apparatus was designed to apply a simple shearconstant volume-constant degree of saturation mode of strain to a cuboidal specimen as shown in Figure 1. This mode of strain involves zero horizontal extension in the direction of shear, εy = 0, together with plain strain in the orthogonal direction, εx = γxy = γxz = 0 (simple shear), zero vertical strain, εz = 0 (constant volume), and constant water content which implies
89
3.1 Vertical force distribution during compression
Figure 2.
Vertical forces measured by the biaxial load cells during compression should be ideally uniform. Differences may arise from non-uniform soil density, and hence non-uniform soil stiffness, non-uniform stiffness of the biaxial load cells, and improper coupling between the soil specimen and the confinement system. In turn, this is associated with the unevenness of the specimen surface and the non-coplanarity of the biaxial load cells. All these effects were separately investigated through specific tests. After installation, the 10 biaxial load cells were not perfectly coplanar and the bottom surface was shown to have a step-like profile. Due to these steps not all biaxial load cells came into contact with the specimen at the same average vertical force and this clearly caused a non-uniform distribution of vertical stresses. To eliminate steps between the biaxial load cells, these were mounted on the sliding base using a dynamometric key to control the torque and the surface formed by the biaxial load cell was ground. Although the biaxial load cells and relative bolt junctions are virtually equal, stiffness is not uniform due to bending of the sliding base. Initially, two pairs of sliders were positioned at the ends of the sliding base causing the sliding base to have greater deflections at its centre. As a result, the central cells (3a and 3b) were less stiff than the lateral cells (2a, 2b, 4a and 4b) which were in turn less stiff than the cells at the edge (1a, 1b, 5a and 5b) as shown in Figure 3a where the forces recorded by the biaxial load cells are plotted against the average vertical force in a test carried out on a rubber specimen. In order to reduce bending of the sliding base, 3 pairs of sliders were added in between the 2 external pairs of sliders for a total of 10 sliders. With such a configuration, the biaxial load cells exhibited a more uniform stiffness. The beneficial effect of grinding and of the additional sliders is shown in Figure 3b, where the vertical force measured by the biaxial load cells is again plotted against the average vertical force. The figure shows a relatively simultaneous loading of the biaxial load cells and changes in local vertical force with respect to the applied vertical force appear to be more uniform. Similar compression tests were performed on soil specimens, previously compacted outside the simple shear apparatus. A test performed when the biaxial load cells had not yet been ground and with only 2 pairs of sliders supporting the sliding base is shown in Figure 4a. It can be observed that the local vertical force may vary up 50% with respect to the average value. Figure 4b shows the vertical force distribution after grinding the base and adding 3 pairs of sliders for a total of 10 sliders. It can be observed that a more uniform stress distribution was achieved and that unloading of central biaxial load cells is less
Schematic layout of the simple shear apparatus.
the ends of the specimen. To perform tests at constant water content, a system to prevent soil-water evaporation was designed. 2.2
Simple shear apparatus
The simple shear apparatus is shown schematically in Figure 2. Its main components are: – a horizontal support carrying a linear motion system; – a sliding base incorporating load cells sliding horizontally over the horizontal support; – 10 biaxial load cells 60 mm long and 30 mm wide arranged in a matrix 5 × 2 used to simultaneously measure the shear and normal forces at the base of the specimen; – stacked steel plates to prevent horizontal deformation during both compression and shearing; – a loading cap constrained to move vertically by two vertical sliders; – a piston moved by a pneumatic-cylinder to apply the vertical load during the compression stage; – two lock nuts to lock the loading cap in order to prevent vertical deformation during shearing; – a frame to carry the piston and the lock nuts; – two lateral supports mounting the two vertical slider guideways and blocking the horizontal movement of the cap during shearing; – a stepper motor to horizontally move the sliding base. 3
PRELIMINARY TESTS
A series of preliminary tests on rubber and soil specimens were performed to investigate the force distribution at the base of the specimen both during compression and shearing stages and to improve the uniformity of shear and normal force distribution.
90
2
2 5b 1b
1.5
1.6
4a 1a
vertical force (kN)
local vertical force (kN)
5a
4b
2b
1 2a
3b
0.5
P = 795 kPa
1.2
P = 493 kPa
0.8
3a
0.4
P = 287 kPa
no contact
0 2
2 0
5b
1a 1b 2a
1
local vertical force (kN)
local vertical force (kN)
P = 800 kPa 5a
1.5
4a
4b 2b
3b
3a
0.5
1.6
1.2
P = 594 kPa
0.8
P = 288 kPa
0.4
0 0
0
0.4
0.8
1.2
1.6
0
average vertical force applied (kN)
10
20
30
lenght of the sample x (cm)
Figure 3. Test on a rubber specimen. (a) with non-coplanar biaxial load cells and 4 sliders (b) with coplanar biaxial load cells and 10 sliders.
Figure 4. Test on soil specimen compacted outside the SSA. (a) with non-coplanar biaxial load cells and 4 sliders (b) with coplanar biaxial load cells and 10 sliders.
pronounced especially at high vertical forces. Despite the significant improvement, non uniformities still remained. This was attributed to inadequate coupling between the surface of the specimen and the confinement system associated with surface unevenness and nonparallelism between the matching surfaces. To improve coupling it was decided to compact the soil powder directly in the simple shear apparatus. The uniformity of stress distribution improved significantly and deviations from the average vertical force were less than 20%. Non-uniform soil density results in non-uniform soil stiffness and, hence, non-uniform distribution of vertical forces. To cope with this problem, four vertical separators were placed in the stacked plates in order to obtain five compartments, each one including one pair of biaxial load cells, where equal amounts of powder were placed. This procedure improved the uniformity of vertical stress distribution. After this last adjustment, the maximum deviation from the average vertical force was found to be equal to 10%.
3.2 Vertical and shear force distribution during shearing Preliminary shear tests at constant vertical stress were carried out on rubber specimens to test the response of the biaxial load cells during shearing. A significant difference was observed between the total horizontal force measured by the external load cell and the sum of the shear forces measured by the biaxial load cells. It was inferred that the resin squeezing out of the specimen during compression formed bridges between the sliding base and the biaxial load cells and the biaxial load cells themselves. To tackle this problem, narrow tape bands were placed to cover the gaps between the biaxial load cells and the sliding base and the biaxial cells themselves prior to spreading the epoxy resin over the biaxial load cells. The tape was 0.1 mm thick and remained incorporated into the epoxy resin layer. Since the tape is more flexible than the epoxy layer, possible interaction between the load cells will only be associated with flexural stiffness of the epoxy layer.
91
4
VALIDATION OF THE APPARATUS
0.5
local shear forces (kN)
To validate the simple shear apparatus, tests were carried out on saturated kaolin specimens. Two saturated tests are presented herein. Tests were carried out on samples directly compacted in the stacked steel plates at a water content of 0.3 and vertical pressure of 300 kPa. After installing the tensiometers, the specimens were saturated under 300 kPa vertical stress and then consolidated in steps to different final vertical stresses: 590 and 820 kPa respectively. The specimens were finally sheared at constant horizontal displacement rate of 5 mm/day. The vertical force distribution at the different total vertical forces applied during consolidation and after locking the nuts is shown in Figure 5. It can be noted that at the end of the tightening process, deviations from the average vertical force were less than 7% if only the 3 central pairs of biaxial load cells are considered. Vertical forces measured by the 10 biaxial load cells during shearing are plotted versus horizontal shear strain in Figure 6 for the specimen compressed to 590 kPa vertical stress. Vertical force decreased with increase in horizontal shear strain. Deviations from the average shear force are significant only for the biaxial load cells at the ends of the specimen (1a, 1b, 5a, 5b). Before peak the maximum deviation of local vertical force from the average value is about 5% and 7% for the specimens compressed to 590 kPa and to 820 kPa respectively. A satisfactory uniformity of vertical forces was then achieved. It is interesting to note the marked change in slope exhibited by the local vertical force at shear strain of 0.2 in correspondence with the shear force peak. This seems to suggest that the peak of shear force is associated with strain localization.
local vertical forces (kN)
local vertical forces (kN)
3b
0.8
3a
2b
4a 4b
5a 5b 1a
2a
0.4
0.8
1.2
1.6
Local shear forces measured by the biaxial load cells are shown in Figure 6. All biaxial load cells show a peak at the same horizontal shear strain of 0.2. Before peak the variation of shear force versus the shear strain is very similar for cells with variations with respect to the average value less than 13% and 17% for the first and second test respectively. Data in terms of average vertical and shear force as measured by the 3 pairs of central biaxial load cells also appear to be consistent (Figure 7). For both specimens the vertical force has a marked change in slope at the same horizontal strain. This horizontal strain corresponds in both tests to the peak in the shear force. External observation of the relative position of steel plates confirmed that strains were no longer uniform after the peak in the shear force. This result is also in good agreement with experimental observations made by Airey et al. (1985) in constant volume simple shear tests performed on normally consolidated samples of kaolin. The stress paths of the effective stresses (σyy , τxy ) on the horizontal plane are shown in Figure 8. To interpret these paths, it is necessary to make an assumption
30
lenght of the samplex (cm)
Figure 5. nuts.
1.2
Figure 6. Shear local forces versus shear strain for specimens compressed to 590 kPa.
0 25
1b
shear strain, γxy
0.4
20
2b 0.1
1b
specimen compressed to 590 kPa
15
2a
4b
5a 5b
0
1.2
10
4a 0.2
0.4
1.6
5
3b
3a
1a
specimen compressed to 820 kPa
0
0.3
0 1.6
2
0.8
0.4
Vertical force distributions after tightening lock
92
1.6
400
specimens comp ressed to 590 kPa specimens comp ressed to 820 kPa
vertical force (kN)
( 'yy, yx)
200
15.5˚
0
0.8
-200
( 'xx, xy)
0.4
( 'xx, xy)
0.5
hypotetical failure circle
-400
0.4
shear force (kN)
22.3˚
( 'yy, yx)
1.2
0
200
400
600
800
1000
'yy, 'xx 0.3
Figure 8. Hypothetical circles corresponding to failure on sub-horizontal planes. 0.2
xy = 0.21
respectively. It is unreasonable that horizontal stresses increase by 152 kPa and 232 kPa respectively during shearing. On the other hand, if it is assumed that the plane of rupture was vertical, i.e. the vertical plane is the plane of maximum stress obliquity, then the angle of shearing resistance φ would be given by the following equation:
0.1
0 0.5 xy = 0.34 0.4
/ '
0.3
2 · tan ϕ +
xy = 0.32
0.2
1 1 = tan ϕ tan φ ∗
(1)
where tan φ ∗ is the stress obliquity on the horizontal plane given by:
0.1
R = tan φ ∗ =
0 0
0.4
0.8
1.2
1.6
τxy = 0.377 (φ ∗ = 20.6◦ ) σyy
(2)
shear strai n , xy
According to Equation (1), an angle of shearing resistance of 35◦ was obtained, which is also unreasonable for kaolin. It may then be concluded that failure occurs on planes that are not planes of zero extension (vertical or horizontal). To interpret the tests, an alternative assumption needs to be made for the horizontal stress. According to Oda (1975) and Wood et al. (1979) the stress ratio R mobilized on the horizontal planes ratio can empirically be obtained as:
Figure 7. Vertical force, shear and stress ratio measured by the 3 pairs of central biaxial load cells during shearing for specimens compressed to 590 kPa.
either of the failure mechanism or of the horizontal effective stress. If it is assumed that the plane of rupture is hori zontal, then the measured stress (σyy , τxy ) should lie on the failure envelope. In this case, however, the resulting horizontal stress would be equal to 552 kPa and 772 kPa for the two tests respectively, which is significantly greater than the maximum expected horizontal stress at the end of consolidation, which was estimated to be about 400 kPa and 540 kPa
R=
τxy = k tan ψ σyy
(3)
where ψ is the angle between the major principal stress and the vertical direction and k is a constant equal to
93
0.387 for kaolin (Borin, 1973). The horizontal stress can then be expressed as a function of the vertical stress and R as follows:
degree of saturation of the macropores instead of the overall degree of saturation. SrM can be expressed as follows:
R2 − k 2 σxx · σyy = 1+ k
SrM =
(4)
If the Mohr circles at shear stress peak is drawn according to this criterion for the two tests, we obtain Figure 8. The two circles thus obtained can be enveloped by a straight line passing through the origin having a slope of 22.3◦ which is a reasonable angle of shearing resistance for kaolin also according to triaxial data by Dalbosco (2005) (φ = 22◦ ) and simple shear data from Airey and Wood (1987) (φ = 22◦ ). Failure planes form at an angle of 12◦ with the horizontal in both circles. The same orientation of rupture bands was detected by a polarizing microscope on longitudinal sections of soil specimens removed from the cell at peak and impregnated with resin. The Mohr circles drawn in Figure 8 are characterized by σx ∼ = σy . If it is tentatively assumed that σx ∼ = σy at the critical state, then ψ = 45◦ at the critical state according to Equations (3) and (4). In other words, the principal axes of stress and strain increment would be coincident at the critical state. Accordingly, the horizontal plane would be the plane of maximum shear stress and the angle of friction mobilized would be given by: R=
5
τxy = sin φ σyy
e − ewm ew − ewm
(7)
where e is the void ratio, ew is the water ratio, and ewm is the ‘microstructural’ water ratio, which separates the region of inter-aggregate porosity from the region of intra-aggregate porosity. Tarantino (2007) showed that ultimate shear strength of compacted unsaturated soils can be described by an equation similar to that of saturated soils with the effective stress replaced by the modified average skeleton stress σ and with ewm determined as best-fit parameter: τ = σ tan φ
(8)
For the compacted kaolin, a value ewm = 0.40 was estimated from data presented by Wheeler & Sivakumar (1995), a value confirmed by triaxial tests carried out at the University of Trento (Dalbosco 2005). The stress path interpreted in terms of σ and the associated Mohr’s circle at peak traced assuming that σx = σy are shown in Figure 9 together with the stress paths recorded in the saturated tests. The Mohr circle at peak for the unsaturated specimen appears to be tangent to the saturated envelope suggesting that shear strength recorded for the unsaturated specimen is consistent with Eq. 8.
(5)
PRELIMINARY TEST ON UNSATURATED SPECIMEN saturated tests unsaturated tests
400
One test was performed on an unsaturated specimen having initial (before shearing) water content w = 0.22 and initial degree of saturation Sr = 0.6. The effectiveness of the anti-evaporation system was checked by verifying that suction measured by tensiometers installed in the loading cap remained constant over a period of time after installation. During shearing, suction remained approximately constant which was expected as void ratio and water content did not change during shearing. Initially the test was interpreted in terms of modified average skeleton stress σ (Tarantino & Tombolato 2005):
( ''yy, yx)
22.3˚
( ''xx, xy)
hypotetical failure circle
200
0
-200
-400
σ = (σ + SrM s) tan φ
(6) 0
where φ is the saturated critical state parameter, σ is the net stress, s is the suction, and SrM is the degree of saturation of the macropores. In the modified average skeleton stress, suction is weighed by
200
400
600
800
1000
', '' Figure 9. Stress paths relative to unsaturated tests interpreted in terms of modified average skeleton stress.
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6
CONCLUSIONS
Airey, D.W. & Wood, D.M. 1987. An evaluation of direct simple shear tests on clay, Géotecnique 37 (1): 25–35. Borin, D. 1973. The behaviour of saturated kaolin in the simple shear apparatus. PhD thesis, University of Cambridge. Dal bosco, A. 2005. Studio sperimentale del comportamento meccanico di un’argilla costipata non satura e generalizzazione della teoria di stato critico ai terreni non saturi. Graduate Thesis, University of Trento. Oda, M. 1975. On the relation τ/σn = k · tan ψ in the simple shear test. Soils and Foundations, 15 (4): 34–41. Tarantino, A. & Mongiovì, L. 2002. Design and construction of a tensiometer for direct measurement of matric suction. In Proceedings 3rd International Conference on Unsaturated Soils (eds J.F.T. Jucá, T.M.P. de Campos and F.A.M. Marinho), Recife 1, pp. 319–324. Tarantino, A. 2007. A possible critical state framework for unsaturated compacted soils. Géotechnique, 57 (4): 385–389. Tarantino, A. & Tombolato, S. 2005. Coupling of hydraulic and mechanical behaviour in unsaturated compacted clay. Géotechnique, 55 (4): 307–317. Tombolato, S. 2007. A simple shear apparatus for testing unsaturated soils from medium to large shear strains, PhD thesis, University of Trento. Wheeler, S.J. & Sivakumar, V. 1995. An elasto-plastic critical state framework for unsaturated soil. Géotechnique, 45 (1): 35–53. Wood D.M., Drescher A. & Budhu M. 1979. On determination of stress state in the simple shear apparatus. Geotechnical Testing Journal, 2 (4): 211–221.
The paper has presented an apparatus to test unsaturated soils in simple shear mode of deformation. The apparatus and the experimental procedure were set up to obtain uniform stress distribution within the specimen. Experimental data from the tests on saturated specimens are in good agreement with data available in the literature. It has been shown that failure planes are neither horizontal nor vertical and it would appear that principal axes of stress and strain increment are coincident at the critical state. For a correct interpretation of simple shear tests, it is necessary to detect rupture bands and their orientation. ACKNOWLEDGEMENTS The authors are grateful to Marco Bragagna for his support in designing and setting up the apparatus. They also wish to express their gratitude to Dr. Giacomo Mele from CNR—ISAFOM (Naples, Italy) for carrying out the photos of thin polarized sections of the resin-impregnated samples. REFERENCES Airey, D.W., Budhu, M. & Wood, D.M. 1985. Some aspects of the behaviour of soils in simple shear. In Developments in soil mechanics and foundation engineering (eds. P.K. Banerjee and R. Butterfield), Vol. 2, pp. 185–213. London:Elsevier.
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A device for simultaneous measurement of acoustic and hydraulic properties in unsaturated soils L.A. George & M.M. Dewoolkar School of Engineering, University of Vermont, Burlington, Vermont, USA
C. Wei Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, China
ABSTRACT: Accurately predicting and modeling flow through unsaturated soils is difficult due to the complexities that stem from the heterogeneities inherent in soil deposits. In simulating subsurface nonequilibrium flow, it is possible to take into account the heterogeneous nature of the material by using a rate dependent, dynamic capillary pressure saturation relationship (water retention relationship). A theoretical kinetic constitutive model which describes the dynamic capillary pressure saturation relationship has been developed. This model depends on variables which can all be measured in the laboratory. All of these variables have been previously measured, except for the capillary relaxation time. The capillary relaxation time can be determined using the velocity and attenuation of low frequency acoustic waves. A device has been developed which will allow for simultaneous measurement of the acoustic velocity and attenuation as well as the hydraulic properties, including the static capillary pressure saturation relationship and the unsaturated hydraulic conductivity function. This paper describes the details of this device and some preliminary measurements.
1
capillary relaxation times and the sizes of local structures in porous media (Wei & Dewoolkar 2006; Wei & Muraleethanan 2006; Wei & Muraleetharan 2002). This paper describes the experimental equipment and procedures which will be used to verify this procedure.
INTRODUCTION
Heterogeneities in porous media occur at a range of scales, from the macro-scale to the micro-scale. Macro-scale heterogeneity can be described in numerical models using varying material properties at the element level, but intermediate scale or meso-scale heterogeneity occurs at the sub-element level. These meso-scale heterogeneities may occur either due to variations in the structure, such as clay inclusions, or the distribution of moisture content, in the case of partially saturated media. Characterization of mesoscopic heterogeneities that may occur in macroscopically homogeneous porous media is fundamental to understanding the behavior of the material, and considering the effect heterogeneities have on flow and transport could vastly improve predictive models. Acoustic techniques provide a powerful means to characterize meso-scale heterogeneity in porous media in a non-destructive manner. Several models which describe wave induced flow have been developed and applied to evaluate the details of the mesoscopic structures in porous media (Johnson 2001; White 1975), but none are used to determine the dynamic effects of capillarity. A procedure has been proposed which would explicitly evaluate the dynamic capillary effects, and has been successfully used to infer the
1.1
Acoustic characterization of mesoscale heterogeneities
When a mesoscopically or locally heterogeneous porous medium is subjected to an external disturbance, fluids in different regions respond with different pressures, resulting in local fluid flow (Pride et al. 2003). Consequently, the macroscopic capillary pressure is generally a dynamic quantity. The local flow induced by a stress wave dissipates wave energy, resulting in intrinsic wave attenuation and velocity dispersion (velocity depending upon frequency). Such acoustical signatures play a key role in determining the characteristics of local flow and dynamic capillarity. A visco-poroelastic model that is capable of characterizing the relaxation processes associated with local fluid flow has been developed (Wei & Muraleethanan 2006). Given the measured acoustical data, specifically the velocity and attenuation of the compressional wave, the model can be used to determine the characteristic time of local flow. Since local flow is governed
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explain the development and operation of this device, developed at the University of Vermont.
by the details of local heterogeneities, the obtained characteristic times can in turn be used to infer the information on local heterogeneities, and their effects on macroscopic fluid flow through the dynamic capillary pressure saturation relationship (or water retention relationship) which is described in the next section. 1.2
2
THE EXPERIMENTAL DEVICE
The laboratory device is capable of housing a cylindrical soil sample 100 mm in diameter and up to 125 mm in height. This large sample size is necessary to allow the low frequency acoustic wave to travel through the media for a distance larger than its wavelength. The sample is confined by cell pressure in a semi-flexible Viton® rubber jacket equipped with an acoustic transmitter and receiver (see Figures 1 and 2). The rubber jacket was made flexible enough to conform to the sample under confinement, but also rigid enough to house the transducers. The transducers were placed on the side of the sample so they would not interfere with the end caps or come in contact with the pore fluid. The device is also capable of utilizing a rigid walled sample when the acoustic measurements are not needed. The acoustic equipment developed by New England Research, Inc. (NER) of White River Junction, Vermont, includes flat piezo-ceramic transducers, a waveform function generator, an oscilloscope and the data acquisition system, as seen in Figure 3. The peizoceramic crystals are mounted on titanium heads that are shaped to the radius of the sample. Canada Balsam, a non-soluble acoustic couplant, is used between the titanium head and the soil sample. An absorptive backing is mounted on the outside of the transducers to reduce reflection of the received waves within the transducer. The flat piezoceramic transducers were chosen because they can produce both shear and
Dynamic capillary pressure saturation relationship
Generally, unsaturated soil properties e.g. the capillary pressure saturation relationship and the unsaturated hydraulic conductivity function, are measured at static or steady state conditions. The capillary pressure saturation relationship describes the relationship between the capillary pressure and the level of saturation in an unsaturated porous media, it is also known as the water retention curve, soil water characteristic curve, or the pressure saturation relationship. These static properties are then used to analyze both steady-state and transient flow. An early study by Topp et al. (1967) showed that these properties are rate dependent, and the assumption that static properties can be used in a transient analysis may be incorrect. Recently, experimental studies have shown that pressure saturation relationships obtained through inverse modeling of one-step and multi-step outflow experiments were influenced by the flow rate (Schultze et al. 1997; Wildenchild et al. 2001). Other models have been developed to explain this dynamic relationship, i.e. (Hassanizadeh & Gray 1993); this model includes a material coefficient thought to depend on both saturation and the rate of saturation change, but the coefficient is impossible to measure experimentally. The coefficient has been found to vary between 104 and 107 Pa.s (Hassanizadeh et al. 2002) by analyzing experimental data reported in the literature, but this formulation has yet to be verified. A new dynamic capillary pressure saturation relationship has been developed (Wei & Dewoolkar 2006) which includes the rate dependence, describes the hereditary effect of capillarity, and is based on the characterization of local flow caused by heterogeneities. The dynamic capillary pressure saturation relationship which has been developed is formulated with commonly known and relatively commonly measured soil properties, (e.g. the static capillary pressure saturation relationship and unsaturated hydraulic conductivity function, the porosity, density, and shear modulus), along with one additional parameter, the capillary relaxation time, which can be determined using acoustic techniques (Wei & Muraleetharan 2007). In order to collect all the parameters needed to determine the dynamic capillary pressure saturation relationship, a device capable of simultaneously measuring the hydraulic and acoustic properties of the porous media is needed. The following sections
Figure 1.
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Schematic of the device.
Figure 2.
that the deformation of the solid is small (strains less than 10−7 ). The response of the partially saturated media is thought to be frequency dependent; therefore the acoustic waves are collected over a range of frequencies. The frequency of interest is in the vicinity to 10 kHz. The confining cell is filled with mineral oil in order to protect the electronic components within the cell. Conically shaped water reservoirs are located on either end of the sample, separated from the sample by the high air entry disc on the bottom and a coarse porous stone on the top. The water reservoirs are conically shaped to aid in removal of diffused air bubbles which may pass through the high air entry disc and are modeled after the work of Lu et al. (2006). The device is capable of utilizing ceramic, metal or nylon porous discs. High air entry discs maintain the sample at a specific saturation by prohibiting air to escape from the sample. The experiments presented in this paper used high entry porous membranes (GE Cellulous Acetate Membranes), with an air entry pressure of 200 kPa and a pore size of 0.45 μm. The membrane is attached to a bronze porous plate, 3 mm in thickness to reinforce the flexible membrane (shown as the HAE disk in Fig. 1). Air pressure is supplied to the sample through the top of the sample. The air can be maintained at atmospheric pressure or can be elevated when using the axis translation technique. A differential pressure transducer is connected between the water reservoir and the air pressure supply tube, to measure the capillary pressure as described in the next section.
Photograph of the confining cell and soil sample.
3 3.1
Figure 3.
PROCEDURES Measurement of the static capillary pressure saturation relationship
The static capillary pressure saturation relationship is a relationship between the level of saturation in a soil sample and the capillary pressure at equilibrium. The relationship is determined using a controlled volume method with the option of axis translation. During a controlled volume method the saturation in the sample is changed by controlling the volume of water which is allowed to leave the sample. Water is withdrawn from the bottom of the sample at a specific rate (Lu et al. 2006; Olsen et al. 1994). The basic concept behind the axis translation technique is to control the capillary pressure (ua − uw ) by elevating the pore air pressure (ua ) and maintaining the pore water pressure (uw ), instead of the traditional method of lowering the pore water pressure and maintaining the pore air pressure. These methods were chosen because of the shortened equilibration time associated with the controlled volume method and the large range of capillary pressures
Photograph of the entire experimental set up.
compressional waves and because of the relatively small strains they produce as compared to other transducers such as bender elements. The linearization used to approximate the governing equations requires
99
possible with the axis translation technique. Other methods may also be employed using this apparatus, such as suction controlled methods. The pore air pressure is maintained at a specific pressure determined by the anticipated capillary pressures of the media being tested. The quantity of water in the sample (i.e., the saturation) is controlled by a flow pump connected to a reservoir on the bottom of the sample. When a volume of water is removed from the sample, the pump is shut off and the capillary pressures are monitored with the differential transducer. When the pressures stabilize it is assumed that equilibrium has been achieved and a point on the static capillary pressure saturation relationship is obtained. The saturation is determined by calculating the volume of water in the sample, and the capillary pressure is measured by the differential pressure transducers connected between the pore air and the lower pore water reservoir. The sample size in this apparatus is much larger than those traditionally used for measurement of the characteristic curve and a few challenges arise when using a large sample. Samples used in Tempe cells are typically approximately 50 mm in diameter and 4–5 mm in height. Generally it is assumed that the saturation distribution along the height of the sample is negligible and the saturation of the entire sample can be taken as an average calculated using the amount of water withdrawn. Since this sample is approximately 100 mm in height there could be a considerable variation in saturation over the height of the sample depending on the pore size distribution of the sample and the capillary pressure at the bottom of the sample. Several soil types are being considered in this research to minimize this variation so that the acoustic measurements are more representative of one level of saturation. The level of saturation at mid height of the sample will be calculated considering the variation in saturation and pressure that occurs over the sample, using a method similar to Liu & Dane (1995). 3.2
Measurement of the unsaturated hydraulic conductivity function
Measurement of the unsaturated hydraulic conductivity function has not yet been attempted using this apparatus. It is expected that the procedures for measuring the capillary pressure saturation relationship will have to be modified from that described in the previous section, in order to also measure the hydraulic conductivity function simultaneously. There are two possible methods which will be investigated. The first approach would use the apparatus as described above; a constant flow rate would be imposed by withdrawing water from the bottom of the sample. This withdrawal would serve to lower the saturation and determine the hydraulic conductivity. The rate of withdrawal will
have to be high enough to impose a gradient across the sample. Assuming Darcian flow, the hydraulic conductivity could be calculated from the flow rate and the imposed gradient. The second approach would require modification of the apparatus including a second high air entry disk on the top of the sample. With this modification, the methods described by Olsen, et al (1994) and Lu & Likos (2006) could be utilized. Here the same amount of water would be injected and withdrawn from the top and bottom of the sample. Simultaneously one flow pump withdraws while the other injects the same volume of water at the same rate. The pressure head difference that this flow causes across the sample would be measured by a differential pressure transducer connected to both water reservoirs, and the head loss across the porous membranes is considered negligible. The flow rate and pressure head loss could be used to calculate the hydraulic conductivity for each saturation level. Both approaches will be tested and evaluated. 3.3
Measurement of the acoustic properties
The acoustic properties are measured at the same time as the capillary pressure saturation relationship and the unsaturated hydraulic conductivity function. Compressional and shear waveforms for a range of frequencies are taken at each saturation. The compressional and shear waves are produced with the transducers, which are excited by a waveform function generator. The received wave is displayed on an oscilloscope and the data acquisition system collects the raw data. The compressional wave velocity and attenuation is determined from the compressional waveform and is used to determine the capillary relaxation time. The shear wave velocity can be determined from the shear waveform and be used to determine the shear modulus of the soil sample, if desired. 4
PRELIMINARY RESULTS
Preliminary hydraulic testing has been performed on a sand sample and the static capillary pressure saturation relationship found is shown in Figure 4. This relationship was found using the procedure outlined in section 3.1, and the capillary pressures at a point were computed using software, TrueCell (Liu & Dane 1995), which corrects for the large height of the sample. Preliminary acoustic measurements have been taken on sand samples during separate experiments from the hydraulic measurements using the device described above. Figure 5 show an example compressional waveform. The preliminary results indicate that the device is measuring the acoustic properties of the sample, without adverse effects from the jacket or end caps. The procedures which will be used to determine
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Once both the velocity and attenuation have been determined the capillary relaxation time can be calculated, and used to predict the dynamic capillary pressure function using the procedure outlined by Wei & Muraleethanan (2007). The hydraulic properties of the sample must also be measured using the procedures outlined earlier.
5
Figure 4.
CONCLUSIONS
The development of a new type of laboratory device capable of making simultaneous measurements of acoustic signatures and hydraulic properties, including the static capillary pressure saturation relationship and the hydraulic conductivity function on relatively large soil specimens was presented. The acoustic properties include the compressional wave speed and attenuation. The measurements of acoustic and hydraulic properties will be used to quantify the effects that meso-scopic heterogeneities have on non-equilibrium flow in macroscopically uniform soil deposits.
Static capillary pressure saturation relationship.
ACKNOWLEDGMENTS
Figure 5.
Example waveform.
the velocity and attenuation from the waveforms are currently being developed, but the preliminary measurements are within the range of expected values, and the trends seen in the velocity as a function of saturation is as expected and as previously shown in partially saturated limestone samples (Cadoret et al. 1995). The attenuation of these waveforms will be determined using a waveform matching procedure developed by NER, which performs time domain minimization of the measured waveforms fit to a constant Q-propagation model prediction. The waveform matching algorithm estimates the time-shift and the attenuation that is needed to convert a reference (source) pulse into a received waveform that best matches the observed waveform. The mathematical basis of the algorithm is straightforward and is just a matter of computing the effect of passage through a substance with a band limited constant Q rheology. This process is superior to traditional spectral ratio methods in that it provides information on both velocity and attenuation while providing a more robust test of model assumptions by fitting the actual waveform rather than just its power spectrum (Smith 1993).
The study presented here was supported by Vermont Experimental Program to Stimulate Competitive Research (VT EPSCoR), (grant EPS 0236976) and the Vermont Space Grant Consortium. The authors are grateful to Dr. George Pinder for his time and advice, Floyd Vilmont and Kurt Anthony of UVM for assistance in the apparatus development and Gregory Boitnott, of New England Research, Inc. for collaboration on acoustic data collection and analysis.
REFERENCES Cadoret, T., Marion, D. and Zinszner, B. 1995. Influence of frequency and fluid distribution on elastic wave velocities in partially saturated limestones. Journal of Geophysical Research 100(B6): 9789–9803. Hassanizadeh, S.M., Celia, M.A. and Dahle, H.K. 2002. Dynamic Effects in the Capillary Pressure-Saturation Relationship and its Impact on Unsaturated Flow. Vadose Zone Journal 1: 38–57. Hassanizadeh, S.M. and Gray, W.G. 1993. Thermodynamic basis of capillary pressure in porous media. Water Resour. Res. 29: 3389–3405. Johnson, D.L. 2001. Theory of frequency dependent acoustics in patchy-saturated porous media. Journal of the Acoustic Society of America 110(2): 682–694. Liu, H.H. and Dane, J.H. 1995. Improved Computational Procedure for Retention Relations of Immiscible Fluids Using Pressure Cells. Soil Science Society of America Journal 59: 1520–1524.
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Lu, N., Wayllance, A., Carrera, J. and Likos, W.J. 2006. Constant Flow Method for Concurrently Measuring SoilWater Characteristic Curve and Hydraulic Conductivity Function. Geotechnical Testing Journal 29(3): 256–266. Olsen, H.W., Willden, A.T., Kiusalaas, N.J., Nelson, K.R. and Poeter, E.P. 1994. Volume-Controlled Hydrologic Property Measurements in Triaxial Systems. Hydraulic Conductivity and Waste Contaminant Transport in Soil, ASTM STP 1142, D.E. Daniel and S.J. Trautwein, eds., American Society for Testing and Materials, Philadelphia, 482–504. Pride, S.R., Harris, J.M. and Johnson, D.L. 2003. Permeability dependence of seismic amplitudes. The Leading Edge 22: 518–525. Schultze, B., Ippisch, O., Huwe, B. and Durner, W. 1997. Dynamic Nonequilibrium During Unsaturated Water Flow, Characterization and Measurement of the Hydraulic Properties of Unsaturated Porous Media; Proc. Intern. Workshop., Riverside, CA, 22–24 October, 1997, Riverside, CA: University of California. Smith, M.L. 1993. Ultrasonic Waveform Matching, NER Application Note AN93-1, AutoLab Users Manual: New England Research, Inc. Topp, G.C., Klute, A. and Peters, D.B. 1967. Comparison of Water Content-Pressure Head Data Obtained by Equilibrium, Steady-State, and Unsteady-State Methods. Soil Science Society of America Journal 31: 312–314.
Wei, C. and Dewoolkar, M. 2006. A Continuum Theory of Nonequilibrium Two-Phase Flow through Porous Media with Capillary Relaxation, Advances in Unsaturated Soil, Seepage, and Environmental Geotechnics, Proceedings of Sessions of GeoShanghai, Shanghai, 6–8 June 2006, Shanghai: ASCE. Wei, C. and Muraleethanan, K.K. 2006. Acoustic characterization of fluid-saturated porous media with local heterogeneities: Theory and application. International Journal of Solids and Structures 43: 982–1008. Wei, C. and Muraleetharan, K.K. 2002. A continuum theory of porous media saturated by multiple immiscible fluids: II. Lagrangian description and variation structure. International Journal of Engineering Science 40: 1835–1854. Wei, C. and Muraleetharan, K.K. 2007. Linear viscoelastic behavior of porous media with non-uniform saturation. International Journal of Engineering Science 45: 698–715. White, J.E. 1975. Computed seismic speeds and attenuation in rocks with partial gas saturation. Geophysics 40: 224–232. Wildenchild, D., Hopmans, J.W. and Simunek, J. 2001. Flow rate dependence of Soil Hydraulic Characteristics. Soil Science of America Journal 65: 35–48.
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A modified triaxial apparatus to reduce testing time: Equipment and preliminary results J.C. Rojas, C. Mancuso & F. Vinale Department of Geotechnical Engineering, University of Napoli Federico II, Italy
ABSTRACT: Two triaxial apparatuses capable of testing unsaturated samples under suction-controlled conditions (USPv2) have been developed at the University of Napoli Federico II with the objective of testing time reduction. Triaxial tests have been performed on reconstituted samples of a pyroclastic silty sand typical of flow slides in Campania region, Italy. Tests are addressed to evaluate the USPv2 apparatuses and to investigate the rate of loading influence on the mechanical behaviour of the material. The tests performed with two USPv2 apparatuses, modified in order to control matric suction at both the ends of the soil specimens by the axis translation technique, presents shorter equalization times with respect to the previous version of the device (USP). Isotropic compression tests have been performed under a constant suction value of 300 kPa applying different rates of loading (2, 8 and 32 kPa/h). The experimental procedures adopted and the first results obtained are presented and discussed in the paper.
1
INTRODUCTION
The mechanical laboratory testing of unsaturated soil is usually very time-consuming, causing difficulties in the application to engineering problems. In suctioncontrolled CRL (constant rate of loading) triaxial tests, the length of the drainage path and the rate of loading influences the testing time. As in saturated soil mechanics, the shorter the drainage path the shorter the time required to equalize externally applied net stresses and suctions to the values acting on the soil skeleton. In unsaturated soils, inappropriate load or deformation rates have a pronounced effect on matric suction (Cho & Santamarina 2001, Macari & Hoyos 2001, Huat et al. 2006), and may cause loss of its effects on the soil structure, and deviation of the observed behaviour from that expected in constant suction conditions. The best choice when selecting the testing rate is to select a value high enough to reduce the testing time but sufficiently low to avoid excess pore water or air pressures. Few studies in the literature address the determination of an adequate rate of loading during triaxial tests (e.g. Macari & Hoyos 2001; Huat et al. 2006), and more studies are required in order to increase understanding of the complex phenomena involved. With the purpose of reducing testing time, suction controlled triaxial apparatuses with water and air control systems at both the ends of the soil specimen have recently been developed. In these devices suction is controlled by the simultaneous application of
pore-water pressure, uw , and pore-air pressure, ua , at both ends of the specimen (e.g. Sharma 1998, Romero 1999, Barrera 2002, Schanz & Alabdullah 2007). From 1994, a triaxial device (USP) has been developed at the University of Napoli Federico II in order to test soils under unsaturated conditions (Rampino et al. 1999). In the original version of this cell, a modified version of a Bishop & Wesley (1975) apparatus and the axis-translation technique (Hilf 1956) were used, with pore-air and pore-water pressures controlled at the top and bottom of the sample, respectively. The USP device has been used during several testing campaigns to date, for example Aversa & Nicotera (1999), Bilotta et al. (2005), Vassallo et al. (2007), Casini et al. (2007), Cattoni et al. (2007) and Papa et al. (2008). A new design of the apparatus is proposed in this paper including modifications introduced to reduce testing time. Also discussed are the experimental procedures adopted during the tests and some preliminary results obtained on a moist compacted pyroclastic silty sand. 2
TRIAXIAL APPARATUSES
Two triaxial apparatuses capable of testing unsaturated samples under controlled-suction condition have been developed at the University of Napoli Federico II in association with the company Megaris. A schematic of the triaxial apparatus, named USPv2 (Unsaturated Stress Path, 2nd version), is presented in Figure 1. The cell design is based on the Bishop & Wesley (1975)
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Figure 1.
Scheme of USPv2 triaxial apparatus for unsaturated soils.
hydraulic triaxial apparatus for controlled stress path testing, with a moving pedestal (Y in Figure 1) that pushes the soil sample against a stationary internal load cell. The suction is controlled by means of the axis translation technique (Hilf 1956). The apparatus is designed to test unsaturated samples of 38 mm in diameter and 76 mm in height in both axial compression and axial extension under either controlled rate of loading or controlled rate of strain. The stress state on the tested samples is obtained by regulating the air pressure supplied by an air compressor (at a constant value of 1100 kPa) through four electro-pneumatic pressure converters (A, B, C, D in Figure 1), and controlled in feedback through the pressure transducers W and R for the pore-air and pore-water pressures, respectively, and by the pressure transducer G and the load cell M, for the cell (σc ) and deviatoric (q) stresses, respectively. The output range of pressure converters is 14 kPa to 800 kPa. The double cell technique is used to monitor the sample volume changes. An open-top inner cell (E), made of stainless steel to avoid water absorption from the measuring device itself, is used inside a conventional perspex cell (F). Pressurized air is used to provide the confining pressure above the inner cell E filled with water. The electro-pneumatic converter C controls the cell pressure and the pressure transducer G measures the cell pressure. The volume change of the specimen is monitored by the change in the volume of water
inside the inner cell. The differential pressure transducer (H) registers the pressure difference between the water level in the water bath surrounding the soil sample and the water level of an external reference double walled burette (I). To minimize water evaporation, a thin layer of silicone oil above the water surfaces of the inner cell and the reference burette is applied. The axial sample deformations are measured by means of a displacement transducer LVDT (J). The LVDT is fixed to the top of the external cell and monitors the position L moves relative to the external cell, allowing the calculation of the axial sample deformation. The electro-pneumatic converter (A) controls the axial stress: the air pressure passes through the air-water interface K and is converted to hydraulic pressure controlling the moving pedestal L and pushes the soil sample against a stationary load cell M. The submersible electric load cell (M) is placed inside the cell and used to measure the deviator load on the soil specimen. The valve N allows switching from stress to strain control thanks to a dual axial control. A stepping motor (O) driven screw pump is used for the axial strain control. The main changes introduced in the USPv2 with respect to the existing USP (Rampino et al. 1999) is the inclusion of a double drainage system to shorten testing time. The bottom pedestal (Q) and the topcap (P) in Figure 1 incorporate a combination of two different porous disks (Figure 2).
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Figure 2.
Base platen details.
These disks comprise a peripheral standard porous stone (3 mm thick porous stainless steel) connected to the pore-air pressure line and an internal HAEV disk (7 mm thick and 24 mm in diameter) connected to the pore-water pressure line. Operating with such a system suction control and the drainage of air and water is allowed at both the sample ends. The new design includes the possibility to change the base pedestal and the top cap in order to select different values of the air entry pressure of the HAEV disk. The electro-pneumatic converter D (Fig. 1) controls the sample pore-water pressure, and the pressure transducer R measures it. Changes in soil water content are obtained via measuring the water volume by means of two double walled burettes (S and T) connected to the HAEV disks (P and Q). Any change between the level of water in the reference burette (S) and in the measurement burette (T) is determined by means of the differential pressure transmitter (U). A peristaltic pump (V) is used to eliminate the air diffused in the water drainage line. The speed of the pump can be adjusted with a trim potentiometer, in order to obtain flow rates from 0.3 l/h to 1.0 l/h. The peristaltic pump acts on the drainage line flushing water through the spiral circuit carved inside the base pedestal (Fig. 2) and top cap, driving the air bubbles into the burette T and expelling them, acting as an air trap. The arrows on Figure 1 shows the water path followed during the flushing process. The pore-air pressure in the soil sample is controlled in feedback by the electro-pneumatic converter B and measured by the pressure transducer W. The tests are controlled, monitored and recorded by a data acquisition and control boards data logger connected to a personal computer. All the required pressures (i.e. axial load, cell pressure, air pressure and water pressure) are controlled through a feedback loop mechanism, the sensors M, G, W and R provide the feedback readings. The pressures are controlled to within ±1 kPa of the target value. During each testing stage the time, axial load, cell pressure, pore water pressure, air pressure, total volume change, water volume change and axial displacement are continuously recorded.
Figure 3.
Top-cap assembling.
All the electronic, pneumatic and hydraulic parts, including the pressure gauges and the valves to accomplish the test and check the operation are contained in a control box. Some measures have been introduced to allow an accurate sample positioning prior to the tests. The inner cell hinders the contact between the sample and the top-cap and connections are required between the top-cap itself, the water and air drainage. For this reason the design of top-cap has been split into a loading cup containing the porous elements and a top part hosting the joints of the water and air lines (Fig. 3). During the assembly process, the loading cup is mounted on the upper part of the sample, and the rubber membrane is positioned. Subsequently the inner cell is placed and the top cap is screwed on the top of the loading cap. On screw tightening, compressive stress is avoided using an auxiliary split collar to resist the torque and consequently to eliminate torsion acting on the soil sample. This design greatly simplifies and speeds up the test set-up.
3
MATERIALS AND METHODS
3.1 Tested soil The tested soil comes from a flow slide in Cava dei Tirreni (Italy) having the grading curve represented in Figure 4. It consists of pyroclastic sand with pumice, and corresponds to a non-plastic silty sand (SM) in the Unified Soil Classification System.
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3.2
Preparation procedure
Reconstituted samples have been selected for two reasons: (a) to minimize the samples heterogeneity and potentially obtain a more consistent set of data and (b) to allow comparison with the laboratory data for the analysis of the tests performed on a large scale prototype of slope recently developed by Pagano et al. (2008) where the same material is used. The choice to use reconstituted specimens introduces the problem of selecting an appropriate preparation method, since the behaviour of granular soils is strongly affected by the procedure selected, especially in the case of sands containing fines. Air pluviation (AP), water pluviation (WP) and moist tamping (MT) are the methods found in the literature and considered here. According to Kuerbis & Vaid (1998) WP and AP techniques result in segregation when used with silty sands as revealed by the presence of thin lenses of fine particles. In contrast to Vaid et al. (1999) some research indicates that specimens reconstituted by the MT method tend to be non-uniform compared to the WP and AP methods (Frost & Park 2003) in the case of the soil under study here the MT method
Figure 4. Table 1.
Grain-size distribution of Cava dei Terreni soil.
appeared the most appropriate due to the high content of fines (i.e. 40 %). In the Campania region (Italy), pyroclastic soils are characterized by high void ratios, ranging from 0.7 to 2.3 (Pellegrino 1967). According to this, two void ratios have been selected in this study: e = 1.30, to validate the improved triaxial apparatuses; and e = 1.66 for soil characterization. For samples of 1.30 void ratio, consolidated drained triaxial tests were carried out in order to verify the repeatability of tests, comparing data obtained with two USPv2 available at the Department of Geotechnical Engineering of the University of Napoli Federico II or by a single apparatus when similar samples under analogous testing conditions are used. Isotropic compression tests applying different constant rates of loading were performed on samples of 1.66 void ratio. Test details are presented in Table 1. The letter L (left) and R (right) identify the two USPv2 apparatuses available in the laboratory.
4
EVALUATION TESTS
In the first stage of all the tests the desired suction value is imposed by means of the air and water pressure control systems while the specimen is subjected to a low isotropic pressure (p − ua ) = 20 kPa. During equalization the variation of the water volume of the sample is measured through the twin burettes connected to the base and top of the sample. The suction equalization between the soil sample and the values imposed through the drainage lines is observed. Figure 4 shows the two curves corresponding to tests performed on samples having similar initial conditions and using the first version of the device and the USPv2 triaxial cell. The test performed with the ‘‘old’’ version of the device (Rampino et al. 1999) having the capacity to drain water only from the bottom pedestal indicates that for a suction increasing of 100 kPa equalization
Experimental program and main samples characteristics. Matric suction (ua − uw )
Net mean stress (p − ua )
Isotropic compression rate
Test
kPa
kPa
kPa/h
L-s100pn100 a L-s100pn100 b L-s100pn200 L-s150pn200 R-s100pn200 R-s150pn200 s300 (2) s300 (8) s300 (32)
100 100 100 150 100 150 300 300 300
100 100 200 200 200 100 100 100 100
2 2 2 2 2 2 2 8 32
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Initial characteristics e γd
1.30 1.30 1.28 1.30 1.28 1.28 1.68 1.68 1.68
w
kN/m3
%
11.1 11.1 11.2 11.1 11.2 11.2 9.9 9.9 9.9
28.0 28.1 28.0 28.2 28.0 28.2 28.5 28.5 28.5
Figure 5. Comparison of suction equalization stage when similar samples are used (suction variation = 100 kPa).
what has been achieved is 11/2.5 = 4.4 which is very satisfactory. Figure 6 illustrates the results obtained during some deviatoric tests performed with the L and R devices USPv2. These deviatoric stages follow appropriate equalization and isotropic compression stages under constant suction carried out increasing the net mean stress (p − ua ) at a constant rate (2 kPa/h). The shearing stage was performed at a constant suction, constant radial stress and strain controlled conditions (0.15 mm/h), slow enough to obtain drained condition. These preliminary tests performed on unsaturated pyroclastic soil shows the capacity of the systems to reproduce the experimental results since a similar sample under similar conditions shows similar results independently of the apparatus used. 5
Figure 6.
Results of drained shear tests (e = 1.30).
takes 11 days (Fig. 5). Using the triaxial with double drainage (USPv2) the equalization stage corresponding to the same suction variation just requires 2.5 days. Theoretically, introducing double end drainage should reduce equilibration time by a factor of 4. In fact,
PRELIMINARY TEST: RATE OF LOADING EFFECT
Figure 7 presents some test rsults aimed at the evaluation of the influence of rate of loading on the mechanical behaviour of pyroclastic soils. Similar samples with a constant suction of 300 kPa were loaded isotropically applying different constant rate of loading (i.e. 2, 8 and 32 kPa/h). In contrast with the observations reported in Huat et al. (2006), for the studied pyroclastic soil the higher the rate of loading the lower the sample compressibility. The observed behaviour is similar to the data reported in Crawford (1964), where different time intervals were applied during incremental loading (IL) oedometer tests performed on saturated Leda clay. The reason for such variation is that as time, t, is increased the amount of creep of the specimen is also increased. The data in Figure 7 clearly show that deformation at constant mean net stress is present in the final stage of the tests performed at 8 kPa/h and 32 kPa/h. It is worth nothing that these deformations are likely to be due to creep phenomena and not to suction variation. In fact, if a high rate of loading is used, pore water pressure increases and hence a suction decrease should be expected during the ‘‘high’’ rate of loading isotropic compression tests. If this was the case, an increase of soil compressibility with rate of loading must be expected in opposition to what has been observed during the tests. Since creep deformations should have developed during all the tests duration, it is quite obvious that for the sample s300 (2) compression effects occurred during the 185 h employed to reach the final net mean stress (i.e. (p − ua ) = 370 kPa). In samples s300 (8) and s300 (32) this phenomenon is less evident and the compressibility is lower since a significantly shorter time (46 h and 12 h, respectively) is required to reach the same isotropic compression stress. Figure 7 also
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significantly shorten the equalization stage, introducing an important improvement of the cell when testing low permeability unsaturated soils. During isotropic compression stage, the tested pyroclastic soil showed rate of loading dependent behaviour. The excess porewater pressure generated during the loading process, that may reduce the suction value, is less significant than the creep phenomena for the pyroclastic soil studied. Further studies, including isotropic compression tests at lower suction values, are necessary to generalize the observed behaviour produced by the presented testing program.
ACKNOWLEDGEMENTS The authors wish to acknowledge the support of the European Commission via the ‘‘Marie Curie’’ Research Training Network contract number MRTNCT-2004-506861.
REFERENCES
Figure 7. Rate of loading influence (s = 300 kPa; e = 1.68).
shows that it is possible to obtain three different values for the preconsolidation pressure dependent upon the choice of rate of loading. The water content variation at the end of the loading process is similar for samples s300 (2) and s300 (8), but lower for sample s300 (32). However, after a period of time, the water content variation of sample s300 (32) tends to reach the variation observed for the another samples.
6
CONCLUSIONS
The University of Napoli Federico II has recently improved the design of the triaxial cell USP with the objective of reducing significantly the duration of tests. This work has resulted in the design of a new triaxial cell (USPv2) capable of reducing tests duration in comparison with the previous version. The capacity to apply both fluid pressures to the top and the bottom of the sample has been demonstrated to
Aversa, S. & Nicotera, M. 2002. A triaxial and oedometer apparatus for testing unsaturated soils. Géotech Testing J 25(1): 3–15. Barrera, M. 2002. Estudio experimental del comportamiento hidro-mecánico de suelos colapsables. Ph.D. thesis. Universitat Politecnica de Catalunya, Spain. Bilotta, E., Cascini, L., Foresta, V. & Sorbino G. 2005. Geotechnical characterization of pyroclastic soils involved in huge flowslides. Geotechnical and Geological Engineering, 23:365–402. Bishop, A.W. & Wesley, L.D. 1975. A hydraulic apparatus for controlled stress path testing. Géotechnique, 25(4): 657–670. Casini, F., Vaunat, J., Callisto L. & Desideri, A. 2007. Comportamento meccanico di un limo parzialmente saturo utilizzato per una sperimentazione in centrifuga. Incontro Annuale dei Ricercatori di Geotecnica. Fisciano, 4–6 luglio 2007. Cattoni, E., Cecconi, M. & Pane V. 2007. Geotechnical properties of an unsaturated pyroclastic soil from Roma. Bull Eng Geol Environ 66: 403–414. Cho, G.C. & Santamarina, J.C. 2001. Unsaturated Particulate Materials—Particle-Level Studies. J. Geotech. and Geoenvir. Engrg. 12(1): 84–96. Crawford, C.B. 1964. Interpretation of the consolidation test. Journal of the Soil Mechanics and Foundations Division, ASCE, 90: 87–102. Frost, J.D. & Park, J.Y. 2003. A critical assessment of the moist tamping technique. J. Geotechnical Testing, 26(1): 57–70. Hilf, J.W. 1956. An investigation of pre-water pressure in compacted cohesive soils. Ph.D. dissertation, Tech. Memo. No.654, U.S. Dep. of the Interior, Bureau of Reclamation, Design and Construction Div., Denver.
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Huat, B.B.K., Ali, F.H.J. & Choong, F.H. 2006. Effect of loading rate on the volume change behaviour of unsaturated residual soil. Geotechnical and Geological Engineering 24: 1527–1544. Kuerbis, R. & Vaid, Y.P. 1998. Sand sample preparation—the slurry deposition method. Soils and Foundations, 28(4): 107–118. Macari, E.J. & Hoyos, L.R. Jr. 2001. Mechanical behaviour of an unsaturated soil under multi-axial stress states. Geotechnical Testing Journal 24(1): 14–22. Pagano, L., Zingariello, M.C. & Vinale, F. 2008. A large physical model to simulate flow-slides in pyroclastic soils. First European Conference on Unsaturated Soils. Durham, UK, 2–4 July 2008. Papa, R., Evangelista A., Nicotera, N.V. & Urcioli G. 2008. Mechanical properties of unsaturated pyroclastic soils affected by fast landslide phenomena. First European Conference on Unsaturated Soils. Durham, UK, 2–4 July 2008. Pellegrino, A. 1967. Proprietà fisico-meccaniche dei terreni vulcanici del napoletano (in italian). VIII Convegno Nazionale di Geotecnica, Cagliari, Italy.
Rampino, C., Mancuso, C. & Vinale, F. 1999. Laboratory testing on an unsaturated soil: equipment, procedures, and first experimental results. Can. Geotech. J. 36: 1–12. Romero, E. 1999. Characterisation and thermo-hydromechanical behaviour of unsaturated Boom clay: an experimental study. Ph.D. thesis. Universitat Politecnica de Catalunya, Spain. Sharma, R.S. 1998. Mechanical behaviour of unsaturated highly expansive clays. Ph.D. thesis, University of Oxford, UK. Schanz, T. & Alabdullah, J. 2007. Testing unsaturated soil for plane strain conditions: A new double wall biaxial device. In Schanz (ed.) Experimental Unsaturated Soil Mechanics. SpringerProceedingsinPhysics112:169–178. Vaid, Y.P., Sivathayalan, S. & Stedman, D. 1999. Influence of specimen-reconstituting method on the undrained response of sand. Geotechnical Testing Journal, 22(3): 187–195. Vasallo, R., Mancuso, C. & Vinale, F. 2007. Effect of net stress and suction history on the small strain stiffness of a compacted clayey silt. Can. Geotech. Journal 44: 447–462.
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A large physical model to simulate flowslides in pyroclastic soils L. Pagano, M.C. Zingariello & F. Vinale Department of Geotechnical Engineering, University of Naples Federico II, Italy
ABSTRACT: This paper describes a large physical model built at the University of Naples Federico II. The equipment has been developed to study those factors affecting flowslides in pyroclastic soils. The physical model is presented along with procedures adopted up to now during the first tests; typical results concerning changes in weight of the sample, soil suction and volumetric water content are plotted and discussed.
1
INTRODUCTION
In the Campania region the number of rain induced flowslides has significantly increased in the last decades. Flowslides involve pyroclastic soil layers no thicker than 2 meters inclined between 30◦ –45◦ , mantling carbonaceous and tuffaceous slopes close to the Vesuvius volcano and the volcanic area of the Campi Flegrei Soils involved are non plastic silty sands with high porosity (ranging between 60–80%). The high porosity, the lack of electrochemical forces between soil particles and conditions at saturation or near saturation are considered to be the main factors determining soil liquefaction upon failure (Olivares & Picarelli, 2003). As a consequence, the sliding mass accelerates significantly, transforming into a rapid flowslide. The high kinetic energy associated to the soil mass is what mainly causes damages to buildings and infrastructures, along with casualties. In the last years the increasing of risks has stimulated studies aimed at deeply investigating the slide triggering factors. Some of these factors, such as the layer thickness, the slope inclination and the soil porosity, do not change significantly during a rain event and are typically used to build up susceptible maps of areas where flowslides are likely to be generated. Other factors, such as soil suction and water content, may vary significantly during a rain event; since a slide trigger is determined by their changes, they are now going to be used, along with the rain itself, in early warning systems. The above mentioned factors may be investigated either theoretically, by using mathematical models solved through numerical approaches, or experimentally, by reproducing such phenomena in laboratory in quite controlled conditions. This latter approach inspired the development at the Department of Geotechnical Engineering of University of Naples
of a physical model to simulate flowslides. The work has been made possible thanks to the financial support of Società Autostrade Meridionali. The model is much larger than other ones developed in the past (Olivares & Damiano, 2005) in order to permit extending experimental results directly to site conditions, without dealing with typical troubles related to scaled tests. The paper describes the physical prototype in all its components and presents the first experimental results. 2
TESTING DEVICES AND EXPERIMENTAL PROCEDURE
Since the slide velocity represents a crucial matter in the hazard evaluation, the prototype design was conceived to investigate how different factors influence not only the slide triggering but also the slide postfailure behaviour. According to these aims, the core of the physical prototype is made up of two parts supported by a steel frame: the upper one, where the flowslide is generated (Fig. 1, tank A); the lower part, located downstream of the upper one, where the postfailure behaviour may be observed. This in order to identify if the kinematics is that of a slow-dry flowslide or that of a rapid one (Fig. 1, tank B). The two tanks may also be inclined differently each other (Fig. 2), to make possible studying geometries where the inclination that regulates the slide trigger differs from that governing the post-failure behaviour. Inclination is provided by two couple of hydraulic rams, pressurized by a plunger. A first couple or rams connects part B to the steel plinth and may incline both parts up to 45◦ with respect to the horizontal plane; the second couple of rams connects the part A with the part B and may incline the former with respect to the latter. In this way, inclination of the sample may reach 70◦ , or may be reduced down to 0◦ , thanks to the
111
Figure 1.
Figure 2.
Figure 3.
Plan view of conveyer belt around the apparatus.
Figure 4.
A schematic section of the whole set of apparatus.
Figure 5.
Bucket carrier.
Physical model scheme.
Traveling pluviation system.
particular position at rest of the rams allowing them to be shortened or enlarged. Both tanks A and B are 3 × 3 m in plant. The whole structure has been designed to be loaded by 12 t, so that samples up to 0.7 m thick may be tested. In the tests carried out up to now the samples have been fully restrained at the lower boundary, where also free drainage has been ensured through a geosyntetic sheet. The soil has been glued (on the base of tank A) at the bottom contact, in order to make the sliding mechanism fully regulated by the soil friction angle. The bottom of the tank A has been left impervious during the tests. Downstream of the part B a third tank collects and stores the mud after the slide has occurred (Figs. 3 and 4). In order to put in place samples characterized by high porosity, a pluvial deposition system has been designed. To obtain an uniform pyroclastic fall the soil needs to be preliminary disaggregated and dried. The whole deposition system is therefore made of various components, which are outlined below in the same sequence as they are usually used during sample making procedure: – a vibrating sieving, used to break soil particles aggregates, typically forming in the drying stage due to soil suction increase;
– a oven 8 m long and 0.8 m large, up to which soil is raised through a buckets carrier (Fig. 5); soil runs through the oven on a conveyer belt; the oven air temperature may be raised up to 150◦ C; – a hopper of around 3 m3 of volume of the same width as the part A; the hopper puts in place the soil on part A (Figs. 3 and 4) after has collected it from the oven; the hopper climbs vertically along four tracks and runs horizontally above part A along two beams; the hopper velocity may be set automatically as well as the start and the end of the hopper run; the hopper produces the pyroclastic fall through the opening; to influence the soil density both the fall height and the opening width may be regulated automatically. The rain is produced in very small drops falling on the sample surface. The water is nebulized to reduce erosion of the sample surface during the test (actually, erosion is reduced by vegetation which protects the soil surface). The rain comes out from four nozzles located at the end of the four arms overhanging the part A
112
Figure 6.
Figure 7.
Rain simulation system.
A detail of the load cell.
inward (Fig. 6). Rain intensity may be controlled and varied in the range from 20 to 200 mm/h. During a test the typical measurements carried out are: – – – –
changes in weight of the sample; surface displacements; water content; soil suction.
Some of monitoring instruments are part of the physical model and have been designed along with it; other ones are ‘‘external’’, and consist of devices suitable to monitor the behaviour of a real slope The instruments which are part of the model consist of: – four load cells (Fig. 7), installed as support of part A; each cell measures continuously in time the six reaction force components; as a result, changes in weight of the part A may be obtained; such changes may be used to derive the sample unit weight during the soil deposition, the changes in the water mass stored by the sample during the test (as a result of the rain, seepage processes and run off), the losses of soil mass associated to the occurrence of landslides or limited earth flows; – a 2D laser scanner device (Figs. 8, 9), that acquire with the triangulation technique the position of the sample surface, with a depth of scanning of few centimeters; the scanner is moved parallel to the sample surface by a mechanical system; measure accuracy (less that ±0.5 mm) is fully satisfactory, while the time period needed to scan the entire sample surface is significant (about six minutes), and makes such technique only suitable to characterize the pre-failure stages; – a Particle Image Velocimetry (P.I.V.) technique based on the interpretation of images taken by a videocamera pointing normally to the sample surface at a distance of about three meters; results are in terms of sequence of two-dimensional velocity fields; these measures are characterized by a good time resolution (up to 25 images per second may be acquired and interpreted) but by a poor accuracy
Figure 8. Plan view of the laser scanner supported by the moving system.
Figure 9.
Laser scanner apparatus.
(approximately 20 mm); however the P.I.V. technique integrates to some extent the laser scanner technique: it is suitable to monitor the failure and post-failure stages, when the occurrence of rapid movements requires high time resolution and the significance of displacements makes poor accuracy acceptable. The external instruments are used to characterize the sample hydraulic behavior; they consist of tensiometers and TDR probes to measure soil suction and water content, respectively. They are installed during the deposition process at three or four different depths.
3
EXPERIMENTAL PROCEDURES
The soil tested is a volcanic ash, made of non plastic silty sand with gravel (see Fig. 10); it is the same soil involved in a significant rapid flowslide of 33000 m3
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4
PRELIMINARY RESULTS
During each test the sample hydraulic response has been characterized by measuring evolution of the sample weight, soil suction (approximately 20 measurement points) and soil volumetric water content (4 measurement points). Typical trends of such quantities are plotted in Figures 11, 12, 13.
0.9 0.7 Weight changes (kN)
occurred on 4th March, 2005 and affected a slope inclined of 37◦ close to the Nocera town (Salerno). In the 10 tests carried out up to now, samples 40 cm thick have been reconstituted, with soil porosity ranging between 60% and 70% (see Tab. 1). The samples have been put in place taking the part A horizontally; once put in place, the sample has been wetted about a week, to decrease suction until to reach the suction level wished at the beginning of the test. The sample has been inclined only before the start of the test. Inclinations ranging between 32◦ and 40◦ have been adopted for the samples (part A). Part B has instead been slightly inclined (10◦ ), in order to make more easy to identify the post-failure behaviour, by maximizing differences in the time needed to cover the trench between a rapid flowslide and a slow-dry one. Up to now, layer thickness, rain history (rain intensity = 30 mm/h) and inclination of the tank B have been kept constant, while the initial state in terms of soil porosity and soil suction, along with the sample inclination, have been varied.
0.5 0.3 0.1 -0.1 0
50
100
150
200
250
300
350
400
450
-0.3 -0.5 Time (min)
Figure 11. Sample weight changes measured by load cells (the weight at the start of the test is assumed as zero reference).
Tensiometer vertical position HOPPER
5 2 1
Side direction
15
4
12
14
11
3
sample surface
13
-2.00
35.0 20
70
120
170
220
Ten_13
30.0
0.00
-u w (kPa)
20.0 4.00 15.0 6.00 10.0
Figure 10.
8.00
5.0
10.00
0.0
Slide
Rain intensity (mm/h)
Development with time of soil suction at three
Sample characteristics. Slope
w
n
TDR probe s ve rtical pos ition
Sr
HOPPE R
S ide dire ction 1
Test
Ten_15
Time (min)
Soil grading. Figure 12. points.
Table 1.
Ten_14
Rain intensity (mm/h)
25.0 2.00
◦
%
%
2
3
4
s a mple s urfa ce
%
0.60
35 .0
0.50
30 .0
31.09 33.21 31.38 25.83 – – 41.89 36.35 39.21 26.58
66.72 70.73 70.02 68.33 – – 62.24 66.22 62.83 67.91
41.10 36.43 35.62 31.74 – – 67.59 49.34 64.71 33.29
25 .0
0.40
20 .0 0.30 15 .0 0.20
10 .0
0.10
5.0
0.00
Rain inte ns ity (mm/h)
32 35 32 35 37 – 37 40 35 37.5
Volumetri c water content
TDR 1
1 2 3 4 5 6 7 8 9 10
TDR 2
TDR 3
TDR 4
S lide
Ra in inte ns ity (mm/h)
0.0 20
70
120
170
220
Time (min)
Figure 13. Development with time of volumetric water content at four points.
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Increments in weight of the sample during the test (Fig. 11) indicate that the sample stores water. It is important to note that the small drops in weight correspond to lost in run off water from the sample surface and empting of tubes when the rain has been stopped in order to make possible working with the laser scanner. Storing water capability under constant rain intensity however reduces with time, as indicated by the decreasing of the derivative of the curve. This effect is manly due to the progressive reduction of soil suction within the sample (Fig. 12). This reduction lowers the hydraulic gradients (driving the water drops within the sample) acting at the sample top surface between the exterior and the interior of the sample. In the initial stages, an additional contribution to the same effect is provided by the time needed for the seeping water to reach downstream the draining boundary. As well known, soil permeability increases during the wetting process. In the initial stages, while the water does not yet drain through the permeable boundary, soil permeability increments should enhance water adsorption. However Figure 11 indicates that permeability effects are not so relevant as that produced by the gradient reductions. Consistently to what expressed by Figure 11, initially the rain appears to the naked eye fully adsorbed by the sample surface and, then increasingly rejected by it, with enhancing run off. The tensiometers (Fig. 12) (installed at the three different depths of 10, 25, 40 cm from the sample surface) along with TDR probes (installed at a depth of 25 cm), indicate the arrive of the saturation front (i.e. suction goes to zero as show in Fig. 12 and volumetric water content goes to zero in Fig. 13). Since the rain intensity adopted is significant the wetting front correspond to a saturation front that lowers soil suction to the null value. The flowslide trigger is clearly indicated by the load cells with an abrupt decrease in the sample weight (Fig. 11). The size of the weight drop is related to the quantity of soil lost in the landslide.
On the other hand, the flowslide trigger is anticipated by soil suction and water content changes. Suction at the bottom of the sample goes down to zero before the triggering time (see tensiometer N. 13 in Fig. 12). In this kind of test, where the sample inclination is slightly less than the soil friction angle, triggering is caused by positive pore pressures developing at the bottom of the sample.
5
CONCLUSION
In this work a physical model to simulate rain induced flowslides has been presented, explaining how such device allows one in taking into account the main factors affecting such phenomena. In the paper the experimental procedures adopted up to now have been illustrated. The apparatus may be used also differently to study the influence of factors such as static and hydraulic boundary conditions differing from those adopted, samples thicker, presence of vegetation. First results have evidenced the effectiveness of load cells in indicating, through changes in the sample weight, the history of test in terms of water mass adsorbed and losses by the sample. Tensiometers and TDR measures may be used to characterize the hydraulic behavior and to estimate the time after which the landslide may trigger.
REFERENCES Olivares L. & Damiano E. 2007. Postfailure Mechanics of Landslides: Laboratory Investigation of Flowslides in Pyroclastic Soils. J. Geotech. and Geoenvir. Engrg., 133(1): 51–62. Olivares L. & Picarelli L. 2003. Shallow flowslides triggered by intense rainfalls on natural slopes covered by loose unsaturated pyroclastic soils. Géotechnique, 53(2): 283–288.
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Climatic chamber to model soil-atmosphere interaction in the centrifuge J. Tristancho & B. Caicedo Universidad de los Andes, Bogotá, Colombia
ABSTRACT: The behaviour of geotechnical structures located close to the surface of the ground, e.g. shallow foundations, retaining walls, embankments, slopes and pavements is highly affected by water content and pore pressure of the soil located near the surface where it is in contact with the atmosphere. The objective of this paper is to describe the design, construction and instrumentation of a climatic chamber used to simulate the tropical atmospheric variables for small scale models in centrifuge.
1
INTRODUCTION
Compressible soils of lacustrine origin in Bogotá region and other sites around the world show high deformations originating from the interaction between the soil and the atmosphere. These deformations can produce settlements (compaction) or swelling (expansion). These problems are of such magnitude that according to Jones & Holtz (1973), the economic losses produced by expansive soils surpass the sum of the losses originated by earthquakes, floods and hurricanes. Nowadays, a phenomenon of drying accompanied by cracking of soils and expansive soil appearance has been observed in Bogotá (Colombia). As a consequence a great amount of construction and infrastructure constructed in the city and its suburbs may be expected to undergo problems of unpredictable settlements. The drying and later expansion of soils in Bogotá and elsewhere takes place by a complex interaction between soil and atmosphere. This phenomenon is associated with the heat and water transference that affects, in a nonlinear way, the deformation of the soil. For this physical problem, centrifuge modeling is an appropriate tool to study the effects of multiannual climatic conditions in geotechnical structures since centrifuge modeling allows acceleration of the time of the physical process. This paper contains a brief description of climatology, its main variables and the method of how the climatic simulation was implemented in the geotechnical centrifuge. The objective of this project is to simulate the main atmospheric variables (for tropical and subtropical countries) according to the scale laws that govern centrifuge modelling. Bolton (2002) proposed that the control of atmospheric boundary conditions as one of the major
challenges in centrifuge modelling. Since 2003 the University of los Andes, Bogota has been working on the design of a new device to control the atmospheric boundary conditions in the centrifuge. 2
THE CLIMATE
The climate is the long term effect of the solar radiation on the earth surface. Climate and its parameters can be characterized for long periods of time (generally greater than 30 years), the weather can be characterized instead for short windows of time. The physical variables measured to determine the weather conditions at a certain site are (Holton, 1992): – Insolation: A measurement of the solar energy entrance to the atmosphere. – Air temperature: Direct consequence of the solar radiation. – Atmospheric pressure: Pressure exerted by the atmospheric mass in the earth’s surface. – Wind speed: Horizontal air movement with respect to the earth surfaces, caused by the atmosphere differential pressure. – Rain intensity: The earth’s water is in constant process of transformation and movement. – Humidity: Relation between the dry air and water vapour that exists in the atmosphere. The main objective of the new device is to simulate the typical meteorological parameters present in the Bogotá region. Therefore the simulation of extreme climatic parameters such as snow, hail or very strong winds are outside the scope of this project. Table 1 summarizes the characteristic averages (maximum, minimum and average) of the principal meteorological variables for Bogotá’s region based on the information provided by the weather station of the
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‘‘El Dorado’’ Airport and the IDEAM (Institute of hydrology, meteorology and environmental studies from Colombia). Each variable is modelled by independent pieces of equipment which were integrated to perform the complete simulation. The following sections present a description of the testing equipment used to reproduce each climatic parameter. 2.1
Wind, air temperature and humidity
Temperature and humidity are the fundamental variables used to determine the weather state of a site (Wang, 1999). The existing relation between temperature, humidity and atmospheric pressure, is complex and is known as psychrometry (Wang, 1999). A Climatic Simulation Chamber (CSC) located on the upper part of the soil container is designed to control these weather parameters. The principle of operation is based on heat transfer for convection, an effective method for heat transfer (Lienhard, 2004). The relative humidity is controlled by means of the extraction of moisture by condensation (dew point) and humidification by dispersion. Figure 1 shows the internal structure of the Climatic Simulation Chamber (CSC). The air that is inside the Table 1.
Climatic variables for Bogotá: IDEAM.
Variable
Max.
Min.
Average
Insolation (MJ/m2 day) Air temperature (◦ C) Atmospheric pressure (Bar) Wind speed (m/s) Rain intensity (mm/year) Relative humidity (%)
16.75 20
14.65 0
15.7 12 0.75 2.2 1250 70
Figure 1.
container moves towards the chamber driven by three axial discharge fans. Later the air passes through a dehumidifier prism, based on the psychrometric process of latent heat elimination by condensation. The dehumidifier prism was constructed using the Peltier effect (Tellurex, 2003), which reduces the temperature in the plate receiving condensation (a lower temperature than the dew point). The condensed water generated by the loss of latent heat is canalized by gravity to a closed deposit, and monitored by an ultrasonic level sensor. The air is then canalized to the heating prism that increases its temperature using again the Peltier effect. The use of thermoelectric devices (Peltier plates) facilitates the design of the power unit and the control system. An additional advantage of the use of the Peltier boards in two prisms (dehumidifier and heater) is the possibility of inverting its functions: allowing two heaters or two dehumidifiers working simultaneously to enhance the power of the chamber. Once the humidity and temperature of the air are adjusted, the air is driven by means of three fans towards the container inside. The Peltier plates are attached to a heat dissipater and exposed to the outside to allow a more efficient heat transfer (Tellurex, 2003). The fans installed are capable of generating a wind speed the order of 7.2 m/s (Approx. 26 km/h). The system at full load is able to make the complete air interchange on the model every 2 sec. The calculation of the power needed by the CSC is based on the day-night cycles typical of Bogotá. Cycles from 0 to 20◦ C and HR (Humidity Relative) of 79% represents an energy change of 145 kJ for the air inside the chamber (approx. 10 Kg of air). The CSC has 10 Peltier plates of 80 W each one. The entire time needed for heat addition is 182 sec. One day at prototype using 20 g corresponds to 216 sec according to scaling law in the centrifuge.
Internal structure and operational functions of the Climatic Simulation Chamber (CSC).
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radiation (without the typical indirect effect of warming). Taking into account the power needed to simulate sun radiation respecting scaling laws in the centrifuge it would be necessary to use optic technologies to concentrate the light. Another effect is the influence of the electromagnetic radiation of the solar light on the soil. Due to these technological constraints, the present version of the CSC does not have the capability to simulate sun radiation.
2.50 LEDs app roach Solar Irradiance (sea level)
Irradiance [W/m²μm]
2.00
1.50
1.00
0.50
0.00 0
200
400
600
800
1000
1200
1400
1600
1800
2000
2200
2400
2600
2800
Wavelength [μm]
Figure 2. Solar radiation at the sea level and modeling approach.
The atmospheric pressure was not taken into account for the modelling due to technical difficulties in making changes on the pressure inside the container. The development of systems to control the pressure in centrifuges can help to increase the mechanical and electrical efficiency of the machine as well as to improve modelling (Craig et al., 1991).
2.2
Solar radiation
The sun is the fundamental source of energy for the climate. The transference of energy from the sun to the ground occurs by radiation (Holton, 1992). Solar radiation is produced by electromagnetic waves having different wavelengths (visible, infrared and ultraviolet light). Figure 2 shows the solar spectrum for sea level (dark line). Modelling of solar radiation can be performed by means of light sources. Each source of light has its own characteristic spectrum: the illumination lamps are optimized for the visible light; the greenhouse lamps have a spectrum with a high level of infrared and some parts of the visible spectrum but without ultraviolet light (spectrum with high efficiency in plant photosynthesis); ultraviolet lamps are used in disinfection and finally infrared lamps are used in medicine. To obtain the best approximation to the solar light it is necessary to create a lamp composed of several types of light. A new method of lighting is based on high power Light Emitting Diodes (LEDs). Every LED has a determined wavelength (i.e. colour) and power. By means of optimization software and by changing the number of LEDs, it is possible to achieve a combination shown in Figure 2 (gray line). The obtained approach is near 75% of the real spectrum of the sun. The mean total radiation at Bogotá is 15.7 MJ/m2 day (approximately 182 W/m2 for one day of 12 hours of light). According to the laws of scaling in centrifuge it would be necessary to generate a power in the model of 1.3 kW. This value of radiation is huge considering that it must be effective
2.3
Rain
Rainfall is one of the mechanisms by which soil is humidified the soil and is a very important factor in the determination of water tables, saturation of soils and erosive processes (Craig et al., 1991). The typical size of a water drop is 4 mm. According to the laws of scaling the approximate diameter of a drop must be of 20 μm at 20 g. Systems of nebulization for greenhouses were used in this work to simulate the size of the drops which have on average a diameter less than 50 μm depending on the pressure. The control system is based on a pressurized line of water with 12 sprinklers, controlled by an electro valve. The rain is generated by opening of the electro valve and controlling the rainfall over specific times. 2.4
Other variables
During testing heat transference appears between the container and the atmosphere. This loss of heat can be significant (Lienhard, 2004). Good performance of the CSC in controlling the climatic variables during testing depends on the limitation of this additional load. With this energetic condition, the design of a new container that allows a minimum loss of heat was carried out (adiabatic container). Metals have high coefficients of thermal conductivity, thus a new material is needed to replace the steel casing. Materials based on fibre-glass present good features in terms of strength, stiffness and low thermal conduction but their high hardness made them inappropriate for this application (Lienhard, 2004). The selected material is a phenolic resin with cotton fibre, used commercially as a dielectric but also has a high mechanical resistance, a good workability and low absorption. This material combined with a metallic external structure is retained for the container design. The container is designed to support pressures up to 0.5 MPa without any significant deflection in order to respect adequate conditions for plane strain models. Figure 3 shows the results of the finite element simulation (FEM) of the final design. The accumulated maximum deflection obtained is 0.5 mm at 1 MPa internal pressure. The basket has a total mass of 65 kg and a total capacity of 0.09 m3 . The maximum heat flux is 0.02 W/cm2 .
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Step motor X axis
Step motor Y axis
Laser displacement
Additional
sensor
Sensors
Figure 4.
Three-dimensional laser profilemeter.
Figure 3. FEM analysis of the basket for maximum deformation (Pressure of 0.5 MPa).
3
CSC
INSTRUMENTATION
The control system set inside the CSC is a closeloop system (Ogata, 2004). All the variables that are controlled are measured. The CSC has the following instrumentation: – – – – –
Three-dimensional
Basket
laser profilemeter 550mm
2 Relative humidity sensors 3 Contact thermometers 1 Infrared thermometer 1 Pressure sensor 1 Wind velocity sensor
664mm 550mm
The interaction between the atmosphere and the soil induces water migration and volumetric changes. These volumetric changes generate heave or settlement causing cracks to appear at the soil surface. A positioning table of two degrees of freedom with a non-contact laser sensor is used to perform the displacement measurements during flight (Doebelin, 1993). The surface level is measured for different positions of the laser sensor and the measurements are carried out periodically to determine the evolution of the soil surface movements. Figure 4 shows the final design for the three-dimensional laser profile-meter. The positioning table has a longitudinal precision of 0.1 mm and transverse precision of 10 μm and effective stroke of 430 mm and 230 mm. In addition to the displacement sensor, the following sensors are installed: – Infrared thermometer: with this sensor is possible to generate thermal maps of the surface – Relative humidity sensor – Contact thermometer (air temperature) – Wind velocity sensor
Figure 5. trifuge.
Climatic modelling system for geotechnical cen-
The total assembly of the designed system for the physical modelling of the soil-atmosphere interaction in centrifuge is presented in Figure 5.
4
CONCLUSIONS
Climatic conditions in tropical countries have a strong influence on civil engineering constructions. All weather parameters affect the soil in a non-linear way that makes numerical modelling difficult. Centrifuge modelling instead could be a useful way to study soil atmosphere interaction in these situations. The climatic chamber presented in this paper is a first approximation to simulate geotechnical problems related with weather since the chamber reproduces the atmospheric parameters at the soil surface. However additional works are necessary to enhance the capacity of the chamber.
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The centrifuge accelerates processes like wetting and drying therefore important future effort in the development of control systems is needed to reproduce cyclic behaviour. The simulation of sunlight radiation needs light concentration in order to respect the scaling laws in centrifuge. REFERENCES Bolton, M. 2002. An atmospheric chamber for the investigation of the effect of seasonal moisture changes on clay slopes. Physical modeling in Geotechnics: ICPMG’02, Tokyo 765–770. Craig, W., Bujang, B. & Merrifield, C. 1991, Simulation of Climatic Conditions in Centrifuge Model Tests. Geotechnical Testing Journal, GTJODJ, Vol. 14, No. 4, 406–412.
Doebelin Ernest. 1993. Diseño y aplicaciones de sistemas de medición. DIANA (ed.). Holton, J.R. 1992. An introduction to dynamic meteorology. Academic Press (ed.). Jones, D. & Holtz, W. 1973. Expansive soils-the hidden disaster. Civil Engineering, pp. 49–51. Lienhard, J. 2004. A Heat Transfer TextBook. PHLogiston Press (ed.). pp. 141–171. Ogata, K. 2004. Ingeniería de Control Moderna. Prentice Hall. Tellurex Corporation, 2003. A guide to temperature Control of thermoelectric systems. Tellurex. Vargas, J. 2003. Modelación Física en Centrífuga, de un Muro Pantalla Apuntalado en Suelos Blandos de Bogotá, Universidad de los Andes. Wang, S.K. & Lavan, Z. 1999. Air-Conditioning and Refrigeration. Mechanical Engineering Handbook. Frank Kreith (ed.). pp. 11–13. White, Frank. 2001. Fluid Mechanics. McGrawHill.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Experimental determination of unsaturated hydraulic conductivity in compacted silt J.J. Muñoz, V. De Gennaro & E. Delaure Ecole des Ponts (Université Paris-Est, Navier Inst. – CERMES), Paris, France
ABSTRACT: Experimental data of unsaturated hydraulic conductivity were determined in aeolian silt taken from Jossigny, east Paris. This test was performed by means of the instantaneous profile method (Daniel 1982). An infiltration column of 50 mm in diameter and 200 mm height was used. The soil was statically compacted by means of the double piston method. The suction profiles were measured with four home-made high capacity tensiometers located at different heights. The tangent of the suction isochrones permits the determination at each point of the hydraulic gradient i = ∂ψ/∂z, with ψ being the water potential or suction head. Consequently, the variation of hydraulic conductivity as a function of suction has been determined. A reduction of two orders of magnitude of unsaturated hydraulic conductivity was determined. 1
INTRODUCTION
In order to determine the hydraulic conductivity in unsaturated soil, more complex experimental methods are required than in saturated soils. As in saturated soils, these methods can be performed in transitory or stationary conditions. Existing techniques to determine the permeability of unsaturated soils can be broadly categorized in three main methodologies. The first one, the so-called Gardner’s method (Gardner 1956), proposes the use of the Richards’s cell (Richards 1931). This method determines the hydraulic conductivity in transitory conditions. It consists in measuring the time evolution of the water volume that moves out of the sample due to a gas pressure increment, which in turns means a suction increment, as the suction s = pg − pw where pg and pw are the gas pressure and the water pressure, respectively. The second method, the so-called Corey’s method (e.g. Green & Corey 1971), determines the hydraulic conductivity in stationary condition. A constant suction is applied to the sample by means of axis translation technique. Positive gas pressure (pg ) and water pressure (pw ) are applied at the bottom of sample, where pg − pw > 0. The same pressure increment is applied to both gas and water at top of sample pg = pw . The gas pressure and water pressure are respectively pg + pg and pw + pw at top of sample, and pg and pw at bottom of sample. A constant value of suction is applied in whole sample. The hydraulic conductivity is determined from the water volume evolution measured during a given time interval due to gradient of pressure applied at each fluid.
Finally, the third method, also known as the instantaneous profile method (Daniel 1982), consists in measuring the variation of the suction profile within an infiltration column as a function of time during the infiltration process. The suction measurements can be performed by means of tensiometers or psychrometers, depending of the expected suction range. The knowledge of the water retention curve (WRC) of the soil allows the determination of the water content profile from the suction profiles and its correlation with the corresponding hydraulic conductivity. In this paper, the determination of the hydraulic conductivity of compacted unsaturated silt by means of the instantaneous profile method will be presented. 2
MATERIAL
The laboratory test was performed on aeolian silt taken from the eastern region of Paris, near to Jossigny village. Jossigny silt can be classed as low plasticity soil in the Casagrande chart. The clay minerals contained in Jossigny silt are illite, kaolinite and inter-stratified illite-smectite (Cui & Delage 1996). The geotechnical properties of Jossigny silt are given in Table 1. The WRC of the Jossigny silt was determined in confined conditions with a suction-controlled oedometer by means of axis translation technique following a wetting path (Casini et al. 2007; Figure 1). No significant swelling properties have been observed on wetting. Experimental data of WRC were fitted adopting the expression proposed by Van Genuchten (1980).
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Table 1. Geotechnical properties of Jossigny silt (after Cui & Delage 1996). wL
wP
(%)
(%)
37
19
IP
18
%
%
γs
<2 μm
>80 μm
kN/m3
34
4
27.2
Suction [kPa]
1000 100 10 1 0.1
Experimental data Van Genuchten 0
0.2
0.4 0.6 Degree of Saturation
0.8
1
Figure 1. Water retention curve in wetting path of Jossigny silt (data after: Casini et al. 2007).
1 −λ s 1−λ Sl = Srl + (Sls − Srl ) 1 + P
(1)
where Sls = 1.0 is the maximum saturation, Srl = 0.0 is residual saturation, s is the suction [kPa], P = 8.67 kPa and λ = 0.217 are the soil parameters. The soil was oven-dried at 40◦ C. Afterwards, soil aggregates were mechanically broken up to pass an 800 μm sieve. The dry soil powder was wetted to a water content of 12.5%, equivalent to an initial suction of 400 kPa. Subsequently, the wetted soil was stored in an airtight container for 24 hours in order to homogenize the soil moisture. The soil was then statically compacted in an infiltration column of 50 mm in diameter and 200 mm height at a dry unit weight of γd = 14.5 kN /m3 . The double piston technique was used in the compaction process (Cui & Delage, 1996).
3
Figure 2. Suction measurements with four tensiometers installed in the infiltration column.
Suction is measured by means of a saturated high air entry value ceramic porous stone (capillary pressure threshold equal to 1500 kPa). The tensiometers were saturated in a saturation cell filled with de-mineralized and de-aired water. A positive pressure of 2000 kPa was applied by means of a pressure-volume control system (GDS) during 24 hours. The calibration curve of the tensiometers was determined by means of the applied positive pressure and the electrical signals of the strain gauge. The water content profiles of each suction isochrone were determined by means of the water retention curve (equation 1). For a given time t, the determination of tangents of one suction isochrone gives at every point the hydraulic gradient (2).
EXPERIMENTAL METHOD
The time evolution of suction profile during the infiltration process was measured inside of an infiltration column of 50 mm in diameter and 200 mm height (Cui et al. 2001). Suction measurements were performed by means of four homemade high capacity tensiometers (Mantho 2005; Cui et al. 2007), placed at 40, 80, 120 and 160 mm from the base of the column (Figure 2).
i=
∂ψ ∂z
(2)
where i is the hydraulic gradient, ψ the water potential or suction head and z is the height. The water volume (V ) infiltrated between two instants t and t + t at a given point, was deduced from
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⎛ H ⎞ H V = A⎝ θt+ t dz − θt dz ⎠ zi
Water pressure [kPa]
the difference between the water content isochrones corresponding to both instants, that is:
(3)
zi
where: A is the sectional area of the column, w is the water content, H is the total height of the column and zi is the current height considered. The water flux q between time t and t + t was computed as indicated in equation (4).
H
θt+ t dz −
zi
q=A
H
0 -50 -100 -150 -200 -250 -300 -350 -400 -450 0
12
θt dz
t
(4)
60
72
Figure 3. Time evolution of suction measured at four different elevations during equalization phase (48 hours) and subsequent wetting phases.
The unsaturated hydraulic conductivity K was calculated from the ratio between the water flux and the hydraulic gradient following Darcy’s law. An average value of hydraulic gradient between two distinct time increments was considered, as shown in the following equation:
0 -50 Water pressure [kPa]
1 2q K= A (it + it+ t )
36 48 Time [hours]
Tensiometer 6 (z = 40 mm) Tensiometer 7 (z = 80 mm) Tensiometer 9 (z = 120 mm) Tensiometer 10 (z = 160 mm)
zi
24
(5)
-100 -150 -200 -250 -300 -350 -400 -450 48
4
EXPERIMENTAL RESULTS
Figure 3 shows the time evolution of suction measured at four different elevations during the equalization phase. Forty eight hours were required for suction equalization in the 350 kPa–400 kPa suction range, until reach a uniform suction profile. Suction equalization was followed by subsequent wetting up to full saturation. Figure 4 shows the details of the time evolution of suction during the wetting phases shown in Figure 3. The advancing front of water saturation is clearly depicted from the tensiometers measurements. More than three hours were required to reach almost full water saturation (i.e. nearly zero suction values) on the top of the soil column at an elevation z = 160 mm (tensiometer 10, Fig. 4). Figure 5 shows both the isochrones of suction (Fig. 5a) and the isochrones of water content (Fig. 5b), determined after 0.46, 0.94, 1.83, 3.08 and 7.0 hours of water infiltration. The suction distribution with the elevation has been computed by means of the equation (6): s = s0
1 −β z 1−β 1− 1+ α
(6)
49
50 51 Time [hours]
52
53
Tensiometer 6 (z = 40 mm) Tensiometer 7 (z = 80 mm) Tensiometer 9 (z = 120 mm) Tensiometer 10 (z = 160 mm)
Figure 4. Time evolution of suction measured during the infiltration phase.
where z is the column elevation and so is the initial suction. The parameters α and β have been determined adopting the minimum square method in order to fit the measured suction profile. The isochrones of water content were determined from suction isochrones using the water retention curve shown in Figure 1 and equation (1). It is worth noting that important suction changes occur within the first 1.83 hours up to an elevation of 120 mm. In this zone the mass transfer occurs mainly in the liquid phase, whereas above 120 mm the likely mechanism of mass transfer is related to the water vapour. Since the former is generally quicker than the latter suction changes in the upper part of the column are recorded later on, after 3.08 hours of elapsed time. For this condition the corresponding change of water content is of about 2% (Fig. 5b). Condition of almost full water saturation along the whole column height
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Height [mm]
200
200
160
160
120
120
80
80
40
40
0
Initial state t = 0 sec Tensiometer (t = 0.46 hours) t = 0.46 hours Tensiometer (t = 0.94 hours) t = 0.94 hours Tensiometer (t = 1.83 hours) t = 1.83 hours Tensiometer (t = 3.08 hours) t = 3.08 hours Tensiometer (t = 7.0 hours) t = 7.0 hours
0 0
100
200 300 Suction [kPa]
400
0.3
a)
0.2 0.1 Water content
0
b)
Figure 5.
Water infiltration test: (a) isochrones of suction and (b) isochrones of water content.
1
1E-006
Relative permeability K/Ksat
Hydraulic conductivity [m/s]
Saturated hydraulic conductivity
1E-007
1E-008
Y = 8.5187E-08*X-0.591 R2 = 0.992 1E-009 1000
100
10
1
0.01
0.001
0
0
Suction [kPa] Unsaturated hydraulic conductivity Saturated hydraulic conductivity
Figure 6.
0.1
0.2 0.4 0.6 0.8 Degree of saturation
1
Hydraulic conductivity Fit
Hydraulic conductivity as a function of suction.
Figure 7. Relative hydraulic permeability as a function of degree of saturation.
(i.e. almost null suction values) is attained for an elapsed time of 7.0 hours. The variation of the hydraulic conductivity as a function of suction is shown in Figure 6. In this work the gradients were obtained graphically from Figure 5. Eight data points were obtained taking the average gradients between two isochrones at every height (40, 80, 120 and 160 mm. Also the gradients could be obtained differentiating equation (6).
The saturated hydraulic conductivity was determined by applying a positive pressure at the base of the column by means of a pressure-volume controller GDS® . The corresponding value was 3.67 × 10−7 m/s. The evolution of the hydraulic conductivity with suction (i.e. saturation) seems to reflect the general findings observed in saturated and partially saturated
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soils. Note that these results suggest a reduced effect of the hydraulic gradient and the general reliability of Darcy’s law when coupled with the instantaneous profile method. This is not necessarily the general trend observed when important microstructural changes are associated with suction changes, as in the case of high swelling soils (e.g. Cui et al. 2001). Finally, Figure 7 shows the variation of the relative permeability computed as a function of degree of saturation. Data on relative permeability were fitted by equation (7). Kr =
β n Sl 1 − 1 − Slλ
(7)
where Sl is the degree of saturation. The parameters λ = 0.138, β = 2.0E − 04 and n = 0.55 have been determined adopting the minimum square method in order to fit the relative hydraulic conductivity.
5
CONCLUSIONS
An infiltration test was conducted on remoulded silt statically compacted in an undeformable column. The results were analysed using the instantaneous profile method (Daniel 1982). The suction profiles were derived from the suction measurements obtained by means of four high capacity tensiometers equally spaced along the column height. The reliability of suction tensiometers was successfully verified. A saturated permeability of 3.67 × 10−7 m/s was found considering constant head condition and stationary flow. The variation of the unsaturated hydraulic conductivity derived following Daniel’s method showed an increase of soil hydraulic conductivity for decreasing values of suction, as is often observed in partially saturated conditions. For suction values of 400 kPa a hydraulic permeability of 3.11E−09 m/s was obtained. Note that this unsaturated hydraulic conductivity is two orders of magnitude smaller than the saturated permeability (1.18E+02). Within the explored suction range, from 0 kPa to 400 kPa (i.e. Srw varying between 100% and 33%), results obtained on Jossigny silt indicate reduced
effects of the hydraulic gradient and the applicability of Darcy’s law. This might not be the case when higher suction levels are considered, as possible influence of microstructural changes could be involved in the assessment of the hydraulic properties. ACKNOWLEDGEMENTS The financial support of EU RTN ‘‘MUSE’’— Mechanics of Unsaturated Soils for Engineering, RTN—Marie Curie Actions) is kindly acknowledged. Authors wish to thank Prof. Y.J. Cui for providing the suction probes used during this study. REFERENCES Casini, F., Muñoz, J.J., Lourenço, S., Vaunat J. & Pereira, J.M. (2007). Technical Report: Results of the first centrifuge campaign al LCPC facilities, Nantes, France. Cui, Y.J. & Delage, P. (1996) Yielding and plastic behaviour of an unsaturated compacted silt. Géotechnique 46, N◦ 2, pp. 291–311. Cui, Y.J., Loiseau, C. & Delage, P. (2001). Water transfer through a confined heavily compacted swelling soil. In Proc. 6th Int. Workshop on Key Issues in Waste Isolation research-KIWIR, ENPC Paris), 43–60. Cui Y.J., Tang A.M., Mantho A. & de Laure E. (2007). Monitoring field soil suction using a miniature tensiometer. Geotechnical Testing Journal, vol. 31 (1), doi:10.1520/GTJ100769. Daniel D.E. (1982). Measurement of hydraulic conductivity of unsaturated soils with thermocouple psychrometers. J. of Soil Science Society of America, 20 (6): 1125–1129. Gardner, W.R. (1956). Calculation of capillary conductivity from pressure plate out-flow data. Soil Science Society of America Proceedings 20, 317–320. Green, R.E., & Corey, J.C. (1971). Calculation of hydraulic conductivity: a further evaluation of some predictive models. Soil Science Society of America Proceedings, 35: 3–8. Mantho, A.T., (2005) Echanges sol-atmosphère application à la sécheresse. PhD. Thesis, Ecole Nationale des Ponts et Chaussées, Paris, France. Richards L.A. (1931). Capillary conduction of liquids through porous mediums. Physics, 1 (5), 318–333. Van Genutchen, M.T. (1980). A close-form equation predicting the hydraulic conductivity of unsaturated soils. Journal Soil Science Society of America 44, pp. 892–898.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Testing for coefficient of permeability of a sandy soil in the residual state zone N. Ebrahimi-Birang Department of Civil and Geological Engineering, University of Saskatchewan, Saskatoon, SK, Canada
D.G. Fredlund Golder Associates Ltd., Saskatoon, SK, Canada
L. Samarasekera Department of Civil and Geological Engineering, University of Saskatchewan, Saskatoon, SK, Canada
ABSTRACT: A series of evaporation tests were conducted in an environmentally controlled room in order to determine the unsaturated coefficient of permeability function for Beaver Creek sand in the residual state zone. Two boundary conditions were applied at the top of the evaporation column; namely, i) ‘‘radiation and wind’’ treatment, and ii) ‘‘wind’’ treatment. The results of the tests indicated that the ‘‘wind’’ treatment was more suitable method for the determination of the unsaturated coefficient of permeability function in the residual state zone. Further tests also revealed that the steady state conditions that appeared to be reached in a fairly short period of time (i.e. 3 to 4 days) might be an ‘‘apparent steady state’’ condition.
1
INTRODUCTION
An understanding of the permeability function for an unsaturated soil is required in modeling the unsaturated seepage problems. Estimation methods have often been used to determine the permeability function. Most of the available estimation methods show a continuous decrease in unsaturated coefficient of permeability, kw , with increasing suction (or decreasing water content). A continuous decrease in the kw with an increase in soil suction can cause numerical instability because of the high nonlinearity and the computing difficulties associated with extremely small numbers. More importantly, an unlimited decrease in the value of kw fails to simulate actual water flow conditions since other moisture transfer mechanisms may cause moisture flow at relatively high soil suctions (Wilson et al. 1994, Gitirana Jr. & Fredlund 2003). Ebrahimi-Birang et al. (2004) suggested a lower limit of 10−14 m/s for kw . Due to restrictions associated with experimental measurements, the unsaturated permeability behaviour of soils remains largely unknown in and beyond the residual state zone. Amongst the methods that have been used for the measurement of the unsaturated coefficient of permeability, the evaporation method can be used to measure small coefficients of permeability in the residual state zone.
The primary objective of this research project was to measure the unsaturated coefficient of permeability in and beyond the residual state zone and also to investigate the mechanism of flow in a porous media when using an evaporation test. During the steady state evaporation method some interesting results were observed. The presentation and discussion of these results are the scope of the current paper. 2
BACKGROUND
The evaporation method to simultaneously measure the soil-water characteristic curve and permeability function was first introduced by Wind (1968). The method was a transient method and involved iterative calculations. Arya (2002) provided information regarding the modifications, commercial equipment, procedure and calculations associated with determining the unsaturated coefficient of permeability. The advantages and disadvantages of the method were also presented. Mehta et al. (1994) used the steady state evaporation method to determine the unsaturated coefficient of permeability. Recently Fujimaki & Inoue (2003) applied the method with some modifications. The principle of the method is based on the assumption that the evaporation rate will start from the maximum
129
rate (i.e. potential evaporation) when the soil column is saturated and will reduce with time and stay constant as the rate of the evaporation reaches the constant inflow rate which is applied from the bottom of the column. The inflow rate is always less than the potential evaporation rate. The test must be run in an environmentally-controlled room. In other words, the potential evaporation must be constant throughout the test. Equation 1 is used to calculate the coefficient of permeability. It must be noted that the soil-water characteristic curve must be measured separately. Research results have shown that steady state conditions appear to be reached within 2 to 3 days for a sandy soil.
k(ψ) =
q−
aτ Dva ρv∗ ρw Rv T ∂ψ ∂z
exp Rψv T ∂ψ ∂z
(1)
−1
where q = ql + qv , ql and qv = the liquid-water and water-vapour fluxes respectively, cm/s; z = depth, cm; a = the air-filled porosity, cm3 /cm3 ; τ = the tortuosity factor; Dva = the diffusion coefficient of water vapour in free air, g/(cm2 · s); ρv∗ = saturated water vapour density; ρw = the density of water, g/cm3 ; Rv = gas constant for water vapour, 4697 cm/K; T = temperature, K; and ψ = soil suction. 3
EXPERIMENTAL PROGRAM
The soil-water characteristic curve for Beaver Creek Sand and details of the evaporation tests procedure are presented in the following sections. 3.1
Soil used
The Beaver Creek sand was used in this research study. The sand was air dried, passed through the sieve #10 (2 mm) and washed thoroughly in order to minimize the amount of salt. Then the properties of the soil were measured. Table 1 summarizes some of the properties of the Beaver Creek Sand. The soil will be referred to as ‘‘Sand’’ throughout the paper. 3.2
SWCC
Hanging column method, Pressure plate (Tempe Cell and Fredlund Cell) and Chilled Mirror Dewpoint Table 1.
Properties of Beaver Creek sand.
Soil properties
Beaver Creek sand
Sand Silt and Clay Specific gravity
99.5 % 0.5 % 2.65
technique (WP4-T apparatus) were used to measure the soil-water characteristic curve of the sand for entire range of suction from zero to 1,000,000 kPa. The equation proposed by Fredlund & Xing (1994) was used to fit the experimental data. Figure 1 shows the experimental data and fitting SWCC for the sand. The air entry value for the sand was 1.7 kPa and residual suction state was reached at about 5 kPa. 3.3 Evaporation test The soil column design, preparation of soil specimens and the evaporation test procedure are presented in the following sections. 3.3.1 Soil column Figure 2 shows a schematic diagram of the soil column used in this study. The column is made of a Plexiglass tube with an inside diameter of 70 mm and a length of approximately 160 mm. Several holes were drilled along the column for the installation of the thermocouples. Eight thermocouples could be installed horizontally at different depths. These depths were: 4.5, 14.5, 24.5, 34.5, 49.5, 72, 112.5, and 147 mm. Some ports were also drilled around the perimeter of the tube to retrieve water content and electrical conductivity samples. The sampling ports in the top 40 mm of the column were smaller (5 mm in diameter) allowing sampling in closer proximity. There were three sampling ports for each depth in the top section of the column. The ports in the lower part of the column had a diameter of 10 mm. Soil samples could be taken from 16 different depths (i.e. 5.5, 10.3, 15.4, 20.5, 25.6, 30.7, 35.8, 40.9, 50.5, 60.4, 70.3, 80.5, 90.5, 100.5, 110.5, 120.5, 130.5, and 140.5 mm). The sampling ports were plugged using rubber stoppers during the test. A heat insulation jacket was used to prevent horizontal heat transfer in the upper part of the column. A porous plate with low air entry value was placed on a grooved pedestal. The column was attached to the pedestal using five bolts and nuts. 3.3.2 Preparation of the soil sample The air-dried sand was mixed with a given amount of water to produce a gravimetric water content of 17%. The soil was left in a plastic container with a tight lid for a day. A Plexiglass tube with a diameter equal to that of the soil column was taped to the column to increase its height. The soil was placed into the column. In order to create a uniform soil, a vertical force was applied on top of the soil through a load cap. Extra soil was trimmed from top of the column. The column was slowly placed on the pedestal and fastened using the bolt and nuts. It should be noted that samples for the SWCC tests (section 3.2) were prepared using a similar procedure. However, the soil
130
Hanging column
Gravimetric water content (%)
30 25 Vapour pressure method method
Tempe Cell and Fredlund SWCC apparatus
20 15
Fredlund and Xing equation 10 Experimental data 5 0 0.1
1
10
100
1000
10000
100000
1000000
Soil suction (kPa)
Figure 1.
Soil-water characteristic curve of Beaver Creek sand.
70 mm
Relay
Electric Fan
Rubber stoppers
150 mm
Sampling ports
Heat insulation jacket
Thermocouples
70 mm
150 mm
Rubber stoppers
Sampling Thermocouples ports
Heat insulation jacket
Bulb
O-rings
GDS Data Logger Porous plate Grooved pedestal
Electronic Balance
O-rings Figure 3.
Porous plate
Grooved pedestal
Figure 2. Schematic diagram of the soil column used in the evaporation test.
samples were extruded into stainless steel rings for the SWCC test. 3.3.3 Test procedure The soil column was placed on an electronic balance (Fig. 3). Thermocouples were horizontally installed
Schematic diagram of the evaporation tests.
through rubber stoppers at specified depths along the column. The thermocouples were attached to a CR1000 Campbell Scientific data logger to monitor temperature during the test. The temperature of the ambient air above the soil column was also monitored using two thermocouples. The soil column was saturated by applying slow flow of distilled water from the bottom of the column. After saturation, the top of the soil was covered with a plastic sheet. The system was left overnight to reach equilibrium. A fiberglass tube was cut and placed around the top part of the column. Two pieces of Velcro were used to tighten the fiberglass around the column. A syringe pump (GDS apparatus) was attached to the column from the bottom through a plastic tube and a needle. The pump was programmed
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4
2560 Weight of the column (g)
2540 2520 2500 2480 2460 2440 2420 2400 0
1
2 3 4 Elapsed time, day
5
6
Figure 4. Change in the weight of the column for ‘‘wind and radiation’’ treatment.
Temperature, ˚C 20
22
24
26
28
30
0 20 Depth (mm)
to apply a specified amount of distilled water into the column (0.36 cm3 /hr). The bottom porous plate had an air entry value of 1.8 kPa. The evaporation test was initiated by removing the plastic cover. An electric fan was used above the column to promote the evaporation. The weight of the soil column was recorded during the test using an electronic balance connected to a computer. The readability of the balance was 0.01 g. The evaporation tests were conducted using two types of top boundary conditions; namely, i) ‘‘radiation and wind treatment’’ and ii) ‘‘wind’’ treatment. In the ‘‘radiation and wind treatment’’ an attempt was made to keep the temperature constant and equal to the room temperature along the soil column using a lamp and a relay. All tests were conducted in an environmentallycontrolled room. The room temperature was about 25.5◦ C and the relative humidity was about 26%. To minimize the effect of the radiation on evaporation, all lights were turned off during the test. The temperature and relative humidity in the room were also recorded using a hygrometer.
RESULTS AND DISCUSSIONS
40 T = 25.4°C
60
t = 100 min
80
t = 2830 min
100 120
4.1
Weight of the column
140 160
Figure 4 shows the change in the weight of the column during the evaporation test for the ‘‘wind and radiation’’ treatment. Steady-state conditions appear to have been reached after 3 to 4 days. A similar result was obtained for the case of the ‘‘wind’’ treatment. Further investigations have shown that this condition may not be a ‘‘true steady state’’ condition (see section 4.4). Further study is required with regard to ‘‘true steady state’’ conditions.
19
21
23
25
0 20
Temperature profiles
t = 7000 min
40 60
t = 400 min
80 100 120
Figure 5 shows temperature profiles during early stages of the evaporation and after what appears to be ‘‘steady state’’ conditions. Temperature gradients are greater for the case of the ‘‘wind treatment’’. For the case of the ‘‘radiation and wind’’ treatment the temperature profile did not change substantially after ‘‘apparent steady state’’ conditions were reached. As can be seen in Figure 5a, the attempt to control temperature seems to be successful. The temperature gradients appear to be small. Further investigation is needed to determine the effect of temperature gradient on the flow through the soil. 4.3
t = 100 min
Temperature, °C 17
Depth (mm)
4.2
t = 2830 min 5a. “Radiation and wind” treatment
Water content profiles
Water content profiles are shown in Figure 6 for both cases. For the case of the ‘‘radiation and wind’’
140 160 t = 7000 min
t = 400 min
5b. “Wind” treatment
Figure 5. Temperature profiles for a) ‘‘radiation and wind’’ treatment, b) ‘‘wind’’ treatment.
treatment it can be inferred that the coefficient of permeability cannot be determined for water contents below 5%. The corresponding suction for a water content of 5% is about 5 kPa (see Fig. 1). However, the water content profile for the ‘‘wind’’ treatment shows that it is possible to determine the corresponding coefficient of the permeability for water contents below 5%.
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Gravimetric water content (%) 0
5
10
Time (min) 15
20
0
0
0 Decrease in weight (g)
20
Depth (mm)
1000 2000 3000 4000 5000 6000 7000 8000 9000 10000
40 60 80 100 120 140 160
20 40 60
Removing a layer of Soil from the surface
80 100 120 140 160
6a. “Radiation and wind” treatment
Figure 7. Weight of the column versus time for the ‘‘wind’’ treatment.
Gravimetric water content (%) 0
5
10
15
20
25
0
EC (ds/m) 0
40
80 100 120 140 160
Figure 6. Water content profiles for a) ‘‘radiation and wind’’ treatment b) ‘‘wind’ treatment.
Steady state condition
Equation 1 can be used along with the soil-water characteristic curve and the water content profile to calculate the coefficient of permeability provided a ‘‘true steady state’’ condition is reached. Further tests must be conducted to determine if the observed steady state condition was truly a steady state condition. The evaporation test with the ‘‘wind’’ treatment was continued for a longer time after reaching an apparent steady state condition. The results of the change in the weight of the sand column are shown in Figure 7. After initiating the evaporation process, the weight of the column started to decrease. Then the weight remained constant for a couple of days (i.e. the steady state condition appeared to be reached). After a day or so the weight of the column started to increase indicating that the outflow rate (evaporation rate) was becoming less than the inflow rate. In other words the evaporation rate was still decreasing. There are two possible reasons for the increase of the weight: i) accumulation of the salts in the top layer of the soil and/or ii) break in the liquid-water continuity between the top and bottom of the column. These two reasons are discussed in the following sections. 4.4.1 Salts accumulation Measurement of the salt profile after reaching the apparent steady state condition showed that the
0.4
0.6
0.8
1
1.2
1.4
20 40 60 80 100 120 140 160
6b. “ Wind” treatment
4.4
0.2
0
60
Depth (mm)
Depth (mm)
20
Figure 8. Electrical conductivity profile for the ‘‘radiation and wind’’ treatment (soil:water = 1:5).
electrical conductivity, EC, of the soil in a thin layer of the soil surface was much higher than the EC for the bottom layers (Fig. 8). Electrical conductivity was measured for the samples with soil to water ratio of 1 to 5. It is possible that this may be related to the reason why the weight starts to increase. If so, then the ‘‘steady-state condition’’ should resume by removing a thin layer of the soil from top of the column. As can be seen in Figure 7 this did not happen and the weight of the column continued rising at the same rate. 4.4.2 Break in the hydraulic continuity of liquid water To examine the hydraulic continuity of the liquid water throughout the soil column, a separate evaporation test was conducted. A soil column was prepared in a similar manner as before except that the porous plate with an air entry value of 100 kPa was used. The inflow rate was also increased to 0.9 cm3 /hr. After the apparent steady state condition passed and the weight of the column started to increase, the inflow rate was reduced to zero. As was expected a decrease in the weight of the column was observed after stopping the inflow rate as shown in Figure 9. The slope of the weight change line corresponds to a rate of evaporation of 0.0101 cm3 /min. The rate of evaporation did not change when compared with the rate before reducing the inflow rate to zero. This may be attributed to
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Time (min) 0
500
1000
1500
2000
2500
3000
3500
Decrease in weight (g)
0 5 w = 0.0101t + 0.2718 RR22= 0.9999
10 15 20 25 30 35 40
Figure 9. Decrease in the weight of the column (evaporation) versus time after reducing the inflow rate (inflow rate = 0).
Gravimetric water content (%) 0
5
10
15
20
25
Depth (mm)
0 20 40
Porous plate (AEV = 1.8 kPa) Inflow rate = 0.36 cm3/hr
60
Porous Plate (AEV =100 kPa) Inflow rate = 0.9 cm3/hr
80 100 120 140
REFERENCES
160
Figure 10. Water content profiles for two different conditions at the bottom of the column.
the fact that there was no hydraulic continuity of liquid water between the top and bottom of the soil column. Plotting the water content profiles for the two different cases provides further evidence that it is possible that the liquid water was not hydraulically connected between the top and bottom parts of the column (Figure 10). The two cases created the same water content profile at the top of the soil while the bottom parts were different due to the change in inflow rate and the bottom plate. In other words, the top portion of the column was solely controlled by the ambient conditions. 5
was promoted with an electric fan above the soil column. While controlling of the temperature seemed to be successful, the water content profiles indicated that the ‘‘radiation and wind’’ treatment might not be a suitable method in order to measure the coefficient of permeability for the range of water content below 5%. On the other hand, the results for the ‘‘wind’’ treatment were encouraging. Continuing the evaporation test for a long time showed that the ‘‘true steady state’’ condition may not have been reached during the short run of the evaporation tests. Two hypothesis were examined for the reason why the steady state condition may not have been attained; namely, i) accumulation of the salt in the surface of the soil and reducing the evaporation as a result, and ii) break in the hydraulic continuity of the liquid water between the bottom and top of the soil. Further investigation showed that the latter reason may provide the best explanation. Further tests are currently being conducting where the water table will be held constant within the soil column at a shallow depth. Hopefully, ‘‘hydraulic continuity’’ will be maintained between the top and bottom of the column.
SUMMARY AND CONCLUSIONS
A series of the evaporation tests were conducted on a sand column in an environmentally controlled room. The aim was to reach steady-state conditions during the evaporation tests and to determine the permeability function in the residual state zone. Two boundary condition treatments were tested, i) ‘‘radiation and wind’’ treatment, and ii) ‘‘wind’’ treatment. In the case of the ‘‘radiation and wind’’ treatment, an attempt was made to control the temperature of the soil column using a relay and lamp system. In both cases the evaporation
Arya, L.M. 2002. Wind and hot air methods. In J.H. Dane & G.C. Topp (eds), SSSA Book Series: 5, Methods of Soil Analysis, Part 4—Physical Methods: 916–926. Madison, Wisconsin: Soil Science Society of America Inc. Ebrahimi-Birang, N., Gitirana, Jr. G.F.N., Fredlund, D.G., Fredlund, M.D. & Samarasekera, L. 2004. A lower limit for the water permeability coefficient. Proceedings of the 57th Canadian Geotechnical Conference: 12–19, 24–27 October 2004. Quebec city, Canada. Fredlund, D.G. & Xing, A. 1994. Equations for the soil water characteristic curve. Canadian Geotechnical Journal 31(3): 521–532. Fujimaki, H. & Inoue, M. 2003. A flux-controlled steadystate evaporation method for determining unsaturated hydraulic conductivity at low matric pressure head values. Soil Science 168(6): 385–395. Gitirana, Jr., G.F.N. & Fredlund, D.G. 2003. From experimental evidences towards the assessment of weather-related railway embankment hazards. Keynote address, Proc. of the International Conference on ‘‘From Experimental Evidences Towards Unsaturated Soil Practice’’, Sept. 18–19 Weimar, Germany. Mehta, B.K., Shiozawa, S. & Nakano, M. 1994. Hydraulic properties of a sandy soil at low water contents. Soil Science 157(4): 208–214. Wilson, G.W., Fredlund, D.G. & Barbour, S.L. 1994. Coupled soil-atmosphere modeling for soil evaporation. Canadian Geotechnical Journal 31(2): 151–161. Wind, G.P. 1968. Capillary conductivity data estimated by a simple method. In P.E. Rijtema & H. Wassink (eds), Proc. Wageningen Symp. on Water in the Unsaturated Zone, Paris, June 1966, Vol. 1: 181–191 Int. Assoc. of Scientific Hydrol., Gent/Brugge/UNESCO.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Preparation of unsaturated soils by oedometric compression B. Caicedo, J.C. Ulloa & C. Murillo Universidad de Los Andes, Bogotá D.C., Colombia
ABSTRACT: The study of unsaturated soils for laboratory tests or physical modeling requires a well controlled preparation method. Usually the procedures for unsaturated soil preparation include different compaction methods controlling water content and voids ratio. However the traditional compaction techniques using blows or kneading reduces the possibility of controlling the stress path during soil compaction. Although a uniaxial compression process allows soil preparation under controlled vertical stress, the whole stress path remains unknown. This paper describes a fully instrumented oedometric apparatus that allows the measurement of vertical and horizontal stress as well as the suction and water content during the oedometric compression test. This new oedometric apparatus is used to prepare unsaturated soils made of mixtures of sand and kaolin. The sensors on the oedometric cell allow the measurement of suction and water content during soil preparation. The results obtained confirm the satisfactory operation of the oedometer and show that this apparatus could be an important tool to investigate the anisotropic response of the unsatrated compacted soils.
1
INTRODUCTION
The increasing interest in physical modelling of unsaturated soils has heightened the need for soil preparation techniques suitable to predict the behaviour of soils during modelling. Of particular interest is the prediction of the expansive or collapse behaviour of soils prepared using different compaction techniques. Studies have been carried out in order to establish controlled methodologies to reproduce intermediate unsaturated soils. These procedures can be grouped into two main techniques: (i) the inclusion of a cementing material in sandy soils (Abdulla et al. 1994, Dupas et al. 1979, Ismail et al. 2000) and (ii) mixtures of clay and sand compacted by uniaxial compression (Brandon et al. 1991, Kimura et al. 1994, Boussaid et al. 2005, Murillo et al. 2006). However these methods suffer from some limitations mainly concerning the possibility of controlling the stress path during compaction. In fact, traditional compaction techniques using blows or kneading make impossible any knowledge of the stress path during compaction. Although uniaxial compression allows soil preparation under controlled vertical stress, the whole stress path remains unknown. Compacted materials are fundamentally unsaturated soils having expansive or collapsible behaviour which is strongly dependent on their negative pore water pressure and their stress history. These soils have been traditionally studied using a set of suction controlled triaxial and oedometric tests. During
these tests soils are submitted to different stress paths and different cycles of drying and wetting in order to analyze their compressibility behaviour. Since these tests are suction controlled tests, the time necessary to characterize the soil takes several weeks or months. As an alternative suction monitored apparatus (triaxial or oedometer) allows the characterization of unsaturated soils in a fraction of time compared with suction controlled apparatus (Blatz and Graham 2003, Jotisankasa et al. 2007). The main objective of this paper is to present a method to investigate the stress—strain—suction paths during the preparation of unsaturated soils by vertical stress compaction. For this purpose this paper presents a new oedometer apparatus having the capability to measure the horizontal stress, suction and water content during compaction. Tests on samples made of a mixture of sand and kaolin are carried out in order to verify the performance of this new oedometer apparatus, however the results in this paper focus on kaolin. 2 2.1
MATERIAL AND EQUIPMENT Material properties
The materials used for the tests are different mixtures of sand and clay. The sand is rounded, well graded silica sand having a specific gravity of 2.45. The clay is kaolin having liquid limit w1 = 55, plasticity index Ip = 29, and a specific gravity of 2.8. The mixtures
135
are obtained by combining different dry masses of silica sand and kaolin with water. Previous standard compaction tests were performed in order to measure the optimum water content and the maximum dry density of the samples. Table 1 shows the sand and clay proportions of the mixtures and the proctor standard results: water content, dry density and void ratio at the optimum water content. 2.2
New suction monitored oedometer apparatus
Figure 1 shows the oedometric cell used for the testing. The cell was designed to measure the stress-strain and suction-water content paths during Table 1.
Soil properties.
Sample
Sand %
Kaolin %
wopt %
ρd kN/m3
E
1 2 3
88 65 0
12 35 100
12 13 29
18.5 18.8 14.5
0.258 0.269 0.482
Figure 1.
Modified oedometric cell.
vertical compression. The modifications to perform the path measurements include: – A capacitive cylindrical water content sensor installed in the centre of the sample (Figure 2). – Three psychrometers to independently measure the suctions. – A linear variable differential transducer (LVDT) to measure the vertical displacement. – A load cell to measure the vertical load. – Three miniature load cells to measure the horizontal stress. The psychrometers are monitored using a Campbell Scientific CR7 data acquisition and control system. The displacement and loads were measured using an Advantech ADAM data acquisition system. The oedometric cell is installed on a Wykeham Farrance press in order to perform oedometric tests with controlled strain rate.
3
TESTING PROGRAMME
Two tests were carried out for each mixture. One of these tests was performed at the optimum water content and compacted up to 9 kN vertical load (2.62 MPa vertical stress). On the other test the soil is mixed at 70% of the optimum water content and compacted up to 3 kN vertical load (0.90 MPa vertical stress). The vertical compression test was performed having one unloading/reloading stage and the oedometric test was a constant rate of displacement test. This type of test allows the continuous measurement of the vertical and horizontal stresses as well as the water content and suction. Increase in water content is allowed after the unloading—reloading process by opening the bottom saturation valve and applying 20 kPa water pressure. During this process the loading piston remains at the same position as at the end of the compression stage; therefore the expansive or collapse behaviour appears as the vertical load increases or decreases.
4
RESULTS AND DISCUSION
4.1 Results for kaolin with high compaction stress Figures 3 to 9 show the results of the sample comprising 100% kaolin and compacted up to 2.62 MPa. On these figures the different phases during the test are identified by the points A to D:
Figure 2.
– Initial state – Loading – Unloading – Wetting
Capacitive water content sensor.
136
point A point B point C point D
2500
800
q kpa
B
400 C
D
1500 1000 500
200
A
0 A 0
C
-500 1000
2000 v
3000
0
(kpa)
400
800
1200
1600
p (kpa)
Vertical and horizontal stress.
Figure 4.
The oedometric cell has a set of miniature load sensors that allows the measurement of the horizontal stress. Figure 3 shows measured vertical and horizontal stresses and it appears there is different behaveiour depending on the direction of loading. The first stage (A-B) corresponds to the loading stage; this stage could be characterized by two linear stages that probably correspond to an overconsolidated stage and a normally consolidated stage. During unloading (B-C) the horizontal stress at first remain constant and then decreases. When the vertical stress reaches zero a horizontal stress of 200 kPa is measured. The reloading path (C-B) is almost linear, corresponding to elastic behaviour. Finally, during wetting, a small decrease in vertical stress and a more importantly an increase in the horizontal stress are apparent. These results show an important anisotropic behaviour since it appears to show a small collapse in the vertical direction and expansion on the horizontal direction. One of the main advantages of measuring the horizontal stress during loading is the possibility of calculating the p-q path. Figure 4 shows the p-q path during loading, unloading, reloading and wetting. This figure shows a number of features: non-linear behaviour during loading, mainly at low stress levels, then approximate linear behaviour for high levels of stress. During unloading and reloading the p-q path is fairly linear but shows a hysteresis. During wetting, the deviatoric stress decreases and the isotropic stress remains almost constant. Figure 5 shows the relationship between axial strain and deviatoric stress. As the test starts with the soil in a loose state, the initial part of the loading stage (A–B) shows a large axial strain without a significant increase in deviatoric strain; however for small strain (ε1 < 0.01) the deviatoric stress grows at higher rate than in the second part of the loading stage corresponding to intermediate strains (0.01 < ε1 < 0.1). This higher slope could be the trace of an initial elastic domain. After unloading (point C) a negative deviatoric stress is measured which is the consequence of combining
p-q path.
2500
B
2000
q kpa
0
Figure 3.
B
2000
600
h
(kpa)
D
D
1500 1000 500
A
0 C
-500 0
0.1
0.2
0.3
1
Figure 5. stress.
Relationship between axial strain and deviatoric
zero axial stress with positive horizontal stress. Finally on wetting a reduction in deviatoric stress appears with any change in axial strain. Figure 6 shows the relationship between specific volume and mean stress. This figure appears to show a clear elastic domain in the first part of the loading stage. As compression starts with the soil in a loose state, this elastic domain is the consequence of an overconsolidated behaviour due to the initial suction. This initial elastic domain is characterized by a line parallel to the unloading reloading stage (B–C). After this initial elastic phase the specific volume reduces at higher rate, during which the degree of saturation of the sample grows and the suction reduces. During wetting an insignificant change in mean stress is recorded therefore on Figure 6 points B and D are superimposed. Figures 7 and 8 show the evolution of suction during testing. Figure 7 shows the relationship between the suction and the volumetric water content θw , and Figure 8 shows the relationship between suction and isotropic stress. As observed on these figures, the new oedometric cell allows the measurement of the suction curve during compression.
137
A
2.8 2.6
V
Loading
2.4
Wetting Initial state Unloading reloading
2.2
B, D
C 2 1
10
100
1000
10000
p (kpa) Figure 6. Relationship between specific volume and isotropic stress.
Figure 9. p − q − s path during oedometric compression. 250
A
4000
(kpa)
6000
150 100
B2 B1
C
50
2000
A
0
D 0
0
24
28
32
36
B C
4000 2000 D 0 0
400
800
1200
1200
domains, an initial elastic domain where the deviatoric stress shows a more important increment as a function of isotropic stress and a normally consolidated domain where the deviatoric stress grows slowly almost for the intermediate strains (0.01 < ε1 < 0.1). This initial compression shows the highest evolution in suction value. During unloading (B-C), the stress path shows a reversible behaviour with minor change in suction value. Finally during wetting a major decrease in suction is evident, as well as an increase of the isotropic stress and a reduction of the deviatoric stress.
A
6000
800
(kpa)
Figure 10. Vertical and horizontal stress for low compaction stress material.
Figure 7. Relationship between suction and volumetric water content. 8000
400 v
w
Suction kpa
D
200
h
Suction kpa
8000
1600
p (kpa) Figure 8.
Relationship between suction and isotropic stress.
Finally it is possible to draw the oedometric compression test on a p−q−s plot (Figure 9). On this curve it is possible to observe all the features described using Figures 3 to 8. The initial state (point A) is characterized by a high suction value and zero p − q stress. The high suction value creates an overconsolidated soil. The loading stage (A-B) is characterized by two
4.2 Results for kaolin with low compaction stress Figures 10 to 12 show the results of the sample comprising 100% kaolin and compacted up to 0.9 MPa. In this tests the reloading phase progresses up to point B2 . This test shows differences to the test carried out with a high compaction stress, mainly in the wetting stage. In fact, on wetting the vertical stress reduces although the horizontal stress remains almost constant (Figure 10). As a consequence for this low compaction stress the collapse behaviour is noticeable on the p-q
138
1000
q kpa
800
The results obtained indicate the apparatus to be responding well in the tests and shows that this kind of apparatus may be an important tool to investigate the anisotropic response of unsaturated compacted soils. The measurement of all the variables involved during the compression of an unsaturated soil allows a better understanding of the preparation of expansive or collapsing soils by static compression. Complementary work is necessary to analyze and model the whole behaviour of compacted soils focusing on their anisotropic response.
B2
B1
600 400
D
200
A
0
C
-200 0
100
200
300
400
500
p (kpa) Figure 11.
REFERENCES
p-q path for low compaction stress material.
A
2.8
V
2.6 2.4 B1
2.2 C
D
2 1
10
100
B2
1000
p (kpa) Figure 12. Relationship between specific volume and isotropic stress, low compaction stress.
path (Figure 11), and on the curve relating the specific volume and the isotropic stress (Figure 12). 5
CONCLUSIONS
This paper presents some details of a suction monitored oedometer to investigate the stress—strain and suction—water content paths during vertical compaction.
Abdulla W.A., Goodings D.J. 1994. Study of sinkholes in weakly cemented sand. Centrifuge 94, Leung, Lee and Tan (eds) Balkema, Rotterdam. Blatz J.A., Graham J. 2003. Elastic—plastic modelling of unsaturated soil using results from a new triaxial tests with controlled suction. Géotechnique 53. No 1. Boussaid K., Thorel L., Garnier J., Ferber V., David J.P. 2005. Comportement mécanique de sols intermediaries reconstitutes: Influence de la teneur en eau et du percentage d’argile. Congrès fancais de mécanique, Troyes, France. Brandon T.L., Clough G.W., Rahardjo P.P. 1991. Fabrication of silty sand specimens for large and small scale tests. Geotechnical testing Journal, Vol. 14 No 1. Dupas J.M., Pecker A. 1979. Static and dynamic properties of sand—cement. ASCE Journal of Geotechnical Engineering Vol. 105, GT3. Ismail M.A., Joer H.A., Randolph M.F. 2000. Sample preparation technique for artificially cemented soils. ASTM Geotech. Testing J., 23(2), 171–177. Jotisankasa A., Ridley A., Coop M. 2007. Collapse behavior of compacted silty clay in suction—monitored oedometer apparatus. Journal of Geotechnical and Geoenvironmental Engineering. ASCE, 133(7), 867–877. Kimura T., Takemura J., Hiro–Oka A., Okamura M. 1994. Mechanical behaviour of intermediate soils. Centrifuge 94. Singapore, Leung et al. (Ed), Balkema. Murillo C. 2006. Caraterización Geotécnica en Centrífuga de Macizos Multicapa de Suelo Parcialmente Saturado usando Ondas de Superficie. PhD. Thesis Universidad de los Andes, Bogotá Colombia.
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Influence of sample height on the soil water characteristic curve C.N. Khoury & G.A. Miller School of Civil Engineering & Environmental Science, University of Oklahoma, Norman, Oklahoma, USA
ABSTRACT: The Soil Water Characteristic Curve (SWCC), one of the fundamental relations to describe unsaturated soil, has been studied extensively; however, not much emphasis has been placed on the effect of sample geometry on the SWCC. The study described in this paper was originated to evaluate the effect of sample height on the SWCC for various soils with the intent of optimizing testing efficiency. A custom made device was built to obtain the SWCC (wetting/drying paths) using automated pore-water pressure and pore-air pressure controllers. Specimens with two heights, 25 mm and 6.35 mm and having a diameter of 63.5 mm, were compacted with similar initial dry density and moisture content. Samples were saturated and then subjected to drainage approaching residual saturation followed by wetting back to a zero suction state. Experimental results thus far demonstrate that the SWCC primary drainage and wetting curves compare favorably for different sample heights. However, an essential distinction in equilibrium time was observed. As expected, tests with smaller sample heights reached equilibrium much faster than larger sample heights. Preliminary results indicate that a 75% reduction of sample height reduced equilibrium time by about 50%. Implications of reducing the sample height are discussed and some general improvements in SWCC testing with the custom made device are presented.
1
INTRODUCTION AND BACKGROUND
The Soil Water Characteristic Curve (SWCC) expresses the relationship between water content and suction in a soil. It is an important relationship in unsaturated soil, and thus obtaining SWCCs experimentally is a crucial yet time consuming endeavor. Extensive research on the SWCC and its importance to unsaturated soil behavior is reported in the literature (e.g. Barbour 1998, Fredlund & Rahardjo 1993, Fredlund et al. 1996). Various test procedures and equipment have been developed to investigate the SWCC (e.g. Olson & Langfelder 1965, Fredlund & Xing 1994, Kawai et al. 2000) such as the filter paper method, pressure plate, Tempe Cell, and many others. However, it seems little research has been conducted to study the effect of sample geometry on the SWCC. Since laboratory testing generally requires significant time to generate a SWCC, there are major advantages to reducing the sample dimensions, particularly the sample height. For example, very little experimental data are available in the literature showing hysteretic behavior of the SWCC; most reported data represent a single branch of the SWCC, typically the primary drainage curve. Probably, time required for completing the SWCC test is the main reason for the lack of reported hysteretic
data; thus, reducing testing time will encourage more extensive testing to fully define hysteretic behavior of the SWCC. This was precisely the motivation for the current authors to pursue this study. This paper presents results of a study to investigate the effect of sample height on the SWCC for a silty soil. The goal was to optimize the testing geometry while shortening the equilibrium time. A preliminary set of experimental results are presented for sample heights of 25.4 mm and 6.35 mm; resulting SWCCs include primary drying and wetting curves. Results clearly demonstrate the time advantage to be gained by reducing sample height. 2
TEST PROCEDURE
The Soil Water Characteristic Curves were experimentally obtained using a custom made test cell built at the University of Oklahoma. Schematic and photographic views of the test cell are shown in Figure 1. The pore-water pressure was digitally controlled using a commercially available high precision motorized piston pump and transmitted to the soil via a high air entry porous disc (HAEPD). A similar pump having a larger piston volume was used to control the air
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size distribution similar to that of fine silt with sand having about 30% fine sand (0.075–0.25 mm), 62% silt (0.002–0.075 mm), and 8% clay size material (≤0.002). A series of tests was conducted to determine the effect of soil sample height on the SWCC. The sample heights tested in this study were 25.4 mm and 6.35 mm with a diameter of 63.5 mm. Each sample was prepared in an identical manner to achieve nominally the same initial void ratio (0.60) and gravimetric moisture content (17.2%) in the test specimens. Samples were compacted into the test cell on top of the pre-conditioned high air entry porous stone using volume-based moist tamping. The test cell was then flooded with water and water was pushed under low pressure through the sample by increasing the air pressure (ua ) above the water in the cell. This process continued until a minimum of three pore volumes of water had flowed through the sample to remove entrapped air. Following saturation, the drying (drainage) and wetting cycles were initiated. The drying curve is obtained by applying ua in increments to obtain different values of matric suction; the amount of pore water volume expelled out of the soil sample is automatically recorded in the system to estimate the gravimetric water content corresponding to each increment of suction. Equilibrium was assumed to occur when negligible water volume (i.e. less than 1% change over a period of 4 hours) occurred for each suction increment. For each height, samples were subjected to wetting and drying cycles under zero net normal stress to obtain the primary drying and primary wetting curves.
GDS Digital Air Pressure Controller
Test Cell
Porous stainless steel top platen Soil sample High air entry porous disc (HAEPD) GDS Digital Water Pressure Controller
Figure 1.
Schematic and photographical view of test cell.
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TEST RESULTS AND DISCUSSIONS
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pressure in the cell. These pumps can accurately control pressure and volume changes to a resolution on the order of 1 kPa and 1 mm3 , respectively. The experimental apparatus allowed for continuous control and measurement of the pore-air pressure and pore-water pressure throughout testing. A porous stone with a relatively low air entry value was used (i.e. 3 bar) to gain maximum efficiency with respect to water transmission into and out of the soil. A commercially available ground silica, Sil-Co-Sil 250 (SCS-250) manufactured by U.S. Silica Company was used as the test soil. The grain size distribution of the SCS-250 is given in Figure 2. As shown, the test soils have a grain
Plots of the Soil Water Characteristic Curves (SWCC) in terms of matric suction (ua − uw ) versus gravimetric water content for tests having heights of 25.4 mm and 6.35 mm are presented in Figure 3 and Figure 4, respectively. Each data point in these figures represents an increment of suction and corresponding measurement of water volume change at equilibrium. Equilibrium was assumed to occur when negligible water volume change occurred for each suction increment. In Figure 5 an example of water volume change versus time for primary drainage of the 25.4 mm sample height is shown; water volume changed fairly rapidly following application of an increment of suction followed by a more gradual change until equilibrium was observed. In Figure 6, a comparison of the primary drainage and primary wetting curves for each (25.4 mm and 6.35 sample height) test is shown. In examining Figure 6 it is apparent that the SWCCs for both sample heights were practically the same.
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Figure 5. Water volume change versus time for primary drainage during testing for 25.4 mm height.
SWCC for the sample of 25.4 mm height.
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Figure 6. SWCC comparison for the two sample heights (25.4 and 6.35 mm).
Figure 7 shows a comparison of water volume change versus total test time for both sample heights. The total time for testing, including primary drainage and primary wetting curves for the 25.4 mm height was about 30 days compared to 15 days for the reduced sample height (6.35 mm). It can be noted that the time required to complete testing was reduced by about 50% when the sample height was reduced from 25.4 mm to 6.35 mm. Results indicate that a reduction in sample height can be an effective way of achieving considerably faster equilibrium test times. However, other considerations remain when reducing the test specimen height, such sample uniformity, and minimum vertical deformations required for accurate measurements on the specimen under vertical loading (i.e. for a given strain shorter heights mean smaller displacements). The reduction in testing time gained by reducing the sample height was a major achievement in that it allowed researchers at the University of Oklahoma to efficiently obtain in a reasonable time frame a complete set of SWCCs including the hysteretic behavior;
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Figure 7. Water volume change versus time for both 25.4 mm to 6.35 mm sample height.
this included primary drying, primary wetting, secondary drying and scanning curves (Fig. 8). This is part of an on-going study of the coupled mechanicalhydraulic behavior of unsaturated soils.
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produced for two different sample heights. By reducing the sample height by 75%, the time required to complete a SWCC was reduced by about 50%. Furthermore, there was virtually no difference in the SWCCs produced using different samples heights.
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Figure 8. 200 kPa.
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SWCC showing hysteresis for normal stress of
CONCLUSIONS
Experiments were conducted in a specially fabricated testing cell and used to examine the effect of sample height on the SWCC relationship in an unsaturated silty soil. The soil water characteristic curves, including primary drainage and wetting curves were
Barbour, S.L. 1998. Nineteenth Canadian Geotechnical Colloquium: The soil-water characteristic curve: a historical perspective, Canadian Geotechnical Journal, Vol. 35, pp. 873–894. Fredlund, D.G. and Rahardjo, H. 1993. Soil mechanics for Unsaturated soils. John Wiley & Sons Inc., New York. Fredlund, D.G. and Xing, A. 1994. Equations for the soil-water characteristic curves, Canadian Geotechnical Journal, Vol. 31, pp. 521–523. Fredlund, D.G., Xing, A., Fredlund, M.D. and Barbour, S.L. 1996. The Relationship of the Unsaturated Soil Shear Strength Functions to the Soil-Water Characteristic Curve, Canadian Geotechnical Journal, Vol. 33, pp. 440–448. Kawai, K., Karube, D. and Kato, S. 2000. The Model of Water Retention Curve Considering Effects of Void Ratio, In: Rahardjo, H., Toll, D.G., Leong, E.C. (Eds.), Unsaturated Soils for Asia, Balkema, Rotterdam, pp. 329–334. Olson, R.E. and Langfelder, L.J. 1965. Pore-Water Pressures in Unsaturated Soils, Journal of Soil Mechanics and Foundation Div., Proc. ASCE, Vol. 91, SM4, pp. 127–160.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Observations of unsaturated soils by Environmental Scanning Electron Microscopy in dynamic mode S.D.N. Lourenço, D.G. Toll & C.E. Augarde School of Engineering, Durham University, Durham, UK
D. Gallipoli Department of Civil Engineering, University of Glasgow, Glasgow, UK
A. Congreve & T. Smart Department of Chemistry, Durham University, Durham, UK
F.D. Evans Controls Testing Equipment Ltd, Wykeham Farrance Division, Tring, Hertfordshire, UK
ABSTRACT: The Environmental Scanning Electron Microscope (ESEM) allows observation of hydrated samples in their original state. Imaging can be done at a constant vapour pressure and temperature or in dynamic conditions to observe a sample response to changes of water vapour pressure and/or temperature. This paper focuses on the use of the dynamic ‘mode’ for unsaturated soils studies. Examples are presented on the hydraulic and structural response of kaolin and silica microspheres to cycles of relative humidity at constant temperature. Qualitative observations were made throughout the cycles and focused on the particle level phenomena (e.g., meniscus shape) and mesoscale phenomena (e.g., particle re-arrangements and emptying and filling of pores). Some quantification was also possible: the contact angle between the air-water and water-solid interfaces was measured. Other applications of the ESEM technique to unsaturated soils and limitations are discussed.
1
INTRODUCTION
The Environmental Scanning Electron Microscope (ESEM) allows hydrated samples to be observed in their original state, unlike the conventional Scanning Electron Microscope (SEM) where samples dry during observation. The ESEM, therefore, provides an essential tool for the study of unsaturated soils, since the arrangements of water within the soil can be observed. ESEM imaging has normally been done in static ‘mode’, under constant relative humidity and constant temperature (i.e. under a constant total suction), to observe a specimen in that particular state. However, it is also possible to use the ESEM in a dynamic ‘mode’ to observe a sample response to changes of relative humidity and/or temperature (i.e. to a change of total suction). This allows the possibility of using the ESEM for ‘‘testing’’ rather than just ‘‘observing’’. Dynamic testing can be carried out in situ,
i.e. without removing the sample from the microscope chamber. There is a need to start developing techniques for ‘‘testing’’ at particle level. The particular techniques to be used will depend on: • the accuracy required: whether measurements (quantitative) or estimations (qualitative) are obtained • the parameter to be measured: stress, strain, suction, water content • particle size scale: mm (sand) to μm (clay) • number of particles to be tested: single particle to particle contact or group of particles. This paper investigates the use of ESEM for unsaturated soil testing. It focuses on dynamic tests where relative humidity is changed at constant temperature in order to change the value of total suction imposed on the sample. Examples are presented for kaolin as well as for samples made of artificial microspheres (around
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6 μm diameter) and the limitations of the technique are also discussed. 2
PREVIOUS WORK
A range of visualisation techniques have been used to study the fabric of unsaturated soils. These include optical microscopy and video methods, X-ray computed tomography (CT), scanning electron microscopy and more recently environmental scanning electron microscopy. Cho and Santamarina (2001) studied samples made of 1.6 mm glass beads and observed the meniscus strain at failure for different rupture modes (shear, extension and rotation). Tests were conducted at the particle-to-particle level by using optical microscopy. Strain was measured directly from the images while water content was estimated for cubic packing. Reinson et al. (2005) observed the drying process of 12 mm glass beads to determine the unsaturated hydraulic conductivity and the soil water retention curve. Observations were made by digital videography in grouped glass beads to capture the meniscus formation and to track the movement of a dye tracer. Suction was estimated by using the Laplace equation based on the observations for a cubic packing arrangement. Computed tomography was used by Wong and Wibowo (2000) to estimate the 3D spatial distribution of porosity, air and water saturation during water flow in a silty sand soil column. Wildenschild et al. (2002) showed that the air-water interfaces in sands could be observed by CT while Cnudde et al. (2006) reviewed the potential to use CT in geo-disciplines. The conventional SEM uses high vacuum to obtain good resolution images. As a result, imaging of wet samples is not possible and special sample preparation procedures are needed. In unsaturated soils, the SEM has traditionally been used for fabric studies, mostly to observe the orientation and packing of particles (e.g. Delage and Lefebvre, 1984; Gasparre et al., 2007). The conventional SEM was later improved to the Environmental SEM, which permits observation of hydrated samples in their original state (e.g. Donald, 2003; Redwood et al., 2005). This increased versatility allowed application of the ESEM to various research fields including, for example, the study of colloids (e.g. Donald et al., 2000). In rock and soil mechanics, the studies conducted so far using the ESEM have focused on: wettability of reservoir rocks in petroleum engineering (e.g. Combes et al., 1998; Buckman et al., 2000; Skauge et al., 2006); hydraulic behaviour of mine marls (Sorgi and De Gennaro, 2006; Sorgi and De Gennaro, 2007); hydration of geopolymer concrete (Zhang et al., 2005). In unsaturated soils, the ESEM was used in the static ‘mode’ to observe the structure of bentonites by Musso et al. (2003), Baker
et al. (1995) and Agus and Schanz (2005). Montes-H. (2004) and Montes-H. et al. (2005) seem to have been the first to use the ESEM for dynamic studies in unsaturated soils. They imposed wetting-drying cycles on bentonite MX80 aggregates while monitoring the structural changes and volume variations. The swelling-shrinkage was measured by a coupled digital image analysis program. Due to the aggregated nature of the material the scale of observation was relatively large (20 μm) and the study was conducted more at a mesoscale rather than at a microscale. Regarding the fabric changes, it was possible to observe cracking and swelling of the aggregates and to quantify the swellingshrinking potential by measuring volume changes. The authors, however, do not report any details about the water menisci, which are present at the interparticle contacts. 3
ESEM WORKING PRINCIPLE
The conventional SEM works by emitting an electron beam towards a conductive sample in high vacuum conditions. Secondary electrons are released from the sample, collected by a detector and amplified to produce an image. The conductive coating of the sample (usually made of gold) improves the image quality and the vacuum ensures the effective operation of the electron gun. In the presence of water vapour inside the microscope chamber, the emitted secondary electrons collide with the water molecules generating positive ions that are directed towards the sample. This causes overcharging of the sample surface and the consequent loss of image quality. In the ESEM a high vacuum condition is ensured only in a limited zone surrounding the electron gun while the relative humidity around the sample stays relatively high. This working mode ensures imaging of hydrated samples in their natural state. Further details about the physical principles governing the operation of the ESEM can be found in Donald (2003) and Stokes (2003). The ESEM is able to induce changes of relative humidity, i.e. water condensation in the sample or evaporation from the sample, by controlling the values of water vapour pressure and temperature. The temperature is controlled by means of a Peltier cooling stage, which can impose temperatures up to 20◦ C (however temperatures are usually kept at low values between 2◦ C and 6◦ C during tests) while the value of vapour pressures can be increased up to 2.339 kPa. The control of relative humidity (RH) inside the microscope chamber is based on the phase diagram of water. Fig. 1 shows the boundary of this diagram separating the region in which vapour pressure at equilibrium is saturated (RH = 100%) from the region where vapour pressure at equilibrium is not saturated (RH < 100%).
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Phase diagram of water.
DYNAMIC TESTING OF UNSATURATED SOILS BY ESEM
As discussed previously, changes in the relative humidity of the pore air can be induced by changing both temperature and water vapour pressure. However, when testing soils, it is preferable to keep the temperature constant and change the water vapour pressure because many soils exhibit a temperature dependent behaviour (e.g. bentonites). 4.1
Examples of tests
Dynamic experiments relevant to unsaturated soils conducted in a FEI XL-30 model have been performed as follows: 1. Clay aggregates under changes of RH Dry Speswhite kaolin was placed in the ESEM chamber in dry conditions and subjected to an increase of relative humidity from 93% to 96% at a constant temperature of 5◦ C. The sequence in Fig. 2 shows an aggregate composed of clay platelets being enclosed in a water film as relative humidity increased from 93% to 96%. In Fig. 2c the clay platelets can still be seen through the water film. Note that both Figs. 2b and 2c refer to the same imposed relative humidity of 96%. The differences between these two images are therefore attributable to the fact that in Fig. 2b equilibrium had not yet been achieved under the imposed value of relative humidity. 2. Microspheres (6 μm) under changes of RH Fig. 3 shows a wetting sequence of three silica microspheres (6 μm diameter) subjected to an increase of relative humidity from 80.1% to 82.3% at a constant temperature of 5◦ C. The water phase is neatly distinguished from the spheres, including the shape of the menisci (concave)
Figure 2. ESEM micrographs of kaolin aggregates at increasing RH.
and its radius. As relative humidity increases the meniscus curvature decreases from a concave shape but without becoming convex (Fig. 3a to Fig. 3b) until it ‘‘bursts’’ in Fig. 3c. Contact angles between the water-solid interface and the air-water interface can be measured directly and are in the range 20◦ –30◦ . Again, the differences between Figs. 3b and 3c (both at the same value of relative humidity) are due to the fact that these figures refer to two different instants in time during the transient phase. 3. Fabric deformation under changes of RH
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Figure 4. ESEM micrographs of silica spheres after a wetting-drying sequence. Arrows in (b) indicate displacement of the spheres.
Figure 3. ESEM micrographs of silica spheres at increasing RH. The spheres, water menisci are identifiable and the contact angle (θ) measurable in (b).
Observations were carried out to detect displacements of the silica microspheres during cycles of relative humidity. All tests were carried out at a temperature of 5◦ C. The sequence in Fig. 4 shows interparticle movements occurring as the microspheres were submitted to the wetting-drying cycle. Distances and directions of movements are measurable and are indicated in Fig. 4b (for the case of the bottom spheres the movement was <1 μm).
4.2 Discussion This research has demonstrated that contact angles, meniscus curvatures and particle movements can be measured for a simple material subjected to cycles of relative humidity. Quantification of ESEM images for these features can be obtained as the relative humidity is changing. In a similar study of clay samples, Montes-H. (2004) observed bentonite aggregates at a larger scale (20 μm). Based on the 2D image of the aggregates, Montes-H. was able to estimate the volume increase during swelling with a digital image analysis software. Lampenscherf et al. (2000) also studied monosized spheres and were able to observe growing menisci in a
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single layer of spheres as relative humidity increased. They were also able to measure indirectly the meniscus force by fixing the spheres to a deformable substrate and measuring its deflection. Schenk et al. (1998) observed the formation of meniscus water at the contact of a cantilever tip of an atomic force microscope and a flat substrate. They were able to validate Kelvin’s law by comparing the imposed relative humidity to the meniscus radius. This shows a range of potential applications for the ESEM, which could be used to validate theories, e.g. the saddle shaped meniscus proposed by Molenkamp and Nazemi (2003). Mechanical testing could be possible for larger materials by fitting the Peltier stage into a straining stage inside the ESEM’s chamber that can be operated either in compression or extension. Stokes and Donald (2000) obtained stress-strain curves for breadcrumbs at different relative humidities. Testing was conducted in unconfined conditions, i.e. with only water vapour pressure surrounding the sample. The ESEM technique could also be useful for the investigation of processes where drying and wetting are due to vapour transfer, including the study of hysteresis (by relative humidity cycles) or wettability (involving contact angle measurements). One of the challenges related to the ESEM is the sample preparation at the microscale. Assembling micron sized particles individually or even in a group might require special manipulation techniques. 4.3
Limitations
One of the main issues in ESEM imaging is the time required for thermodynamic equilibrium. The waiting time should only depend on the volume of the material and imposed relative humidity. However, published results show varied times. For instance, Montes-H. et al. (2005) waited 10 mins for equilibrium conditions with bentonite aggregates 95 μm large under a relative humidity of 95%; Weeks and DeYoreo (2006) waited the same time for water to condense (under RH = 98%) at the tip of an atomic force microscope cantilever and a flat substrate (with the microscope tip width smaller than 1 μm). Other factors might also affect the accuracy of the measurements of water vapour pressure and temperature in the ESEM chamber. Temperature, for instance, is imposed by the Peltier stage, which means that temperature gradients could develop in the material if the sample dimensions are relatively large. The need to test at low temperatures (to obtain a higher image definition) might be a disadvantage in some situations because water properties change with temperature. At 4◦ C, near the temperature at which
most ESEM studies are conducted, water is near its highest density. This could influence cavitation or air entry. Some soils are also sensitive to temperature and testing at low temperatures could therefore change the response of the material. Another limitation is that the ESEM controls the water vapour pressure in 0.1 torr steps (at least in the FEI XL-30 models), which for RH > 90% corresponds about to 1.5% RH changes. These steps are rather coarse and evaporation or condensation can therefore occur too fast leading to a loss of important information during the wetting/drying process. For fabric studies, care must be taken due to different water vapour pressure and temperature conditions between the ESEM chamber and the room. Errors could lead to changes in the fabric as the sample is moved into the ESEM chamber. 5
CONCLUSIONS
This study has demonstrated the potential usefulness of the Environmental Scanning Electron Microscope (ESEM) for unsaturated soils. In the examples shown, water menisci are neatly distinguished from the solid surfaces and details such as the meniscus curvature and contact angle are easily traced and quantifiable. The ESEM allows observation of the effect of changes in total suction on the fabric of unsaturated soils. The ESEM has the capability of conducting dynamic experiments where the total suction imposed to the sample can be varied by changing the relative humidity and temperature inside the microscope chamber. The analysis of images from the ESEM allows the direct measurement of contact angle during wettingdrying cycles. Moreover, published studies have also shown that stress-strain testing inside the ESEM is possible. One limitation of ESEM is however the impossibility of obtaining direct measurements of water content inside the sample. Despite this, the potential of this technique for the study of the engineering behaviour of unsaturated soils is considerable. ACKNOWLEDGEMENTS The authors thank David Beamer (FEI Instruments), Helen Riggs (Durham University) and Dr Jim Buckman (Heriot-Watt University) for helping with the ESEM observations. This research is supported by the Engineering and Physical Sciences Research Council (UK) and Wykeham Farrance Ltd. The support from the European Commission via the ‘‘Marie Curie’’ Research Training Network contract number MRTN-CT-2004–506861 is also acknowledged.
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REFERENCES Agus, S.S., Schanz, T. (2005). Effect of shrinking and swelling on microstructures and fabric of a compacted bentonitesand mixture. Proc. Int. Conf. on Problematic Soils (2) 543550. Baker, J.C., Grabowska-Olszewska, B., Uwins, P.J.R. (1995). ESEM study of osmotic swelling of bentonite from Radzionkow (Poland). Applied Clay Science 9, 465–469. Buckman, J.O., Todd, A.C., Hill, P.I. (2000). Observations on a reservoir rock wettability using an environmental scanning electron microscope. Microscopy and Analysis 14, 2, 35–37. Cho, G.C., Santamarina, J.C. (2001), Unsaturated particulate materials— particle level studies. J. Geotech. Geoenv. Eng. 127, 1, 84–96. Cnudde, V., Masschaele, B., Dierick, M., Vlassenbroeck, J., Van Hoorebeke, L., Jacobs, P. (2006). Recent progress in X-ray CT as a geosciences tool. Applied Geochemistry 21, 5: 826–832. Combes, R., Robin, M., Blavier, G., Aidan, M., Degreve, F. (1998). Visualization of imbibition in porous media by environmental scanning electron microscopy: application to reservoir rocks. J. Petroleum Sc. and Eng. 20, 133–139. Donald, A.M., He, C., Royall, C.P., Sferrazza, M., Stelmashenko, N.A., Thiel, B.A. (2000). Applications of environmental scanning electron microscopy to colloidal aggregation and film formation. Colloids and Surfaces A: Physicochemical and Eng. Asp. 174, 37–53. Donald, A.M. (2003). The use of environmental scanning electron microscopy for imaging wet and insulating materials. Nature Materials 2, 511–516. Gasparre, A., Nishimura, S., Coop, M.R., Jardine, R.J. (2007). The influence of structure on the behaviour of London Clay. Geotechnique 57, 1, 19–31. Lampenscherf, S., Pompe, W., Wilkinson, D.S. (2000). Stress development due to capillary condensation in powder compacts: a two-dimensional model study. J. Am. Ceram. Soc., 83 6, 1333–1340. Montes-H., G. (2005). Swelling—shrinkage measurements of bentonite using coupled environmental scanning electron microscopy and digital image analysis. J. Colloid and Interface Sc. 284, 271–277. Montes-H., G., Geraud, Y., Duplay, J., Reuschle, T. (2005). ESEM observations of compacted bentonite submitted to hydration/dehydration conditions. Colloids and Surfaces A: Physicochem. Eng. Aspects 262, 14–22. Molenkamp, F., Nazemi, A.H. (2003). Interactions between two rough spheres, water bridge and water vapour. Geotechnique 53, No. 2, 255–264.
Musso, G., Morales, E.R., Gens, A., Castellanos, E. (2003). The role of structure in the chemically induced deformations of FEBEX bentonite. Applied Clay Sc. 23, 229–237. Redwood, P.S., Lead, J.R., Harrison, R.M., Jones, I.P., Stoll, S. (2005). Characterization of humic substances by environmental scanning electron microscopy. Env. Sc. and Tech. 39, 7, 1962–1966. Reinson, J.R., Fredlund, D.G., Wilson, G.W. (2005). Unsaturated flow in coarse porous media. Can. Geotech. J. 42, 252–262. Schenk, M., Futing, Reichelt, R. (1998). Direct visualization of the dynamic behavior of a water meniscus by scanning electron microscopy. J. App. Phys. 84, 9, 4880–4884. Skauge, A., Spildo, K., Hoiland, L., Vik, B. (2006). Theoretical and experimental evidence of different wettability classes. J. Petroleum Sc. and Eng. (in press). Sorgi, C., De Gennaro, V. (2006). Observations at the Environmental SEM of the water influence in the behaviour of marls. Proceedings Journ. Nat. de Geotech. et de Geol. de l’Ing., Lyon, France, pp. 9 (in French). Sorgi, C., De Gennaro, V. (2007). ESEM analysis of chalk microstructure submitted to hydromechanical loading. Comptes Rendus de l’Academie des Sciences—serie Geoscience (accepted) (in French). Stokes, D.J. (2003). Recent advances in electron imaging, image interpretation and applications: environmental scanning electron microscopy. Phil. Trans. R. Soc. Lond. A 361, 2771–2787. Stokes, D.J., Donald, A.M. (2000). In situ mechanical testing of dry and hydrated breadcrumb in the environmental scanning electron microscope (ESEM). J. Mat. Sc. 35, 599–607. Zhang, Y.S., Sun, W., Li, J.Z. (2005). Hydration process of interfacial transition in potassium polysialate (K-PSDS) geopolymer concrete. Mag. Concrete Res. 57, 1, 33–38. Weeks, B.L., DeYoreo, J.J. (2006). Dynamic meniscus growth at a scanning probe tip in contact with a gold substrate. J. Phys. Chem. B 110, 10231–10233. Wildenschild, D., Hopmans, J.W., Vaz, C.M.P., Rivers, M.L., Rikard, D. and Christensen, B.S.B. (2002). Using X-ray computed tomography in hydrology: systems, resolutions and limitations. J. Hydrology 267, 285–297. Wong, C.K., Wibowo, R. (2000). Tomographic evaluation of air and water flow patterns in soil column, Geotech. Test. J. GTODJ 23, 4, 413–422.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Recent advances in ESEM analysis of partially saturated geomaterials C. Sorgi INERIS, Verneuil-en-Halatte, France (now RATP, Paris, France)
V. De Gennaro Ecole des Ponts (Université Paris-Est, Navier Inst. – CERMES), Paris, France
H.D. Nguyen Ecole des Ponts (Université Paris-Est, Navier Inst. – CERMES), Paris, France INERIS, Verneuil-en-Halatte, France
P. Delalain INERIS, Verneuil-en-Halatte, France
ABSTRACT: The Environmental Scanning Electron Microscope (ESEM) allows the observation of microstructural changes of geomaterials in their natural state, under controlled conditions of temperature and pressure. Unlike the traditional Scanning Electron Microscopy (SEM), ESEM technology does not require any preliminary treatment of the observed samples (i.e. previous dehydration and eventually conductive coating) reducing possible procedure compliances. Although ESEM applications are nowadays recurrent in many research fields related to materials science, this investigation tool is still seldom used in geomechanics. In this paper we discuss some aspects associated with this technology when used for partially saturated geomaterials. Examples of applications on chalks are presented and some perspectives on the development of this instrument in relation with geomechanical applications are discussed.
1
INTRODUCTION
It is now well recognized that the characterization of a geomaterial’s microstructure and the analysis of its evolution under the effect of applied loadings and/or environmental conditions can provide valuable information for the interpretation and the prediction of mechanical behaviour. The objective of this paper is to present some recent developments and examples of application of the Environmental Scanning Electron Microscope (ESEM) for the study of the microstructure of geomaterials and its relationship with the macroscopic behaviour. So far the observation and the microstructural analysis of geomaterials have been conducted successfully with the Scanning Electron Microscope (SEM); a synthesis of the results obtained in this area of investigation has been presented recently by Mitchell & Soga (2005). Undoubtedly attractive, this technique however requires a preliminary preparation of the samples, submitted to high vacuum during the observation, consisting of dehydration and gold coating to improve the interaction between the electrons and the matter. Sample preparation procedure may have a major impact on
the structure of the material, particularly in clays, for which the dehydration process can harm the integrity of the initial microstructure of the soil sample and lead to important modifications because of shrinking due to drying (e.g. Tessier & Berrier 1978, Delage et al. 1982). Also, this situation prevents the observation of materials at their natural moisture content. In order to demonstrate the potential of the ESEM to investigate behaviour of geomaterials we will focus our investigation on a chalk from the shallow mine of Estreux, located near Valenciennes (France, North department). This chalk is the object of an ongoing research programme conducted by INERIS, devoted to the study of water-rock interaction mechanisms and ageing processes in geomaterials, in relation to the risk assessment of sudden collapses and subsidence originated by the breakdown of shallow abandoned mines. 2
MATERIAL CHARACTERISATION
Under the effect of environmental agents (e.g. temperature, pressure) microstructural evolutions in
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geomaterials often occur. These evolutions can affect the integrity of the solid skeleton and eventually change the mechanical behaviour of the material at the macroscopic scale. The result of these microscopic processes is often identified with the progressive ‘‘ageing’’ of the microstructure and is mainly related to the interaction between the solid skeleton and the fluids which saturate partially or completely the porous network. The intrinsically dynamic nature of these processes is at odds with the static character of SEM imaging. It is thus clear the interest that ESEM can present, allowing observation of samples in their natural state (i.e. saturated, partially saturated or dry) and under variable environmental conditions (temperature, pressure, moisture content), by letting the vapour reside inside the observation chamber (Danilatos 1998). Some phenomena observed during wetting and drying processes in chalk are presented herein.
100 Hr = 83.5% ( s = 24.9 MPa)
10
SUCTION, s :MPa
Hr = 98.2% ( s = 2.5 MPa)
1 Hr = 99.8% ( s = 1.5 MPa)
0.1
Dry path Wetting path Initial state
0.01
0.001 0
Figure 1.
2.1
Hr = 97% ( s = 4.2 MPa)
0.2
0.4 0.6 DEGREE OF SATURATION, Srw
0.8
1
Water retention curve of Estreux chalk.
Physical properties of Estreux chalk
The chalk used in this work originates from the Estreux abandoned underground mine in Northern France. The mine is located 15 km East of Valenciennes (France). Estreux chalk is a gluconite rich chalk. Glauconite is an allumino-silicate of iron, potassium and sodium. Its mineral composition is close to the illite, although glauconite is not hydrated, with the additional presence of sodium and strong isomorphism by substitution of aluminium atoms with Fe2+ and Fe3+ iron atoms (Amouric 1990). Glauconite is often present in chalk deposits in northern France (Masson 1973). The porosity of Estreux chalk is of about 37%, its specific gravity is Gs = 2.74 and the average water content is equal to 20.7% when the rock is water saturated. At microstructural level the solid matrix is made up of small micrometric grains which are principally fragments of coccolithes. Sometimes intact coccolithes also occur. The chalk is then principally made up of calcite (i.e. calcium carbonate CaCO3 ), which often constitutes also the cementing agent at the intergranular contacts. Microfossils and mineral impurities are also frequently observed.
the atmospheric pressure pa ) and the water pressure pw , as st = pa − pw = −
ρw pv RT ln Mv pvs
(1)
where ρw is the water density, Mv the molar mass of the water vapour, R the universal constant of an ideal gas (8.314 Jmol−1 K−1 ), T the absolute temperature, pv the vapour pressure and pvs the pressure of the saturating vapour at temperature T (hr = pv /pvs ). It is well known that any change in total suction induces a change in the degree of water saturation Srw as quantified via the Water Retention Curve (WRC) of the material. The WRC of Estreux chalk is presented in Figure 1 (De Gennaro et al. 2006). As can be observed, important changes in Srw occur when suction varies between 1 and 2 MPa, causing nearly complete material desaturation. This occurs when the corresponding relative humidity reduces from 100% to 98.2%. Since similar changes of hr are possible in the underground mine, the relative humidity may have a significant effect on the state of saturation of the material.
2.2 Retention properties of Estreux chalk Estreux chalk samples were completely saturated when extracted; mine temperature was 11◦ C and the relative humidity hr ∼ = 100% (owing to the 2% accuracy of the hygrometry resistive sensors). It should be noted that relative humidity inside the mine can vary seasonally between 80% and 100% (Sorgi 2004). Based on Kelvin’s law, the change in relative humidity modifies the total air-water suction st , the difference between the water vapour pressure (assumed equal to
3
ESEM ANALYSIS
Changes in Srw can be reproduced with the ESEM controlling sample temperature and pressure following the state diagram of water (Fig. 2), being simultaneously correlated to the corresponding microstructural evolutions. A further step of the analysis consists of the investigation of the microstructure while the material is
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hr = 100% 95 % 85%
1400 LIQUID
PRESSURE (Pa)
1200 1000
60%
A≡D
800
50%
600 B 400 C
200
GAS
0 0
2
4
6
8
10
12
14
TEMPERATURE (°C)
Figure 2.
State diagram of water.
subjected to a micromechanical loading under constant or variable relative humidity by means of ESEM micromechanical in situ tests. In this study a FEI Quanta 400® ESEM equipped with a Deben® microtesting facility has been used as a tool for the microstructural and micromechanical characterization of chalk. Three types of observations are presented: (i) the observation of changes in microstructure under wetting, (ii) the observation of samples submitted to saturation/desaturation cycles starting from their natural state of saturation and (iii) the observation of samples submitted to unconfined compression microtests under variable states of water saturation.
(a)
3.1 Sample preparation Samples were extracted from available blocks of Estreux chalk retrieved from the underground mine, sealed and stored in a thermo regulated chamber. This ensured the preservation of in situ conditions in terms of water content and saturation. Observations (i) and (ii) were conducted on chalk plugs having a square section (about 10 mm side) and a thickness varying from 2 mm to 4 mm. Samples were fixed on the observation stage by means of carbon conductive glue. The small plug thickness allowed for a uniform temperature distribution within the sample. Temperature was controlled using a thermo-electric cooler (Peltier’s effect). The corresponding value of the pressure in the observation chamber was used to define the level of hygrometry hr based on the state diagram of water (Fig. 1). 3.2
Microstructural changes under wetting
The changes in microstructure under wetting when passing from hr = 97% (chalk in its natural state at sampling with w = 20.7%) to hr = 100% are observed by comparing Figures 3a and 3b. A reference network has been superimposed on the micrograph and
(b) Figure 3. Modifications of the porous network in chalk during wetting: (a) initial state, (b) intermediate state before complete saturation.
the boundary of one characteristic pore has been plotted. Since the condition in the chamber corresponds to hr = 100% (p = 705 Pa, T = 2◦ C), hydration takes place as time passes. In Figure 3b, the same pore is visualised after the in-situ hydration. As can be seen, hydration produces a progressive enlargement of the pore boundaries due probably, but not exclusively, to the loss of capillary bridges between the grains. Progressive saturation of smaller pores is also observed on the left side of the photo in Fig. 3b. This observation still remains rather qualitative, though it provides a qualitative picture of the ongoing phenomena. It should be emphasized that
153
(a) 1st wetting
(b) 1st drying
(c) 2nd wetting (start)
(d) 2nd wetting (end)
Figure 4. (a) & (b) fracture opening in chalk specimen during drying; (c) & (d) fracture closing following the second saturation.
pore enlargements are certainly amplified by the specific condition reproduced in the ESEM environment, namely the absence of any external loading and the observation of the external surface of the sample. It is expected that the extent of this phenomenon could reduce for the inner (invisible) pores. 3.3
Saturation-desaturation cycles with ESEM
A series of tests was carried out on samples submitted to saturation-desaturation cycles following the path indicated in Figure 2. During these tests a constant temperature condition was chosen (T = 2◦ C). Relative humidity was modified changing the level
of vacuum inside the chamber between 705 Pa and 346 Pa, corresponding to an hr varying between 100% et 50% (path A-B-C-D Fig. 2). Observations were conducted at 1500 magnification starting from the saturated state (i.e. hr = 100%). During the pressure changes images were captured every 2 minutes and later mounted as a video clip. The observed zone was characterised by the presence of a rigid inclusion (crystal) embedded in the chalk porous matrix (Fig. 4a). The analysed cycles included: Phase 1: saturation & stabilization; sample was left 90 minutes at T = 2◦ C and p = 705 Pa, hence hr = 100% (Fig. 2). The reference image is captured after 90 minutes of elapsed time.
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3.4 Micromechanical in situ testing The combined use of the ESEM technique and a micromechanical testing apparatus was investigated by means of unconfined compression tests. A loading module Deben MICROTEST® allowed the application of a maximum compression load of 5000 N at a constant strain rate of 1 × 10−5 s−1 . A specific set up was developed to carry out micromechanical tests under controlled total suction (i.e. controlling the level of relative humidity during the tests). Cylindrical samples approx. 8 mm in diameter and 15 mm in height were used. Samples were obtained by means of highprecision coring. Upper and lower base parallelism was ensured by means of a high-precision slicer having the accuracy of the order of 1 μm. A first series of preliminary micromechanical tests was conducted on samples saturated, partially saturated and dry in order to verify the agreement between the micromechanical
12 DRY CHALK 10
UCS (MPa)
Phase 2: desaturation; pressure is decreased instantaneously down to 599 Pa (hr = 85%, path A-B-C in Fig. 2). Sample is left to stabilize during 60 minutes. Phase 3: 2nd saturation; the pressure inside the chamber is increased up to 705 Pa (Fig. 2, path CD) and sample is left to stabilize during 60 minutes at hr = 100%. During the first phase of saturation (Phase 1) the initial condition corresponding to full water saturation was reproduced inside the samples (Fig. 4a). The successive drying process (Phase 2) induced a fracture opening at the contact between the crystal and the chalk matrix (indicated by an arrow in Fig. 4b). The presence of this fracture wasn’t observed at the beginning of the test (Fig. 4a). This phenomenon seems to be associated with the changes in suction induced by wetting and drying cycles, admitting that capillary effects could be at the origin of this microstructural modification (swelling/shrinkage of the material). In other words, wetting would have brought to fracture closing whereas drying caused chalk matrix shrinkage around the crystal inducing fracture opening. Fracture opening could then be the consequence of increasing capillary bridges (hence air-water interfaces) inside the chalk matrix during drying. In opposition to this mechanism, wetting decreased the number of air-water menisci between the chalk matrix and the crystal leading to a progressive fracture seal (Figs. 4c, 4d). If related to material ageing, the evolution of this phenomenon with time following consecutive wetting and drying cycles could help in assessing the microstructral feature associated with material degradation. This type of observation could also be assisted by advanced techniques of 2D and 3D image analysis, allowing for a more quantitative characterisation of the morphological modifications induced by changes in water saturation (e.g. Sorgi & De Gennaro 2007).
8 6 PARTIALLY SATURATED CHALK (s = 4.2 MPa)
4 2
SATURATED CHALK
0 0
1 2 AXIAL STRAIN (%)
3
Figure 5. ESEM in situ unconfined compression tests on dry and water saturated chalk.
test results and the laboratory test results performed on samples having standard dimensions. Preliminary results of unconfined compression microtests are presented in Figure 5 which indicates tests results on dry samples to show good reproducibility. The linear slopes of the compression curves (eventually after a first tightening phase) allow the quantification of the Young’s modulus at various states of saturation. It is worth noting that the Young’s modulus for dry chalk was Edry = 1.1 GPa, as compared with that of saturated chalk Esat = 0.71 GPa. The ratio Edry /Esat = 1.6 is the same obtained from other researchers by means of standard laboratory unconfined compression tests (e.g. Raffoux & Ervel 1980). At a suction level so = 4.2 MPa the value of Young’s modulus Eo is between Edry and Esat ; a value of 0.78 GPa. Concerning material strength, the comparison between the Unconfined Compression Strength (UCS) values obtained at saturated and dry states gives a ratio UCSdry /UCSsat ∼ = 2 in agreement with available data on North French chalk (e.g. Bonvallet 1979). Results from the sample tested under constant suction equal to 4.2 MPa (i.e. Sr ∼ = 97%, Fig. 1) show that higher suction levels strengthen the rock by means of additional bonding due to capillary effects. This seems in good agreement with the general pattern of behaviour observed for this chalk in oedometric compression tests under controlled suction conditions (Nguyen et al. 2007). Also of note is that Nguyen et al. (2007) also found a ratio of 2.1 between the yield stress in dry and saturated conditions, close to the ratio UCSdry /UCSsat ∼ = 2 found during ESEM micro-testing. Also, the ratios between the yield stress at a suction level of 4.2 MPa and that at saturated
155
3
2.5
UCS (MPa)
2
1.5
1
0.5
0
Figure 6.
0
0.5
1 1.5 AXIAL STRAIN (%)
2
Failure pattern during ESEM in situ unconfined compression test on water saturated chalk.
and dry state were 1.5 and 0.7, respectively. Similar ratios obtained by micromechanical testing using ESEM were equal to 1.5 and 0.75, showing a notable agreement with the oedometric tests results. Finally, Figure 6 shows some preliminary results of ESEM in situ testing with simultaneous visualisation of the deformation pattern and the failure mode. The direction of compression is vertical, as indicated on the ESEM image (A). At peak strength (image B) the sample surface is still apparently unchanged. At about 0.9% axial strain, in the softening regime, a pseudovertical fracture is visible (image C) followed by a progressive opening in the post-peak phase (images D and E). The aim of these preliminary tests was to explore the possibility to have a characterisation of the local strain field during hydro-mechanical loading using ESEM. Some possible developments like Digital Image Correlation (DIC) technique (e.g. Vales et al. 2007) could be envisaged to aid a quantitative characterisation of the local deformation at microstructural (few hundreds μm) and mesostructural (some mm) levels.
4
2.5
CONCLUSIONS
In this paper some basic applications of the ESEM for the microstructural characterisation of partially saturated geomaterials have been presented. The ESEM allows the observation of microstructural changes of geomaterials in their natural state, under controlled conditions of temperature and pressure. Change in saturation can be easily reproduced in
the observation chamber by means of a thermo-electric cooler based on the Peltier’s effect. This allows for an analysis of the microstructural modifications induced by the saturation/desaturation cycles in the absence of mechanical loading. Suction controlled in situ tests are also possible. The validation of a specific experimental technique is in progress. Further developments are needed to characterize quantitatively the effects of the mechanical and physico-chemical processes associated with the waterrock interaction. In the specific case of the carbonated rocks these developments could improve characterization of some fundamental processes like dissolution, precipitation, crystallization and solid transport under stress, often at the origin of the degradation mechanisms of the rock under the effect of environmental and mechanical agents. ACKNOWLEDGEMENTS The results on Estreux chalk have been obtained during the French National Project BCRD coordinated by INERIS. The collaborations of Mr. P. Delalain (INERIS) and Mr. J.M. Taulemesse (Ecole des Mines d’Alès) are kindly acknowledged. REFERENCES Allais L., Bornert M., Bretheau T. & Caldemaison D. 1994. Experimental characterization of the local strain field in a heterogeneous elastoplastic material. Acta Metallurgica et Materallia, 42 (11): 3865–3880.
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Amouric M. 1990. La transformation gel—smectite— glauconite. Matériaux Agileux: Structure, Propriétés et Applications—SFMC (A. Decarreau, editor): 451 461 Danilatos G.D. 1998. Foundations of environmental scanning electron microscopy, Advances in Electronics and electron physics, 71: 109–250. De Gennaro V., Sorgi C. & Delage P. 2006. Water retention properties of a mine chalk. Proc. 4th International Conference on Unsaturated Soils (UNSAT 2006), Phoenix (USA): 1371–1381. Delage P., Tessier D. & Marcel-Audiguier M. 1982. Use of the Cryoscan apparatus for observation of freeze-fractured planes of a sensitive Quebec clay in scanning electron microscopy. Canadian Geotech. J., 19: 111–114. Masson M. 1973. Pétrophysique de la craie. Bulletin des Laboratoires des Ponts et Chaussées, Spécial V: 23–48. Mitchell J.K. & Soga K. 2005. Fundamentals of Soil Behavior, 3rd Edition, John Wiley & Sons, Hoboken, NJ: 577 pp. Nguyen H.D., De Gennaro V., Sorgi C. & Delage P. (2007). Retention and compressibility properties of a partially saturated quarry chalk. Proc. 1st European Conf. on Unsaturated Soils (E-UNSAT), Durham (UK). Raffoux, J.F. & Ervel, C., 1980. Stabilité générale de la carrière souterraine d’Estreux. Rapport CERCHAR, 8 pp.
Sorgi C. (2004). Contribution méthodologique et expérimentale à l’étude de la diminution de la résistance des massifs rocheux par veillissement. BCRD Rapport Final (2001–01111) INERIS-DRS: 132 pp. Sorgi C. & De Gennaro V. 2007. ESEM analysis of chalk microstructure submitted to hydromechanical loading. C.R. Géosciences 339: 468–481. Stockes D.J. & Donald A.M 2000. In situ mechanical testing of dry and hydrated breadcrumb in the environmental scanning electron microscope (ESEM). Journal of Materials Science, 35: 599–607. Tessier D. & Berrier J. 1978. Observation d’argiles hydratées en microscopie éléctronique à balayage. Importance et choix de la technique de preparation. Proc. 5th Int. Work.—Meet. on Soil Micromorphology: 117–135. Tovey D. & Wong K. 1973. The preparation of soils and other geological materials for the SEM. Proc. Int. Symp. on Soil Structure: 59–67. Valès F., Bornert M., Gharbi H., Nguyen Minh D. & Eytard J.C. 2007. Micromechanical investigations of the hydro-mechanical behaviour of argillite rocks by means of optical full field strain measurement and acoustic emission techniques. Proc. 11th ISRM Congress, Lisbon, July 2007: in press.
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Study of desiccation crack evolution using image analysis S. Costa & J. Kodikara Department of Civil Engineering, Monash University, Australia
N.I. Thusyanthan Schofield Centre, Department of Engineering, University of Cambridge, UK
ABSTRACT: Desiccation cracking can be heavily detrimental on the performance of clay soils in various engineering applications. Typical engineering applications include compacted clay barriers in waste containment, dam cores, canal liners and road pavements. The evolution of desiccation cracks has not been clearly understood and explained. A series of laboratory tests were conducted using Merri-Creek clay. The evolution of cracks was captured by automated digital photography. It was revealed that under the conditions tested, the cracks occurred sequentially subdividing the overall surface area into cells. The relationship between desiccation rate, average cell area, thickness of the specimen and crack initiation are examined and discussed.
1
INTRODUCTION
Clay soils undergo shrinkage cracking during desiccation. Cracks can be a major unwanted feature in a number of geoengineering applications as well as in some other disciplines. For instance, in geoengineering shrinkage cracking is significant in earth embankments, slopes, foundations and roads. In agricultural engineering, cracks can stimulate the water and solute flow through soil in irrigated land. Clay liners are commonly used for lining and covering waste landfills in geo-environmental engineering. Shrinkage cracks can highly compromise the primary function of these clay liners by promoting water and leachate migration. A substantial amount of research work has been conducted in materials engineering on this issue to study the glazing and thermal fracturing in ceramics (e.g. Chiu & Cima, 1993) and printing, painting & washing (e.g. Deegan et al. 1997). Despite the significance of cracking on these applications, the essential understanding of soil shrinkage crack evolution and propagation is still far from satisfactory. The majority of previous research has been qualitative and behavioural (Corte & Higashi 1960, Muller 1998, Kodikara et al. 2000). Many researchers have work on the final state of the cracking process (Morris et al. 1991, Konrad & Ayad 1997, Kodikara et al. 2000). Nahlawi and Kodikara (2006) presented results of cracking tests, where they measured the onset of the first crack, cracking water content and subsequent crack evolution. A similar study was undertaken by Lakshmikantha et al. (2006). In contrast, using time-lapse video technology, it was
possible to capture the complete process of shrinkage cracking in laboratory test specimens. Results are presented in image format as well as in video clips. These videos will be uploaded to a web link in near future.
2
LABORATORY CRACKING TESTS
Merri-Creek clay was used in the experiments. MerriCreek clay is found in Northeastern Melbourne. This very heavy and sticky grey to black clay soil has been used by other researchers (e.g., Chan et al. 2007) and its basic properties includes: LL = 74%, PL = 33%, PI = 41%, Linear shrinkage = 13%. The Merri-Creek clay used for the tests was processed for commercial use and contained a considerable amount of tiny plant roots. This clay is commonly used for construction of cricket pitches in Melbourne, including the Melbourne Cricket Ground. 2.1 Merri-Creek clay A series of tests were conducted with Merri-Creek clay. The unprocessed clay samples were lightly crushed using a rubber hammer and sieved through a 1.45 mm sieve. The plant roots were removed as much as possible for the soil samples. The initial moisture content of soil was determined using the oven drying method. The material that passed a 1.45 mm sieve was mixed with water to its liquid limit (74%), and stirred well until it attained a visibly homogeneous state. The prepared clay mixture was placed in a plastic tray, which was then placed into two polythene bags and was
159
sealed for moisture leakage. The tray was kept in a cool, damp place for 48 to 72 hours allowing the clay paste to gain adequate moisture homogenization. Circular glass containers of 140 mm diameter were used to make the specimens. An air vibrator was used while preparing the specimen in order to remove entrapped air. Then the glass container was placed on an electronic balance which was connected to a computer. This system automatically measured and stored the weight of the specimen every 30 minutes. Specimens were dried using flood lamps each of 500 watts. Four lamps were placed above, surrounding the specimen at a distance of 50 cm. A digital camera, which was operated by a computer, was positioned directly above the specimen. The camera was programmed to take photos at 30 second intervals and the data were automatically saved in the computer. The tests were conducted at varying lamp distances (35, 50 & 75 cm) as well as with varying specimen thicknesses (5, 10 & 20 mm). Although the tests were not performed in a temperature or humidity controlled environment, both surrounding temperature and relative humidity were reasonably constant at 50◦ C and 20% respectively owing to the constant heat emitted by lamps. 3
RESULTS
It is interesting to observe that all specimens produced predominantly sequential, orthogonal crack patterns (Figs 1 & 2), leading to subdivision of the crack area into smaller cells.
(a)
(c) Figure 2. Crack pattern for 35, 50 & 75 cm lamp distances (a, b & c respectively) for 20 mm thick specimen. Table 1.
(b)
(c) Figure 1. Crack patterns for 5, 10 & 20 mm thick specimens (a, b & c respectively) at 50 cm lamp distance.
Statistical features of clay specimens.
Lamp distance cm
Thickness of the specimen mm
Desiccation rate g/hr · cm2
Average cell area mm2
35
5 10 20 5 10 20 5 10 20
0.1939 0.0884 0.0574 0.1196 0.0420 0.0252 0.0677 0.0298 0.0220
224 217 296 113 326 481 134 294 362
50
75
(a)
(b)
For the clay cracking shown in Figures 1 & 2 the number of cracked cells and the average cell area are found to be dependent on the specimen thickness and the lamp distance (or the desiccation rate). As the thickness of the specimen increases, number of cracked cells decreases, in turn increasing the average cell area. Similarly, an increased desiccation rate (or decreased lamp distance) will result in an increase of number of cracked cells and a decrease in the average cell area. Some statistical features of cracked specimens are given in Table 1. An exceptional situation can be seen at 35 cm lamp distance, where for 5 mm thick specimen, the average cell area is larger than that for the 10 mm thickness. The desiccation rates for each test condition were computed on the basis of the automatic weight measurements during drying.
160
4
DISCUSSION 3
3
4.1
8
8
The average cell area of the final crack pattern was dependent on the desiccation rate and the thickness of the specimen. It can be seen from Table 1, that the desiccation rate increases when the lamp distance decreases or the clay thickness decreases. In general, the higher the desiccation rate, the lower the average cell area. At higher desiccation rates, more cracks are needed to release the rapid increase of stress in the specimen, subsequently reducing the crack spacing and the size of the cells. With a low desiccation rate, the specimen has enough time to release the stress increment with a few slowly opening cracks.
10
4
10
5
2
2 1
6
1
9
(a)
4.3
3
3
7
Generally, the evolution and propagation of shrinkage cracks cannot be categorized as purely orthogonal or non-orthogonal patterns. The final state of the crack pattern is generally a mixture of orthogonal, non-orthogonal, simultaneous and sequential cracks (Kodikara et al. 2000). However, crack patterns in all the clay specimens contained almost all orthogonal, sequential cracks where subdivision was the dominant feature in propagation. Figure 3 highlights some of the main features of cracking process. Onset of cracking is dependent on tensile stress distribution was well as the flaw distribution within the material. As theorized by Kodikara and Choi (2006), the maximum stress is likely to occur at the middle of a layer or cracked cell, if cracks have already formed, otherwise predominantly uniform stress conditions might prevail, as applicable to initial cracking. However, the exact location of crack formation will depend on the existence of a flaw that can be propagated with the prevailing stress level at
7
8 10
8 4
10
5
4
5 2
2
6 9
1
6 9
(d)
Specimen thickness
Crack evolution
6 9
(b)
1
The decrease of the average cell area with reducing specimen thickness has been presented by several previous researchers (Nahlawi & Kodikara 2006, Lakshmikantha et al. 2006). The exceptional behaviour (noted in the previous section) of the 5 mm thick specimen at 35 cm lamp distance is being further investigated using thinner specimens. Kodikara et al. (2007) theorized that the spacing between cracks decreases when the specimen thickness decreases up to a certain critical thickness, below which the spacing between cracks becomes larger, increasing the area of the cells. It may be possible that this behaviour is relevant for interpreting the current experimental results, or it may be one-off result dependent on the specific conditions of testing.
4
5
(c)
4.2
7
7
Desiccation rate
3
3
7
7
8 10
8 4
10
2 1 (e)
4
5
5
2
6 1
9
6 9
(f)
Figure 3. Evolution and propagation of shrinkage cracks in 5 mm thick clay specimen at 75 cm lamp distance.
that location. Therefore, the initial cracking is generally associated with edge cracking, where the material can be weakly attached to the container. However, it is possible for several cracks to initiate simultaneously because the stress conditions are relatively uniform at the beginning. Thereafter, cracks can occur somewhere in the vicinity of the centre of a layer or cracked cell, although theoretically, the tensile stress development would likely to be a maximum at the centre. Numbers 1, 2, & 3 in Figure 3(a) refers to the onset of first three cracks respectively. Once a crack is open, it tends to spread in both directions until it intersects another crack or the boundary. It is hardly seen that two cracks meet at an angle of 120◦ to form one crack, or an existing crack bifurcates to form a 120◦ nucleation. This can be identified by following the crack no. 1, 2, 3, 4 & 5 in Figure 3(a) to (f). Crack no. 7 & 8 in Figures 3(c) & (d) are examples for subdivision. Instead of subdivision, only rarely do cracks appear to bifurcate to form new cracks. In Figure 3, crack no. 9 appears to bifurcate into two cracks. A certain few cracks appear to start from one point simultaneously and propagate in three directions making approximately 120◦ angles among them. Crack no. 6 in Figures 3(b) to (f) is an example of
161
4.4
Percentage crack length / (%)
The distribution of cumulative crack length over the drying period illustrates a similar behaviour for specimens with same thickness at different lamp distances. Figure 4 shows the increase in crack length as a percentage of the final crack length for 5 mm thick specimens as the drying progressed. All the specimens were prepared at their liquid limit (74%). The specimen under highest desiccation rate (lamp distance = 35 cm) starts cracking first as expected. These results show that the average cracking water content (as determined from overall weight measurements) is also higher when the first crack occurred. However, the actual cracking water content may be different and was not measured in these tests. Once the cracks are initiated, they grow rapidly to the final state where the crack length becomes stabilized. When desiccation rate is low, cracks open up reasonably late, but continue to grow until the soil is almost fully dried. Using the photos taken at various time intervals, the frequency of crack initiation was analyzed within each hour. A typical distribution is shown in Figure 5. Almost all the cracks have opened up within the initial stage of drying. This distribution shows the likely distribution of flaws that were propagated at various moisture contents. In other words, it represents the flaw distribution with associated fracture stress given by the corresponding moisture content. This analysis
120.00
75cm
100.00
50cm
80.00 60.00
35cm
40.00 20.00 0.00 10
20
60
50
40
30
20
10
0 0
1
2
3
4
5
6
Time/(hr)
Figure 5. Number of cracks initiated during the first few hours of the drying of 5 mm thick specimen at 75 cm lamp distance.
Crack initiation
0
No. of cracks initiated within the hour
such a formation. However, closer examination of these crack formations reveals that these can very well be explained by the presence of certain flow orientations and the influence of stress relief caused by other already formed cracks. In this regard, the crack formation observed in these tests can be considered to form generally orthogonal patterns. This is very common when cracks propagate in subdivision, as a requirement of the prevailing stress regimes influenced by formed cracks. An example is shown in Figures 3(b) to (f) by crack no.10.
30
40
50
60
70
80
Water Content / (%)
Figure 4. Variation of percentage crack length with average water content of a 5 mm thick layer—the legend shows the lamp distance.
Figure 6. Displacement vectors of a cracked specimen generated using PIV analysis.
can be extended further to develop detailed flaw distributions as well as flaw orientations that are required for numerical modelling of crack evolution. 4.5 Strain analysis Particle Image Velocimetry (PIV) is becoming a powerful tool in the study of failure mechanisms and material failure parameters in geomechanics (White et al. 2003, Thusynathan et al. 2007). This paper presents some preliminary results of the application of this technique to study desiccation crack evolution. Figure 6 shows the displacement vectors of a cracked specimen of Merri-Creek clay analyzed using the PIV technique. The PIV image software developed at the University of Cambridge, UK (White, 2002, Take, 2003) was used here. It is clear that despite the large deformations cracked cells have experienced, it is possible to track their strains and displacements provided that additional texture is provided to the cracking surface. In this instance, fine white sand was randomly distributed on the clay surface at the beginning to provide sufficient textural properties for image tracking by the software.
162
Cracks
Figure 7.
Cracks analyzed with PIV technique.
PIV can produce plots of strain contours which distinguish the strain localization prior to the crack initiation. For example, analysis focused on the initiation of a selected single crack in the specimen shown in Figure 7. Plots generated from a preliminary analysis are shown in figure 8a–c. Initially, soil was undergoing almost uniform strain over the entire region as shown in Figure 8a. Strain localization close to the top right and left corners of the region before the crack initiation can be seen in Figure 8b. The grayscale code on the right of the each figure refers to the value of strain in pixels as the images were not calibrated. In Figure 8c, the crack has already opened increasing the maximum strain from 1.8 to 18.
5
(a)
Cracks
(b)
CONCLUSION
This paper presents the results of laboratory cracking tests undertaken on a reactive clay. The evolution of crack patterns was studied using image analysis, and time-lapse videographs were produced giving a complete picture of crack evolution. Tensile stress distribution within the material and the flaw distribution govern the crack evolution. The spacing between cracks or the average cell area decreased the increasing of either the desiccation rate and (or) the specimen thickness. In line with previous observations on desiccation cracking, clay specimens cracked mainly orthogonally by sequential subdivision after the crack initiation, which was associated with some simultaneous cracking, influenced by flaw and tensile stress distributions. Preliminary analyses were undertaken using Particle Image Velocimetry (PIV) technique in order to capture the development of strain prior to crack initiation. This technique will further be used in future experiments for further studies.
ACKNOWLEDGEMENTS The support given by ARC Discovery Scheme is gratefully acknowledged. Thanks are also rendered to Drs White and Take and Cambridge University for providing PIV software.
Cracks
REFERENCES
(c)
Figure 8a–c. opening.
Plots of strain build-up around the crack
Chiu, R.C. and Cima, M.J. 1993. Drying of granular ceremic films: II, Drying stress and saturation uniformity. J. American Ceremic Society, 76(11), 2679–2777. Corte, A. and Higashi, A. 1960. Experimental research on desiccation crack in soil. U.S. Army Snow Ice and PermafrostResearch Establishment. Research report No.66. Corps of Engineers. USA.
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Deegan, R.D., Bakajin, O., Dupont, T.F., Huber, G., Negal, S.R. and Witten, T.A. 1997, Capillary flow the cause of ring stains from dried liquid drops, Nature, 389, 827–829. Chan, D., Kodikara, J.K., Ranjith, P.G. and Choi, X. 2007. Data analysis and laboratory investigation of the behaviour of pipes buried in reactive clay, 10th AustraliaNew Zealand Conference on Geomechanics, Brisbane, Australia. Kodikara, J.K., Barbour, S.L. and Fredlund, D.G., Choi, X. 2007, Theoretical analysis of desiccation cracking of a long soil layer, under review. Kodikara, J.K. and Choi, X. 2006. A simplified analytical model for desiccation cracking of clay layers in laboratory tests, Proceedings of UNSAT2006 Conference, Edited by G.A. Miller, C.E. Zapata, S.L. Houston and D.G. Fredlund, ASCE Geotechnical Special Publication, Unsaturated Soils Vol. 2, pp. 2558–2567. Kodikara, J.K., Barbour, S.L. and Fredlund, D.G. 2000. Desiccation cracking of soil layers, Proceedings of Asian Conference on Unsaturated Soils: From Theory to Practice, A. A. Balkema, pp. 693–698. Konrad, J-M. and Ayad, R. 1997. Desiccation of a sensitive clay: field experimental observations, Canadian Geotechnical Journal, 34, 929–942. Lakshmikantha, M.R., Prat, P.C. and Ladesma, A. 2006. An experimental study of cracking mechanisms in drying
soils, Proceedings of 5th International Conference on Environmental Geotechnics, Thomas Telford, London. Lee, S.L., Lo, K.W. and Lee, F.H. 1982. A Numerical model for crack propagation in soils, Proceedings of the International Conference on Finite Element Methods, Shanghai, China, pp. 412–418. Morris, P.H., Graham, J. and Williams, D.J. 1992. Cracking in drying soils, Canadian Geotechnical Journal, 29, 263–277. Muller, G. 1998. Experimental simulation of basalt columns, J. Volcanology and Geothermal Research, 86, 93–96. Nahlawi, H., and Kodikara, J.K. 2006. Laboratory experiments on desiccation cracking of thin soil layers, Journal of Geotechnical and Geological Engineering, GEGE2281, Springer Netherlands, Vol. 24, No. 6, pp. 1641–1664. Take, W.A. 2003. The influence of seasonal moisture cycles on clay slopes, PhD dissertation, University of Cambridge, UK. Thusyanthan, N.I., Take, W.A., Madabhushi, S.P.G. and Bolton, M.D. 2007. Crack initiation in clay observed in beam bending, Géotechnique, Vol. 57, No. 7, 581–594. White, D.J. 2002. An investigation into the behaviour of pressedin piles. PhD dissertation, University of Cambridge, UK. White, D.J., Take, W.A. & Bolton, M.D. 2003. Soil deformation measurement using particle image velocimetry (PIV) and photogrammetry, Géotechnique, 53, No. 7, 619–631.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Theoretical analysis of the effect of temperature, cable length and double-impedance probe head on TDR water content measurement A. Tarantino & A. Pozzato Dipartimento di Ingegneria Meccanica e Strutturale, Università degli Studi di Trento, Italy
ABSTRACT: The TDR method for volumetric water content determination is based on the measurement of the soil apparent permittivity from travel time analysis of a reflection waveform. This is in turn related to water content through a calibration curve. Methods for travel time determination and calibration equations have been developed in the laboratory under conditions that often differ from those in the field, where longer cable are used and temperature fluctuations are significant. This paper presents a theoretical analysis of the effect of temperature, cable length, and double-impedance probe head on signal travel time. This is made by solving the transmission line equations in the frequency domain and by obtaining the time domain waveform by inverse Fast Fourier Transform. It is shown that multiple reflections associated with double-impedance probes may significant affect TDR travel time-based water content determination.
1
INTRODUCTION
Water content measurement in the laboratory and the field is a key to understanding the hydraulic and mechanical behaviour of unsaturated soils. The method based on Time Domain Reflectometry (TDR) may be considered as the most accurate and versatile technique. TDR measurement involves a fast rise-time step pulse generator, a coaxial cable, a two or three-rod probe inserted into the soil, and a sampling oscilloscope. The step pulse is launched into the transmission line, travels along the coaxial cable and probe rods. It is then reflected at the end of the rods and travels backward along the rods and coaxial cable. The time taken to the pulse to travel forth and back the probe rods depends on the volumetric water content of the soil but also on soil dry density, clay content, temperature, soil conductivity, cable length and rise-time of step pulse. Reviews of TDR technique for water content measurement can be found in O’ Connor & Dowding (1999), Gardner et al. (2001), Noborio (2001), Dane & Topp (2002), Jones et al. (2002), Robinson et al. (2003), Tarantino et al. (2008). Conventional interpretation of TDR measurement consists of determining the pulse travel time along the rods and relating it to the volumetric water content through a suitable calibration curve. This can be the Topp’s equation (Topp et al. 1980) or Ledieu’s equation (Ledieu et al. 1986) or a soil specific calibration curve. Conventional interpretation of TDR measurement lies on the assumption that travel time is only affected by volumetric water content and is independent of
other factors such as temperature, cable length. This assumption is clearly a source of error in water content measurement especially in the field, where long cable are often used and temperature fluctuations are significant particularly in surface installations. The paper presents a theoretical analysis to assess the effect of temperature and cable length on TDR signal travel time and, hence, on water content measurement. In addition, the effect of multiple reflections occurring at the probe head is analysed. Probe heads of current commercially available probes are formed by two series impedances which cause the waveform to first descend and then ascend when the signal travels along the probe head. This form of the wave at the interface between cable and soil is somehow different from the classical ‘single rising limb’ form (single-impedance head) reported in the literature (Heimovaara & Bouten 1990). A question that might be asked is whether the methods for travel time determination developed for single-impedance heads still hold for double-impedance heads. The theoretical analysis was carried out by solving the transmission line equations in the frequency domain and then obtaining the time domain waveform by inverse Fast Fourier Transform. Soil permittivity was represented by a four-component mixing model and free and bound water were assumed to have frequency-dependent complex dielectric permittivity. The cable was modelled by assuming that its permittivity is complex and frequency-dependent. The analysis is here limited to soils having pore water with low electrical conductivity and negligible
165
amount of bound water (soils having low cation exchange capacity). 2
SIMULATING TDR WAVEFORMS
2.1
Uniform transmission line
Let us consider an equivalent circuit for a uniform transmission line as shown in Figure 1. The line is terminated with an independent voltage source VS at z = 0 and a source impedance ZS and with a load impedance ZL at z = l (ZL = ∞ for the open-ended TDR probe). Electromagnetic wave propagation inside the uniform transmission line is described by the line current I and the voltage V between the conductors. If V and I are time-harmonic cosine functions with angular frequency ω and the symbolic representation of sinusoidal signal is adopted, the following transmission line equations can be obtained (Kraus & Fleisch 1999): ⎧ + −γ z+jωt + V0− eγ z+jωt ⎪ ⎨ V (t, z) = V0 e (1) V+ V− ⎪ ⎩ I (t, z) = 0 e−γ z+jωt − 0 eγ z+jωt Z Z where t is the time, z is the position along the line, and V + and V − are complex constants to be determined for given boundary conditions. The two complex terms in each equation denotes travelling waves in positive and negative direction respectively. The propagation constant, γ , and the characteristic impedance of the line, Z, are the two complex parameters governing the propagation of electromagnetic waves along the transmission line and can be expressed for the case of non-ferromagnetic materials as follows: γ =
jω ∗ εr ; c
Zp Z= √ ∗ εr
(2)
where c is the speed of an electromagnetic wave in free space (c = 3 · 108 m/s), εr∗ is the equivalent permittivity of the medium between the inner and outer conductor, and Zp the characteristic impedance in vacuum, which is only a function of the crosssectional geometry of the transmission line and can ZS Vs
+
+ V(0) Characteristic impedance, Z
z=0 Figure 1.
Uniform transmission line.
ZL
z=l
be assumed, as a first approximation, to be equal to the characteristic impedance in air. The boundary conditions for the uniform transmission line shown in Figure 1 can be written as follows: V (0) = VS − ZS I (0) (3) V (l) = ZL I (l) By combining the second of these boundary conditions with Equation 1, we can obtain the impedance that the oscilloscope sees at z = 0 (Kraus & Fleisch 1999): Z(0) = 2.2
V (0) ZL + Z tan h(γ l) =Z Z + ZL tan h(γ l) I (0)
(4)
TDR multi-section transmission line
The equivalent circuit for the TDR system is shown in Figure 2. It includes a multi-section transmission line consisting of a cable, a probe head split in two sub-sections, head 1 and head 2, and a probe. Each section of the transmission line is characterised by an impedance Z, a propagation constant γ , and a length l. The solution for the multi-section transmission line can be obtained by writing Equation 1 for each section of the line and by considering the continuity constraints at the discontinuities between the terminations of each section and by imposing the boundary conditions at z = 0 and z = l given by Equation 3. Rather than simultaneously solving Equation 1 for each section of the line, we will use the explicit procedure suggested by Lin (2003a, 2003b), which involves determining the input impedance at the end of the line and transforming the impedance successively to the subsequent discontinuity until the source is reached at z = 0: Z(4) = ZL Z(3) = Zprobe
Z(4) + Zprobe tan h(γprobe · lprobe ) Zprobe + Z(4) tan h(γprobe · lprobe )
Z(2) = Zhead2
Z(3) + Zhead2 tan h(γhead2 · lhead2 ) Zhead2 + Z(3) tan h(γhead2 · lhead2 )
Z(1) = Zhead1
Z(2) + Zhead1 tan h(γhead1 · lhead1 ) Zhead1 + Z(2) tan h(γhead1 · lhead1 )
Z(0) = Zcable
(5)
Z(1) + Zcable tan h(γcable · lcable ) Zcable + Z(1) tan h(γcable · lcable )
The impedance Z(0) obtained from Equation 5, which is the impedance that the oscilloscope sees at z = 0, controls the voltage V (0) in the frequency
166
suggested by Heimovaara (1994) and Jones & Or (2001), provided the input function was zero padded with the addition of a number of zero samples equal to 4 N/8 N. To verify that the FFT of the sampled input function after zero-padding was not affected by noise, we compared the discrete Fourier transform with the continuous Fourier transform of the input function obtained from the Fourier integral (Brigham 1974). The following expression for the input function in the frequency domain was derived:
Cable Head 1 Head 2 Probe ZS Z(0) Z(1) Z(2) Z(3) Z(4) Vs
+ Zcable V(0) γcable lcable
+
Zhead1 γhead1 lhead1
l1 z=0
Figure 2.
l2 z=z1
Zhead2 γhead2 lhead2
Zprobe γprobe lprobe
l3 z=z2
ZL
l4 z=z3
z=l
Multisection transmission line.
V
H( f ) = V0 V0
j −j2π f T e−j2π f t1 − e−j2π f t0 e + 2 (t1 − t0 )(2πf ) 2πf
(7)
where f is the frequency and V0 the voltage amplitude. t0
Figure 3.
Δt
t1
T
t
ΔT
3
Ideal input step function.
domain sampled by the oscilloscope at z = 0 (Lin 2003a, 2003b): V(0) = Vin +
Z(0) − ZS · Vin Z(0) + ZS
(6)
where Vin is the incident waveform in the frequency domain (Vin = Vs /2). 2.3
Numerical modelling of TDR reflection waveform
According to Lin (2003a, 2003b), the TDR waveform can be obtained by standard spectra analysis that involves (i) transforming the incident step input in the frequency domain to determine Vin ; (ii) determining the frequency response of the output V (0) using Equations 5 and 6 and (iii) transforming the frequency response back into the time domain. The Fourier and Inverse Fourier Transforms were performed using the Fast Fourier Transform (FFT) and inverse FFT (IFFT) algorithm. Appropriate zero padding and suitable window size were selected. 2.4
Input function
We considered the ideal input step function shown in Figure 3, where T = T − t0 is the pulse length and t = t1 − t0 is the pulse rise time ( t = 200 ps). We assumed that the pulse length T is finite, with T greater than the time required for complete reflections of waves traveling forth and back the TDR probe. When transforming the sampled input function into the frequency domain by FFT, we found that it was not necessary to introduce any algorithm as earlier
TRANSMISSION LINE PARAMETERS
The propagation constant, γ , and the characteristic impedance, Z, are the parameters governing the signal propagation through each section of the line. According to Equation 2, these parameters depend on the dielectric permittivities of the media filling the sections of the transmission line. These permittivities are discussed in the following sections. 3.1 Soil permittivity The permittivity of the soil εm∗ was described by the four-component complex dielectric mixing model presented by Heimovaara et al. (1994): ρd √ ∗ εm∗ = εs + (θ − δρd As ) εfw ρs √ ρd ∗ + δρd As εbw + 1− −θ εa (8) ρs where εs and εa are the permittivities of soil solids ∗ ∗ and air respectively, εfw are the equivalent and εbw permittivities of free and bound water respectively, ρd is the bulk dry density of the soil, ρs is the average density of the solid phase, the product δρd As represents the volumetric bound water content, with As and δ being the specific surface of the soil and thickness of the bound water layer respectively. ∗ The equivalent permittivity of free water εfw was assumed to be described by a Debye-type equation (Hasted 1973): ∗ εfw = εfw,∞ +
167
−j
εfw,s (N , T ) − εfw,∞ 1 + j ffw,relf(N ,T )
σfw,dc (N , T ) 2πf ε0
(9)
Table 1. Debye parameters for free water at N = 0.05 (moderately saline water). T (◦ C)
σfw,dc (S/m)
εfw,s –
ffw,rel (GHz)
εfw,∞ –
0 20 40
0.28 0.47 0.69
86.8 79.2 72.3
9.0 17.1 27.5
4.2 4.2 4.2
where f is the frequency, ffw,rel is the relaxation frequency, εfw,s the static permittivity, εfw,∞ the permittivity at infinite frequency (refractive index), ε0 is the permittivity in free space, σfw,dc the direct current electric conductivity. The parameters εfw,s , ffw,rel , and σfw,dc depend on temperature T and normality N of the aqueous solution according to the relationships given by Stogryn (1971). Table 1 show the values of the free water dielectric parameters for three different temperatures T for the case of an aqueous solutions having N = 0.05 (moderately saline water). A similar Debye relationship was used to represent the equivalent permittivity of bound water. Since the relaxation frequency of bound water is well below the TDR bandwidth (Tarantino et al. 2008), the Debye ∗ permittivity of bound water εbw was simplified to: ∗ εbw = εbw,∞ − j
σbw,dc 2π f ε0
(10)
where εbw,∞ and σbw,dc were assumed to be temperature-independent. We assumed εbw,∞ = 5 and σbw,dc = 15 S/m according to Heimovaara et al. (1994). The permittivities of soil solids and air were assumed to be real and frequency independent (εs = 5, εa = 1). 3.2
Cable permittivity
The permittivity of the cable was modelled according to Lin & Tang (2007), who presented the following expressions for the propagation constant, γ , and the characteristic impedance, Z: j2π f √ αR εcable 1 + (1 − j) γcable = c f Zp,cable αR 1 + (1 − j) Zcable = √ εcable f
(11)
(12)
where εcable is the dielectric permittivity of the medium filling the cable assumed to be real and frequencyindependent, and the αR is the resistance loss factor
representing the combined effect of geometric factors and surface resistivity. We determined the parameters εcable , αR , and Zp,cable with reference to the cable RG58A/U connected to the TDR probes manufactured by Campbell Scientific. These parameters were determined by fitting the frequency-dependent nominal attenuation (dB/m), the nominal velocity of propagation, and the nominal impedance reported in the cable datasheet. We obtained αR = 130 sec−0.5 , εcable = 1.62, and Zp,cable = 63.6. 3.3 Head permittivity We assumed that the head permittivity was real and frequency-independent. For sake of simplicity, we assumed that the head permittivity was equal to the cable permittivity (εhead = 1.62). 4
EFFECT OF DOUBLE-IMPEDANCE PROBE HEAD
To investigate the effect of the double-impedance probe head, we considered different combinations of Zhead1 and Zhead2 (Table 2). For each impedance combination, we simulated the waveform in water, air, and soil at different volumetric water contents. The waveform in air and water was used to calibrate the probe according to Heimovaara (1993). The water content was then derived from travel time analysis using Ledieu’s calibration and compared with the theoretical value used to generate the waveform. To isolate the effect of multiple reflections occurring at the double-impedance head, we assumed that both cable and soils were non-dissipative (αR = 0, As = 0, σfw,dc = 0). The waveforms obtained by considering a single impedance probe head are reported in Figure 4(a) (combinations No. 1 and 2 in Table 2) whereas the waveforms obtained by considering a double-impedance probe head with different values of Zhead1 and Zhead2 are reported in Figure 4(b) (combinations No. 3 to 5 in Table 2). It can be observed that the waveform can change significantly if there is a high impedance mismatch between the two head sub-sections. Table 2. Combinations of impedances of probe head sub-sections. No.
Cable L(m)
Head1 L(m)
Zp()
Head2 L(m)
Zp()
1 2 3 4 5
0.08 0.08 0.07 0.07 0.07
– – 0.01 0.01 0.01
– – 28 6 6
0.02 0.02 0.02 0.02 0.02
57 285 57 171 57
168
0.7
0.5
0.6
No.1
0.5
No.2
0.4
0.3
'MEASURED'
reflection coefficient, ρ
0.4
0.2 0.1
(a)
0 0.1
0.3
0.2
combination No.1 No.2 No.3 No.4 No.5
0.2 0.3
0.1
0.4 0.5 9
10
11
12
13
14
15
16
0
t [ns]
0
0.5 0.4
No.3
0.3
No.4
reflection coefficient, ρ
0.2
0.3
0.4
0.5
IMPOSED
Figure 5. Comparison between ‘measured’ water content and water content used to generate the waveform for different combinations of head sub-section impedances.
No.5
0.2
0.1
0.1 0 0.1
0.4
(b)
0.2 0.3 0.4
0.6
'MEASURED'
0.5 ρd=1.5 g/cm3; ρs=2.65 g/cm3
0.7 0.8 9
10
11
12
13
14
15
16
0.3
t [ns]
cable length 1m
0.2 Figure 4. Waveforms in water. (a) single-impedance probe head; (b) double impedance probe head.
10 m 50 m
Finally, the ‘measured’ water content is compared with the water content used to generate the waveform (Fig. 5). For the two single-impedance combinations (No. 1 and 2), the ‘measured’ water contents are close to each other and close to the values used to generate the waveform. However, deviations from the ‘true’ water content may be significant for the case where the probe head has two sub-sections having high impedance mismatch. 5
0.1 0.1
0.3
0.4
IMPOSED
Figure 6. Comparison between ‘measured’ water content and water content used to generate the waveform for different cable length.
considering in Equation 11 an equivalent resistance loss factor αR∗ determined as follows:
EFFECT OF CABLE LENGTH
The effect of cable length on signal travel time was investigated by considering a dissipative cable (αR = 130 sec−0.5 ). We investigated the cable lengths lcable = 1, 10, and 50 m. The different cable lengths were simulated by con∗ sidering a single fictitious length lcable = 1 m and
0.2
αR∗ = αR
lcable ∗ lcable
(13)
This approach was adopted because the time domain window becomes extremely large for excessive cable length and the Fourier Inverse Transform becomes problematic.
169
Since the cables acts as a low-pass filter, the case of dissipative soil was considered. In particular, we assumed As = 66.7 m2 /g, ρd = 1.66 g/cm3 , ρs = 2.71 g/cm3 and the free water parameters corresponding to N = 0.05 and T = 20◦ C (Table 1). These values of As , ρd , ρs are those used to simulate the waveforms measured in the clayey silt reported by Pozzato et al. (Ibid.). For each cable length, the waveform in air and water was used to calibrate the probe according to Heimovaara (1993). The water content derived from travel time analysis using Ledieu’s calibration was then compared with the theoretical value used to generate the waveform. Results from this analysis are shown in Figure 6. It can be observed that for a soil moderately dispersive (σfw,dc ∼0.5 S/m), the effect of cable length is not significant. This may not be the case for pore-water with high electrical conductivity and significant amount of bound water (soils having high cation exchange capacity).
6
The effect of temperature was investigated by considering a non-dissipative cable, a zero-length probe head, and As = 0. In this way, the signal losses are only associated with electrical conductivity of free water. We considered three different temperatures (T = 0, 20, and 40◦ C) and a moderately saline pore-water (Table 1). The waveform in air and water at T = 20◦ C was used to calibrate the probe according to Heimovaara (1993). The water content was then derived from travel time analysis using Ledieu’s
'MEASURED'
0.4
0.3
temperature 0 °C 20 °C 40 °C
0.1 0.1
0.2
7
CONCLUSIONS
The paper has presented a theoretical analysis to investigate sources of error in TDR water content measurement. It has been shown that double impedance probes may considerably affect the measurement for the case where sub-section head impedances are significantly different. For non-dispersive soils characterised by porewater with low electrical conductivity and negligible amount of bound water (low cation exchange capacity), temperature and cable length do not appear to have significant effect. REFERENCES
EFFECT OF TEMPERATURE
0.2
calibration and compared with the theoretical value used to generate the waveform. Again, it can be observed (Fig. 7) that for a soil moderately dispersive (σfw,dc ∼0.5 S/m), the effect of temperature is not significant.
0.3
0.4
IMPOSED
Figure 7. Comparison between ‘measured’ water content and water content used to generate the waveform for different combinations of T and N .
Brigham, E.O. 1974. The fast Fourier transform. PrenticeHall, Inc., Englewood Cliffs, N.J. Dane, J.H. & Topp, G.C., eds. 2002. Methods of soil analysis. Part 4-Physical Methods. SSSA Books Ser. 5. SSSA Madison, WI, USA. Gardner, C.M.K., Robinson, D.A., Blyth, K. & Cooper, J.D. 2001. Soil water content measurement. In K. Smith & C. Mullins (eds), Soil and Environmental Analysis: Physical Methods (Second Edition): 1–64. Marcell Dekker, Inc., 270 Madison Ave, New York. Jones, S.B., Wraith, J.M. & Or, D. 2002. Time domain reflectometry measurement principles and applications. Hydrol. Process. 16: 141–153. Hasted, J.B. 1973. Aqueous dielectrics. London: Chapman and Hall. Heimovaara, T.J. 1993. Design of triple-wire time domain reflectometry probes in practice and theory. Soil Sci. Soc. Am. J. 57: 1410–1417. Heimovaara, T.J. 1994. Frequency domain analysis of TDR waveforms 1. Measurement of the complex dielectric permittivity of soils. Water Resources Research. 30(2): 189–199. Heimovaara, T.J. & Bouten, W. 1990. A computer-controlled 36 channel time domain reflectometry system for monitoring soil water contents. Water Resour. Res. 26: 2311–2316. Heimovaara, T.J., Bouten, W. & Verstraten, J.M. 1994. Frequency domain analysis of time domain reflectometry waveform. 2. A four-component complex dielectric mixing model for soils. Water Resour. Res. 30(2): 201–209. Jones, S.B. & Or, D. 2001. Frequency-Domain methods for extending TDr measurement range in saline soils. Symposium and Workshop on TDR for Innovative Geotechnical Applications. Available at http://www.iti.northwestern. Kraus, J.D. & Fleisch, D.A. 1999. Electromagnetics with applications. McGraw-Hill.
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Lin, C.P. 2003a. Analysis of nonuniform and dispersive time domain reflectometry measurement systems with application to the dielectric spectroscopy of soils. Water Resour. Res. 39 DOI:10.1029/2002 WR001418. Lin, C.P. 2003b. Frequency domain versus travel time analyses of TDR waveforms for soil moisture measurement. Soil Sci. Soc. Am. J. 67: 720–729. Lin, C.-P. & Tang, S.H. 2007. Comprehensive wave propagation model to improve TDR interpretation for geotechnical applications. Geotech. Testing J. 30(2): 90–97. Ledieu, J., De Ridder, P., De Clerck, P. & Dautrebande, S. 1986. A method of measuring soil moisture by time domain reflectometry. Journal of Hydrology. 88: 319–328. Noborio, K. 2001. Measurement of soil water content and electrical conductivity by TDR: a review. Computers and Electronics in Agriculture. 31: 213–237. O’ Connor, K.M. & Dowding, C.H. 1999. Geomeasurements by pulsing TDR cables and probes. CRC Press.
Pozzato, A., Tarantino, A., McCartney, J. & Zornberg, J. (Ibid). Effect of dry density on the relationship between water content and TDR-measured apparent dielectric permittivity in compacted clay. This conference. Robinson, D.A., Jones, S.B., Wraith, J.M., Or, D. & Friedman, S.P. 2003. A review of advances in dielectric and electrical conductivity measurement in soils using TDR. Vadose Zone Journal 2: 444–475. Stogryn, A. 1971. Equations for calculating the dielectric constant of saline water. IEEE Trans Microwave Theory Tech 19: 733–736. Tarantino, A., Ridley, A.M. & Toll, D.G. 2008. Field measurement of suction, water content, and water permeability. Geotechnical and Geological Engineering. In press. Topp, G.C., Davis, J.L. & Annan, A.P. 1980. Electromagnetic determination of soil water content: Measurements in coaxial transmission lines. Water Resour. Res. 16: 574–582.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Effect of dry density on the relationship between water content and TDR-measured apparent dielectric permittivity in compacted clay A. Pozzato & A. Tarantino Dipartimento di Ingegneria Meccanica e Strutturale, Università degli Studi di Trento, Italy
J. McCartney & J. Zornberg University of Texas, Austin, TX, US
ABSTRACT: The paper presents an experimental investigation of the effect of dry density on dielectric apparent permittivity. It was observed that the effect was not significant, but not negligible for sensitive applications. It is shown that the effect of dry density can be successfully modeled using a three-phase ‘refractive index’ model. It is also shown that Topp’s equation can accurately predict water content provided bulk electrical conductivity is accounted for.
1
INTRODUCTION
The volumetric water content, θV , is a key variable in unsaturated soil mechanics and needs to be measured both in the laboratory and the field. Time domain reflectometry (TDR) is a technique that can be successfully used for this purpose. This technique is based on the measurement of the dielectric permittivity of the soil, Ka , which is in turn related to the volumetric water content through a suitable calibration curve. An empirical calibration curve was presented by Topp et al. (1980) suggesting a unique relationship between Ka and θV . However this curve was developed for agriculture soils which have dry densities typically lower than compacted soils used in geotechnical engineering. The purpose of this study is to investigate the effects of dry density on the Ka − θV relationship.
To prepare the samples for calibration, dry soil was placed in a motorized mixer and sprayed with a predetermined amount of demineralised water while continuously mixing the soil. Samples were prepared at water contents ranging from 9.7% to 17.7%. The moistened soil was stored for at least two days to allow moisture equilibration. A PVC mold having a diameter of 103 mm was used to compact the soil. The soil was compacted in six layers 19.4 mm thick using a drop hammer to obtain
2.2
2
MATERIAL AND SPECIMEN PREPARATION
A low plasticity compacted clay (RMA soil) was selected for use in investigating the impact of density on the TDR calibration. The soil has a plastic limit wP = 0.12, liquid limit wL = 0.27 and hygroscopic water content wH = 0.02. The grain size distribution showed it to have 0.24 clay fraction, 0.36 silt fraction, and 0.4 sand. The specific gravity of the soil is 2.71, and the saturated hydraulic conductivity is about 5 ∗ 10−6 m/sec. The maximum dry density, ρd , obtained using the standard Proctor compaction effort is 1.9 g/cm3 , and the optimum water content, wC was 12.9% (McCartney 2007).
d
2
[gr/cm^3]
1.9 1.8
proctor standard compaction rd = 1.4 gr/cm3 rd = 1.5 gr/cm3 rd = 1.7 gr/cm3
ZAV
(S =
2.1
S= S=
S=
100
%)
70% 60%
50%
1.7 1.6
S=
40%
1.5
S= 1.4
30%
1.3 9
10
11
12
13
14
15
16
17
wC [%]
Figure 1. Samples prepared for TDR calibration (the standard Proctor compaction curve is shown for reference).
173
specimen 116.4 mm high. Each layer was compacted which a same target dry density. Three series of samples were prepared, each with a different dry density. The dry densities and the gravimetric water content of the samples used in the TDR measurements are shown in Figure 1. 3 3.1
cable
Voltage, mV
2400
1600 TRANSIT TIME
1200
400
TDR installations
Three types of measurements were performed; measurements in demineralised water and air, in layers of water and air, and in compacted soil. For measurement in soil, the TDR probe was inserted centrally into the cylindrical specimen still in the mould (Figure 2). For measurement in water and in layers of air and water, the probe was inserted centrally in a container of the same size as the mould. The measurements were performed in a temperature-controlled laboratory (22 ± 1◦ C).
w ave guide
soil
PVC cylinder
end of waveguide
start of waveguide
2000
800
Instrumentation
116.4 mm
2s
103 mm Figure 2.
reflections in cable tester
2800
EXPERIMENTAL PROCEDURE
The TDR system used in this study consists of an electromagnetic step pulse generator with a fast rise time, a time equivalent sampling oscilloscope, and a trifilar waveguide. A commercially available TDR system was used in this study (MiniTrase). The oscilloscope and the step pulse generator were incorporated into the MiniTrase (6050X3) and the waveforms were collected via serial port with the TraseTerm software. An uncoated, 8-cm buriable probe (Model 6111, Soil Moisture Equipment Corp., Santa Barbara, CA) was used in this study. The probe had three 3 mm stainless steel rods having spacing, s, of 12.5 mm. A 3 m of low-loss RG-58 coaxial cable was used. 3.2
3200
Probe installation in the compacted soil.
start of incident pulse
0 0
4
8
12
16
20
24
t [ns]
Figure 3.
Complete reflection waveform.
3.3 TDR measurement A typical reflection waveform with a large time window, obtained from measurement in water, is shown in Figure 3. At t = 2ns, the voltage step pulse launched into the transmission line is recorded by the oscilloscope. The oscillations following the rising step are perhaps aberrations due to the internal circuit and reflection from the front panel. The signal becomes stable while travelling down the cable. At t = 15ns, a drop in voltage amplitude is detected when the signal enters the probe. This is associated with the impedance mismatch between the probe and the cable. A voltage rise is then observed at t = 18ns when the signal reaches the end of the rods (open-ended termination). Finally, multiple reflections occurs until a steady state is attained (not shown in the figure). The time required for the step pulse to travel along the waveguide is used to measure the apparent dielectric permittivity of the soil. The higher is the water content, the higher is the soil bulk permittivity and, hence the lower is the velocity at which the wave propagates into the guide (Robinson et al. 2003). The portion of the waveform of interest for travel time determination (box in Fig. 3 ) is shown in Figure 4. In the same figure, the waveforms in air and soil are also shown. The initial dip and the following bump are associated with the transit of the signal through the probe head. The time corresponding to the second ascending limb is associated with signal reflection at the end of the probe (Figure 4). In Figure 4 it can be observed that the waveforms are shifted with respect to time and voltage. This instrument response is surprising. The time at which the signal enters the probe after traveling along the cable should always be the same. Nonetheless, if the waveforms are ideally superposed, one would observe that the first descending limb (valley) is equal for
174
4000 air
3600
0.8
2800
reflection coefficient,
Voltage, V
3200 soil DVc-p
2400
water
2000 1600
DVc-p
DVc-p
air
Dt AIR
0.6
water
0.4
Dt*
0.2 0
baseline -0.2
tangent
1200 -0.4
6
7
8
9
10
11
12
8
t [ns]
Figure 4.
Dt WATER
t IN
800
8.5
9
9.5
10
10.5
t FIN 11
11.5
12
t [ns]
Figure 6. form.
Waveforms in air, water, and soil.
The Heimovaara interpretation of a TDR wave-
reflection coefficient
0.2 moving apex a
0.1
w
0 –0.1 –0.2
ascending limb dip in probe head
66% air 33% air ~3% air
Figure 5. Waveforms measured as the probe is moved from air to water as surrounding medium.
all waveforms whereas the subsequent first ascending limb (bump) is different. This suggests that the bump cannot be taken as a reference for the beginning of the rods as suggested by other authors (e.g. Or et al. 2002). To better understand the nature of the bump located after the first valley of the waveform, a series of measurements was carried out with the probe inserted vertically downward into a low permittivity layer (air) over a high permittivity layer (water). The waveforms collected with the probe sequentially dipped into water are presented in Figure 5. The apex of the bump is observed to move forward in time as the probe is removed from water. This confirms that the bump depends on the permittivity of the medium surrounding the rods and it cannot be taken as reference for the beginning of the rods. This has been demonstrated by Robinson et al. (2003). A different approach should be therefore developed to identify the beginning of the rods. It would be expected that the beginning of the rods lies somewhere along the first descending limb.
the signal enters the rods. The signal is represented in term of reflection coefficient, ρ. The time tIN is the time at which the signal enters the head of the probe. The time tFIN , obtained by the intersection between the line tangent to the second ascending limb is the time at which the signal is reflected at the end of the probe. The time t ∗ , which is the time taken by the signal to travel along the probe head to reach the beginning of the rods, and the effective length of the rods L∗ are determined by calibration in air and water. It is assumed that the reflection in water is the slowest, while the reflection in air is the fastest, providing bounds on the possible travel times. The relationship between the apparent permittivity Ka and the propagation velocity vP of the signal along the rods can be written as follows: vP =
tFIN
L∗ c = √ − tIN − t ∗ KA
(1)
where c is the speed of light in vacuum and (tFIN − tIN − Dt ∗ ) determines the value of DT. By combining measurements in air (Ka = 1) and water (Ka = 79.1), the values for t ∗ and L∗ equal to 0.136[ns] and 0.0792[m], respectively, were obtained. The time at which the signal enters the rods, (tIN + Dt ∗ ), was found to be very close to the first waveform valley. We therefore assumed this time could alternatively be taken as reference for the beginning of the rods. 4.2 Waveform interpretation
4 4.1
WAVEFORM INTERPRETATION Calibration
The approach suggested by Heimovaara (1993), shown in Figure 6, was used to determine the time at which
Two methods were considered to calculate the transit time from the reflected waveform. In method 1, the time tIN and tFIN were taken as shown in Figure 6, and the apparent permittivity was calculated by considering the values of L∗ and t ∗ derived from Equation 1. In method 2, the length of the rods L∗ was assumed to
175
be equal to the physical length (0.08 m). In this case, the time t ∗ was set to zero and tIN is taken at the first waveform valley.
5
The two methods are essentially equivalent. It may be concluded that, for this TDR system, the time associated with the first waveform valley can be successfully used to identify the beginning of the rods, for cases when TDR measurements in water and air are not available. The relationship between the apparent permittivity and the volumetric water content for the three series of samples, which are characterized by nominal dry densities of 1.4, 1.5, and 1.7 g/cm3 respectively, is shown in Figure 8. Topp’s equation (Topp et al. 1980) is also plotted as a reference (dotted line). It can be observed that the higher the dry density ρ d , the higher the apparent permittivity Ka at a given θV . This is expected because when ρ is increased, the air (Ka = 1) is replaced by solids having higher dielectric permittivity (Ka ∼ 5). Overall, all data are located above Topp’s equation.
RESULTS
A comparison between the two procedures used to determine Ka value is shown in the Figure 7. 14 13
Ka (method 1)
12 I1I
11 10
6
9
DISCUSSION
8
To assess the effect of dry density on dielectric permittivity, the three-phase Litchteneker ‘refractive index’ mixing model was considered:
7
√ 7
8
9
10 11 12 Ka (method 2)
13
14
Figure 7. Comparison of the two procedures used to obtain Ka.
ation ( as re 1980) feren ce
14
Topp ´s Eq u
13
12 rd = 1.7 g /cm3
Ka
11
10
rd = 1.5 g /cm3
rd = 1.4 g /cm3 8
7 0
0.05
0.1
0.15
0.2
0.25
0.3
qV measured
Figure 8. Ka versus θv for the three different dry densities (Ka determined using method 1).
ρREFd + ρd Ks − 1 + ϑ Kw − 1 ρs (2)
where K denotes the real part of the apparent permittivity, Ks and Kw are the permittivity of solids and water, respectively, ρs is the density of solids, ρREFd is a reference bulk dry density and ρd is the variation of dry density with respect to ρREFd . The real part of the apparent permittivity K was used in place of the apparent permittivity Ka to denote the fact that Equation 2 is written by assuming that the complex part (which reflects the electrical conductivity) is negligible. This model has been found to satisfactorily capture experimental data for the case of soils having low clay content and/or low specific surface (Roth et al. 1990; Robinson et al. 1999). The Equation 2 can be written as follows: √
9
K − 1=
K =
ρ KREFd + Ks − 1 ρs
(3)
where KREFd is the permittivity for ρd = 0. We assumed ρREFd equal to 1.5 g/cm3 because KREFd calculated using Equation 2 equals KTOPP for this value of ρREFd (Tarantino et al. 2008). In Figure 9, the measured apparent permittivities corrected by the factor ρ(Ks0.5 − 1)/ρs are plotted versus the volumetric water content θV together with the uncorrected data. It can be observed that corrected
176
3.8 3.6
(Ka') ^ 0.5
3.4 3.2 3 2.8
Topp's equation K'a
2.6
K'a , corrected for r effect D
2.4
qV measured 0.15
0.2
0.25
0.3
Figure 9. Apparent permittivity Ka data corrected for the effect of dry density.
a period of time of only 24 ns, which is not enough to measure the reflection coefficient at t ∼ ∞. To extrapolate the recorded waveform to higher times, we simulated the waveform according to the approach presented by Lin (2003) for multi-section transmission lines as described by Tarantino and Pozzato (Ibid.). For sake of simplicity, an ideal input function was considered. The specific surface As , was estimated from hygroscopic water content according to Dirksen and Dasberg (1993) assuming that a monomolecular layer of water envelops the clay particles. A value of 67 m2 /g was thus obtained. The measured and simulated waveforms are shown in Figure 11. We tentatively assumed the following values for the permittivity of free water, bound water and
a)
0.3 reflection coefficient,
data have significant lower dispersion suggesting that the ‘refractive index’ model adequately captures the effect of dry density. Nonetheless, data are located above Topp‘s equation. We checked whether bulk electrical conductivity could explain this discrepancy. In fact, a relative high electrical conductivity tends to increase dielectric permittivity as shown by the equation of apparent permittivity for a sinusoidal plane wave (Von Hippel, 1954):
0 –0.1 –0.2
10% of risetime
–0.3
tR~0.4ns
reflection coefficient,
0.1 0 –0.1
90% of risetime
–0.2
10% of risetime
–0.3 –0.4
tR~0.6ns
–0.5 8.5
9
9.5
10
10.5
11
11.5
12
t [ns]
Figure 10. Determination of risetime, tR , from the TDR waveform using the 10%–90% values in water (a) and soil (b).
measured waveform (r D = 1.67gr/cm3, w= 11.94%, qV = 19.9%) simulated waveform
0.2
(5)
where tR can be obtained according to the construction shown in It was observed that the effective frequency decreases from about 800 MHz to 550 MHz from water to soil respectively. This signal dispersion is due to a non-negligible electrical conductivity. Lower frequency waves are slowed down (see Equation 4, producing less steep second ascending limb. According to Topp et al. (1988), the bulk electrical conductivity, σa , can be calculated from reflection at t ∼ ∞. Unfortunately, waveforms were recorded by the Trase over
0.1
8
reflection coefficient,
ln(0.9/0.1) 2π · tR
ascending limb
b)
fEFF =
90% of risetime
0.2
–0.4
ε εa = (1 + 1 + ((εRELAX + σ/2πfEFF ε0 )/ε )2 ) 2 (4) where εa is the measured apparent permittivity, ε and ε are the real and imaginary part of the soil dielectric permittivity, respectively, εo the dielectric permittivity in the vacuum, σ is the bulk electrical conductivity and fEFF is the effective frequency in Hz. The effective frequency fEFF of the signal propagating in water and soil was calculated according to Strickland (1970) as follows:
0.4
0.1
0 –0.1 –0.2 –0.3 –0.4 8
8.5
9
9.5 t [ns]
10
10.5
11
Figure 11. Measured (ρs = 2.71 g/cm3 , ρD = 1.67 g/cm3 , θV = 0.2) and predicted waveform for soil (As = 66.7, εfw = 80.2, εs = 5, σbw = 15 S/m, σfw = 1.1 S/m).
177
0.3
3.8 t
3.6 3.4
0.1
3.2
0
(Ka') ^ 0.5
reflection coefficient
0.2
0.1 0.2
3 2.8 Topp's equation K'a
2.6
0.3
2.4 20
30
40
50
60
K'a, corrected
t [ns]
2.2
Figure 12. Simulated reflection coefficient from the plotted reflection at t ∼ infinite.
2 0.1
solids, εfw = 80.2, εfw = 5, and εs = 5, respectively, and σfw = 1.1 S/m and σbw = 15 S/m for the electric conductivity of free water and bound water, respectively. The entire simulated waveform was plotted and the value of the reflection coefficient was determined as equal to ∼0.2 (Figure 12). The bulk conductivity, σa , was calculated according to Topp et al. (1988): 1 ε0 cZ0 1 − ρ∞ 1 ε0 cZ0 2V0 σ = −1 ≡ 1 + ρ∞ Zc L VF Zc L (6) where ε0 is the permittivity of free space (8.854 · 10−12 F m−1 ), c is the speed of light in a vacuum (3 · 108 m s−1 ), L is the probe length (0.08 m), ρ∞ the reflection coefficient at infinite time (∼0.2), V0 is the voltage entering the head of the probe, VF the final voltage recorded by the oscilloscope after all multiple reflections had taken place, Zc is the characteristic impedance of the cable tester (50 W), and Z0 is characteristic impedance of the probe (220 W). A value of 1dS/m was obtained. To account for the effect of electrical conductivity on apparent permittivity, the empirical approach proposed by Wyseure et al. (1997) was considered: Ka = K + 1.432σ
(7)
where σ is the electrical conductivity in dS/m. If Equation 7 is substituted in Equation 3, the following equation is obtained: KTOPP =
√ 2 Ks − 1 Ka − ρd − 1.432 · σ ρs (8)
The values of Ka measured using TDR and the values corrected to account for the combined effect of
0.15
0.2
0.25
0.3
qV measured
Figure 13. Apparent permittivity Ka as result of the correction in term of dry density and bulk electrical conductivity.
ρd and σ (KTOPP in Equation 8) are plotted against volumetric water content θV . It can be observed that the corrected data collapse on Topp’s calibration curve. This demonstrates again that deviations from Topp’s equation occur for dry densities and bulk electrical conductivities outside the range investigated by Topp et al. (1980). Nonetheless, simple corrections could be introduced to account for these deviations.
7
CONCLUSIONS
An experimental investigation of the effect of dry density on dielectric apparent permittivity was carry out in this study. It was observed that the effect was not significant, but not negligible for sensitive applications. The effect of dry density was successfully modeled using a three-phase ‘refractive index’ model. Nonetheless, the measured permittivity corrected for dry density was still underestimated by Topp’s equation. We observed a decrease in effective frequency when measuring the waveform in the soil and we inferred the soil had non-negligible electrical conductivity. Since the waveform was recorded over a short period of time that was insufficient to reach steady-state conditions, the waveform was simulated to capture the reflection coefficient that would have been recorded at infinite time. This made it possible to estimate the bulk electrical conductivity and to further correct the measured Ka using an empirical equation. Topp’s equation was shown to match the corrected data.
178
REFERENCES Dirksen, C. and Dasberg, S. (1993). Improved calibration of time domain reflectometry soil water content measurements. Soil Sci. Soc. Am. J., 57: 660–667. Heimovaara, T.J. 1993. Design of triple-wire time domain reflectometry probes in practice and theory. Soil Sci. Soc. Am. J., 57: 1410–1417. Lin, C.P. (2003a). Analysis of nonuniform and dispersive time domain reflectometry measurement systems with application to the dielectric spectroscopy of soils. Water Resour. Res. 39. McCartney, J.S. (2007). Determination of the Hydraulic Characteristics of Unsaturated Soils using a Centrifuge Permeameter. Ph.D. Dissertation. The University of Texas at Austin. Or, D., VanShaar, T., Fisher, J.R., Hubscher, R.A. and Wraith, J.M. 2002. WinTDR99—Users guide. Utah State University – Plants, Soils & Metereology, Logan, UT. Robinson, D.A., Gardner, C.M.K. and Cooper, J.D. (1999). Measurement of relative permittivity in sandy soils using TDR, capacitance and theta probes: comparison, including the effects of bulk soil electrical conductivity. Journal of Hydrology, 223: 198–211. Robinson, D.A., Schaap, M., Jones, S.B., Friedman, S.P. and Gardner, C.M.K. (2003b). Considerations for Improving
the Accuracy of Permittivity Measurement using Time Domain reflectometry: Air-water calibration, effects of cable length. Soil Sci. Soc. Am. J., 67: 62–70. Roth, K., Schulin, R., Flühler, H. and Attinger, W. (1990). Calibration of TDR for water content measurement using a composite dielectric approach . Water Resources Research, 26 (10): 2267–2273. Strickland, J.A. (1970). Time-domain reflectometry measurements. Tektronix Inc., Beaverton, Oregon: 11–13. Tarantino, A., Ridley, A.M. and Toll, D. (2008). Field measurement of suction, water content and water permeability. Geotechnical and Geological Engineering, in press. Tarantino, A. and Pozzato, A. (Ibid). Limitations of travel time interpretation of reflection waveform in TDR water content measurement. Topp, G.C., Yanuka, M., Zebchuk, W.D. and Zegelin, S. (1988). Determination of Electrical conductivity using TDR: soil and water esperiments in coaxial lines.. Water Resources Research, 24(7): 945–952. Topp, G.C., Davis, J.L. and Annan, A.P. (1980). Electromagnetic determination of soil water content: Measurements in coaxial transmission lines. Water Resour. Res., 16:574–582. Wyseure, G.C.L., Mojid, M.A. and Malik. (1997). Measurement of volumetric water content by TDR in saline soils. European. Journal of Soil Science, 48: 347–354.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Spatial Time Domain Reflectometry (Spatial TDR) – Principles, limitations and accuracy R. Becker IMKO Micromodultechnik GmbH, Ettlingen, Germany
A. Scheuermann Institute for Soil Mechanics and Rock Mechanics, University of Karlsruhe (TH), Germany
S. Schlaeger Schlaeger Mathematical Solutions & Engineering, Horn, Bad Meinberg, Germany
C. Huebner University of Applied Sciences, Mannheim, Germany
N. Wagner Institute of Material Research and Testing (MFPA) at the Bauhaus University Weimar, Germany
ABSTRACT: Monitoring of transient soil moisture profiles yields valuable insight into soil hydraulic processes. A recently developed reconstruction algorithm allows deriving water content profiles along extended moisture probes from Time Domain Reflectometry (TDR) signals. Based on inverse modelling of the wave propagation along a transmission-line the algorithm calculates electrical parameter distributions. The method named Spatial TDR will be explained and the accuracy as well as the spatial and temporal resolution defining the possibilities and limitations of the procedure will be presented on practical examples.
1
INTRODUCTION
Many applications in geotechnical engineering, hydrology and agriculture require determining the transient water content profile characterizing soil hydraulic processes in unsaturated soils. However the monitoring of a sufficient number of soil moisture profiles can be costly, laborious and extraordinary invasive, especially if the profiles are determined point-wise by a large amount of single probes buried in soil. A recently developed reconstruction algorithm (Schlaeger 2005) allows computing complete soil water content profiles along elongated single moisture probes from time domain reflectometer (TDR) measurements in a short time. This method leads to a reduction of the number of probes accompanied by a higher spatial resolution of moisture profiles. The whole technology of soil moisture profile retrieval—including measurement devices and probes, reconstruction algorithm and calibration procedure—has been named Spatial TDR (Becker 2004, Huebner et al. 2005). This method is being developed and applied by the Soil Moisture Group (SMG),
an interdisciplinary research group at the University of Karlsruhe. This article gives a brief introduction into the fundamentals of TDR before the basic concept of STDR is explained with the emphasis on its algorithm and the initial probe calibration by way of a coated 3-rod-probe. The theoretical accuracy of the measured moisture profiles is assessed by means of electromagnetic (EM) field simulations. Laboratory and large-scale experiments were realized to evaluate the method and to compare the reconstructed water content profiles with comparable information of the real soil.
2 2.1
MEASUREMENT METHOD Dielectric properties of soils
Soil as a typical porous medium consists of three phases: solid particles (clay minerals and granulates) pore air and pore water in different forms of bounding (cf. Fig. 1). The fractions of the soil phases vary both in space—due to composition and density of
181
pulse generator voltage
oscilloscope
coaxial cable
length l
two wire transmission line (metallic fork)
incident signal reflected signal sum signal two wire line travel time
soil
time
Figure 2. Basic TDR set-up and signals. Oscilloscope and pulse generator are usually integrated in a single TDR device.
Figure 1. Dielectric (permittivity) and electric (resistivity) properties of the soil phases.
soil—and time—due to changing of water content and temperature. For the determination of the water content, one utilizes the fact that the effective relative dielectric permittivity of the soil depends on the fractions of the soil phases (Robinson 2004). The relation between water content and effective permittivity can be performed using specific laboratory calibration with gravimetric sampling. (e.g. Topp et al. 1980). Alternatively empirical, semi-empirical and theoretical mixing rules can be used as a relationship between dielectric properties of the soil and its water content (Tuncer et al. 2002). For highly conductive soils—e.g. for fine grained soils with clay contents—general empirical calibration equations fail due to the strong frequency dependency of the effective dielectric permittivity, whereas soil and probe specific calibration function or theoretical models can provide a satisfactory estimate of the water content (Cosenza & Tabbagh 2004, Kupfer et al. 2007). 2.2
Time Domain Reflectometry (TDR)
A TDR instrument, which consists of a pulse generator and an oscilloscope, emits a voltage step pulse VI(m) (t) via a feeding cable into a waveguide (e.g. a moisture probe) buried in the soil. When the propagating electromagnetic (EM) wave hits the transition between cable and probe it is generally split due to impedance discontinuity. One part is reflected and traveling back and the rest of the signal is transmitted into the waveguide, interacting with the surrounding soil. When the pulse reaches the probe end it is reflected again. Hence the incident signal VI(m) (t) (input, measured) excites the system under test (SUT, probe/soil) which reacts with voltage reflections whose superposition V0(m) (t) (output, measured) is sampled by the TDR instrument as a sum of both signals (schematic description in Fig. 2).
Figure 3.
Flat band cable as moisture probe.
The elapsed time between first and second main reflection is the pulse travel time along the SUT. This travel time can be transformed into average soil moisture or water content by appropriate calibration functions and/or mixing rules. This is the common evaluation procedure for TDR measurements.
2.3 Moisture probes (transmission line) The length of standard, non-insulated metallic forks as transmission lines are restricted to about 30 cm because of high electrical attenuation. For longer investigation areas insulated 2- or 3-wire transmission lines as rod-probes (cf. Becker 2004) or insulated flat band cables are used (Huebner et al. 2005). Such insulated flexible flat band cables are proposed for the use as elongated moisture probes with lengths of more than 0.5 m. In the past several cables with different geometries have been developed and manufactured, from simple concentric insulation to sophisticated multiwire structures with unilateral sensitivity. The flat band cable used in the most experiments within the SMG is shown in Figure 3. The cable consists of three copper wires covered with polyethylene insulation. The sensitive area around the cable extends approximately 3 to 5 cm. For the near surface observation of moisture profile changes 3-rod-probes are frequently used which are described in the next chapter.
182
Figure 5. The simplified moisture probe model consisting of bulk electronic parts. Above: coated 3-rod-probe as an example for a moisture probe (TDR waveguide); below: infinitesimal section of an equivalent circuit of the transmission line.
Figure 4. TDR-signals measured at a flat band cable, half of the cable is located in saturated soil.
3 3.1
propagation of a voltage pulse V (x, t) along the buried waveguide:
SPATIAL TDR PROCEDURE
∂ ∂2 + L(x)G (x) ∂t ∂t 2 ∂2 ∂L(x)/∂x ∂ V (x, t) = 0 − + L (x) ∂x ∂x2
L(x)C (x)
The inverse problem
The measured TDR signal contains far more than the travel time of the reflected electromagnetic signal. The reflectogram, especially the part between first and second main reflections at the probe’s beginning and end, is a finger print of the dielectric profile along the waveguide, which is mainly ruled by the water content. Figure 4 shows TDR signals measured with a flat band cable as sensor up to the half of the length located in saturated soil. Unfortunately the moisture distribution cannot be calculated directly from the TDR signal but has to be estimated indirectly. The basic idea of STDR is to transform the measured output signal V0(m) (t) into the soil moisture profile θ (x) along the probe by means of inverse modeling. The essence of this approach is to simulate the propagation of the TDR signal along the waveguide in time domain by employing a numerical model (forward problem) based on the telegraph equations. This simplified model assumes that the relevant properties of the transmission-line can be described by bulk electronic parts like resistors, inductors, and capacitors (Figure 5). Among the conditions for this electronic circuit model to hold the most important are: wave modes other than the transversal-electromagnetic (TEM) mode and frequency dependence of transmission-line properties may be neglected. The first condition requires a wellbehaving waveguide with little distortion on the signal propagation, the second is only met, if the losses in the SUT are not too large. Schlaeger (2005) derived the following wave equations from the circuit model for describing the
(1)
Capacitance C (x) and effective conductance G (x) are influenced by the soil water content distribution θ(x) along the waveguide. Inductance L (x) is a function of the transmission-line only and constant and known for coaxial cable and moisture probe. The spatial derivative of L (x) in (1) describes the change of inductance between coaxial cable and probe. Resistance R along the waveguide has been neglected. All parameters are given per unit length. Strictly spoken the equivalent circuit of Figure 4 is not totally correct, because the conductor G should be enclosed by two capacitors due to the rod coating. Therefore G is not the real ionic conductance of the soil but a kind of correcting parameter in the determination of C . According to former results we assume that this simplification does not have a large influence on the results. Equation (1) is solved numerically with appropriate initial and boundary conditions to simulate a TDR measurement V0(s) (t) for given C (x) and G (x). The result of the simulation is compared to the TDR measurement V0(m) (t). An optimization algorithm is used to modify the electrical parameters C (x) and G (x) until the simulated TDR reflectogram V0(s) (t) matches the measurement V0(m) (t)sufficiently well. The final parameter distributions resulting from the simulation are the best estimates of the electric properties along the probe in soil.
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3.2
Empirical relationship between capacitance and effective conductance
The wave equation (1) needs two parameter distributions C (x) and G (x). These parameter distributions could be found simultaneously by inverse modeling, if two independent TDR measurements were available for the same moisture probe, which is best possible with probes connected from both sides (double sided). Those kinds of probes can be constructed using flat band cables, which are frequently in use for monitoring purposes with elongated probes in earth structures like dikes (cf. Scheuermann et al. 2008, Huebner et al. 2005). In case of single sided probes it is reasonable to assume a relationship between C (x) and G (x), since both parameters are linked by soil moisture: higher water content leads to higher dielectric permittivity and higher conductivity. The following relationship is proposed:
1/C (ε) = 1/(ε · C1 ) + 1/C2
(3)
The rods of the 3-rod-probe presented here consist of stainless steel cores of 6 mm diameter with a 1 mm thick PVC coating. The rods are 30 mm apart. They are screwed into the probe head which connects them to a 50 Ohms coaxial cable. According to the equations (1) and (3) it is necessary to get the three parameters C1 , C2 and L for the rod probe. This can be done empirically by TDR pulse propagation velocities vi = v (εi ) measured for two different media with well known dielectric permittivities ε 1 and ε 2 , respectively. The pulse propagation velocity along the coated probe rods is: v(ε) = 1/ L · C (ε)
G (C ) G∞ · (1−exp(−(C −C0 )/Cd ), if C ≥ C0 , = 0, if 0 ≤ C ≤ C0 . (2) The parameters G∞ , C0 and Cd can be determined by soil and probe dependent calibrations.
3.3
as a probe specific calibration which can be easily solved for ε with the constant capacitances C1 and C2 :
The pulse velocity is determined empirically by measuring the time between the two main reflections in the TDR reflectogram. Combining equation (4) with (3) for the two materials one yields: C1 = (ε2 − ε1 )/(ε2 ε1 (v12 − v22 ) · L ) C2
From capacitance to dielectric permittivity
To derive the volumetric water content profile θ (x) the dielectric permittivity profile ε(x) of the soil/water/air mixture has to be extracted from the capacitance profile C (x) first. For the design of a simple moisture probe (cf. Figure 6) it is possible to find analytically a convenient parametric form for C (ε)
(4)
= (ε2 −
ε1 )/((ε2 v22
−
ε1 v12 )
and
·L)
(5)
The rod impedance Z can be used to get L : Z(ε) =
L /C (ε)
(6)
The impedance mismatch between coaxial cable and probe rods leads to a partial reflection of the incident excitation pulse. The amplitude of incident and reflected signal are denoted by AI and AR , respectively. Then the reflection coefficient yields: r(ε) = AI /AR = (Z(ε) − Z0 )/(Z(ε) + Z0 )
(7)
which can be determined experimentally from TDR measurements. Z0 = 50 Ohms is the impedance of the coaxial cable. The combination of the equations (5) and (6) yields: Figure 6. Capacitance C of a 3-rod-probe as a function of the soil’s dielectric permittivity ε. (a) segment of three parallel rods encompassed by soil; light gray: PVC coating; dark gray: metallic core; (b) equivalent circuit. C1 , C2 : constant capacitance parameters determined by the probe’s geometry and material.
L = (1 + r(ε))/(1 − r(ε)) · Z0 /v(ε)
(8)
The equations (5) and (7) are sufficient to determine the dielectric parameter ε of the soil from TDR signals when a coated rod-probe is used (cf. Fig. 6).
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3.4
From dielectric permittivity to water content
The second step performs the transition from dielectric permittivity to water content based on the phase fractions of the soil solid particles, water and air. An empirical relationship between ε and θ often used in TDR applications was found by Topp (1980). For the presented example a more simple but also less general empirical formula was found derived from laboratory experiments with a loamy sand: θ(ε) = 30.1 · ε 0.31 − 41.1(%vol)
4
Figure 7 displays the TDR reflectograms simulated with MWS and reconstructed by the Spatial TDR algorithm. The predefined and reconstructed soil moisture profile for the sequence wet/moist/dry is shown in Figure 8. Two cases were realized: one with and the other without consideration of ionic conductivity σ (lossy and lossless case). Although the difference between simulated and measured TDR reflectogram is very small, the deviation in the moisture profile can be quite large.
(9)
ACCURACY OF SPATIAL TDR
4.1 Electro-dynamic simulation To test the Spatial TDR method with 3-rod-probes several TDR reflectograms were simulated with Microwave Studio (MWS), an EM simulation tool based on the full wave solution of Maxwell’s equations. In the numerical model the 3-rod-probe is embedded in a three layer material, whose dielectric permittivity and ionic conductance can be modified. A step pulse of 1 Volt amplitude and 1 GHz bandwidth is fed into the probe. The simulated TDR reflectograms are used for three purposes: 1. determination of the probe parameters according to (4) and (6), 2. determination of the empirical C − G -relationship (7), and 3. generation of test reflectograms to assess the quality of the Spatial TDR algorithm.
4.2
Figure 7. TDR reflectograms simulated by MWS and the corresponding signal approximations resulting from the reconstruction algorithm. Material sequence wet/moist/dry. Energy losses due to ionic conductance lead to a strong falling trend of the TDR signals.
Numerical investigations
To assess the quality of the algorithm which determines the water content profile from a TDR reflectogram by inverse parameter estimation, the MWS is fed with three soil layers of different moisture. Table 1 shows the applied soil parameters. Each simulated reflectogram together with the excitation pulse was fed into the Spatial TDR algorithm and a reconstruction process was conducted to retrieve the soil moisture profiles, which should match the predefined one as close as possible.
Table 1.
Material parameters used in Microwave Studio. Moisture state
‘dry’ ‘moist’ ‘wet’
θ (%vol)
ε (−)
σ (mS/m)
0.5 8 13.5
2.9 4.9 6.8
0 14 23
Figure 8. Moisture profile, sequence wet/moist/dry, predefined in the MWS model and reconstructed by means of the Spatial TDR algorithm.
185
transient soil moisture profiles under irrigation with high spatial and temporal resolution (Becker 2004, Scheuermann et al. 2008).
5 5.1
Figure 9. Spatial TDR application to a real soil moisture profile. Measured and reconstructed TDR reflectograms for short and long coaxial cable as connecting cable.
Figure 10. Spatial TDR application to a real soil moisture profile. Material sequence dry/moist/wet. Reconstruction results compared to volumetric water content of soil samples determined by oven drying. Differences up to 3%vol are due to imperfect calibration of the real 3-rod-probe.
4.3
SPATIAL AND TEMPORAL RESOLUTION OF SPATIAL TDR Sensitivity of TDR Probes
A simplification frequently utilized in TDR applications is the use of an idealized equivalent circuit (c. f. Fig. 5) for the sensor without consideration of losses due to the skin-effect or radiation from the sensor as well as the assumption of a homogeneous sensitivity distribution along the sensor (Heimovaara et al. 2004, Huebner & Kupfer 2007). In addition, a frequently arising problem in various applications is the direct contact between sensor and surrounding material. For these reasons the sensitivity of a flat band cable as moisture probe was investigated with 3D electromagnetic finite element modeling under consideration of the frequency-dependent complex dielectric permittivity (Wagner et al. 2007). One main result of this investigation is that coupling problems caused by air or water gaps lead to dramatic travel time distortion even for very small gaps. An air filled gap with a thickness of 0.25 mm on both sides of a flat band cable sensor already leads to the drastic underestimation of water content of approximately 36%. In contrast a drastic overestimation occurs in the case of a water filled gap for the same gap size. Therefore, an accurate installation of the moisture probes is stringently necessary for the quantitative in situ water content determination.
Laboratory investigation
To test Spatial TDR in laboratory a box with three chambers of 0.2 m length each was prepared in accordance to the MWS numerical model and filled with soil of predefined moisture (see Table 1). A 3-rod-probe of 0.6 m length (Figure 4) was installed such that it crossed all chambers. TDR measurements were performed with a Tektronix metallic cable tester 1502B. A comparison between measured and reconstructed TDR-signals for different lengths of the connecting coaxial cables is given in Figure 9. With each material sequence four soil samples of known volume were taken from each chamber. Their volumetric water content was determined by oven drying. Figure 10 shows the result for the material sequence dry/moist/wet. The overall accuracy of Spatial TDR with coated rod probe is sufficient for many applications in soil science. A lysimeter experiment with 1 m3 loamy sand showed that the method is capable of tracking
5.2
Laboratory and in situ comparison
An experiment for the investigation of transport of volatile organic compounds in a medium grained sand (grain size 0.2 to 1 mm) was conducted under different moisture conditions to verify the spatial variations of the water content distribution. For the Spatial TDR measurements flat band cable connected from both sides were used. Figure 11 shows the temporal process of redistribution of water after a one hour lasting irrigation from top. Graph d) of Figure 11 shows a comparison of the volumetric water content between the reconstruction and results from the oven-drying technique at 105◦ C. An average uncertainty of ±2.3% was determined. Figure 12 shows the result of Spatial TDR measurements in a full-scale dyke model (cf. Scheuermann et al. 2008) in comparison with water pressure measurements conducted at the water-proof base of the dyke.
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correct installation of probes in soils plays a decisive role for the accuracy of the measurement results. The examples show clearly the functional capability of Spatial TDR for the measurement of water content distributions. REFERENCES
Figure 11. a)—c) Redistribution of the moisture profile after an irrigation to the steady state (dashed line) and d) comparison with gravimetric measurement of several soil samples (∗).
Figure 12. Saturation distribution inside a dyke as result of Spatial TDR measurements.
The measured phreatic line and the location of the transition from the wet to the dry zone correspond very well. Underneath the phreatic line in the ‘saturated’ zone different values below full saturation can be recognised indicating a fairly high residual rate of air remaining in the pores. This observation was also verified by independent measurements during the steady state condition. The changes in water content are reconstructed with a spatial accuracy of about 3 cm and an average deviation of ±2% compared to independent water content measurements.
6
CONCLUSION
Spatial TDR is a new innovative method for the investigation of moisture distributions in porous materials with high resolution in space and time. However the accurate use of Spatial TDR requires calibration procedures both for the probe and the soil. Furthermore the
Becker, R. 2004. Spatial Time Domain Reflectometry for Monitoring Transient Moisture Profiles. Ph.D. thesis, Inst. for Water and River Basin Management, Univ. of Karlsruhe. Cosenza, P. & Tabbagh, A. 2004. Electromagnetic determination of clay water content: role of the microporosity. Applied Clay Science, 26 (1–4):21–36. Heimovaara, T.J., Huisman, J.A., Vrugt, J.A. & Bouten, W. 2004. Obtaining the spatial distribution of water content along a TDR probe using the SCEM-UA bayesian inverse modelling scheme. Vadose Zone J. 3:1128–45 Huebner, C. et al. 2005. Advanced measurement methods in TDR for soil moisture determination. In K. Kupfer (ed.), Electromagnetic Aquametry: 317–347. Springer. Huebner, C. Kupfer, K. 2007. Modelling of electromagnetic wave propagation along transmission lines in inhomogeneous media. Meas. Sci. Technol. 18:1147–1154. Kupfer, K., Trinks, E., Wagner, N. Huebner, C. 2007. TDR measurements and simulations in high lossy bentonite materials, Meas. Sci. Technol. 18:1118–1136. Robinson, D.A. 2004. Calculation of the Dielectric Properties of Temperate and Tropical Soil Minerals from Ion Polarizabilities using the Clausius-Mosotti Equation. Soil Sci. Soc. Am. J. 68:1780–1785. Scheuermann, A. et al. 2008. Spatial Time Domain Reflectometry (Spatial TDR)—On the use in geotechnics and geohydraulics. First European Conference on unsaturated soils; Proc. intern. symp. Durham, 2–4 July. Schlaeger, S. 2005. A fast TDR-inversion technique for the reconstruction of spatial soil moisture content. Hydrol. Earth Sys. Sci. 9:481–492. Topp, G.C., Davis, J.L. & Annan, A.P. 1980. Electromagnetic determination of soil water content: Measurement in coaxial transmission lines. Water Resour. Res. 16 (3):574–582. Tuncer, E., Serdyuk, Y.V. & Gubanski, S.M. 2001. Dielectric mixtures—electrical properties and modelling. IEEE Transactions on Dielectrics and Electrical Insulation 9:809–828. Wagner, N., Trinks, E. & Kupfer, K. 2007. Determination of the spatial TDR-sensor characteristics in strong dispersive subsoil using 3D-FEM frequency domain simulations in combination with microwave dielectric spectroscopy. Meas. Sci. Technol. 18:1137–1146.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Spatial Time Domain Reflectometry (Spatial TDR) – On the use in geohydraulics and geotechnics A. Scheuermann, A. Bieberstein & Th. Triantafyllidis Institute for Soil Mechanics and Rock Mechanics, University of Karlsruhe (TH), Germany
C. Huebner University of Applied Sciences, Mannheim, Germany
R. Becker IMKO Micromodultechnik GmbH, Ettlingen, Germany
S. Schlaeger Schlaeger Mathematical Solutions & Engineering, Horn, Bad Meinberg, Germany
N. Wagner Institute of Material Research and Testing (MFPA) at the Bauhaus University Weimar, Germany
ABSTRACT: Time Domain Reflectometry (TDR) is a widely-used tool for the point-wise determination of water contents in soils, especially in hydrology and soil-physics. Another well-known field of application of TDR is the observation of deformation processes in soils or rocks. The development of Spatial TDR offers new fruitful possibilities in geohydraulics and geotechnics. With Spatial TDR it is possible to determine physical properties of the soil along elongated transmission lines. The paper presents completed and ongoing research projects in which the determination of the spatial and temporal evolution of state variables like water content and pressure play an important role.
1
INTRODUCTION
The hydraulic and the mechanical behavior of unsaturated soils depend on several state variables. Firstly water content and suction should be named, which are both connected to each other via the soil water retention curve. Others are the soil density and the stresses involving deformations preferentially along shear zones. For the safety assessment of earth structures the experienced geotechnical engineer has to rely on quantitative information on the spatial as well as temporal evolution of these state variables. The electromagnetic measurement method Time Domain Reflectometry (TDR) offers different helpful solutions for the observation of these state variables. The most well known application of TDR is the measurement of water content at a single point, for example for the monitoring of landfill covers (e.g. Schofield 2001). Furthermore, water content measurements with TDR on a field scale are used for intensive sampling
(e.g. Long et al. 2002) and also for the determination of soil hydraulic properties (e.g. Heathman & McAfee 2006). TDR is also well-known in geotechnical monitoring for the shear zone localization, e.g. in rock masses (Dowding et al. 1989) as well as in landslides (Kane et al. 2001). In this regard the accuracy of the so-called TDR extensometers is better than ±0.5 mm. With the development of Spatial TDR, for the first time it is possible to determine the spatial distribution e.g. of water contents for practical purposes along elongated transmission lines. An introduction to the Spatial TDR procedure is given in Schlaeger (2005) and Becker et al. (2008). In this paper the use of Spatial TDR as a monitoring system for dams and dykes is presented first. Another major application is the measurement of moisture in small catchment areas in order to improve flood forecasting. Finally, a novel application of TDR is presented to determine the spatial distribution of mechanical pressure along transmission lines.
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2 2.1
MONITORING OF DAMS AND DYKES Full-scale dyke model
The transient seepage through dykes due to a hydraulic stress depending on the initial moisture condition was investigated on a full-scale dyke model (Fig. 1). The dyke is built up homogeneously with sand (grain size 0.2–2 mm) and has a waterproof sealing consisting of plastic sheeting as a base, so that the water within the dyke body flows to a drain at the toe of the landside slope. In order to simulate flood events, a basin is included in the construction. The dyke is equipped with pore water gauges at the base for measuring the hydraulic head and with flat band cables for measuring the spatial water content distribution using Spatial TDR (cf. Fig. 2). The TDRsystem consists of 12 flat band cables from 1 to 3 m in length, which are installed vertically inside the dyke. They are connected with coaxial cables at both ends to a multiplexer and a TDR device in a box on the crest of the dyke. The data collection and controlling equipment (PC) of the multiplexer and the TDR device are placed in a measuring container at the toe of the landside slope (Figs. 1, 2). 2.2
Measurement results
Different physical flood simulation tests were carried out on the dyke model (Scheuermann & Bieberstein 2006). Figure 3 shows water content measurements
Figure 1. Full-scale dyke model at the Federal Waterways and Research Institute in Karlsruhe during a flood simulation test in December 2000 (steady state of seepage condition).
Figure 2. Setup of measuring devices with positions and length of the flat band cables and positions of piezometer gauges on the base of the dyke model.
Figure 3. Distributions of saturation during a flood simulation test on the full-scaled dyke model.
as distributions of saturation indicating different hydraulic situations during the transient hydraulic process of water infiltration. The positions and lengths of the flat band cables are shown as dots and the values beside the dots show the measured saturation at these locations (cf. Fig. 2). For better clarity the water content distributions are interpolated over the cross-section of the dyke. These kinds of measurements during the experiment are available at a temporal resolution of 15 min. On the basis of these experiments, it was possible to demonstrate the influence of initial water content distributions on the transient seepage through dykes. However, with this system it is also possible to measure small changes in the distribution of the water content. Since 2000, water content has been measured on the dyke model almost continuously with Spatial TDR. Apart from any sprinkler irrigation during the summer time to water the grass cover, the water content changes are mainly influenced by precipitation and evapotranspiration. Depending on these hydraulic boundary conditions it is possible to use the dyke as a lysimeter to characterize and investigate the water balance processes. Figures 4 and 5 show the moisture situation inside the dyke with the precursory precipitation events as well as the discharge measured near the drain at the downstream slope. As can be seen from Figures 4 and 5, the water content distributions show distinctive differences not only concerning the mean saturation (given in the graphs), but also concerning the distribution of the water inside the dyke. In particular it should be mentioned that during long periods with precipitation that occurred several times in March 2001 (see Fig. 5) the water
190
Figure 6. Plan of the measurement site at the river Unstrut in Thuringia, Germany.
Figure 4. Moisture distribution inside the dyke on the 31st May 2002 with precursory meteorology over 16 days.
Figure 5. Moisture situation inside the dyke on the 26th March 2001 with precursory meteorology over 16 days.
content primarily increased within a certain depth from the dyke surface, forming an area in the middle of the dyke cross-section, which is almost unchanged with respect to the water content compared to the rather dry situation shown in Figure 4. One explanation for this observation is the lateral movement of water in the wet zone, which occurs frequently in combination with fingering effects. During a precipitation experiment, observations were made indicating such phenomena (Scheuermann & Bieberstein 2007). 2.3
Monitoring system for real dykes
The long-term measurements on the full-scale dyke model have proven that the preliminary hydrological and meteorological events lead to a water content
distribution inside the dyke, which is characteristic for the previous hydrologic events. Furthermore, the investigations on the dyke model have shown that the transient seepage is influenced considerably by the initial moisture content inside the dyke. Due to these findings, it confirms that Spatial TDR can be used to develop a monitoring system for river dykes, which can also be adapted to other embankments or earth structures like slopes. In cooperation with the Institute of Material Research and Testing (MFPA) at the Bauhaus University in Weimar, two measurement systems have been installed in real dykes along the river Unstrut and the river Elbe. Along the river Elbe one dyke section is monitored on 6 cross-sections over a distance of 250 m. The smaller measuring location on the Unstrut (cf. Fig. 6) can be used as a reference object, since flood events can be artificially initiated using a water retaining structure. This project is being carried out within the national research program ‘‘Risk management of extreme flood events—RIMAX’’.
3
MOISTURE SENSING IN HYDROLOGY
3.1 Lysimeter investigations Especially in small catchments, the development of flooding depends on the initial moisture situation within the catchment area due to a reduced storage capacity of the soil. The moisture distribution in the top few decimeters is decisive for surface runoff generation. To investigate the development of water content distribution near the top surface 3-rod-probes were developed and tested using Spatial TDR (Becker 2004, Becker et al. 2008). In order to test the suitability of Spatial TDR for the observation of the small-scale variability of water content distributions, infiltration experiments were conducted in a lysimeter (Fig. 7).
191
The soil used for the experiments was a silty sand with a saturated hydraulic conductivity of kf ≈ 10−5 m/s. The artificial precipitation was achieved using a spray nozzle bar. For comparative purposes additional moisture measuring devices were included in the lysimeter. Figure 8 shows the results of water content profile measurements at two different 3-rod-probes during an infiltration experiment. Since deliberate inhomogeneities were included in the sample in the lysimeter the moisture profiles show different temporal evolutions. At time step 0 both moisture profiles show disturbances, most probably due to differences in the density within the soil sample. These disturbances were persistent over the whole experiment. The graph
on the right in Figure 8 shows a more or less continuous infiltration of water into the sample. The moisture front passed the end of the probe after 180 min. In contrast, the temporal evolution of the moisture profile on the left of Figure 8 shows completely different temporal behavior. After 60 min. the infiltration seemed to stop at a depth of about 10 to 12 cm. After 180 min. the profile evolution indicated horizontal water movement. Only the combination of measurement results from several probes provides a good basis for the assessment of water movements.
Figure 7. Lysimeter holding 1 m3 of soil. 1: tubular steel frame, 2: soil; 3: probe connecting coaxial cables; 4: probe multiplexer; 5: spray nozzle bar; 6 and 7: additional smallscale moisture measuring devices.
Figure 9. Interpolated soil moisture distribution on two different measurement dates registered at 46 2-rod-probes. Dark grey: wet, light grey: dry condition. A cross-section along the black line is given in Figure 10.
Figure 8. Water content profiles measured at two 3-rodprobes during an. infiltration experiment lasting 360 min.
Figure 10. Water content distribution in the cross-section along the black line shown in Figure 9.
3.2 In situ application A first in situ application of the system was carried out at the Goldersbach catchment near Tübingen (Figs. 9 and 10). In this case 46 2-rod-probes were installed. The aim of this application was to measure the extension of a saturation zone both horizontally as well as vertically. An ephemeral creek divides the measurement site, which is dominated by podzolic soils.
192
The TDR measurements were reconstructed yielding water content profiles along the 60 cm long 2-rodprobes. For a quasi three-dimensional soil moisture distribution, the results were interpolated between the probes. Figure 9 shows a two-dimensional map of the average moisture for a dry (A) and wet (B) condition. The growth of the zone of high average water content is evident. An example of a vertical cross-section through the soil is given in Figure 10. A wet zone in the deeper soil regions can be clearly seen.
4 4.1
MEASUREMENT OF PRESSURE PROFILES
Figure 12. Measured and reconstructed TDR reflections for profile measurements of buckled steel strips.
Laboratory experiments
Many applications in geotechnical engineering require the knowledge of total pressure distributions. A novel sensor makes it possible to determine pressure profiles from Spatial TDR data. The design of the sensor is based on a rubber-insulated transmission line. Due to mechanical forces, the distance between the conductors of the transmission line is changed, which leads to a spatial distribution of the capacitance and inductance of the sensor properties. The resulting partial reflections of an incident step pulse are used to reconstruct the physical parameter distributions. Detailed information on the reconstruction algorithm are given in Scheuermann & Hübner (2008). The reconstruction procedure was validated in a simplified laboratory experiment. Steel strips (20.5 mm in width and 1.1 mm thick) were used as conductors for a 102 cm long transmission line (see Figure 11). The TDR signal was launched at a distance of 1 cm from the end of the strips into the transmission line. In this way, the actual length available during a TDR-measurement was reduced to 101 cm. The steel strips were bent at regular intervals of 25 cm. Thus four areas were adjusted at a more or less constant distance. The transmission line was calibrated by means of TDR measurements with even steel strips, in order to obtain a calibration function between conductor distance and capacitance. The results of the test were verified by numerical calculations (Scheuermann & Hübner 2008).
Figure 13. Measured and reconstructed distances between the conductors for the profile measurement.
The validation of the reconstruction algorithm is conducted with TDR-measurements, which are recorded for different profiles of the steel strip distances. Figure 12 shows an example of a measured reflected signal (solid line) of a profile and its reconstruction (dashed line). The calibration function mentioned is used to determine the distance between the conductors from the inversely adjusted capacitance profile (cf. Fig. 13). When compared, the reconstructed and measured distance profiles agree satisfactorily. The overshoot at steep edges and other deviations can be attributed to the spatial resolution of 2.5 cm of the algorithm, timing/amplitude errors in the TDR instrument, end capacitance effects and other non-ideal properties of the transmission line. 4.2 Prototype development
Figure 11. sion line.
Bent steel strips as inhomogeneous transmis-
A prototype sensor for geotechnical applications has been developed and investigated. It consists of two
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Figure 14.
to minimize outer influences on the electromagnetic field (cf. Fig. 14). The aim of the investigations with the prototype design is to demonstrate the general use of this measurement technique under real conditions. In order to prove the spatial sensitivity for the localisation of pressure changes, simple experiments were conducted with a sensor of the prototype design 113 cm in length. For this purpose, the sensor was placed in a loading frame. The sensor was loaded at four different positions using flat weights and rigid polystyrene blocks to distribute the load over a specific section (20 cm). The step-wise load at the different positions was achieved with weights of 10 kg each. After each load step TDR measurements were conducted from both sides of the sensor, which increases the information content of a measurement for each load condition. Figure 15 shows the evolution of the TDR traces for every load condition of the loading phase. The initial condition without load (0 0 0 0) forms the upper border of the graph. With every load step the TDR trace changes due to the changing capacitance respectively due to the changing impedance. The resulting difference forms an area which is highlighted in a grey colour (cf. legend top right). The photo shows the load conditions 10 30 20 10. The top graph shows the TDR measurements from position 1 and the graph in the middle the measurements from position 4. The bottom graph shows the differences of the superposed TDR traces compared to the initial condition. The evolution of the TDR traces shows clearly the changes of the conductor distance due to the mechanical load. In contrast to the distinct changes in the distances on the profiled transmission line presented above, the changes in the distance are smoother, which can be also seen in the evolution of the TDR traces. In particular, the presentation of the differences implies a parabola like distribution of the distances below the polystyrene blocks at each load position.
Diagram of the prototype sensor.
5
Figure 15. Stepwise loading test with the long prototype sensor: photo: load configuration 10 30 20 10 (for illustration purposes) above: TDR traces measured from left end (near position 1) middle: TDR traces measured from right end (near position 4) below: differences of the superposed TDR traces relative to the initial condition (0 0 0 0).
steel-strips (15 mm in width and 0.4 mm thick) with rubber foam (approx. 9.7 mm thick) as dielectric material. At the free surfaces of the steel strips (above and below the sensor) 6.9 mm thick rubber sealings are fastened with glue serving as electric insulation in order
CONCLUSIONS
The applications of Spatial TDR presented clearly show the wide applicability of this new method. The great advantage of Spatial TDR is its high resolution both in space and time, which is required for monitoring purposes, especially for transient processes. Hence Spatial TDR is applicable on different scales, from a laboratory scale of several decimeters (cf. Becker et al. 2008) up to a field scale of several meters (Scheuermann & Bieberstein 2006). In this respect it should be emphasized that— besides the reconstruction algorithm—Spatial TDR includes hardware components like multiplexers, probes and additional electronic devices and the
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corresponding controlling software (cf. Becker 2004, Hübner et al. 2005). Although the observation of the unsaturated water movement is still the major field of application, other applications—especially in geotechnics—are under development, such as the measurement of pressure distribution.
REFERENCES Becker, R. 2004. Spatial Time Domain Reflectometry for Monitoring Transient Moisture Profiles. Ph. D. thesis, Inst. for Water and River Basin Management, Univ. of Karlsruhe. Becker, R., Scheuermann, A., Schlaeger, S., Hübner, C. & Wagner, N. 2008. Spatial Time Domain Reflectometry (Spatial TDR)—Principles, limitations and accuracy. First European Conference on unsaturated soils; Proc. First European Conference on Unsaturated Soils, Durham. Dowding, C.H., Su, M.B. & O’Connor, K. 1989. Measurement of rock mass deformations with grouted coaxial antenna cables. Rock Mechanics and Rock Engineering, 22:1–23. Heathman, G.C. & McAfee, J. 2006. Measuring soil hydraulic properties using dielectric sensors. TDR 2006, Purdue University, Proc. https://engineering.purdue.edu/ TDR/Papers. Huebner, C., Schlaeger, S., Becker, R., Scheuermann, A., Brandelik, A., Schaedel, W. & Schuhmann, R. 2005. Advanced measurement methods in Time Domain
Reflectometry for soil moisture determination. In Klaus Kupfer (ed.), Electromagnetic Aquametry: 317–347. Springer. Kane, W.F., Beck, T.J. & Hughes, J.J. 2001. Applications of Time Domain Reflectometry to landslide and slope monitoring. TDR 2001, Proc. http://www.iti.northwestern.edu/ tdr2001/proceedings. Long, D.S., Wraith, J.M. & Kegel, G. 2002. A heavyduty Time Domain Reflectometry soil moisture probe for use in intensive field sampling. Soil Sci. Soc. Am. J. 66:396–401. Scheuermann, A. & Bieberstein, A. 2006. Monitoring of dams anddikes—watercontentdeterminationusingTimeDomain Reflectometry (TDR). 13. Danube European Conference on Geotechnical Engineering: Ljubljana, Slovenia, Mai 29–31, 2006, ISBN 961-90043-8-8, 2: 493–498. Scheuermann, A. & Bieberstein, A. 2007. Preferential water movement in homogeneous soils. Proc. Int. Symposium on Mechanics of Unsaturated Soils, March 7–9, Weimar, 461–473. Scheuermann, A. & Hübner, C. 2008. On the feasibility of pressure profile measurements with Time Domain Reflectometry (TDR). IEEE Trans. Instr. Meas. (accepted). Schlaeger, S. 2005. A fast TDR-inversion technique for the reconstruction of spatial soil moisture content. Hydrology and Earth System Sciences 9: 481–492. Schofield, T.G. 2001. Long-term stability of Time Domain Reflectometry measurements in a multi-layer field experiment. TDR 2001, Proc. http://www.iti.northwestern.edu/ tdr2001/proceedings.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Water content dynamics in unsaturated soils – Results of experimental investigations in laboratory and in situ A. Scheuermann Institute for Soil Mechanics and Rock Mechanics, University of Karlsruhe (TH), Germany
ABSTRACT: The unsteady movement of water frequently involves so-called ‘‘dynamic effects’’. So far, most investigations regarding these effects have been mainly focused on the drainage processes starting from full saturation, which represents only one aspect concerning questions on dynamic effects. The contribution presents measurements obtained during laboratory and in situ experiments revealing new aspects of these effects in conjunction with infiltration and alternating hydraulic stresses.
1
2
INTRODUCTION
Dynamic effects in connection with multi-phase or unsaturated water flow have been observed many times in experimental investigations, which generally arise as temporarily delayed changes in the water content (Topp et al. 1967) or in the outflow (Hollenbeck & Jensen 1998). However, most of the experiments conducted were not designed especially to investigate these effects. They were carried out in order to verify Richards’ equation (Biggar & Taylor 1960), to investigate the soil properties affecting soil water characteristics (Elzeftawy & Mansell 1975) or to determine the parameters describing the soil water characteristic curve (Wildenschild et al. 2001). An overview of experiments showing dynamic effects is given by Hassanizadeh et al. (2002). These experimental investigations clearly show that dynamic effects are significant in both granular and fine-grained soils in drainage and infiltration. However, in the literature (cf. Wildenschild et al. 2001, Hassanizadeh et al. 2002) the mechanisms discussed as being the cause of these dynamic effects are focussed mainly on drainage. The possible mechanisms for the occurrence of dynamic effects during infiltration or even for cyclic hydraulic conditions, i.e. the alternate infiltration and drainage of water, have not been investigated in detail so far. In the following, measurement results are presented, which were observed in the laboratory using column test apparatus. In situ experiments on a full-scale dyke model are also shown.
SOIL USED IN THE EXPERIMENTS
The soil used in the experiments was a well graded sand with grain sizes between 0.2 and 2 mm. The densities of the sand in both experiments were similar corresponding to a density index Dr = (nmax − n)/ (nmax −nmin ) ≈ 0.6 with porosity n of the material, the maximum being nmax and the minimum nmin . Based on this density index, the pore constriction size distribution of the sand was calculated using a numerical method (cf. Scheuermann et al. 2008). Both the grain size and the pore constriction size distributions are shown in Figure 1. With regard to the well graded distribution of the grain size as well as the distribution of the pore constriction size, the soil water retention curve of the sand
Figure 1. Grain size and pore constriction size distribution of the well graded sand used for the experiments.
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Figure 2. Primary drainage und main wetting curve of the sand with fitting curves using the model acc. to Mualem (1976). Figure 4. Diagram of the column test apparatus with the measuring devices used.
Figure 3. Unsaturated hydraulic conductivity of the sand ac-cording to the model of Mualem (1976).
shows a distinct transition from a saturated to an unsaturated condition (see Figure 2). The corresponding air entry value |ψAEV | of the sand is about 1 kPa. Figure 2 shows the primary drainage and the main wetting curves of the sand measured in the laboratory under a state of equilibrium using a Buchner funnel set-up. In addition a fitting curve is included with the parameterization according to Mualem (1976). The saturated hydraulic conductivity of the sand is kf = 2.1 · 10−4 m/s. The correspond-ing evolution for the unsaturated condition is shown in Figure 3 (based on the primary drainage curve).
3
COLUMN TEST APPARATUS
3.1 Experimental set-up and instrumentation In order to determine the soil hydraulic parameters depending on the density, the soil water retention curve and the unsaturated hydraulic conductivity, a column test apparatus was developed to carry out multi-step inflow and outflow experiments under de-fined stress conditions on samples 40 cm in height and 19 cm in diameter (cf. Scheuermann et al. 2003). Figure 4 gives
a diagram of the experimental set-up of the column test apparatus. The soil sample is located in a plastic-bag, which is embedded in a pipe of fiber glass. The plastic-bag is sealed with closing plates at both ends. In order to induce a hydraulic stress on the sample, a filter of sintered porous glass is installed in the lower plate. In contrast, the upper plate has a small opening to ensure atmospheric boundary conditions at the opposite end of the sample. As a result of this arrangement, the fiber glass pipe is unsupported and it floats, only held by the friction between the plastic-bag and the pipe. The interface between the plastic-bag and pipe is lubricated with Vaseline in order to reduce the friction and to allow the sample to deform axially with as little hindrance as possible (oedometric-like condition). In order to vary the density of the material, the sample is mechanically loaded using a hydraulic pump using the steel frame as a reaction. A position encoder records the deformation of the sample. For the purpose of the experiment, the hydraulic stress is imposed on the lower closing plate by means of a hanging water column. An overflow connected to a water reservoir is used to keep the hydraulic stress constant (cf. Figure 4). The column is equipped with different measuring devices, including four tensiometers installed in order to measure the matric suction at four different points along the column. For this reason, small windows are located in the pipe. Furthermore, two flat band cables are placed between the pipe and the plasticbag, which make it possible to measure the spatial distribution of the water content in the soil using a newly developed measuring method called ‘Spatial TDR’ (see Becker et al. 2008, Scheuermann et al. 2008). A detailed description of any further equipment is given in Scheuermann et al. (2003). With the above mentioned measuring devices continuous observation of both the matric suction and the water content is
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possible, thus describing the transient changes of the hydraulic conditions inside the soil sample.
Table 1. Mechanic load, deformation and stored water after each hydraulic cyle.
3.2
Hydraulic cycle
Mech. load kPa
Deformation mm
Stored water ml
1 2 3 4
0 100 200 300
0 6 2 1
580 560 350 350
Performing the experiment
The following experiment differs firstly from conventional multi-step experiments regarding the conditions and secondly from the experiment originally planned using this set-up. Thus the test started with infiltration under quite dry initial conditions of θi ≈ 3 vol-% roughly corresponding to the residual water content θr (cf. Figure 2). Furthermore, the density of the sand was initially too high to compact the sample normally with increasing mechanical loads. Only small deformations were observed. In this way an experiment was performed, whereby the sample was hydraulically stressed in cycles with repeated infiltration and drainage phases. Below the performance of the experiments is illustrated taking as an example the last (4th) hydraulic cycle, which was carried out with a mechanical load of 300 kPa (cf. Table 1). The corresponding time-variations of the experiment (with a hydraulic cycle consisting of infiltration followed by drainage) is given in Figure 5. In the upper diagram the imposed steps in hy-draulic stress are shown. The reference level is at the top edge of the lower closing plate. As can be seen, the infiltration path as well as the drainage path were carried out in four steps each consisting of 2 kPa beginning with an initial matric potential of −4 kPa. A new hydraulic stress was set before the state of equilibrium was reached. In the second graph the cumulative discharge is shown. The mean volumetric water content measured with the TDR sensors (symbols) and calculated from the discharge (line) is plotted in the third graph in Figure 5. It can be seen, that there is a difference in the values of up to 3 vol-%. One reason for this discrepancy is the fact that the lower part of the sample (ca. 5 cm) was not observed by the sensor. The last four graphs show the time-variation of the matric suction measured with the tensiometers. The positions of each tensiometer are given in the graph. Altogether four identical hydraulic cycles (infiltration and drainage with four steps each with 2 kPa) were carried out with four different mechanical loads. Two experiments were carried out every day; thus there was a break over night between the second and the third experiments. After each hydraulic cycle a certain amount of water was stored in the sample as can be seen from the graph for the cumulative discharge in Figure 5. This water could not flow out of the sample, since the outlet was closed during the break, when the new mechanic load was also adjusted. The volume of water stored after each hydraulic cycle is given in Table 1 together with the deformations for each mechanical load. The same observation can be seen
Figure 5. Time-variation curve of the measured values of the last (4th) hydraulic cycle with a mechanical load of 300 kPa.
in Figure 6, in which the temporal evolution of the mean volumetric water content for each experiment is presented. After each hydraulic cycle, the mean hydraulic water content throughout the sample increased. Furthermore, it can be seen from the graph that the final condition of each experiment corresponded to the initial condition of the next one. This also means that
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Figure 6. Time-variation of the mean volumetric water content along the soil sample measured at different load stages.
the mechanical load increased in stages had no influence on the water content measurements. Below these results are presented in detail and discussed in relation to the observed dynamic effects. 3.3
Figure 7. Water content profiles at different time steps of the 4th hydraulic cycle during infiltration (left) and drainage (right) with readings of the water level measured with tensiometers.
Results and discussion
Figure 7 shows the profiles of volumetric water content for the different time steps of the 4th hydraulic cycle during the experiment (cf. Figure 6 and Table 1) for the phases of infiltration (left) and drainage (right). The time of measurement and the appropri-ate level of the hydraulic zero potential (z-coordinate in regard to the lower boundary of the sample) is indicated in each legend. The zero potential is derived from the tensiometer readings and corresponds to the water level under the assumption that there is a state of equilibrium. It indicates the situation under transient conditions when matric suc-tion is lost. A comparison between the water content profiles for the infiltration and the drainage shows, that completely differing pore water pressure conditions can be observed for similar water content distributions. For example, during infiltration a zero potential and thus a loss of matric suction can be measured even for small volumetric water contents (cf. water content profile for t = 59 min.). However, for a similar water content distribution at t = 107 min. in the drainage phase, there is still an area with a fairly high volumetric water content above the level of hydraulic zero potential. This observation is not only caused by the hysteresis of the soil water retention curve. Another reason can be found in effects caused by the transient or dynamic conditions, prevailing during the experiment. Figure 8 shows a synoptical description of the overall conditions of the 4th hydraulic cycle at tensiometer 2 (z = 18 cm) during the experiment. In the graph on the top left, the cumulative discharge is shown. In this regard it should be mentioned that the
Figure 8. Multi-step-inflow and outflow-experiment of the 4th hydraulic cycle: Time-variation curve of recorded measure-ments at tensiometer 2 (2nd from below, cf. Figure 4).
time axis runs from right to left. The hydraulic potentials as lower boundary conditions are highlighted in grey (cf. data in the bend of the diagram at the bottom on the left).
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The matric potential readings at tensiometer 2 are presented in the central graph on the left. Here both negative and positive pore water pressures are included in the graph. The corresponding water con-tents at this location are presented in the lower graph on the right. A mean volumetric water content is calculated from the Spatial TDR measurements over a range of 2 cm on the elevation of tensiometer 2. By combining the matric suction readings and volumetric water contents, the graph in the centre on the right with the white background can be taken as a kind of soil water retention curve, whereby ‘a kind of ’ merely highlights the fact that also positive matric potential readings are included here. Finally the graph shows the relationship between pore water pressure and water content as a closed hysteresis loop. For comparative purposes the quasi-static soil water retention curve from Figure 2 is included in the graph. As can be seen from the graph, neither result can really be compared with the other. For example, the primary drainage curve (grey triangles) is located above the transient drainage curve (black rhombuses). Earlier experimental investigations (cf. Hassanizadeh et al. 2002, Mohamed & Sharma 2007) have shown, that the curve for dynamic conditions should be located above the quasi-static curve and not conversely. The reason for this contradiction lies on the one hand in the densities of the samples. The quasi-static water retention curve was measured with a density index Dr ≈ 0.95 under very dense conditions, whereas the density index of the sample in the column was Dr ≈ 0.6. On the other hand, the quasi-static drainage curve was determined starting at full saturation. The highest saturation during the transient experiment in the column was circa 80%. Nevertheless, the infiltration curve especially shows distinctive devolution influenced by the tranient or dynamic boundary conditions. The loss of negative matric potential happens at a volumetric water content of circa θ = 17 vol-%, which corresponds to a saturation of not even S = 50%. For this reason, the soil water retention curve of the column experiment is located considerably below the quasi-static curve. Another impressive effect caused by dynamic—and in special cases cyclic—hydraulic boundary conditions is given in Figure 9. It shows the soil water retention curves for all hydraulic cycles conducted with in column test apparatus. As can be seen from the graph, the soil water retention curves reflect the same cumulative response as indicated by the stored water volume (cf. Table 1) or by the mean volumetric water contents of Figure 6. The volumetric water content of the 1st hydraulic cycle is particularly surprising, when the negative matric potential was lost. At circa θ = 9 vol-% it does
Figure 9. Step-wise increase in the water content inside the soil sample with repeated infiltration of water (measurements at tensiometer 2).
not even correspond to a saturation degree of S = 25%, and the highest volumetric water content measured in this experiment was roughly θ = 18 vol-% (S = 50%). Although these degrees of saturation are quite small, it is perfectly conceivable that positive matric potentials could occur, since both the air and water phases form continuous phases during these degrees of saturation. Both values (water content at loss of suction and maximum water content) increased from cycle to cycle with repeated infiltration and drainage of the sample, indicating an accumulation of water. Under the supposition that the hydraulic boundary conditions remain constant, it can be expected that with additional hydraulic cycles a limit cycle would be reached, leading to a constant hysteresis loop. This kind of pumping effect was also qualitatively ob-served in column experiments with clayey material (Delov & Diankov 1998). One possible explanation for this observation is based on the sintered porous glass plate at the lower end of the sample. The saturated hydraulic conductivity of the glass plate at kf = 2.5 · 10−6 m/s is roughly 100times smaller than the hydraulic conductivity of the sand. Nevertheless, in a dry condition the sand strives to soak up water. If during infiltration a degree of saturation is reached, which is high enough to transport the water upwards for the existing hydraulic gradients, the water content should stay constant. It can be expected that primarily small pore-channels will be activated in such a process. The subsequent drainage of the sample leads to an incomplete desaturation of the sand and some pores remain filled with water. During subsequent infiltration under the existing conditions (hydraulic gradient and initial saturation of the sample) further porechannels are activated and more water can flow into the sample.
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This explanation is just a hypothesis for the observation presented, which needs to be verified in controlled experimental investigations. Nevertheless, the observations in the column experiments demonstrate a new aspect concerning dynamic effects. Even if the absolute values of the water con-tent measurements may be inexact, the relative changes are given and they are significant. Confirmation of these observations is given in the next section, in which measurements in a full-scale dyke model are presented.
4
FULL-SCALE DYKE MODEL
Physical flood simulation tests were carried out in a full-scale dyke model. The dyke was built up with the same sand used for the investigations with the column test apparatus and with a similar density. Figure 10 shows the positions and lengths of the flat band cable used as TDR-sensors inside the dyke cross-section. Tensiometers are installed at different depths along the first sensor from the crest of the down-stream slope side (see crosses in Figure 10). A de-tailed description of the dyke model and its instru-mentation is given in Scheuermann et al. (2008). The readings of the water content measured with Spatial TDR and the recorded matric potentials were analyzed in the same manner as for the experiments with the soil column. Figure 11 presents the corresponding relationship between the volumetric water content and the matric potential. As can be seen from the graph, the volumetric water content, at which the matric suction is lost, increases with the height of the observation point. The measurements were conducted during the transient seepage through the dyke. The velocity of the moving phreatic surface during infiltration decreases with increasing in-filtration. The closer the phreatic surface is situated to the stationary condition, the slower is the velocity. Thus, the differences in the soil water retention curves measured in situ must be caused by the different velocities of the phreatic surface. These independently measured observations verify the results from the laboratory investigations in the soil column.
Figure 11. Measurements of matric potential during a flood simulation experiment on a full-scale dyke model.
5
OUTLOOK
The experiments presented were not originally designed for investigating dynamic hydraulic effects. However, the observations clearly show several phenomena resulting from the particular dynamic conditions. Thus it could be seen that, during the transient infiltration of water, matric suction may be lost even at very small water contents. This phenomenon depends on the velocity of the infiltration, as could be seen from the results when in the dyke model. A new aspect with regard to dynamic effects is the cumulative storage of water during cyclic hydraulic boundary conditions. The velocity of the in-filtrating water is only one influencing factor for this phenomenon. Another might be the availability of water during infiltration. The observations presented in this paper were only possible with the help of the new measuring method, Spatial TDR. In future laboratory experiments and large-scale experiments this method will also be used for the targeted investigation of hydraulic dynamic effects. REFERENCES
Figure 10. Set-up of measurement devices with positions and lengths of the flat band cables and positions of tensiometers.
Becker, R., Scheuermann, A., Schlaeger, S., Huebner, C. & Wagner, N. 2008. Spatial Time Domain Reflectometry (Spatial TDR)—Principles, limitations and accuracy. First European Conference on Unsaturated Soils; Durham.
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Biggar, J.W. & Taylor S.A. 1960. Some aspects of the kinetics of moisture flow into unsaturated soils. Soil Sci. Soc. Am. Proc. 24: 81–85. Delov, K. & Diankov, Z. 1998. Einfluss des Lufanteiles auf die Hysteresisparameter bei der Bodenbewaesserung. Dresdner Wasserbauliche Mitteilungen, Inst. f. Wasserbau und Techn. Hydrom., TU Dresden, 13: 391–400. Elzeftawy, A. & Mansell, R.S. 1975. Hydraulic conductivity calculations for unsaturated steady-state and transientstate flow in sand. Soil Sci. Soc. Am. Proc. 39: 599–603. Hassanizadeh, S.M., Celia, M.A. & Dahle, H.K. 2002. Dynamic effect in the capillary pressure-saturation relation-ship and its impacts on unsaturated flow. Vadose Zone J. 1: 38–57. Hollenbeck, K.J. & Jensen, K.H. 1998. Experimental evidence of randomness and nonuniqueness in unsaturated outflow experiments designed for hydraulic parameter estimation. Water Resour. Res. 34: 595–602. Mohammed, M.H.A. & Sharma, R.S. 2007. Role of dynamic flow in relationships between suction head and degree of saturation. J. of Geot. and Geoenviron. Engin. 133: 286–294.
Mualem, Y. (1976). Hysteretical models for prediction of the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12(6): 1248–1254. Scheuermann, A., Bieberstein, A., Triantafyllidis,Th., Huebner, C., Becker, R, Schlaeger, S. & Wagner, N. 2008. Spa-tial Time Domain Reflectometry (Spatial TDR)—On the use in geotechnics and geohydraulics. Proc. First European Conference on Unsaturated Soils, Durham. Scheuermann, A., et al. 2003. Column test apparatus for the inverse estimation of soil hydraulic parameters under de-fined stress condition. ISBN 3-540-21121-7, Springer, Ber-lin, 33–44. Topp, G.C, Klute, A. & Peters, D.B. 1967. Comparison of water content-pressure head data obtained by equilibrium, steady-state, and unsteady-state methods. Soil Sci. Soc. Am. Proc. 31: 312–314. Wildenschild, D., Hopmans, J.W. & Šim˚u,nek. 2001. Flow rate dependence of soil hydraulic characteristics. Soil Sci. Soc. Am. J. 65: 35–48.
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A new high capacity tensiometer: First results J.C. Rojas, L. Pagano, M.C. Zingariello & C. Mancuso University of Naples, Federico II, Italy
G. Giordano & G. Passeggio INFN, Naples, Italy
ABSTRACT: A high capacity tensiometer has been developed at the University of Napoli Federico II that allows substitution of the High Air Entry Value (HAEV) filter and, hence, the variation of the probe measurement range and response time. The device has been also designed to allow initial saturation without removal from the high vacuum temperature-controlled pre-conditioning chamber. Regardless of the HAEV filter (5 bar and 15 bar), the probe has been saturated under a saturation pressure of 800 kPa and then calibrated applying positive pressure values. To evaluate the performance of the tensiometer free evaporation tests, prolonged high suction measurements and pressure reversal tests were carried out. The tensiometer layout, the pre-conditioning setup and the saturation process are described in the paper. The results obtained during some preliminary tests are also presented and discussed.
1
INTRODUCTION
In recent years, several designs of high capacity tensiometers have been presented in the literature. According to the original proposal from Ridley & Burland (1993), all these devices use a fixed high air entry value (HAEV) filter to protect the water reservoir against de-saturation (Fig. 1). This introduces however two contrasting requirements: (a) the need to maximize the air entry value (AEV) of the filter, in order to extend as much as possible the suction measured, and (b) the need to limit the AEV of the filter in order to reduce the response time of the tensiometer. In addition, the need for high pressurization during the saturation of the HAEV filter and water reservoir (i.e. 4 MPa after Ridley & Burland 1999),
Figure 1. 1995).
Model of mini-tensiometer (Ridley & Burland
makes unfeasible the use of high sensitivity thin diaphragms due to the possibility of them yielding during pressurization. This paper discusses the above two problems, presenting a new high capacity tensiometer developed at the University of Napoli Federico II (UNINA). The design of the new tensiometer addresses the contrasting requirements associated with the functioning and pre-conditioning of the probe. Also discussed are the performance of the probe when a saturation pressure of 800 kPa is used and ceramic filters of 5 and 15 bar AEV are adopted. 1.1 Cavitation When water is subjected to a pressure lower than its vapour-saturation value, it usually transforms into vapor (causing cavitation). However, in a tensiometer, if pure water is used to saturate the HAEV and water reservoir, and hydrophilic materials are adopted to build a very smooth measuring chamber, cavitation may occur only in appropriate circumstances far beyond thermodynamic equilibrium. As a matter of fact, the maximum tension that pure water can stand ranges from 200 MPa, as measured by Imre (2002), to 400 MPa, as theoretically predicted by Tabor (1979). Under a tension of 200 MPa the pure water is not in equilibrium but can remain in this metastable condition for a long time. To explain this fact it is worth recalling that cavitation is a non-equilibrium process triggered at a
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cavitation nucleus, that brings an unstable system to a new equilibrium condition through a process of phase transition by heterogeneous density fluctuations. Cavitation may be triggered at the site of microscopic heterogeneities in the liquid, such as suspended dirt particles, gas micro-bubbles, etc. (i.e. heterogeneous nucleation), or it may arise randomly in the liquid itself (i.e. homogeneous nucleation) if the required conditions of pressure and temperature exists. In nature and in technical applications heterogeneous nucleation is the most common trigger of cavitation. If sufficient numbers of ‘‘nucleation sites’’ of sufficient size are present, when a liquid is subjected to a pressure reduction the liquid will become vapor and cavitation rapidly occurs. On the contrary, if no nucleation site is present, the depressurization of the liquid may lead to a metastable state down the theoretical isotherm, since imperfections may cause instability and transition to the vapor phase. In the particular case of high capacity tensiometers, even if pure water is used, a weakness will still exist in the microscopic bubbles of gas present in crevices at the water-solid contact (Brennen 1995) (i.e. at the contact between the water and the reservoir), and inside the water filling the pores of the HAEV filter. To understand how this weakness may be reduced, the crevice model proposed by Harvey et al. (1944) may be helpful. As a matter of fact, this model establishes that if a small volume of gas is trapped in minute crevices at the contact between the water and a solid, the application of an appropriate water tension may cause the expansion of the gas until the bubble stability is lost and uncontrollable expansion occurs. In this situation it is likely that the bubble will move from the solid-liquid surface into the liquid and will dissolve if a new pressurization stage is applied (Atchley & Prosperetti 1989). A higher water tension is now necessary to cause the expansion of the micro-bubble that remains within crevice (Harvey et al. 1944), though, in water, microbubbles of air seem to persist almost indefinitely and are almost impossible to remove completely (Brennen 1995). All the above suggests that subjecting a high capacity tensiometer to cycles of high depressurization and high pressurization may improve its saturation, reducing the size of heterogeneous cavitation nuclei by extracting ‘‘air fractions’’ from the cavities and dissolving them in the water. Trevena (1982) summaries the experimental results reported in the literature regarding the effects of time in cavitation. Their conclusions can be outlined as: a) if the nucleation site is the solid surface, the breaking tension decreases as the pressure rate increases with time; b) when the cavitation starts in the liquid itself, the breaking tension increases as the stressing rate increases; c) the longer the time of pressurization the greater is the tension needed for cavitation; d) the breaking tension increases steadily as the number of
cycles of cavitation and pressurization increases until it levels-off at an upper limit. 1.2
Direct suction measurement: previous studies
As mentioned, many studies considering direct suction measurements with high capacity tensiometers have been published. Table 1 summarizes some basic information on the type of HAEV filter, assembly method, etc. used by various Authors. All these studies seem to indicate that the design of a tensiometer is crucially important as it influences its robustness, sensitivity, ease of saturation, speed of response, and cavitation resistance (Take & Bolton 2003). Equally clear is that the design of appropriate saturation setups and procedures is also critical. With reference to the probe design, previous experience recognizes the important role of the water reservoir volume, as this is in direct contact with the internal area of the diaphragm. In particular it is generally recognized that the use of water reservoirs as small as possible will reduce the probability of cavitation (Ridley & Burland 1993; Marinho & Pinto 1997). In particular, Guan & Fredlund (1999) suggested that there is a cavitation tension for a particular pre-pressurization procedure and a particular suction probe. Ridley & Burland (1999) found, on the contrary, that for a thoroughly saturated suction probe the stress required to cause a tension breakdown in the reservoir water is uniquely related to the AEV of the filter. Most of these probes can stand very high values of suction but, as Take & Bolton (2003) mentioned, there are many applications where small suction values (i.e. 300 kPa) are of interest. This implies the requirement for sensitive lower-pressure-range devices that are likely to be damaged when a high pressure is applied. According to the previously described crevice model, Tarantino & Mongiovì (2001) observed that saturation of the ceramic filter is achieved mainly through cycles of cavitation and subsequent pressurization, and that an inadequate initial saturation simply increases the number of cycles required to obtain a satisfactory performance of the probe. Contrarily, Guan & Fredlund (1999) indicated that repeated cavitation of the sensor appeared to reduce the maximum sustainable tension. Finally, Chiu et al. (2005) and Lourenço et al. (2006) show unclear evidence to support the hypothesis of an increase of cavitation suction with cycles of cavitation and pressurization. In summary, after Marinho & Chandler (1994), the main requirements to avoid cavitation in the measurement system and improve the ability to measure negative water pressure seems to be: a) water and all surfaces within the measurement system must be pure and clean (Henderson & Speedy 1980), b) the surfaces in contact
206
Table 1.
Saturation process data used in previous studies.
Tensiometer
Filter AEV (bar)
Assembly
Vacuum saturation
Pre-pressurization pressure (kPa)
Pre-pressurization cycles
Ridley & Burland (1999) Guan & Fredlund (1997) Tarantino & Mongiovì (2002) Meilani et al. (2002) Take & Bolton (2003) Chiu et al. (2005) He et al. (2006) Lourenço et al. (2006) Mahler & Diene (2007)
15 15 15 5 3 5 5 15 5, 15
dry under water dry dry oven dried dry dry or saturated dry dry
yes (60 min) no yes no yes (20 min) yes (60 min) no yes yes (15 h)
4000 (24 h) 12000 (1 h) 4000 (24 h) 800 (4 days) 1000 (1 h) 700 (24 h) 2000 (1 month) 800 (72 h) higher than filter AEV
no yes (6 cycles) no no yes no no no yes
with the water system must be as smooth as possible to avoid or reduce the number and size of crevices, c) the system should be air-evacuated by vacuum application prior to the pre-pressurization in order to remove the maximum amount of air entrapped into the crevices (Jones et al. 1981), d) pre-pressurization of the system to high pressure is required in order to dissolve all the free air (Harvey et al. 1944), e) the HAEV disk must be brought to a low initial moisture content prior to the application of initial saturation, as this has been demonstrated a crucial factor for the saturation of the disk itself (Take & Bolton 2003). All these factors should be considered in the design of a saturation setup and saturation procedure adopted for any probe.
2
THE UNINA PROBE
A high capacity tensiometer has been developed at the University of Naples Federico II using a design layout similar to that initially proposed at the Imperial College of London (Ridley & Burland 1995) but including some variants to allow the substitution of HAEV disk without changing the whole probe. This measure has been adopted in order to easily tune the measurement capacity of the tensiometer and its response time to the particular application under study. The UNINA probe (Fig. 2), utilizes a circular clamped-edge diaphragm. The strain-gauged diaphragm is 6 mm in diameter and 0.4 mm in height. The strain gauge has a rosette-like design with the radial strain gauges next to the rim and tangential strain gauges adjacent to the radial ones, generating the highest sensitivity when combined in a Wheatstone bridge. The circular trim diameter of the strain gauge covers a considerable area of the micro diaphragm. To produce the maximum allowable output signal the strain gauge is bonded to the non-pressurized side of the diaphragm. The novel piece is an interchangeable filter cap containing a HAEV ceramic disk of 7.4 mm in diameter
Figure 2.
UNINA high capacity tensiometer.
and 6.0 mm in height. The operating range is determined by the filter’s AEV (e.g. 5 or 15 bar), allowing a single unit to operate in different suction ranges by changing the filter. The water reservoir between the ceramic disk and the strain-gauged diaphragm has a volume of approximately 3 mm3 . Two stainless steel housings are used (Fig. 2), one to hold the diaphragm, and another one to provide a support and isolate the electrical connectors. A vented waterproof sheating ensures atmospheric pressure is maintained in the back of the strain-gauged diaphragm and isolates the electronic parts from water and dust. The strain-gauge measurements are acquired through a bridge amplifier static strain indicator and stored in a digital data logger. The recorded data (i.e. up to 1 per second of observation) are stored on a memory card and transferred by a USB port to a PC. The strain gauge is connected to the acquisition system through appropriate input terminals. An undefined full-bridge circuit is used as input, selected on the basis of the net output of the active strain gauges without mathematical corrections for either bridge configuration or nonlinearity being applied. Operating in this way, the nonlinearity errors will have to be determined by direct calibration against a previously calibrated transducer. Table 2 shows the design parameters that characterize the UNINA probe, determined assuming 2000 kPa as the maximum
207
Table 2. Characteristics corresponding to a maximum applied pressure of 2000 kPa. Parameter
Symbol
Critical magnitude
Units
Radial strain Total gage output Sensitivity Deflection Radial stress
εR Eo – Yc σR
3.8 × 10−4 0.125 0.28 2.1 × 10−3 54, 210
– mV/V μV/kPa mm kPa
pre-pressurization pressure. The maximum radial strains in the diaphragm are well-suited with the reference of the strain gauge manufacturer (i.e. >−2 × 10−3 ). The maximum expected deflection is very little compared with the water reservoir depth (0.1 mm) and therefore the design ensures the free deformation of the diaphragm. Also, the maximum radial stress remains below the yielding stress for the stainless steel.
3
Figure 3.
Saturation system.
Figure 4.
Tensiometer calibration curve.
SATURATION SYSTEM
As the initial saturation procedure of high capacity tensiometers has been demonstrated to be very important, a saturation system (Fig. 3) has been designed to saturate and calibrate the UNINA probe. The apparatus consists of two chambers (c1 and c2), a vacuum generator (g), a vacuum gauge (m), two heaters (h1 and h2), and five valves (v1–v5). Initially valve v1 is opened to drive distilled water into the chamber c1. The water is then de-aired keeping all the valves closed except valve v2 and applying a relative pressure of −95 kPa to the chamber c1 through a pressure p1 = 600 kPa applied to the vacuum generator g. The water is de-aired for at least 3 hours. The tensiometer T is then screwed into the chamber c2. To dry the tensiometer, the heaters h1 and h2 are switched on to bring the tensiometer chamber to constant temperature of 70◦ C. Opening the valve v3 vacuum is applied to the chamber c2. After 16 hours the heaters are switched off and valve v5 is opened to slowly introduce water into the chamber c2 (and, hence, into the HAEV filter and water reservoir) while under vacuum. Four hours after, the vacuum is released and further time is allowed for saturation of the filter and water reservoir under atmospheric pressure. The valve v4 is then opened and the valves v3 and v5 closed in order to pressurize the chamber c2 at a pressure p2 = 800 kPa and to force any residual amount of air into solution. The pressurization stage is applied for 72 hours. It is important to note that a maximum pressure of 800 kPa has been applied during saturation, independently of the AEV used. A weakness of the saturation system is the absence of an interface membrane between air and water in
the pre-pressurization chamber, allowing potential air diffusion. The tensiometer is finally calibrated inside the chamber c2 varying the pressure p2 from 0 to 800 kPa. During cyclic pressure loading the probe shows a linear response without appreciable hysteresis (Fig. 4). The calibration curve in the negative pressure range was extrapolated from the calibrated positive range. As Tarantino & Mongiovì (2002) observe, sensitivity resulting from calibration is not so different from the expected value, 0.25 μV/kPa and 0.28 μV/kPa (Table 2), respectively. 4
EVALUATION TESTS
To check the performance of the tensiometer some evaluation tests have been conducted in a 22◦ C constant temperature room. 4.1 Comparison measurements against known suction values Comparisons of the tensiometer measurements against known values of suction were conducted to verify its
208
4.2
Figure 5.
Long time suction measurements on soil samples.
time response, its ability to stand high suctions for a long time and to roughly verify the calibration data. The data presented in Figure 5 were obtained using a 15 bar filter. Similar results were obtained when a 5 bar filter was used. The equilibration time of the tensiometer was examined using silty-sand. Matric suctions of 200, 250 and 350 kPa were generated in different samples of this material using a modified Wisa oedometer working under the axis translation technique. Matric suction of the sample was then measured dismounting the oedometer, putting the sample to the atmospheric pressure and using the UNINA probe. A thin layer of the soil paste was used to improve contact between the soil sample and the miniature tensiometer. During the tests the samples remained isolated to avoid large suction changes associated with environmental conditions. The observed trend of matric suction with time may be subdivided into three parts and explained following Guan & Fredlund (1999). In Part I, a sudden increase of readings is observed to reach suction values slightly less than those expected on the basis of the suction applied by the axis translation technique. Afterward, in Part II of the tests, a slow process of suction equalization is observed. In Part III, following a period in which the suctions are almost constant at the expected values, slow increases in the tensions are observed. These are mainly attributed to moisture losses due to evaporation from both the samples and the suction probes during the measurements. The measurements performed on the sample preconditioned to a suction of 350 kPa present some cyclic variations. It is worth noting that large variations are observed during days I, II, V and VI, while no variations were registered in days III and IV corresponding to Saturday and Sunday, respectively. This seems to suggest that the observed variations are related to small temperature changes in the controlled temperature room during working days. The tests were stopped when the probe measured constant suction for a time long enough to validate the capacity of the probe to withstand high suction for a long time.
Evaporation tests
Evaporation tests were performed to determine the maximum measurable suction. The maximum suction values registered are 450 kPa (Fig. 6a) and 720 kPa (Fig. 6b) when 5 bar and 15 bar filters were used respectively. For the 5 bar filter the maximum value registered was approximately the expected one (i.e. ≈500 kPa). This implies that the saturation process for this AEV seems to have worked properly. However, the maximum suction obtained for the 15 bar filter was almost one half of the expected value, but very near to the pre-pressurization pressure applied during the saturation process (i.e. 800 kPa). It is worth noting that Figure 6 indicates that, on cavitation, the pressure increases to −100 kPa, indicating good accuracy of the probe’s calibration. Table 3 presents the values of suction measured at cavitation when the 15 bar filter is used. According to Tarantino & Mongiovì (2001), the data in Table 3 seem to indicate that an enhanced saturation of the ceramic filter is achieved through cycles of cavitation and subsequent pressurization. Moreover, according to Trevena (1982) the upper limit of the tensiometer is of about 645 kPa. Obviously, if a probe is saturated at its upper limit the cycles of cavitation will not improve the probe’s performance. However higher pre-pressurization pressures may improve its response. Then, analogous to observations by Atchley & Prosperetti (1989) in their crevice model of bubble
Figure 6.
209
Cavitation tests: maximum measurable suction.
Table 3.
(Fig. 7a). However, if the probe had not been properly saturated, the offset decreased after every reversal (Fig. 7b).
Tension breakdown values using 15 bar filter.
Test
Tension breakdown (kPa)
1st 2nd 3rd 4th 5th 6th 7th
330 481 566 647 646 720 635
5
CONCLUSIONS
A new high capacity tensiometer has been developed at University of Naples Federico II. The novel design of the probe allows the substitution of the HAEV filter without changing the whole probe. The objective was to study the behaviour of the UNINA probes when they had been saturated under a reduced pressure (i.e. 800 kPa), well below the maximum allowable prepressurization pressure (i.e. 2000 kPa). The response of the new high capacity tensiometer when a 5 bar filter was used was found to be excellent during free evaporation tests, cyclic evaporation tests and equilibration time tests. On the other hand, the 800 kPa pressure applied during the saturation stage was not enough to properly saturate the 15 bar filter. The maximum suction registered seems to be approximately equal to the minimum of either the pre-pressurization pressure used or the AEV of the filter.
REFERENCES
Figure 7.
Response of the probe to suction reversals.
nucleation, the maximum cavitation suction depends on the past history of the tensiometer. Contrarily to the observations in Berthelot tube tests, the tension breakdown value seems not to be affected by the rate at which the tension increases (Fig. 6a, b). 4.3
Cyclic evaporation tests
The probe’s ability to register rapid suction changes was examined using cyclic evaporation tests. Figure 7 shows several evaporation cycles, consisting in free evaporation stages up to prescribed suction values (i.e. lower than the nominal filter’s AEV) and stages in which the atmospheric pore water pressure was applied by immerging the tensiometer tip in water. A probe’s response to reversals of suction was found to be excellent for properly preconditioned probes
Atchley, A.A. & Prosperetti, A. 1989. The crevice model of bubble nucleation. J. Acoustical Society of America 86(3): 1065–1084. Brennen, C.E. 1995. Cavitation and bubble dynamics. Oxford University Press. Chiu, C.F., Cui, Y.J., Delage, P., De Laure, E. & Haza, E. 2005. Lessons learnt from suction monitoring during centrifuge modeling. Proc. intern. symp. on advanced experimental unsaturated soil mechanics EXPERUS 2005. Trento, Italia, June 27–29: 3–8. Guan, Y. & Fredlund, D.G. 1997. Use of the tensile strength of water for the direct measurement of high soil suction. Canadian Geotechnical Journal 34: 604–614. Guan, Y. & Fredlund, D.G. 1999. Use of the tensile strength of water for the direct measurement of high soil suction: Reply. Canadian Geotechnical Journal 36: 181. Harvey, E.N., Barnes, D.K., McElroy, W.D., Whiteley, A.H., Pease, D.C. & Cooper, K.W. 1944. Bubble Formation in Animals. J. Cellular and Comparative Physiol. 24(1): 1–22. Henderson, S.J. & Speedy, R.J. 1980. A Berthelot-Bourdoon tube method for studying water under tension. J. of Physics E: Scientific Instrumentation 13: 778–782. Imre, A.R., Maris, H.J. & Williams, P.R. 2002. Liquids Under Negative Pressure, NATO Science Series. Jones, W.M., Overton, G.D.N. & Trevena, D.H. 1981. Tensile strength experiments with water using a new type of Berthelot tube. J. of Physics D: Applied 14: 1283–1291. Lourenço, S.D.N., Gallipoli, D., Toll, D.G. & Evans, F.D. 2006. Development of a commercial tensiometer for triaxial testing of unsaturated soils. In Miller et al. (eds.).
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ASCE Geotechnical Special Publication No. 147(2): 1875–1886. Mahler, C.F. & Diene, A.A. 2007. Tensiometer development for high suction analysis in laboratory lysimeters. In Schanz (ed.), Experimental unsaturated soil mechanics; Springer proceedings in physics No. 112: 103–115. Marinho, F.A.M. & Chandler, R.J. 1994. A new instrument for the measurement of soil moisture suction: Discussion. Geotechnique 44(3): 551–556. Marinho, F.A.M. & Pinto, C.d.S. 1997. Soil suction measurement using a tensiometer. In Almeida (ed.), Recent developments in Soil and Pavement Mechanics 1: 249–254. Rotterdam: Balkema. Meilani, I., Rahardjo, H., Leong, E. & Fredlund, D.G. 2002. Mini suction probe for matric suction measurements. Canadian Geotechnical Journal 39: 1427–1432. Ridley, A.M. & Burland, J.B. 1993. A new instrument for the measurement of soil moisture suction. Géotechnique 43: 321–324. Ridley, A.M. & Burland, J.B. 1995. Measurement of suction in materials which swell. Applied mechanics reviews 48(10): 727–732. Ridley, A.M. & Burland, J.B. 1999. Use of the tensile strength of water for the direct measurement of high soil
suction: Discussion. Canadian Geotechnical Journal 36: 178–180. Tabor, D. 1979. Gases, liquids and solids. Cambridge University press. Take, W.A. & Bolton, M.D. 2003. Tensiometer saturation and the reliable measurement of soil moisture suction. Geotechnique 53(2): 159–172. Tarantino, A. & Mongiovì, L. 2001. Experimental procedures and cavitation mechanisms in tensiometer measurements. Geotechnical and Geological Engineering 19: 189–210. Tarantino, A. & Mongiovì, L. 2002. Design and construction of a tensiometer for direct measurement of matric suction. In Jucá, de Campos & Marinho (eds.) Unsaturated Soils; Proc. 3rd inter. conf., Recife, 10–13 March 2002: 319–324. Lisse: Balkema. Tarantino, A. 2004. Direct measurement of soil water tension. In Jucá, de Campos & Marinho (eds.) Unsaturated Soils; Proc. 3rd inter. conf., Recife, 10–13 March 2002, 3: 1005–1017. Lisse: Balkema. Trevena, D.H. 1982. Time effects in cavitation experiments. J. Phys. D: Applied Physics 15: L111–L114.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Evaluation of suction measurement by the tensiometer and the axis translation technique S.D.N. Lourenço, D.G. Toll & C.E. Augarde School of Engineering, Durham University, Durham, UK
D. Gallipoli Department of Civil Engineering, University of Glasgow, Glasgow, UK
F.D. Evans Controls Testing Equipment Ltd, Wykeham Farrance Division, Tring, Hertfordshire, UK
G.M. Medero Department of Civil Engineering, Heriot-Watt University, Edinburgh, UK
ABSTRACT: The axis translation technique is a well-established method for imposing values of suction in unsaturated soil samples. High-suction tensiometers are more recently developed devices used for measuring pore water pressures in soils, including negative pore water pressures (i.e. suctions) below absolute zero. Both these techniques are comparable in terms of the suction range in which they operate. In this work a tensiometer has been used to measure suction values imposed by the axis translation technique in kaolin samples inside a pressure plate and a triaxial cell. The tensiometer has been kept in contact with the soil sample to track pore water pressure variations throughout the duration of the tests. The suctions measured by the tensiometer have been compared to those imposed by the axis translation technique and it was found that the suction measured by the tensiometer was always smaller than that imposed. Two scenarios are proposed to explain this. The first scenario considers the presence of water inside and below the high air entry value ceramic plate whereas the second one hypothesises the lack of equilibrium in terms of soil water content when suction is measured. The latter scenario seems to be supported by the evidence in the literature of equilibration times for pressure plate tests that are significantly longer than those reported for the present testing programme. Implications of both scenarios for laboratory testing are discussed.
1
INTRODUCTION
The axis translation technique (Hilf, 1956) is commonly used in unsaturated soil mechanics for imposing matric suctions in samples. In this technique, the pore air pressure and the pore water pressure are raised by the same amount so that the matric suction (given by their difference) is kept constant. In this way, the pore water pressure can become positive, thus avoiding water cavitation inside the experimental set up. The technique is employed in the pressure plate device, which consists of a high air entry value ceramic plate saturated by water and acting as a separation filter between the air above and the water below. Soil samples are placed on the ceramic plate and the suction is imposed by controlling independently both the air pressure and the water pressure on the two sides of the plate. The range of suction over which the technique
can be applied depends on the air entry value of the ceramic plate (usually between 500 kPa and 1500 kPa) and the capacity of the compressor controlling the air pressure. High-suction tensiometers (Ridley and Burland, 1993) are relatively new devices used for the direct measurement of pore water pressures in soils, including negative pore water pressures below absolute zero. Tensiometers are usually employed under conditions where the air pressure is atmospheric and the matric suction is given by pore water under tensile stress, which is directly measured by the tensiometers. High suction tensiometers can be schematically divided into three parts (Figure 1): a miniature water reservoir, a pressure transducer measuring the water pressure inside the reservoir and a high air entry value porous stone acting as a separation filter between the reservoir on one side and the soil on the other side.
213
reservoir
transducer
porous stone Figure 1. Schematic of the tensiometer used for this research (Lourenço et al., 2006).
Work done by Guan (1996) and reported in Guan and Fredlund (1997) used a modified pressure plate to perform a standard drying test by increasing pore air pressure in an initially saturated sample to impose a given value of suction (water pressure was at atmospheric pressure). Subsequently, the air pressure was instantaneously released to atmospheric pressure while a high suction tensiometer, placed in contact with the soil, simultaneously measured the corresponding drop in pore water pressure. This procedure was used to assess the accuracy of the tensiometer calibration over the negative range of pressures. The authors observed that the suction measured by the tensiometer was less than the suction imposed via the pressure plate. The same was observed by Lourenco et al. (2006) in similar tests. The tests conducted by Guan and Fredlund (1997) had a unique feature: water in the compartment below the porous stone of the pressure plate was flushed out before the air pressure decrease. No details are provided but it is believed that this was to avoid water flowing from the water compartment to the sample and therefore to avoid a further decrease of suction during the air pressure decrease. It is the purpose of this paper to evaluate the suction measurement of samples prepared at the same initial conditions by the tensiometer and the pressure plate. In this work, a conventional pressure plate sold commercially by Soil Moisture Corporation as well as a triaxial cell, whose pedestal was fitted with a high air entry value ceramic plate, were used. In the pressure plate the compartment below the ceramic plates was always full of water. In the triaxial cell, the compartment could be full or empty of water (but with the ceramic plates always saturated) (Figure 2). In the following part of this paper, the working principle of both the tensiometer probe and the axis translation technique will be initially reviewed in more detail including limitations and terminology. Then the procedures and results of the testing programme will be shown and the implications for laboratory testing of unsaturated soils will be discussed.
Figure 2.
2
Experimental set-up.
DIRECT SUCTION MEASUREMENT VERSUS AXIS TRANSLATION TECHNIQUE
The axis translation technique imposes a value of suction by raising the air pressure above atmospheric value with the water phase kept either at atmospheric or at a given positive value smaller than the air pressure. This forces water to move from (or into) the soil through the ceramic plate. Water will move to or from the compartment below the plate depending on whether the imposed suction is smaller or higher than that initially present in the soil sample. Once equalisation is achieved, no more transfer should occur and the water content in the sample should remain constant at the equilibrium value corresponding to the imposed suction (Figure 3). The tensiometer measures directly the water tensile stress existing in the soil pores. After the porous stone of a tensiometer is placed in contact with a soil sample with a negative pore water pressure, an initial equilibration phase takes place whereby a small volume of water is sucked out from the reservoir through the porous stone into the soil producing a deformation of the transducer diaphragm in the direction of the soil. This deformation is transferred to a strain gauged diaphragm from which pressure can be measured. Once this transfer ends, all water inside the tensiometer as well as in the soil will have the same value of negative pressure. The volume of water transferred from the reservoir to the soil is small enough so that it can be considered negligible, and therefore the water content of the sample is not affected. The working principle for both the axis translation technique and the tensiometer are schematically illustrated in Figure 3.
214
Figure 3. Working principle for the tensiometer (above) and pressure plate (below).
One of the main limitations of the pressure plate device is related to the presence of air diffusion through the ceramic plate (e.g. Padilla et al., 2006), which needs to be accounted for when the change in water content of the sample is measured by means of volume gauges connected to the water compartment below the ceramic plate. For the tensiometer, the range of measurable suctions is primarily limited by the occurrence of cavitation inside the probe, which is in turn governed by the degree of saturation of the porous stone and reservoir (e.g. Guan and Fredlund, 1997; Lourenco et al., 2006). Suction measurements by the tensiometer also appear to be sensitive to temperature as shown by Toker et al. (2004).
3
TESTING PROGRAMME, EQUIPMENT AND MATERIAL
in contact with the sample to track pore water changes throughout the test. A kaolin slurry was prepared at a water content of 200% and was deposited directly on the previously saturated ceramic plates inside the triaxial cell and the pressure plate. In order to avoid spreading, the slurry was placed in a cylindrical mould (diameter 38 mm) with open top and bottom ends. The tensiometer was then set directly on the top surface of the kaolin slurry and a plastic mesh was also used to keep the tensiometer in the right position during the test, i.e. to avoid it falling or tilting. The tensiometer used in this work has a nominal measuring capacity of 1000 kPa in both the positive and negative ranges. The tensiometer was previously saturated and calibrated according to procedures described in Lourenço et al. (2006). Suction was imposed in the sample inside the pressure plate by quickly raising the air pressure to the required value while pore water pressure was maintained at the atmospheric value. As soon as the air pressure was raised, the tensiometer (placed on the top of the sample) recorded a positive excess pore water pressure, which subsequently started to dissipate. Once the pore water pressure read by the tensiometer dropped back to zero, it was assumed that equilibrium was achieved throughout the sample. The air pressure was then reduced to the atmospheric value and the corresponding negative pore water pressure generated inside the sample was measured by the tensiometer. Increasing values of suction were applied and measured on the sample in a sequence up to a maximum value of 500 kPa corresponding to the air entry value of the ceramic plates in both the triaxial cell and the pressure plate. The tests performed in the pressure plate and in the triaxial cell differed in one respect. In the triaxial cell, after pore water pressure equalized at 0 kPa and before releasing the air pressure to zero, water was flushed out below the ceramic plate by air circulation. Once the air pressure was dropped and the reading from the tensiometer was taken, water was restored below the ceramic for the application of the next suction stage. In the pressure plate, water at atmospheric pressure was present in the compartment below the ceramic plate throughout the entire test.
4
If a given suction is imposed in a soil sample by using the axis translation technique, one would expect that an equal value of suction would be read by a tensiometer when placed in contact with the same sample. In order to verify this, tests were conducted by imposing given values of suction on Speswhite kaolin samples in the pressure plate while a tensiometer was placed
RESULTS AND DISCUSSION
Figure 4a shows the results for the test performed in the pressure plate. Inspection of Figure 4a indicates that, after the air pressure was increased to 187.6 kPa, the pore water pressure measured by the tensiometer instantaneously increased by 170 kPa and then progressively dissipated back to zero. After equilibrium was achieved, air pressure was reduced to zero
215
a)
400
pressure (kPa)
200
Table 1. Difference between the imposed and measured suctions for each test.
ua =396.5 kPa ua =187.6 kPa
0 uw =-149.2 kPa
-200
uw =-278.5 kPa -400 0
100 time (min)
150
200
Device
Difference (%)
T14 T17 T31 T35 T36 T38 T39 T40
Pressure plate Pressure plate Triaxial cell Triaxial cell Triaxial cell Triaxial cell Triaxial cell Triaxial cell
20.4–30.5 12.5–18.2 10.5–11.0 4.6–10.5 12.5–16.25 14.2–17.2 4.3–6.0 4.3–4.6
600 400 400
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Figure 4. Axis translation tests with uw measured with the tensiometer. (a) Test T14 conducted in the pressure plate and, test T40 conducted in the triaxial cell.
and this induced a reduction of the pore water pressure from zero to −149.2 kPa, i.e. a reduction about 20% smaller than the corresponding reduction in air pressure. Subsequently, the air pressure was increased again to a higher level of 396.5 kPa and, after dissipation of the excess pore water pressure from 160 kPa, was reduced again to zero. Also in this case, the corresponding reduction of pore water pressure from zero to −278.5 kPa was about 30% smaller than the corresponding reduction of air pressure. For the case of Figure 4b, the air pressure was increased in 4 stages to 99.6 kPa, 200 kPa, 299.4 kPa, and 400 kPa. The measured water pressures were 95.7 kPa, 191.4 kPa, 284.9 kPa, and 381.6 kPa, respectively. Comparing to Figure 4a, the imposed and measured suctions are smaller. Table 1 shows for each test the difference, in percentage, between the applied suction and measured suction. This difference was seen to vary throughout the air pressure releases. For instance, for test T14 in Figure 4a for the first air pressure release the ratio 149.2/187.6 gives 20.4%. In the second release this ratio gives 30.5%. Therefore during each air pressure release this difference became greater. Results from all tests are shown in Figure 5 where the suction imposed by the axis translation technique is plotted against the suction measured by the
Figure 5.
100 200 300 imposed suction (kPa)
400
Imposed versus measured suctions for all tests.
tensiometer. The difference between the measured and imposed suction were larger when the pressure plate was used. Previous work by Guan and Fredlund (1997) showed similar results, with the suction measured by the tensiomer smaller than the suction imposed by the axis translation technique by a margin ranging between 0.5% to 8.5%. Figure 6a shows an expanded view of the final part of the test shown in Figure 4a. It can be seen that, after the instantaneous initial drop in pore water pressure, the pore water pressure slowly rises over a period of about 20 minutes until it stabilises at a value of approximately −73 kPa. A similar result is shown in Figure 6b, which presents part of a test carried out in the triaxial cell where the pore water pressure recorded by the tensiometer, after an initial instantaneous drop, rises under constant air pressure and stabilises at a value of −335 kPa. This was a common feature of behaviour observed in all tests where the air pressure was maintained at zero for some time, after reducing it from the imposed value of suction. This result might be a consequence of the availability of free water inside the ceramic plate or below it. This water is sucked into the sample under the action of the negative pore water pressures generated by the air pressure drop, thus increasing water content and reducing soil suction.
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pressure (kPa)
a)
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ua = 396.5 kPa
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-200 uw = -278.5 kPa -400 125
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ua =599.4 kPa
0 -400 uw =-473.5 kPa
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Figure 6. Kaolin response after releasing the air pressure. a) Suction measured by the tensiometer continuously decreasing and, b) stabilizing at a 335 kPa.
A consistent result emerging from this work, as well as previous work by Guan (1996), is that the instantaneous pore water pressure decrease recorded by the tensiometer is generally smaller than the imposed drop of air pressure (Figure 6a and Figure 6b). Two possible explanations are provided here to interpret this result. One possibility is that, despite the air pressure drop being applied almost instantaneously, some water is still sucked back into the sample, which limits the magnitude of the measured pore water pressure reduction. This explanation seems consistent with the observation that pore water pressure reductions tending to be proportionally smaller for tests carried out in the pressure plate, where water is permanently present below the ceramic plate, than for tests carried out in the triaxial cell, where water below the ceramic plate is flushed out before each air pressure drop. A second possibility is that the water content in the soil sample had not yet come to equilibrium, despite the pore water pressure having done so. Equilibrium was assumed to be achieved at each imposed value of suction when the tensiometer read a value of zero pore water pressure. After this condition was attained, the air pressure was decreased and the corresponding negative pore water pressure drop was measured by the tensiometer. However, although the pore water pressure is equal to zero throughout the specimen, it is
possible that water content is still reducing inside the sample due to a slow rearrangement of water menisci at the interface between gas and liquid phases inside the pores. Such a hypothesis seems to be supported by the observation that pressure plate tests published in the literature (where the achievement of equilibrium is based on the measurement of the sample mass during equalisation) usually require significantly longer time than the tests reported in this work (where the achievement of equilibrium is based on the dissipation of the excess pore water pressures measured by the tensiometer). For example, the tests shown in Figure 4a and Figure 4b, both of which involved imposing more than one suction value to the sample, took overall 4 hours and 5 days respectively. Tinjun et al. (1997) and Vanapalli et al. (1997) reported equalisation times for clay samples of 5–8 days and 6–7 days respectively for each imposed value of suction in the pressure plate. However, both authors did not measure the sample’s mass, equilibrium conditions were ensured when the outward flow of water from the sample stopped. If the above hypothesis were true, the dissipation of pore water pressure to zero would not be enough to conclude that a given suction ‘is imposed’ on the sample, as assumed by Guan and Fredlund (1997) and Lourenço et al. (2006). Hence, the difference between the measured and imposed suction is simply due to lack of equilibrium in terms of water content. The tensiometer would be expected to measure suctions closer to the imposed ones if longer periods of time are waited during equalisation. A testing program is on the way to confirm this. 5
CONCLUSIONS
This paper presents a series of measurements performed by high suction tensiometers on kaolin samples, which were previously subjected to different suction levels by using the axis translation technique. It was found that the suction measured by the tensiometers was always smaller than that imposed by the axis translation technique. Two different hypotheses have been put forward to justify such discrepancy. One possibility is that the smaller measured suctions are due to the absorption of water by the sample from the ceramic plate and/or the compartment below it. However, another possibility is that for each imposed value of suction equilibrium conditions had only been achieved in terms of pore water pressure but not water content. This idea is suggested by comparison with published data on the equilibrium times for pressure plate tests, which have required longer times. This might be explained by considering that water menisci at the interface between the gas and liquid phases inside soil pores take longer to re-arrange in a stable configuration after the pore water pressure has come to
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equilibrium. Should this hypothesis hold, then it would not be correct to assume achievement of equilibrium based on the pore water pressure read by the tensiometer but equilibrium should be assessed on the basis of subsequent sample mass measurements during the equalisation phase. Further testing is currently being undertaken to confirm or refute such a hypothesis. ACKNOWLEDGEMENTS This research was funded by the Engineering and Physical Sciences Research Council of the United Kingdom through a CASE research grant, with additional financial support from Controls Testing Equipment Ltd. Support from the European Commission via the ‘‘Marie Curie’’ Research Training Network contract number MRTN-CT-2004-506861 is acknowledged. Technical support was given by Mr. C. McEleavy and Mr. S. Richardson. REFERENCES Guan, Y. 1996. The measurement of soil suction, PhD Thesis, University of Saskatchewan, pp. 331. Guan, Y., Fredlund, D.G. 1997. Use of the tensile strength of water for the direct measurement of high soil suction, Can. Geotech. J. 34: 604–614. Hilf, J.W. 1956. An investigation of pore water pressure in compacted cohesive soils, US Bureau of Reclamation, Tech. Mem. 654, Denver: US Bureau of Reclamation.
Lourenço, S., Gallipoli, D., Toll, D.G., Evans, F. 2006. Development of a commercial tensiometer for triaxial testing of unsaturated soils, Geotechnical Special Publication (ASCE) No. 147, Vol. 2, 1875–1886. Lourenço, S.D.N., Gallipoli, D., Toll, D.G., Evans, F., Medero, G. 2007. Determination of the Soil Water Retention Curve with tensiometers, Weimar, Germany, Experimental unsaturated soil mechanics, T. Schanz (Ed.), Springer, 95–102. Oliveira, O.M., Marinho, F.A.M. 2006. Study of the equilibration time in the pressure plate, Geotechnical Special Publication (ASCE) No. 147, Vol. 2, 1865–1874. Padilla, J.M., Perera, Y.Y., Houston, W.N., Perez, N., Fredlund, D.G. 2006. Quantification of air diffusion through high air-entry ceramic disks, Geotechnical Special Publication (ASCE) No. 147, Vol. 2, 1852–1863. Ridley, A.M., Burland, J.B. 1993. A new instrument for the measurement of soil moisture suction, Geotechnique 43, No. 2, 321–324. Tinjun, J.M., Benson, C.H., Blotz, L.R. 1997. Soilwater characteristic curves for compacted clays, ASCE J. Geotech. Geoenv. Eng. 123, 11, 1060–1069. Toker, N., Germaine, J., Sjoblom, K., Culligan, P. 2004. A new technique for rapid measurement of continuous soil moisture characteristic curves, Géotechnique 54, 3:179–186. Vanapalli, S.K., Fredlund, D.G., Pufahl, D.E. 1999. The influence of soil structure and stress history on the soil-water characteristics of a compacted till, Geotechnique 49, 2, 143–159.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A system for field measurement of suction using high capacity tensiometers J. Mendes, D.G. Toll & C.E. Augarde School of Engineering, Durham University, Durham, UK
D. Gallipoli Department of Civil Engineering, University of Glasgow, Glasgow, UK
ABSTRACT: This paper presents a new system to measure suction in the field using high capacity tensiometers recently developed through collaboration between Durham University and Wykeham Farrance Limited. The system comprises a borehole probe locator where five tensiometers can be inserted allowing the measurement of suction at different depths. Since the tensiometers are left in place, rather than being used for a single ‘‘spot’’ measurement, suctions can be observed continuously with the aid of a logger and a computer. This enables the measurement of variations of suction due to seasonal changes and the observation of the immediate response to a rainfall event. Two borehole probe locators have been installed at different points in an embankment to measure suction in the fill material. The instrumented embankment was built for research purposes at Nafferton farm, near Newcastle, UK, as part of a cooperative project (BIONICS) investigating the biological and engineering impacts of climate change on slopes. The paper describes the installation and some preliminary observations obtained using the system.
1
INTRODUCTION
Field measurements of suction in unsaturated soils have been made using different approaches: directly (using tensiometers) or indirectly (using techniques such as porous blocks) or by collection and measurement of suction in recovered samples. A direct approach is always to be preferred as the measurement is made in situ and avoids errors in defining indirect relationships (e.g. between suction and resistivity or thermal conductivity). It also avoids concerns that the quality of the suction measurement on recovered samples may be jeopardized because measurements are made in a different stress or water content condition. Conventional tensiometers have been widely used for direct measurement of suction in the field, but they have a cavitation limit of −100 kPa. On the other hand, high capacity tensiometers (i.e. tensiometers capable of measuring pore water pressures lower than −100 kPa) have been mainly used for the measurement of suction in the laboratory rather than in the field. This paper describes the use of a commercial high capacity tensiometer, manufactured by Wykeham Farrance Limited, for the measurement of suction in the field. This tensiometer has been developed through collaboration between Wykeham
Farrance Limited and Durham University and can measure water pressures directly down to −1.2 MPa or even lower (Lourenço et al., 2006). Like other high capacity tensiometers that can be found in the literature (e.g. Ridley & Burland, 1993), the design of the Wykeham Farrance—Durham University tensiometer includes a high air entry value porous filter, a water reservoir and a pressure transducer (see Figure 1).
Figure 1. Wykeham Farrance—Durham University high capacity tensiometer (after Lourenço et al., 2006).
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Previous field observations using high capacity tensiometers (Ridley et al., 2003) have used ‘‘spot’’ measurements where the tensiometer has been placed in contact with the soil to take a suction reading at a particular time, i.e. the tensiometer was not left in place to take continuous readings with time. Cui et al. (2008) have used high capacity tensiometers for the continuous measurement of suction but their system does not allow installation of multiple tensiometers at different depths at the same location. The system reported in this paper provides multiple tensiometers at different depths as well as the possibility of taking continuous readings with time from each tensiometer. In the proposed system, the tensiometers can also be easily removed if required for re-saturation or replacement. A total of ten high capacity tensiometers have been installed to observe the variation of soil suction with depth at two different locations in an experimental embankment. The embankment is located at Nafferton farm, near Newcastle, UK and has been built as part of a cooperative project (BIONICS) aimed at investigating the biological and engineering impacts of climate change on slopes. The paper describes the installation of the tensiometers in the BIONICS embankment and reports on some preliminary observations of suction using the system.
2 2.1
THE EQUIPMENT Design of the high capacity tensiometer
The operation of the Wykeham Farrance—Durham University tensiometer is based on the same general principles as other versions of high capacity tensiometer proposed in the literature. The device measures soil suction through a high air entry value filter connected to a small water reservoir, which is in contact with a pressure transducer. The tensiometers used in this work were saturated prior to calibration inside a high pressure vessel (Figure 2). The tensiometers were fixed inside the vessel, which was then filled with de-aired water and pressurized to about 1000 kPa. The tensiometers were left exposed to this pressure for a period of two weeks which is assumed to be enough for the first saturation while for subsequent re-saturations 24 hours should be enough (depending how dry the tensiometer is). In this work, however, the tensiometers were re-saturated for a longer period of two weeks given that site visits took place fortnightly. Calibration was performed by submerging the tensiometers inside a triaxial cell and reading the voltage from the tensiometers at different values of (positive) cell pressure. The ability to calibrate in the positive range and extrapolate to the negative range has been verified by Lourenço
Figure 2. Saturation vessel with a set of 5 Wykeham Farrance—Durham University field tensiometers.
et al. (2007) for the Wykeham Farrance—Durham University tensiometer and confirms the observations by Tarantino & Mongiovi (2003) for another type of high capacity tensiometer. High capacity tensiometers are limited by cavitation and air entry. Although tensiometers can sustain high suctions for short periods, they may not be able to sustain these suction values when installed in the ground for a long periods (usually, after two to three weeks the tensiometer cavitates, if a value much greater than −100 kPa is continuously read as observed from other laboratory tests). Therefore, any reliable system for the field measurement of suction has to account for the possibility of cavitation occurring in the tensiometers and it must allow removal of the probes so they can be re-saturated and re-installed whenever necessary. Some minor modifications were made to the original version of the Wykeham Farrance—Durham University tensiometer to adapt it to field conditions. The electrical cable that connects the tensiometer to the logger was covered with nylon tubing (10 m long by 8 mm diameter) to provide a stronger, stiffer connection that would allow the tensiometer to be pushed in (without buckling) during installation and pulled out during removal. The nylon tubing had the dual purpose of protecting the electrical cable from damage. The edges of the tensiometers were also smoothed for easy removal and installation.
2.2 Borehole probe locator The borehole probe locator included five suction stations at depths of 0.5 m, 1 m, 1.5 m, 2 m and 3 m, with each suction station fitted with a high capacity tensiometer. The borehole probe locator consisted of a PVC pipe 3 m long with an
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outer diameter of 90 mm and an inner diameter of 70 mm. Five guide tubes were inserted inside the borehole probe locator to individually connect each suction station to the surface. These guide tubes were made from flexible hose with an inner diameter of 19 mm. A small tapered aluminium cylinder was fitted at the end of each hose reducing the inner diameter from 19 mm down to 14 mm (this is about the same as the external diameter of the tensiometer). The aluminium fitting helped to hold the tensiometer in place and prevented movement of soil into the hose. Such a design enabled the tensiometers to be removed and inserted individually whenever necessary (see Figure 3). Due to the small inner diameter (70 mm) of the borehole probe locator the exit angle of the suction stations had to be 45◦ with the exception of the suction station located at the bottom which was vertical (see Figure 3). The top of the borehole probe locator was sealed with foam and silicone to avoid any infiltration of water or other kind of material from the surface.
3
INSTALLATION AND USAGE
Figure 3. Borehole probe locator (a) with enlarged views of the suction stations on the side (b) and bottom (c).
Figure 4. Plan view of BIONICS embankment and borehole probe locators (after Glendinning et al., 2006).
3.1 The BIONICS embankment The objective of the BIONICS project is to investigate what could happen to infrastructure embankments in the UK when subjected to climate change. As part of the project, an experimental embankment has been built in four panels (Figure 4) separated by vertical impermeable membranes and constructed by using different compaction efforts. Panels A and D are poorly compacted (intended to represent old rail embankments constructed in Victorian times) while panels B and C are well compacted (representing modern embankments). The compactive effort has two roles in the suction measurement: (i) changes in void ratio can affect the
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3.3
Figure 5. Cross section of the BIONICS embankment and borehole probe locator showing suction station depths.
water retention properties of the soil, and (ii) the permeability will also be affected (which will influence infiltration, evaporation and internal flow throughout the fill material). Current measurements of suction have been obtained during natural rainfall conditions. In the near future, a climate control system will be used to impose expected future climate patterns on the embankment. 3.2
Equipment at the embankment
One borehole probe locator was installed in the poorly compacted panel A while the second was installed in the well compacted panel B (see Figure 4). Both were located close to the south facing slope of the embankment at about 1 m from the edge of the crest (see Figure 5). Boreholes were drilled in the embankment to a depth of 3 m with a diameter of 110 mm, which is slightly larger than the outer diameter of the borehole probe locators of 90 mm. The borehole probe locators were subsequently lowered into the embankment while the suction stations were sealed using plugs with a similar shape and dimension as the tensiometers to avoid soil particles from the fill material entering the guide tubes. A period of two weeks was allowed to elapse to promote the natural closure of the borehole walls around the probe locator. During this time the plugs were kept in place to avoid entry of fill material inside the guide tubes. Subsequently the plugs were replaced with the tensiometers, which were firmly pushed into place (using the stiff nylon tube around the electrical cable) to ensure good contact between the tensiometer and the soil. Each tensiometer was fitted with an 11 m long electrical cable connected to a data logger inside a waterproof steel box placed on the top of the embankment between the two borehole probe locators. The data logger was connected to a computer in a field hut near the embankment for direct real-time downloading of data.
Maintenance of tensiometers
As discussed previously, cavitation is a possible problem for tensiometers operating over long periods of time. Regular fortnightly visits were therefore made to the site in order to verify the correct functioning of the equipment. If a tensiometer cavitates, it can be removed from the suction station and replaced by a plug. The tensiometers should not be allowed to dry so the saturation vessel is taken to the field (filled with de-aired water) to transport back the cavitated tensiometer (s); in this way a long re-saturation is avoided and after two weeks it is possible to re-install the tensiometer back in its position.
4
IN-SITU OBSERVATIONS
Preliminary suction measurements in the embankment are available from May to July 2007. Figures 6 and 8 show measurements for the well compacted panel and the poorly compacted panel respectively. Values of daily rainfall are also shown as spikes in Figures 6 and 8 for the period May to June 2007 (the record of daily rainfall for the month of July 2007 was not yet available at the time of submission of the manuscript). Note that the tensiometer for the 3 metre deep suction station in the poorly compacted panel has yet to be installed; therefore, there are only four recorded values down to 2 metres depth. It can be observed from the two figures that during the initial drier period (May) both panels had values of suction that increased with depth. However, that trend has changed for the poorly compacted panel during the wetter period (June-July). The well compacted panel shows greater suctions (20–40 kPa at 3 m) whereas in the poorly compacted panel suctions are less than 5 kPa and generally pore water pressures are positive (in the wetter period since June).
Figure 6. Pore water pressure records for the well compacted panel suction (SS indicates suction station at different depths). Vertical spikes show daily rainfall.
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Pore water pressure (kPa) –35 0 0.5
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Figure 7. Well compacted panel pore water pressure profiles for different weather conditions.
pressures approaching zero within the top 1 m (and becoming positive at 1 m). In the well compacted material the tensiometers do not show rapid responses to rainfall events, although there is a general increase in pore water pressure (reduction in suction) with time. This could be because of the lower permeability of the well compacted material is restricting infiltration, perhaps suggesting there is greater runoff from this section (runoff is not yet being measured so there are no measurements to corroborate this). It seems that it is taking some time for infiltration to slowly wet the fill material (see Figure 6) gradually decreasing the value of suction over time. 4.2
Figure 8. Pore water pressure records for the poorly compacted panel suction (SS indicates suction station at different depths). Vertical spikes show daily rainfall.
The tensiometers in the poorly compacted panel can be seen to respond almost immediately to weather changes (see Figure 8), especially during the second half of June. Note that the gaps in the curves of Figures 6 and 8 correspond to periods when data are missing because either the tensiometers were temporarily removed from the site or a mains power cut occurred causing the computer and logger to shut down. To avoid loss of data, a backup uninterruptible supply has recently been installed to power the computer in the occurrence of electrical cuts.
Poorly compacted panel
The pore water pressure readings for the poorly compacted panel (see Figure 8) within the top 1 m show a similar pattern to those for the well compacted panel. As in the well compacted panel the pore water pressure at 0.5 m is close to zero (or with small positive values). Pore water pressures at 1 m were initially around −5 kPa but have increased with time and by July show positive pore water pressures approaching 10 kPa. Initially in May, pore water pressures in the poorly compacted panel showed a reduction with depth to around −20 kPa at 2 m depth, quite similar to the well compacted panel (cf. Figures 9 and 7). However, after the rainfall events of 11–16 June, the responses of the poorly compacted panel changed and small suctions or positive pore water pressures were recorded at 1.5 and 2 m depth (see Figure 8). The reaction of the tensiometers to rainfall is clearly observed during the period 13 to 26 June. It can be seen that during this period there was a decrease on the pore water pressure measured in the shallow zone (0 to 1 m) when it rained, while the deeper tensiometers showed quite significantly increased pore water pressures, recovering to former pore water pressure values when there was less rainfall (see Figure 8). These overall trends can also be seen in the pore water pressure
Pore water pressure (kPa) -35 -30 -25 -20 -15 -10 -5 0 5 10
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Well compacted panel
31/07/2007
The pore water pressure records for the well compacted panel (see Figures 6 and 7) show a value close to zero at 0.5 m. At 1 m the initial pore water pressure was −20 kPa but has increased with time to just above zero. Below 1 m, pore water pressures reduce with depth but the values of pore water pressure have been gradually rising with time (see Figure 6). The changes in pore water pressure profiles can be seen in Figure 7. This shows a progressive wetting up, since the initial readings in May; with pore water
0.5 24/05/2007 Depth (m)
4.1
1 1.5 2 2.5 28/06/2007 3
13/06/2007 after heavy rainfall
Figure 9. Poorly compacted panel pore water pressure profiles for different weather conditions.
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be seen that the tensiometers in the switched positions gave consistent (if not identical) readings. After this test, from 26 July, both tensiometers were returned to their initial position recording similar values with those recorded previous to the shift in the position. The lack of identical readings could suggest some shift in zero values for the tensiometers. This is now being investigated by regularly removing the tensiometers (every two weeks) and immersing them in a container of water to check the zero values.
Figure 10. siometers.
5
Scattering caused by poor saturation of ten-
Figure 11. Shift in position of tensiometers at 0.5 m and 3 m in the well compacted panel.
profiles in Figure 9. It is expected that further measurements will help to provide explanations for this seemingly anomalous behaviour. 4.3
Tensiometer issues
Figure 10 shows an enlarged view of the readings plotted in Figure 6. A high degree of scattering is observed in the values measured by the tensiometer at 2 m depth, much worse than the scatter seen from other tensiometers (this scattered data was removed from Figure 6). This large fluctuation was overcome by re-saturating the tensiometer, suggesting that the tensiometer was initially not well saturated. This confirms the importance of tensiometer saturation in ensuring good quality readings. It can be observed from Figure 6 that after the re-saturation this same tensiometer showed less scatter and behaved similarly to other tensiometers. In order to check the reliability of the equipment, two tensiometers in the well compacted panel were changed in position for a period of 2 weeks (the tensiometer that was initially in the suction station at 0.5 m was swapped with tensiometer that was initially in the suction station at 3 m). From Figure 11 it can
CONCLUSIONS
The paper presents a system to measure suction in the field using Wykeham Farrance—Durham University tensiometers. The wide measuring range of the tensiometers (up to −1.2 MPa) allows usage of the proposed system in most natural and manmade earth structures. A borehole probe locator has been designed and installed. This allows the user to easily remove tensiometers for their re-saturation whenever necessary, overcoming one of the major limitations associated with the use of high capacity tensiometers in the field. The proposed borehole probe locator also allows readings at different levels in a single borehole, permitting observations of the variation of suction with depth. Two borehole probe locators have been installed in the BIONICS embankment with the intention of measuring suction in two different areas constructed by using different compactive efforts. This has allowed the observation of the variation of suction with depth in both areas and the suction changes to rainfall events. Preliminary results (from three months of monitoring) show that there are different patterns of suction measurements from the tensiometers installed in the well compacted part of the embankment compared to those installed in the poorly compacted part. It has been observed that tensiometers installed in the poorly compacted part of the embankment react rapidly to rainfall. The well compacted panel instead shows a slower change of suction and does not respond rapidly to rainfall. To check the validity of measurements, two tensiometers were swapped in position. The values measured by the two tensiometers at the same depth were consistent but not identical. This suggests there may have been some shift in the calibration zero, which is now being investigated. ACKNOWLEDGMENTS The authors gratefully acknowledge the financial support from Engineering and Physical Sciences Research Council (EPSRC) for the BIONICS project (Grant
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GR/S87430/01). The support from the European Commission via the ‘‘Marie Curie’’ Research Training Network contract number MRTN-CT-2004–506861 is also acknowledged. Thanks are also due to Dr. Paul Hughes from Newcastle University and the laboratory technicians at Durham University: Mr. McEleavey and Mr. Richardson for assistance with the experimental work. REFERENCES Cui, Y.J., Tang, A., Mantho, A.T. & De Laure, E., 2008. Monitoring Field Soil Suction Using a Miniature Tensiometer, Geotechnical Testing Journal 31 (1), (available online). Glendinning, S., Rouainia, M., Hughes, P. & Davies, O., 2006. Biological and engineering impacts of climate on slopes (BIONICS): The first 18 months, In Proc. 10th IAEG Congress, Nottingham, Paper 348 (on CD).
Lourenço, S.D.N., Gallipoli, D., Toll, D.G., Augarde, C.E., Evans, F.D. & Medero, G.M., 2007. Calibration of high suction tensiometers, submitted to Géotechnique August 2007. Lourenço, S.D.N., Gallipoli, D., Toll, D.G. & Evans, F.D., 2006. Development of a commercial tensiometer for triaxial testing of unsaturated soils. In Proc. 4th International Conference on Unsaturated Soils, Carefree, USA, Geotechnical Special Publication No. 147, ASCE, Reston. Vol. 2, 1875–1886. Ridley, A.M. & Burland, J.B. 1993. A new instrument for the measurement of soil moisture suction, Géotechnique 43 (2), 321–324. Ridley, A.M., Dineen, K., Burland, J.B. & Vaughan, P.R., 2003. Soil matrix suction: some examples of its measurement and application in geotechnical engineering, Géotechnique 53 (2), 241–253. Tarantino, A. & Mongiovi, L., 2003. Calibration of tensiometer for direct measurement of matric suction, Géotechnique 53 (1), 137–141.
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Engineering behaviour Water retention behaviour and hydraulic properties
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Water retention properties of Boom clay: A comparison between different experimental techniques T.T. Le, P. Delage, Y.J. Cui & A.M. Tang Ecole des ponts – CERMES (I. Navier, Université Paris-Est), Marne la Vallée, France
A. Lima, E. Romero & A. Gens Department of Geotechnical Engineering and Geosciences, Universitat Politècnica de Catalunya, Barcelona, Spain
X.L. Li EURIDICE, c/o SCK-CEN, Mol, Belgium
ABSTRACT: The water retention properties of Boom clay samples extracted at a depth of 223 m have been determined in ENPC Paris and UPC Barcelona using different experimental techniques. Boom clay is a stiff clay in which an underground laboratory devoted to carry out research in radioactive waste disposal has been excavated near the city of Mol (Belgium). The retention properties of Boom clay have been investigated for two reasons: i) in good quality samples, a high suction develops in the saturated sample during extraction and its value is correlated with the sampling depth; ii) possible desaturation due to gallery venting during the operational phase may occur in the clay. Various suction control and measurement techniques have been used: osmotic, vapour equilibrium, filter paper, high-range tensiometer and chilled-mirror dew-point psychrometer readings. Some volume changes have also been measured along the equalisation or measuring stages. The values obtained are discussed according to the techniques used. They are compared with previous data on compacted Boom clay samples. The air entry value is estimated close to 4–5 MPa and the shrinkage-swelling properties are also examined. The sample suction at saturation is compared to the in-situ stress state.
1
INTRODUCTION
Various investigations have been and are being carried out on the coupled thermo-hydro-mechanical behaviour of Boom clay in relation with the research conducted on radioactive waste disposal at the Mol Underground Research Laboratory (URL). This URL has been excavated in a layer of Boom clay at a depth of 223 m by SCK-CEN, the Belgian organisation for nuclear studies, near the city of Mol. Various researches on Boom clay are presently being carried out by the EURIDICE group in Mol. Special attention has been devoted to the water retention properties of Boom clay, a lightly overconsolidated saturated stiff clay. On the one hand, the examination of suction effects in samples is a relevant indicator of the quality of the sampling (Skempton & Sowa 1963, Doran et al. 2000). On the other hand, water retention properties have to be investigated to better assess possible desaturation effects due to the venting of the galleries in the operational phase of the disposal facility during which the wastes will be disposed (one to three hundreds of years).
In this paper, various suction control techniques used on intact Boom clay samples at both ENPCCERMES (Paris) and UPC (Barcelona) are described and the results obtained are compared. The following control and measurement techniques have been used to cover a wide suction range: the vapour equilibrium method, the filter paper method, high-range tensiometer and chilled-mirror dew-point psychrometer readings. The paper also includes and discusses water retention properties of compacted Boom clay obtained with vapour equilibrium technique at an equivalent void ratio to that of the in situ state.
2 2.1
MATERIALS AND EXPERIMENTAL METHODS Boom clay
The Boom clay formation belongs to the Rupelian geological period in the Tertiary sub-era, which dated from 36 to 30 million years before present. This moderately swelling clay presents 20%–30%
229
kaolinite, 20%–30% illite and 10%–20% smectite. The geotechnical properties of Boom clay are presented in Table 1. In-situ water content measurements were made on excavated blocks during the excavation in the URL (Connecting Gallery, excavated between 23 January and 23 April 2002). Figure 1 presents the water content of soil samples excavated at different distances from the wall of the gallery, measured just when the excavation was made. It is observed that at distances smaller than 1 metre from the wall, the water content values vary between 24.3% and 25.9%. The value stabilises around 24.8% at a distance larger than of 1.5 m from the wall, showing a possible perturbation of the water content due to gallery excavation.
Table 1.
Geotechnical properties of Boom clay. Belanteur Dehandschutter et al. et al. (1997) (2005) UPC
Unit mass of solid (Mg/m3 ) 2.67 Unit mass (Mg/m3 ) Liquid limit wL 59–76
1.9 70
22–26 37–50
25 45
Plastic limit wP Plastic index IP Water content (%) Natural porosity (%) Poisson’s ratio Internal friction angle (◦ ) Permeability (m/s)
2.67 1.99 to 2.05 56 using SBCW (∗ )
25–30
23–25
35 0.4
38–39
18 10−12
Excavated blocks (2002) were immediately vacuum packaged in reinforced aluminium foil and thermowelded. They were stored in Mol in a room with temperature ranging between 15 and 20◦ C under an average relative humidity of 45% before being sent (2005) to the two laboratories. 2.2 Suction control and measurement techniques The experimental study carried out at ENPCCERMES was based on the use of the vapour equilibrium method, the filter paper method and high range tensiometers. The initial water contents of the sample used at CERMES are described in Table 2. Samples were trimmed from block 3 and 4 with respective water contents equal to 23 and 23.4 respectively. When considering i) the in-situ water content and ii) the age of the samples (excavated in 2002), the light decrease in water content from the average values given in Table 2 shows a reasonably good conservation of the sample with around 1 point of decrease in water content during 3 years. Note however that some drying occurred in the laboratory during sample preparation and trimming, resulting in water contents finally equal to 21.6% and 21.8% for blocks 3 and 4 respectively. The initial suction of the sample was measured by using the filter paper method and a value of 2 MPa was obtained. Along the drying path, starting from initial water contents close to 21%, rectangular clay samples were manually trimmed (30 × 30 × 10 mm approximately) and submitted to different values of suction by using the vapour equilibrium method (see for instance Delage et al., 1998). 5 saturated saline solutions were used, as shown in Table 3. Triplicate specimens were used at each suction level to determine the water content at equilibrium.
3 × 10−12 Table 2. Initial water contents. Changes in water content during the soil sample preparation.
(∗ ) SBCW: synthetic Boom clay water.
CERMES
UPC
26.0
w (%)
25.6
After package opening During sample preparation End of sample preparation
25.2 24.8
w (%) Block 3
w (%) Block 4
w (%) Block 2
23.0 22.6 21.6
23.4 – 21.8
23.9 – –
24.4
Table 3. Saturated saline solutions used in the vapour equilibrium method.
24.0 0
0.5
1
1.5
2
2.5
3
Distance from the gallery (m)
Salt
Figure 1. Water contents measured at different distances from the gallery’s wall (Li, 2007).
CuSO4
Suction (MPa) 2.8
230
K2 SO4
KNO3
NaCl MgCl2
4.2
8.5
37.8
152.8
The volume changes of the rectangular specimens were determined by hydrostatic weighing after having immersed the samples in a non aromatic hydrocarbon liquid called Kerdane. Along the wetting path, the three oedometer specimens (cylindrical oedometer samples: d = 70 mm, h = 20 mm) were smoothly wetted (from initial water content of 21%) by putting them in contact with humid filter papers and the resulting suction was afterwards measured by using a high range tensiometer. This tensiometer is based on the principle proposed by Ridley and Burland (1993) with some special adaptations carried out at CERMES (Mantho 2005). The volume changes of these samples were determined with a precision calliper. At UPC, laboratory tests were carried out on natural and compacted samples. The natural sample was trimmed from block 2 (Table 2) with dimensions of 15 mm in diameter and 12 mm high. Water retention properties of the natural sample under unstressed conditions were determined using a chilled-mirror dewpoint psychrometer (WP4 dewpointmeter, Decagon Devices, Inc, USA) and the vapour equilibrium technique. The volume changes were not registered. On the other hand, when preparing the compacted sample, Boom clay powder was left in equilibrium at a relative humidity of 40% to achieve a water content of around 2.5%. A soil sample (15 mm in diameter and 12 mm high) was one-dimensionally compacted at this water content to a dry density of 1.7 Mg/m3 (similar to the natural dry density). Details on the working principle of the dew-point psychrometer, as well as the different calibrations carried out, have been extensively described in Cardoso et al. (2007). A multi-stage drying path was first performed by allowing the natural sample to progressively dry for one hour in each step under controlled relative humidity (around 40%). After this period, the dried sample was equilibrated for one day under hermetic conditions before taking the reading with the psychrometer. The total suction measuring time was around 5 minutes. During this period some small drying occurred inside the measuring chamber, as shown in Cardoso et al. (2007). Water contents were determined using the initial and final weights (average values). After reaching a maximum total suction of around 130 MPa, a multi-stage wetting path was carried out. The path was performed by wetting the sample with small drops of distilled water. An equalisation period of one day under hermetic conditions was afterwards performed, before the determination of the total suction. The sample was trimmed from block 2, starting from an initial water content of 21.8%. An equivalent multi-stage drying path was carried out by letting the natural material to further dry for one hour in each step under a low relative humidity using LiCl. H2 O powder (around 11%). Progressive readings on
drying were taken with the psychrometer up to a maximum total suction of 330 MPa. Afterwards, the dried sample was progressively wetted by keeping it for one hour in each step under a controlled relative humidity of around 40%. Again, progressive readings on wetting were taken with the psychrometer (Pineda et al. 2008). The vapour equilibrium technique was also used to complement the information of the wetting and drying branches of natural and compacted samples. Partially saturated aqueous solutions of NaCl were used to apply different relative humidity values (Romero 1999) below a total suction of 38 MPa. In the upper total suction range, a saturated solution of NaBr.2H2 O was also used to apply a total suction of 75 MPa (Delage et al. 1998, Romero 2001). Multistage drying and subsequent wetting paths at the following steps 5, 10, 20, 38 and 75 MPa were carried out on the natural sample placed in a hermetic jar. At specific intervals of the equalisation process the mass of the sample was registered. An equivalent procedure was followed on a compacted sample. In this case, a multi-stage wetting path followed by a drying path was performed. Samples were allowed to equilibrate for a constant period of two weeks at different relative humidity values, corresponding to the following total suctions: 32, 10, 8, 6 and 3 MPa. 3
EXPERIMENTAL RESULTS
With regard to the CERMES results, Figure 2 presents the changes in water content observed under the various suctions values imposed by using the vapour equilibrium technique. As commented before and as seen in the Figure, three samples were used at each suction value. Stabilisation is observed after around two weeks with good repeatability at the two high values (37.8 and 152.8 MPa). Some fluctuations are observed at 8.5 MPa whereas the curves at 4.2 and 2.8 MPa are superimposed with a tendency of increasing water content along a wetting path. After drying in the oven (suction s estimated to 1 GPa), the dried samples (w = 0) were used to determine a wetting branch from the dry state by using the vapour equilibrium method. Figure 3 presents the water retention properties of Boom clay in terms of both water content (w) and degree of saturation (Sr ) as a function of the logarithm of suction (log s). Starting from initial water contents of 20.2–21.6%, three points were obtained along a wetting path (with measured suctions by tensiometer equal to 180, 280 and 600 kPa respectively). The data obtained along the drying path show a good compatibility between the various points obtained under the same suction, both in terms of water content and degree of saturation. Some hysteresis is observed
231
CuSO4 (2.8 MPa)
16
w (%)
KNO3 (8.5 MPa)
12 NaCl (37.8 MPa)
8
MgCl2 (152.8 MPa)
4
0
4
8
12
16
20
Time (days) Figure 2. Water content equilibration with the vapour control method. 35
Air entry value
w (from initial state) w (Romero et al., 1999)
30 25
100
w (from dry state) Degree of saturation
20 Initial water content w i = 20.2 - 21.6%
15
80 60 40
10
20
5 Drying
Wetting
0 0,1
Degree of saturation (%)
Filter paper
Water content (%)
120
w (Bernier et al., 1997)
1
10
100
0 1000
Suction (MPa)
Figure 3.
Water retention properties of intact Boom clay.
between the two branches of the water content versus suction (w − s) curve, one wetting from dry state, the other drying form initial state. The Sr -log s plot shows that the two points obtained along the drying path at suctions equal to 2.8 and 4.2 MPa indicate that the samples remained saturated. Desaturation starts above 4.2 MPa and the degree of saturation at a suction of 8.5 MPa is 90%. As shown in the figure, the air entry value of Boom clay can be estimated at approximately 5 MPa. At the highest suction (152.8 MPa), the degree of saturation is equal to 31%. Along the wetting path, the curve shows that, curiously, the degrees of saturation at suctions smaller than 1MPa are lying between 90 and 100% whereas samples under suctions of 2.8 and 4.2 MPa were saturated. This point is related to the volume measurement technique (precision calliper) used at lower suction. As compared to the hydrostatic weighing (used at
0.90
-20 -15
Wetting: de /dlogs = - 0.5
0.80
-10
0.70 -5 0.60
0 5
0.50 Drying: de /dlogs = -0.10
0.40
10
Volumetric deformation (%)
20
suction values of 2.8 and 4.2 MPa), precision calliper measurements are thought to be less precise, leading to under-estimated values of the degree of saturation. Under the hypothesis of saturated state, the increase in water content obtained along the wetting path corresponds to some swelling. Conversely, up to the air entry value pressure (5 MPa) drying occurs with some shrinkage under a saturated state. The curve follows the main drying path at suction higher than 5 MPa when the sample starts desaturating. At a suction as high as 152.8 MPa, Boom clay is able to retain 5% water content as a consequence of the smectite content. Water retention data obtained by Bernier et al. (1997) and Romero et al. (1999) on compacted Boom clay samples at a dry unit mass of 1.7 Mg/m3 are also represented for comparison. The data show that the curve of Romero et al. (1999) is parallel, with less water being retained by the compacted sample on a drying path at the same suction. The wetting curve of Bernier et al. (1997) is similar to that of Romero et al. (1999) at high suction. Figure 4 shows the volume changes with respect to suction that correspond to the drying and wetting paths of Figure 3. A significant swelling of 18% is observed when suction is reduced to 180 kPa. A shrinkage of 15% is observed at a suction of 152.8 MPa. The slope that characterises swelling (average slope e/ log s = −0.5) is larger than the shrinkage slope (average slope e/ log s = −0.1). Bernier et al. (1997) found a similar trend on compacted Boom clay specimens subjected to change in suction under a small vertical load in the oedometer. Regarding UPC data, Figure 5 presents the time evolution of the changes in soil mass (natural Boom clay) along the different wetting steps using vapour transfer with pure diffusion. The different wetting steps were 75 MPa to 38 MPa (corresponding to a relative humidity change from 58% to 76%), 38 MPa to 20 MPa (76% to 86%), 20 MPa to 10 MPa (86% to 93%) and 10 MPa to 5 MPa (93% to 96%). Vapour mass transfer rate for a given temperature, vapour
Void ratio
K2SO4 (4.2 MPa)
15 0.30 0.1
1.0
10.0
100.0
1000.0
Suction (MPa)
Figure 4. Variation in void ration and volume with respect to suction change during drying and wetting.
232
WP4 dewpointmeter Low-suction range drying wetting High-suction range (Pineda et al. 2008) drying wetting
1000
Wetting steps: ψ = 10 MPa to 5 MPa Total suction (MPa)
ψ = 20 MPa to 10 MPa ψ = 38 MPa to 20 MPa ψ = 75 MPa to 38 MPa
Soil mass change (g)
0.30
0.20
100 Vapour equilibrium drying wetting
10
1 0
5
10 15 Water content, w (%)
20
25
Figure 6. Retention curves of natural Boom clay using different techniques (WP4 psychrometer and vapour equilibrium technique).
0.10
0.00 0.1
1
10
Time (day)
Figure 5. Time evolution of changes in soil mass along different wetting steps.
diffusivity and sample size is assumed proportional to the relative humidity change applied in a wetting step. As observed in the figure, longer equalisation periods are required for the lower relative humidity changes at elevated total suctions. Equalisation time is observed after around three weeks for the total suction step 10 MPa to 5 MPa, whereas equalisation is completed in less than one week for the total suction step 75 MPa to 38 MPa. A good agreement with CERMES results is observed. Figure 6 summarises the water retention results obtained by UPC on natural Boom clay using psychrometer readings and vapour equilibrium results. As detected in the hysteresis loops in the figure, the shifting towards lower water contents of the wetting branches is more obvious at total suctions lower than 10–20 MPa. In addition to the hydraulic hysteresis, the irreversible shrinkage undergone by the sample on first drying is also affecting the water storage capacity of the sample at low suctions. This low-suction zone of the retention curve (below 10 to 20 MPa) is dependent on void ratio and is consequently sensitive to the stress paths followed (Romero & Vaunat 2000). As observed in the figure and with reference to psychrometer readings on drying, important changes in water content occur when total suction is increased over 5 MPa (air-entry value in terms of water content). Regrettably, degrees of saturation were not determined that could allow for a further reconsideration of this
value. Equivalent water retention results were obtained when comparing vapour equilibrium data and psychrometer readings at total suctions over 38 MPa. The lower water contents determined with vapour equilibrium technique compared to WP4 readings for suctions below 38 MPa, appear to be a matter of the equalisation process. As shown in Figure 5, the equalisation process is still ongoing after 30 days for total suctions below 20 MPa. In addition, the systematic higher total suctions measured with the psychrometer for specific water contents can be explained in terms of the hydraulic path undergone by the soil during the measurement process. As discussed by Cardoso et al. (2007), the sample placed inside the equalisation chamber of the WP4 psychrometer undergoes some drying along the main drying curve during equalisation, which can explain the systematic higher suction values. Figure 7 summarises the water retention results on drying obtained by CERMES and UPC on natural Boom clay, as well as the results measured by UPC on the compacted material at an equivalent void ratio to that of the in situ state. A quite good agreement is observed between both laboratories when comparing results on natural Boom clay using vapour equilibrium technique. Small discrepancies can be explained in terms of the testing protocols adopted by each laboratory (time to reach equilibrium, sample dimensions, and so on). Psychrometer results displayed slightly larger values compared to vapour equilibrium results, as previously discussed. When comparing natural and compacted states, systematically lower water retention capacity has been observed in the case of the compacted material. These differences are more important at total suctions below 10 MPa. Differences at this low-suction range can be explained as a consequence of the different pore size distributions of
233
REFERENCES
1000 Drying paths
Total suction (MPa)
WP4 psychrometer UPC Vapour equilibrium UPC
100
Romero (1999) Vapour equilibrium CERMES
10
1 0
5
10 15 Water content, w (%)
20
25
Figure 7. Retention curves on drying. Comparison between different states (natural and compacted) and different techniques (WP4 psychrometer and vapour equilibrium technique).
the material. The compacted material displays larger dominant macropore dimensions, which are associated with a lower air-entry value (around 0.7 MPa, according to Romero 1999).
4
CONCLUSIONS
The retention properties of Boom clay have been investigated by using various suction control and measurement techniques including the vapour equilibrium method, the filter paper, high-range tensiometer readings and the chilled-mirror dew-point psychrometer. The values obtained are discussed according to the techniques used. They are compared with previous data on compacted Boom clay samples. The swellingshrinkage behaviour under changes in suction was investigated. The water retention curves determined show that the air-entry value of the natural material is closed to 4–5 MPa, much higher than the corresponding one to the compacted state at equivalent void ratio. This feature explains the lower water retention capacity of the compacted material compared to the natural state for total suctions between 3 and 10 MPa.
ACKNOWLEDGEMENT EURIDICE (European Underground Research Infrastructure for Disposal of nuclear waste In Clay Environment, Mol, Belgium) is gratefully acknowledged for funding the work presented in this paper. This work has also been conducted within the MUSE European Research and Training Network (Marie Curie Action).
Belanteur, N., Tacherifet, S. and Pakzad., M. (1997). Étude des comportements mécanique, thermo-mécanique et hydro-mécanique des argiles gonflantes et non gonflantes fortement compactées. Revue Française de Géotechnique 78, 31–50. Bernier, F., Volckaert, G., Alonso, E. and Villar, M. (1997). Suction-controlled experiments on Boom clay. Engineering Geology 47, No. 4, 325–338. Cardoso, R., Romero, E., Lima, A. and Ferrari, A. (2007). A comparative study of soil suction measurement using two different high-range psychrometers. Proc. 2nd Int. Conf. Mechanics of Unsaturated Soils. Weimar, T. Schanz (ed.). Springer-Verlag, Berlin, 79–93. Dehandschutter, B., Vandycke, S., Sintubin, M., Vandenberghe, N. and Wouters, L. (2005). Britlle fractures and ductile shear bands in argillaceous sediments: inferences from Oligocen Boom Clay (Belgium). J. Structural Geology 27, 1095–1112. Delage, P., Howat, M.D. and Cui, Y.J. (1998). The relationship between suction and swelling properties in a heavily compacted saturated clay. Engineering Geology 50, 31–48. Doran, I.G, Sivakumar, V., Graham, J. and Johnson, A. (2000). Estimation of in-situ stresses using anisotropic elasticity and suction measurements. Géotechnique 50, No. 2, 189–196. Li (2007). Personal communication. Mantho, A., (2005). Echanges sol-atmosphère. Application à la sécheresse. PhD Thesis, Ecole des ponts, Paris. ONDRAF/NIRAS, (2001). Aperçu technique du rapport SAFIR 2. Safety Assessment and Feasibility Interim Report 2. Publication NIROND 20001–05 F, p. 280. Pineda, J., Lima, A. and Romero, E. (2008). Influence of hydraulic paths on the low-strain shear modulus of a stiff clay. Proc. 1 st Eur. Conf. Unsaturated Soils. Durham, United Kingdom. Ridley, A.M. and Burland, J.B. 1993. A new instrument for measurement of soil moisture suction. Géotechnique, 43, no. 2, 321–324. Romero, E. (1999). Characterisation and thermo-hydromechanical behaviour of unsaturated Boom clay: an experimental study. PhD Thesis. Universitat Politècnica de Catalunya, Spain. Romero, E. (2001). Controlled suction techniques. Proc. 4◦ Simposio Brasileiro de Solos Nao Saturados. Gehling and Schnaid (eds.). Porto Alegre, Brasil, 535–542. Romero, E., Gens, A. and Lloret, A. (1999). Water permeability, water retention and microstructure of unsaturated compacted Boom clay. Engineering Geology 54, 117–127. Romero, E. and Vaunat, J. (2000). Retention curves of deformable clays. Proc. Int. Workshop on Unsaturated Soils: Experimental Evidence and Theoretical Approaches, Trento, Tarantino & Mancuso (eds). Balkema, Rotterdam, 91–106. Skempton, A.W. and Sowa, V.A. (1963). The behaviour of saturated clays during sampling and testing. Géotechnique 13, No. 4, 269–290.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Determination of soil suction state surface in pure and composite clays by filter paper method M. Biglari, A. Shafiee & I. Ashayeri IIEES, International Institute of Earthquake Eng. & Seismology, Tehran, Iran
ABSTRACT: Filter paper method is used to measure total suction of compacted clay and clay-sand mixture. The samples are prepared by static compaction to the desired initial void ratio and degree of saturation to investigate effects of initial compaction on the drying soil water characteristic curves. Additionally, volume change of samples was measured during the drying process and its effect was considered in obtaining SWCC. The suction measurements were plotted in e-Sr space and equal suction lines obtained. These lines represent a surface in a 3D plot.
1
INTRODUCTION
The development of unsaturated soil mechanics based on the concept of using two independent stress state variables requires measurement of the soil suction. Several techniques have been developed to measure soil suction at laboratory and in-situ. The total soil suction is known to be summation of the osmotic suction and the matric suction. Osmotic suction is influenced by salt concentration in the pore water that is present in both saturated and unsaturated soils. Osmotic suction changes have an effect on the mechanical behaviour of a soil. Krahn & Fredlund (1972) studied variation of total, matric and osmotic suction of compacted Regina clay and glacial till respect to soil water content and showed the total and matric suction curves have almost similar variations, particularly in the higher water content range (Fig. 1). Matric suction is defined as the difference between the pore air pressure above the contractile skin and the water pressure below the contractile skin. The contractile skin is consisted of water molecules at the interface layer between the water and the air, where the surface tension of the water molecules presents. The maximum matric suction that can be maintained across contractile skin is called air entry value and can be determined using Kelvin equation (Eq. 1) ua − uw =
2Ts Rs
The use of filter paper for estimating the water potential was first reported by Gardner (1937) for agricultural applications. Currently, the filter paper method is a standard test method for measurement of soil suction in ASTM D 5298-94. The filter paper method is an inexpensive and relatively simple soil suction measurement technique. In addition, it can be applied for a wide range of suction values. With the filter paper method both total and matric suction can be measured. If the filter paper is allowed to absorb water through vapor flow (noncontact method) then only total suction is measured. Otherwise, if the filter paper is allowed to acquire
(1)
where; Ts is the surface tension of the contractile skin and Rs is radius of the maximum pore size distribution. Rahardjo & Leong (2006) have presented summary of several suction measurements techniques.
Figure 1. Variation of total, osmotic and matric suction of Regina clay by water content (after Krahn & Fredlund 1972).
235
2
MATERIALS AND TESTING PROGRAM
Two basic materials are used in this study; clay and sand. The suction measurements were performed on the samples of pure clay and artificial materials composed of 60 percent clay and 40 percent sand by weight. The pure clay is classified as medium plastic Kaolinite clay. The liquid limit of the clay soil is 42 percent, the
plasticity index is 18 percent, the specific gravity of particles is 2.69 and from hydrometer analysis the clay size fraction (finer than 2 μm) is about 60 percent and the remaining 40 percent is smaller than 75 μm (sieve No. 200). The sand is classified as medium to fine uniformly graded sand (SP in USCS) and its fine content is about 1 percent. The specific gravity of the material is 2.69. Figure 2 represents particle size distribution of sand. Different samples were prepared from pure clay (C100) and the composite material (C60). The soils were compacted statically to a disc shaped samples
100 90 80 70
Percent Passing
water through fluid flow (contact method), then only matric suction is measured. Meanwhile, the provision of contact between filter paper and the pore fluid is difficult in low water content samples, the contact filter paper method may measure either the total or the matric suction, depending on the degree of contact between the soil and the filter paper. The most commonly used filter papers for suction measurement are Whatman No. 42 and Schleicher & Schuell (S&S) No. 589-WH. The calibration curve for these two filter papers is given in ASTM D 5298-94 and is used in the measurements of the present investigation. The variation of matric suction in an identical soil specimen during drying and wetting versus soil specimen gravimetric water content, degree of saturation or volumetric water content is called soil-water characteristic curve (SWCC) or soil water retention curve. It has been found that at a given matric suction the soil water content during the wetting and drying process are different, that is known as the hysteretic behaviour of SWCCs. Furthermore, recent investigations revealed that there is no single, unique relationship between volume change and water content change for an unsaturated soil. The volume change and the water content change in an unsaturated soil are controlled by two independent mechanisms; the stress strain behaviour and the adsorption-drainage behaviour (Fredlund & Pham 2006). Conventionally, the SWCC is determined at zero net normal stress and the volume changes of soil specimen during the determination of SWCC are ignored. Ho et al. (2006), in a recent experimental studies, have used a volumetric pressure plate extractor and provided state dependent soil water characteristic curves (SDSWCC) where the degree of saturation is expressed by two stress state variables. In the present study, the total suction of pure and composite clay-sand mixture is measured by the filter paper method and the effects of initial degree of saturation and void ratio on the total suction are investigated. Furthermore, the soil samples were allowed to dry gradually and the variation of total suction is measured while considering volume changes of the specimen. The total suction measurements are presented by contour lines in e-Sr space for both materials and the possible state surfaces are shown in 3D plot.
60 50 40 30 20 10 0 0.001
Figure 2.
0.01
0.1 1 Particle Size (mm)
10
100
Particle size distribution of pure sand.
Table 1. Initial void ratio and degree of saturation for samples. Sample no.
e0
Sr 0 (%)
Sample no.
e0
Sr 0 (%)
C100-1 C100-2 C100-3 C100-4 C100-5 C100-6 C100-7 C100-8 C100-9 C100-10 C100-11 C100-12 C100-13 C100-14 C100-15 C100-16 C100-17 C100-18 C100-19 C100-20 Max Min
0.684 0.672 0.688 0.666 0.723 0.667 0.774 0.640 0.630 0.698 0.733 0.663 0.691 0.661 0.637 0.655 0.572 0.584 0.575 0.600 0.774 0.572
33.0 47.0 58.5 76.9 85.9 37.9 45.8 64.4 82.4 94.6 38.2 56.6 63.0 75.6 88.8 44.9 62.4 70.6 81.9 87.5 94.6 33.0
C60-1 C60-2 C60-3 C60-4 C60-5 C60-6 C60-7 C60-8 C60-9 C60-10 C60-11 C60-12 C60-13 C60-14 C60-15 C60-16 C60-17 C60-18 C60-19 C60-20 Max Min
0.677 0.705 0.762 0.835 0.767 0.673 0.660 0.724 0.772 0.729 0.624 0.688 0.648 0.643 0.659 0.534 0.557 0.572 0.589 0.603 0.835 0.534
30.6 36.4 44.1 49.4 65.3 29.9 40.2 42.7 50.2 61.2 35.1 40.7 49.2 54.4 63.4 38.8 44.7 47.4 54.6 59.6 65.3 29.9
236
with approximate diameter of 50 mm and height of 20 mm. In order to investigate effects of initial void ratio and degree of saturation on the suction, the samples were compacted to different e and Sr. Twenty samples were prepared for each soil group. Table 1 presents the initial conditions of the samples. The samples were weighted by a digital balance with 0.0001 gr accuracy and the average diameter and height of the sample for volume measurements were measured with 0.05 mm accuracy. Filter paper tests were performed according to ASTM D 5298-94 and total suction was measured in the samples. Whatman No. 42 filter paper was used for suction measurements and the corresponding standard calibration curve was applied. For the vapor equalization time the samples and two filter papers were placed into sealed jars and the jars were kept in an isolated container for 10 days. According to Marinho (1994) 7 to 15 days is suitable equalization time for total suction measurement in the range of 250 to 30000 kPa. The filter papers were placed above a piece of PVC pipe with height of 20 mm, itself placed above the soil sample in the jar. After 10 days the weight of filter papers was measured with the digital balance and then the filter papers were placed into oven with 110 ± 5◦ C for 10 hours. After 10 hours the dry weight of filter paper was measured. Detail of the procedure is presented by Bulut et al (2001).
Accordingly, the soil samples were placed into a desiccator for 3 days to reduce water content. In order to facilitate desiccation silica gel was used. After three days the soil samples weighted with the digital balance and their volume was measured. Afterward, they were placed into jars with new filter papers again. The procedure explained above was repeated four times for C100 samples and three times for C60 samples.
3
DISCUSSION OF TEST RESULTS
Figure 3 presents the drying SWCCs for both soils. It is clearly shown that the samples of the same material follow different drying curves according to their different initial conditions. The comparison between SWCC of C100 and C60 reveals that the SWCCs of C100 are more deviated than C60s’, although the deviation in e0 of C60s is more than C100s (Table 1). Furthermore, the average SWCC of C60 has smaller suction than the average C100 one. Figures 4 & 5 plot the variation of void ratio versus total suction along the drying path for C100 and C60 respectively. It is observed that again initial void ratio affects significantly the suction of the sample when the sample’s suction is less than a specific value. This specific value corresponds to the sample’s shrinkage limit. For instance, samples of C100 with suction more
100 90 80
Degree of saturation
70 60 50
C100-1
C100-2
C100-3
C100-4
C100-5
C100-6
C100-7
C100-8
C100-9
C100-10
C100-11
C100-12
C100-13
C100-14
C100-15
C100-16
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C100-18
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C60-1
C60-2
C60-3
C60-4
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C60-14
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C60-16
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C60-20
40 30 20 10 0 100
1000
10000 Total Suction (kPa)
Figure 3.
Drying SWCC for C100 and C60.
237
100000
0.8
C100-1 C100-2 C100-3
0.75
C100-4 C100-5
0.7
C100-6 C100-7
Void Ratio (e)
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C100-8 C100-9
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0.4 100
1000
10000
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C10010 C10011 C10012 C10013 C10014 C10015 C10016 C10017 C10018 C10019 C10020
Total Suction (kPa)
Figure 4.
Void ratio variation in drying SWCC for C100.
50
C100-1 C100-3 C100-5 C100-7 C100-9 C100-11 C100-13 C100-15 C100-17 C100-19 C60-1 C60-3 C60-5 C60-7 C60-9 C60-11 C60-13 C60-15 C60-17 C60-19
45
Volumetric water content
40 35 30 25 20 15 10 5 0 100
Figure 5.
1000
10000 Total Suction (kPa)
Void ratio variation in drying SWCC for C60.
238
100000
C100-2 C100-4 C100-6 C100-8 C100-10 C100-12 C100-14 C100-16 C100-18 C100-20 C60-2 C60-4 C60-6 C60-8 C60-10 C60-12 C60-14 C60-16 C60-18 C60-20
0.9
C60-1 C60-2 C60-3 C60-4 C60-5 C60-6 C60-7 C60-8 C60-9 C60-10 C60-11 C60-12 C60-13 C60-14 C60-15 C60-16 C60-17 C60-18 C60-19 C60-20
0.85
0.8
Void Ratio (e)
0.75
0.7
0.65
0.6
0.55
0.5 100
1000
10000
100000
Total Suction (kPa)
Figure 6.
Volumetric water content versus suction for C100 and C60.
C100-1
0.9
C100-2 0.85
C100-3 C100-4
0.8
C100-5 C100-6
0.75
C100-7
Void Ratio (e)
C100-8 0.7
C100-9 C100-10
0.65
C100-11
1MPa
C100-12
0.6
C100-13 2MPa
0.55
C100-14 C100-15 C100-16
0.5
C100-17
5MPa
C100-18
0.45 20MPa
15MPa
C100-19
10MPa
C100-20
0.4 0
10
20
30
40
50
60
Degree of Saturation
Figure 7.
Contour lines of equal suction in e-Sr space for C100.
239
70
80
90
100
0.9
C60-1 C60-2 C60-3 C60-4 C60-5 C60-6 C60-7 C60-8 C60-9 C60-10 C60-11 C60-12 C60-13 C60-14 C60-15 C60-16 C60-17 C60-18 C60-19 C60-20
0.85
Void Ratio (e)
0.8 0.75 0.7 1MPa 0.65 0.6 3MPa
0.55 15MPa 10MPa 7MPa 5MPa 0.5 0
Figure 8.
10
20
30
40 50 60 Degree of saturation
70
80
90
100
Contour lines of equal suction in e-Sr space for C60.
than 5 MPa shows no correlation to void ratio and similarly, the samples with suction more than 3 MPa for C60s. Figure 6 presents drying SWCC of both materials by volumetric water content versus suction. Although different drying curves are observed for different samples, the volumetric water content versus suction looks less deviated than Figure 3. This can be interpreted as the incorporated presence of void ratio or porosity and degree of saturation in the volumetric water content definition. The variation of soil suction versus void ratio and degree of saturation (or volumetric water content) expresses that soil suction can be plotted versus these two parameters. Figures 7 & 8 present the positions of all samples in the e-Sr space. The dashed lines represent contour lines of equal suctions. These lines resemble a 3D surface in suction versus void ratio and degree of saturation space (Fig. 9). It is illustrated that total suction is more influenced by void ratio for an intermediate range of degree of saturation. The contour line of equal suction tends to vertical as the degree of saturation decreases and the variation of suction decreases as the degree of saturation tends to one. Comparison between Figures 7 and 8 reveals the shrinkage of this intermediate range by increasing sand content. Figures 10 & 11 replot variation of degree of saturation versus suction for some of the test results presented in Figures 7 & 8 respectively, where the void
Figure 9.
Suction state surface in 3D plot for C100.
ratio of samples are constant. These figures illustrate possible drying SWCCs for the samples that have similar void ratio. The lower the void ratio of the samples, the larger the air entry values and the larger the suction. Figure 11 represents increasing sand content of the material up to 40 percent has eliminated effect of void ratio to some extent. 4
CONCLUSION
Filter paper method is an inexpensive and relatively simple technique for measurement of both total and matric suction of soil. In addition, it can be applied for a wide range of suction values. In the present study, filter paper method was applied to investigate effect of initial void ratio on drying SWCCs. The material tested was composed of pure clay and clay-sand
240
100 90 Lower void ratio
80
Degree of Saturation
70 60 50 Higher void ratio 40 30 20 10 0 100
1000
10000
100000
Total Suction (kPa) Ave(e)=0.463, Stdev(e)=0.001 Ave(e)=0.635, Stdev(e)=0.006
Figure 10.
Ave(e)=0.499, Stdev(e)=0.005 Ave(e)=0.666, Stdev(e)=0.003
Ave(e)=0.561, Stdev(e)=0.007 Ave(e)=0.682, Stdev(e)=0.005
Drying SWCC at constant void ratio for C100.
100 90 80
Degree of Saturation
70 60 50 40 30 20 10 0 100
1000
Total Suction (kPa)
Ave(e)=0.685, Stdev(e)=0.005 Ave(e)=0.627, Stdev(e)=0.005
Figure 11.
10000 Ave(e)=0.658, Stdev(e)=0.003 Ave(e)=0.574, Stdev(e)=0.007
Drying SWCC at constant void ratio for C60.
241
100000
mixture. The tests results revealed that the initial condition of the samples significantly affects SWCCs but increasing sand content has reduced the extent of effects. Additionally, presenting SWCC by volumetric water content, instead of degree of saturation, results into less deviated SWCCs. Meanwhile, considering volume change of sample during measurement of total suction is found to be more important for an intermediate range of degree of saturation of samples and this range shrinks by increasing sand content. More accurate numerical modeling can be achieved by using 3D constitutive surfaces or constant void ratio SWCCs instead of single SWCC. REFERENCES Bulut, R., Lytton, R.L. & Wary, W.K. 2001. Suction Measurements by Filter Paper, Expansive Clay Soils and Vegetative Influence on Shallow Foundations, ASCE Geotechnical Special Publication No. 115 (eds. C. Vipulanandan, M.B. Addision, and M. Hasen), ASCE, Reston, Virginia, pp. 243–261.
Fredlund, D.G. & Pham, H.Q. 2006. A Volume-mass Constitutive model for Unsaturated Soils in Terms of Two Independent Stress State Variables, Unsaturated Soils, ASCE, Geotechnical special publication No. 147. pp. 105–134. Gardner, R. 1937. A Method of Measuring the Capillary Tension of Soil Moisture over a Wide Moisture Range, J. Soil Science. Vol. 43, No. 4, pp. 277–283. Ho, K.M.Y., Ng, C.W.W., Ho, K.K.S. & Tang, W.H. 2006. State-dependent Soil-water Characteristic Curve (SDSWCCs) of Weathered Soils, Unsaturated Soils, ASCE, Geotechnical special publication No. 147, pp. 1302–1313. Krahn, J. & Fredlund, D.G. 1972. On Total Matric and Osmotic Suction, J. Soil Science. Vol. 114, No. 5, pp. 339–348. Marinho, F.A.M. 1994. Medicao de succao com o metodo do papel fitro, In Proc. X Congresso Brasileiro de Mecanica do Solos e Engenharia de Fundacoes. Vol. 2, pp. 516–522. Rahardjo, H. & Leong, E.C. 2006. Suction Measurements, Unsaturated Soils, ASCE, Geotechnical special publication No. 147, pp. 81–104.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Soil water retention curves for remolded expansive soils K.C. Chao, J.D. Nelson, D.D. Overton & J.M. Cumbers Engineering Analytics, Inc., Fort Collins, Colorado, USA
ABSTRACT: Volume change in expansive soils occurs due to changes in the soil water system that change the stress equilibrium of the soil. Consequently, when determining the Soil Water Retention Curve (SWRC) of an expansive soil, it is important to consider the volume change that occurs as the suction, and hence water content, changes during the test. Experiments using the Fredlund SWCC device and the filter paper method were conducted to take into account the effect of the volume changes on the soil water retention relationship of expansive soils. Claystone samples of the Denver and Pierre Shale Formations obtained near Denver, Colorado, USA were used in the study. A moist tamping system was used to obtain ‘‘identical’’ soil specimens. The observed experimental data were used to evaluate the previously published mathematical equations of SWRC. It is shown that the Fredlund and Xing equation is in the best agreement with the experimental data among the equations. In addition, a bilinear form was used to express the SWRC for the expansive soils. It is concluded that the bilinear form of the SWRC gives the best fit to the measured experimental data.
1
INTRODUCTION
The soil water retention curve (SWRC) has played a dominant role in unsaturated soils in disciplines such as soil science, soil physics, agronomy, and agriculture. There is some discussion within the soil water research community regarding the use of the term soil water retention curve (SWRC) as opposed to the term soil water characteristic curve (SWCC). The term soil water retention curve (SWRC) has been adopted in this paper. However, when reference is made to the Fredlund SWCC device and test results therefrom, the term SWCC has been retained in connection with that device. The SWRC has been identified as the key soil information required for the analyses of seepage, shear strength, and volume change problems involving unsaturated soils. The SWRC is usually measured assuming no volume change of the soil specimen. This is not the case for an expansive soil. When determining the SWRC of an expansive soil, it is important to consider the volume change that occurs as the suction changes during the test. The SWRC of a soil is hysteretic. Therefore, depending on whether the process being simulated in the field is a wetting or drying process, an appropriate wetting or drying curve needs to be determined for the soil. Heaving of expansive soils/bedrock is related to the wetting process. Consequently, a wetting curve should be utilized in simulations of the migration of water in the subsoils/bedrock for modeling heave
phenomena. This paper focuses on an evaluation of the wetting curves of the expansive claystone of the Denver and Pierre Shale Formations. A moist tamping system was used to obtain identical soil specimens. The Fredlund SWCC device and the filter paper test were utilized in the experiments. The observed experimental data were used to evaluate previously published mathematical equations for the SWRC. This paper presents the results of the experimental data of the claystone and a proposed equation for the SWRC curve. 2 2.1
EXPERIMENTAL PROGRAM Soil description and index properties
Samples of claystone of the Denver and Pierre Shale Formations were obtained using drilling with a continuous core sample at sites near Denver, Colorado, USA. The boring log of the claystone of the Denver Formation indicates that the claystone bedrock was slightly moist and consisted of yellowish brown, hard claystone with some oxidation and occasional silty claystone lenses. The boring log of the claystone taken from the Pierre Shale Formation indicates that the claystone bedrock was slightly moist and consisted of light olive brown and gray claystone with oxidation along the bedding planes. The results of the laboratory tests are provided in Table 1. The samples of the claystone of both the Denver and Pierre Shale Formations were classified
243
Table 1.
Summary of geotechnical properties of Denver and Pierre Shale formations. Consolidation-Swell Test(2)
Formation of claystone bedrock
Natural water content (%)
Natural dry density (Mg/m3 )
LL/PL(1) (%)
Percent swell (%)
Swell pressure (kPa)
Denver Pierre shale
20.1–26.5 15.2–16.3
1.54 –1.67 1.81–1.92
56–68/32–43 60–61/41–42
6.5–7.4 3.1–5.7
1150–2550 710–1300
Notes: (1) LL = Liquid Limit, PL = Plastic Limit. (2) Inundation Pressure, σi = 48 kPa.
as high plasticity clay (CH). They exhibited moderate to very high swell potential. 2.2
Specimen preparation
A variety of methods have been developed for reconstituting soil specimens in the laboratory. The moist tamping method is one of the successful methods proposed for preparing nearly identical soil specimens (Mulilis, et al., 1975). The early implementation of the moist tamping method involved the soil specimen being prepared using a number of layers of equal dry weight and volume wherein each layer was being compacted to the same target density. Mulilis, et al. (1975) found that this could result in the lower portion of the specimen becoming denser than the desired specimen density because the compaction of each overlying layer also resulted in the densification of underlying layers. Noorany (2005) proposed to prepare a soil sample with a number of layers of equal soil weight and volume when compacting each layer into a compaction mold, as shown in Figure 1. Noorany (2005) found that this modified moist tamping method was successful in preparing uniform soil specimens for the oedometer test. The modified moist tamping method was utilized to prepare and compact soil specimens for the laboratory testing. The soil specimens were prepared for testing by compacting them to 100% of the maximum Standard Proctor dry density at a water content 3% less than the optimum water content. The sample rings used for the experiment have dimensions of 6.2 cm inside diameter and 3.1 cm thick. The thick steel plate shown in Figure 1 is 0.5 cm in height. The soil sample at the completion of compaction within each ring was 2.5 cm in height. In addition, four (4) layers with each layer being 0.6 cm in height were selected for the compaction process.
2.3
Experimental procedure
2.3.1 Filter paper test The filter paper method was used to obtain the soil water retention relationship of both soil types for a soil suction ranging from approximately 1 to 175,000 kPa.
Figure 1. Schematic of Moist Tamping System (modified from Noorany, 2005).
This range corresponds to a pF of 1.01 to 6.25. Whatman No. 42 filter paper was used in this study. The weight of the filter paper was measured to the nearest 0.0001 g during the test. The filter paper method was adopted to measure total and matric suctions of soil specimens in accordance with both non-contact and contact techniques described in ASTM D5298-94. ASTM D5294-94 recommends a minimum equilibration time of 7 days for running the filter paper contact and non-contact tests. However, in examining the required time for filter paper to reach equilibrium, it was found that the equilibration time is dependent on suction source, measured suction type (contact or non-contact method), material type, water content of soil specimen (suction level), number of pieces of filter paper used, relative humidity of the air, and soil mass and space in the container. The time required for equilibration of the filter paper when measuring the suction of the claystone from the Pierre Shale Formation was evaluated in Chao (2007). For determining the boundary wetting curve, the soil specimen was initially air-dried in the laboratory. The weight and volume of the air-dried sample were
244
measured. Calipers were used to measure the height and diameter of the sample in order to determine the volume. A filter paper test was performed on the airdried sample to obtain a soil suction corresponding to the lowest water content of the sample. At the completion of the first filter paper test, water was sprayed onto the soil specimen to obtain a desired water content of the sample for the next filter paper test. The values of water content of the sample were increased at intervals of approximately 5%. The wetting curve test continued until the last desired value of water content of the soil specimen was reached. Measurements of the weight and volume of the sample at equilibrium were taken throughout the experiment. In addition, five remolded samples of the Pierre Shale claystone were oven-dried to obtain the soil suction of the claystone at oven-dry water content conditions using the filter paper method. The sample was cut in two pieces and filter papers were placed between the pieces. A rubber band was placed around the sample to ensure contact between the filter papers and the soil. 2.3.2 Fredlund SWCC test The Fredlund SWCC device was utilized to determine the SWRC over a range of soil suction from 2 to 900 kPa for the claystone of the Denver formation. This soil suction range overlapped the range used in the filter paper tests to verify the measured laboratory data from each other. A schematic of the Fredlund SWCC device used in this study is shown in Figure 2. The sample rings used for the test are 6.4 cm in diameter and 2.5 cm in height. The Fredlund SWCC device was calibrated to account for compressibility of the device, filter paper, and porous stone (Chao, 2007). Similar to the filter paper test, the soil specimen was compacted to 100% of the maximum Standard Proctor dry density at a water content 3% less than the optimum water
content, and then air-dried until a minimum water content was reached in the laboratory. The weight and volume of the air-dried sample were measured. The air-dried soil specimen was transferred to a ceramic stone placed in the pressure cell of the Fredlund SWCC device. The water below the ceramic stone was maintained at atmospheric pressure. A specified air pressure was applied into the pressure cell. In response to the applied suction, the water was drawn into the soil specimen through volume indicator tubes and through the ceramic stone until equilibrium was established. It was possible for air to diffuse through the ceramic stone and collect on the bottom of the cell. Therefore, the diffused air was flushed out before reading the levels in the volume indicator tubes. The water content of the specimen was calculated using the volume indicator tube readings. The change in height of the soil specimen was measured from an attached dial gauge. This procedure was repeated for successive pressure decrements to obtain a series of data points on the wetting curve. The pressure values that were used were 900, 400, 100, 10, and 2 kPa. At the end of the wetting curve test, the soil specimen was removed from the cell and its water content and dry density were determined. 2.4 Experimental results Figures 3 and 4 present the SWRCs in terms of volumetric water content from the average values of the experimental data for the Denver and Pierre Shale Formation samples, respectively. The osmotic suction curves shown in Figures 3 and 4 were computed by subtracting the matric suction values from the total suction values. None of the SWRCs shown in Figures 3 and 4 exhibit a distinct point of bifurcation to define the displacement pressure head. This trend of not having a distinct displacement pressure head for expansive soil has also been reported by others (Chao, 1995;
Volumetric Water Content (%)
50 45
Total Suction
40
Matric Suction
35
Osmotic Suction
30 25 20 15 10 5 0 1
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100000 1000000
Soil Suction (kPa)
Figure 2. Schematic of Fredlund SWCC device (from GCTS 2004).
Figure 3. Wetting SWRC—Total, matric and osmotic suctions from Filter Paper test—Remolded claystone of Denver formation.
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60
45 40
Total Suction Matric Suction
35
Osmotic Suction
Volumetric Water Content (%)
Volumetric Water Content (%)
50
30 25 20 15 10 5
Measured Data Burdine (1953), r^2 = 0.8980
50
Gardner (1958), r^2 = 0.9559 Brooks & Corey (1964), r^2 = 0.8960
40 30 20 10 0
0 1
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Soil Suction (kPa)
Figure 4. Wetting SWRC—Total, matric, and osmotic suctions from Filter Paper test—Remolded claystone of Pierre Shale formation.
10
100 1000 Soil Suction (kPa)
10000 100000
1000000
Figure 6. Burdine, Gardner, and Brooks & Corey equations fitted to experimental data—Claystone of Denver formation.
60 Volumetric Water Content (%)
Volumetric Water Content (%)
60 Measured Data from Filter Paper Test 50
Measured Data from Fredlund SWCC Test
40 30 20 10
1
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100000 1000000
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Soil Suction (kPa)
Soil Suction (kPa)
Figure 7. Mualem, van Genuchten, and Fredlund & Xing equations fitted to experimental data—Claystone of Denver formation.
Figure 5. Comparison of wetting SWRCs from Filter Paper test and Fredlund SWCC test—Remolded claystone of Denver formation.
Al-Mukhtar, 1995; Alonso, et al., 1995; Wan, et al., 1995; and Miller, 1996). The Fredlund SWCC test was conducted on the remolded claystone of the Denver Formation and the results were compared with those obtained using the filter paper method. Figure 5 shows that the filter paper test reproduced the results obtained from the Fredlund SWCC test.
3.1
40
0
0
3
Measured Data Mualem (1976), r^2 = 0.9136 van Genuchten (1980), r^2 = 0.9559 Fredlund & Xing (1994), r^2 = 0.9685
50
ANALYSIS OF EXPERIMENTAL DATA Curve fitting with previously published SWRC equations
The observed experimental data were fitted to the previously published mathematical equations for the SWRC. Selected mathematical equations include those proposed by Burdine (1953), Gardner (1958), Brookes and Corey (1964), Mualem (1976), van Genuchten (1980), and Fredlund & Xing (1994). Figures 6 and 7 show the curve fitting for the claystone of the Denver Formation. Figures 8 and 9
show the curve fitting for the claystone of the Pierre Shale Formation. The values of r 2 for regression analyses of the equations are also shown in the figures. Comparison of Figures 6 through 9 indicates that among all equations considered, the Brooks and Corey equation provides the least agreement with the experimental data. The reason for the poor fit of the Brooks and Corey equation is that this curve exhibits a sharp break at the air entry value. This is more representative of sandy soil having a relatively narrow grain size distribution. It should be noted that this equation was developed for a rigid porous medium (i.e. no volume change). It is seen in Figures 6 through 9 that the Fredlund and Xing equation exhibits the best agreement with the experimental data. An interesting observation is that the four-parameter equations (such as the van Genuchten and Fredlund & Xing equations) performed a better curve fitting than the three-parameter equations (such as the Burdine, Brooks and Corey, and Mualem equations). This observation was also made by Leong and Rahardjo (1997) for other soil types.
246
(%)
Measured Data Burdine (1953), r^2 = 0.9108
50
Volumetric Water Content,
Volumetric Water Content (%)
60
Gardner (1958), r^2 = 0.9574 Brooks & Corey (1964), r^2 = 0.8819
40 30 20 10 0 1
10
100
1000
10000
30 = -2.3404Ln( ) + 43.396 r2 = 0.9957
20 10
= -5.3991Ln( ) + 69.37 r2 = 0.9875
? 10
100 1000 Soil Suction,
10000 (kPa)
100000 1000000
Figure 11. Bilinear equation fitted to experimental data— Claystone of Pierre Shale formation.
and Miller, 1996). The results of the experimental data plotted in bilinear form are shown in Figures 10 and 11 for the claystone of the Denver and Pierre Shale Formations, respectively. It is shown in Figures 10 and 11 that the bilinear form of the SWRC gives the best fit to the measured experimental data compared to the published mathematical equations discussed previously. The question mark by the point at zero water content indicates that this point was not used in the curve fitting procedure.
60 Volumetric Water Content (%)
40
1
Figure 8. Burdine, Gardner, and Brooks & Corey equations fitted to experimental data—Claystone of Pierre Shale formation.
Measured Data Mualem (1976), r^2 = 0.9213 van Genuchten (1980), r^2 = 0.9570 Fredlund & Xing (1994), r^2 = 0.9727
40
Measured Data
50
0
100000 1000000
Soil Suction (kPa)
50
60
30 20 10 0 1
10
100
1000
10000
100000 1000000
4
Soil Suction (kPa)
Figure 9. Mualem, van Genuchten, and Fredlund & Xing Equations fitted to experimental data—Claystone of Pierre Shale formation.
Volumetric Water Content (%)
60 50
Measured Data
40 30 = -2.5853Ln( ) + 46.686 r2 = 0.982
20 10
= -6.2348Ln( ) + 80.671 r2 = 0.9865
?
0 1
10
100 1000 10000 Soil Suction (kPa)
100000 1000000
Figure 10. Bilinear equation fitted to experimental data— Claystone of Denver formation.
3.2
Curve fitting with bilinear equation
Chao, et al. (1998) indicated that a bilinear form gives a good agreement to the observed experimental data for expansive soils. The bilinear relationship of the SWRC for expansive soils has also been reported by others (McKeen and Neilsen, 1978; Marinho, 1994;
DISCUSSION AND CONCLUSIONS
Fredlund (2002) stated that matric suction dominates the lower suction portion of a SWRC, while osmotic suction dominates the high suction portion of the SWRC. Capillary effects dominate when there is a significant amount of liquid water in the soil, whereas the osmotic suction related to the adsorbed salts dominates the behavior of the soil at a high suction range. It was shown by van der Raadt, et al. (1987) that filter paper results used both in contact and noncontact modes were similar for values of suction above 1,000 kPa, but were different for values of suction less than 1,000 kPa. Leong et al. (2002) suggested that for ‘‘up to 1000 kPa suction, the contact filter paper method can be used to measure matric suction reliably, while the noncontact method can be used to measure total suction. Beyond 1,000 kPa suction, the filter paper method measures only total suction, regardless if the contact or the noncontact procedure is used.’’ Figures 3 and 4 indicates that this limit is much higher (closer to 10,000 kPa). The soil suction at zero water content is used as a boundary point in heave prediction using the soil suction method proposed by McKeen (1992). The soil suction at zero water content was stated by McKeen (1992) to be near 174,385 kPa (6.25 pF). Fredlund and Xing (1994) introduced a correction function, C(ψ),
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in their SWRC fitting equation to force the SWRC to pass through a soil suction of 106 kPa (7.0 pF) at zero water content. The measured average total suction of the five oven-dried claystone samples shown in Figure 5 is approximately 245,000 kPa (6.40 pF) at oven-dry water content. This value of measured soil suction at oven-dry water content is closer to that expressed by McKeen (1992). The bilinear form used in this study is representative of the observed experimental data for expansive soils. At stress above 100 MPa, the curve tends to increase in slope to a limiting suction value of about 245,000 kPa (6.40 pF). Cumbers (2007) measured points that fell on a straight line between suction values of about 100,000 kPa and 245,000 kPa. Thus, the curves are in fact tri-linear, but for suction values below 100,000 kPa they will be referred to as being bi-linear. The change in slope of the SWRC for expansive soil has been attributed to the transition from macropore spaces, where water retention is governed by capillary mechanisms, to micropore spaces, where water retention is governed by thermodynamic forces (Miller, 1996). REFERENCES Al-Mukhtar, M. (1995). ‘‘Macroscopic Behavior and Microstructural Properties of a Kaolinite Clay Under Controlled Mechanical and Hydraulic State.’’ Proceedings, 1st International Conference Unsaturated Soils, Paris, I, 3–9. Alonso, E.E., Lloret, A., Gens, A., and Yang, D.Q. (1995). ‘‘Experimental Behavior of Highly Expansive Double-Structure Clay.’’ Proceedings, 1st International Conference Unsaturated Soils, Paris, I, 11–16. Brooks, R.H., and Corey, A.T. (1964). ‘‘Hydraulic Properties of Porous Media.’’ Hydrology Paper No. 3, Colorado State University, Fort Collins, Colorado. Burdine, N.T. (1953). ‘‘Relative Permeability Calculations from Pore Size Distribution Data.’’ Journal of Petroleum Technology, 5, 71–78. Chao, K.C. (1995). ‘‘Hydraulic Properties and Heave Prediction for Expansive Soil.’’ Maters Thesis, Colorado State University, Fort Collins, Colorado. Chao, K.C., Durkee, D.B., Miller, D.J., and Nelson, J.D. (1998). ‘‘Soil Water Characteristic Curve for Expansive Soil.’’ Thirteenth Southeast Asian Geotechnical Conference, Taipei, Taiwan. Chao, K.C. (2007). ‘‘Design Principles for Foundations on Expansive Soils.’’ Dissertation submitted in partial requirement for the Ph.D. Degree, Colorado State University, Fort Collins, Colorado. Cumbers, J.M. (2007). ‘‘Soil Suction for Clay Soils at Oven-Dry Water Contents and the End of Swelling Conditions.’’ Thesis submitted in partial requirement for the Mater Degree, Colorado State University, Fort Collins, Colorado. Fredlund, D.G. (2002). ‘‘Use of Soil-Water Characteristic Curves in the Implementation of Unsaturated Soil Mechanics.’’ Third International Conference on Unsaturated Soils. Recife, Brazil.
Fredlund, D.G. and Rahardjo, H. (1993). ‘‘Soil Mechanics for Unsaturated Soil.’’ John Wiley & Son, Inc., New York, NY. Fredlund, D.G. and Xing, A. (1994). ‘‘Equation for the Soil-Water Characteristic Curve.’’ Canadian Geotechnical Journal, 31(3), 521–532. Gardner, W.R. (1958). ‘‘Some Steady State Solutions of the Unsaturated Moisture Flow Equation with Application of Evaporation from a Water Table.’’ Soil Science, 85(4), 228–232. Geotechnical Consulting and Testing Systems, Inc. (GCTS). (2004). ‘‘Fredlund SWCC Device Operating Instructions.’’ Tempe, Arizona. Jefferson County GIS Department. (1997). ‘‘Designated Dipping Bedrock Area. 1: 62,500 scale.’’ Jefferson County, Colorado. Leong, E.C. and Rahardjo, H. (1997). ‘‘Review of Soil-Water Characteristic Curve Equations.’’ Journal of Geotechnical and Geoenvironmental Engineering, 123(12), 1106–1117. Leong, E.C., He, L., and Rahardjo, H. (2002). ‘‘Factors Affecting the Filter Paper Method for Total and Matric Suction Measurements.’’ Geotechnical Testing Journal, 25(3), 322–333. Marinho, F.A.M. (1994). ‘‘Shrinkage Behavior of Some Plastic Soils.’’ Ph.D. Dissertation, University of London, Imperial College of Science, Technology and Medicine. McKeen, R.G. (1992). ‘‘A Model for Predicting Expansive Soil Behavior.’’ Proceedings of 7th International Conference on Expansive Soils, Dallas, Texas. 1, 1–6. McKeen, R.G. and Nielson, J.P. (1978). ‘‘Characterization of Expansive Soils for Airport Pavement Design.’’ U.S. Dept. of Transportation, Federal Aviation Administration, Report No. FAA-120-78-59. Miller, D.J. (1996). ‘‘Osmotic Suction as a Valid Stress State Variable in Unsaturated Soils.’’ Ph.D. Dissertation, Colorado State University, Fort Collins, Colorado. Mualem, Y. (1976). ‘‘A New Model for Predicting the Hydraulic Conductivity of Unsaturated Porous Medial.’’ Water Resources Research, 12, 513–522. Mulilis, J.P., Chan, C.K., and Seed, H.B. (1975). ‘‘The Effects of Method of Sample Preparation on the Cyclic Stress Strain Behavior of Sands.’’ EERC Report, 75–78. Noorany, I. (2005). E-Mail Letter to Kuo-Chieh Chao Regarding ‘‘Moist Tamping Equipment.’’ January 10th. SoilVision Systems Ltd. (2006). ‘‘SoilVision Software, Version 4.0.’’ Saskatoon, Saskatchewan, Canada. Tinjum, J.M., Benson, C.H. and Blotz, L.R. (1997). Soil-Water Characteristic Curves for Compacted Clays. Journal of Geotechnical and Geoenvironmental Engineering. November. 1060. van der Raadt, P., Fredlund, D.G., Clifton, A.W., Klassen, M.J., and Jubien (1987). ‘‘Soil Suction Measurement at Several Sites in Western Canada.’’ Transportation Res. Rec. 1137, Soil Mechanics Considerations in Arid and Semi-Arid Areas, Transportation Research Board, Washington, D.C., 24–35. van Genuchten, M.T. (1980). ‘‘A Closed-Form Equation for Prediction the Hydraulic Conductivity of Unsaturated Soils.’’ Soil Sci. Soc. Am. J. 44, 892–898. Wan, A.W.L., Gray, M.N. and Graham, J. (1995). ‘‘On the Relations of Suction Moisture Content and Soil Structure in Compacted Clays.’’ Proc. 1st Intern. Conf. Unsaturated Soils, Paris, I, 215–222.
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Hydromechanical couplings in confined MX80 bentonite during hydration D. Marcial Instituto de Materiales y Modelos Estructurales, Universidad Central de Venezuela, Caracas, Venezuela
P. Delage & Y.J. Cui CERMES, Ecole Nationale des Ponts et Chaussées, Paris, France
ABSTRACT: In order to characterize the hydromechanical (HM) properties of a MX80 bentonite, used as an Engineered Barrier (EB) material for nuclear waste disposal facilities, a 7 months infiltration column test with coupled measurement of swelling pressure and suction was carried out. The hydraulic conductivity was obtained using the Instantaneous Suction Profile (ISP) method (Daniel 1983) in an initial highly compacted unsaturated state (γd = 1.7 Mg/m3 ; w = 8.2 %), and the swelling pressure was monitored at different heights of the column. Also, some mercury intrusion porosimetry measurements were conducted at the end of the test to better understand the observed coupled behaviour. Important effects of suction gradients were observed; the transitory hydraulic conductivity values are higher when the bentonite is hydrated from very high suctions because of gradient effects. Then it drastically reduces as the hydration front advances and the microstructure is reorganized. Concerning the couplings of suction and swelling pressure, a softening threshold suction value was systematically observed at a value of 90 MPa. Also, low changes of stresses with suction δσ/δs were observed for a high range of suction values. These experimental evidences permit to better understand hydromechanical couplings during hydration of engineered barrier materials in confined conditions.
1
INTRODUCTION
Figure 1 presents a schema of an engineered barrier (EB) section of a disposal pit according to the concept of deep nuclear waste disposal. One can appreciate the EB surrounding the waste container (C) and filling up the void zone between the pit walls crossed in the host rock (HR) and the container. The EB is composed of specially shaped compacted bentonite bricks arranged in such a way that void zones (joints) are minimized. The joints are present in the EB-EB, EB-C and EB-RH contact surfaces and their presence within the barrier highlight the importance of the swelling potential of the EB material. The self sealing capacity of bentonites is particularly important to ensure an adequate isolation of the waste (Pusch 1982). Marcial et al. (2006) have shown with a reduced model test, that in bentonite based EB, such joint system could heal very soon with hydration if the joint sizes are small enough, even for a relatively low EB dry density. However, higher periods of time could be necessary as the joint size increases. Extensive experimental hydromechanical studies were done by the Soil and Rock Mechanics Research Centre, at the Navier Institute in France, on FoCa7 clay and a Kunigel VI bentonite—sand mixture in the recent past (See Yahia-Aissa 1999 and Loiseau 2001).
Figure 1. Cross section of a disposal pit with schematic representation of joints and an EB radial element.
Furthermore, advances in the characterization of compacted unsaturated MX80 bentonite has been achieved by incorporating the measurement of lateral stresses. This work concerns the suction—swelling pressure coupling observed in a 7 months infiltration column
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test with measurement of swelling pressure and suction. The experimental set-up correspond to a reduced model that take into account the HM behaviour of an EB radial element, perpendicular to the disposal pit axis (axis symmetrical problem). Figure 1 also shows a radial EB element where the stress state, defined by σθ and σr , is dependent of the suction changes within the EB due to hydration. Since the test was conducted in isothermal conditions (T = 20◦ C) and temperature changes are present in a nuclear waste repository, it is not representative of the initial saturation cycle. However, the results obtained in this work permit an initial approach to the understanding of HM couplings in EB materials. 2
MATERIAL AND EXPERIMENTAL SET-UP
2.1
Index properties and initial conditions
The chosen material was a commercial MX80 bentonite whose index properties are summarized in Table 1. Concerning the initial conditions, a dry density γd = 1.7 Mg/cm3 and a water content w = 8.2 % (corresponding to a suction of 103 MPa) were fixed. The γd value was chosen to be high enough to obtain high swelling pressures, and low enough to have double porosity microstructure (Delage et al. 1996) permitting to observe interesting and complex phenomena concerning micro—macro fabric coupling as it will be shown later. 2.2
Experimental set-up
The experimental set up was essentially composed of an infiltration column (see Figure 2) with a 50 mm internal diameter, and a 250 mm height. Five resistive sensors were used to monitor relative humidity (RH) changes with water uptake, permitting to adequately estimate the hydraulic conductivity by the ISP method. Four of these sensors were placed in the column cylinderv at a distance of 4.5, 9.5, 14.5 Table 1.
MX80 bentonite index properties.
Property
Value
Mineralogy
(1)
C.E.C (meq/100 g) Liquid limit, % Plastic limit, % ρs (Mg/m3 ) Skempton’s activity Specific surface, m2 /g (1)
82% montmorillonite (Na/Ca=5.5) 69.6 (1) 520 42 2.65(1) 5.8 800(2)
Sauzeat et al. (2000) (2) Pusch (1982).
Figure 2. Infiltration column: (1) holes for RH sensors location (2) split head piston (3) piston cap (4) 2 mm thick zones for lateral stress monitoring (5) column base (6) porous stone (7) water intake circuit.
and 19.5 cm from the infiltration point. A fifth sensor is placed inside the piston at the top of the column, located at a distance of 25 cm from the infiltration point. The lateral stress changes were monitored by incorporating reduced thickness zones, where deflections were measured with highly sensitive strain gages. To do so, the column cylinder was mechanized in such a way that five thin wall zones (2 mm thick) were incorporated at the heights of 2, 7, 12, 17 and 22 cm. These zones, which work as semi rigid membranes, have 5 mm in height and were designed to experience a deflection of 5 μm under a 60 MPa pressure. Elsewhere, a global measure of the axial stress was done with an external 50 kN load cell. The soil was statically compacted in a rigid mould with an internal diameter slightly lower than 50 mm to avoid any unknown initial soil stress state due to friction (see Marcial et al. 2006). Compaction was done step by step adding 25 mm thick layers, and the target density was obtained after soil rebound, with a 39 MPa compaction stress. Three cylindrical bricks were placed to fill the column, with a height of 125, 75 and 50 mm. Figure 3 shows the progressive placement of the bricks in the column. After the insertion of each brick, the RH sensors corresponding to the filled height were carefully placed. Once the column was filled, special care was taken to guarantee the system sealing, which is particularly important in the ISP method (see Figure 4).
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At this point, the infiltration test was ready to run. The compacted soil was hydrated from the base of the column with a volume—pressure controller, which was set at a 10 kPa water pressure. The hydration time was extended to 208 days.
3
Figure 3. View of a 75 mm height compacted brick (a) and the progressive placement of bricks to fill the column (b, c and d).
RESULTS AND DISCUSSION
To determine the hydraulic conductivity with the ISP method, it is necessary to register the changes of relative humidity with time, and to know the water retention curve (WRC) at constant volume conditions. Because of space limitations, the procedure for the determination of the WRC is not presented. However, for the interest of the readers, the curve is presented in Figure 5. The changes in RH with time are presented in Figure 6 for all measurement sections. A global typical trend is observed; the increase of RH is higher as the section of measurement is closer to the water source. Notice that all curves are superposed at time zero and they progressively separate for increasing times. The acceleration in the RH increase corresponds to
Suction (MPa)
1000 100 10 1 0.1 0
Figure 4. View of the experimental set-up. (1) Sealing detail at the head piston cap (2) sealing details at RH sensor caps (3) final view of the experimental set-up with thermal isolation.
The head piston was left free of movement during 13 days, until the stabilization of the relative humidity was reached along the whole length of the column. A relative humidity value of 46.7% was registered at a controlled room temperature of 20◦ C, corresponding to the initial condition of the test before hydration starts (103 MPa suction). Once the suction stabilized, the column was placed in a 50 kN digitally controlled press, and the head piston was blocked against the reaction frame. A 50 kN load cell was placed between the head piston and the reaction frame to obtain a global measure of the axial stress (swelling pressure). In order to avoid the test to be affected by temperature changes, the unit press—column was isolated with 50 mm polystyrene walls, and a 5 mm glass screen was left at its front face.
10
20 30 Water content (%)
40
Figure 5. Water retention curve obtained at constant volume conditions with a dry density of 1.7 Mg/m3 .
Figure 6.
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Changes of relative humidity with time.
the arrival of liquid phase water, as the hydration front advances with time. Before liquid water arrives, RH curves stay superimposed because hydration is only done by vapour phase through macroporosity. The monotone and regular increase of RH with time shows that the system was adequately sealed. The suction profiles are shown in Figure 7; they were obtained with the RH—t curves and the WRC. To do so, polynomial functions were fitted at different time periods with the RH—t curves and the condition of zero suction at the bottom of the column, corresponding to the infiltration point. In order to get fitting curves less perturbed by measures taken away from a particular section of the column, only 3 points were considered. Thus, the corresponding profiles are also reported in sections, as shown in Figure 7. This aspect is very important because is from the slope of the suction profiles that hydraulic gradients are obtained. The profiles shown in Figure 7 correspond, from top to bottom to t = (0, 5, 10, 15, 20, 25, 30, 35, 40, 45, 50,
55, 60, 65, 70, 80, 90, 100, 110, 120, 130, 140, 150, 160, 170, 180, 190, 200 and 208) days respectively. For the 0–9.5 cm section, the profiles are presented only to 120 days because at this time the RH sensor corresponding to 4.5 cm height was damaged due to an excess of humidity. As shown in Figure 6, at this height the RH sensor reads a value of 97.4% at the time of 126 days. The derivate of fitted polynomial functions of suction profiles, at each measurement point, and for each time, gives the changes of hydraulic gradient i with time. Figure 8 shows that i values are very high (about 116000 in the extreme case), specially when the distance to the hydration source is small. It is evident that i values do not correspond to the hydration pressure of 10 kPa. They are due to the strong hydrophilic character of the bentonite brick, initially equilibrated to a very high suction (103 MPa). Changes on i values are strongly influenced by the distance h and suction s. On the one hand, the higher is h, the lower is i. On the other hand, the increase rate of i slows down, and is even reversed as suction decrease. Both effects concern the hydrophilic character of the bentonite brick. As closer the considered section is to the hydration point, and higher is the thickness of non hydrated soil, higher is the hydraulic gradient. In addition, as suction reduces, the hydrophilic character of the soil reduces also, slowing down the increase of the gradient. The combination of both factors gives rise to the shape of the i − t curves shown in Figure 8. In the case of h = 4.5 cm, the thickness of the soil that participate in the adsorption process is important and the gradient is high. Otherwise, because the section is very close to the hydration point, the suction and the gradient reduce drastically (Figure 7) when hydration front approaches. These effects being less important when h is higher the changes observed in the gradient occur in a more progressive manner.
Figure 7. length.
Figure 8. hole test.
Suction profiles at different times for the whole
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Changes of hydraulic gradient with time for
The hydraulic conductivity kw is obtained with the generalized Darcy’s law: kw = −
q 1 · A 1/2 · (it + it+dt )
(1)
where A is the infiltration section, i is the hydraulic gradient, t is the time and q is the flow rate, through the section A, established in the time interval dt . The q value in an unsaturated soil is obtained with the following expression: H q=A·
hi
θt+dt dh − dt
H hi
θt dh
(2)
The volumetric water content is obtained with the expression: θ=
w · ρd ρw
Figure 9. times.
Volumetric water content profiles at different
(3)
The volumetric water content profiles (Figure 9) were obtained for the same times of suction profiles. Notice that after 208 days, only the first 61 mm were saturated. Also, the degree of saturation reduces drastically as the distance to the saturation front increases to further stabilize at low values. This permits to better understand the gradient changes presented in Figure 8. For h = 4.5 cm, the lowest i values are obtained when hydration front approach this section. However, the gradient keeps high for h = 9.5 and 14.5 cm because in these sections suction changes are still important. For h = 19.5 cm hydration front is far enough, suction changes are less important and gradient changes are more progressive. With the volumetric water content profiles and Equation 1, the hydraulic conductivity at h = 4.5, 9.5, 14.5 and 19.5 cm was obtained. Figure 10 shows the changes of hydraulic conductivity with suction for different h values. First of all, notice that the highest kw values are obtained for the highest suctions. Then, kw values reduce drastically to stabilize later and even increase at lower suction values. These observations confirm the global trends obtained by Loiseau et al. (2002), with a Kunigel VI—sand mixture. Concerning global kw − h changes, a progressive reduction of kw values is observed as h increases. This trend is due to the effect of hydraulic gradient. For low h values, the thickness of unsaturated material is higher. Remember that it is not the 10 kPa hydration pressure of water source that impose hydraulic gradient, but the hydrophilic character of the unsaturated compacted bentonite brick. Thus, the influence of hydraulic gradient reduces as the h value increases, as shown by Loiseau et al. (2002). Also, notice the
Figure 10. Changes of hydraulic conductivity with suction at different sections.
increase of kw as suction decrease, at the lower suction range, like currently observed in unsaturated soils. Figure 11 presents the pore size distribution observed at the end of the test at different h values. This is a typical trend observed when bentonite based materials are hydrated at constant volume conditions. When hydration is important (lower h values), microstructure hydrate and accessible porosity reduces. Because of the constant volume condition, microstructure swelling reduces macroporosity. Notice a well defined inter—aggregate pore group for h = 25 cm at r = 3 μm that gradually disappears at more hydrated sections (h = 4.5 and 9.5 cm). These microstructure observations confirm the hypothesis that RH curves shown in Figure 6 stay superimposed while hydration occurs by vapour phase through macroporosity. Concerning the coupling of suction and swelling pressure, a typical trend with two maxima was
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Figure 11. Pore size distribution at different sections of the column at the end of the test.
Figure 13. Changes of vertical stress with suction for different sections of the sample.
is observed until saturation approaches and the δσ/δs rate progressively increases to a value of about 0.1.
4
Figure 12. Changes of lateral stress and suction with time for different sections of the sample.
observed for lateral stress measurement at h = 2, 7, 12 and 17 cm. Particular attention was taken to the first maxima, corresponding to a softening point of clay aggregates due to hydration (Pusch 1981). Figure 12 presents the first maxima observed at different h values. Notice that all maxima occur systematically at a suction value of about 90 MPa. The repeated apparition of these maxima is important to confirm the existence of a softening threshold value. Figure 13 shows vertical stress changes with suction at sections located close to hydration point (h = 2, 3 and 4.5 cm). Notice that stress changes with suction δσ/δs are very high when hydration starts, but rapidly slow down as suction decrease. See that the maximum curvature occurs close to a suction value of approximately 90 MPa when the softening threshold is approached. Then, a low and quasi regular δσ/δs rate
CONCLUSIONS
The infiltration test permitted to confirm the results obtained by Loiseau et al. (2002), concerning the effects of suction gradients on hydraulic conductivity, but with a different EB material. The hydraulic conductivity is higher as the EB material is submitted to higher suction gradients. Then, hydraulic conductivity reduces drastically as the hydration front advances and microstructure is reorganized. When suction decreases enough, the hydraulic conductivity increases as typically observed in unsaturated soils. Obtained results suggest that, during the hydration phase, water transfers in the EB should be partially governed by the strong hydrophilic character of unsaturated zones, where suction values keep being high enough. Concerning the suction—swelling pressure coupling, a softening threshold was systematically observed at a suction of 90 MPa. This threshold value must be associated to the particular initial conditions of the studied material (γd = 1.7 Mg/cm3 and s = 103 MPa). The observed results show that above the threshold value the δσ/δs rate is very high, decreasing to a very low and quasi regular value when suction reduces below this point. When suction is low enough and saturation approaches, the δσ/δs rate progressively increases to a value of about 0.1. The study of some HM properties and microstructure of a compacted MX80 bentonite, in confined condition, permits to state a complex and highly coupled HM behaviour of EB materials. The results presented
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herein give some elements to improve constitutive models that consider these aspects. REFERENCES Daniel. D.E. (1983). Permeability test for unsaturated soil. Geotechnical Testing Journal. 2, 81–86. Delage et al. (1996). Microstructure of compacted silt. Canadian Geotechnical J. 33, 150–158. Loiseau C. (2001). Transferts d’eau et couplages HM dans les barrières ouvragées. PhD. Thesis, ENPC, Paris, France. Loiseau et al. (2002). The gradient effect on the flux through a compacted swelling soil. 3rd Int. Conf. on Unsaturated Soils, Brazil. 1, 395–400. Marcial et al. (2006). Application of vertical strain control to measure swelling pressure of clayey soils. 4th Int. Conf. on Unsaturated Soils. Arizona, EE. UU.
Marcial et al. (2006). A laboratory study of the self sealing behaviour of a compacted sand-bentonite mixture. Geomechanics and Geoengineering An International Journal. 1, 73–85. Pusch R. (1981). Unsaturated and saturated flow in swelling clay. 10th IFSMFE, Session 6/14, Stockholm. pp. 369–373. Pusch R., (1982). Mineral-water interactions and their influence on the physical behavior of highly compacted Na bentonite. Canadian Geotechnical Journal. 19, 381–387. Sauzeat et al. (2000). Caractérisation minéralogique, cristallochimique et texturale de l’argile MX-80. LEM-CREGU. ANDRA Technical Report. France. Yahia-Aissa, M. (1999). Comportement HM d’une argile gonflante fortement compactée. PhD Thesis, ENPC, Paris, France.
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Effect of temperature on the water retention capacity of FEBEX and MX-80 bentonites M.V. Villar & R. Gómez-Espina CIEMAT, Madrid, Spain
ABSTRACT: The retention curves of the FEBEX and MX-80 bentonites compacted at dry densities from 1.3 to 1.8 g/cm3 have been determined using methods that allow the volume of the samples to remain constant during the determination. The methods have been upgraded to use them at high temperatures, and thus the range of temperatures between 20 and 120◦ C has been explored. For a given density and water content, suction decreases as temperature increases at a rate that is larger than that predicted on the basis of the water surface tension change with temperature. Hysteresis on heating/cooling cycles has been observed, especially in the MX-80 bentonite. For suctions higher than 10 MPa and for a given temperature and water content, the suction measured is slightly higher for higher dry density of the bentonite. However, for lower suctions this trend clearly inverts. The water retention capacity is lower for the MX-80 bentonite, although the difference is lessened for low suctions. The retention capacity of the FEBEX bentonite is more affected by temperature than that of the MX-80.
1
countries as reference materials for the sealing of HLW repositories.
INTRODUCTION
This research has been carried out in the context of projects concerning the engineered clay barrier of underground repositories for high-level radioactive waste (HLW). The barrier, made of compacted bentonite (a highly swelling material), will be placed between the waste canisters and the host rock, and will get saturated by the groundwater while it is subjected to high temperatures due to the radioactive decay of the wastes. These temperature changes affect the hydraulic and mechanical response of the bentonite, which has important implications on the design and performance of the repository. Particularly, the changes in the water retention capacity of the bentonite affect the hydration kinetics of the barrier and the time needed for its full saturation. The water retention capacity of a material is usually evaluated by determining its water retention curve, which relates suction and water content for a given temperature along a suction span as broad as possible. Previous investigations have shown that the retention curve, for the same initial conditions of the material, differs significantly depending on the volume restriction imposed to the sample during the determination (Yahia-Aissa, 1999; Villar, 2002). Thus the effect of temperature on the water retention curve of two natural compacted bentonites, the FEBEX and the MX-80, has been analysed by means of laboratory tests in which the volume of the samples has been kept constant. Both bentonites have been selected by different
2
MATERIAL
Two bentonites have been used in this investigation: the Spanish FEBEX bentonite and the American MX-80 bentonite. The FEBEX bentonite comes from the Cortijo de Archidona deposit (Almería, Spain) and its characterisation can be found in ENRESA (2006), Villar (2002) and Lloret et al. (2004). The smectite content of the FEBEX bentonite is higher than 90 percent (92 ± 3%) and it contains variable quantities of quartz (2 ± 1%), plagioclase (2 ± 1%), K-felspar, calcite and opal-CT. The CEC varies from 96 to 102 meq/100 g, and the major exchangeable cations are Ca (35–42 meq/100 g), Mg (31–32 meq/100 g), Na (24–27 meq/100 g) and K (2–3 meq/100 g). The liquid limit of the bentonite is 102 ± 4 percent, the plastic limit is 53 ± 3 percent, the total specific surface area is 725 ± 47 m2 /g and the specific gravity 2.70 ± 0.04. The hygroscopic water content in equilibrium with the laboratory atmosphere is 13.7 ± 1.3 percent. The MX-80 bentonite is extracted from Wyoming (USA). It is a worldwide known material supplied in the form of powder homoionised to sodium. The MX-80 bentonite consists mainly of montmorillonite (65–82%). It also contains quartz (4–12%), feldspars (5–8%), and smaller quantities of cristobalite, calcite
257
and pyrite. The CEC is 74 meq/100 g, and the major exchangeable cations are Na (61 meq/100 g), Ca (10 meq/100 g) and Mg (3 meq/100 g). The liquid limit of the bentonite as determined in CIEMAT laboratories is 526 percent, the plastic limit is 46 percent, the total specific surface area is about 512 m2 /g and the specific gravity is 2.82. The hygroscopic water content at laboratory conditions is 8–11 percent. The saturated permeability to deionised water of samples of these bentonites compacted at different dry densities is exponentially related to the dry density. The values of permeability to deionised water for dry densities of 1.6 g/cm3 are in the order of 10−14 m/s for the FEBEX bentonite and of 10−13 m/s for the MX-80 bentonite. The swelling pressure of bentonite samples compacted at their hygroscopic water content and flooded with deionised water up to saturation at room temperature can be related exponentially to dry density. For dry density 1.6 g/cm3 the swelling pressure of the FEBEX bentonite is about 6 MPa and of the MX-80 bentonite is about 8 MPa. 3
METHODS
To determine the water retention curve of the compacted bentonite at constant volume, two methodologies, the theoretical principle of which is different, have been followed. The cell method is carried out in special cells designed to avoid the swelling of the clay in wetting paths (Villar, 2002; Villar and Lloret, 2004). The cells consist of a corrosion-resistant stainless steel cylindrical body with two perforated covers joined by bolts. Granulated clay is compacted directly inside the cell ring at room temperature using static uniaxial compaction. The length of the specimen is 1.20 cm and its cross section, 11.34 cm2 . The cells are placed in desiccators with a sulphuric acid solution or with a NaCl solution. There are temperature-dependent experimental relations between the concentration of the solution and its water activity (aw ). The calculation of suction on the basis of relative humidity (RH = aw /100) is accomplished through Kelvin’s equation. In the cell method the suction is, therefore, imposed through the control of relative humidity. The perforated covers allow the exchange of water in the vapour phase between the clay and the atmosphere of the desiccators. Once the water content of the clay is stable (approximately 2 to 3 months, what is checked by periodic weighing), the solution in the desiccators is changed in order to apply a different suction. To determine the curve at different temperatures, the desiccators are placed inside ovens. At the end of the tests the final water content of the specimens is measured by oven drying.
The sensor/cell method consists on the compaction of a bentonite block with the clay previously mixed with the desired quantity of deionised water and the measurement of its relative humidity by means of a capacitive sensor while the bentonite is kept inside a hermetic cell made of stainless steel (Villar et al., 2005; 2006). To convert the values of RH to suction values, Kelvin’s law is used. The clay was used either with its hygroscopic water content, mixed with deionised water, or slightly dried at temperatures below 50◦ C, so as to obtain water contents between 4 and 22 percent. The block is introduced in the cell, the dimensions of the block being equal to the internal volume of the cell, 7 cm diameter and 10 cm height. A hole is drilled in the central upper part of the block to insert the sensor and the cell is closed. The external wall of the cell is covered with a silicone-rubber laminated heater that fixes the temperature all over the cell. After measuring the suction corresponding to the laboratory temperature, the temperature of the external heating mat was increased up to 120◦ C in intervals of 20◦ C. Each target temperature was kept for about two days, although the RH equilibrium is reached very quickly (in a few hours). Afterwards, the temperature was decreased according to the same pattern. This allows, in a single test, the determination of the change of suction with temperature for a given density and water content. At the end of the test, the block is extracted and its water content and dry density are measured. The drawback of the cell method is the duration of the tests, because the time to reach equilibrium for each suction is very long, this is why the sensor/cell method was fine-tuned. The results obtained with both methods are largely consistent, although the sensor/cell method is unsuitable for the very low and very high suctions (Villar & Gómez-Espina, 2007).
4
RESULTS
4.1 FEBEX bentonite The effect of dry density on the water retention capacity of the FEBEX bentonite has been checked using the cell method. It has been observed that there is a suction threshold value above which, for a given water content, the suction of the higher density samples is higher, and below which the trend inverts. For 20◦ C this threshold value is about 12 MPa (Figure 1). Tests with different densities have been also performed at different temperatures using both methods. Some of the results obtained are plotted in Figure 2. For the range of suctions considered, the retention capacity of the sample of dry density 1.7 g/cm3 is higher than of 1.5 g/cm3 . Also, the samples tested at 80◦ C have lower retention capacity than those tested at 20◦ C
258
140
1.4
1.6
1.7 Suction (MPa)
Suction (MPa)
Dry density (g/cm )
100 80 60 40
140 120 100 80 60 40 20 0
20
20
0 10
15 20 25 Water content (%)
30
100
1.5, 26 1.5, 80 1.7, 20 1.7, 80
1
15 20 25 Water content (%)
80
100
120
140
Figure 3. Evolution of suction with temperature (heatingcooling paths) for FEBEX samples compacted with different water content at dry density 1.6 g/cm3 (open symbols) and 1.5 g/cm3 (filled symbols).
4.2 MX-80 bentonite
0.1 10
60
the range of suctions considered, which could be a consequence of the closeness of the densities tested (1.5 and 1.6 g/cm3 ) and points also to the higher influence of temperature over density on the retention capacity. Anyway, the smaller slope of the curves for the dry density 1.5 g/cm3 would indicate a smaller effect of temperature on the retention capacity for the low density samples.
1000
10
40
Temperature (˚C)
35
Figure 1. Retention curves of FEBEX bentonite compacted at different dry densities obtained at 20◦ C following wetting paths with the cell method.
Suction (MPa)
11% 14% 16% 18% 19% 20% 21%
180 160
3
120
30
Figure 2. Retention curves obtained for the FEBEX bentonite compacted to different dry densities (indicated in g/cm3 ) and temperatures (indicated in ◦ C).
(Lloret et al. 2004, Lloret & Villar 2007). The effect of temperature on the retention capacity is greater for the higher dry density. Figure 3 shows the evolution of suction with temperature in samples compacted to different dry densities with various water contents tested with the sensor/cell method. The decrease of suction with temperature is significant, especially for temperatures above 60◦ C. There is also a small hysteresis between the initial heating and the subsequent cooling, the suctions measured during cooling being slightly higher. On the other hand, the influence of dry density is not very clear in
The influence of dry density on the retention capacity of the MX-80 is highlighted when the cell method is used. Figure 4 shows the results obtained at 60◦ C for a broad range of dry densities (Villar 2005). For suctions above approximately 20 MPa the behaviour of the different densities is similar, but below this value, the higher the dry density the lower the suction for a given water content. Although, for the sake of clarity, the drying paths are not included in the figure, it was observed that the hysteresis in wetting/drying paths is not very important. The dry densities 1.5, 1.6 and 1.75 g/cm3 have been tested with the sensor/cell method. The hysteresis on heating/cooling was found to be more important than for the FEBEX bentonite (Villar & Gómez-Espina, 2007). Some of the results obtained are plotted as retention curves in Figure 5, where the decrease of the retention capacity with temperature is noticeable, as well as the effect of dry density: since the suctions tested with the sensor/cell method are above the threshold mentioned before, the retention capacity is higher for the samples of higher dry density.
259
1000
Suction (MPa)
100
1.30
1.37
1.60
1.79
10
1
0.1 0
10
20
30
40
Water content (%) Figure 4. Retention curves of MX-80 bentonite compacted to different dry densities (indicated in g/cm3 ) obtained with the cell method in wetting paths at 60◦ C (Villar 2005).
Suction (MPa)
1000
100
1.75, 39 1.75, 99 1.50, 40 1.50, 100
10
basis of the change of surface tension of water with temperature. For the MX-80 bentonite it has been checked that the actual suction change measured is higher than the change computed by introducing in the Laplace equation the temperature dependence of the surface tension of water (Jacinto et al., in press a). The same has been checked for the FEBEX bentonite, as shown in Figure 6, in which the measured and computed evolution of suction with temperature have been plotted. This discrepancy (which is more significant for temperatures above 60◦ C) is probably due to the fact that capillarity is not the main mechanism of water retention in bentonite. Instead, physico-chemical interactions between the clay particles and the water tightly attached to them are responsible of the soil retention capacity, especially in the high suction range. In this low water content region, changes in the interaction mechanisms between the clay and water are considered the main temperature effects on water retention capacity (Romero et al., 2001; Villar & Lloret, 2004; Villar et al., 2005). Ma & Hueckel (1992, 1993) state that an increase in temperature produces a transfer of water from the interlayer region to the pores between the clay aggregates (macropores). Since the density of the interlayer, tightly-bound water in smectites is higher than one (Villar, 2002; Marcial, 2003; Jacinto et al., in press b), the volume occupied by the interlayer water transferred to the macropores will be higher and the degree of saturation of the sample will increase (provoking a suction decrease) when the temperature is increased (Villar & Lloret, 2004).
1
180
3
8 13 18 Water content (%)
23
160
14%
17%
21%
140
-0.33 -0.26
120 Suction (MPa)
Figure 5. Retention curves obtained with the sensor/cell method for the MX-80 bentonite compacted to different dry densities (in g/cm3 ) and temperatures (in ◦ C).
5
11%
-0.53 100 80
-0.16
-0.40
40
DISCUSSION
-0.57
60 -0.05
20
Although it is generally acknowledged that suction in clayey soils is not exclusively a capillary process, the Laplace equation, which relates the capillary pressure and the pore size distribution, is a first approximation to explain the water retention processes in soils. Thus, for the prediction of the effect of temperature on the retention capacity, the change of surface tension of water with temperature is usually included in this equation. However, the observed evolution of suction with temperature cannot be explained on the
-0.27
0 20
40
60
80
100
120
140
Temperature (ºC)
Figure 6. Change of suction with temperature for FEBEX bentonite compacted with different water contents to dry density 1.6 g/cm3 as measured with the sensor/cell method (continuous lines) and as computed by the change in water surface tension (dashed lines). The slope of the lines is indicated.
260
1.5 1.6 1.75
1.0 0.8
MX, 26˚C MX, 80˚C FBX, 27˚C FBX, 81˚C
160 Suction (MPa)
Relative suction change
200
1.2
0.6 0.4 0.2
120 80 40
0.0 3
8
13
18
23
0
Water content (%)
3
Figure 7. Relative suction change when temperature increases from 26 to 100◦ C in the FEBEX (filled symbols) and MX-80 (open symbols) bentonites compacted to different dry densities (indicated in g/cm3 ) and tested with the sensor/cell method.
8
13
18
23
Water content (%) Figure 8. Retention curves obtained with the sensor/cell method for the FEBEX (FBX) and MX-80 (MX) bentonites compacted at dry density 1.5 g/cm3 .
180 -0.53
160
FBX, 11%
140
Suction (MPa)
Figure 7 represents the relative change of suction experienced by samples of different dry density and water content tested with the sensor/cell method when the temperature was increased from 26 to 100◦ C. The suction decrease with temperature tends to be higher for the higher dry densities, both for the FEBEX and the MX-80 bentonites. It is known that the proportion of water in the interlayer of the smectite increases with the density of the bentonite (Pusch et al. 1990). This would explain the larger effect of temperature on high density samples. On the other hand, the retention capacity of the FEBEX bentonite is higher than that of the MX-80, as it can be observed in Figure 8 for the dry density of 1.5 g/cm3 . Numerous authors have pointed out that the retention capacity of predominantly divalent (Ca and Mg) smectites is higher than that of sodic ones, except for the lowest suctions (Hall & Astill, 1989; Saiyouri et al., 2004). This figure also shows how the difference between the two bentonites attenuates towards the low suctions, and this has been checked for several temperatures (Villar & Gómez-Espina, 2007; Villar, 2007). Also, Figure 9 shows that the effect of temperature on suction is higher for the FEBEX bentonite than for the MX-80 (note the higher slope of the lines that relate suction with temperature for the FEBEX bentonite). This would be a consequence of the predominance of interlaminar porosity (in which high-density water is placed) in the Ca-Mg bentonite, whereas in the Na bentonite the porosity among primary particles (in which ‘‘free’’ water is placed) prevails, since these particles are formed by fewer laminae (Pusch et al., 1990).
FBX, 14%
120
-0.32
100
FBX, 21%
-0.57
MX, 6%
80
MX, 11%
-0.37
60
-0.28
MX, 15%
40 -0.27
20
MX, 21%
-0.03
0 20
40
60 80 100 Temperature (˚C)
120
140
Figure 9. Evolution of suction during heating for FEBEX (FBX) and MX-80 (MX) bentonites compacted at dry density 1.6 g/cm3 and tested with the sensor/cell method. The slope of the lines is indicated.
6
SUMMARY AND CONCLUSIONS
The retention curves of two natural compacted bentonites have been determined trying to reproduce as well as possible the conditions of the engineered barrier of a HLW repository, for which reason the bentonites were used in their natural state (without previous drying or grinding), kept at constant volume during the determination and submitted to high temperatures. Results for dry densities from 1.3 to 1.8 g/cm3 and temperatures from 20 to 120◦ C have been reported. The suctions involved ranged from 0 to 200 MPa.
261
The effect of density on the retention capacity varies according to the suction range. For suctions below a threshold value (which is about 12–20 MPa) for a given water content and temperature the suction of the higher density samples is lower, and above this suction value the trend inverts. Anyway, the effect of dry density on the water retention capacity seems lower than that of temperature. The water retention capacity of the bentonite decreases clearly with temperature, especially when it is above 60◦ C and when the density of the bentonite is high. This decrease cannot be explained on the basis of the changes of water surface tension with temperature. Instead, mechanisms related to the physico-chemical interactions that take place at microscopic level (in particular the transfer of interlayer water to the macropores triggered by temperature) seem to explain qualitatively the experimental observations. There are also differences in the behaviour of the two materials tested. The FEBEX bentonite, which has mainly bivalent cations in the exchange complex, has a higher retention capacity than the MX-80 bentonite, which is predominantly sodic. Also, the effect of temperature on the water retention capacity is more noticeable for the FEBEX bentonite.
ACKNOWLEDGEMENTS Part of the work on the FEBEX bentonite has been co-funded by ENRESA (Spanish National Agency for Waste Management) and the European Commission (EC Contracts FI4 W-CT95-006 and FIKW-CT-200000016). The research agreements CIEMAT/ENRESA 00/271 and CIEMAT/CIMNE 04/113 have financed the research related to MX-80 bentonite. The laboratory work was performed by R. Campos and J. Aroz at CIEMAT (Madrid, Spain). The second author has a grant of the Spanish Ministry of Education.
REFERENCES ENRESA 2006. Full-scale Engineered Barriers Experiment. Updated Final Report 1994–2004. Publicación Técnica ENRESA 05-0/2006. 590 pp. Madrid. Hall, P.L. & Astill, D.M. 1989. Adsorption of water by homionic exchange forms of Wyoming montmorillonite (SWy-1). Clays and Clay Minerals 37(4): 355–363. Jacinto, A., Villar, M.V., Gómez-Espina, R. & Ledesma, A. in press a. Influence of temperature and density on the retention curve of compacted bentonite: modifications to the van Genuchten expression. Applied Clay Science. Jacinto, A., Villar, M.V. & Ledesma, A. in press b. Influence of water density on the water retention curve of expansive clays. Géotechnique.
Lloret, A. & Villar, M.V. 2007. Advances on the knowledge of the thermo-hydro-mechanical behaviour of heavily compacted FEBEX bentonite. Physics and Chemistry of the Earth, Parts A/B/C 32 (8–14): 701–715. Lloret, A., Romero, E. & Villar, M.V. 2004. FEBEX II Project. Final report on thermo-hydro-mechanical laboratory tests. Publicación Técnica ENRESA 10/04. 180 pp. Madrid. Ma, C. & Hueckel, T. 1992. Stress and pore pressure in saturated clay subjected to heat from radioactive waste: a numerical simulation. Can. Geotech. J. 29: 1087–1094. Ma, C. & Hueckel, T. 1993. Thermomechanical effects on adsorbed water in clays around a heat source. Int. J. Numer. Anal. Methods Geomech. 17: 175–196. Marcial, D. 2003. Comportement hydromécanique et microstructural des matériaux de barrière ouvragée. Ph. D. thesis. École Nationale des Ponts et Chausées, Paris, 316 pp. Push, R., Karnland, O. & Hökmark, H. 1990. GGM—A general microstructural model for qualitative and quantitative studies of smectite clays. SKB Technical Report 90-43. Romero, E., Gens, A. & Lloret, A. 2001. Temperature effects on the hydraulic behaviour of an unsaturated clay. Geotech. Geolog. Eng. 19: 311–332. Saiyouri, N., Tessier, D. & Hicher, P.Y. 2004. Experimental study of swelling in unsaturated compacted clays. Clay Minerals 39: 469–479. Villar, M.V. 2002. Thermo-hydro-mechanical characterisation of a bentonite from Cabo de Gata. A study applied to the use of bentonite as sealing material in high level radioactive waste repositories. Publicación Técnica ENRESA 01/2002. 258 pp. Madrid. Villar, M.V. 2005. MX-80 bentonite. Thermo-hydromechanical characterisation performed at CIEMAT in the context of the Prototype Project. Informes Técnicos CIEMAT 1053. 39 pp. Madrid. Villar, M.V. 2007. Water retention of two natural compacted bentonites. Clays and Clay Minerals 55(3): 311–322. Villar, M.V. & Lloret, A. 2004. Influence of temperature on the hydro-mechanical behaviour of a compacted bentonite. Applied Clay Science 26: 337–350. Villar, M.V. & Gómez-Espina, R. 2007. Retention curves of two bentonites at high temperature. In Experimental Unsaturated Soil Mechanics. Springer Proceedings in Physics, vol. 112: 267–274. Berlin: Springer. Villar, M.V., Martín, P.L. & Lloret, A. 2005. Determination of water retention curves of two bentonites at high temperature. In Tarantino, A., Romero, E. & Cui, Y.J. (eds.), Advanced experimental unsaturated soil mechanics. EXPERUS 2005. pp 77–82. London: A.A. Balkema Publishers. Villar, M.V., Gómez-Espina, R. & Martín, P.L. 2006. Behaviour of MX-80 bentonite at unsaturated conditions and under thermo-hydraulic gradient. Work performed by CIEMAT in the context of the TBT project. Informes Técnicos CIEMAT 1081. 45 pp. Madrid. Yahia-Aissa, M. 1999. Comportement hydromécanique d’une argile gonflante fortement compactée. Ph.D. thesis, École Nationale des Ponts et Chaussées, CERMES, Paris.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Soil-water characteristic curves and void ratio changes relative to suction for soils from Greece M.E. Bardanis & M.J. Kavvadas National Technical University, Athens, Greece
ABSTRACT: The paper presents the drying portions of the soil-water characteristic curves of five soils from Greece, along with the void ratio vs suction curves over the same drying portion, the one-dimensional compression curves of the same soils and their comparison. The curves were measured using the pressure plate extractor technique. The soils tested included one silt, two clays and two marls. Soil specimens used for soil-water characteristic curve determination were first reconstituted, reconsolidated under one-dimensional conditions to the in-situ vertical stress of each soil, and then unloaded. Undisturbed samples were available for one soil as well and the drying portion of the undisturbed material was measured for this soil too. The soil-water characteristic curve data presented are the first for soils from Greece and among the few presented for marls.
1
INTRODUCTION
Despite climatic conditions favouring the presence of unsaturated soils in Greece, the research in this subject has lagged behind research in fully saturated soils. This paper constitutes one of the first efforts to report unsaturated soil properties for soils from Greece. The property considered first and presented here is the drying portion of the soil-water characteristic curve (SWCC) of five soils. The SWCC constitutes a fundamental property for the study of unsaturated soils. It represents the relation between the distribution of solid, liquid and air phase in the volume of soil (as expressed by degree of saturation, Sr , gravimetric or volumetric water content, w or θ, and void ratio, e), as well as the total volume of the soil itself, and the negative pressure sitting on the liquid phase until desaturation occurs, or suction after desaturation has occurred. The soils tested included marls and other soils containing large amounts of calcite, for which it is hard to find SWCC data presented in the literature. Given that the compressibility properties of the soils have also been studied, and that the SWCC tests involved measurement of both void ratio and water content changes with suction, the comparison between void ratio changes with suction and vertical stress increase under one-dimensional conditions of loading is also presented. 2
THE SOILS TESTED
The soils studied were Ioannina Lake Silt, Corinth Marl, Chania Clay and Kifissia Clay and Marl.
The names used to describe the soils are empirical and the actual physical properties dictating the nature of each soil are presented in this section. Samples from all soils were disturbed samples from excavation materials or relatively low quality borehole cores, except for the samples of Corinth Marl which were carefully cut and preserved samples removed from the toe of the north slope of the Corinth Canal. For this reason, the soil-water characteristic curve of undisturbed samples was measured only for Corinth Marl, while for the others it was measured on specimens reconstituted, then reconsolidated to the estimated in-situ vertical stress and unloaded. This took place for Corinth Marl as well for comparison with the SWCC of the other soils and the SWCC measured on the undisturbed specimens of this material. Classification tests and mineralogical analyses were carried out on all five soils. The index properties of the soils tested are presented in Table 1 and the basic minerals found by x-ray diffraction and methylene blue methods are presented in Table 2. Ioannina Lake Silt is categorised as SM according to USCS, while all others are categorised as CL. Corinth and Kifissia Marls have the highest percentages of calcite. Kifissia Clay has a considerably high percentage of calcite as well, and Chania Clay has a very high percentage of quartz, despite the fact that both soils are commonly referred to as ‘‘clays’’. Highly active minerals such as illite and montmorillonite are present in all five soils, ranging from 3 to 10% and from 7 to 17% respectively. The absence of kaolinite is typical of most soils from Greece.
263
Table 1.
Index properties of the soils tested.
Soil
wL (%)
Ip –
Gs –
Clay (%)
Silt (%)
Sand (%)
Ioannina Lake Silt Corinth Marl Chania Clay Kifissia Clay Kifissia Marl
24 34 24 41 31
1 12 9 21 16
2.55 2.67 2.68 2.67 2.66
8 11 18 33 25
27 86 50 64 68
65 3 32 3 7
Table 2. Basic minerals of the soils tested (measured on percentage passing through sieve No. 200).
Mineral
Kifissia Ioannina Chania Corinth Lake Silt Clay Marl Clay Marl
Quartz Albite Calcite Dolomite Illite Montmorillonite Halloysite Chlorite Serpentine Muscovite
75 5 2.5 – 3 7 – 3 2 –
3
60 3 3 – 3 9 10 3 – 5
16 3 60 2 7 7 – 1.5 1.5 1
16 – 37 1 10 12 8 4 4 7
18 2 52 – 5 17 – 2 – 3
EXPERIMENTAL METHOD
Soil water characteristic curves were measured using the axis translation technique by means of a conventional Soil-Moisture Inc. pressure extractor with 15 Bar air-entry pressure ceramic porous stones. Air pressure was provided from an air compressor with the necessary filters connected to the air supply for air dehumidification. Different specimens were used for each suction value applied in the pressure extractor, rather than measuring the amount of water being extracted from the same specimen. This was considered important for the measurement of total volume changes (which in combination with water content measurement allow the calculation of void ratio changes with suction), as with the water movement measurements, both system complexities and assumptions involved may limit accuracy. With different samples, accuracy is determined only by soil homogeneity for undisturbed samples and careful preparation of identical reconstituted soil samples. Air pressure is supplied to the pressure extractor during the time needed for the suction to reach equilibrium in the specimens. Afterwards the air pressure is removed and the soil specimens are taken out immediately, cut in half, with one half used for water content measurement and the other half being immersed in melted
paraffin wax for total volume measurement. Assuming that the water content measured on one half is the same throughout the specimen, then the mass of the water in the half used for total volume measurement can be calculated from the total mass of this half. Once the mass of the water is known, the mass of the solid particles is also known, and then their volumes are calculated from the known density of water and specific gravity respectively. Having calculated the volumes of the water phase (Vw ) and the solid phase (Vs ) in the half of the specimen where total volume has been measured (Vtot ), the volume of the voids (Vv ) is calculated (Vv = Vtot − Vs ) and the degree of saturation (Sr ) of the sample is calculated by its definition as a property (Sr = Vw /Vv ). Once the degree of saturation has been calculated and the water content w and specific gravity Gs are already known then void ratio e can be calculated (e = w · Gs /Sr ). These calculations are based on the reasonable assumptions that the water content measured on one half of the specimen and the degree of saturation calculated for the other are the same throughout the specimen. An important detail is that when cutting the specimen, utmost care must be exhibited that the surface of the section in the half used for total volume measurement must be as flat as possible without cavities where air may be trapped. As far as one-dimensional consolidation is concerned, conventional deadweight, front-loading oedometers were used with a 10:1 beam-lever ratio and fixed-ring cells with lightly lubricated, smooth and polished inner surface rings, with a 70 mm internal diameter and 19 mm height. Reconstitution involved breaking of particle aggregations and thorough mixing with de-aired, de-ionised water until a slurry of 1.5wL water content was prepared. All slurries were left to hydrate under vacuum for sufficient time with occasional measurement of their water content and drying or addition of water to ensure homogeneity of the slurries prepared for each soil and consistent initial conditions for all reconstituted soils. As a general rule, a water content of ±10% from the target value of initial slurry water content was set, which has been found to ensure homogeneity of later consolidated specimens of reconstituted soils, provided the maximum vertical stress exceeds 50–100 kPa (Bardanis, 1999) as was the case for all 5 soils. All soils were consolidated to a maximum vertical stress corresponding approximately to the depth they came from and then unloaded; Ioannina Lake Silt to 100 kPa, Chania Clay to 200 kPa, and Kifissia Clay and Marl to 600 kPa. Corinth Marl specimens were consolidated to 800 kPa and then unloaded, mostly on the basis that this stress history created the same initial void ratio that was measured on the undisturbed specimens removed from the toe of the Corinth Canal slopes (approximately 70–75 m high).
264
As far as the samples of the undisturbed Corinth Marl are concerned, these were carefully preserved in a controlled humidity chamber. Larger blocks were taken out of the chamber when specimens had to be trimmed from them in order to be put in the pressure extractor. Corinth Marl as a geological formation may by no means be considered a homogeneous material; still the largest possible block of visually homogeneous material was used. Homogeneity within this block was later verified by numerous index tests on specimens from various positions in the block. The blocks came from the toe of the canal slope just above sea level (ca. 0.50 m) and in-situ suction was measured with a Quickdraw Tensiometer and found to be approximately 10 kPa. 4
RESULTS AND DISCUSSION
In Figure 1(a) degree of saturation is plotted against suction for Ioannina Lake silt, while in Figure 1(b) void ratio is plotted against the corresponding value of water content during drying. The solid line in 100
Sr (%)
80 60 40 20 0 10
100
(a)
1000
10000
s (kPa)
Figure 1(b) is the full saturation line corresponding to the specific gravity, Gs , of the material (e = w · Gs , for Sr = 100%). As seen in Figure 1(a), desaturation occurred between 25 and 30 kPa, while the second inflection point occurred between 150 and 200 kPa corresponding to a degree of saturation between 45% and 50%. This value seems too high to be the residual value of the degree of saturation. Specimens of the soil left to dry completely in the air yielded a value of the degree of saturation on average 7%. This value seems more likely to reflect residual conditions, whereas the value of 45%–50% observed on the SWCC corresponds most probably to the point where water retention characteristics start to be dictated primarily by the finer fraction of the soil’s grains. The grain size distribution of this soil (Fig. 2) is gap-graded, although slightly and only for the small percentage passing through sieve No.200. Still, this type of grain size distribution would justify a ‘bimodal’ SWCC with one inflection point at Sr 45%–50% and a second one at approximately 7%, which was not observed however as the maximum applied suction was 1500 kPa. Also as seen in Figure 1(b), the scatter of void ratio values is very large, as this is probably the coarsest material for which immersion in melted paraffin wax for total volume measurement may be applied. In Figures 3(a) & 3(b) degree of saturation is plotted against suction and void ratio against the corresponding water content during drying respectively for both reconstituted/reconsolidated and undisturbed Corinth Marl. As seen in Figure 3(a), desaturation occurred for both types of Corinth Marl, although a second inflection point was not observed for either soil up to the maximum applied suction of 1500 kPa. Similarly, a clear departure from the full saturation line can be observed for both types of this soil in Figure 3(b). Two other observations can be made. First, the scatter of measured values is larger for the
0.80
.
0.70
Percentage passing (%)
0.60
e
0.50 0.40 0.30 0.20 0.10 0.00 0
(b)
5
10
15
20
25
100 90 80 70 60 50 40 30 20 10 0 0.001
30
0.010
0.100
1.000
10.000
Sieve diameter (mm)
w (%)
Figure 1. (a) Degree of saturation Sr vs suction s, and (b) void ratio e vs water content w for Ioannina Lake Silt.
Figure 2. Lake Silt.
265
Grain-size distribution curve of Ioannina
100
80
80
60
60
Sr (%)
Sr (%)
100
40 20
20 0
0 10
100
1000
10
10000
100
(a)
s (kPa)
0.80
0.70
0.70
0.60
0.60
0.50
0.50
0.40
0.40
0.30
1000
10000
s (kPa)
0.80
e
e
(a)
0.30
0.20
Rec/Rec
0.20
0.10
Undisturbed
0.10
0.00
0.00
0
(b)
40
5
10
15
20
25
30
0
(b)
w (%)
5
10
15
20
25
30
w (%)
Figure 3. (a) Degree of saturation Sr vs suction s, and (b) void ratio e vs water content w for Corinth Marl.
Figure 4. (a) Degree of saturation Sr vs suction s, and (b) void ratio e vs water content w for Chania Clay.
undisturbed Corinth Marl, almost at the point of rendering the results meaningless, especially in the e-w plot of Figure 3(b). Still it is clear in Figure 3(a) that, despite the large scatter, the undisturbed Corinth Marl desaturates at a higher suction than the reconstituted and reconsolidated one (between 200 and 300 kPa as opposed to 100 to 200 kPa) and retains a higher degree of saturation for the same suction after desaturation, although both materials have the same void ratio at the beginning of drying. Bardanis & Kavvadas (2004) have elaborated more on this observation and attributed the observed behaviour to cementation of the undisturbed Corinth Marl, which does not exist in reconstituted/reconsolidated specimens. This is worth further investigation, as experimental results for unsaturated properties of marls (especially focusing on the effect of their cementation in their drying behaviour) are scarce, if any, in the literature. More information on the engineering behaviour of Corinth Marl and the role played by its cementation may be found in Kavvadas et al. (2003).
In Figures 4(a) & 4(b) degree of saturation is plotted against suction and void ratio against water content during drying for Chania Clay. As seen in Figure 4(a), desaturation seems to start occurring at approximately 1000 kPa but this is not supported by a similarly clear departure from the full saturation line in Figure 4(b). The observed departure is not considered clear given the accuracy of measurements. Still the picture is that the air entry pressure of Chania Clay must be between 1000 and 1500 kPa, although a few measurements at slightly larger values would have ascertained whether desaturation did actually occur or not. In Figures 5(a) & 5(b) degree of saturation is plotted against suction and void ratio against water content during drying for both Kifissia Clay and Marl. Given the same stress history of both materials, the Clay retains a higher void ratio, in agreement with its higher liquid limit. Kifissia Clay seems to desaturate close to 1000 kPa (Fig. 5(a)), which is supported by signs of departure from the full saturation line (Fig. 5(b)). Both the departure from line Sr = 100% in Figure 5(a) and
266
0.80
100
0.70 0.60 0.50
60
e
Sr (%)
80
40
0.40 0.30 0.20
SWCC
0.10
1D Compression
20
0.00
0 10
100
1
10000
s (kPa)
(a) 0.80
0.70
0.70
0.60
0.60
0.50
0.50
0.40
0.40
1000
10000
0.20
Clay
0.20
SWCC
0.10
Marl
0.10
1D Compression
0.00
0.00 0
5
10
15
20
25
1
30
w (%)
(b)
Figure 5. (a) Degree of saturation Sr vs suction s, and (b) void ratio e vs water content w for Kifissia Clay and Marl.
the full saturation line in Figure 5(b) are rather obscure relative to the accuracy achieved. As far as Kifissia Marl is concerned, desaturation has not occurred, as no departure is observed from the line Sr = 100% or the full saturation line. The opposite would have been expected given that the Marl contains slightly less clay-size material than the Clay (25% vs 33%), slightly more sand (7% vs 3%) and less clayey minerals in the fraction passing sieve No. 200 (a total of 27% vs 45%). The observed lack of desaturation up to 1500 kPa may therefore be attributed either to the presence of more montmorillonite (17% vs 12%) or to experimental error with the results of Kifissia Clay. 5
100
0.30
0.30
(b)
10
Suction/Vertical stress (kPa)
0.80
e
e
(a)
1000
VOID RATIO CHANGES WITH SUCTION AND VERTICAL STRESS
Given that the one-dimensional curves of most of the soils had already been studied, a comparison was attempted between void ratio changes due to suction and due to one-dimensional compression.
10
100
1000
10000
Suction/Vertical stress (kPa)
Figure 6. Void ratio vs suction during drying and one-dimensional compression curves for (a) reconstituted and reconsolidated Corinth Marl, and (b) undisturbed Corinth Marl.
In Figures 6(a) & 6(b) the void ratio-suction curve and the one-dimensional compression curve for reconstituted/reconsolidated specimens and undisturbed specimens of Corinth Marl are plotted. For Corinth Marl, sufficient quantities of the material were available for a special test with a loading-unloading loop, similar to that applied to reconstituted specimens before drying, to be performed. The compression curve for this test is shown in Figure 6(a). The compression curve shown in Figure 6(b) is an average of the one-dimensional compression tests performed on undisturbed Corinth Marl. The larger scatter of void ratio values of undisturbed specimens during drying relative to that of the values of the reconstituted/reconsolidated specimens is apparent in these plots as well. For reconstituted/ reconsolidated specimens there seems to be fair agreement up to 100 kPa. After that value of suction/stress, the void ratio during drying becomes smaller than that for the compression
267
1.20 1.00
e
0.80 0.60 0.40 0.20 0.00 10
100
1000
10000
Suction/Vertical stress (kPa) Figure 7. Void ratio vs suction during drying and onedimensional compression curves for reconstituted and reconsolidated Kifissia Clay. 1.00 0.80
e
0.60 0.40 0.20 0.00 10
100
1000
10000
Suction/Vertical stress (kPa) Figure 8. Void ratio vs suction during drying and onedimensional compression curves for reconstituted and reconsolidated Kifissia Marl.
curve, up to the value of stress where the intrinsic compression curve is reached and the opposite seems to happen. In Figures 7 and 8 the same curves are compared for Kifissia Clay and Marl respectively. Limited quantities of the samples from each material did not allow for special one-dimensional compression tests to be carried out with a loading-unloading loop to the maximum stress applied to reconstituted specimens before drying. One point on the void ratio-suction curve of Kifissia Clay corresponding to 1100 kPa (Fig. 7) departs significantly from the curve the rest of the points seem to follow. This point corresponds to the point indicating desaturation in the curves on Figures 5(a) & 5(b). This seems to support that either
the particular specimen had different properties or there has been some experimental error. Therefore it will not be considered that Kifissia Clay achieved desaturation. Returning to the comparison between void ratio vs suction and one-dimensional compression curves for each of the two materials, two observations can be made. First, the void ratio vs suction curves are for all practical purposes (and at least up to the maximum stress applied to specimens used for SWCC measurement) parallel to the unloading branches of the one-dimensional curves. This point seems to support that void ratio decrease with increasing suction up to the air-entry pressure during drying and increasing vertical stress during one-dimensional loading may be described by the same indices. The second observation regards the void ratio vs suction curve of Kifissia Clay, which seems to exhibit a change in its slope at 600 kPa (if the point at 1100 kPa is omitted). Unfortunately this has not been observed on the same curve for Kifissia Marl. Still it would be logical to expect such a change of slope when such conditions occur, i.e. a maximum preconsolidation pressure smaller than the air-entry pressure and a zero total stress suction path extending to suctions higher than the preconsolidation pressure. These observations need certainly to be supported by further experimental research (especially with tests where high values of suction will be applied so that desaturation does actually occur) as they are of considerable value in constitutive modelling of unsaturated soils. Void ratio vs suction curves described by the same indices as with compression curves could mean that κs could be substituted by κ in the Barcelona Basic Model (Alonso et al. 1990) family of constitutive models for air-entry pressure smaller than the maximum preconsolidation pressure. This would itself change to λ for air-entry pressure larger than the maximum preconsolidation pressure, in the suction range between preconsolidation pressure and the air-entry pressure. 6
CONCLUSIONS
The drying portions of the soil-water characteristic curve presented constitute the first ones for soils from Greece. Except for this they are among the few such results presented for marls and generally clay-size soils containing large amounts of calcite. Although they may by no means be considered representative of the properties of soils found throughout Greece or soils with high calcite fractions, they draw attention to the properties of such materials. The most important aspect needing further research is the possibility that cementation of undisturbed marls leads to retaining higher degrees of saturation for the same suction in the same soils with the same loading history but without
268
cementation. Further investigation into the decrease of void ratio with increasing suction for soils with a maximum preconsolidation pressure smaller and higher than their air-entry pressure may also help redefine the parameters used in constitutive modelling to describe these changes. ACKNOWLEDGEMENTS Part of the research by M.E. Bardanis has been funded by the National Scholarship Foundation (IKY) of Greece. REFERENCES
Bardanis, M.E. 1999. An experimental study of the properties of intrinsic compressibility of one clay and one marl, Proc. 13th Young Geotechnical Engineers Conference, Santorini, Greece, 23–25 September 1999, 88–97, Athens: Minoas. Bardanis, M.E., Kavvadas, M.J. 2004. Laboratory investigation of the virgin drying of the Corinth Marls, in T. Schanz (ed.), Unsaturated Soils: Experimental Studies, Proc. of the Int. Conf. ‘‘From Experimental Evidence towards Numerical Modelling of Unsaturated Soils’’, Weimar, 17–18 September 2003, 421–432, Berlin: Springer. Kavvadas, M.J., Anagnostopoulos, A.G., Georgiannou, V.N., Bardanis, M.E. 2003. Characterisation and engineering properties of the Corinth Marl, in Tan et al (eds.), Proc. Int. Workshop ‘Characterisation and Engineering Properties of Natural Soils’, Singapore, 2002, 2, 1435–1459, Lisse: Swets & Zeitlinger.
Alonso, E.E., Gens, A., Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique 40(3): 405–430.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Prediction of soil-water retention properties of a lime stabilised compacted silt M. Cecconi University of Perugia, Perugia, Italy
G. Russo University of Cassino, Cassino, Italy
ABSTRACT: The applicability of semi-empirical prediction methods of the water retention properties of unsaturated soils has been examined in detail. Among these methods, those based on the particle size distribution of samples seem to be very effective in predicting the soil water retention curve, as well as being very advantageous for their simplicity. On the other hand, other methods allow predicting indirectly the soil water retention curve from the mercury intrusion porosimetry technique. In the paper experimental soil water retention curves (swrcs) of a natural and lime stabilised compacted silt, obtained from pressure plate tests and mercury intrusion porosimetry tests, are respectively compared with those predicted by pore size distribution model and mercury intrusion porosimetry models. The comparison allows a critical review of the prediction methods and highlights the consistency of the predicted and the observed water retention properties of both natural and lime stabilised samples.
1
INTRODUCTION
The relationship between suction, s, and volumetric water content, θ , or degree of saturation, i.e. the soil water retention curve SWRC, can be experimentally measured in the laboratory by means of pressure plate or volumetric pressure plate extractor. Several mathematical expressions, both empirical and theoretical in nature, have also been proposed in the literature to describe the SWRC (see Scott et al., 2001). Moreover, the soil water characteristic curve can also be computed from the particle size distribution (PSD); this approach is based mainly on the similarity between shapes of the cumulative grain size distribution and the s(θ ) curves. The methods originally proposed in the field of soil physics by Arya & Paris (1981) and Arya et al. (1999) seem to be very effective in predicting the SWRC, as well as being very advantageous for their simplicity. However, since most predictions models are based on PSD information, the accuracy of a PSD curve may affect the estimate of s(θ). At present, there are a few attempts to quantitatively investigate the effect of the choice of a PSD model on the prediction of the soil water retention curve as well as the conductivity function k(s). A review of such models is critically examined in Hwang et al. (2002) and Hwang & Powers (2003). The water retention properties can be also obtained indirectly from the mercury porosimetry technique
(Aung et al., 2001; Kong & Tan, 2000; Prapaharan et al., 1985; Purcell, 1949; Penumadu & Dean, 1999), since the SWRC is intrinsically linked with the pore size distribution of the material (the equivalent pore radius can be somehow related to matric suction through the capillarity equation). Porosimeter tests in fact allow evaluating the pore size, their amount and their distribution, and in a much shorter time compared to pressure plate tests. In the paper, experimental soil water retention curves (SWRCs) of a natural and lime stabilised compacted silt, obtained from pressure plate tests and mercury intrusion porosimetry tests, are respectively compared with those predicted by Arya & Paris (1981) and Prapaharan et al. (1985) models. The pressure plate test results are reported in detail in a companion paper (Tedesco & Russo, 2008). The comparison allows a critical review of the prediction methods, and highlights the consistency of the predicted and the observed water retention properties of both natural and lime stabilised samples. 2
EXPERIMENTAL PROCEDURES AND RESULTS
Laboratory tests were performed on remoulded samples of an alluvial silty soil. The physical characteristics (grain size distribution, specific weight,
271
Table 1. (MIP).
Pressure plate tests (PP) and porosimetry tests
Test type
Test #
Sample
Curing time
PP PP PP PP MIP MIP MIP MIP MIP MIP MIP MIP
STDN01 STD02 L43CCT07(∗) L43CCT28(∗) L4NOF01 L4NOF02 L4NOF04 L43OF00 L43OF07 L43OF14 L43OF28 L43OF77
nat 3% lime 3% lime 3% lime natural natural natural 3% lime 3% lime 3% lime 3% lime 3% lime
− variable 7 days 28 days − − − 0 days 7 days 14 days 28 days 77 days
(∗ ) CCT: constant curing time.
Table 2. samples.
Natural 3% Lime
Physical properties of natural and stabilised γs (kN/m3 )
wL (%)
PI
wopt (%)
γdmax (kN/m3 )
26.4 26.1
25.0 24.0
8 –
14.5 17.5
18.6 17.3
1.0
0.8
no rm
plastic limit, liquid limit) of the natural soil were determined and standard Proctor tests were performed. Lime treated samples were prepared by hand mixing the oven dried soil with 3% quicklime powder and distilled water, allowing the quicklime to hydrate for 24 hours. The selected percent by weight of quicklime allowed the development of pozzolanic reactions (Rogers et al., 1997). The samples were finally compacted at optimum (wopt ) initial water content. Pressure plate tests were performed on both natural and lime stabilised samples. With reference to the standard testing procedure, the duration of the test does not allow the control of the curing time of the stabilised samples. Therefore, a new testing procedure was developed in order to obtain constant curing time water retention curves. Details of the procedure can be found in a companion paper (Tedesco & Russo, 2008). Two types of water retention curves of the stabilised samples have been considered, namely the standard retention curve, characterised by a variable curing time, and the ‘‘constant curing time’’ curves, for which the experimental data are determined at the same curing time (CCT tests). In particular, 7 and 28 days curing times were set for stabilised samples, traditionally considered in order to evaluate the effectiveness of lime stabilisation. In order to perform mercury intrusion porosimetry, samples were dehydrated by freeze-drying technique (Delage & Pellerin, 1984), that is rapid freezing in liquid nitrogen (boiling point −196◦ C) followed by sublimation in a true vacuum. Freezing was accelerated using small pieces of soil (1–2 mg in weight), as stated by Delage & Lefebvre (1984). The dehydrated lime stabilised samples were then cured for fixed time intervals under controlled conditions before performing MIP tests. The curing intervals of time selected were t = 0, 7, 28 days. In Table 1 pressure plate tests (PP) and mercury intrusion porosimetry tests (MIP) are summarized. Table 2 reports the main physical properties of both natural and lime stabilized samples. In Figure 1 the water retention curves of natural (STDN 01) and lime stabilised samples, at variable (STDN 02) and constant curing time (L43CCT07, L43CCT28), are reported. It can be seen that the addition of lime generally increases the water retention of the soil, and this increase is strongly affected by the curing time (Tedesco, 2007). Figure 2 and Figure 3 show the results of MIP tests respectively on natural and lime stabilised samples, the latter performed at constant curing time. A relevant modification of porosity for lime stabilised samples takes place immediately after the addition of lime. A subsequent reduction of this effect occurs increasing the curing time of the stabilised samples, bringing back the pore size distribution towards the
S TD02 L43CCT07 L43CCT28
0.6
S TDN01 Va n Ge nuchte n (1980)
0.4 1
10
100
1000
10000
s (kP a ) Figure 1. SWRCs of natural and lime stabilised samples (from pressure plate tests).
distribution of the natural samples. After a curing time of 28 days the stabilised samples show a very similar porosity and pore size distribution comparable with those of natural samples. More details on the observed behaviours can be found in Russo et al. (2007).
272
sands yields to a computed parameter α not depending on particle size (constant α = 1.38). Later investigations by Arya et al. (1999) were aimed to investigate on the variation of α with particle size distribution parameters. However, in the following α is assumed to be constant. In order to produce a mathematical representation of the complete PSD, the single-parameter unimodal Jaky model was used in the present study (Jaky, 1944):
L4NOF0 1 L4NOF02 L4NOF04
0.12 0.08 0.04
10
100
2 1 d P(d) = exp − 2 ln k d0
1000
diameter ( m)
Figure 2.
Results of MIP tests on natural samples.
cumulative volume (cc/g)
0.25 L43OF00 L43OF07 L43OF14 L43OF28 L43OF77
0.20 0.15 0.10 0.05 0.00 0.001
Figure 3.
3
0.01
0.1
1 10 diameter ( m)
100
1000
Results of MIP tests on lime-stabilised samples.
PREDICTIONS
3.1
Particle size distribution method
Very briefly, in the model proposed by Arya & Paris (1981) it is assumed the solid grains spherical and the pore volume approximated to that of cylindrical capillary tubes. For each ith particle-size class, the pore radius (ri ) can be related to the mean grain radius (Ri ), according to: ri = Ri [2eni (1−α) /3]1/2
where d0 represents the diameter corresponding to the 100% of passing in weight (P), and k the fitting parameter. The value of k was found to vary from 5 to 3 when passing from natural to lime stabilised soil (Fig. 4). The calculated PSD was then divided into thirty size fractions and values of s(θ) were then calculated by means of the procedure outlined by Arya & Paris (1981). The predicted SWRCs are shown in Figures 5a and b) in comparison with those obtained from standard and constant curing time pressure plate tests and fitted through Van Genucthen (1980) equation. The results are plotted in terms of the ratio = θ/θ0 , where θ0 represents the initial volumetric water content of the sample. For the material in its natural state (Fig. 5a), it can be noted that the predicted SWRC (α = 2.5) is twisted and smoothed with respect to the measured SWRC and the air entry value is questionable. The predictions improve for the stabilised samples. In this case, a larger value of Arya and Paris parameter α is needed (α = 4). By comparing the dotted curves in Figure 5b with the model prediction, it is found that the slope of the predicted SWRC is very similar to that obtained from a standard pressure plate test (test STDN02, see Table 1), even if the predicted curve is shifted downward.
(1)
1.0
where ni , e and α are respectively the number of spherical grains, the voids ratio and a constant parameter larger than unity. Then, for a tube of radius ri , the capillarity equation holds:
gravel
sand
silt
0.8
passing in weigth
(ua − uw )i = si = 2Tw /ri
(2)
0.6 0.4
nat
0.2
with Tw the surface tension of water (Tw = 7.27 × 10 N/m at 20◦ C). For a given grain size distribution, Equations 1 and 2 allow to calculate the value of suction required to desaturate a given fraction of pores. The application of the model to different soils varying from silty clays to
(3)
=3
1
y, k
0.1
Jak
0.01
=5
0.0 0 0.00 1
y, k
0.16
Jak
cumulative volume (cc/g)
0.20
lime-stabilised
−2
0.0 0.00 1
0.01
0.1
1
10
10 0
d (mm)
Figure 4. Grain size distributions and Jaky model for natural and lime-stabilised samples.
273
with Tm the surface tension of mercury (Tm = 480 × 10−3 N/m at 20◦ C) and δm the contact angle between mercury and soil (δm = 139◦ ). The soil gravimetric water content that should correspond to each intruded pore radius can be calculated from Equation 5:
1.0 nat.
= 2.5
norm
0.8
0.6
w=
pressure plate-nat. samples - - - - - - Van Genuchten (1980) 0.4 1
10
10 0
100 0
with n the soil porosity and n˜ the ratio of the volume intruded by mercury to pore radii as small as r to the total volume of the sample. Equation 5 is well-founded by assuming implicitly that the pressure um − ua intruding the air pores (Va ) of a soil sample of volume V and porosity n corresponds—through Equations 4—to the matric suction s required to desaturate an initially saturated sample with the same total volume and porosity. Experimental data obtained from MIP tests have been inferred and then ‘‘converted’’ to swrcs according to Equations 4 and 5. Figures 6a and 6b show the model
a)
1.0 lime s
tab.
=4
norm
STDN02
L43CCT28
0.6
(5)
10000
s (kPa)
0.8
n − n˜ (1 − n)Gs
L43CCT07 - - - - - - Van Genuchten (1980) 0.4 1
10
10 0
100 0
10000
1.0
s (kPa)
b)
Figure 5. Model predictions for a) natural and b) lime stabilised samples (from grain size distribution data). norm
0.8 STDN01 - - - - - - Van Genuchten (1980)
0.6
However, for the material at hand, the Arya and Paris (1981) model predictions are not sufficiently accurate. Further investigations are also required to explore the nature of parameter α; in fact values of α larger than unity render Eqution 1 dimensionally incorrect (Cecconi & Pane, 2002). 3.2
from MIP tests L4NOF01 L4NOF02 L4NOF04
0.4 1
10
100
1000
MIP method 1.0
Van Genuchten STDN02 L43CCT07 L43CCT28
norm 0.6
0.4 1
10
100
1000 s (kPa)
[4.1]
[4.2]
(4)
a)
0.8
– the mercury entry value, mercury entry value and the air entry value of the SWRC are closely related; – the equivalent pores radius (r) from MIP tests and the pores radius from experimental swrcs can be calculated by using the following equations (4.1) and (4.2) derived from Kelvin equations: 2Tm cos δm =− (um − ua )
100000
L43OF00 L43OF07 L43OF14 L43OF28 L43OF77
The method proposed by Prapaharan et al. (1985) was used to derive the SWRC from the results of MIP tests. Such method is based on the following experimental evidence:
2Tw r= (ua − uw )
10000
s (kPa)
10000
100000 b)
Figure 6. Model predictions for a) natural and b) lime stabilised samples (from MIP tests).
274
predictions estimated for natural and lime stabilised samples. From a critical inspection of these figures, the following considerations can be drawn:
4
– the predicted swrcs for tests L43OF00, L43OF07 and L43OF14 are very similar in shape, thus indicating that the short term effects induced by lime persist at least for 14 days; – the subsequent microstructural changes induced by lime with increasing the curing time up to 28 and 77 days (tests L43OF28 and L43OF77 modify the location and the shape of the swrc; due to long term effects (pozzolanic reactions), the increase of the retention properties are probably connected with the reduction of interconnected pores between aggregates and the increase of occluded intra-aggregate pores. – the predicted and experimental soil water retention curves—in Figure 6, the experimental data are fitted through the Van Genuchten equation—are substantially in good agreement. It is noted that data from constant curing time tests are very close to those calculate from MIP tests carried out at low curing time. Also, data from test stdn02 are definitely comparable with those obtained from MIP tests on stabilised samples and cured for four and more weeks. Finally, when comparing the whole set of predictions obtained from MIP tests discussed above and shown in Figure 7, it is synthetically highlighted the relevant dependency of water retention properties of the stabilised samples on the curing time. There are no sensible differences—in terms of retention properties—among natural and stabilised samples, as long as the curing time does not exceed two weeks. After that, the soil water retention curves increase significantly as the pozzolanic reactions develop.
1.0
norm
0.8
0.6 natural 3% stab. 0, 7, 14 days 3% stab. 28, 77 days 0.4
1
10
100
1000
10000
100000
s (kPa)
Figure 7. Model predictions for lime stabilised samples (from MIP tests).
CONCLUDING REMARKS
Two different empirical methods available in the literature for the prediction of the SWRCS of unsaturated soils, namely the models proposed by Arya & Paris (1981) and Prapaharan et al. (1985) have been applied to the experimental results of pressure plate and mercury intrusion porosimeter tests on natural and lime stabilised samples of a compacted sandy silt. By following the approach proposed by Prapaharan et al. (1985), based on the similarity between the pore size distribution and the soil water retention properties, the agreement between experimental results and predictions is very encouraging. The model is capable to capture the very complex evolution with curing time of the microstructure of stabilised samples, due to the development of cation exchange and pozzolanic reactions induced by lime. Moreover, the mercury porosimetry technique requires much shorter test duration than pressure plate tests and this certainly represents a great advantage.
ACKNOWLEDGEMENTS The Authors are very grateful to Prof. Giuseppe Mascolo for the support during the experimental work. Mercury intrusion porosimetry tests were developed at the University of Cassino under the careful supervision of Sebastiana Dal Vecchio. With gratitude the Authors thank Dante Valerio Tedesco for the helpful contribution to the laboratory work.
REFERENCES Arya, L.M., Paris, J.F. 1981. A physicoempirical model to predict the soil moisture characteristic from particle size. Soil Sci. Soc. Am. J. 45: 1023–1030. Arya, L.M., Feike, J.L., van Genuchten, M.T., Shouse, P.J. 1999. Scaling parameter to predict the soil water characteristic from particle size distribution data. Soil Sci. Soc. Am. J. 63: 510–519. Aung, K.K., Rahardjo, H., Leong, E.C., Toll, D.G. 2001. Relationship between porosimetry measurement and soilwater characteristic curve for unsaturated residual soil. Geotechnical and Geological Engineering, 19: 401–416. Cecconi, M., Pane, V. 2002. Comparison of some experimental and theoretical approaches for the determination of the soil water characteristic curve. Proc. of International Workshop on Environmental Geomechanics, Monte Verità, Ascona, Switzerland, 341–346. Delage, P., Pellerin, F.M. 1984. Influence de la lyophilisation sur la structure d’une argile sensible du Québec. Clay Minerals, 19: 151–160. Delage, P., Lefebvre, G. 1984. Study of the structure of a sensitive Champlain clay of its evolution during consolidation. Canadian Geotechnical Journal 21: 21–35.
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Fredlund, M.D., Fredlund, D.G., Wilson, G.W. 1997. Prediction of the soil water characteristic curve from grain size distributions and volume mass properties. Proc. 3rd Brasilian Symp. on Unsat. Soils, Nonsat97, Rio de Janeiro, vol. 1, 13–23. Hwang, S.I., Lee, K.P., Lee, D.S., Powers, S.E. 2002. Models for estimating soil particle size distributions. Soil Sci. Soc. Am. J. 66: 1143–1150. Hwang, S.I. and Powers, S.E. 2003. Using soil particle size distribution models to estimate soil hydraulic properties. Soil Sci. Soc. Am. J. 67: 1103–1112. Jaky, J. 1944. Soil Mechanics. Egyetemi Nyomda, Budapest. Kong, L.W., Tan, L.R. 2000. A simple method of determining the soil-water characteristic curve indirectly. Proc. of the Asian Conference on Unsaturated Soils, Singapore, 341–345. Penumadu, D., Dean, J. 1999. Compressibility effect in evaluating the pore-size distribution of kaolin clay using mercury intrusion porosimetry. Canadian Geotechnical Journal 37: 393–405. Prapaharan, S., Altschaeffl, A.G., Dempsey, B.J. 1985. Moisture curve of compacted clay: mercury intrusion method. Journal of Geotechnical Engineering, ASCE, 111(9): 1139–1143. Purcell, W.R. 1949. Capillary pressures, their measurement using mercury and the calculation of permeability therefrom. Petroleum Transactions, IME 186: 39–48.
Rogers, C.D.F., Glendinning, S., Roff, T.E.J. 1997. Modification of clay soils for construction expediency. Geotechnical Engineering 125: 1–8. Russo, G., Dal Vecchio, S., Mascolo, G. 2007. Microstructure of a lime stabilised compacted silt. In Tom Schanz (ed.), Experimental Unsaturated Soil Mechanics, Proc. of the 2nd Int. Conf. On the Mechanics of Unsaturated Soils, USS2007, Weimar (D), 7–9 March 2007. Heidelberg: Springer, 49–56. Scott Sillers, W., Fredlund, D.G., Zakerzadeh, N. 2001. Mathematical attributes of some soil-water characteristic curve models. Geotechnical and Geological Engineering 19: 243–283. Tedesco, D.V. 2007. Hydro-mechanical behaviour of limestabilised soils. PhD Thesis, University of Cassino. Cassino, Italy. Tedesco, D.V., Russo, G. 2008. Time dependency of water retention properties of a lime stabilised compacted soil. Submitted for publication to First European Conference on Unsaturated Soils, 2–4-July, Durham. Van Genuchten, M. Th. (1980). A closed-form equation for predicting the hydraulic conductivity off unsaturated soils Soil Sci. soc. Am. J. 44: 892–898.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Time dependency of the water retention properties of a lime stabilised compacted soil D.V. Tedesco & G. Russo University of Cassino, Cassino, Italy
ABSTRACT: Lime stabilisation induces the development of chemical reactions which modify the microstructure of treated soils. Cation exchange and pozzolanic reactions are the two main phenomena responsible for those microstructural changes. Among the hydro-mechanical properties of the stabilised soil, the water retention properties are significantly modified with respect to those of the natural ones and are strongly dependent on curing time. An experimental investigation was carried out on a natural and lime-stabilised compacted silty soil. It was found that the water retention capacity increases after the addition of lime independently from the initial water content. The increase is significantly higher for longer curing times. The results of mercury intrusion porosimetry tests highlighted the fundamental influence of lime on the modification of inter-aggregate porosity.
1
INTRODUCTION
Lime stabilisation is widely used in order to improve the engineering properties of natural soils not suitable as construction materials in earthworks. The reuse of those soils represents a great chance in the reduction of the environmental impact of earthworks (Croce & Russo, 2002). Two different chemo-physical reactions take place after the addition of lime, namely cationic exchange and pozzolanic reactions, which develop simultaneously but on different time scales. Cationic exchange between calcium cations, made available by lime addition, and the hydrogen, sodium and potassium cations of the clay minerals takes place in the short period. This reaction induces the flocculation of clay aggregates. On the long term, pozzolanic reactions take place with the development of stable compounds, such as hydrated calcium silicates and aluminates (Eades & Grim, 1960, Glenn & Handy, 1963), responsible of cementation bounds among the soil aggregates. These two mechanisms are respectively referred to as modification and stabilisation of treated soils (Rogers & Glendinning, 1996). On the macroscopic scale, the treated soil shows a different grain size distribution and plasticity, a decrease in compressibility and a corresponding increase of shear strength, the latter being strongly dependent on curing time (Croce & Russo, 2003). The water retention of lime stabilised compacted samples is generally higher in comparison with natural compacted samples at corresponding initial water content (Croce & Russo, 2003). It has been observed
(Russo, 2005) that, as stated for natural compacted samples (Vanapalli et al., 1999), the higher water retention pertains to stabilised samples compacted wet of optimum. Despite the strong dependency of lime stabilised soil properties on the time needed for the development of cation exchange and pozzolanic reactions, the role played by curing time in the increase of water retention of lime stabilised samples is still not clear. In the paper the results of an experimental investigation on the influence of curing time on the water retention of lime stabilised soils are presented. Pressure plate tests on both natural and lime stabilised compacted alluvial sandy silt have been performed at fixed lime content. A new testing procedure has been adopted in order to determine soil water retention curves at constant curing time. The results have been interpreted by means of the Van Genuchten (1980) model. A discussion on the experimental findings has been developed with reference to the results of mercury intrusion porosimetry tests performed on the same natural and lime stabilised soils (Russo et al., 2007). 2
EXPERIMENTAL PROCEDURES
The natural soil used in the investigations is an alluvial sandy silt of low plasticity. The minimum amount of quicklime necessary to the triggering of pozzolanic reactions was about 1.0% by weight, as observed by means of the Lime Fixation Point Method (Hilt & Davidson, 1960, Rogers & Glendinning,
277
1996). A fixed amount of quicklime (3.0% by weight) was set in order to allow the complete development of both cationic exchange and pozzolanic reactions (Rogers & Glendinning, 1996). After the addition of quicklime and distilled water, the samples were cured for 24 hours in order to allow the hydration of quicklime. Grain size distributions, Atterberg limits and specific weights of both natural and lime stabilised soils were determined. The same tests were repeated for stabilised samples at different curing times, namely 0, 7, 28, 60 days. Both natural and lime stabilised samples were compacted following the Standard Proctor procedure (ASTM D698-91ε1 ) at different initial water content, namely dry of optimum, optimum and wet of optimum water contents. It has been supposed that the structure of soils compacted at corresponding initial water contents is comparable (Seed & Chan, 1959, Alonso et al., 1987). Natural and lime stabilised samples (20.0 mm in height and 60.5 mm in diameter) were saturated with distilled water through the application of a hydraulic head and submitted to desiccation tests using a pressure plate apparatus equipped with a high air entry value porous stone (1.5 MPa). For each suction step, four days were needed for the specimens in order to reach the equilibrium between the internal and the applied air pressure. At the end of the tests the specimens were oven dried and the soil water retention curves (SWRCs) determined by back calculation. During the long duration of each test lime treated samples experience continuous changes in microstructure, due to the relevant dependency on curing time (Russo et al., 2007). The variations in soil water
Table 1.
Pressure plate tests (PP).
Sample
Test
Water content
Curing time (days)
Natural Natural Natural 3% Lime 3% Lime 3% Lime 3% Lime 3% Lime 3% Lime 3% Lime 3% Lime 3% Lime
ND NO NW STD STO STW CCTD07(∗) CCTO07(∗) CCTW07(∗) CCTD28(∗) CCTO28(∗) CCTW28(∗)
Dry Opt Wet Dry Opt Wet Dry Opt Wet Dry Opt Wet
– – – Variable Variable Variable 7 7 7 28 28 28
(∗)
For constant curing time (CCT) tests the average values are reported.
retention capacity detected at the end of the test must be considered as determined at variable curing time. Generally, at the end of the test the sample was cured for more than 28 days. In order to carry out tests at constant curing time on stabilised samples, a new experimental procedure was set up (Tedesco, 2007). Each point of the SWRC, corresponding to a fixed value of matric suction, was determined by means of three stabilised samples cured for 7 or 28 days. At the end of each step, the average degree of saturation of the three samples constituted the point of the SWRC at constant curing time. The samples were then removed and substituted by new stabilised samples cured for the same time, in order to perform the subsequent step. The final results formed the water retention curve of stabilised samples at constant curing time. In Table 1 the pressure plate test on both natural and stabilised samples are summarised.
3
RESULTS
The main physical properties of natural samples were initially determined (PI = 9.0%, LL = 23.0%, γs = 26.9 kN/m3 ). The same tests were then repeated on lime stabilised samples, taking into account an eventual time dependency. In Table 2 the Atterberg limits and the specific weights of the stabilised samples at different curing times have been reported. It is noteworthy that for every value of curing time the plastic limit of lime stabilised samples was not determinable. In Figure 1 the grain size distributions of natural and stabilised specimens are reported. The latter were determined as a function of curing time. Stabilised samples are characterised by a sensible decrease in fine grains, which seems to remain constant with curing time (Tedesco, 2007). In Figure 2 the compaction curve of natural and stabilised (for curing time t = 0) samples are plotted. The addition of lime induces a shifting of the curve, with an increase in the optimum water content and a decrease in the maximum dry density. Figures 3–6 show the results of pressure plate tests on natural and lime stabilised samples at constant curing time and at variable curing time. The SWRCs were plotted in terms of ratio between the actual average degree of saturation and the initial average degree of saturation. The experimental points were interpreted by fitting the available data with the Van Genuchten (1980) equation:
S=
278
1 [1 + (aψ)b ]c
(1)
Table 2. Atterberg limits and specific weights of the stabilised samples. Liquid limit (%)
Specific weight (kN/m3 )
0 7 28 60
23 25 29 25
2.66 2.69 2.69 2.67
95 90 85
S/S 0 [%]
Curing time (days)
100
80 ND
75 70
NO
65
NW
60 55 50 1
10
100
1000
100
1000
u a-uw [kPa]
100
Figure 3.
90 80 70 P [%]
SWRCs of natural samples.
natural
60 50
100
3% lime -t=7
95
3% lime -t=28
90
3% lime -t=60
85
S/S 0 [%]
40
3% lime -t=0
30 20 10
80 CCTD07
75 70
CCTO07
65
0 0,0001
0,001
0,01
0,1
1
10
CCTW07
60 55
D [mm]
50
Figure 1. samples.
Grain size distributions of natural and stabilised
1
10 ua-uw [kPa]
Figure 4. SWRCs of lime-treated samples at constant curing time t = 7 days. 1,90 natural 3% lime
1,85
100 95 90
1,75
85
1,70
S/S 0 [%]
g d [g/cm3]
1,80
1,65 1,60
80 CCTD28
75
CCTO28
70 65
1,55
CCTW28
60
1,50 8
10
12
14
16 w [%]
18
20
55
22
50 1
10
100
1000
ua-uw [kPa]
Figure 2. Standard proctor compaction curves of natural and stabilised samples.
Figure 5. SWRCs of lime-treated samples at constant curing time t = 28 days.
where S is the actual degree of saturation, ψ the matric suction, and a, b and c best-fitting parameters, respectively linked to the air-entry value, to the slope of the curve at the inflexion point and to the residual degree of saturation. This equation was modified in order to plot the results in terms of ratio between the actual degree
of saturation and the initial degree of saturation S0 of the samples:
279
1 S = √
C B·C S0 S0 + (Aψ)B
(2)
100 95 90
S/S 0 [%]
85 80 STD
75
STO
70 65
STW
60 55 50 1
10
100
1000
ua-uw [kPa]
Figure 6. time.
SWRCs of lime-treated samples at variable curing
Table 3. Best-fitting parameters of the modified Van Genuchten (1980) equation. Test
A
B
C
aev (kPa)
nd no nw
0.041 0.012 0.009
0.855 1.000 1.373
0.184 0.181 0.158
15 52 91
CCTD07(∗) CCTO07(∗) CCTW07(∗)
0.077 0.016 0.008
0.676 0.727 0.586
0.180 0.200 0.198
4 26 35
CCTD28(∗) CCTO28(∗) CCTW28(∗) STD STO STW
0.056 0.009 0.007 0.040 0.006 0.006
0.453 0.800 0.918 0.551 0.464 0.470
0.200 0.193 0.200 0.109 0.155 0.142
4 14 16 2 9 8
capacity of stabilised samples on the initial water content is relevant for short curing times, while for long curing times this dependency tends to be negligible with respect to the effects of curing time. In order to highlight this point, in Figures 7–9 the water retention curves of stabilised samples are compared with the natural ones at fixed initial water content and as a function of curing time. It can be observed that, for each initial water content, in the short term (t = 7 days) a slight decrease of the retention takes place for suction values lower than 100 kPa, with a reduction in the air entry values, while no significant changes take place for suctions higher than 100 kPa. As the curing time increases (t ≥ 28 days), the retention is higher in the upper suction range (100–1000 kPa), as detected for all the stabilised samples at each initial water content. The highest retention pertains to samples cured for long time intervals. For those samples, the air entry values are considerably reduced.
100
S/S 0 [%]
90 80 ND CCTD07 CCTD28 STD
70 60 50 1
Air-entry values were calculated using the average S0 .
Figure 7.
with A, B and C best fitting parameters. The A parameter can be related to air-entry value (aev) of the samples through the expression: aev =
1 B·C · S0 A
10
100
1000
ua-uw [kPa]
The best fitting parameters are reported in Table 3. From the experimental results the relevant influence of the curing time on the water retention properties of lime stabilised soils can be observed. Increasing the curing time of stabilised samples, water retention increases. The larger increment of water retention pertains to dry of optimum stabilised samples, but optimum and wet of optimum stabilised samples show the final higher water retention, as reported in Figure 6 for SWRCs at variable curing time. It can be stated, as observed for natural compacted samples (Vanapalli et al., 1999), that the dependency of the water retention
SWRCs of dry of optimum samples.
100
(3)
90
S/S 0 [%]
(∗)
80 NO CCTO07 CCTO28 STO
70 60 50 1
10
100 ua-uw [kPa]
Figure 8.
280
SWRCs of optimum samples.
1000
100
0,025
90
0,020 dV/d(logD) [ml/g]
S/S 0 [%]
Nat
80 NW CCTW07 CCTW28 STW
70 60
3%_28
0,015
3%_77
0,010 0,005
50
0,000 1
10
100
1000
0,01
ua-u w [kPa]
Figure 9.
4
3%_7
SWRCs of wet of optimum samples.
0,1
1 D [ m]
10
Figure 10. MIP of optimum samples: incremental distribution of intruded mercury volume.
DISCUSSION 0,25 Nat 0,20 V [ml/g]
The observed hydraulic behaviour of stabilised samples can be explained with reference to the reactions induced by lime. As observed before, those reactions are strongly dependent on curing time and largely modify the microstructure of the natural soil. Russo et al. (2007) carried out mercury intrusion porosimetry tests on natural and lime stabilised samples of the same soil; the stabilised samples were cured for increasing time intervals. Figure 10 and Figure 11 show the results of MIP tests on optimum water content stabilised samples in terms of incremental and cumulative volume of mercury intruded. Immediately after the addition of lime (t = 7 days) a relevant modification of porosity for lime stabilised samples takes place, with the formation of pore of relatively large diameter (between 4 and 40 microns). A subsequent reduction of this effect occurs increasing the curing time of the stabilised samples (t = 28 days), probably due to pozzolanic reactions which induce the development of bonds between the aggregates. A reduction in the frequency of pores with diameters between 0.2 μm and 2 μm can be also detected in the long term. Finally, pores ranging from 0.01 μm to 0.2 μm systematically increase their frequency as the curing time increases. In terms of water retention properties, the increase in frequency of pores of relatively large radius (short time effects mainly induced by cation exchange), together with the increase in the presence of sand sized aggregates in the grain size distribution, reduces both the air entry value and the retention capacity of the stabilised samples for values of suction lower than 100 kPa. The reduction persists for long curing times. For suction values greater than 100 kPa the water retention increases as the curing time becomes higher. A possible interpretation of this result, consistent with the larger amount of small radii pores observed as curing time increases, is that the cementation bonds between aggregates enhance the frequency
3%_7 3%_28
0,15
3%_77 0,10 0,05 0,00 0,01
0,1
1 D [ m]
10
Figure 11. MIP of optimum samples: cumulative distribution of intruded mercury volume.
of ink-bottle pores. In pores of this type, characterised by an entrance radius smaller than the dimension of the inner part of the pore, intrusion cannot occur until sufficient pressure has been attained to force mercury into the narrow neck, whereupon the entire pore will be filled. As ink-bottle pores upon depressurization entrap mercury in the wide inner portion of the pore, upon drying ink-bottle pores contribute relevantly to retain water into the stabilised soil. The smaller the narrow openings of the ink bottle pores, the higher the suction values needed to desaturate the soil.
5
CONCLUDING REMARKS
In the paper some results of an experimental study on the time dependency of lime stabilisation on the soilwater retention capacity of a compacted silty soil are presented. The comparison between water retention curves of natural and lime stabilised samples points out the general increase of the water retention capacity of the
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soil induced by the addition of lime. The role of both initial water content and curing time has been highlighted. From the results it has been found that stabilised samples compacted at optimum and wet initial water content show higher water retention. The microstructure modifications taking place as a function of curing time, assessed by means of MIP tests, allow an insight into the reaction mechanisms induced by lime and an explanation of the observed increase of water retention. The relevance of the MIP technique in this experimental investigations has been underlined, both for the short test duration and for the analogy between the results in terms of mercury intrusion and water outflow. Further research is required in order to assess the role of microstructure and its evolution with curing time on the retention properties of stabilised samples. Intrusion-extrusion cycles, performed through both volumetric pressure plate extractor and mercury intrusion porosimeter, could highlight the role and amount of ink bottle pores on the water retention of stabilised soils. ACKNOWLEDGEMENTS The Authors are very grateful to Prof. Giuseppe Mascolo for the support during the experimental work. Mercury intrusion porosimetry tests were developed at the University of Cassino under the careful supervision of Sebastiana Dal Vecchio. REFERENCES ASTM 1991. Standard Test Method for Laboratory Compaction Characteristics of Soil Using Standard Effort (12, 400 ft-lbf /ft3 (600 kN-m/m3 )), ASTM D698-91ε1 . In Annual Book of ASTM Standards 04.08: 77–84. West Conshohocken: ASTM International. Alonso, E.E., Gens, A. & Hight, D.W. 1987. Special problem soils-General report. In E.T. Hanran, T.L.L. Orr & T.F. Widdis (eds.), Ground effects in geotechnical engineering (3): 1087–1146; Proc. IX ECSMFE, Dublin, 1987. Rotterdam: Balkema.
Croce, P. & Russo, G. 2002. Reimpiego dei terreni di scavo mediante stabilizzazione a calce. In Proc. XXI AGI— Convegno Nazionale di Geotecnica: 211–216. L’Aquila: Patron Editore. Croce, P. & Russo, G. 2003. Soil-water characteristic curves of lime-stabilised soils. In Pieter A. Vermeer, Helmut F. Schweiger, Minna Karstunen & Marcin Cudny (eds.), Geotechnics of Soft Soils—Theory and Practice: 575–580; Proc. Int. Workshop, Noordwijkerhout (NL), 17–19 September 2003. Essen: VGE. Eades, J.L. & Grim, R. 1960. Reactions of Hydrated Lime with Pure Clay Minerals in Soil Stabilization. Highway Research Board Bulletin 262: 51–63. Glenn, G.R. & Handy, R.L. 1963. Lime-clay mineral reaction products. Highway Research Record 29: 70–82. Hilt, G.H. & Davidson, D.T. 1960. Lime fixation in clayey soils. Highway Research Board Bulletin 262: 20–32. Rogers, C.D.F. & Glendinning, S. 1996. Modification of Clay Soils using Lime. In Rogers, C.D.F., Glendinning, S. & Dixon, N. (eds.) Lime Stabilisation: 99–126. London: Thomas Telford. Russo, G. 2005. Water retention curves of lime stabilised soils. In A. Tarantino, E. Romero & Y.J. Cui (eds.), Advanced Experimental Unsaturated Soil Mechanics: 391–396; Proc. of the Int. Workshop on Advanced Experimental Unsaturated Soil Mechanics, Experus 2005, Trento (I), 27–29 June 2005. Rotterdam: Balkema. Russo, G., Dal Vecchio, S. & Mascolo, G. 2007. Microstructure of a lime stabilised compacted silt. In Tom Schanz (ed.), Experimental Unsaturated Soil Mechanics: 49–56; Proc. of the 2nd Int. Conf. On the Mechanics of Unsaturated Soils, USS2007, Weimar (D), 7–9 March 2007. Heidelberg: Springer. Seed, H.B. & Chan, C.K. 1959. Structure and strength characteristics of compacted clays. JSMFD 85 (SM5): 87–128. Tedesco, D.V. 2007. Hydro-mechanical behaviour of limestabilised soils. PhD Thesis at the University of Cassino. Cassino, Italy. Van Genuchten, M. Th. 1980. A closed form equation predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44: 892–898. Vanapalli, S.K., Fredlund, D.G. & Pufhal, D.E. 1999. The influence of soil structure and stress history on the soilwater characteristics of a compacted till. Geotechnique 49 (2): 143–159.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Retention and compressibility properties of a partially saturated mine chalk H.D. Nguyen Ecole des Ponts (Université Paris-Est, Navier Inst. – CERMES), Paris, France INERIS, Verneuil-en-Halatte, France
V. De Gennaro & P. Delage Ecole des Ponts (Université Paris-Est, Navier Inst. – CERMES), Paris, France
C. Sorgi INERIS, Verneuil-en-Halatte, France (now RATP, Paris, France)
ABSTRACT: In relation with the assessment of the stability of underground chalk mines, a preliminary investigation of the behaviour of chalk samples retrieved from the pillars of the abandoned Estreux shallow mine (Northern France) has been conducted. Due to changes in hygrometry and water table (ambient relative humidity comprised between 80% and 100%), pillars are submitted to cyclic variations in degree of saturation. The potential impact of the changes in water content on the mechanical behaviour of the chalk has been assessed based on the methods and concepts of the mechanics of unsaturated soils. Water retention properties and volume change behaviour of the unsaturated chalk were investigated. Suction hardening was clearly identified, resulting in increasing yield stresses with suction, in agreement with the Loading Collapse (LC) yield curve of the Barcelona Basic Model (Alonso et al. 1990). Collapse compression under wetting at constant applied vertical load was also observed. As already discussed in the case of oil-reservoir chalks (De Gennaro et al. 2004), it is confirmed that the methods and concepts of the mechanics of unsaturated soils are relevant to better analyse the water weakening effects in chalks.
1
INTRODUCTION
Research into the stability of abandoned subsurface cavities in chalk is being carried out by the French Institute INERIS (Institut National de l’Environnement Industriel et des Risques) with a special attention devoted to the abandoned underground chalk shallow mine of Estreux (Northern France). The detailed monitoring of the periodic changes in relative humidity (hr ) in the mine showed that values as low as 80% could be reached, giving rise to possible desaturation of the pillars. In this regard, a study of the behaviour of the Estreux chalk under unsaturated states was found necessary. The mechanical behaviour of chalk is known to be significantly sensitive to changes in water content, an effect described as the water weakening effect. Water weakening has been particularly considered in the study of the reservoir chalks of the North Sea (Newman 1983, Andersen 1995; Schroeder et al. 1998, Gutierrez et al. 2000, De Gennaro et al. 2003 and 2004). Pore collapse under water flooding is a particular illustration of water weakening. Various investigations have been carried out on the pore collapse phenomena (Bonvallet 1979, Raffoux & Ervel
1980, Bell et al. 1999, Talesnick et al. 2001, Sorgi 2004, Priol 2005). Reservoir chalks contain two immiscible pore fluids (oil and water). They are comparable to unsaturated soils that contain air and water. In this regard, Delage et al. (1996) showed that the mechanics of unsaturated soil could be fruitfully used to investigate the behaviour of fluids-filled chalks. In underground quarries, low relative humidity (hr = 80%) might possibly dry the chalk pillars at least near the pillar surface, with an introduction of air as the non wetting pore fluid. In this paper, the methods and concepts of the mechanics of unsaturated soils are applied to some specimen of Estreux Chalk. Firstly, the water retention properties are investigated. Secondly, volume changes properties are considered under suction controlled conditions in the oedometer. 2
MATERIAL AND EXPERIMENTAL METHODS
The study was carried out on chalk specimens extracted from the Estreux abandoned underground mine in Northern France, 10 km East of the city
283
of Valenciennes in the vicinity of the Valenciennes—Bruxelles A14 highway. The Estreux chalk formation belongs to the late Cretaceous geological period, which dated from 89 to 94 M years ago. A square pillar (1.4 × 1.4 m with a height of 1.8 m) has been continuously monitored since 2003 in relation within the research programme conducted by INERIS about ‘‘Ageing phenomena in geomaterials’’ (Sorgi 2004), hr measurements showed that the relative humidity inside the mine varied between 80 and 100% with an almost constant temperature of 11◦ C. Cubic blocks of chalk (30 cm each side) were manually retrieved at a 20 meters depth. Table 1 presents the index properties of Estreux chalk. By using a helium picnometer, a specific gravity Gs of 2.74 was obtained. As compared to the specific gravity of pure calcite (Gs = 2.71), this higher value is related to the presence of a fraction of glauconite (with Gs = 2.99). Glauconite is often observed in Northern French chalks (Masson, 1973; Bonvallet, 1979; Hazebrouck & Duthoit, 1979). The glauconite fraction is also linked to the relatively high values of the specific surface (Ss = 13 m2 /g measured using methylene blue absorption, as compared to 9 m2 /g for a pure chalk like for instance Lixhe chalk, Belgium). The average porosity n close to 37% is in good agreement with literature values (Masson, 1973; Bonvallet, 1979). Typical Unconfined Compression Strength (UCS) values for Estreux chalk are UCSsat ∼ = 5MPa when saturated and UCSdry ∼ = 11MPa if dried (typically UCSdry /UCSsat ∼ = 2). The high value of degree of saturation measured in extracted specimens (Srw = 97%) indicates that chalk was probably saturated in the mine at the time extraction was carried out, with some possible further loss of water during testing. The water retention properties of Estreux chalk were determined by using cylindrical samples of 20 mm in diameter and from 20 mm to 25 mm in height. In relation with the relative humidity observed in the mine (hr between 80 to 100%), the suction values applied were taken between 0 and 24.9 MPa by using 3 methods of controlling suction: the osmotic method for low suctions (from 0 to 1.5 MPa) (Williams & Shaykewich 1969, Delage et al. 1998, Marcial 2003), the vapour equilibrium method at
Table 1.
higher suctions (from 2 to 24.9 MPa) (Delage et al. 1998, Marcial 2003) and the filter paper method with contact for sample in their initial state (Fawcett & Collis-George 1967, Chandler & Gutierrez 1986, Houston et al. 1994, Bulut et al. 2001). In the osmotic method, the sample is placed in a tube shaped cellulotic semi-permeable membrane (Spectrapor ® ) and then immersed in an aqueous solution of large sized molecules of Poly Ethylene Glycol (PEG 6000 or 20000) (Figure 1). The imposed suction was derived from the solution concentration by using the calibration data of Williams & Shaykewich (1969) and the correction proposed by Dineen and Burland (1995). Five suctions level (0 MPa using pure water instead of a PEG solution, 0.5, 1, 1.2 and 1.5 MPa) were imposed with the osmotic method. The vapour equilibrium method was carried out by using the device presented in Figure 2, in which desiccators are placed in a temperature controlled bath. As can be seen in the Figure, a circulation of air with a controlled relative humidity is ensured by circulating air in a bottle containing a saturated saline solution. The air is subsequently circulated in the desiccator that contains the sample. Experience showed that circulating air significantly reduced the period of time necessarily to reach equilibrium. Two saturated saline solutions: (NH4 )2 SO4 (hr = 83.5%, s = 24.9 MPa) and K2 SO4 (hr = 97%, s = 4.2 MPa) were used.
Cellulotic semipermeable PEG
Thermostat
Sample
Magnetic stirrer
Figure 1. Determination of the water retention curve by using the osmotic method.
Index data of Estreux chalk.
Properties Density of particles, ρs (Mg/m3 ) Degree of saturation, Srw (%) Dry density, ρd (Mg/m3 ) Porosity, n(%) Natural water content, w(%) Specific surface, Ss (m2 /g)
2.74 97 1.73 37 20.7 14
Pump
Saturated saline solution
Thermostat
Figure 2. Determination of the water retention curve by using the vapour equilibrium technique.
284
Two PEG solutions at controlled concentrations corresponding to 2.5 MPa (hr = 98.2%) and 2 MPa (hr = 98.4%) were also used in the same fashion to impose lower suctions. Two filter papers measurements were carried out to determine the initial suction of the intact sample. In order to avoid any contact with chalk, both papers were placed between two protection papers and then positioned between two halves of chalk samples. The whole system was then isolated from the ambient relative humidity and stored in a temperature controlled room (20◦ C ± 0.1◦ C) for at least 15 days before weighing the filter papers (accuracy 1 × 10−5 g). Finally, a high stress double lever arm oedometer equipped with a suction control system was used (e.g. Marcial et al. 2002) to investigate the compressibility of partially saturated Estreux chalk samples. The control of the suction was carried out either by using the osmotic method (suctions smaller than 1.5 MPa) (see Kassiff & Benshalom 1971, Delage et al. 1992, Dineen and Burland 1995, De Gennaro et al. 2003, Priol 2005). The same cell was also used at higher suctions with the vapour equilibrium method (Esteban 1990, Oteo-Mazo et al. 1995, Oldecop & Alonso 2001, Marcial 2003) for suctions higher than 4.2 MPa. In this case, air with controlled hr was circulated in the oedometer cell through the bottom of the sample (see Figure 3). Samples of 38 mm in diameter and 19 mm ±2 mm in height were reshaped on a lathe. A dry sample was obtained after a period of 48 hours in an oven at 60◦ C following the recommendations of the International Society of Rock Mechanics. Since the mechanical response of chalk is strain rate-dependent (e.g. De Gennaro et al. 2003, Priol et al. 2007), it was decided for multiple loading stages oedometer tests to
consider a period of sustained loading of 48 hours in the pseudo-elastic regime and 7 days in the plastic regime, resulting in total tests durations from 45 to 60 days. Deformation regimes (elastic and plastic) were defined based on results from constant rate of strain oedometer tests (Priol et al. 2007), that allowed to identify the expected yield stress. Isotach behaviour (i.e. only dependent on the strain rate) was adopted to define the compressibility curves obtained by means of oedometer tests. Following this methodology for each loading stage the corresponding vertical strain was measured when the axial strain rate was lower than 10−10 sec−1 . Based on the experimental results from the determination of the water retention properties, four oedometer compression tests were carried out as follows: two tests in dry conditions (T1 & T2), one test at controlled suction (T3: s = 4.2 MPa with the vapour equilibrium method and K2 SO4 salt) and one test at saturated conditions (T4).
3
RESULTS AND DISCUSSION
3.1 Water retention properties The water retention curve of Estreux chalk is shown in Figure 4 in terms of changes in degree of saturation (Srw ) with respect to the logarithm of suction (log s). Beside the points obtained at various controlled suctions along the drying and wetting paths, the initial suction obtained with the filter paper method is also represented. A suction value of 40 kPa with a degree of saturation of 97% indicated that the sample was probably saturated when excavated.
100 Hr = 83.5% ( s = 24.9 MPa)
10
Hr = 97% ( s = 4.2 MPa)
v
Hr = 98.2% ( s = 2.5 MPa)
Sample 1 SUCTION, s :MPa
Sieve
Hr = 99.8% ( s = 1.5 MPa)
0.1
Dry path
0.01
Wetting path Initial state
0.001
Pump
Figure 3.
Saturated saline solution
0
Thermostat
Scheme of the vapour equilibrium oedometer.
Figure 4.
285
0.2
0.4 0.6 DEGREE OF SATURATION, S rw
0.8
Water retention curve of Estreux chalk.
1
SUCTION, s
T2
T3
∼ – Test T1 (ei = 0.575): dry compression (s = 30 MPa) up to 39.7 MPa, unload down to 0.44 MPa, soaking under 0.44 MPa and subsequent loading up to 39.7 MPa. – Test T2 (ei = 0.61): dry compression (s ∼ = 30 MPa) up to 22.41 MPa, unload down to 10.19 MPa, reload to 29.28 MPa and soaking. – Test T3 (ei = 0.602): suction controlled compression (s = 4.2 MPa) up to 39.7 MPa, unload down to 8.82 MPa and reload to 39.7 MPa. – Test T4: (ei = 0.581): saturated compression up to 20.38 MPa, stress release at 0.26 MPa and reload at 40.76 MPa.
s = 4.2 MPa
saturated, s = 0 MPa T4
100
1000 10000 VERTICAL STRESS, v : kPa
Figure 5.
100000
Loading paths.
0.65
0.6
WATER INJECTION
0.55
3.2 Oedometer tests The two independent stress variables commonly used in the investigation of the mechanical behaviour of unsaturated soils are the suction, s = ua − uw (where ua and uw are the air and water pressure respectively) and the mean net stress pnet = p − ua (where p is the total mean stress). The loading paths followed in a vertical stress suction (σv : s) are presented in Figure 5. The compressibility curves in [log σv : e] diagrams are presented in Figure 6. The testing program comprises three compression tests carried out as follows:
Dry, s = 30 MPa
T1
VOID RATIO, e
The slight differences observed between the drying and wetting paths denote a moderate hysteresis effect, also observed in partially air-water saturated Lixhe chalk by Priol (2005). A possible effect of the glauconite fraction in reducing the hysteresis effect is suspected, although a clear explanation of the slight hysteresis is not straightforward. The drying curve shows that the air entry value of Estreux chalk can be estimated at approximately 1.5 MPa. Following desaturation, the degree of saturation exhibits a dramatic reduction with a value as low as 30% at 2.5 MPa. At the highest suction (s = 24.9 MPa, hr = 83.5%) the degree of saturation is as low as 2–5%, showing that chalk is nearly completely desaturated. Based on the water retention curve, the suction of a dry sample can be estimated at 30 MPa. The shape of the water retention curve of Estreux chalk and the sudden decrease in saturation above 1.5 MPa shows that the changing values of the ambient relative humidity in the mine (between 80% and 100%) can definitely lead to significantly unsaturated states, at least at the surface of the pillar directly in contact with the ambient relative humidity. It is then suspected that the mechanical properties of the chalk in unsaturated states have to be considered when addressing the long term stability of the pillars. As a first step, the compressibility properties of the chalk under various controlled suctions are now presented.
WATER INJECTION 0.5 SWELLING 0.45 COLLAPSE
T1 (dry) T2 (dry) T3 (s = 4.2 MPa) T4 (saturated)
0.4
0.35 100
Figure 6. ters.
1000 VERTICAL STRESS,
10000 v : kPa
100000
Compressibility curves obtained with oedome-
The compressibility curves of Figure 6 show some responses that are compatible with that of unsaturated soils:
286
– Increase in yield stress with increased suction. – Increase in compressibility with decreased suction. – Slight suction dependency of the pseudo-elastic compressibility module. – Slight swelling due to suction release in the elastic zone. – Significant collapse when soaking under high stress when the sample is located on the LC curve.
Table 2.
Compressibility data taken from oedometer tests.
State
Elastic
T1 T2
40
Stiffness Plastic
Yield stress (MPa)
LOADING
LC i
LC 1 LC 3
0.0022 0.0055
0.1082 0.094
16 13.5
0.0095 0.0039
0.1137 0.135
11.4 7.5
30 SUCTION, s :MPa
Dry (T1) Dry (T2) Suction controlled (T3) Saturated (T4)
Water injection 20 Collapse
Swelling
10
Interestingly, the position of the collapsed sample is close to the saturated compression sections of tests T2 and T4.
LC 2 LOADING
0
The corresponding numerical values are given in Table 2. These trends illustrate the sensitivity of the mechanical response of the Estreux chalk to change in suction. They are in good agreement with the water weakening effects described by Matthews and Clayton (1993) and with earlier observations on reservoir chalks (with water and oil as pore fluids) by De Gennaro et al. (2004) and Priol (2005). Water sensitivity is denoted by the swelling observed in test T1 (soaking under 441 kPa) and by the collapse observed in T2 when soaking under 29.28 MPa. The increase in compressibility and decrease in yield stress with increased degree of saturation (decreased suction) are two other manifestations of the water weakening effect. 3.3
BBM modelling
The results of Figure 6 are now qualitatively interpreted in the framework of the Barcelona Basic Model (Alonso et al., 1990). Figure 7 shows the Loading Collapse (LC) curve that can be derived from the experimental data of Figure 6. With suction at dry state equal to 30 MPa, the LC curves exhibit fairly regular and satisfactory shapes. A tentative identification of the initial LC curve can be obtained assuming the following constitutive parameters for the BBM: λ(0) = 0.12, pc = 0.002 MPa, p∗o = 8 MPa. Owing to the reduced effect of suction on the virgin compressibility of the material, λ(s) values were found assuming β = 0.5 and r = 0.94. The loading path of test T1 crosses the initial dry LCi curve at (σvo − ua ) = 16 MPa, displacing the LC curve up to LC1 at the maximum 39.7 MPa value (hardening process). After unloading down to 0.44 MPa, water soaking was performed under 0.44 MPa resulting in reducing suction from 30 MPa down to 0 MPa. The swelling under stress release observed (increase in void ratio from 0.466 to 0.476) is also in good agreement with
0
Figure 7.
10
20 VERTICAL STRESS,
30 v: MPa
40
Loading Collapse yield in the test T1 and T2.
the BBM model, the suction release occurring inside the elastic zone delimited by the LC curve. The subsequent compression at zero suction carried out during the T1 test evidenced a yield at 20 MPa that is finally moved towards the LC2 position at 39.7 MPa. Further validation of the BBM is provided by the results of test T2 that defines a yield stress at dry state (σvo − ua = 13.5 MPa). This slightly smaller value is related to the higher porosity of the sample (37.9% instead of 36.5%) as explained by Matthews & Clayton (1993). At s = 30 MPa, the yield curve is moved during dry compression up to the position LC3 (29.3 MPa). The soaking induces here significant collapse (decrease in void ratio from 0.500 to 0.389) that further moves the LC curve to the right, with an intersection with the x axis at 29.3 MPa.
287
4
CONCLUSIONS
The water retention properties and compression behaviour of unsaturated samples of chalk from an abandoned underground mine were investigated in relation with the long term stability of abandoned underground quarries. A slight hysteresis was observed on the water retention curves, together with a significant desaturation that occurred along the drying path just above the airentry value of the chalk (1.5 MPa). This confirmed that the desaturation of the pillars had to be considered when assessing the long term stability of the abandoned mine.
Four suction controlled oedometer tests showed that the volume change behaviour of the unsaturated chalk was fairly comparable to that of unsaturated soils. The Barcelona Basic Model could be successfully used to account to some extent for water weakening effect in partially saturated chalk, both in terms of swelling when releasing suction at low stress and collapse compression during soaking under high stress. It should be mentioned however that the behaviour of Estreux chalk during oedometric loading doesn’t reflect completely the in situ conditions. Further knowledge on the effect of changes in degree of saturation on the collapse behaviour of the material at low stress levels is needed in order to have an insight into the water weakening mechanisms in chalk.
ACKNOWLEDGEMENT The results on Estreux chalk have been obtained during the French National Project BCRD coordinated by INERIS. The collaboration of Dr G. Priol is also acknowledged.
REFERENCES Alonso, E.E., Gens, A. & Josa, A., 1990. A constitutive model for partially saturated soils. Géotechniques 40, No. 3, 405–430. Andersen, M.A., 1995. Petroleum research in North Sea chalk. Joint chalk research, phase IV, 47–153. Bell, F.G., Culshaw, M.G. & Cripps, J.C., 1999. A review of selected engineering geological characteristics of English chalk. Engineering Geology, 54, 237–269. Bonvallet, J., 1979. Une classification géotechnique des craies du nord utilisée pour l’étude de stabilité des carrières souterraines. Revue Française de Géotechnique, 8: 5–14. Bulut, R., Lytton, R.L. & Wray, W.K., 2001. Soil suction measurements by filter paper. Proc. Of Geo-Institute Shallow Foundation and Soil Properties Committee Sessions, ASCE Conference, Geotechnical Special Publication Number 115, 243–261. Chandler, R.J. & Gutierrez, C.I., 1986. The filter papar method of suction measurement. Géotechnique 36, 265–268. De Gennaro, V., Delage, P., Cui, Y.J., Schroeder, Ch. & Collin, F. 2003. Time-dependent behaviour of oil reservoir chalk: a multiphase approach. Soils and Foundations, 43 (4), 131–148. De Gennaro, V., Delage, P., Priol, G., Collin, F. & Cui, Y.J., 2004. On the collapse behaviour of oil reservoir chalk. Géotechnique, 54 (6), 415–420. Delage, P., Suraj De Silva, G.P.R. & Vicol, T. 1992. Suction controlled testing of non saturated soils with an osmotic consolidometer. 7th Int. Conf. Expansive Soils, Dallas, 206–211.
Delage, P., Schroeder, C., & Cui, Y.J. 1996. Subsidence and capillary effects in chalks. EUROCK ’96, Prediction and performance on rock mechanics and rock engineering 2, 1291–1298, Turin, Italy. Delage, P., Howat, M.D. & Cui, Y.J., 1998. The relationship between suction and swelling properties in a heavily compacted unsaturated clay. Engineering Geology, 50, 31–48. Dineen, K. & Burland, J.B., 1995. A new approach to osmotically controlled oedometer testing. Proc. 1 st Int. Conf. on Unsaturated Soils UNSAT’95, Paris, 459–465. Esteban Moratilla, F., 1990. Caracterizacion experimental de la expensividad de una roca evaporitica. Identificacion de los mecanismos de hinchamiento. PhD thesis, Universidad de Cantabria, Santader, 352 p. Fawcett, R.G. & Collis-George, N., 1967. A filter paper method of determining the moisture characteristics of soil. Austr. J. of Exp. Agr. and Animal Husb. 7, 162–167. Gutierrez, M., Øino, L.E. & Hoeg, K., 2000. The effect of fluid content on the mechanical behaviour of the fractures in chalk. Rock Mechanics and Rocks Engineering, 33 (2), 93–117. Hazebrouck, R. & Duthoit, B., 1979. Particularité du comportement mécanique des craies: rôle de l’eau—rupture sous contrainte hydrostatique. Revue Française de Géotechnique, 8, 45–50. Houston, S.L., Houston, W.N. & Wagner, A.M., 1994. Laboratory filter paper suction measurements. Geotechnical Testing Journal, 17 (2), 185–194. Kassiff, G. & Ben Shalom, A., 1971. Experimental relationship between swell pressure and suction. Géotechnique, 21, 245–255. Marcial, D., Delage, P. & Cui, Y.J., 2002. On the high stress compression of bentonites. Can. Geotech. J. 39, 812–820. Marcial, D., 2003. Comportement hydromécanique et microstructural des matériaux de barrières ouvragées. PhD Thesis, Ecole Nationale des Ponts et Chaussées, Paris: 316 p. Masson, M., 1973. Pétrophysique de la craie. In La craie, Bull. Labo. Ponts et Chaussées, Special V, 23–48. Matthews, M.C. & Clayton, C.R.I, 1993. Influence of intact porosity on the engineering properties of a weak rock. Proc. Geotechnical engineering of hard soils—soft rocks, vol. 1, Anagnostopoulos et al. (eds), Balkema, 693–702. Newman, G.H., 1983. The effect of water chemistry on the laboratory compression and permeability characteristics of some North Sea chalks. J. of Petroleum Eng., 976–980. Oldecop, L.A. & Alonso, E.E., 2001. A model for rockfill compressibility. Géotechnique 51, No. 2, 127–139. Oteo Mazo, C., Saez Aunon, J. & Esteban, F., 1995. Laboratory tests and equipment with suction control. Proc. 1st Int. Conf. on Unsaturated Soils UNSAT’95, 3, Paris, Balkema, Rotterdam, 1509–1515. Priol, G., De Gennaro, V., Delage, P. & Cui, Y.J. 2004. On the suction and the time dependent behaviour of reservoir chalks of North sea oilfields. Proc. 2nd Int. Workshop on Unsaturated Soils, Capri (Italy), 43–54. Priol, G., 2005. Comportement mécanique différé et mouillabilité d’une craie pétrolifère. PhD Thesis, Ecole Nationale des Ponts et Chaussées, Paris, 217 p. Priol, G., De Gennaro, V., Delage, P., & Servant T., 2007. Experimental investigation on the time dependent behaviour of a multiphase chalk. Springer Proceedings
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Physics 112, Experimental Unsaturated Soil Mechanics, T. Schanz (ed.), 161–167. Raffoux, J.F. & Ervel, C., 1980. Stabilité générale de la carrière souterraine d’Estreux. Rapport CEECHAR, 8 p. Schroeder, Ch., Bois, A.P., Maury, V. & Halle, G., 1998. Water/chalk (or collapsible soil) interaction: Part II. Results of tests performed in laboratory on Lixhe chalk to calibrate water/chalk models. SPE/ISRM (SPE 47587) Eurock’98, Trondheim. Sorgi, C., 2004. Contribution méthodologique et expérimentale à l’étude de la diminution de la résistance des massifs
rocheux par vieillissement. BCRD Final Report (conv. 2001–01111), INERIS-DRS (in French), 132 p. Talesnick, M.L., Hatzor, Y.H. & Tsesarsky, M., 2001. The elastic deformability and strength of a high porosity, anisotropic chalk. Int. J. of Rock Mech. & Min. Sci., 38, 543–555. Williams, J. & Shaykewich, C.F., 1969. An evaluation of polyethylene glycol PEG 6000 and PEG 20000 in the osmotic control of soil water matric potential. Can. Geotech. J., 102 (6), 394–398.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Effect of grain size distribution on water retention behaviour of well graded coarse material C. Hoffmann & A. Tarantino Dipartimento di Ingegneria Meccanica e Strutturale, Università degli Studi di Trento, Italy
ABSTRACT: The paper presents an experimental investigation on water retention behaviour of well graded coarse-grained soils. Two ‘reduced’ grain size distributions were tested to investigate how the removal of the larger grain size fraction needed to reduce field samples to appropriate grain size for laboratory testing affects water retention behaviour. As expected, the removal of larger particles significantly modified the water retention characteristics of the soil. An approach to ‘scale’ water retention curves obtained in the laboratory to the soil in the field is then presented. This approach was successfully tested against the soil investigated in this programme.
1
INTRODUCTION
Coarse well graded unsaturated soils often compose earthen constructions (earth dams, road and railway embankments, and flood defence embankments). These soils also compose shallow landslides that evolve into debris-flows. Their water retention behaviour is a key to understanding the effect of changing boundary hydraulic conditions (rainfall, water table, water reservoir level, river level) on shear strength and, hence, on stability. Water retention behaviour of coarse well graded soils is often inferred from index properties (grain size distribution and dry density) in preliminary design and large area projects. These indirect methods are also used when direct laboratory measurements are costly and/or time consuming. A number of methods have been proposed in the literature for the estimation of the water retention curve based on statistical and physico-empirical approaches. However, these methods have essentially been validated on agricultural soils (Vereecken et al. 1989, Arya and Paris 1981). A very limited database is available for coarse well graded materials. Another problem arising when investigating water retention behaviour of coarse-grained materials is the need of reducing field samples to appropriate grain size for laboratory testing. A question that might be asked is how to extrapolate the water retention curves obtained in the laboratory on reduced-size samples to the soil in the field. This paper presents an experimental investigation on the water retention behaviour of a well graded coarse material. Two different ‘reduced’ grain size distributions were considered to investigate how the
removal of the larger grain size fraction affects water retention behaviour. The soil was tested along wetting paths under different void ratios to investigate the main wetting surface in the space suction-void ratio-degree of saturation. The experimental data were then compared with the water retention curves estimated using indirect methods presented in the literature.
2
EXPERIMENTAL EQUIPMENT
The box illustrated in Figure 1, which is equipped with one Trento high-capacity tensiometers (Tarantino &
Tensiometer
O-rings Compacted specimen
Spacer
Figure 1.
291
Schematic layout of suction measurement box.
Tensiometer support
CLAY
Tensiometers Weight
SAND
GRAVEL
d10 (d < 10 mm) d25 (d < 25 mm)
0.8
Fraction finer
75-85 mm
Membrane
SILT
1
Compacted sample
0.6
0.4
0.2
Ø = 252 mm 0 0.0001
0.001
0.01
0.1
1
10
Particle size, d: mm
Figure 2. Schematic layout of the oedometer cell used to measure suction of statically compacted specimens.
Figure 3. ‘Reduced’ grain size distributions investigated in this programme.
Mongiovì 2002), was used to carry out matric suction measurement on dynamically compacted samples. Tensiometers were locked in place to ensure contact with the sample by using caps tightened to the cell upper base (not shown in the figure). O-rings ensured air tightness so that water vapour could reach equilibrium with the soil water. Matric suction measurements on statically compacted samples were carried out in the same oedometer cell used to compact the sample (Figure 2). Two tensiometers were installed through a metal support connected to a flexible membrane used to ensure air tightness. To ensure contact of the tensiometers with the sample, two weights obtained by filling plastic bags with steel spheres were placed over the metal support. 3
MATERIAL AND SPECIMEN PREPARATION
Two ‘reduced’ grain size distributions having maximum particle size of 10 and 25 mm respectively were tested in this experimental programme (Figure 3). These soils will be referred to as d10 and d25 respectively. Air-dried soil was laid in a large plastic basin and sprayed with demineralised water to reach the target water content. The moistened powder was handmixed and then wrapped inside two sealed plastic bags, placed in a plastic container and stored in a high-humidity room for 1 day. The soil d10 was dynamically compacted into a 101.6 mm diameter mould in three layers to 30%, 50%, or 100% of Proctor energy. The sample was trimmed to 117 mm height, extruded and stored for 2 days at least to allow moisture equalisation. A first series of samples were directly put into the suction
Figure 4. ‘As-compacted’ states of statically and dynamically compacted samples. Arrows show the path followed by the samples wetted after compaction.
measurement box for tensiometer measurement (specimens compacted to 100% and 50% Proctor energy in Figure 4). A second series of samples were wetted by spraying demineralised water to reach a target water content checked by weighing. The wetting stage was then followed by a period of 2 days for moisture equalisation. The samples were then put into the suction measurement box for tensiometer measurement (specimens compacted to 30 % Proctor energy in Figure 4). The soil d25 was statically compacted into the 252 mm diameter oedometer cell shown in Figure 2. The moistened powder was placed in the oedometer and compressed by increasing the air pressure in
292
the upper compartment of the cell. A rigid plate (not shown in the figure) was interposed between the flexible membrane and the top surface of the sample to ensure uniform vertical deformation. The sample was compacted in stages to four different vertical stresses: 75, 150, 300, and 600 kPa. The as-compacted states of the statically compacted samples are shown in Figure 4.
Degree of saturation, Sr
1 0.8 0.6 100% Proctor 50% Proctor 30% Proctor(wetted) 75 kPa 150 kPa 300 kPa 600 kPa 75 and 150 kPa
0.4 0.2
(a)
300 and 600 kPa
0
EXPERIMENTAL PROCEDURE
Tensiometers were calibrated in the positive range of water pressure and the calibration curve was then extrapolated to the negative range of water pressure according to Tarantino & Mongiovì (2003). Before testing, the saturation of the tensiometer porous ceramic was checked following the procedure illustrated by Tarantino (2004). After assembling the suction measurement box (Figure 1) or the oedometer cell (Figure 2), the tensiometers were installed and fixed by screws. To improve contact with the sample a paste made by the finer fraction of the soil was applied on the porous stone of the tensiometer. A single suction measurement was performed on each dynamically compacted specimen (d10) . In contrast, multiple suction measurements were performed on each statically compacted specimen (d25). After applying the 75 kPa vertical stress, the loading pad was removed and the tensiometers were installed as shown in Figure 2. Afterwards, the tensiometers were removed, the specimen was compacted to 150 kPa vertical stress, and suction measurement was carried out again. This procedure was repeated for the vertical stresses of 300 and 600 kPa. 5
EXPERIMENTAL RESULTS
The experimental results in terms of degree of saturation are shown Figure 5a. All these data may be assumed to be ‘main’ wetting data. Compaction produces an increase in the degree of saturation by reducing void ratio at constant water content. This mechanism can be referred to as ‘mechanical’ wetting. Since compaction induces the lowest void ratio, compacted samples also experience the highest degree of saturation. Data relative to ‘as-compacted’ states (statically compacted samples and samples dynamically compacted to 50 and 100% Proctor energy) can therefore be assumed to be ‘main wetting’ data. Samples compacted at 30% Proctor energy were further wetted by spraying water. This mechanism of degree of saturation increase can be referred to as ‘hydraulic’ wetting. Since hydraulic wetting followed a mechanical ‘main’ wetting, these data can
Effective water ratio, ew-ewh
4
(b) 0.1
1
10
100
Matric suction, s: kPa
Figure 5. Water retention data for statically and dynamically compacted samples.
still be assumed to be ‘main wetting’ data. Here, we are implicitly assuming that the two modes of degree of saturation increase, hydraulic and mechanical, are equivalent as demonstrated by Tarantino & Tombolato (2005) and Tarantino (2008). Figure 5a shows that the relationship between suction and degree of saturation for the d10 and d25 soils is not unique but depends on void ratio. The higher the compaction energy, the lower the void ratio, and the higher the air-occlusion suction. This is consistent with the capillary model which predicts an increase in the air-occlusion suction as the diameter of the capillary tube decreases. Data shown in Figure 5a therefore suggests that main wetting data should be modelled in the space suction, void ratio, and degree of saturation. Figure 5b shows the same data plotted in terms of effective water ratio, which is defined as the difference between water ratio ew and hygroscopic water ratio ewh , the water ratio being the volume of water to volume of solids ratio (ew = Vw /Vs ) . The effect of void ratio is now much less pronounced and data seems to converge in a log-log plot at high suctions. This was also observed by Tarantino (2008) for a number of different soils. This means that the effective water ratio ew − ewh at high suction is described by a power function of suction. The power interpolation is shown in Figure 5b for d10 and d25 soils.
293
MODELLING VOID-RATIO DEPENDENT WATER RETENTION BEHAVIOUR
1 d10(d<10mm) d25(d<25mm) Estimated degree of saturation, (Sr)estimated
6
Let us assume that the effective water ratio ew − ewh at high suctions for ‘main wetting’ paths can be described by a power function of suction, s: ew − ewh = as
−b
(1)
where ew is the water ratio, ewh is the hygroscopic water ratio, and a and b are two parameters associated with the intercept and slope of the straight line interpolating experimental data in plane ln(s) − ln(ew − ewh ). Consider now the water retention equation of the type proposed by van Genuchten (1980):
0.2
0.2
0.4
0.6
0.8
1
Measured degree of saturation, (Sr)
(2)
measured
Figure 6. Performance of the water retention model for the grain size distributions d10 and d25.
1
ew − ewh e − ewh
⎞n ⎤− nb ⎛ 1 ⎢ ⎜ e − ewh b ⎟ ⎥ s⎠ ⎦ = ⎣1 + ⎝ a
0.4
0
where Sre is the effective degree of saturation, e is the void ratio, and α, n, and m are soil parameters. If the van Genuchten’s model is constrained to converge at high suctions to the water ratio curve given by Equation 1, the following model for ‘main wetting’ behaviour is obtained: Sre =
0.6
0
Degree of saturation, Sr
−m ew − ewh Sre = = 1 + (αs)n e − ewh
0.8
⎡
(3)
e=0.38 e=0.28
e=0.28 0.8
(a)
0.6 e=0.38 0.4 0.2 0.1
1
100 10 Matric suction, s: kPa
1000
Degree of saturation, Sr
1
Full derivation of Equation 3 and its validation can be found in Tarantino (2008). It can be seen that the dependency of effective degree of saturation on void ratio naturally appears in the modified van Genuchten’s water retention equation. It is worth noticing that void ratio e controls the α parameter (compare Eq. 2 with Eq. 3) which is, in turn, the van Genuchten’s parameter that essentially affects the air-occlusion suction. In other words, the void ratio controls the water retention behaviour through the air-occlusion suction. The capability of Equation 3 to capture the experimental data is shown in Figure 6 and Figure 7 for the d10and d25 grain size distributions. The main wetting retention curves at the same void ratio e = 0.4 for the two grain size distributions d10 and d25 as predicted by Equation 3 are shown in Figure 8. As expected, two different grain size distributions produce two different water retention curves. However, there is a similarity between the water retention curves for d10 and d25in Figure 8 and the grains size distributions shown in Figure 3.
e=0.51 ± 0.01 e=0.42 ± 0.01
0.8 0.6
e=0.42 (b)
0.4 0.2 0 0.1
e=0.51
10 1 Matric suction, s: kPa
1000
Figure 7. Main wetting water retention curves at constant void ratio (a) soil d10; (b) soil d25.
The steepest grain size distribution, d10, also produces the steepest water retention curve. This is in agreement with the observations made by Arya & Paris (1981). Indirect methods for predicting water retention behaviour based on grain size distribution and dry density should be therefore able to account for this effect.
294
0.6 0.4
d25
1
Degree of saturation, Sr
d10
0.8
(a)
0.8
Vereecken et al. (1989)
Eq. (3) 0.6 0.4 Arya & Paris (1981) 0.2
e=0.28 e=0.38
0
0.2 0.1
0.1
1
10 100 Matric suction, s: kPa
1
1000 (b)
1
Degree of saturation, Sr
Degree of saturation, Sr
1
0.8
10 Matric suction, s: kPa
100
1000
Vereecken et al. (1989)
Figure 8. Predicted main wetting retention curves at the same void ratio (e = 0.4) for the grain size distributions d10 and d25.
7
ESTIMATING WATER RETENTION BEHAVIOUR FROM GSD
Eq. (3)
e=0.42 e=0.51
0.6 0.4 0.2
Arya & Paris (1981)
0
According to Cornelis et al. (2001), there are three main approaches to estimate the water retention curve. The Group 1 methods estimate the water content of the soil at certain suctions using multiple linear regression or artificial neural networks. The Group 2 methods predict the parameters of a closed-form analytical equation such as the model of Brooks and Corey (1964) or the van Genuchten equation (1980). This is done through multiple linear regression or artificial neural networks. The Group 3 methods are based on a physical-conceptual approach of the water retention phenomenon and may use fractal mathematics and scaled similarities. We selected one method from Group 2 (Vereecken et al. 1989, 1992) and one method from Group 3 (Arya & Paris 1981). The method presented by Vereecken et al. (1989, 1992) estimates van Genuchten’s parameters by regression equations that use the grain-size distribution and the dry density. In particular, three grain size fractions are considered, clay fraction (<2 μm), silt fraction (2–50 μm), and sand (50–2000 μm). The large database of 40 soil horizons used by Vereecken et al. (1989, 1992) to develop their regression equations did not include soils with grain size greater than 2 mm. As a result, this method may give inconsistent results when applied to coarse-grained materials. Nonetheless, it was selected as it appears to give the best results among the methods in Group 2 (Cornelis et al. 2001). The method by Arya & Paris (1981) consists in translating the grain size distribution into a pore-size distribution. The cumulative pore volume and the corresponding suction are then determined by assuming spherical particles and cylindrical pores. This method was originally developed from a small database and then extrapolated to larger database.
0.1
1
10
100
1000
Matric suction, s: kPa
Figure 9. Assessment of indirect methods for predicting water retention behaviour form grain size distribution. (a) soil d10; (b) soil d25.
An average value of 1.38 was originally suggested for the scaling parameter α. Later investigations by Arya et al. (1982) showed that the average scaling parameter α ranged from 1.1 for fine-grained soils to 2.5 for coarse-grained soils. A value of α = 2 was selected for the well graded coarse materials d10 and d25. The water retention curves predicted by these two methods are shown in Figure 9 for the soils d10 and d25. As expected, prediction using the approach by Vereecken et al. (1989) is not satisfactory especially for the soil d25. The degree of saturation is significantly overestimated at low suctions and even the shape of the predicted water retention curve differs from the one derived from the experimental data (Eq. 3). This confirms that empirical methods should be applied to the same class of grain size distributions used to validate such methods. The model by Arya & Paris (1981) gives better results and the shape of the predicted water retention curve appears to be similar to the one derived from experimental data.
8
FROM LABORATORY SCALE TO FIELD SCALE
The water retention curve derived form the Arya & Paris (1981) approach is satisfactory at a qualitative level. This suggests a simple approach to extrapolate
295
the water retention behaviour experimentally determined in the laboratory on a ‘reduced’ grain size distribution to the soil in field. Let us assume that the soil d25 is the original soil in the field and that the grain size distribution d10 is the ‘reduced’ grain size distribution to be tested in the laboratory. The water retention curve for d10is determined experimentally and one has to predict the unknown water retention curve for the soil d25. The curve from the Arya and Paris (1981) method can be first scaled to match the experimental data available for soil d10. We scaled the suction according to the following relationship: ln s∗ = A · ln
sAP s0
+ ln s0
(4)
where s∗ is the scaled suction, sAP is the suction derived from the original Arya and Paris (1981) method, s0 and A are two best-fit parameter. Equation 4 indicates a rotation of the water retention curve around the point having suction s0 . We selected s0 = 1000 kPa and determined the parameter A by matching the experimental curve Figure 10a). The scaling provided by Equation 4 was then applied to the Arya & Paris water retention curve estimated for the soil d25 based on grain size 1 Degree of saturation, Sr
Eq. (3)
Arya & Paris (1981) 0.4
1 10 Matric suction, s: kPa
100
CONCLUSIONS
The paper has presented an experimental investigation of water retention behaviour of well graded coarsegrained soils. Two ‘reduced’ grain size distributions, d10 and d25 respectively, were tested. Each soil was compacted to different void ratios. It has been shown that water retention behaviour is significantly affected by void ratio and a water retention equation has been used to model main wetting behaviour in the space suction, void ratio, and degree of saturation. Two indirect methods were then investigated to derive water retention curve from grain size distribution. The statistical approach provided mean results because it was validated against a different class of soils. The physical-conceptual model was closer to experimental data and could be used as a basis to extrapolate the water retention behaviour experimentally determined on a ‘reduced’ grain size distribution (d10) to a soil including a larger grain size fraction (d25).
The authors wish to acknowledge the support of the European Commission via the ‘‘Marie Curie’’ Research Training Network contract number MRTNCT-2004–506861. They also wish to thank Ms Giulia Pisoni and Mr Martin Monnier who carried out the tests on soil d10 and Mr Marco Campana who carried out the test on soil d25.
(a)
0.6
e=0.4 0.2 0.01 0.1
9
ACKNOWLEDGEMENTS
Arya & Paris (1981) scaled 0.8
distribution (Figure 10b). The agreement is not excellent but may be considered acceptable in many practical applications.
1000
1 Degree of saturation, Sr
Arya & Paris (1981) scaled
REFERENCES
0.8 Eq. (3) 0.6
(b)
0.4 Arya & Paris (1981) 0.2 e=0.4 0 0.001 0.01
0.1 1 10 Matric suction, s: kPa
100
1000
Figure 10. A simple approach to derive field water retention curve from laboratory ‘reduced’ grain size water retention curve. (a) determining the scaling parameter by fitting experimental data on d10; (b) predicting water retention curve for d25.
Arya, L.M. & Paris, J.F. 1981. A physicoempirical model to predict the soil moisture characteristic from particle size. Soil Sci. Soc. Am. J. 45: 1023–1030. Arya, L.M., Richter, J.C. & Davidson, S.A. 1982. A comparison of soil moisture characteristic predicted by the Arya-Paris model with laboratory-measured data. Agristars Technology Report SM-L1-04247, JSC-17820, NASA-Johnson Space Center, Houston, Texas. Brooks, R.H. & Corey, A.T. 1964. Hydraulic properties of porous media. Hydrology Paper 3. Colorado State Univ., Fort Collins, CO. Cornelis, W.M., Van Meirvenne, M. & Hartmann, R. 2001. Evaluation of Pedotransfer Functions for Predicting the Soil Moisture Retention Curve. Soil Sci. Soc. Am. J. 65: 638–648.
296
Tarantino, A. 2004. Panel report: Direct measurement of soil water tension. In Proceedings 3rd International Conference on Unsaturated Soils (eds J.F.T. Jucá, T.M.P. de Campos and F.A.M. Marinho), Recife, 3, pp. 1005–1017. Rotterdam: A.A. Balkema. Tarantino, A. 2008. A water retention model for deformable soils. Submitted for publication. Tarantino, A. & Mongiovì, L. 2002. Design and construction of a tensiometer for direct measurement of matric suction. In Proceedings 3rd International Conference on Unsaturated Soils (eds J.F.T. Jucá, T.M.P. de Campos and F.A.M. Marinho), Recife, 1, pp. 319–324. Tarantino, A. & Mongiovì, L. 2003. Calibration of tensiometer for direct measurement of matric suction. Géotechnique, 53(1): 137–141.
Tarantino, A. & Tombolato, S. 2005. Coupling of hydraulic and mechanical behaviour in unsaturated compacted clay. Géotechnique 55(4): 307–317. van Genuchten, M.T. 1980. A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of American Journal 44, 892–898. Vereecken, H., Feyen, J., Maes, J. & Darius, P. 1989. Estimating the soil moisture retention curve characteristic from texture, bulk density, and carbon content. Soil Science 148: 389–403. Vereecken, H., Diels, J., Van Orshoven J., Feyen, J. & Bouma J. 1992. Functional evaluation of pedotransfer function for the estimation of soil hydraulic conductivity. Soil Sci. Soc. Am. J., 56: 1371–1378.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Water retention functions of sand mixtures E. Imre & I. Laufer St. István University, Ybl Miklós School of Engineering and Geotechnical Dept., BME, Budapest, Hungary
K. Rajkai Hungarian Academy of Sciences, Research Institute for Soil Sc. and Agricultural Chem., Budapest, Hungary
A. Scheuermann Institute for Soil Mechanics and Rock Mechanics, University of Karlsruhe (TH), Germany
T. Firgi & G. Telekes St. István University, Ybl Miklós School of Engineering, Budapest, Hungary
ABSTRACT: The water retention curves of three sand fractions and 12 continuous and gap-graded 2-component sand mixtures were measured. Due to the unexpectedly long equalization times, the tests (involving 11 suction steps) lasted longer than two years. In this paper, two methods for predicting the water retention properties are considered which use the grain size distribution as primary input. In particular, the data are used to validate a pedo-transfer model which is based on the pore size distribution of a soil.
1
2
INTRODUCTION
The experimental determination of the water retention curve or soil water characteristic curve (SWCC) and the unsaturated hydraulic conductivity is time consuming and costly. However, these properties are the primary input for the assessment of infiltration processes in unsaturated soils. Consequently the soil hydraulic properties are often estimated rather than measured. In this paper, research concerning two methods is considered which use the grain size distribution as primary input. Method 1 is the application of a transfer function generation method based on grading entropy (Imre et al, 2008). It consists of the following steps. (i) The soil function is experimentally determined for some controlled grading curves (ii) The measured data are mathematically described using the best possible model (iii) The mathematical description is extended to all grading curves. In this paper—the 6th in a series (Imre et al, 2003 to Imre et al, 2008) —some measured data are presented. This adds to the data on a duplicate sample set that was stopped after 7 suction steps, reported in Imre et al. (2007). This new data is used for the validation of method 2, which is based on the calculation of the pore size distribution (Scheuermann & Bieberstein, 2007).
2.1
THEORETICAL METHODS Method 1—grading entropy approach
A transfer function generation method for sands, describing the relationship between the grading curve and the soil properties (property functions) was suggested (Imre et al, 2008). It is based on the grading entropy concept of L˝orincz (1986). The grading curve is characterized by two entropy coordinates: base entropy So and entropy increment S (in normalised form ‘‘A’’ and ‘‘B’’, respectively). This can be related to the number of particle size fractions, N , identified within the grading curve. A normalised entropy diagram (Fig. 1) can be used to identify soils that are stable, or subject to piping or suffusion (particle migration). Soils for testing in this research were identified to represent different entropy states (Fig. 2). 2.2 Method 2—capillary method based on the pore constriction size distribution The pore constriction distribution is calculated approximately using a method proposed by Schuler (1996). Based on the assumption that the soil consists of spherical particles, the grain size distribution (finer by weight) is recalculated into a distribution of ‘‘finer by surface’’. The grain size distribution finer by surface
299
particles. In this way a pore constriction distribution is calculated dependent on the soil density. Based on the pore constriction distribution, the water retention curve is calculated using the YoungLaplace equation. For the presented study the residual water content is approximated as retained water in the contact zones of the particles. Adhesive forces are neglected. A detailed description of the method is given in Scheuermann & Bieberstein (2007).
entropy maximum for N=2 3
4
Entropy increment, B[-]
1 .2
5 6
Zone Zone II.
I. 0 .8
7 III.
0 .4
0 .0
minimum B lin e N = 3 to 7
3
0 .6 0 .8 Relative base entropy, A[-]
1 .0
Figure 1. Half of the normalized entropy diagram for various numbers of grading fractions (N ). Legend: Zones: I: piping. II: stable. III: stable with suffusion.
stage I, II
Entropy increment, B[-]
stage III 1.2
MEASUREMENT METHODS
For the determination of the transfer function with method 1, some experiments were needed. The testing conducted previously was carried out on soils composed from the fractions shown in Table 1. Optimal mixtures (with entropy parameter ‘‘A’’ = 2/3) were tested (Table 2). In the first part of the research (Imre et al, 2003) seven fractions were used and the standard method for suction determination of the Soil Science Institute was adopted. This method uses sand boxes (for ua − uw ≤ 50 kPa) and a pressure membrane extractor (1500 kPa > ua − uw > 50 kPa) (Várallyay, 1973; Rajkai 1993). In addition, a pressure-plate extractor was used. Due to the problems with the high air entry disc, this method was not applied later on.
0.8 Table 1.
0.4 lower bounding lines for N = 2 to 7 0.0
0.0
0.2 0.4 0.6 0.8 Relative base entropy, A[-]
1.0
Fractions in the research.
Simplified notation
Grain size d (mm)
1 2 (C) 3 (B) 4 (A) 5 6 7
2.0–4.0 1.0–2.0 0.50–1.0 0.25–0.50 0.125–0.25 0.06–0.125 0.03–0.06
Figure 2. The normalized entropy diagram (showing the soils tested in the research).
includes information about the probability with which individual particles with a specific surface will touch each other. The pore constriction in the area between the particles is determined based on the density index of a soil Dr = (nmax − n)/(nmax − nmin ) (where n is porosity and nmax and nmin are the maximum and minimum porosities) by considering a group of four particles touching each other. In this sense the pore constriction is defined as the largest 1-dimensional circle that can be constructed in the pore throat between the four
Table 2. The mixtures used in the first part of the research (Imre et al, 2003). The number of fractions N [-]
Fractions in the mixture
2 3 4 5 6 7
1-2, 2-3, 3-4, 4-5, 5-6, 6-7 1-2-3, 2-3-4, 3-4-5, 4-5-6, 5-6-7 1-2-3-4, 2-3-4-5, 3-4-5-6, 4-5-6-7 1-2-3-4-5, 2-3-4-5-6, 3-4-5-6-7 1-2-3-4-5-6, 2-3-4-5-6-7 1-2-3-4-5-6-7
300
Percentage passing S [%]
(a) 100 100B 100 A
0
100C 1.00 d [mm]
Table 3. 2005).
A section through the sand box.
The mixtures used in the second part (Imre et al,
N [-]
Fractions in the mixture
2 3 4
1-2, 2-3, 3-4 1-3, 2-4 1-4
Table 4.
(c) Percentage passing S [%]
Figure 3.
Percentage passing S [%]
(b)
Mixtures used in the third part (reported here).
N [-]
Fractions in the mixture
3
C-B, C-A, B-A
100 100A 80A20B 60A40B 40A60B 20A80B 100B 0
1.00 d [mm] 100B
80B20C 60B40C 40B60C 20B80C 100C 1.00 d [mm]
(d) S, Percentage passing [%]
0.10
100
0
The sand box (Figure 3) was originally built with a filter of fine sand with about 0.01 m of thickness (that acts as a semi-permeable layer) and a lower filter material (asbestos) below the sand with about 0.01 m of thickness. Kaolinite can be used for a semi-permeable layer for higher suctions. Suction is applied by gravitational means (hanging column of water) for suctions less than about 2.5 kPa and vacuum above this. Water content is measured by weighing of the samples about every third day. In the second part of the research (Imre et al, 2005) only fractions 1 to 4 were used. Two-component mixtures were tested in the suction range 0 to 50 kPa using some new suction steps and sand boxes. In the third part of the research (reported here) 2-component soils were used consisting of fractions A [0.25–0.5 mm], B [0.5–1.0 mm] and C [1.0–2.0 mm] (these are the same as fractions 2 to 4 used in the previous research). The relative base entropy ‘‘A’’ varies from 0 to 1 (Table 4 and Fig. 2). It follows from the definition of the entropy parameter ‘‘A’’ (e.g. Imre et al,
0.10
0.10
100 100A 80A20C 60A40C 40A60C 20A80C
0
100C 1.00 d [mm]
0.10
Figure 4. Composition of soils in the third part of the research (intended curves in dashed lines). (a) B-A mixtures, (b) C-B mixtures and (c) C-A mixtures.
2008) that for a 2-component soil the value of ‘‘A’’ is equal to quantity of the larger fraction (Fig 2). The soil composition is shown in Figure 3 in terms of grading curve and in terms of symbols (e.g. 20A80B indicates
301
Suction steps in the sand box.
1.0
Suction steps (in 0.1 kPa)
Semi-permeable layer
Suction load
1, 2.5 4, 6* , 7, 8*, 10, 13*, 15, 16*, 20, 20*, 23*, 26*, 29*, 31.5, 32*, 35*
Sand fine sand
Gravitational vacuum
0.8
w [-]
Table 5.
* Additional suction steps in this research—third part.
0.6 4/A 0.4
2003 2007
1 2/C 5 6 7
3/B
0.2 20% from fraction A and 80% from fraction B in terms of dry mass). The intended and the actual grading curves slightly differ. The difference can be attributed to suffusion and segregation (the entropy parameter ‘‘A’’ was varying from 0 to 1 exceeding the segregation safe zone, ‘‘A’’ = 0.4–0.7). Suffusion was observed in the first mass measurements. The testing was carried out with a single new fine sand box with varying suction load that required stages with much longer durations (more than two months were needed for larger suction loads instead of 2–3 weeks) than in the case of the boxes with specified constant suction load. The sand box is shown in Figure 3. The filter material was changed in the third part of the research. The asbestos material was replaced with a copy of the original material which is not dangerous. The suction steps were decided on the basis of the experimental results throughout the previous parts of the program (Table 5). At least two samples were prepared for each mixture. The sand was poured in the loosest possible dry state in a container then it was saturated. Samples were gained by pushing the samplers with 2.5 cm of height and 3.8 cm of diameter into the saturated layer. The mass of the samples was measured regularly during each suction step and at the end of the test they were oven dried. From these data, the water content was back-computed for each measured mass value. Because of the time consuming nature of the experiment, half of the duplicate soil samples were opened after load step 7 (at 2.6 kPa) and part of the results were presented earlier (Imre et al, 2007).
4
RESULTS
0.0 1E-1
1E+0
1E+1
1E+2
1E+3
ua-uw [kPa] Figure 5. Water retention curves, results from Imre et al (2003) and Imre et al (2007) (w—gravimetric water content).
According to the results, the water retention data are situated in the same order as the grading curves in Figure 4, however, the ‘‘spacing’’ is not equal. The various fractions have significantly different slopes in the quasi-linear, steep part, getting steeper for the finer fractions. Constant-valued (flat) parts (sections where the suction changes without a change in the water content) were observed in the curves for fraction B and for some mixtures A-B and A-C. Comparing the results of the fraction with the results measured in the first part of the research (Fig. 5) the following can be observed. The result for fraction C (same as fraction 2) is identical, for fractions B (i.e. 3) and A (i.e. 4) some difference was found basically due to the additional suction steps. Slightly different sample sizes and suction increments were used. The measurements were made in different sand boxes since the filter material was changed in the third part of the research. Comparing the results of the double soil samples, the slight difference between the first and second samples is acceptable (the first samples were opened after step 7, at 2.6 kPa suction load, see Fig. 6).
4.2 Comparison with the pedo-transfer method
4.1 Water retention curve data The water retention data of the fractions measured in the first and some from the third part of the research are compared in Figure 5. The water retention curves measured in the third part of research are shown in Figure 6.
Figure 7 shows calculations of the water retention curves (lines) using method 2 described in section 2.2 in comparison to the presented experimental data (symbols). Since the samples are tested in a loose condition a density index of Dr = 0.3 was chosen. The saturated water contents of the experimental investigation are used for the calculation.
302
C-B-A fractions (2nd part) A-B samples 1&2 (3rd part)
(a) 1
w [-]
0.8 0.6 0.4
C
B A
0.2
(a)
0 1E-1
1E+0
1E+1
ua-uw[kPa] C-B-A fractions (2nd part) C-B samples (3rd part)
(b) 1
w [-]
0.8
B
0.6 0.4
(b)
A
C
0.2 0 1E-1
1E+0
1E+1
ua-uw[kPa] (c)
fractions C, B, A, 2nd part of the research C-A samples 1&2, 3nd part of the research 1
w [-]
0.8
(c)
0.6 0.4
B
C
Figure 7. Comparison between measured (symbols) and calculated (lines) water retention curves. (a) B-A mixtures, (b) C-B mixtures and (c) C-A mixtures.
A
0.2 0 1E-1
1E+0
consideration of the density index which was estimated and not measured for the calculation.
1E+1
ua-uw[kPa]
Figure 6. Measured water retention results (a) B-A mixture, (b) C-B mixture, and (c) C-A mixture curves (w—gravimetric water content).
The comparison of Figure 7 between calculated and measured retention curves shows in the most cases quite good agreement. In particular, the suction at the air entry value, which is characterized by the largest pore constriction (i.e. the greatest possible exit of a pore) was calculated with satisfactorily accordance. The discrepancy between the calculation and the measurement are mainly caused by the inaccurate
5
DISCUSSION AND CONCLUSIONS
Some results of two ongoing research projects are reported in this paper where water retention curve models are planned to be elaborated. 5.1 Method 1 (grading entropy approach) The water retention curves of three sand fractions and 12 continuous and gap-graded 2 component sand mixtures were measured. The mixtures constituted some one-parameter grading curve series (optimal,
303
gap-graded, selected on the basis of grading entropy theory) with diameter being larger than 0.25 mm. The main conclusion can be summarized as follows: i. The water retention curves were measured in a sand box with varying suctions applied gravitationally since the residual suction was less than 10 kPa in every case. Some additional suction steps were adopted with respect to previously reported parts of the research (Table 5). The measured data indicated that the applied suction increment system was acceptable and the ‘‘precise’’ shape of the retention curves for the tested sands were determined (except that the intended and the actual grading curves differed slightly due to segregation and suffusion). ii. According to the results, the middle part of the retention curve of the fractions was extremely steep. The slope was steeper for finer fractions than for coarser fractions which conflicts with the previous assumption (i.e. it was assumed that these were equal). iii. The water retention curve for fraction B and some mixtures contained some constant valued (flat) parts. The reason was probably partly due to non-perfect fractions and partly the non-uniform distribution of the grains or of the pores within a fraction. Further experimental research is suggested on the determination of the grain and pore size distribution curves, using artificial soils. iv. Very long stage durations (about 3 months) were observed which was attributed to the fact that the suction was varied within the sand box. The widths of the sand layer in the sand box is comparable with the height of the sample (0.025 m) since the width of the fine sand is about 0.01 m and the filter material below the sand is also about 0.01 m in thickness. v. A slight shift was found between the results of the second and the third stage data measured in different sand boxes. Further research is planned on the slight difference between the old and the new boxes. 5.2 Method 2 (the ‘‘capillary method’’) validation In this research the measured data were used to test a capillary method for the calculation of the water retention curve based on an approach for the
approximate determination of the pore constriction size distribution. The first results indicate a fairly good agreement between calculation and measurement reflecting the fact that the samples may have different compactness ratio, which was not directly determined in the laboratory tests. Further experimental research is suggested, in particular on the determination of the minimum and maximum dry density of the tested mixtures. Future investigations are aimed to develop and improve both the pedo-transfer methods.
REFERENCES Imre, E., Rajkai, K., Genovese, R., Jommi, C., L˝orincz, J., Aradi, L., Telekes, G. 2003. Soil water-retention curve for fractions and mixtures. Proc. of UNSAT-ASIA, Osaka 451–456. Imre, E., Havrán, K., L˝orincz, J., Rajkai, K., Firgi, T., Telekes, G. 2005. A model to predict the soil water characteristics of sand mixtures. Int. Symp. on Advanced Experimental Unsat. Soil Mech. Trento June 27–29. Imre, E., Rajkai, K., Firgi, T., Trang Q.P., Telekes, G. 2006. Closed-Form Functions For The Soil WaterRetention Curve of Sand Fractions and Sand Mixtures The Fourth Int. Conference On Unsaturated Soils, Arizona. 2408–2419. Imre, E., Laufer, I., Trang, Q.P., L˝orincz, J., Rajkai, K., Firgi, T., Telekes, G. 2007. The soil water characteristics of 2-component sand mixtures, 2nd International Conference Mechanics of Unsaturated Soils, 2007 Weimar 2:45–59. Imre, E., L˝orincz, J., Rózsa, P. 2008. Characterization of some sand mixtures. Proc. of the 12th Int. Conference of International Association for Computer Methods and Advances in Geomechanics (IACMAG) 1–6 October, 2008 Goa, India (submitted). Rajkai, K. 1993. A talajok vízgazdálkodási tulajdonságainak vizsgálati módszerei. Búzás I. (ed): Talaj-és agrokémiai vizsg. INDA4321 Kiadó, Bp. 115–160. Scheuermann, A., Bieberstein, A. 2007. Determination of the Soils Water Retention Curve and the Unsaturated Hydraulic Conductivity from the Particle Size Distribution. Experimental Unsaturated Soil Mech. Springer. 421–433. Schuler, U. 1996. Scattering of the composition of soils—an aspect for the stability of granular filters. In J. Lafleur & A.L. Rollin (ed.), Geofilters ’96, Montréal, May 1996. Várallyay Gy. 1973. A talajok nedvességpotenciálja és új berendezés annak meghatározására az alacsony tenziótartományban. Agrokémia és Talajtan 22. 1–22.
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Permeability of a heavily compacted bentonite-sand mixture as sealing and buffer element for nuclear waste repository S.S. Agus Civil, Geotechnical and Geoenvironmental Engineering Consultant, Singapore
T. Schanz Bauhaus-University Weimar, Germany
ABSTRACT: The most important issue pertaining to the performance of sealing and buffer elements in nuclear waste repository is permeability of the elements. Heavily compacted bentonite-sand mixtures are amongst the materials suggested to be used as sealing and buffer elements. When these materials are in contact with water at low stress levels, swelling takes place and void ratio increases. Generally, permeability of a soil increases with void ratio. However, the compacted bentonite-sand mixtures used for this purpose would most probably undergo wetting under constant volume conditions or under limited volume change. In this paper, a method to calculate possible changes in permeability of a heavily compacted bentonite-sand mixture is presented. The method is based on the micro-macro interaction model for expansive soils.
1
INTRODUCTION
There are urgent needs of establishing a final repository for hazardous waste (including nuclear waste) in many countries in the world. The concept of storing the hazardous waste in containers buried at great depths becomes popular. In Germany, since 1979, Deutsche Gesellschaft zum Bau und Betrieb von Endlagern fuer Abfallstoffe mbH (DBE) or the German Company for Construction and Operation of Waste Repository, an organization by the Federal Government, has been appointed to establish final repositories for the German hazardous waste (Enviros, 2003). AkEnd (2002) set up the requirements for selecting a suitable site for the final repository in the country, which are mainly related to the characteristics of host rocks where the repository will be located. The design concept of the deep geological repository includes buffering and sealing the canister where the waste will be stored. Among the favorable materials proposed to be used as sealing and buffer elements for the repository are compacted bentonite-sand mixtures. Several favorable characteristics of compacted bentonite-sand mixtures include low permeability, good thermal properties, and high self-sealing capability. However, the most important issue pertaining to the use of compacted bentonite-sand mixture in a repository is its permeability. Wittke et al. (1998) indicated that the intrinsic permeability of the material for sealing and buffer of the hazardous waste repository
should be as low as 2 × 10−16 m2 , also considering other factors that may affect the characteristics of the material such as moderate-to-high temperature development and the influence of solutions flowing from the host rocks. It is well understood that the buffer and sealing material located close to the canister would experience an increased temperature generated by the stored waste. On the other hand, the material, which would be located close to the host rocks, would be under influence of saline solutions. The material at this location would possibly swell due to water ingress since initially there would be a gap between the bricks and the host rocks. As soon as the gap is sealed, the material will be under constant volume conditions and swelling pressure is exerted. In this paper, possible variation of permeability of a heavily compacted bentonite-sand mixture which includes the variation under constant volume and unconfined conditions is presented. 2
THEORETICAL BACKGROUND
Bentonite is an expansive material and it swells when it is in contact with fluid, in this case water, under low stress level, resulting in an increase in its void ratio. Generally, permeability of material increases with increasing void ratio. The classical concepts of permeability, such as Kozeny-Carman model (Kozeny, 1927 and Carman, 1938) clearly indicate the dependency of
305
permeability on void ratio soils. The Kozeny-Carman model is expressed as follows: ks = K
ρw g μw
=
ρw g μw
1 CK−C
1 So2
e3 (1 + e) (1)
where ks is the saturated coefficient of permeability, K is the intrinsic permeability, ρw is the density of water, g is the gravitational acceleration, μw is the absolute viscosity of water, CK−C is the KozenyCarman empirical coefficient (i.e., equal to 5), So is the specific surface area of soil particles per unit volume of the soil, and e is the soil void ratio (or total void ratio, eT ). However, the Kozeny-Carman model is inaccurate when used for predicting the permeability of soils with platy (or clay) particles such as bentonite (Olsen, 1962). Factors that influence the inaccuracy of the Kozeny-Carman model for clays were described in Olsen (1962), which included possible errors in Darcy’s law used as basis for developing the model, electro kinetic coupling, and variation of water viscosity between clay particles, non-constant tortuosity, and the existence of clusters in the clayey soils. However, Olsen (1962) found that the main cause of discrepancy between the Kozeny-Carman model prediction and the measured data is the existence of clay clusters in the soils. The existence of cluster in clayey soils has been shown by Environmental Scanning Electron Microscopic (ESEM) photos in Agus and Schanz (2005) for a calcium bentonite, Calcigel. Another assumption in the Olsen model is that void ratio (or total void ratio, eT ) of the soil consists of cluster void ratio (em ) and inter-clusters void ratio (ep ). The em can also be called the intra-cluster or micro void ratio while ep can be regarded as macro void ratio. The Olsen model is expressed in the following equation. 3 1 − eemT Kmeasured qmeasured = = N 2/3 qK−C KK−C (1 + em )4/3
(2)
where qmeasured is the measured flow rate of water, qK−C is the predicted flow rate using the KozenyCarman model, kmeasured is the measured intrinsic permeability, KK−C is the Kozeny-Carman intrinsic permeability, N is the average number of clay particles per cluster, em (or ec in the original model) is the cluster void ratio (i.e., the intra-cluster or the intraaggregate or the micro-pore void ratio), and eT is the total void ratio. To compute the saturated coefficient of permeability of clay using the above equation, the parameter N and the two void ratios (i.e., em and eT ) must be known. The number of clay particles per cluster
(N ) can be assumed to be constant for a specific soil permeant system. The clay-permeant dispersion system is considered to affect the decrease in both em and the magnitude of initial cluster void ratio (emo ). Olsen (1962) assumed relationships between the eT , em , and ep in which em begins to reduce upon compression when ep ratio is equal to 0.43. However, when expansive soil such as bentonite is subject to changes in suction (or wetting-drying processes), the changes in em are governed by the changes in micro-structural effective stress following Barcelona Expansive Model or BExM (Alonso et al., 1999): dem κm d pˆ d pˆ = = Km (1 + em ) (1 + em ) pˆ = βm exp −αm pˆ d pˆ
e = dενm
(3)
e is the elastic micro-structural volumetric where εvm strain, em is the micro void ratio, Km is the coefficient of volume change for the microstructure, κm is the compressive index for the microstructure, αm and βm are material parameters, and pˆ is a micro-structural effective stress and is defined as pˆ = p + s with p is the net mean stress and s is suction. Normally, only the changes in eT are measured when soil undergoes loading-unloading or dryingwetting cycles. The value of ep can be calculated when em is known or vice versa. Thus by utilizing the BExM model, the prediction of permeability using the Olsen model can be done with a better scientific basis for the relationship between eT , em , and ep . The κm value in the BExM model can be obtained from cyclic drying-wetting tests. After several cycles of drying and wetting, the response of expansive soil to drying and wetting processes in terms of changes in void ratio is generally elastic or reversible. By knowing κm and the variation in eT , the intrinsic permeability of expansive soil can be computed for any loading-unloading or drying-wetting processes. Although the intra-cluster void is always (or is deemed to be) fully saturated (Alonso et al., 1999), the inter-cluster void may also be filled with air leading to unsaturated state of the expansive soil. Hence, the computation of coefficient of permeability of the expansive soil with respect to each phase (i.e., water and air phase) can only be done by incorporating an unsaturated soil concept for permeability. In this paper, two models; namely, van Genuchten-Mualem model and Fredlund and Xing-Mualem model are discussed. Many other models are available but not discussed in this paper. The two models were derived based on the statistical distribution of pores in the soil. The relationship between suction and degree of saturation or volumetric water content (i.e., soil-water characteristic curve or SWCC) is required for the computation. In the first unsaturated permeability model, the van
306
Genuchten SWCC equation (van Genuchten, 1980) is used whereas in the second model, the Fredlund and Xing SWCC equation (Fredlund and Xing, 1994) is used, both in combination with the Mualem statistical model (Mualem, 1976). The assessment of accuracy of both methods for predicting the unsaturated permeability function can be found in Agus et al. (2003). Van Genuchten: m Sr − Sres 1 n Se = = Sr max − Sres 1 + as 1 −m s m−1 = 1+ (4) a
calcium bentonite, Calcigel, and the sand was quartz sand with a maximum grain size of 2 mm. The properties of the bentonite and sand and the preparation of heavily compacted specimens for laboratory tests have been described in Agus and Schanz (2005, 2005a). Saturated compression rebound data were obtained for saturated specimens by also accounting for deformation of the test system (Schanz et al., 2005) and the results are presented in Fig. 1. Wetting curves were obtained for the heavily compacted material by incorporating both axis-translation and vapor equilibrium techniques. Two different test conditions were considered in the experimental program; namely, testing under constant volume conditions and unconfined swelling conditions. Details of
where Se is the effective degree of saturation, Sr is the degree of saturation, Sres is the residual degree of saturation, Sr max is the maximum degree of saturation, a (kPa), n and m are fitting parameters. Parameter a in the above equation is also called the reference suction. Fredlund and Xing:
0.70 0.65 0.60
Void ratio, e
0.55
Sr max
Sr = C(s) n m ; ln exp (1) + as ln 1 + ssr C (s) = 1 − ln 1 + 1 000sr 000
0.50 0.45 0.40 0.35
(5)
0.30
compression rebound
0.25 0.20 1
kw (Se ) =
1000 v -ua)
10000
100000
(kPa)
100 95
r
0 s2 Sr max dSr 0 s2
100
Figure 1. Results of the compression-rebound test for saturated specimen.
The computation of unsaturated coefficient of permeability using the Fredlund and Xing-Mualem model is not straightforward but involves an integration of the Fredlund and Xing SWCC equation combined with the Mualem model as follows (Mualem, 1976): ' Sr dS (2 ks Se1/2
10
Net vertical stress, (
Degree of saturation, S r (%)
where sr represents the suction corresponding to the residual volumetric water content (or residual degree of saturation). The unsaturated coefficient of permeability for water phase based on the van Genuchten-Mualem model is expressed in the following closed-form equation (van Genuchten, 1980). ⎧ ⎫ 1 m 2 Se ⎨ Se m ⎬ kw (Se ) = ks 1− 1− (6) ⎭ 100 ⎩ 100
(7)
90 85 80 75 70 65 60
constant volume unconfined
55 50 1
3
LABORATORY TEST DATA
10
100
1000
10000
100000
Suction, s (kPa)
A heavily compacted bentonite-sand mixture was investigated in this study. The bentonite used was a
Figure 2. Degree of saturation versus suction obtained from the wetting tests.
307
1E-19
0.34 loading 2
Intrinsic permeability, K (m )
wetting-drying cycles unloading
0.32
Void ratio, e
initial void ratio 0.30
0.28
1E-20
1E-21
1E-22
compression (cluster model) rebound (cluster model)
0.26
Kozeny-Carman
1E-23 0.24 1000
0.1 10000
100000
0.2
0.3
0.4
0.5
0.6
0.7
Void ratio, e
1000000
Total suction, s t (kPa)
Figure 4. Intrinsic permeability versus void ratio for the compression-rebound test specimen.
(a) 0.34 loading
1E-20
drying-wetting cycles 0.32
cluster model
Void ratio, e
2
Intrinsic permeability, K (m )
unloading
0.30
0.28
0.26
Kozeny-Carman
1E-21
1E-22 1 0.24 1000
10
100
1000
10000
100000
Suction, s (kPa) 10000
100000
1000000
(a)
Total suction, s t (kPa) 1E-18
cluster model
2
Intrinsic permeability, K (m )
(b) Figure 3. Results of the cyclic wetting-drying tests under (a) 200 kPa and (b) 1500 kPa net vertical stress.
the procedures adopted were described in Agus and Schanz (2004). Figure 2 shows results of the wetting tests. To obtain the microstructural compressive index (κm ), two cyclic wetting-drying tests were performed at 200 kPa and 1500 kPa net vertical stress, respectively. The suction cycles were imposed using vapor equilibrium technique and the results are presented in Fig. 3. 4
1E-19
Kozeny-Carman
1E-20
1E-21
1E-22
1E-23 1
10
100
1000
10000
100000
Suction, s (kPa)
(b) Figure 5. Intrinsic permeability versus void ratio for: (a) the constant volume wetting test specimen and (b) the unconfined wetting test specimen.
COMPUTATION OF INTRINSIC PERMEABILITY UNDER DIFFERENT LOADING CONDITIONS
The κm value was derived from the cyclic wettingdrying test data in the last cycle for each test. The value is 0.0087 and 0.0117 for the test at 200 kPa and 1500 kPa net vertical stress, respectively. In this
study, the average value of 0.0102 was used in the computation. The number of clay particle per cluster (N ) can be approximated by the ratio of the total specific surface area to the external specific surface area.
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The Kozeny-Carman computation which is based on total void ratio (eT ) results in greater value of intrinsic permeability than that computed using the cluster model. The difference is more obvious at low void ratios since the inter-cluster void ratio (ep ) is compressed leaving only nominal space for water channel. The evolution of intrinsic permeability during constant volume wetting test shown in Figure 5(a) indicates that the Kozeny-Carman model almost consistently predicts intrinsic permeability to be one order of magnitude higher compared with the cluster model. The cluster model computation shows a decrease in the intrinsic permeability when the heavily compacted specimen was wetted to about 1000 kPa suction which is captured in the cluster model prediction but not in the Kozeny-Carman’s. Further wetting was incorporated by a large increase in swelling pressure which resulted in the larger deformation of the constant volume cell used in the test. Thus, the intrinsic permeability increased as eT increased. Interestingly, both the Kozeny-Carman model and the cluster model give almost similar prediction of the intrinsic permeability for the unconfined wetting test specimen (Figure 5(b)). This is due to the fact that the change in eT during wetting under free swell conditions was accompanied by the change in ep whereas em was essentially constant. Figure 6 illustrates the evolution of specimen void ratio during wetting tests.
0.35
0.3
Void ratio, e
0.25
0.2
0.15
0.1 total 0.05
intra-aggregate inter-aggregate
0 10
100
1000
10000
100000
Suction, s (kPa)
(a) 1.2
total
1
intra-aggregate inter-aggregate
Void ratio, e
0.8
0.6
0.4
0.2
0 10
100
1000
10000
100000
5
Suction, s (kPa)
(b) Figure 6. Change in void ratio during wetting under: (a) constant volume conditions and (b) unconfined conditions.
This approximation is with a basis that the measurement of total specific area using for instance Ethylene Glycol Monoethyl Ether (EGME) method accounts for the surface area of clay particles in the clay clusters while the Brunette-Emmett-Teller (BET) method for the external specific surface area measurement can only measure the surface area of the clay clusters. Thus the ratio of the two specific surface areas provides indication of the number of clay particles per cluster. The total and external specific surface areas of Calcigel have been reported in Schanz et al. (2005) and the value is 651 m2 /g and 69 m2 /g, respectively. In this case, the N value is taken as 10. The computation of intrinsic permeability using a cluster model requires the Kozeny-Carman model prediction based on Equation (1). The change in intrinsic permeability of specimen during the saturated compression-rebound test is shown in Fig. 4.
COMPUTATION OF UNSATURATED COEFFICIENT OF PERMEABILITY FOR WATER PHASE
The computation of unsaturated coefficient of permeability commenced with the curve-fitting of the van Genuchten and Frendlund and Xing SWCC equations to the experimental wetting data. The following van Genuchten SWCC equations were obtained for the wetting test data. For the constant volume test: s 1.626 −0.385 Se = 100 1 + ; 1201 Sr max = 86.1%;
(8)
Sres = 80%
For the unconfined test: s 1.451 −0.311 ; Se = 100 1 + 272 Sr max = 100%;
(9)
Sres = 82%
The following Fredlund and Xing SWCC equations were obtained for the wetting test data.
309
For the constant volume test:
Unsat. coeff. of permeability, kw (m/s)
1.E-11 1.E-12 1.E-13
kw (Se ) = ks
1.E-14 1.E-15 1.E-16 1.E-17
For the unconfined test:
1.E-18 1.E-19 1.E-20
kw (Se ) = ks
1.E-21 van Genuchten-Mualem model
1.E-22
⎧ 0.311 ⎫2 ⎬ Se 3.215 Se ⎨ 1− (13) ⎭ 100 ⎩ 100
Fredlund and Xing-Mualem model 1.E-23
The computation of unsaturated coefficient of permeability using the Fredlund and Xing-Mualem model involves integration procedures and no closed-form solutions are available to date. Figure 7 shows the comparison between the van Genuchten-Mualem prediction and the Fredlund and Xing-Mualem prediction for the unsaturated coefficient of permeability of the heavily compacted bentonite-sand mixture. It should be noted that the saturated coefficient of permeability used in the computation were based on the cluster model prediction. The above figures reveal that both the van Genuchten-Mualem model and the Fredlund and Xing-Mualem model generally give almost similar results. The unsaturated coefficient of permeability for the specimen wetted under unconfined conditions is generally one to two orders of magnitude higher than that under constant volume conditions, which is partly due to the difference in the saturated coefficient of permeability.
1.E-24 1
10
100
1000
10000
100000
10000
100000
Suction, s (kPa)
(a) 1.E-11
Unsat. coeff. of permeability, kw (m/s)
⎧ 0.385 ⎫2 ⎬ Se ⎨ Se 2.597 (12) 1− ⎭ 100 ⎩ 100
1.E-12 1.E-13 1.E-14 1.E-15 1.E-16 1.E-17 1.E-18 1.E-19 1.E-20 1.E-21 van Genuchten-Mualem model
1.E-22
Fredlund and Xing-Mualem model 1.E-23 1.E-24 1
10
100
1000
Suction, s (kPa)
(b)
6
Figure 7. Unsaturated coefficient of permeability (water phase) prediction for the specimen tested under: (a) constant volume conditions and (b) unconfined conditions.
For the constant volume test: 86 Sr = ) * , s 0.634 + 0.111 ln exp (1) + 2607
(10)
For the unconfined test: 100 Sr = ) * , s 1.147 + 0.106 ln exp (1) + 202
(11)
The unsaturated coefficient of permeability can be computed using the following closed-form solution based on the van Genuchten-Mualem unsaturated permeability functions.
CONCLUSIONS
A study on the permeability of a heavily compacted bentonite-sand mixture for waste repository applications has been presented. The following conclusions can be drawn: 1. The flow of water in saturated expansive soils is through the channels available for water flow. These channels are mainly the inter-cluster pores (i.e. the pores located between the clay clusters). 2. A cluster model (Olsen, 1962) can be used to describe the flow of water by taking into account the presence of clusters in expansive soils. 3. The inter-cluster void ratio can be calculated by utilizing the micro-macro-structure interaction as described in the Barcelona Expansive Model (BExM) (Alonso et al., 1999). 4. The Kozeny-Carman model for saturated permeability predicts the intrinsic permeability to be about one order of magnitude higher for the studied material than the cluster model prediction.
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5. Under constant volume conditions, the intrinsic permeability of the compacted bentonite-sand mixture may drop during wetting. The drop in the intrinsic permeability may be more obvious for lower density compacted mixtures due to a greater difference in the inter-cluster void ratio of the mixtures at initial and saturated states. 6. The computation of unsaturated coefficient of permeability can be performed by combining the cluster model prediction for saturated coefficient of permeability with either the van GenuchtenMualem model or the Fredlund and Xing-Mualem model. Both models give almost similar results. 7. The proposed predictive model for saturated and unsaturated coefficient of permeability is at the moment merely at conceptual stage. No verification has been made with measured data. There is room for improvement to this method such as extending the model for solutions other than water that occur in the deep geological waste repository. REFERENCES Agus, S.S., Leong, E.C., and Schanz, T. (2003) Assessment of statistical models for indirect determination of permeability functions from soil-water characteristic curves. Géotechnique, 53(2): 279–282. Agus, S.S. and Schanz, T. (2004) Swelling pressures and wetting-drying curves of a highly compacted bentonitesand mixture. In Proceedings of the International Unsaturated Soil Conference, From Experimental Towards Numerical Modelling of Unsaturated Soils, Weimar, Germany, 2003 (Ed. T. Schanz), Lecture Notes in Applied Mechanics, Springer: 241–256. Agus, S.S. and Schanz, T. (2005) Effect of shrinking and swelling on microstructures and fabric of a compacted bentonite-sand mixture. In Proceedings of International Conference on Problematic Soils (GEOPROB 2005), Eastern Mediterannian University, Northern Cyprus, 2005 (Ed. N. Famagusta), 2: 543–550. Agus, S.S. and Schanz, T. (2005a) An investigation into hydro-mechanical behavior of an expansive soil using axis-translation and vapor equilibrium techniques. In Proceedings of International Symposium on Advanced Experimental Unsaturated Soil Mechanics (EXPERUS 2005), Trento, Italy, 2005 (Eds. A. Tarantino, E. Romero, and Y.J. Cui), Balkema, Rotterdam: 53–60.
AkEnd (2002) Site selection procedure for repository sites. Recommendation of the AkEnd Committee on a Site Selection Procedure for Repository Sites. Arbeitskreis Auswahlverfahren Endlagerstandort. W&S Druck GmbH, Collogne. Alonso, E.E., Vaunat, J., and Gens, A. (1999) Modelling the mechanical behaviour of expansive clays. Engineering Geology, 54: 173–183. Carman, P.C. (1938) Fundamental principles of industrial filtration—A critical review of present knowledge. Transaction of Institution of Chemical Engineering, 16: 168–188. Enviros (2003) The virtual repository of nuclear information. Public Access Area. Enviros Consulting Ltd. www.enviros.com/repository Fredlund, D.G. and Xing, A. (1994). Equation for the soil-water characteristic curve. Canadian Geotechnical Journal, 31: 521–532. Kozeny, J. (1927) Über kapillare Leitung des Wassers im Boden. Akademie der Wissesschaften. Wien, 136(2a): 271. Mualem, Y. (1976). A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research, 12: 513–522. Olsen (1962) Hydraulic flow through saturated clays. Clays and Clay Minerals, 9: 131–161. Schanz, T., Tripathy, S., Datcheva, M., Agus, S.S., Gruner, M., Sitz, P., Herbert, H.-J., Moog, H., und Kolditz, O. (2005) Schlussbericht zum BMBFForschungsvorhaben—Experimentelle und numerische Untersuchungen des Langzeitverhaltens von Abschlussbauwerken im Salinar mit Bentonitegemischen als Dichtelement. Förderkennzeichen 02 C 0881 (01.08.2001 bis 31.07.2004), Bauhaus-Universität Weimar, Weimar, Deutschland. van Genuchten, M.T. (1980). A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 44: 892–898. Wittke, W., Schmitt, D., Gattermann, J. (1998) Verschlieβkonzept für Untertagedeponien—Entwurf und geotechnische Nachweis. Geotechnik, 21(3): 212–216.
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Volumetric behaviour
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Volumetric behaviour of compacted London Clay during wetting and loading R. Monroy Ramboll Whitbybird, London, UK (formerly Imperial College London, London, UK)
L. Zdravkovic Imperial College London, London, UK
A. Ridley Geotechnical Observations Ltd, London, UK
ABSTRACT: In this study, the mechanical behaviour of a compacted clay in equilibrium with the atmospheric pressure was investigated. Samples of London Clay were compacted to the same initial conditions, corresponding to dry of optimum moisture content on a Proctor plot, and were taken along complex stress paths, involving wetting under a constant vertical stress, wetting under a condition of zero volumetric strain, and loading and unloading at a constant value of matric suction. Tests were performed with a combination of standard and osmotic oedometers—the latter developed specifically at Imperial College London to test unsaturated soils under atmospheric conditions. Samples taken along different hydration paths displayed similar post-yield behaviour when loaded at a constant suction, suggesting that common yield surface in the e: s: σv space (where e denotes void ratio, s is the matric suction, and σv is the vertical stress) controls the plastic volumetric behaviour of unsaturated London Clay during loading following monotonic hydration.
1
INTRODUCTION
When an unsaturated soil is loaded at different values of constant matric suction, one invariably finds that this has a fundamental effect on the mechanical response of the material: higher values of suction result in higher values of measured yield stress; additionally, suction has a fundamental impact on the location and shape of the normal compression line. The type of elasto-plastic framework first introduced by Alonso et al (1987) to describe the mechanical behaviour of unsaturated soils, defines a yield surface which can model the above phenomenon. This surface, labelled as the Loading-Collapse (LC) yield surface in the original elasto-plastic constitutive model developed from the original framework (Alonso et al, 1990), separates elastic from plastic processes, both during loading as well as wetting. The fundamental assumption of this, as well as all subsequent formulations, is that all irreversible volumetric strains due to a reduction in suction or an increase in load are associated with yielding on a unique LC yield surface. The above surface has been thoroughly investigated in the laboratory, and it is now believed that there is conclusive experimental evidence supporting its existence and qualitative shape (Wheeler and Karube,
1995). In most investigations, it has been identified by performing loading tests at different values of constant suction (Maatouk et al, 1995; Wheeler & Sivakumar, 1995; Cui & Delage, 1996; amongst others). Loading at constant suction has usually followed an initial equalization stage, in which the sample has been brought from the original state to the desired equilibrium suction, by wetting (or sometimes drying) under the effect of a nominal load or under no applied stress. Under these circumstances, it has been assumed that the locus of points joining the yield stresses associated with the different values of suction, define unequivocally the position and shape of the LC yield surface, proving its existence and uniqueness. In the original formulation, the LC yield surface is assumed to be independent of the stress path. This means that a sample taken along different wetting path should yield along the same surface, when loaded to sufficiently high stresses. To the authors’ knowledge, there is, to date, limited experimental evidence which shows that this is the case. The purpose of this paper is to present and compare a number of experimental results, in which similar samples were taken along different hydration paths prior to loading at constant suction. The results are believed to provide conclusive evidence of the uniqueness of the LC yield surface.
315
2
EXPERIMENTAL PROCEDURE
Top Cap
IC Tensiometer
The soil selected for this study was weathered London Clay. The following properties were measured in the laboratory: specific gravity, 2.70; liquid limit, 83%; plasticity index, 54%; clay content, 58%; fines content, 98%. Tests were performed with a combination of standard lever arm oedometers and osmotic oedometers. The latter were specifically developed at Imperial College London to test unsaturated soils under atmospheric conditions (Dineen & Burland, 1995). The standard oedometers were slightly modified in order to be able to test samples of similar size in all cases (corresponding to a sample height of 30 mm and a diameter of 75 mm). The use of standard equipment allowed comparisons to be made between tests results derived from both sets of apparatuses. The use of an osmotic system to control matric suction allowed samples to be tested under atmospheric conditions. This approach was adopted in preference to the better known axis translation technique (widely used in experimental studies on unsaturated soil behaviour), since it was felt that it provided a better way of replicating field conditions. The use of elevated air pressures to test unsaturated soils appears to have important theoretical and technical limitations, which remain unsolved to date (Burland & Ridley, 1996; Baker & Frydman, unpub.). It is acknowledged, however, that there is also a certain degree of uncertainty regarding the precise influence of the osmotic system on a sample’s response, particularly with regards to the effect of migrating solute molecules across the semi-permeable membrane. Despite this the authors feel that, at present, the objections associated with this method of testing are fewer that those attached to the axis translation technique. The osmotic oedometers had, inter alia, the following characteristics (Fig. 1): – Matric suction was controlled at the bottom of the sample by placing a poly-ether sulfonate ultra filtration (PES-UF) semi-permeable membrane over a woven mesh at the base of the oedometer cell, as shown in Figure 1. Osmotic solutions—consisting of different concentrations of polyethylene glycol (PEG) 35,000 molecular weight mixed with distilled water—were circulated continuously underneath the membrane, in order to vary the value of suction. Further details on the osmotic system can be found in Monroy (2006) and Monroy et al (2007). – Matric suction was measured independently and continuously at the top of the sample, by means of IC tensiometers (Ridley & Burland 1995). In the context of the present study, in which the soil was in equilibrium with the atmospheric air pressure, soil matric suction was measured as a tensile hydraulic
Upper Clamping Ring
Strain-gauged Diaphram
Oedometer Cell
Soil Sample
Semi-permeable membrane
Oedometer Base
Figure 1.
Lower Clamping Ring
Woven Mesh
Inlet and Outlet PVC Tubes (filled with osmotic solution)
Osmotic oedometer cell.
stress in the water filling the saturated tensiometer, when this had its porous tip making intimate contact with the pore fluid (Ridley et al, 2003). This tensile stress, however, must not be interpreted as the actual tension existing in the pore fluid, as pointed out by Baker & Frydman (unpubl.), but rather as a measure of the attraction that the soil exerts on the water (Ridley et al, 2003)—attraction which results from the combined effect of capillary action and surface adsorption effects (Alonso et al, 1987). – All processes of control and data acquisition were automated. – Loading and unloading of samples was carried out as a continuous process, by the application of small increments/decrements of load over the full length of a test. Samples were statically compacted to the same initial conditions, corresponding to an average moisture content of 23.6%, dry density of 1.384 Mg/m3 , degree of saturation of 67%, void ratio of 0.952, and matric suction of 1,000 kPa. These were equivalent to a sample compacted on the dry side of optimum moisture content on a Proctor curve. Selection of the above was based on considerations regarding the maximum suction the IC tensionmeter could measure for long periods of time, as well as the maximum vertical stress the osmotic oedometer was capable of delivering. A total of seven samples were used in this study. They were all tested starting from the same initial conditions described above, and were made to follow two different sets of stress paths: (i) wetting under a constant nominal load to different equilibrium values of suction (0, 120 and 405–430 kPa), followed by loading and unloading at constant suction; and (ii) wetting under conditions of zero volumetric strain
316
to the same equilibrium suctions, followed by a single loading-unloading cycle at constant suction.
3
EXPERIMENTAL RESULTS
Figure 2 presents results from samples tested in the osmotic and conventional oedometers and loaded in the fully hydrated state, at a measured value of zero matric suction. A total of three tests are shown in the figure: two osmotic (o9 and o17) and a third conventional (c13). This last test is included for comparison purposes. Sample o17 was allowed to swell under a nominal vertical stress of 7 kPa whilst water was circulated through the osmotic system. After reaching equilibrium—when no significant further changes in void ratio, suction, horizontal stress, or degree of saturation were noticeable—the sample was loaded to 600 kPa vertical stress, and thereafter unloaded to 70 kPa. This process took place slowly and continuously, in order to ensure that the suction remained always close to zero. Sample o9, on the other hand, was wetted—using the above method—whilst ensuring that the volume remained constant through the full hydration stage. During this process, the vertical stress was observed to reach a maximum of 150 kPa at some intermediate value of suction, before dropping to the final equilibrium value of 130 kPa. Due to high rate at which the sample was hydrated (the full drop in suction from 1000 to 0 kPa took place in a single stage), it was not possible to determine the exact value of suction corresponding to this maximum vertical stress.
c13 (free swell - conventional) o17 (free swell - osmotic) o9 (confined wetting - osmotic) 1.2
s = 0 kPa
Void ratio
1.1
s = 0 kPa
1
s = 0 kPa 0.9
Starting point 0.8
0.7 1
10
100
Applied vertical stress (kPa)
Figure 2.
Loading-unloading tests at zero suction.
1000
After reaching equilibrium, the soil was loaded to 700 kPa and unloaded to 50 kPa. This last stage was performed in steps, rather than continuously as in the case of Sample o17, by applying increments, and thereafter decrements, of 100 kPa. Test o9 was the only one performed in the osmotic oedometer in which this approach was followed (in all other cases the load was applied continuously in small increments). Sample c13 was tested in the conventional oedometer and was initially hydrated under a vertical stress of 7 kPa. In order to replicate conditions in the osmotic equipment—where hydration could only take place from the bottom of the sample—just enough water to cover the lower porous stone was placed inside the oedometer pot. After reaching equilibrium—when no further volumetric strains were recorded—the sample was loaded to 440 kPa and unloaded to 30 kPa in stages in the standard way. Figure 2 shows two interesting results. Firstly, the osmotic and conventional oedometers yield very similar results. There is a good agreement in the shape and location (given due account of experimental variations) of the loading-unloading curves corresponding to samples o17 and c13. When first commissioned, the design of the osmotic oedometer had been criticised for the inclusion of a woven mesh at the bottom of the sample (which served to improve circulation of the osmotic solution), since it was believed that this would have a considerable impact on the measured vertical strains. It was argued that since the woven mesh could deform, as well as, more importantly, penetrate the sample, vertical deformations would be overestimated in the osmotic oedometer. Figure 2 shows that this is not the case, or at least the effect is minimal, when a compacted sample is tested in the fully hydrated state. Secondly, for a fully hydrated sample, the method of hydration had no effect on the post yield response during loading. The normal compression lines for all three samples are coincident (allowing again for experimental variations). Figure 3 shows the response during a single loadingunloading cycle for two further samples tested in the osmotic oedometer (o10 and o11). As before, results from the conventional oedometer (sample c13) have been included as a reference. Sample o10 was allowed to swell freely under a constant vertical stress of 7 kPa whilst the suction was reduced in stages—by circulating increasingly more diluted solutions of PEG—until it reached an equilibrium value close to 120 kPa. This was followed by a full loading-unloading cycle at this constant value of suction, to a maximum vertical stress of 420 kPa. Sample o11 was also allowed to hydrate in stages to a final suction of 120 kPa, whilst the volume was kept constant. After reaching equilibrium, this second sample also underwent a complete cycle of loading and unloading, to a maximum stress of 510 kPa. During the
317
1.2
c13 (free swell-conventional) o10 (free swell-osmotic) o11 (confined wetting-osmotic)
1.2
s = 0 kPa
1.1
1.1
c13 (free swell-conventional) o14 (free swell-osmotic) o13 (confined wetting-osmotic) s = 0 kPa
Void ratio
Void ratio
s = 120 kPa Starting point
1
s = 120 kPa 0.9
1
s = 430 kPa s = 405 kPa
0.9 Starting point 0.8
0.8
0.7
0.7 1
10
100
1
1000
Figure 4. suction.
Loading-unloading tests at 120 kPa suction.
initial hydration stage, the vertical stress required to maintain the constant volume increased monotonically to a maximum of 185 kPa. Figure 3 shows that good agreement exists in the location and shape of the normal compression lines traced by both samples o10 and o11, and which are associated with different methods of hydration. Results from two further samples loaded at higher values of suction are shown in Figure 4. As in the two previous cases, one of the samples (o14) was allowed to swell under a nominal vertical load of 7 kPa, whilst the suction was decreased in stages to an equilibrium value of 430 kPa. The second sample (o13) was hydrated under a condition of zero volumetric strain to an equilibrium suction of 405 kPa. After reaching equilibrium, both samples were loaded and unloaded to 600 kPa and 220 kPa respectively (o14), and 630 kPa and 105 kPa (o13) respectively. During hydration of sample o13, the vertical stress required to maintain constant volume increased monotonically to a maximum value of 105 kPa. The results shown in Figure 4 are consistent with previous observations reported in this paper: the postyield during loading at constant suction is similar, regardless of hydration path. Figure 5 shows, in a single plot, the load-unload response of all six samples tested in the osmotic oedometer. By approximating the compression and swelling lines in Figure 5 by straight lines (an otherwise reasonable approximation), it is possible to follow their evolution with suction. This has been done and the results are shown in Figure 6. Due to their similarity, the loading curves associated with suctions of 405 and
100
1000
Loading-unloading tests at 405 kPa and 430 kPa
1.2 s = 0 kPa 1.1
Void ratio
Figure 3.
10
Applied vertical stress (kPa)
Applied vertical stress (kPa)
s = 120 kPa
1
s = 405 430 k Pa Starting point
0.9 0.8 0.7 1
10 100 Applied vertical stress (kPa)
1000
Figure 5. Summary of loading-unloading curves following free swelling and confined wetting.
430 kPa have been combined into a single line. Figure 6 shows how an increase in suction translates in steeper loading and flatter swelling lines. The measured values of compression and swelling indices associated with the different values of suction are given in Table 1. The results shown in Figure 6 are consistent, at least in qualitative terms, with earlier findings using axis translation. Wheeler & Sivakumar (1995) presented data for compacted kaolin loaded isotropically at different values of suction using this procedure. They found the normal compression lines to be straight (in the v: ln p plane; where v represents the specific volume and p the mean net stress, defined as the mean stress minus the pore air pressure), with the value of
318
Yield points:
s = 0 kPa s =120 kPa s = 405-430 kPa
400
Matrix suction (kPa)
2
Void ratio
Free swell Confined wetting
500
Cc
1.5
300
200
1
Cs
100
0.5 1
10
100
0
1000
Applied vertical stress (kPa)
0
100
200
300
400
500
Applied vertical stress (kPa)
Figure 6.
Normal compression and swelling lines. Figure 7. Loci of yield points associated with each method of hydration.
Table 1.
Compression and swelling indexes.
Suction kPa
Cc
Cs
0 120 405–430
0.349 0.583 0.723
0.081 0.034 0.032
1000 900 800
Sample o9 o11 o13
λ(s) increasing as the suction was augmented from 0 to 200 kPa. The yield stresses associated with each of the two different methods of hydration investigated in this study—free swell and confined wetting—are presented in Figure 7 in a plot of matric suction versus applied vertical stress. In all cases, the yield stress has been defined, rather arbitrary, as the intersection between the normal compression line and a second line parallel to the swelling curve and having as origin the start of the loading path. Each of the two sets of yield points can be joined together to form two yield curves, associated with the onset of plastic deformations during loading (following the two different methods of hydration considered). These two yield lines, however, must not be confused with the Load-Collapse (LC) yield line defined by Alonso et al (1990), since the full elastic behaviour of the material along a wetting-drying path is not known in the present case. Nevertheless, both yield curves in Figure 7, as well as the LC yield line, form part of the same LC yield surface defined in the e: s: σv space, as proposed by Alonso et al (1987).
Matric suction (kPa)
700 600 500 400 Free swell yield line
300 200
Confined wetting yield line
100 0 0
100
200
300
400
500
600
700
Applied vertical stress (kPa)
Figure 8.
Wetting paths at constant volume.
It is interesting to look at the constant volume wetting paths, now that the position of the LC yield surface has been established. This is shown in Figure 8. Sample o9 was wetted in a single stage, and therefore only the final equilibrium position is representative. The paths described by samples o11 and o13—having been hydrated at a much slower rate—can be expected to represent real soil behaviour. The figure shows
319
how, had the suction in sample o11 decreased to zero, the vertical stress would have had to reduce from the maximum value of 185 kPa at 120 kPa suction, to the final equilibrium value of 130 kPa at zero suction. This would be consistent with the proposition that any wetting path crossing the LC yield surface would cause the sample to yield—hence the necessary reduction in vertical stress to maintain the volume constant.
4
CONCLUSIONS
The purpose of this paper was to present strong experimental evidence which could be used to support the idea that, for a compacted, unsaturated soil, all irreversible volumetric compressive strains due to a reduction in suction or an increase in load are associated with a unique LC yield surface—as assumed in some of the most popular elasto-plastic models for unsaturated soil behaviour. Tests on samples of compacted clay, taken along two different hydration paths prior to loading at constant suction (free swelling under a nominal load and constant volume hydration), have shown that the post-yield response during loading is unaffected by the method of hydration. The similarity in position and shape of the normal compression lines in both cases, for different values of suction, is taken to be indicative of the uniqueness of the LC yield surface. Additional confirmation of the uniqueness of this surface was also provided by the shape of the wetting paths followed during constant volume hydration. As the wetting path approached the yield surface defined during loading, the sample was observed to start yielding, which translated into a reduction in the applied stress necessary to keep the volume constant. The present study has been limited to suctions in the range of 0 to 430 kPa, and to Ko loading. However, the results and conclusions are believed to be representative of soil behaviour at higher values of suction and under different loading conditions. Additionally, the tests have been performed under atmospheric pressure and, therefore, are believed to closely represent actual soil behaviour in the field. No consideration has been given to the effect of wetting-drying cycles on subsequent mechanical response. The findings and conclusions presented in this paper are, therefore, necessarily limited to the particular case of monotonic hydration from an initial compacted state.
ACKNOWLEDGEMENTS This research project was funded by the Engineering and Physical Science Research Council (UK). REFERENCES Alonso E.E., Gens A. & Hight D.W. 1987. Special problem soils. General Report. Proceedings of the 9th European Conference on Soil Mechanics and Foundation Engineering, Dublin, Ireland, 3, 1087–1146. Alonso, E.E., Gens, A. & Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique, 40, 3, 405–430. Baker, R. & Frydman, S. Unpubl. Unsaturated soil mechanics: Critical review of physical foundations. Submitted to the Canadian Geotechnical Journal for publication. Burland, J.B. & Ridley, A.M. 1996. Keynote address: The importance of Suction in Soil Mechanics. Proceedings of the 12th Southeast Asian Geotechnical Conference, Kuala Lumpur, Malaysia, 2, 27–49. Cui, Y.J. & Delage, P. 1996. Yielding and plastic behaviour of an unsaturated compacted silt. Géotechnique, 46, 2, 291–311. Dineen, K. & Burland, J.B. 1995. A new approach to osmotically controlled oedometer testing. Proceedings of the 1st International Conference on Unsaturated Soils, Paris, 2, 459–465. Maatouk, A., Leroueil, S. & La Rochelle, P. 1995. Yielding and critical state of a collapsible unsaturated silty soil. Géotechnique, 45, 3, 465–477. Monroy, R. 2006. The influence of load and suction changes on the volumetric behaviour of compacted London Clay. PhD Thesis, University of London. Monroy, R., Ridley, A., Dineen, K. & Zdravkovic, L. 2007. The suitability of the osmotic technique for the long term testing of partly saturated Soils. Geotechnical Testing Journal, 30, 3, pp. 220–226. Ridley, A.M. & Burland, J.B. 1995. A pore water pressure probe for the in situ measurement of a wide range of soil suctions. Proceedings of the International Conference on Advances in Site Investigation Practice, ICE, London, 510–520. Ridley, A.M., Dineen, K., Burland, J.B. & Vaughan, P.R. 2003. Soil matrix suction: some examples of its measurement and application in geotechnical engineering. Geotechnique, 53, 2, 241–253. Wheeler, S.J. & Karube, D. 1995. State of the art report: Constitutive modelling. Proceedings of the 1st International Conference on Unsaturated Soils, Paris, 3, 1323–1356. Wheeler, S.J. & Sivakumar, V. 1995. An elasto-plastic critical state framework for unsaturated soil. Geotechnique, 45, 1, 33–53.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Stress path dependence of hydromechanical behaviour of compacted scaly clay in wetting and drying suction controlled oedometer tests at constant vertical net stress C. Airò Farulla Università degli Studi di Palermo, Italy
ABSTRACT: The results are presented of an experimental programme devoted to investigating the volumetric strain and water ratio (volume of water to volume of solids) evolution of a compacted scaly clay stressed by wetting and drying cycles in suction-controlled oedometer tests. The stress paths applied included loading and unloading cycles at constant matric suction and suction controlled wetting-drying cycles at constant vertical net stress. The test results show that during wetting and drying cycles the samples experienced irreversible shrinkage or swelling strains depending on the stress path applied. Irreversible water ratio increases were always observed in these cycles. However, a quasi-reversible response both in terms of volumetric and hydraulic behaviour was approached as the number of cycles increased. The main characteristics of material behaviour are delineated and discussed.
1
INTRODUCTION
The analysis of the mechanical behaviour of compacted unsaturated clays subjected to cyclic wetting and drying paths has been receiving increasing attention owing to their use as construction material in many Civil and Environmental Engineering applications. Wide experimental evidence shows that in wetting and drying cycles compacted clays can accumulate irreversible volumetric swelling or irreversible volumetric shrinkage depending on stress history and the applied net confinement stress and cyclic suction change (Alonso et al., 2005; Sharma & Wheeler, 2000). Different mechanisms have been suggested in order to explain the observed volumetric behaviour and devise conceptual models reproducing test results. They refer to interactions between multiple levels of material structural arrangements at microscopic scale (Gens & Alonso, 1992; Alonso et al., 1999; Alonso et al., 2005) or to hydraulic hysteresis and void ratio dependence of material retention curves (Buisson & Wheeler, 2000; Vaunat et al., 2000). With reference to these questions, experimental research was developed at the University of Palermo in order to characterize the hydromechanical behaviour of a compacted scaly clay, which is often used for isolation of industrial and domestic waste banks. Selected experimental results related to volumetric strains and water content changes of the compacted scaly clay samples subjected to different stress paths and several
wetting and drying cycles in suction controlled oedometers are presented and discussed. The paper underlines the most important aspects of the volumetric and hydraulic behaviour of the material tested and its dependence on the stress paths applied.
2 2.1
EXPERIMENTAL PROGRAMME Material tested
The samples tested were prepared using a scaly clay outcropping near Palermo (Italy). The material is a kaolinitic-illitic clay with liquid limit wl = 58% and plasticity index Ip = 30%. The specific gravity is Gs = 2.78. The air-dried clay with a hygroscopic water content wh = 0.05 was disaggregated by a rubber pestle, and the fraction passing at no. 4 ASTM sieve (425 μm) was selected. Distilled water was added and carefully mixed. After a curing time of 2 or 3 days, the samples were compacted dynamically with a non-standard Proctor procedure to a target dry density. Some of the initial physical characteristics (water content, w0 ; dry density, γd0 ; void ratio, e0 ; saturation degree, S0 ) of the tested samples are collected in Table 1. The initial matric suction of the tested samples was in the order of 2 MPa as inferred from Fig. 1, which represents variation of the matric suction, detected by filter paper technique, of the as-compacted material
321
Table 1.
Initial characteristics of the tested samples.
Sample
w0
γd0 [kN/m3 ]
e0
S0
DMA DMB LC8 LC4
0.15 0.15 0.15 0.15
17.56 17.66 17.07 17.56
0.55 0.54 0.60 0.55
0.74 0.77 0.71 0.74
10000
s [kPa]
Figure 2.
Stress path layout applied.
1000
100 10
11
12
13
14
15
16
17
18
19
20
21
22
23
w [%]
Figure 1. Initial matric suction (filter paper method) of the as-compacted material.
(γd0 = 16.7 − 17.6 kN/m3 ) versus water content (Airò Farulla, 2004). The compacted scaly clay displayed a clear double structure pore network as observed from MIP results reported by Airò Farulla & Jommi (2005). A dominant macro-pore size of 30–40 μm was detected in these tests, while the micro-porosity dominant mode was in the range of 0.025–0.1 μm.
2.2 Controlled-suction technique and applied stress paths The experimental programme included loading and unloading tests at constant matric suction, s, and wetting and drying tests at constant net vertical stress, σv . Tests were carried out in two controlled-suction oedometers. Suction was controlled by means of the axis translation technique according to the air overpressure technique (Romero, 2001). After translation of the reference air pressure, the samples were allowed to equalize at a reference suction value, s0 , equal to 800 kPa for DMA, DMB and LC8 samples and 400 kPa for LC4 sample, respectively. The wetting and drying cycles on DMA and DMB samples started after the application of a vertical net stress, σv, equal to 50 kPa and 200 kPa, respectively, changing the applied suction between 800–10 kPa
(Fig. 2). The applied vertical stress and the first wetting stage (from the initial suction to 10 kPa) ensured an adequate contact with the oedometer ring, prior to the first drying stage. Subsequent suction increase from 10 to 800 kPa (lower than initial suction) is expected to induce shrinkage without lateral contact being lost. Romero (1999) presented results on a lateral stress oedometer showing that suction increase still maintained lateral contact (even at relatively low vertical stresses) if a first wetting stage is performed starting from a high initial suction. The LC8 sample underwent a loading-unloading cycle to the maximum value σvmax = 1600 kPa at constant suction s0 = 800 kPa and afterwards a cyclic suction variation in the interval of 800–10 kPa at constant σv = 200 kPa (Fig. 2). In the case of the LC4 sample, the applied stress path included multiple steps of loading-unloading cycles to the maximum value σvmax = 2800 kPa at constant suction s0 = 400 kPa and two series of wetting-drying cycles in the suction interval of 400–10 kPa at constant σv = 200 kPa, referred to as LC4B, and σv = 50 kPa referred to as LC4A, respectively (Fig. 2). To reduce test duration, suction was changed in a single step. The different loading steps, related to both vertical net stress or suction changes, were allowed to equalize until the rate of volumetric straining had reduced to a limit strain rate equal to or lower than 0.1%/day at a constant temperature of T = (20±1)◦ C. Water content variations were determined by measuring water inflow or outflow by a burette with a resolution of 0.02 cm3 .
3
ANALYSIS OF EXPERIMENTAL RESULTS
Volumetric strains, εv , and water ratios, ew (volume of water to volume of solids), measured at the end of each wetting and drying step, were collected versus applied
322
matric suction, s, in the diagrams in Fig. 3. Swelling volumetric strains are considered negative. With reference to mechanical behaviour, DMA and DMB samples accumulated compressive volumetric strains during wetting and drying cycles (more evident for DMB), while the LC8 and LC4 samples, owing to the previous loading and unloading cycle, developed high irreversible swelling strains (Fig. 3). Most of the irreversible strains developed in the first wetting-drying cycle, while volumetric behaviour became reversible more or less quickly as the cycles accumulated. Water content evolution (Fig. 3) showed the same trend in all the samples tested. An irreversible water ratio increment was measured for the most part in the first cycle, whereas an almost fully reversible behaviour occurred in successive cycles. General material behaviour appeared to be ruled by hydraulic hysteresis, while stress state appeared to influence water content change values. A deeper evaluation of the evolution of the mechanical and hydraulic behaviour of the compacted scaly clay can be obtained by analysing volumetric strain increments, εv , and water ratio increments, ew , measured at the end of each wetting and drying step. In the diagrams in Fig. 4, εv values are represented as absolute values, while ew values are represented together with the corresponding void ratio increments e, in order to point out the relationships between water and void ratio variations as suction was cycled. Vertical net stress influence on material behaviour was investigated by comparing results of tests DMADMB and LC4A-LC4B, respectively. Swelling strain and shrinkage strain increments for the DMA sample were quite high and almost equal. In contrast, the DMB sample, sharing a nearly similar stress history, showed a high irreversible shrinkage strain in the first cycle. Swelling strains then increased, shrinkage strains decreased, and its volumetric behaviour became almost fully reversible. When reversible behaviour was attained, DMA volumetric strain increments were more than double the DMB corresponding values. In terms of water ratio changes the samples behaved in a very similar way. They showed an evident irreversible water ratio increment in the first cycle, and reversible ew changes in the successive steps. In both irreversible and reversible conditions, DMA water ratio increments were greater than DMB water ratio increments. In the reversible condition a well-defined relationship can be detected between ew and e values (Fig. 4). Both increased as the applied vertical net stress decreased; also, the ew /e ratios were almost constant as the cycles accumulated, equating to about 3 for DMA and 4 for DMB.
LC4A and LC4B tests results indicate that in the first cycle the samples showed irreversible swelling strain increments that were much higher in the LC4A test owing the greater over-consolidation ratio. However, starting from the second cycle, volumetric behaviour in both tests became fully reversible. A quite similar behaviour was observed also in terms of water ratio increments. The diagrams in Fig. 4 show that elastic volumetric strain and water ratio increments in the LC4A test were higher than the corresponding LC4B values. In the elastic range, the ew /e ratios were 1.4 for LC4B and 1 for LC4A, since the sample approached or attained saturation during wetting and drying cycles. In conclusion, at the lesser vertical net stress applied (LC4A test), greater irreversible and reversible volumetric strain and water ratio increments occurred. The influence of stress history on mechanical and hydraulic behaviour at the same constant vertical net stress (σv = 200 kPa) and suction change (s = 800 kPa) can be elucidated by analysing DMB and LC8 test results. This influence was only significant in the first cycle when samples showed irreversible volumetric strains of different sign (DMB settled whereas LC8 swelled) and different irreversible water ratio increments (higher for DMB). However, starting from the second cycle, their behaviours were almost identical in terms of both εv and ew intensities. Irreversible volumetric strain and water content variations in the first cycle appears to cancel the effects of the previous stress history. It was possible to detect a proof of the effects of the applied suction change s on the volumetric strain and water content changes through the comparison between LC8 and LC4B samples, which shared a nearly similar stress history, bore the same vertical net stress (σv = 200 kPa), but were subjected to a suction increment of 800 kPa and 400 kPa respectively. The data collected in the diagrams in Fig. 4 indicate that in the first wetting the samples showed almost equal swelling strain increments, but that in the first drying LC8 settled much more than the LC4 sample as well as in the successive cycles when volumetric strains became reversible. Also with reference to the water ratio evolution, the LC8 sample showed greater irreversible and reversible water volume changes. These data indicate that the volumetric strain and water ratio increments depended on the intensity of the applied suction variation. However, in the first wetting, the effects of density (determined by the previous loading and unloading cycle) on volumetric swelling prevailed over the suction effects—in fact, the LC4B void ratio at the beginning of wetting was ei = 0.40 while the LC8 void ratio was ei = 0.51. A very similar result was obtained by comparing DMA (ei = 0.55) and LC4A (ei = 0.41) tests, which
323
0.6
–3
DMA
DMA –2
ew
v%
0.5 –1
0.4 0
v
= 50 kPa
s = 10–800 kPa 0.3 0.60
1 0
DMB
DMB 1
ew
v%
0.50 2
0.40 3 v
= 200 kPa
s = 10–800 kPa 0.30 0.6
4 2
LC8
LC8 3
ew
v%
0.5 4
0.4 5
v
= 200 kPa
vmax
0.3 0.5
6 4 LC4A
= 1600 kPa
s = 10–800 kPa LC4A
5
v%
6
0.4 ew
7 8
0.3 v
9
= 50 kPa = 2800 kPa
vmax
s = 10–400 kPa
0.2 0.5
10 6
LC4B
LC4B
7
ew
v%
0.4 8
0.3 9
v
initial point 10
Figure 3.
100
200
300
400
500
600
700
800
900
= 2800 kPa
s = 10–400 kPa
0.2 0
= 200 kPa
vmax
0
100
200
300
400
500
600
700
800
900
Volumetric strain (εv ) and water ratio (ew ) evolution versus matric suction (s) in wetting and drying cycles.
are characterized, as noted above, by a very different stress history, different s, and equal σv (50 kPa). In the first wetting LC4A swelled much more than DMA, but in the first drying and successive cycles the DMA volumetric strain increments were significantly higher. In terms of water content variations, DMA
always showed greater water ratio variations both in the first cycle and in the successive reversible cycles. The effects of higher density (or higher OCR) appear to overcome those of higher suction change only with reference to the volumetric swelling strain at the first wetting.
324
0.20
4
DMA DMA
0.16
v%
ew , e
3
0.12 0.08
2 0.04 0.00
1 0
1
2
3
4
0
5
1
2
3
4
5
6
0.12
3
DMB
DMB 0.10 0.08
v%
ew , e
2
0.06 0.04
1
0.02 0.00
0 0
1
2
3
4
0
5
3
1
2
3
4
5
6
0.12 LC8
LC8 0.10 0.08
v%
ew , e
2
0.06 0.04
1
0.02 0.00
0 0
1
2
3
4
0.00
5
5
1.00
2.00
3.00
4.00
5.00
0.12 LC4A
LC4A 0.10
4 ew , e
v%
0.08 3
0.06 0.04
2
0.02 1 0
1
2
3
4
0.00
5
0
3
2
3
4
5
0.12 LC4B
LC4B
0.10
2
ew , e
v%
1
1
0.08 0.06 0.04 0.02
0
0.00 0
1
2
3
4
5
0
1
2
cycles wetting
Figure 4.
4
3
4
5
cycles drying
ew
e
Increments of volumetric strain (εv ), water ratio (ew ) and void ratio (e) versus cycle number.
DISCUSSION OF RESULTS
With regard to volumetric behaviour it is evident that the material tested, depending on the stress path
applied, can manifest either a net compressive strain or a net swelling strain. Most irreversible or plastic volumetric strains develop in the first cycle, while in successive cycles, more or less quickly, volumetric
325
behaviour becomes reversible. A distinctive feature of the reported test results is the strong dependence of mechanical behaviour in the first suction cycle on the stress history and material density at the beginning of wetting. In the reversible range, stress history effects seem to disappear and elastic volumetric strains are governed by the vertical net stress and suction increment applied. More precisely, volumetric strain changes increase as σv decreases and s increases. The evolution of water ratio with wetting and drying cycles develops in a quite similar way for all tested samples, which accumulate irreversible water content increments in the first cycle and share an almost fully reversible behaviour in successive cycles. The irreversible water ratio variations are an evident consequence of hydraulic hysteresis. However, the stress paths applied influence water volume changes which increase, both in the irreversible and the reversible range, as σv decreases or s increases. These experimental results could easily fit, at least qualitatively, in the B.Ex.M. frame (Alonso et al., 1999; 2005; Gens & Alonso, 1992). Such an interpretation has been proved effective with reference to volumetric behaviour, although with the constraint of simplified hypotheses (Airò et al., 2007). A quantitative simulation of some of the above data, related to volumetric strain evolution, is at present in progress. However, in order to try to model irreversible and reversible water content changes in suction wetting and drying cycles, the effects of hydraulic hysteresis and void ratio changes are to be considered in a fully coupled hydromechanical model (Vaunat et al., 2000). 5
CONCLUSIONS
This paper presents detailed information on volumetric strain and water ratio evolution of a compacted scaly clay stressed by wetting and drying cycles at constant vertical net stress in suction controlled oedometers. The analysis of the test results aims to characterize some particular aspects of material mechanical and hydraulic behaviour and its dependence on the stress paths applied. In this connection it is evidenced that the compacted unsaturated scaly clay, when stressed cyclically in wetting and drying, underwent irreversible volumetric swelling or shrinkage strains and irreversible water ratio (or saturation degree) increases. Irreversible volumetric strain and water ratio changes developed for the most part in the first cycle; starting from the second suction cycle the material behaviour became reversible more or less quickly. In the first wetting and drying cycle the overall volumetric behaviour appeared to be strongly dependent on previous stress history and the σv and s applied. Water ratio increments, which must have been related to hydraulic
hysteresis, showed dependence on the stress paths applied. In the reversible range both volumetric strain and water ratio increments shared the same trend: they depended on the σv and s applied. The complexity of the material volumetric and hydraulic behaviour requires a conceptual model in which the different characteristic aspects can be rationally and consistently related. In this respect, the interpretation by B.Ex.M. of the volumetric behaviour of compacted scaly clay has been proved to be effective. A quantitative simulation of volumetric strain evolution is now in progress. REFERENCES Airò Farulla, C. 2004. Comportamento idraulico e meccanico dell’argilla a scaglie compattata del nucleo delle dighe Scanzano e Rossella. AGI XXII Conv. Naz. di Geotecnica, Palermo 22–24 Settembre: 445–452. Bologna: Patron Ed. Airò Farulla, C., Ferrari, A. & Romero, E. 2007. Mechanical behaviour of compacted scaly clay during cyclic controlled-suction testing. In T. Schanz (ed.), Experimental Unsaturated Soil Mechanics: 345–354. Berlin: Springer. Airò Farulla, C. & Jommi, C. 2005. Suction controlled wetting-drying cycles on a compacted scaly clay. Proc. Int. Conf. on Problematic Soils: 229–238. Eastern Mediterranean University, Famagusta, N. Cyprus. Alonso, E.E. Vaunat, J. & Gens, A. 1999. Modelling the mechanical behaviour of expansive clays. Engineering Geology 54: 173–183. Alonso, E.E., Romero, E., Hoffmann, C. & GarciaEscudero, E. 2005. Expansive bentonite-sand mixtures in cyclic controlled-suction drying and wetting. Engineering Geology 81: 213–236. Buisson, M.S.R. & Wheeler, S.J. 2000. Inclusion of hydraulic hysteresis in a new elasto-plastic framework for unsaturated soils. In A. Tarantino & C. Mancuso (eds), Experimental Evidence and Theoretical Approaches in Unsaturated Soils: 109–119. Rotterdam: Balkema. Gens, A. & Alonso, E.E. 1992. A framework for the behaviour of unsaturated expansive clays. Can. Geotechnical J. 29: 1013–1032. Romero, E. 1999. Characterisation and thermo-hydromechanical behaviour of unsaturated Boom clay. An experimental study. Doctoral Thesis, Universidad Politécnica de Cataluna, Barcelona. Romero, E. 2001. Controlled-suction technique. In W.Y.Y. Gehling & F. Schnaid (eds.), Proc. 4◦ Symp. Brasil. Solos Nao Saturados, Porto Alegre, Brasil, 535–542. Sharma, R.S. & Wheeler, S.J. 2000. Behaviour of an unsaturated highly expansive clay during cycles of wetting and drying. In H. Rahardio, D.G. Toll & E.C. Leong (eds), Unsaturated Soils for Asia. 721–726. Rotterdam: Balkema. Vaunat, J., Romero, E. & Jommi, C. 2000. An elastoplastic hydro-mechanical model for unsaturated soils. In A. Tarantino & C. Mancuso (eds), Experimental Evidence and Theoretical Approaches in Unsaturated Soils. 121–138. Rotterdam: Balkema.
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Long-term behaviour of lime-treated expansive soil submitted to cyclic wetting and drying O. Cuisinier & D. Deneele Laboratoire Central des Ponts et Chaussées, Centre de Nantes, France
ABSTRACT: Lime addition is a widely used technique to improve the engineering behaviour of soils and is known to reduce the swelling potential of expansive soils. However, in the long term, the permanence of the effect is questionable. This question is of interest since lime might be used to prevent swelling of expansive soils in earthworks. An experimental study was undertaken to assess the effects of successive wetting/drying cycles on the swelling behaviour of lime-treated expansive soils. This study was conducted both on three-year-old field samples from an experimental backfill and samples reconstituted in the laboratory. Osmotic suction-controlled oedometers were used to determine the swelling/shrinkage behaviour when submitted to wetting/drying cycles. The results obtained for reconstituted samples showed that lime treatment can reduce dramatically the swelling capacity of an expansive soil. However, the lime-treated samples taken from the experimental backfill exhibited important swelling and shrinkage deformations when submitted to successive wetting and drying. The results clearly indicate that treatment efficiency decreases with time. This tendency was confirmed by several cyclic wetting/drying tests.
1
INTRODUCTION
Quicklime addition is a common technique to improve the physical properties of fine soils. The first benefit of quicklime addition to a soil is related to the hydration reaction of quicklime that is highly exothermic causing the evaporation of water, further increasing the workability of the soil. Secondly, this hydration reaction results in an increase of Ca2+ and OH− concentrations in the soil. In the short term, this induces cation exchange of Ca2+ from the exchangeable cations existing in clay lattices that causes the flocculation of the particles (e.g. Abdi & Wild 1993) further affecting soil plasticity (e.g. Locat et al. 1990). Moreover, in the long term, the release of hydroxyl anions increases the soil pH up to 12.5, leading to the dissolution of silica and alumina of soil minerals that react with calcium, permitting the formation of cementitious compounds. These compounds cement soil particles together, this increasing the soil mechanical properties, like shear strength (e.g. Little 1995, Bell 1996). These reactions are named pozzolanic reactions. In addition to the immediate modification and the long term mechanical improvement, lime treatment is also known to significantly reduce the swelling ability of expansive soils (e.g. Brandl 1981, Rao & Thyagaraj 2003). Hence, this kind of soil treatment would be of interest in order to prevent swelling of clayey soils. One of the main mechanical concerns
with this practice, is the maintenance of the reduction of the swelling/shrinkage potentials associated with the lime addition. However, there is a lack of knowledge of the very long term efficiency of lime treatment, especially when lime-treated soils are submitted to a succession of wet/dry seasons. A few field studies have attempted to evaluate the performance of lime stabilized roads, earthfill, etc., several years after the construction of the infrastructure (e.g. Gutschik 1978, Kelley 1988). From these studies, there is a general agreement indicating that the alternation of wet/dry period could be detrimental to the efficiency of lime treatment. It is however difficult to generalize these results since little information is available on the soil types, lime treatment and compaction conditions, etc. in these studies. Experiments conducted on samples reconstituted in the laboratory are also reported in the literature. Guney et al. (2007) performed successive wetting/drying cycles on lime-treated expansive clay. They showed that the swelling/shrinkage potential of the clay is reduced by lime treatment only when the first cycle is considered. The swelling potential of the lime-treated clay increased significantly with the number of wet/dry cycles. The study presented by Khattab et al. (2007) concluded that successive cyclic wetting and drying cycles can be detrimental to lime effects on swelling properties. This seemed to be related to the curing time before the first water content cycle is
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performed. As a conclusion, these studies tend to indicate that suction cycles can alter the effects of lime treatment on swelling potential of clays. However, it should be considered that, in these studies, the samples were submitted to cycles between null suction (samples exposed to free water) and very low relative humidity (i.e. high suctions). These experimental conditions are rather severe compared to field conditions where suction variations are less pronounced below a few tens of centimetres from the outer surface of the backfill. In this context, an experimental programme was undertaken to evaluate the long term efficiency of lime treatment on the swelling/shrinkage properties of an expansive soil when submitted to suction variations in a more realistic range. Osmotic suctioncontrolled oedometers were used to determine the swelling/shrinkage behaviour of soils submitted to wetting/drying cycles in the range of suctions comprised between 0 and about 8 MPa. This study was conducted on two kinds of samples. Firstly, samples were taken in July 2006 inside an experimental backfill constructed in July 2003 with lime-treated expansive soil. Secondly, additional experiments were carried out with the same expansive soil, untreated or lime-treated but cured only one month to evaluate the short term efficiency of the lime treatment.
2 2.1
TESTED MATERIALS
In parallel, untreated clayey soil of the A34 was also sampled in order to conduct laboratory experiments on reconstituted lime-treated A34 clay reconstituted in the laboratory. 2.2 Untreated A34 clay properties The identification properties of the A34 soil (before lime addition) are given in Table 1. The compaction properties were also determined. The optimum mass water content was 27.0% that gave a dry density of 1.46 Mg · m−3 . With 3% of lime, on a dry weight basis, the optimum mass water content of the A34 soil was equal to 24.5%, and the dry density was about 1.37 Mg · m−3 . The determination of the methylene blue value of a soil (VBS) by means of the stain test evaluated the argillaceous fraction activity and quantity. These characteristics were used for the in situ compaction of the backfills. The particle size distribution analysis result is given on Figure 1. 2.3 Field samples characterization Only the central parts of the cores were used for the experiments presented in this study. Their water content was between 32 and 36%, the dry density between 1.14 and 1.28 Mg · m−3 and the degree of saturation between 70 and 80%. These characteristics are very different to the density and water content of the backfill built in 2003. This could be related (i) to field
Experimental backfills
An important amount of swelling clay was identified on one section of the A34 highway in the Ardennes (northern France) before its construction. This clay was found to be unsuitable to build the backfills of the highway according to French technical recommendations. One possible way to use this kind of clayey soil was to add quicklime. In this case, extensive studies were required to demonstrate the feasibility of the lime treatment. In this context, two experimental backfills (100 m length, 10 m width and 1.5 m height) were constructed in 2003, several compaction methods were considered. The variations of the backfill properties were monitored until now. In the framework of the present paper, different cores were sampled in those backfills in order to evaluate the swelling properties of the expansive soil three years after the lime treatment and the backfills construction. Those backfills were submitted to climatic conditions during three years and the sampling was performed in July 2006. In the selected backfill the A34 clay was mixed with 3% of quicklime, on a dry weight basis, and compacted at the optimum water content. The lime percentage was recognized, from the laboratory design study, to be sufficient to suppress the swelling potential of the A34 clay.
Table 1.
Identification properties of the untreated A34 clay.
wL %
wP %
Ip %
γs Mg · m−3
VBS g/100 g
<2 μm %
98.1
37.1
61.0
2.67
10.7
66.1
Figure 1. Particle size distributions of the untreated A34 clay compared with that of sample taken in the backfill.
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compaction that was less efficient in the field than in the laboratory, (ii) to a swelling of the soil after its compaction, or (iii) to a swelling related to the effect of climatic conditions and the increase in water content. Particle size distribution analysis (PSD) was carried out. Figure 1 compares the mean PSD of the untreated A34 clay and of the treated A34 clay coming from the experimental backfill. It can be seen that, after three years, the lime treatment induced a strong reduction of the amount of the clay particles (i.e. lower than 2 μm) from 66.1% down to 30%. The VBS value for the limetreated soil after 3 years is comprised between 5.1 and 7.1 g/100 g of dry soil that is significantly lower than the untreated soil (see Table 1). These considerations tend to indicate that the limetreated A34 clay sampled within the backfill is less active than the untreated soil. 2.4
Laboratory-reconstituted samples (lab-samples)
Some samples were reconstituted in the laboratory and several kinds of specimen preparations were considered: (i) untreated A34, (ii) lime-treated A34 with 3% of lime without curing and (iii) treated-A34 with 1 month of curing at 40◦ C. This temperature was chosen to speed up the chemical reactions and promote the secondary formation of hydrated cementitious products. The preparation of the lime-treated samples followed French technical recommendations. The lime and the soil at a water content equal to the optimum water content were thoroughly mixed together. The mixture was left for one hour in an airtight container before compaction to allow the development of immediate reactions between lime and the soil particles. Then, the soil was dynamically compacted directly in the desired oedometric cell. The compaction energy corresponded to the normal Proctor energy. The dynamic compaction procedure was scaled for the volume of the oedometric cell. A minicompaction device similar to the one presented by Sridharan & Sivapullaiah (2005) was used. When a curing period was required, the sample was wrapped with plastic sheets in order to prevent any water loss. All the reconstituted samples were compacted at their respective optimum water content and density. 3
water, and therefore the suction, is controlled by the macromolecule concentration: the higher the concentration, the higher the suction. In this method, only the matric suction of the sample is controlled. The exchange of water is due to the process of osmosis. The macromolecule commonly used is the polyethylene glycol (PEG) with a molecular weight of 20 000 or 6000 Da (1 Dalton, Da = 1.6605 10−24 g). An extended calibration curve for suctions ranging between 0 up to 8.5 MPa is given by Delage et al. (1998) and Cuisinier and Masrouri (2004). To fit these data, the following empirical calibration equation was proposed by Delage et al. (1998): s = 11 c2
(1)
where s is the suction and c the concentration of the PEG solution expressed in g of PEG per g of water. In order to limit this effect, the temperature was maintained at 20 ± 1.5◦ C. The basic principle of the osmotic oedometer used in this study is presented in Figure 2. A peristaltic pump circulates the macromolecules solution through the base of the oedometer cell, which is designed to allow fluid to circulate all around the bottom of the sample. Between the sample and the PEG solution, a semi-permeable membrane is introduced to prevent PEG macromolecules from passing into the sample. The diameter of the sample is 7 cm, and its initial height about 1 cm. With that material, 7 days were needed for deformation equilibrium to be reached. Mechanical loading was performed in the
OSMOTIC TECHNIQUE
In order to study the swelling/shrinkage behaviour of the samples, suction-controlled oedometers were used. They use the osmotic technique for suction imposition. Its basic principle is to introduce a semi-permeable membrane between a solution of macromolecules and the soil sample. The amount of exchanged
Figure 2.
329
Sketch of the osmotic oedometer.
same manner as in a typical oedometer test. All the wetting and drying phase were performed under a vertical stress of 10 kPa to ensure a good contact between the semi-permeable membrane and the lower face of the sample. The osmotic technique was also used to determine the water retention properties of the tested material. Cubic-shaped samples with a volume of approximately 1 to 2 cm3 were obtained from compacted samples of the different materials used in this study. They were inserted in the semi-permeable membrane. Then the membrane was hermetically sealed and further immersed in the desired PEG solution. Seven days were required to reach moisture equilibrium. Then, the water content of the samples was determined and the PEG concentration measured to determine the imposed matric suction.
4
BEHAVIOUR OF THE SAMPLES FROM THE EXPERIMENTAL BACKFILLS
4.1 Water retention curves The matric suction of the field samples was determined with the filter paper method. Samples were cut into two parts, three filter papers being inserted between them. After 10 days in an airtight container in order to reach equilibrium, the central filter paper was used for the suction determination. The mean value of the initial matric suction was between 800 and 1000 kPa. In a second test, the retention properties of the field samples were determined between 10 kPa and about 8 MPa. The retention curve test was performed in
Figure 3.
duplicate. Each sample was cut into small pieces of approximately 4 to 5 cm3 . Several pieces were used for each imposed suction. The pieces were inserted in a semi-permeable membrane and after 7 days in the osmotic solution, the water content of each piece was determined. The results are given in Figure 3. The results show a good reproducibility between duplicates. We note that the imposition of suction lower than the initial suction did not induce a significant increase of the water content.
4.2 Swelling characteristics of field samples Several series of tests were performed to evaluate the swelling properties of the field samples. First, the swelling potential was determined. This test was performed in a basic oedometer under the load of the piston. The swelling potential was found to be lower than 0.5%. This can be compared to the swelling potential of the untreated A34 clay that is equal to 13% for an initial water content of 35% (i.e. close to the in situ water content). Afterwards, three samples were submitted to successive wet/dry cycles between their initial suction (i.e. about 1 MPa) and 0 kPa. Their initial dry densities are comprised between 1.17 and 1.28 Mg · m−3 . In order to limit the test duration, no intermediate stages of suction were imposed between the initial suction and 0 kPa. It can be seen in Figure 4 that the first hydration induced small height variation between +0.02 and −0.02%. The results show that the first wetting/drying cycle resulted in an accumulation of shrinkage deformation.
Retention curves of the different tested materials.
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from 5.1% to 8.5%, significantly higher than the deformation registered between 0 and 1 MPa with the tests A, B and C (Figure 4). Secondly, it can be seen that the wetting that followed the first drying was associated to a swelling but the samples did not return to their initial state. The first suction cycle induced an accumulation of shrinkage deformations. During the additional suction cycles, it appears that the suction cycles induced only elastic swelling/shrinkage deformations. Therefore, the swelling behaviour of the limetreated expansive soil is related to the magnitude of the suction cycle. Lime treatment is still efficient 3 years after the backfill construction only for the suction cycles conducted between 0 and 1 MPa. 5
Figure 4. Influence of successive suction cycles between 1000 and 0 kPa on three-year-old field samples.
BEHAVIOUR OF THE SAMPLES RECONSTITUTED IN THE LABORATORY (LAB SAMPLES)
In order to assess the effect of lime on swelling properties of the A34 clay, the experimental approach performed with field samples were implemented with laboratory-reconstituted samples. For this, several preparation methods discussed previously were considered (untreated, lime treated without curing period prior to testing and lime treated with 1 month curing at 40◦ C). 5.1 Water retention curves
Figure 5. Influence of successive suction cycles between 8000 and 0 kPa on three-year-old field samples.
In a next step, samples were submitted to wetting/drying cycles, but in the range of suction between 0 and 8000 kPa. The suction of the samples was first increased from their initial suction up to 8000 kPa, and then submitted to suction cycles. The results of these tests are given in Figure 5. The first point to note is that the first drying induced a vertical shrinkage ranging
The influence of lime treatment on the water retention curve of the lab. samples can be seen in Figure 3. It appears that the lime treatment affects significantly the behaviour of the clay. The water retention capacity of the lime-treated clay is lower than that of the untreated clay for suctions lower than 200 kPa. However, it seems that the water retention capacity is higher for the limetreated A34 clay under high suction (>1 MPa). The effect of the curing time can be seen from these results; the water retention capacity tends to decrease with increasing curing time. Moreover, it appears that the water retention curve of the field sample is significantly different from the water retention curves determined with thelab. samples. It is interesting to note that, under a suction of 10 kPa, the water retention capacity of the field sample is equivalent to the water retention capacity of the untreated A34 clay. 5.2
Swelling characteristics of the lab. samples
The swelling behaviour of the lab. samples was determined only in the range of suctions between 0 and about 8 MPa. The results are shown on Figure 6. On this figure, only the results obtained for the limetreated samples after one month of curing at 40◦ C
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Moreover, the water retention capacity under low suction of the A34 field-samples is similar to the water retention of the untreated A34 clay, and significantly higher than those of the untreated clay. However, the water retention curve between 50 kPa up to 8 MPa is still drastically different. The identification properties also clearly indicate that lime is still having an effect on the A34 clay 3 years after the construction of the backfill. Hence, it can be stated that these results tend to indicate that the effect of lime treatment on the swelling properties of an expansive soil still have a significant effect on the behaviour of the A34 clay, 3 years after the backfill construction. Nevertheless, it appears that the lime treatment ‘‘efficiency’’ on the swelling/shrinkage potential of the A34 clay decreases with time. The results show that the behaviour of the A34 fieldsamples depends on the imposed suction range. 7 Figure 6. Influence of successive suction cycles between 8000 and 0 kPa on lab-samples.
are given and are presented for comparison with the untreated A34-sample. First, it can be seen that the untreated A34 clay has a high swelling/shrinkage potential, expected behaviour for an expansive soil. One sample of untreated clay was first submitted to wetting down to 0 while another sample was first submitted to a drying up to 8 MPa. In the first case, the successive suction cycles induce the accumulation of plastic swelling deformation whereas in the second case, there is a slight tendency for the accumulation of shrinkage deformations. Secondly, the lime-treated samples cured one month at 40◦ C exhibited a very different behaviour. It can be seen that the swelling/shrinkage potential is lower than 3% in the studied range of suction. Hence, it can be stated that, after one month of curing, the lime treatment is efficient at reducing the swelling potential of the A34 clay. It appears also that the maximum deformation has taken place during the first cycle, the remaining suction cycles inducing only elastic deformation. 6
DISCUSSION
All these results can be compared to assess the permanence of lime treatment effects on an expansive soil in the very long term. It can be seen that the swelling/shrinkage potential of the A34 clay field samples is significantly higher than those of the laboratoryreconstituted lime-treated A34 samples. However, the swelling/shrinkage potential of the A34 field samples is still lower than the untreated A34 clay.
CONCLUSION
In this study, experimental techniques developed to study the behaviour of unsaturated soils were used to evaluate the long term efficiency of lime-treatment on the swelling/shrinkage behaviour of expansive soils. These techniques demonstrate that the efficiency of lime treatment tends to decrease with time. It is now necessary to determine whether this decrease is linked to particular environmental conditions (weather, drainage, etc.) of the experimental backfill or the lime/soil reactions themselves. Additional investigations on the physico-chemical characteristics of the different tested materials will also be undertaken. ACKNOWLEDGEMENT The authors thank V. Berche from the Laboratoire Régional de l’Équipement of St Quentin (France) for providing both the core samples and data about the backfill construction. REFERENCES Abdi, M.R. & Wild, S. 1993. Sulphate expansion of lime-stabilised kaolinite: I. Physical characteristics. Clay Minerals 28: 555–567. Bell, F.G. 1996. Lime stabilization of clay minerals and soils. Engineering Geology 42: 223–237. Brandl, H. 1981. Alteration of soil parameters by stabilization with lime. 10th int. conf. on soil mechanics and foundation engineering, Stockholm, Sweden, vol. 3: 587–594. Cuisinier, O. & Masrouri, F. 2004. Testing the hydromechanical behaviour of a compacted swelling soil. Geotechnical Testing J. 27: 598–606.
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Delage, P., Howat, M.D. & Cui, Y.J. 1998. The relationship between suction and the swelling properties in a heavily compacted swelling clay. Engineering Geology 50: 31–48. Guney, Y., Sari, D., Cetin, M. & Tuncan, M. 2007. Impact of cyclic wetting-drying on swelling behaviour of limestabilized soil. Building and Environment 42: 681–688. Gutschick, K.A. 1978. Lime stabilization under hydraulic conditions. 4th lime congress, pp. 1–20. Kelley, C.M. 1988. A long range durability study of lime stabilized bases at military posts in the southwest. Bulletin 328, National Lime Association, Arlington, 2nd edition. Khattab, S.A.A., Al-Mukhtar, M. & Fleureau, J.-M. 2007. Long-term stability characteristics of a lime-treated plastic soil. J. of Materials in Civil Engineering 19: 358–366.
Little, D.N. 1995. Stabilization of pavement subgrades and base courses with lime. Arlington: National lime association. Locat, J., Bérubé, M.A. & Choquette, M. 1990. Laboratory investigations on the lime stabilisation of sensitive clays: shear strength development. Canadian Geotechnical J. 27: 294–304. Rao, S.M. & Thyagaraj, T. 2003. Lime slurry stabilisation of an expansive soil. Geotechnical Engineering 153: 139–146. Sridharan, A. & Sivapullaiah, P.V. 2005. Mini compaction test apparatus for fine grained soils. Geotechnical Testing J. 28: 240–246.
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Hydro-mechanical properties of compacted sand-bentonite in a semi-arid climate H. Bilsel & A. Iravanian Eastern Mediterranean University, Famagusta, N. Cyprus
ABSTRACT: This article presents the preliminary findings of an experimental study conducted on uniform sand-bentonite mixtures, focussing on the investigation and prediction of the volume change and hydraulic properties of artificially prepared mixtures of natural bentonite (Na-smectite) and poorly graded fine sand. Compacted specimens of sand-bentonite mixtures with additions of 33%, 50% and 75% sand were tested to demonstrate the change in physical and mechanical properties as compared to the compacted bentonite with no sand, therefore obtaining the most feasible combination for achieving the required properties. Based on the experimental findings of swell-shrink behaviour, saturated hydraulic conductivity and soil-water characteristic behaviour, sand-bentonite mixtures with 75% sand proved to be quite effective in fulfilling the requirements for barriers in a semi-arid climate. 1
INTRODUCTION
The current design criteria for waste containment systems use saturated hydraulic conductivity as a measure of effectiveness of the barrier layers. This, however, can be detrimental to covers in arid and semi-arid regions. In order to achieve a low saturated hydraulic conductivity, the barrier soil must be compacted wet of optimum, which will lead to drying, hence shrinking and cracking, therefore leaving the barrier layer ineffective. These cracks form preferential flow paths, and allow for infiltration of water. In semi-arid and arid climates compacted buffer materials remain unsaturated for a prolonged dry season, therefore suctions are a major factor in influencing the strength, compressibility and hydraulic conductivity of the materials. To minimize the effects of desiccation, clays with lower plasticity should be used, compacted close to optimum water content. Therefore, silty clays, sandy clays, clayey silts and clayey sands are less susceptible to cracking upon desiccation (Benson 1999). The design of the waste containment facilities, which are the cover and liner layers, require an extensive experimental investigation to be able to choose the best solution. The aim of this research is to investigate a long lasting and feasible solution for the environmental problems created by the abandoned copper mine and the landfills, which are not covered in North Cyprus, using the locally existing sources abundantly found on the island: the ‘‘beach sand’’ and naturally found ‘‘Na-smectite’’. Different proportions of sand and bentonite were mixed
and compacted together to form a material with low hydraulic conductivity which can be used as barrier layers. The initial findings of an extensive experimental program will be presented herein, which includes studies on swell potential, shrinkage characteristics, saturated hydraulic conductivity and soil-water characteristics. 2
BACKGROUND
Compacted clay liners are widely used as hydraulic barriers in landfills and other waste containment structures, with the intention of impeding flow. Hence the main goal is to achieve low hydraulic conductivity. Hydraulic conductivity depends mainly on the molding water content and dry unit weight obtained during compaction. Atterberg limits also have significant effect on hydraulic conductivity. Soils with higher plasticity index have lower hydraulic conductivity, since they will possess higher fines content (Benson and Trast 1995). Landfill covers and liners, engineered barriers and buffers need to be made from special materials, which meet the specified requirements, whenever available on-site soils are not suitable. The barriers designed using clays alone should maintain a saturated layer to reduce the rate at which oxygen can diffuse through the cover, therefore reducing the rate at which the oxygen enters into the waste, which creates acid generation in waste rock of mines. Therefore, wherever this method is applicable, it is important to keep the cover material saturated year round (Weeks and Wilson 2005).
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3
MATERIALS AND METHODS
This report includes the research findings on mixtures of natural compacted bentonite and 33%, 50% and 75% by dry mass of uniform sand. The testing program includes determination of physical properties of samples and hydro-mechanical properties including one dimensional free swell, and shrinkage test under vertical pressure, soil suction measurements and consolidation test. SoilVision (1998) software, a knowledge-based system database, was used to fit the models and calculate the fitting parameters of soil-water characteristic curve (SWCC), and shrinkage curves. The materials used in this study is basicly Na-smectite, obtained from the bentonite mine in Yiitler, and poorly graded uniform sand from Silver Beach in North Cyprus. According to the Unified Soil Classification System, grain size data of the sand indicate a mean diameter D50 = 0.20, a uniformity coefficient Cu = 1.53, a coefficient of curvature of Cc = 0.99 and effective diameter D10 = 0.14.
3.1 Atterberg limits The most important physical properties of the sandbentonite samples are the Atterberg limits, which show the reduction in the plastic behaviour with increasing sand content. The tests were performed using all fractions of the mixtures, without sieving through 0.425 mm. Table 1 depicts the plastic limit, liquid limit and the plasticity indices of sand-bentonite mixtures with increasing percentages of sand. The plasticity index values indicate a significant reduction in the plastic behaviour of the mixtures with increasing sand content. 3.2 Compaction test For laboratory investigations on sand-bentonite mixtures, the hydraulic conductivity is significantly influenced by the moulding water content. A thorough mixture of sand-bentonite is essential for reducing the scatter in hydraulic conductivity. In order to achieve a homogenenous distribution of voids within the mixture, the materials must be compacted at water contents either at optimum or just above the optimum. In this study, Standard Proctor tests were performed on natural bentonite alone and on mixtures of natural bentonite and sand. The results of the compaction tests carried out to assess the optimum water contents and maximum dry densities are given in Figure 1. Table 1.
Atterberg limits of sand-bentonite mixtures. Sand
Plastic limit Liquid limit Plasticity index
0
33%
50%
75%
67 117 49
49 77 29
30 57 27
32 24 8
1800 Natural bentonite 33% Sand 50% Sand 75% Sand
1700 Dry density, kN/m3
Various investigators have assessed the suitability of bentonite-based materials to be used as barrier layers for repositories. The use of pure bentonite in liners for water-retention facilities is very common. Particle sizes of the clayey soils such as bentonite are so fine, giving them the ability of being impervious and preventing the leaks. In recent years sand-bentonite mixtures have been used in construction of landfills and waste water ponds, which are observed to perform better than clayey mixtures in semi arid climates. The addition of small quantities of bentonite allows the fulfillment of the hydraulic conductivity requirement without failing in mechanical stability. Using clayey compound with granular soils to be applied as hydraulic or evapotranspirative barriers is a relatively new solution. Bentonite as a fine particle size soil with its specific properties seems to be an appropriate type of material to be used. The bentonite reduces the hydraulic conductivity, while sand reduces problems of bentonite cracking under shrinkage (Kaoser et al. 2006). The percentage of bentonite varies depending on the properties of the soil it will be mixed with. If pure bentonite is to be mixed with uniform sand usually 10–15% of bentonite is adequate. In general the amount of bentonite used in landfill industry varies between 3–15% (Kumar and Yong 2002). However, as the cost of bentonite is high, to determine the minimum percentage of bentonite necessary to achieve the required properties should be the main task. If the bentonite amount is high, the mixture becomes plastic and therefore it will be difficult to compact (Sallfors and Öberg-Högsta, 2002).
1600 1500 1400 1300 1200 1100 1000 0
0.1
0.2
0.3
0.4
Water content Figure 1.
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Compaction curves.
0.5
0.6
As can be observed in the figure, increasing sand content decreases the optimum water content, while increasing the maximum dry density. The bentonite, which forms a gel around sand particles, when reduced causes a reduction in the effective size of particles, hence decreasing the volume of voids. Therefore the dry density is reduced. 3.3
Swell potential
To investigate the swelling characteristics of natural bentonite and sand bentonite mixtures, one dimensional swell tests were carried out using oedometers. Consolidation rings of 50 mm inner diameter and of height 14 mm were pushed into the compacted sand-bentonite prepared at optimum water content, and two samples were obtained for swell testing. Specimens with varying sand-bentonite contents were allowed to swell until the increase in free swell with time became marginal. Figure 2 presents the free swell response with time for different mixtures of sandbentonite. The results depict a significant reduction in free swell with respect to the increasing sand content. 3.4
Soil-water characteristic curve
The compacted sand-bentonite barriers are frequently unsaturated in semi-arid areas. Therefore, suctions are a key factor in influencing the hydraulic properties, volume change and strength. Hydraulic properties consist of soil water characteristic curve (SWCC), and hydraulic conductivity function. SWCC is a measure of water storage capacity of soil for a given soil suction. It describes the relationship between the volumetric water content, θ , or the gravimetric water content, w, and the matric suction, ψm (ua − uw ) or the total suction (that is matric plus osmotic suction), ψt . It has a similar role as the 25 Natural bentonite 33% Sand 50% Sand 75% Sand
Percent Swell
20 15 10 5 0 1
Figure 2.
10
100 1000 Time, min
Free swell test results.
10000 100000
consolidation curve in saturated soil mechanics, and controls the behavior of hydraulic conductivity, shear strength and volume change at different suctions during wetting and drying processes. Therefore, SWCC can be considered as one of the most fundamental hydraulic characteristics of unsaturated soils. The water content of a soil decreases as suction increases following a drying path (desorption). On the other hand, the water content increases when the suction decreases following a wetting path (adsorption). For engineering practice, however, a single valued function, usually the desorption curve, is used in characterizing the hydraulic properties of unsaturated soils. The drying curve has a breaking point corresponding to the matric suction when the soil starts to desaturate, called the air-entry value (AEV), and is identified as the suction at which air enters the largest pores of the soil (Fredlund and Rahardjo 1993, Rahardjo and Leong 1997). In order to predict the performance of sandbentonite barriers, it is essential to determine the suction characteristics. Sand-bentonite mixtures develop very large suctions which cannot be tested by conventional methods, such as axis translation and osmotic techniques. In this study a chilled mirror potentiameter device was used to measure total soil suctions. This equipment was chosen because of its practicality in giving quick response, and the repeatability of the test results with high accuracy. Many other methods for measuring total suction are available such as filter paper and psychrometer methods but assessment made by the Agus & Schantz (2005) showed that the chilledmirror potentiameter gives the most accurate results. A description of the chilled-mirror potentiameter used was given by Leong et al. (2003). This device which also has soil science and agricultural usage has the ability of measuring the suctions between the ranges 500–300 000 kPa and higher within 10 minutes in fairly high accuracy. The dew point potentiometer (Model WP4 T, Decagon Devices, Inc., Pullman, W A 99163 USA) used in this research, determines total suction by measuring the dew point temperature of the head space above sample. It is done by cooling a mirror, the reflectance of which is carefully monitored by an optical sensor. As the mirror reaches the dew point it reflects changes and the device measures the temperature at which the first drop of dew was condensed on mirror. Using this temperature, the device calculates the suction of sample indirectly and shows it on a small monitor within a few minutes. In general it can be said that the chilled mirror potentiameter is an easy to use device giving quick assessments of the moisture state of the soil. Figure 3 depicts the soil-water characteristic curves of different mixtures of sand-bentonite with Fredlund and Xing (1994) models fitted by the use
337
Natural Bentonite 33% Sand 50% Sand 75% sand
0.6
Water content
0.5 0.4 0.3 0.2 0.1 0 10
100
1000
10000 100000 1000000
Suction, kPa Figure 3. Soil-water characteristic curves for different sand-bentonite proportions. Table 2.
Fredlund and Xing model parameters.
Sand (%)
Residual water content (%)
AEV (kPa)
0 33 50 75
29.93 27.67 23.22 9.17
326.25 220.35 213.31 41.02
cracks formed. The bentonite reduces the hydraulic conductivity, while the sand reduces the bentonite cracking under shrinkage. Samples compacted at optimum water content were saturated in one dimensional swell equipment, drained and allowed to desiccate at room temperature. Drying was carried out in a sequential manner. Volume change during shrinkage and suction measurements were carried out at varying time intervals to study the void ratio-water content (shrinkage curve) and soil-water characteristics relationships. The void ratio versus water content relationships are the shrinkage curves given in Figure 4. Increase of sand decreased the shrinkage limit, and hence the volume change. The shrinkage curve provides volumetric data for a soil as it dries and therefore allows calculations of volumetric properties for the SWCC. The shrinkage curve must be consistent with the hyperbolic equation to allow these calculations to proceed. The model parameters of the hyperbolic fit to the shrinkage data are given in Table 3. The parameter ash represents the minimum void ratio the dried specimens attained, and the bsh values are the minimum water content values at which volume change commenced. The latter are also referred to shrinkage limit which decreases with increasing sand percentage.
Void ratio
0.7
of SoilVision (1998) software and Table 2 presents the model parameters. The air entry value obtained by Fredlund and Xing (1994) model decreses with the increasing percentage of sand in the mixtures, which is rather significant for 75% sand. As the percent sand in mixtures gets higher, the amount of water held in saturated condition, ws , reduces. The reduction in the slope of soil-water characteristic curves is due to reduction in the rate of drying, which is an indication of reduced unsaturated hydraulic conductivity. The residual water content, wr , given in the table decreases with increasing sand content. Residual water content, wr , is the maximum gravimetric water content, at which the water capacity (the rate of change of gravimetric water content with respect to matric suction) approaches zero and the unsaturated hydraulic conductivity becomes zero. 3.5
2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
80% saturation 100% saturation Lab data
(a)
Void ratio
0
2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
Sand-bentonite mixtures are less susceptible to damage by desiccation due to the rigid matrix formed by sand and swelling of bentonite to close the
20 30 40 Water content, %
50
60
80% saturation 100% saturation Lab data
(b) 0
Shrinkage
10
10
20 30 40 Water content, %
50
60
Figure 4. Shrinkage curves of (a) natural bentonite, (b) bentonite-sand mixture with 75% sand.
338
Table 3.
Shrinkage parameters.
Sand (%)
ash
bsh
csh
0 33 50 75
0.17 0.43 0.50 0.52
0.0700346 0.1667609 0.1948968 0.1978353
1.33603 2.370018 2.979534 7.211402
Table 4.
Saturated hydraulic conductivity values. Coefficient of saturated hydraulic conductivity (m/s)
Stress range (kPa)
Natural bentonite
33% Sand
50% Sand
75% Sand
0–200 200–400 400–800 800–1569
6.94E-09 3.81E-09 1.74E-09 8.50E-10
1.19E-08 5.06E-09 2.59E-09 1.27E-09
1.11E-08 5.07E-09 2.64E-09 1.15E-09
1.07E-08 3.45E-09 3.28E-09 9.03E-10
There is a significant decrease in volume change. No cracks are observed in the desiccated specimens of sand-bentonite with 75% sand content. 3.6
Hydraulic conductivity
Saturated hydraulic conductivity is usually taken as a measure defining effectiveness of barriers. Barrier layers are expected to block the infiltration. However, in semi-arid and arid areas, macro-pores are formed upon desiccation, providing pathways for the infiltration of water. Therefore, it is of great importance to predict the hydraulic conductivity of barriers at initial stages of their design (Öberg-Högsta, 2002). It is universally accepted that the hydraulic conductivity of liners for hazardous waste should not exceed 10−9 m/s. In this study, saturated hydraulic conductivity was determined from the consolidation test results under different effective consolidation pressures. The estimated values are presented in Table 4. The testing program includes determination of hydraulic conductivity values by direct measurements under varying confining pressures, which is still under progress. 3.7
Figure 5. Scanning electron microscopy images for (a) natural bentonite, and sand-bentonite mixtures with (b) 33%, (c) 50%, and (d) 75% sand.
4
CONCLUSIONS
This study presents the initial findings of an on going research program to assess the most suitable barrier material for waste containment facilities in North Cyprus, where semi-arid climatic conditions prevail. Uniform sand and natural bentonite (Na-smectite) were chosen, which are local materials abundantly found. The results of the experimental program which consists of determination of swell-shrink characteristics and hydraulic properties, indicate that bentonite with 75% sand significantly reduces the volume change upon drying, forming a uniform texture with no desiccation cracks. Studying the soil-water characteristic curves, it is observed that, while the air-entry value decreases with increasing sand content, the slope also reduces indicating a reduction in the unsaturated hydraulic conductivity function with respect to suction. Based on these preliminary results it is anticipated that the naturally recovered bentonite and the uniform beach sand can be efficiently utilized as a barrier material in a semi-arid climate. However, these initial findings will be ascertained upon completion of the testing program.
Scanning electron microscopy
The desiccated specimens of natural bentonite and of mixtures of sand-bentonite were examined by scanning electron microscopy. From the micrographs given in Figure 5, it can be observed that there are large macropores in the pure bentonite, which reduces in size with increasing sand content. In the specimens with 75% sand, the bentonite content is just enough to fill the voids of the mixture completely even in the desiccated state. Therefore, the texture appears to be more uniform.
REFERENCES Agus, S.S. and Schanz, T. 2005. Swelling pressure and total suction of compacted bentonite-sand mixtures. Proceedings of International Conference on Problematic Soils, 25–27 May 2005. Eastern Mediterranean University, Famagusta, N. Cyprus. Benson, C. 1999. Final covers for waste containment systems: A North American Perspective. XVII Conference of Geptechnics of Torino, Nov. 23–25, 1999.
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Benson, C. and Trast, J.M. 1995. Hydraulic conductivity of thirteen compacted clays. Clays and Clay Minerals. 43, No. 6, 669–681. Fredlund, D.G. and Rahardjo, H. 1993. Soil Mechanics for Unsaturated Soils. New York: John Wiley and Sons, Inc. Fredlund, D.G. and Xing, A. 1994. Equations for the soilwater characteristic curve. Canadia Geotechnical Journal: 31, 521–532. Kaoser, S., Barrington, S., Elektorowicz, M. and Ayadat, T. 2006. The influence of hydraulic gradient and rate of erosion on hydraulic conductivity of sand-bentonite mixtures. Soil and Sediment Contamination: 15, 481–496. Kumar, S. and Yong, W.L. 2002. Effect of bentonite on compacted clay landfill barriers. Soil and Sediment Contamination: 11(1): 71–89. Leong, E.C., Tripathy, S. and Rahardjo, H. 2003. Total suction measurement of unsaturated soils with a device using the chilled-mirror hygrometer technique. Geotechnique. 53(2): 173–182.
Rahardjo, H. and Leong, E.C. 1997. Soil-water characteristic curves and flux boundary models. Unsaturated Soil Engineering practice: Geotechnical Special Publication No. 68, edited by Houston, S.L. and Fredlund, D.G., Geo Institute, ASCE, Utah. Sallfors, G. and Öberg-Högsta, A.L. 2002. Determination of hydraulic conductivity of sand-bentonite mixtures for engineering purposes. Geotechnical and Geological Engineering: 20, 65–80. SoilVision Systems Ltd. 1998. User’s Guide—A Knowledge Based System for Soil Properties, Version 2.0, Saskatoon, Canada. Tang, G.X., Graham, J., Blatz, J., Gray, M. and Rajapakse, R.K.N.D. 2002. Suctions, stresses and strengths in unsaturated sand-bentonite. Engineering Geology, 64, 147–156. Weeks, B. and Wilson, W. 2005. Variation in moisture content for a soil cover over a 10 year period. Canadian Geotechnical Journal. 42, 1615–1630.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Grain size effects on rockfill constitutive behaviour A. Ramon, E.E. Alonso & E.E. Romero Department of Geotechnical Engineering and Geosciences, UPC, Barcelona, Spain
ABSTRACT: The elastoplastic compressibility model developed by Oldecop & Alonso (2001) describes rockfill behaviour by means of a few constitutive parameters. Rockfill behaviour depends markedly on particle breakage. Therefore, grain size distribution is expected to control macroscopic behaviour. The purpose of the work developed was to relate specific features of the grain size distribution to changes in constitutive parameters. Experimental work was performed on compacted gravel specimens having different gradings. It was found that grain size uniformity leads to an increasing compressibility and collapse potential. However, elastic parameters and the ratio of the creep index, λt to total compressibility (λi + λd0 ) were not affected by changes in grain size distribution. It was also found that changes in grain size distribution, due to particle breakage, were insufficiently described by the well known indices of Marsal & Hardin.
1
INTRODUCTION
Rockfill mechanical behaviour has some particular features of behaviour such as the development of longterm deformations and collapse strains induced by the increase of humidity. These phenomena are related to particle breakage, which is influenced by the stress level and the action of water. Grain-size distribution is the relevant information. It controls the contact stress level between the rockfill particles and, therefore its probability of breakage. Since rockfill is a granular material constituted by rock particles with a diameter varying between 0.5 to 1.5 metres in practice, it is not possible to test samples of rockfill in a real scale. An alternative is to understand the effect of the grain-size distribution and extend this knowledge to the real situation. The study reported here focuses on investigating the influence of the particle gradation, the addition of a fine fraction and the size effect associated with grain distributions having a common degree of uniformity. A program of oedometer tests was carried out on gradings having different uniformity coefficients and different contents of fine fraction (0.5–0.075 mm) which may reach up to 11% in weight. Gradings with different D50 values were also tested. The interpretation of the tests was performed using the elastoplastic model for rockfill compressibility developed by Oldecop & Alonso (2001). The paper is organized as follows: First, the reference elastoplastic compressibility model for rockfill is briefly described. Then, the test programme carried out, the testing procedures and the main results are described. Several relationships between
model parameters and some grading indices are discussed. Finally, the main conclusions of the study are summarized. 2
REFERENCE MODEL
Figure 1 summarizes the compressibility model. σ is the normal stress applied and ε is the total vertical strain. The model considers two mechanisms producing plastic strains: under dry conditions (at a certain relative humidity) the instantaneous deformation
y
Dry i
Humid collapse i+ d
Figure 1. Isotropic stress—strain behaviour of rockfill. (Oldecop & Alonso, 2001).
341
- ε = λt · ln t t r + ε r
(1)
where t r , εr is a reference point in the time plot.
3
100
80 Percent finer by weight
mechanism (IDM) takes place; under saturated conditions, and beyond a threshold total stress value that defines the onset of particle breakage, σY , the time-dependent deformation mechanism (TDM) is activated. Also a linear strain-stress relationship is assumed for unloading-reloading paths. In the tests performed, strains were recorded in time for each loading step and a creep index, λt was determined. λi , λd0 , κ, χ and λt are the model parameters used to investigate the effect of grain size. λi defines the slope of the linear compression line during IDM, λi + λd0 describes the slope of the normal compression line, under saturated conditions, when both IDM and TDM are active. λi values were obtained from the plot of the strain against vertical stress for each dry oedometer test, whereas the combined value of parameters λi + λd0 was derived from the loading path under saturated conditions. Parameter κ describes the slope of the unloading-reloading path on the strain-stress space, and it has been obtained from the unloading increments of the oedometer tests. χ describes the slope of the existing linear relationship between collapse strains and the logarithm of suction during wetting of the sample, Oldecop & Alonso (2001). Total suction is derived from RH measurements using the psychrometric relationship. The creep index, λt , is given by the expression 1
60
40 M1 M3 M5 M7
20
0 10
Testing procedures The tested material was a quartzitic shale from a Pancrudo River outcrop (Aragón, Spain). After crushing to appropriate particle sizes, four different grain size distributions (gradings M1, M2, M3 and M4) were prepared and adapted to mathematical expressions. Several samples, 1550 grams each, were prepared. Gradings were characterized with different uniformity coefficients and different contents of the fine fraction. Their accumulated grain size distribution curves are shown in Figure 2 and their principal characteristics are summarized in Table 1. Grading M5 has the higher content of fines of all the specimens tested (11% in weight). It has the same accumulated grain size distribution as specimen M1, for the fractions in excess of D50 . Grading M7 has a lower D50 dimension than the other specimens tested. It was defined by means of a constant displacement of the M3 grading density curve. Ramon (2006) provides a detailed description of the experimental work performed.
0.1
Figure 2.
Grain size distributions tested.
Table 1.
Characteristics of tested gradings.
M1 M3 M5 M7
0.01
D50
Dmax
Dmin
mm
mm
mm
Dmax / Dmin
D60 / D10
7.5 7.5 7.5 5.62
20 10 20 8
1 2 0.075 0.12
20 5 266.67 66.67
5.25 2.08 11.05 2.72
Table 2.
EXPERIMENTAL WORK
1 D (mm)
Identification of tests performed.
Dry tests
Saturated tests
Compaction tests
Test
Grading
Test
Grading
Test
Grading
EP 1 EP 3 EP 5 EP 7
M1 M3 M5 M7
EP 2 EP 4 EP 6 EP 8
M1 M3 M5 M7
PC 1 PC 3 PC 5 PC 7
M1 M3 M5 M7
Table 2 summarizes all the tests carried out. Two oedometer tests were performed for each grading in a Rowe-type cell specially adapted for granular materials. Samples were 152 mm in diameter and approximately 50 mm in height. The granular material was initially equilibrated during 24 hours under the laboratory controlled atmosphere, (50% RH and T = 22◦ C). Before compaction, a double layer of polythene with silicone grease inside was placed between the rockfill sample and the inner lateral wall of the oedometer cell in order to reduce the lateral friction during the test. The sample was compacted inside the oedometer ring in two layers, equal in weight, using a Marshall hammer. This hammer has the benefit of
342
Test results Vertical strains were registered with time during each loading increment. Figure 4 shows the time records of deformation for test EP3. The collapse deformation due to the flooding of the sample is also included. A rapid increase of deformation was observed in all the tests after the
application of each load increment, followed by a long-term deformation in time without apparent stabilization. This type of behaviour has already been observed by others (Marsal, 1973; Sowers et al., 1965;
0
0.2
Vertical stress (MPa) 0.4 0.6 0.8 1.0
(%)
EP1 EP3 EP5 EP7
0 2 4 6 8 10 12 14
0
0.2
0.4
Vertical stress (MPa) 0.4 0.6 0.8
0.8
1.0
1.2
Figure 5. Oedometer tests. Vertical strain against vertical stress for (a) the ‘‘dry’’ tests, (b) the saturated tests.
0.2
Vertical stress (MPa) 0.4 0.6 0.8 1.0
1.2
3.55E-04
1.0
1.2
v (%/min)
(%)
0 2 4 6 8 10 12 14
0.2
0.6
EP2 EP4 EP6 EP8
0
0
1.2
0 2 4 6 8 10 12 14
(%)
transmitting the energy to the material through a fixed surface, avoiding a direct impact to the rock particles and the resulting intense breakage of the layer surface. The total compaction energy applied corresponds to the Normal Proctor test (584.3kJ/m3 ). The pair of oedometer tests performed for each grading consists of: 1) a loading oedometer test under dry conditions followed by an induced collapse, at a constant stress level, flooding the sample (tests EP1, EP3, EP5 and EP7), and 2) a saturated oedometer test (tests EP2, EP4, EP6 and EP8). Stresses were applied in increments by means of pressurized air against the top of the upper platen. Each loading increment lasted 24 hours, a long enough time to allow the establishment of a stable creep trend. The maximum pressure reached was 1.1 MPa, and it was followed by wetting of the sample (on the dry tests) and a final unloading. Figure 3 shows plots of vertical strain against vertical stress from two typical dry and saturated tests on the same grading.
2.55E-04 1.55E-04 5.50E-05 –4.50E-05
EP7 Dry test EP8 Saturated test
Saturated tests
Dry tests
Figure 6. Time-dependent strain rate for oedometer dry tests (broken lines) and saturated tests (solid lines).
Figure 3. Loading and unloading during dry (EP7) and saturated (EP8) oedometer tests.
0.1
1
+Patm(Mpa) 10 100
1000
collapse (%)
0 1 2 3 4 5
M1 M3 M5 M7
6 Figure 4. Vertical strains vs. time during consecutive loading increments in the non saturated oedometer test EP3.
Figure 7. Collapse strain plotted against total suction under a vertical stress of 1.1 MPa (tests EP1, EP3, EP5 and EP7).
343
Nobari & Duncan, 1972; Oldecop & Alonso 2001; Montobbio, 2001). Figure 5 shows plots of vertical strain against vertical stress for the eight oedometer tests carried out. The plotted values correspond to the vertical strain measured 24 hours after the application of the loading increment. Table 3.
Initial and final water content of tested samples.
Final water content at the end of the test Test
Final water content (%)
Test
Final water content (%)
EP 1 EP 2 EP 3 EP 4
8.04 8.57 6.14 5.86
EP 5 EP 6 EP 7 EP 8
8.13 7.77 7.08 6.12
Initial water content
0.59
Percent finer by weight
100
Initial EP 2 Post Compacted M1 Final EP2
80
60
4
GRAIN SIZE DISTRIBUTION AND CONSTITUTIVE PARAMETERS
40
20
0 10
D50 (mm)
The time-dependent strain rate, v, was obtained at the end of each loading increment; it was derived by means of a linear regression slope adjusted to the record from 100 minutes to 1440 minutes (with respect to the instant of load application). Results are shown in Figure 6 for all dry tests (broken lines) and saturated tests (solid lines). The strain rate increases with the applied stress. Figure 7 shows plots of collapse strain against total suction for the four different gradings. The measured water content at the end of the oedometer test is indicated in Table 3. Given these values and the water retention curve of the rock provided by Oldecop & Alonso (2001), it was checked that all rock particles were saturated at the end of the tests. Particle breakage induced during oedometer loading was also investigated. The grain size distributions at the end of the tests were obtained as well as the grain size distribution at the end of the compacting processes (tests PC1, PC3, PC5 and PC7; see Table 2). Figure 8 shows plots of the original prepared grading M1, the grading at the end of the compaction process on M1 (PC1) and the grading at the end of the saturated oedometer test EP2. Results indicate that particle breakage occurs both during the compaction process and during the oedometer test. However, it was difficult to derive a clear relationship between the evolution of D50 and the applied work.
1 D (mm)
0.1
8 7.5 7 6.5 6 5.5 5 4.5 4
0.01
M1 M3 M5 M7 0
0.2 0.4 0.6 Applied energy (MPa)
0.8
Figure 8. (a) Specimen M1. Original grading, grading at the end of the compaction process and grading at the end of the oedometer test EP2, (b) evolution of D50 due to the energy applied.
Parameters λi , λd0 , κ, χ and λt , were obtained from the set of oedometer tests described; the main results are summarized in Table 4. Figure 9 and Figure 10 show, respectively, plots of λi and λd0 against the ratio of maximum and minimum particle dimensions in the tested grading (Dmax /Dmin in log scale) for the four non saturated oedometer tests and the four saturated oedometer tests performed. λi and λd0 decreased with the ratio Dmax /Dmin and a quasi linear relation fits the data. Both plots provide the sequence from the more compressible grading to the less compressible grading: M3, M1, M7 and M5. It seems that the IDM and the TDM are controlled by the grading size distribution in a similar manner. Grading M3 was more compressible than grading M1. This is explained by the uniform grading of M3, which implies larger contact forces and a higher probability of particle breakage. In contrast, the continuous distribution of M1 results in an increased number of contacts, reduced contact forces, more limited particle breakage and increased stiffness. Marsal (1973) also observed that more uniform gradings produced more particle breakage.
344
Table 4.
Compressibilty model parameter values of the tests carried out.
Test
λi (MPa−1 )
EP1 (dry) EP2 (saturated) EP3 (dry) EP4 (saturated) EP5 (dry) EP6 (saturated) EP7 (dry) EP8 (saturated)
0.0305 0.0305 0.04196 0.04196 0.02482 0.02482 0.02921 0.02921
λi + λdo (MPa−1 )
λdo (MPa−1 )
0.06653
0.03603
0.08836
0.04641
0.04481
0.01999
0.05849
0.02928
M1
0.03
M7
(MPa–1)
i (MPa–1)
M3
0.04
M5
0.02 0.01 0.00 1
10 Dmax/Dmin
100
1000
0.06 od (MPa–1)
M3 M1
0.04
M7
0.03
M5
0.02 0.01 0.00 1
10 Dmax/Dmin
100
0.008 0.007 0.006 0.005 0.004 0.003 0.002 0.001 0
1000
Figure 10. Compressibility parameter λd0 from the non saturated oedometer tests.
Grading M1 was, in turn, more compressible than grading M5. Grading M5 has a higher fine fraction than M1. It is interpreted that the fine particles of grading M5 were filling the interparticle voids, allowing a better uniform distribution of the external load among particles and hence lower stress levels were concentrated on the individual particle contacts. Also, the more compressible nature of grading M7 with respect to the behaviour of grading M5 was consistent with the previous explanations because of the better gradation and the higher fine content of grading M5 with respect to grading M7.
0.00821 0.00872 0.01229 0.01211 0.00569 0.00499
0.00739 0.00488 0.00333
M3 M1 M5 M7
1
Figure 9. Compressibility parameter λi from the non saturated oedometer tests.
0.05
χ (MPa−1 ) 0.00581
0.06 0.05
κ (MPa−1 )
10 100 Dmax/Dmin
1000
Figure 11. Parameter χ plotted against ratio Dmax /Dmin for the analysed grain size distributions.
Figure 2 shows that grading M7 was nearly parallel to grading M3 for the fractions larger than D50 . It also has a higher fine content than grading M3. Since grading M3 has bigger particles than grading M7, there can be more defects in their particles that could develop the onset of a fracture; this fact, added to the existence of a lower fine content in grading M3, may explain why it was more compressible than grading M7. Montobbio (2001) also reached similar conclusions. The comparison of the response of gradings M1 and M7 suggests that the higher fine content and smaller particles of M7 resulted in a more rigid behaviour. This result is better appreciated in the saturated tests. Figure 11 shows the variation of χ parameter against the ratio Dmax /Dmin . The collapse deformation induced by sample flooding at some stress level is a result of particle breakage and therefore, it was logical to obtain relations between χ and grading similar to the changes in compressibility indices with grading (Figure 11). The values of parameter κ are shown in Figure 12. It appears that the grading distribution had no significant influence on rockfill elasticity; in fact no definite trends were observed between κ and the ratio Dmax /Dmin for the tested specimens during unloading. Time-dependent strain rates plotted in Figure 6 were higher for the more compressible gradings. It was
345
(MPa–1)
0.020 0.015
M5 dry M3 sat. M3 dry M7 dry M7 sat.
0.010 0.005
M5 sat.
0.000 0
Figure 12.
50
100 150 Dmax/Dmin
200
250
300
Values of parameter κ for the tests performed.
Table 5. Ratio of the creep index, λt to total compressibility (λi + λd0 ). Dry conditions λt
/λi
Test
%
EP1 EP2 EP3 EP4 EP5 EP6 EP7 EP8
2.08
Saturated conditions λt /(λi + λd0 ) % 1.60
1.06 1.56 1.59 1.24 1.80 1.42
obtained that the ratio between the creep index parameter λt and the compressibility parameters was nearly constant, and varies from 1.4 × 10−2 to 2 × 10−2 in percentage. Table 5 summarizes the values found in all tests performed. Hardin and Marsal parameters were obtained for all the oedometer tests in order to quantify the particle breakage due to the applied loading path. They were derived considering that the post compacted grading distribution was the initial grading, in order to isolate the effect of the oedometer loading. The analysis indicated that tests exhibiting a higher particle breakage (according to the indices) did not correspond to the more compressible tests. The Hardin index, in particular, quantifies particle breakage by means of the variation in the area below the accumulated grading curve; therefore this index is not useful to compare particle breakage between gradings having different shapes of the accumulated grain distribution curve. 5
controlled by the rockfill grading distribution. The principal aim of the reported research has been the study of the effect of the grading distribution on rockfill behaviour, focusing on the effect of the degree of uniformity of the grain size and the influence of the fine fraction. A programme of oedometer tests have been performed on samples following four different gradings. Strains during each load increment and collapse deformations have been measured. Rockfill response has been described in terms of five parameters which characterize the elastoplastic compressibility model developed by Oldecop & Alonso (2001). The results indicate that gradings with a higher uniformity have a more compressible behaviour and enhanced collapse deformations than well graded distributions when they have in common the D50 dimension. In the case of gradings with the same degree of uniformity, a smaller D50 dimension means a less compressible behaviour and a reduced collapse deformation. It has been observed that the addition of a fine fraction favours the increase of stiffness even in the case of well graded materials. Rockfill deformations are a result of particle breakage. Two factors related with the particle breakage have been considered to understand the obtained results: the concentration of high stress levels on contacts and the defects or flaws contained in rockfill particles. Well graded distributions result in more contact points among particles than uniform gradings. Also, increasing the fine fraction means an increase in the number of contacts between particles and a more uniform distribution of contact forces. A larger number of defects are more likely in bigger particles and this explains the more compressible behaviour and collapse deformations observed in samples with larger D50 (for a similar coefficient of uniformity). It appears also that the elastic (unloading/reloading) behaviour of rockfill is not affected by the grain size distributions analyzed here. It has been observed that poorly graded samples exhibit a higher time-dependent strain rate. This is a trend observed also for the compressibility of the specimens tested. It has also been found that the ratio between λt and the compressibility parameter is nearly constant for all the tests performed. The development of particle breakage due to the oedometer tests performed was also investigated. It was found that Hardin and Marsal indices could not be related in a consistent manner with the compressibility observed in tests.
CONCLUSIONS ACKNOWLEDGEMENTS
Rockfill structures accumulate permanent deformations in time and develop collapse when they are wetted. These deformation characteristics are
The first author acknowledges the support of the ‘‘Comissionat per a Universitats i Recerca del
346
Departament d’Innovació, Universitats i Empresa’’ of the ‘‘Generalitat de Catalunya’’ and the European Social Fund. REFERENCES Marsal, R.J. 1973. Mechanical properties of rockfill. Embankment Dam Engineering. Casagrande Volume. Hirschfeld, R.C. & Poulos, S.J., eds. John Wiley & Sons. Montobbio, D. 2001. Influencia de la granulometria en la compresibilidad de las escolleras. Graduate thesis. UPC.
Nobari, E.S. & Duncan, J.M. 1972. Effect of reservoir filling on stresses and movements in Herat and rockfill dams. Department of Civil Engineering. Report No. TE-72–1. University of California. Oldecop, L.A. & Alonso, E.E. 2001. A model for rockfill compressibility. Géotechnique, 51 (2), 127–139. Ramon, A. 2006. Efecte de la granulometria en el comportament d’esculleres. Graduate thesis. UPC. Sowers, G.F., Williams, R.C. & Wallace, T.S. 1965, Compresibility of broken rock and settlement of rockfills. Proc. 6th ICSMFE, Montreal, 2, 561–565.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
The influence of suction on stiffness, viscosity and collapse of some volcanic ashy soils E. Bilotta, V. Foresta & G. Migliaro Department of Civil Engineering, University of Salerno, Fisciano, Italy
ABSTRACT: This study focuses on the mechanical characterization of the volcanic ashy soils (silty sands) covering the Pizzo d’Alvano massif (Campania Region). Frequently, they are in unsaturated condition with significant suction values, due to the finer portion of their grain size distribution, that strongly influences their mechanical behaviour. The structure of undisturbed samples is the result of their air-fall origin with an open configuration (metastable structure) that induces collapse when saturation occurs. On the contrary, the remoulded material shows a more stable structure. However, these soils show a remarkable creep behaviour and therefore significant secondary settlements. In this work, the experimental data obtained by means of tests performed on unsaturated samples are discussed. The results obtained in a wide range of practical stress level indicate that beside suction, also the initial specific volume of the soil and the overburden pressure influence the magnitude of both time-dependent and collapse settlements. 1
INTRODUCTION
2
Ashy soils represent a remarkable portion of the unsaturated pyroclastic cover that can be found in Campania Region (Southern Italy). Such cover derives from the Somma—Vesuvius volcanic activities both as primary air-fall deposition and as debris colluvial deposition. Frequently, rapid flow type movements triggered by particular intense meteoric events involve pyroclastic soils. The periodic occurrence of depositional events from landslide phenomena is highlighted by the presence, at the toe of the valleys, of alluvial fans of various ages superimposed onto older debris deposits. The soils constituting the older deposits are frequently used in the construction of structures founded or realized with them such as road embankments. The design of suitable works as well as a correct stability analysis aimed at flowslides modelling need a thorough understanding of the mechanical behaviour of the abovementioned soils. To this aim, in situ (Sorbino & Cascini 2002) and laboratory investigations (Bilotta & Foresta 2002, Sorbino & Foresta 2002, Bilotta et al. 2006) were started and they are still in progress at University of Salerno (Italy). The main objective of the research presented in this paper is focused on the investigation of the stress-strain response under two different stress paths (oedometric and triaxial) of both undisturbed and remoulded samples. The influence on compressibility (stiffness, viscosity and collapsibility) of the initial suction (s) and initial specific volume (vini ) of the soil were investigated.
EXPERIMENTAL PROGRAMME
2.1 Tested materials Laboratory tests were performed on a non-plastic ashy soil (Bilotta & Foresta 2002); its main physical properties are summarized in Table 1 and Table 2. This material, in undisturbed state (air-fall deposition), is characterized by a high value of νini and by a metastable structure. These features are caused by its air-fall deposition. On the contrary, remoulded samples (alluvial deposition) show a νini lower than undisturbed materials (Table 2). Table 1.
Composition of tested soils. Clay
Silt
Sand
Gravel
Grain size distribution
%
%
%
%
Upper bound limit Lower bound limit
4.7 1.4
53.6 40.9
40.6 51.3
1.1 6.4
Table 2.
Average index properties of tested soils. Gs
vini
Soil state Undisturbed Remoulded
349
2.549 2.552
3.595 2.982
Sr
γd
%
kN/m3
74.8 92.1
6.93 8.65
Remoulded samples were prepared by hand mixing material at natural water content with distilled water in order to form a slurry with 1.5wL initial water content. This slurry was then statically compressed in a large consolidometer under an effective vertical stress of 10 kPa. The consolidated soil was initially air dried for one day and then used to sample the test specimens.
2.2
Type of performed tests
Different tests were performed to investigate the stressstrain response of the materials. The suction was imposed by the axis translation technique. The layout of the controlled suction apparatuses used in this work is reported by Aversa & Nicotera (2002). The suction equalization stages (either directly caused by changing the suction or indirectly induced as a consequence of loading) were controlled by monitoring the water volume change of the specimens (Fig. 1). It was assumed that the equilibrium was achieved when the rate of water volume change, expressed by εw (Fig. 1) was sufficiently low (about 0.004 log(min)−1 ). Oedometer tests with control of suction were performed to study compressibility, creep and collapsibility. Specimens with diameter of 56 mm and 20 mm high have been tested at several values of suction (0 kPa, 30 kPa, 50 kPa, 100 kPa, 150 kPa, 200 kPa). Vertical stresses ranging from 5 kPa to 2400 kPa were applied both for 24 hours and for 240 hours. A minimum time of 24 hours was selected to ensure the equalization of the water content change induced by loading (Fig. 1b). Collapsibility of the soils was also investigated by triaxial tests with control of suction. Specimens with diameter of 68 mm and 70 mm, respectively 136 mm
time (min) 0.1
1
10
100
0
1000
10000 0
a) -0.05
3.1 Viscosity properties of tested soils The creep behaviour of these material was in part already highlighted in a previous paper (Bilotta et al. 2006). Additional results obtained by performing long term creep tests with 240 hours load permanence are shown in Figure 2. In the figure Δεv represents the difference between total vertical strain and primary consolidation strain that occurs at the end of primary consolidation (teop ). This behaviour was interpreted by using the non-linear creep function proposed by Yin (1999). Such a function, represented with dashed line in Figure 2, was later used to evaluate long term time (min)
-0.01
-0.15
-0.015
0
0
b)
1.0E+00
= V/V
time (min)
1.0E+04
- 0.01
water phase solid phase
1.0E+06
1.0E+08
t load = 10 days
- 0.02
5
-0.03
-0.05
1.0E+02
- 0.00
-0.05
-0.02
-0.04
TEST RESULTS
v
= Vw / V w
3
-0.005
-0.1
-0.01
and 140 mm high, have been tested under suction ranging from 0 kPa to 50 kPa and mean net stress (p − ua ) varying between 10 kPa and 477 kPa. A stress controlled rate of 2.5 kPa/h was chosen to obtain a constant suction loading for both the isotropic and anisotropic tests. The suction equilibrium was checked by monitoring the pore water pressure variation for a time of about 24 hours at the end of the loading stage. In this time, small increase (about 1 kPa) of pore water pressure was registered in respect to the imposed target value. This last circumstance is imputable to the creep deformation of the material. The collapsible behaviour of these soils was studied performing, in both oedometer and triaxial apparatuses, particular tests referred as ‘‘collapse tests’’ in the following. In these tests the specimens were initially subjected to an imposed suction value. After the equalization of the imposed suction was reached, the specimens were compressed either in multiple steps (oedometer tests) or with constant stress rate of 2.5 kPa/h (triaxial tests), until a prefixed stress level. At this point, the suction was reduced, from the initial value to 0 kPa, either gradually in multiple steps (oedometer and triaxial tests) or suddenly by flooding the specimens (in oedometer tests only).
-0.1
- 0.03
-0.15
- 0.04
Figure 1. Examples of equalization stages in oedometer tests: (a) during an imposed suction variation; (b) after a load variation.
t eop
24 hours
240 hours
100 years
Figure 2. Comparison between measured data and fitted curve for a vertical stress of 160 kPa and teop = 2 min.
350
C (mm/log(min))
stiffness of the investigated soils. The final slope of experimental data, commonly denoted by coefficient of secondary consolidation (Cαε ), is represented with a continuous line in the same graph. It appears that a more realistic prediction of the secondary deformation can be performed by using Yin’s model as the curves show a non linear trend of creep strain (Δεv ) with the logarithm of time. However, in this section, the linear creep coefficient (Cα ) was used in order to easily represent the influence of νini , suction and stress levels on the viscous properties of the investigated ashy soils. Figure 3a shows, for undisturbed saturated specimens, a non linear trend of Cα with the logarithm of the effective vertical stress with a maximum average value of 0.11 mm/log (min) for stress level exceeding 300 kPa. On the contrary, for remoulded saturated specimens an almost linear trend of Cα with the logarithm of the stress level can be observed. The values of vertical stress adopted in the performed oedometer tests are reported in Table 3.
(a)
v ini = 3.617 ± 0.076
I;
0.2
Rm; vini = 3.005 ± 0.030
0.15 0.1
Initial stress Final stress Mean stress value value values Line n# Symbol kPa [1] [2] [3] [4] [5] [6] [7]
♦ <*>
− +
19.1 36.9 87.9 160.4 298.1 599.9 1193.1
kPa
kPa
36.9 87.9 160.4 298.1 599.9 1193.1 2379.6
28.0 62.4 124.2 229.3 449.0 896.5 1786.4
The curved shape of the Cα − s relationship at various stress levels (numbers in brackets in Fig. 3b, c)—furnishes Cα values decreasing with the increasing suction for stress levels lower than 600 kPa (Fig. 3b, c). For undisturbed specimens such a trend disappears at stress levels higher than 600 kPa. For remoulded specimens the above mentioned trend is less marked, independently of the stress level (Fig. 3c). Comparing Figure 3b and Figure 3c, at the same stress level, it is possible to note that Cα values for remoulded specimens are lower than those attained by undisturbed specimens. This observation seems to suggest a reduced effect of suction on Cα in remoulded material. 3.2 Short and long term stiffness of tested soils
10
100
1000
10000
The results of confined compression test conducted by using a controlled suction oedometer are used to show the influence of the initial void ratio, νini , the suction, s, and the stress level on the stiffness of soils. Short and long term compressibility is described by means of two different parameters: immediate oedometric modulus (Eimm ) and total oedometric modulus (Etot100 ). The modulus Eimm was calculated as reported in Equation 1:
'v (kPa)
C (mm/log(min))
Vertical stress adopted in oedometer tests.
0.05 0
0.16 0.14 0.12 0.1 0.08 0.06 0.04 0.02 0
(b)
Undisturbed samples "I"
[7] [5] [4] [3] [2] [1]
-10
0
10
20
30
40
50
s = ua
C (mm/log(min))
Table 3.
Eimm =
(c)
Remoulded samples "Rm"
0.1
60
w (kPa)
[7]
0.08 0.06
[5] [4]
0.04
[3]
0.02
[1]
[2]
0 -50
0
50
100
150
s = ua
200
250
w (kPa)
Figure 3. Trend of linear creep coefficient (Cα ), for remoulded and undisturbed specimens, (a) with effective vertical stress, (b, c) with suction and vertical stress applied.
Δσν | Δεc |
(1)
where σν = σν(i+1)−σνi is the net vertical stress variation; εc = (Hc(i+1) − Hci )/Hci is the primary consolidation strain corresponding to the stress interval σν and Hc represents the height of the specimens at the end of primary consolidation. Figure 4 shows, for saturated specimens, the variation of the modulus Eimm as a function of νini at different stress levels (line marked with numbers in brackets). As it can be noted, the modulus Eimm increases as far as νini decreases. A negative exponential law was found to be adequate to interpolate experimental data.
351
30 25
Eimm (MPa)
The increment of the modulus Eimm can be up to 5 times the corresponding saturated value, depending on the stress level. The long term stiffness modulus Etot100 was calculated as reported in Equation 2.
E imm = a + b ×exp ( vini ) 2
[7]
0.928 < R < 0.976
20 [6]
15 10 5
[2]
Etot100 =
[5] [4] [3] [1]
0 2.5
3.0
3.5
4.0
initial specific volume vini
Eimm (MPa)
Figure 4. Immediate oedometric modulus (Eimm ) trend with initial specific volume and vertical stress level.
(a)
Undisturbed samples
18 14 10 6 4
[7] [6] [5]
3 -10
0
10
20
30
40
30
40
[3] [2] [1] 50 [4]
s = ua - uw (kPa)
2
Δσν |Δεtot |
(2)
where εtot = (Hdef − Hci )/Hci , is the total strain corresponding to the stress interval σν and Hdef is the height of the specimens calculated as difference between Hc and the creep settlement evaluated at a time of 100 years by using Yin’s model (Yin, 1999). Figure 6 shows the variation of the modulus Etot100 , under various stress levels (Table 3), as a function of νini (Fig. 6a) and suction (Fig. 6b, c). As already observed for the modulus Eimm , Etot values increase as νini decreases and suction increases. Figure 6b highlights a marked variation of the modulus Etot , as suction increases, for vertical stress not exceeding 300 kPa. On the contrary, the remoulded specimens exhibit a lighter increase of the modulus Etot (Fig. 6c). However, as expected for the viscous behaviour of the tested soils, the modulus Etot is generally very small if compared with the modulus Eimm (Figs 6c, 5c).
1
3.3 Collapsibility
0 -10
0
10
20
imm Eimm E(MPa)
s = ua Remoulded samples
25 20 15
50 60 w (kPa)
(b) [7]
-50
0
50
100
150
200 [6]
s = ua
10 [5] [4] [3] [2] [1]
5 0 -50
0
50
100
150
s = ua
200 250 w (kPa)
Figure 5. Trend of the immediate oedometric modulus Eimm with the applied suction and the vertical stress level.
The variation of the calculated modulus Eimm with the applied suction is shown in Figure 5a, b for undisturbed and remoulded specimens respectively. Up to a certain value of the overburden stress at the end of the load increment, the modulus Eimm increases with suction. The threshold values are respectively 300 kPa (line 4 in Fig. 5a) for the undisturbed specimens and 1193 kPa (line 6 of Fig. 5b) for the remoulded ones. Above such thresholds, the influence of suction seems to be negligible.
It is well known that a more complete investigation of the collapse behaviour of soils must be performed by using different types of testing procedures (Vilar & Davies, 2002). Controlled suction triaxial tests are more time consuming than oedometer tests due to the size of the specimens (see section 2.2). For these reasons, the collapsible behaviour of the investigated soils was mainly studied by using controlled suction oedometer tests. Some preliminary tests were also carried out in triaxial apparatus, with the aim of checking if compression stress paths different from confined ones (oedometer) lead to substantial effects on the magnitude of collapse. A series of tests were interpreted by using the double oedometer procedure. A number of similar specimens, approximately with the same νini were tested. One was saturated by flooding at the beginning of the test while the others were kept under an imposed value of suction. All of them were compressed, in multiple steps, up to a maximum stress level of about 2400 kPa. The difference of vertical deformation between the specimens with imposed suction and the flooded specimen (referred as εcoll in Fig. 7) can be attributed to the soil collapse. As it can be observed from the figure, the magnitude of collapse is a function of both the suction level and the value of νini . In particular, for undisturbed specimens (Fig. 7a), a maximum collapse of 9% is attained
352
Etot 100 (MPa)
20 18 16 14 12 10 8 6 4 2 0
(a) Etot 100 = c + d ⋅ exp ( vini)
[7]
2
0.947 < R < 0.990
-0.02
Etot 100 (MPa)
10
100
1000
- ua (kPa) 10000
coll -0.04 -0.06
[2]
[5] [4] [3] [1]
3.0
3.5
0
10
20
v ini = 3.626 ± 0.076
(b)
Remoulded samples
v
10
100
1000
- ua (kPa) 10000
coll -0.02
[7]
s = 50 kPa
-0.03 [6] [5]
s = 100 kPa
-0.04
v ini = 2.954 ± 0.039
s = 150 kPa -0.05
s = 200 kPa
Figure 7. Results of double oedometer tests performed on undisturbed and remoulded specimens.
30
40
50
s = ua 18 16 14 12 10 8 6 4 2 0
-0.1 0.01
s = 50 kPa
0
[3] [2] [1]
-10
s = 30 kPa
-0.01
(b)
Undisturbed samples 13 11 9 7 5 3 1 2.5 2 -100102030405060 s = ua - uw (kPa) [4] 1.5 1 0.5 0
-0.08
4.0
initial specific volume vini
Etot 100 (MPa)
v
0
[6]
2.5
Etot 100 (MPa)
(a)
Undisturbed samples
0.02
Remoulded samples
60 w (kPa)
10
1000
σv - ua (kPa) 10000
0
(c)
[5] [4]
100
lower bound limit
[7]
-0.02
[6]
-0.04
upper bound limit
εcoll
[3] [2] [1]
-0.06 s = 50 kPa -0.08
-50
0
50
100
150
200
s = ua
250 w(kPa)
-0.1
Figure 6. Trend of the total oedometric modulus Etot100 (a) with the initial specific volume and the vertical stress level, (b, c) with the applied suction and the vertical stress level.
Figure 8. mens. Table 4.
in correspondence to a stress value of 160 kPa. After this stress level, the collapse tends to decrease as the overburden stress increases. A similar trend is shown in Figure 7b for remoulded specimens. For these last ones a maximum collapse of about 4% is attained for a vertical stress of 600 kPa and a suction of 200 kPa. The experimental data obtained by collapse tests are shown in Figure 8. These tests were performed on undisturbed specimens subjected to initial suction of 50 kPa. Such specimens, as already mentioned in section 2.2, were loaded until a target stress value was reached. At this time, the suction was reduced in two manners: either by suddenly flooding the specimens with distilled water (type test 2 in Table 4) or gradually reducing the initial suction by increasing the pore
Results of collapse tests on undisturbed speci-
Type of collapse tests performed.
Symbol Apparatus Type test vini
Stress path
•
k0 k0 isotropic 0.73 < η < 1
oedometer oedometer triaxial triaxial
1 2 3 4
3.172 ± 0.127 3.687 ± 0.091 3.318 ± 0.124 3.429 ± 0.088
water pressure at the base of the specimens (type tests 1,3,4 reported in Table 4). In this last cases, the initial suction was decreased in three steps, respectively with suction values of 20 kPa, 10 kPa and 0 kPa. The magnitude of collapse of the flooded specimens is in good agreement with the trend shown by the
353
calculated collapse curve for undisturbed specimens (double oedometer Fig. 7a). It is worth noting that the other experimental data (black squares in Fig. 8) show a collapse trend much closer to the calculated curve for remoulded specimens (double oedometer Fig. 7b). This last circumstance can be explained by looking at the average initial specific volume of these specimens, which value is closer to the average value of remoulded ones. These results highlight that the magnitude of collapse of this ashy soil is strongly influenced by the value of νini and the stress level. In Figure 8 the preliminary experimental data obtained in collapse tests carried out in controlled suction triaxial apparatus are also reported (type tests 3, in Table 4). The type test 3 were conducted in isotropic conditions while the type test 4 were performed with an obliquity value η = q/(p − ua ) ranging from 0.73 to 1. The collapse exhibited by the last specimens (η = 0) is of the same order of magnitude of that shown by the lower bound limit of the confined specimens (type test 1). This is true despite their average values of νini (3.429 ± 0.088). On the contrary, a different behaviour is shown by the isotropically compressed samples that exhibit negligible collapse values. Such results seem to suggest that the collapse magnitude is also dependent on the stress path performed, as already evidenced by Vilar & Davies (2002). 4
CONCLUDING REMARKS
In order to analyse the influence of suction on the stress-strain behaviour of ashy soils, experimental tests were performed through the use of triaxial and oedometer suction-controlled apparatuses. The results obtained on both undisturbed and remoulded specimens are summarized in the following points: – a maximum average value of Cα for the undisturbed specimens and a linear trend with the logarithm of the applied stress for the remoulded ones were founded; a reduced effect of suction on Cα was evidenced for the remoulded material; – the remoulded specimens exhibit immediate oedometric modulus (Eimm ) and long term stiffness
(Etot100 ) higher than undisturbed specimens. The modulus Eimm is strongly influenced by suction up to a threshold value of the applied overburden stress; the effect of suction on the variation of Etot100 is less marked for remoulded material; Etot100 can be used for a quick evaluation of long term settlements; – if the same conditions (stress level and suction) are considered, the magnitude of collapse is strongly influenced by either the initial specific volume of the material and the stress path performed. REFERENCES Aversa, S. & Nicotera, M.V. 2002. ‘‘A Triaxial and Oedometer Apparatus for Testing Unsaturated Soils,’’ Geotechnical Testing Journal, GTJODJ 25(1): 3–15. Bilotta, E. & Foresta, V. 2002. On the measured shear strength of some pyroclastic soils of Sarno mountains. Proceedings. of the 3rd International Conference on Unsaturated Soils, UNSAT 2002, 10–13 March, Recife, Brazil, 2: 495–500. Rotterdam: Balkema. Bilotta, E., Cascini, L., Foresta, V. & Sorbino, G. 2005. Geotechnical characterization of pyroclastic soils involved in huge flowslides. Geotechnical and Geological Engineering Journal 23: 364–402. Bilotta, E., Foresta, V. & Migliaro, G. 2006. Suction Controlled Laboratory Tests on Undisturbed Pyroclastic Soil: Stiffnesses and Volumetric Deformations. Proceedings of the 4th International Conference on Unsaturated Soils, UNSAT2006 (GSP 147), 2–6 April, Carefree, Arizona, USA, 1: 849–860. Cascini, L. & Sorbino, G. 2002. Soil suction measurement over large areas: a case study. Proceedings of the 3rd International Conference on Unsaturated Soils, UNSAT 2002, 10–13 March, Recife, Brazil, 2: 829–834. Sorbino, G. & Foresta, V. 2002. Unsaturated hydraulic characteristics of pyroclastic soils. Proceedings of the 3rd International Conference on Unsaturated Soils, UNSAT 2002, 10–13 March, Recife, Brazil, 1: 405–410. Rotterdam: Balkema. Vilar, O.M. & Davies, G.I. 2002. Collapse behavior analysis of a clayely sand using different testing procedures. Proceedings of the 3rd International Conference on Unsaturated Soils, UNSAT 2002, 10–13 March, Recife, Brazil, 2: 571–576. Yin, J.-H. 1999. Non linear creep of soils in oedometer tests. Géotechnique 49(5): 699–707.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Role of critical volumetric water content and net overburden pressure on swelling or collapse behavior of compacted soils I. Ashayeri, A. Shafiee & M. Biglari IIEES, International Institute of Earthquake Eng. & Seismology, Tehran, Iran
ABSTRACT: Swelling pressures of clay samples compacted at different values of initial void ratio and degree of saturation were measured using constant volume oedometer tests. In addition, volume change behaviour of compacted samples during wetting was investigated in oedometer tests under various overburden pressures. It was confirmed that collapse behaviour is not observed in samples with pre-wetting volumetric water content more than a critical value. Furthermore, for those samples with volumetric water content less than the critical value, good correlation is found between the volume change percent and the normalized overburden pressure (the pre-wetting overburden pressure divided by the corresponding swelling pressure of an identical sample).
1
INTRODUCTION
Volume change prediction of unsaturated soils is a matter of concern that will help geotechnical engineers to know the mechanisms which occur during saturation (wetting) or desaturation (drying) processes. Expansive and collapsible soils are given extra concern in the context of problematic soils due to the variety of behavior they have shown regarding their initial (prewetting) conditions. Meanwhile, swelling and swelling pressure of plastic clays have been investigated since the mid 20th Century. Holtz and Gibbs (1956) investigated effects of initial water content and dry density on swelling potential and swelling pressure (Figs. 1 and 2). Their results revealed that, both swelling percent and swelling potential generally decrease with increasing water content and increase with increasing dry density, but swelling pressure is more significantly influenced by dry density. Early investigations revealed swelling or collapse behavior of compacted soils is related to pre-wetting (not only as compacted) degree of saturation and overburden pressure (Lawton 1986). It is now well known that, even highly plastic clays can collapse if they form a relatively dry and open structure (i.e. metastable structure) and are subjected to large enough overburden pressure. (Barden et al. 1969 and Lawton et al. 1992). Mitchell (1976), introduced metastable structure as the availability of following conditions in the soil element • An open, partially unstable, unsaturated fabric • A high enough net total stress that will cause the structure to be metastable
• A bonding or cementing agent that stabilizes the soil in the unsaturated condition • The addition of water to the soil, which causes the bonding or cementing agent to be reduced and the interaggregate or intergranular contacts to fail in shear, resulting in a reduction in total volume of the soil mass Jennings and Burland (1962), performed some double oedometer tests to investigate limitations of effective stress definition in unsaturated soils and found Bishop’s effective stress fails to explain the
Figure 1. Effect of initial water content and dry density of swelling potential of compacted clay during wetting (after Holtz and Gibbs 1956).
355
Swelling Pressure (kPa)
600 400 200 0.8 0 1
0.7 0.8
0.6 0.6
0.4 Degree of Saturation
0.5
Void Ratio
0.2 0
0.4
Figure 3. Swelling pressure versus pre-wetting void ratio and degree of saturation.
Figure 2. Effect of initial water content and dry density of swelling pressure of compacted clay during wetting (after Holtz and Gibbs 1956).
volume change behaviour of compacted soils if the degree of saturation is less than a critical value, or in other words, samples with degree of saturation more than that critical value will not collapse during wetting. They stated that the critical degree of saturation varies with grain size characteristics. Lawton et al. (1992) found the critical degree of saturation varies with overburden pressure too and suggested that it approximately follows the line of optimum Proctor compaction test. Matyas and Radhakrishna (1968) proposed volume change behaviour of unsaturated soils to be expressed as a direct function of two independent stress components; applied stress and suction rather than in terms of a single effective stress. Fredlund and Morgenstern (1977) provided further theoretical and experimental justification for the use of two independent stressstate variables i.e. net stress (σ − ua ) and matric suction (ua − uw ) for unsaturated soils based on multiphase continuum mechanics . Additionally, recent investigations on modeling volume change behavior of unsaturated soils have shown that these two opposite behaviors (swelling and collapse) of specific clayey soil can be explained by two independent stress state variable of unsaturated soil element (Tadepalli and Fredlund 1991, Pereira and Fredlund 2000). The literature indicates that the volume change behaviour of compacted clays is affected by the soil structure which can be expressed by degree of saturation and void ratio of element just before wetting. Developed mechanics for unsaturated soils provide constitutive relations representing these variables in terms of two stress-state variables known as net normal
stress and matric suction (Fredlund 2006, Fredlund and Pham 2006). In the recent study volume change behavior of compacted clayey soils are investigated by performing several constant volume swelling pressure oedometer tests (named CVSPO) and constant overburden pressure volume change tests (named COPVC). Soil samples are prepared at different initial degree of saturation and void ratio and are tested at different overburden pressures. The samples experienced swelling when the overburden pressure was smaller that the swelling pressure of the sample. Similarly, the samples experienced collapse when the swelling pressure was smaller than the overburden pressure and the degree of saturation was smaller than the critical value. Swelling pressure of compacted clays is presented as a function of both pre-wetting degree of saturation and void ratio. Figure 3 represents the general swelling pressure state surface of compacted clays in 3D plot (data from Ashayeri & Yasrebi 2005). The aim of this study is to predict volume change behavior of compacted soil by knowing swelling pressure and applied overburden pressure. 2
MATERIALS AND TESTING PROGRAM
The material that has been used was medium plastic clay. The liquid limit of the clay soil is 42 percent, the plasticity index is 18 percent, the specific gravity of particles is 2.69 and from hydrometer analysis the clay size fraction (finer than 2 μm) is about 60 percent. The testing program includes 10 CVSPO tests and 38 COPVC tests. CVSPO tests were carried out on samples compacted to different values of void ratio and degree of saturation. In these tests the samples were allowed to saturate while keeping the volume of the sample constant by increasing overburden pressure
356
0.54 CVSPO tests (Swelling pressure in kPa) COPVC tests (Overburden pressure in kPa, Volume change percent)
0.56
w
0.58
(1280,-1.82%) Sp=500
0.60
Pre-wetting void ratio (e)
= 0.33
500
Sp=400 0.62
Sp=300 300 410 410
250
0.64
(1280,-5.03%) (1280,-6.47%)
0.66
(1280,-0.18%)
Sp=250
(320,0.08%)
0.68
Sp=160
210
(80,0.94%)
165
(160,0.25%)
(160,-0.47%)
0.70
(160,-0.73%)
130
(160,-1.17%) 0.72
(80,0.34%)
(320,-0.95%)
(160,-0.04%)
(80,0.75%)
Sp=100
100
0.74
70
70
96 %
10 0%
92 %
88 %
84 %
80 %
76 %
72 %
68 %
64 %
60 %
56 %
52 %
48 %
44 %
40 %
36 %
32 %
28 %
24 %
20 %
0.76
Pre-wetting degree of saturation (%)
Figure 4.
Summary of Results of CVSPO tests and some COPVC tests.
as much as required. The equalized pressure is known as the swelling pressure. The measured swelling pressures of these samples were used to approximate the equal swelling pressure lines in the e-Sr space. The results of CVSPO tests on pure clay samples are plotted on Fig. 4. The remaining 38 COPVC tests were also carried out on samples compacted to different values of void ratio and degree of saturation. In these tests the soil sample is compacted by applying specific overburden pressure to the pre-wetting void ratio and degree of saturation, then the sample is allowed to saturate by inundation and the volume change of the sample is recorded under the specific overburden pressure. Some of the results of COPVC tests are plotted on Fig. 4 in e-Sr space, the numbers in brackets are overburden pressure in kPa and volumetric strain (expansion positive), respectively. In addition, the results of CVSPO tests were used to try to correlate the volume change of samples in COPVC tests with the ratio of overburden pressure to swelling pressure. 3
DISCUSSION OF TEST RESULTS
As previously explained, CVSPO test results are used to obtain approximate contours of swelling pressure in e-Sr space. These contours are used to interpolate the
corresponding swelling pressure of 38 COPVC tests. Then the volume change percentages of 38 samples are plotted versus the normalized parameter of overburden pressure divided by swelling pressure of sample. This new plot is presented in figure 5. Good correlation is observed between the volume change percent and normalized overburden pressure except for a few samples which showed no collapse compression even though the values of normalized overburden pressure were relatively high. Inspection of these tests indicated that in all such cases the degree of saturation prior to wetting was high and the volumetric water content prior to wetting was correspondingly high. This led to the proposal of a critical value of pre-wetting volumetric water content, above which collapse compression would not occur on wetting, irrespective of the value of overburden pressure. The volumetric water content of selected samples is presented on figure 5. Two samples with volumetric water content around 0.39 have no volume change while the normalized overburden pressure of one is twice the other. The third sample with volumetric water content of around 0.33 has no volume change while the normalized overburden pressure is as high as 3.6. These results support the proposal that if the volumetric water content is more than a critical value the soil shows negligible volume change on wetting regardless of the overburden pressure. The critical volumetric water content seems to be about 0.33 for the clay soil used in
357
8%
6%
4%
V0/V
2% w=
w=
0.392
0.387
0% w=
0.328
-2%
-4%
-6%
-8% 0
1
2
3
4
5
6
7
8
9
10
(Pover)/Sp Figure 5. Correlation between normalized overburden pressure and volume change percent for samples with volumetric water content smaller than the critical value.
this investigation. The line of volumetric water content equal to 0.33 is plotted on figure 4. By using the concept of the soil water characteristic curve, that relates volumetric water content to matric suction, it could be stated that the critical volumetric water content corresponds to a critical value of suction. The volumetric water content versus total suction of the same material is presented by Biglari et al. 2008. The best fitting curve of the remaining COPVC test results is shown in figure 5 and is expressed by the following equation −b
V a(P − 1) = −b V0 P +c
(1)
where; P = Poverburden /SP is the normalized overburden pressure and a, b, c are the correlation parameters. The coefficient of correlation between laboratory measured values and values obtained from equation 1 is R 2 = 0.880 and the correlation parameters for the soil investigated in this study are; a = 0.0419, b = 1.1861 and c = 0.5544. Equation 1 satisfies the CVSPO tests that results no volume change when P = 1. Furthermore, in a free
swelling test where the overburden pressure is very small (i.e. 1 kPa) and the swelling pressure is as high as expected the P approaches zero and the parameter a expresses the volume change percentage of the sample. Similarly, in a collapse potential test where the overburden pressure is very high and the soil structure is as metastable as possible the fraction −a/c expresses the volume change percentage of the sample. The parameter b is the shape parameter and affects the curvature of equation 1. Since all three correlation parameters have physical meaning the following tests are suggested to obtain them 1. Free swelling test on highly compacted soil with initial water content approximately 2∼3 percent dry of optimum. 2. Collapse test on relatively dry sample under high overburden pressure where the normalized overburden pressure exceeds 10. 3. Some COPVC tests with corresponding CVSPO tests. When the correlation parameters of equation 1 are found one can approximate the volume change percent of the sample at various overburden pressures by knowing the swelling pressure only.
358
4
CONCLUSION
A series of constant overburden pressure volume change tests was performed on soil samples with different values of pre-wetting void ratio and degree of saturation. It was confirmed that for samples with volumetric water content more than a critical value negligible volume change occurs during wetting. Normalized overburden pressure was used to predict wetting-induced volume change percentage of soil samples with volumetric water content less than the critical value. Good correlation was found with a proposed equation that needs three correlation coefficients. The physical meanings of the coefficients have been discussed and the required tests to measure the coefficients have been suggested. ACKNOWLEDGMENTS The first author wishes to thank Mr. M. Shirazian and soil mechanics laboratory staff of IIEES for their helps in performing tests.
REFERENCES Ashayeri, I. & Yasrebi, S.S. 2005. Evaluating effects of compaction characteristics on swelling pressure of compacted clays, Proceedings of International Conference on Problematic Soils, GeoProb 2005. Eastern Mediterranean University, Famagusta, N. Cyprus. Barden, L., Madedor, A.O. & Sides, G.R. 1969. Volume change calculations of unsaturated clay, J. Soil Mech. And Found. Div., ASCE, Vol. 95, pp. 33–51.
Biglari, M., Shafiee, A. & Ashayeri, I. 2008. Determination of soil suction state surface in composite clays by filter paper method, 1st ECUS, Durham, England. Fredlund, D.G. 2006. Unsaturated soil mechanics in engineering practice, J. Geotech. And Geoenv. Eng. ASCE, Vol. 132, No. 3, pp. 286–321. Fredlund, D.G. & Morgenstern, N.R. 1977. Stress state variables for unsaturated soils, J. Geotech. Engrg. Div., ASCE, Vol. 103, No. 5, pp. 447–466. Fredlund, D.G. Pham, H.Q. 2006. A volume-mass constitutive model for unsaturated soils in terms of two independent stress state variables, Unsaturated Soils, ASCE, Geotechnical special publication No. 147. pp. 105–134. Holtz, W.G. & Gibbs, H.J. 1956. Engineering Characteristics of Expansive Clays, ASCE Transactions Paper No. 2814, Vol. 121. Jennings, J.E.B. & Burland, J.B. 1962. Limitations to the use of effective stresses in partly saturated soils, Geotechnique, London, Vol. 12, No. 2, pp. 125–144. Lawton, E.C. 1986 Wetting-induced collapse in compacted soils, Ph.D. thesis Washington State Univ., Pullman, Wash. Lawton, E.C., Fragaszy, R.J. & Hetherington, M.D. 1992. Review of wetting-induced collapse in compacted soils, J. of Geotech. Eng., ASCE, Vol. 118, No. 9, pp. 1376–1394. Matyas, E.L. & Radhakrishna, H.S. 1968. Volume change characteristics of partially saturated soils, Geotechnique, London, Vol. 18, No. 4, pp. 432–448. Mitchell, J.K. 1976. Fundamentals of soil Behaviour, Wiley, New York. Pereira, J.H.F. & Fredlund, D.G. 2000. Volume change behaviour of collapsible compacted Gneiss soil, J. Geotech. And Geoenv. Eng. ASCE, Vol. 126, No. 10, pp. 907–916. Tadepalli, R. & Fredlund, D.G. 1991. The collapse behaviour of a compacted soil during inundation, Can. Geotech. J., Ottawa, Vol. 28. pp. 477–488.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
The changes in stress regime during wetting of unsaturated compacted clays when laterally confined J.L. Brown University of Ulster, Belfast, UK
V. Sivakumar Queen’s University, Belfast, UK
ABSTRACT: Compacted clay fills are placed in an unsaturated condition and over time the fill will become saturated if the water table rises. The bimodal pore size distribution often prevails in these soils. This will lead to a combination of aggregate swelling and collapse during wetting, which can considerably change the stress regime in the fill. This paper examines the stress regime within compacted fills during wetting when lateral expansion is restricted. A one dimensional consolidation chamber was used to examine the behaviour of kaolin compacted to different initial bulk densities, representing un-engineered fill, engineered fill and heavily engineered fill. Wetting was performed under overburden pressures of 25 kPa, 50 kPa and 100 kPa. High lateral pressures and sample swelling were observed, which have significant implications on the stress distribution behind retaining structures where compacted clays are used as backfilling materials.
INTRODUCTION
0.20
The presence of two pore fluids in unsaturated soils leads to substantial behavioural differences between unsaturated and saturated soils. Many researchers have examined unsaturated soil behaviour in laboratory experiments (Sivakumar 1993), field studies (Springman et al. 2003), numerical analysis (Georgiadis et al. 2003) and constitutive modelling work (Wheeler & Sivakumar 1995). Previous work has shown a bimodal structure in unsaturated compacted clays consisting of groups of individual particles forming aggregates and these aggregates form an overall structure (Lloret et al. 2003). Wetting of unsaturated soils produces a combination of aggregate swelling, loss of frictional resistance at aggregate contacts and aggregate deformation (Thom et al. 2007). Sivakumar (2005) showed that swelling of heavily compacted clay was significantly influenced by the initial density. Figure 1 shows the increase in specific volume plotted against suction for samples with different initial densities. The graph shows that under wetting heavily compacted soil produced greater swelling than lightly compacted kaolin. This work shows the importance of the initial compaction effort on the volume change behaviour of compacted fills. Clay fills can be used as an economically and environmentally advantageous alternative to granular materials; e.g. these can be placed behind a retaining
Change in specific volume
v
1
Light compaction Heavy compaction
0.15
0.10
0.05
0.00 0.0 0.2
0.4 0.6 0.8 1.0
1.2 1.4 1.6
⎛ s + p atm ⎞ ln p ⎟ ⎜ atm ⎠ ⎝ Figure 1. The volume change behaviour of lightly and heavily compacted fills (after Sivakumar 2005).
wall, as fill surrounding trenches and as road pavements. Figure 2 shows a typical case where fill is placed behind a retaining wall. The fill behind a rigid wall is considered to be ‘at rest’ as lateral movement
361
Ground surface Final groundwater table
A B
Initial groundwater table
C
Figure 2. An unsaturated compacted clay behind a retaining structure.
Figure 3. Twin cell stress path apparatus for laterally confined sample testing.
is restricted. Knowledge of lateral pressures on retaining structures is essential for safe and economical design. In saturated soils K0 the coefficient of at rest earth pressure allows these to be evaluated. Equation 1 defines K0 for saturated soils (Bishop, 1958). K0 =
σh σν
(1)
where σh is the effective horizontal stress and σν is the effective vertical stress in saturated soils. The K0 value is affected by various factors including; internal angle of friction, soil plasticity, previous stress history, and anisotropy (Jaky 1948, Brooker & Ireland 1965, Schmidt 1966, Maine & Kulhawe 1982, Sivakumar et al. 2002). The presence of two pore fluids in unsaturated soils makes the assessment of K0 more complex and limited information is available in this respect. This paper aims to examine K0 in compacted fills using simple one dimensional compression tests in a Rowe cell. The K0 in unsaturated soil is defined using the following relationship: K0 =
σh − ua σν − ua
(2)
where σh is the total horizontal stress, ua is the pore air pressure and σν is the total vertical stress. This equation was used by Habib (1995), who found K0 values up to 7.7 using a looped stress path cell. Compacted fills are unsaturated when placed; however in temporal climates it is common for the groundwater table to rise and consequently reduce soil suction, as illustrated in Figure 2. In a field study, Carder (1988) presented the effects of inundating a clay backfill behind a retaining wall. Surface heave combined with high pressures along the retaining wall were recorded. The horizontal confinement
provided by the rigid wall caused excessive stresses to build up in the compacted fill. These stresses are not considered in current retaining structure design and could be detrimental. Therefore further research is necessary to understand the stress regime in compacted fills. Ongoing research at Queen’s University Belfast focuses on this aspect. A sophisticated stress path system which includes a provision for measuring sample volume change using a twin cell (Sivakumar et al. 2006) has been developed and commissioned for testing recently for examining unsaturated soils under K0 conditions (Fig. 3). A preliminary study has been performed in a standard Rowe Cell, to plan the testing strategy for the main experimental programme. This paper presents data obtained from the preliminary testing.
2
EQUIPMENT AND TESTING PROGRAMME
The preliminary tests were conducted in a one dimensional consolidation chamber of diameter 255 mm (Fig. 4). The cell was instrumented with four XPM10 type transducers. Two pressure cells were used for measuring horizontal pressures at sample mid height in diametrically opposite locations. The other two pressure cells were used to measure vertical pressures on the sample top and bottom. A Novo Technik TR100 type potentiometric displacement transducer was used to measure the change in sample height. Data was logged automatically using a DT50 data-recorder and the De Transfer computer program. Each test required 7.0 kg of kaolin powder. Clay was mixed at 25% moisture content in a domestic food blender before being stored for three days in a temperature controlled environment. This resting period
362
80
Displacement transducer
Horizontal Stress (kPa)
70
Pressure transducer Rubber bellofram Filter disk
Horizontal pressure cell
Horizontal pressure cell
50 50kPa
40 30
25kPa
20 10
Filter disk Vertical Pressure Cell
Figure 4.
100kPa 60
0
Base drainage lines
0
10
20
30
40
50
Time (Hrs)
One dimensional consolidation chamber.
Figure 5. Horizontal stress against time for un-engineered fill.
allowed the clay to reach moisture equilibrium. Samples were statically compressed in three equal layers in the chamber. An un-engineered fill was simulated using a vertical compression pressure of 400 kPa (resulting in an initial void ratio (e) of 1.20), engineered fill case 1 using a compression pressure of 800 kPa (e of 0.99), and engineered fill case 2 with a compression pressure of 1050 kPa (e of 0.91). After the completion of sampling a known overburden pressure of 25 kPa, 50 kPa or 100 kPa was applied to simulate different depths (Fig. 2), prior to wetting. Under these overburden pressures inundation was simulated by applying 15 kPa pore water pressure to the base drainage lines.
160
Vertical Stress ( kPa)
140 120 100kPa 100 80 50kPa
60 40
25kPa 20 0
3
0
RESULTS AND DISCUSSION
10
20
30
40
50
Time (Hrs)
The samples of kaolin prepared at different initial bulk densities were allowed to saturate without any attempt to control the suction. Therefore the discussion presented in this paper is a qualitative assessment of the stress regime in unsaturated soils rather than specific proposals on the subject since the suction change is unknown. The horizontal stress was calculated by averaging the horizontal pressures measured by the two diametrically opposite pressure cells located on the chamber walls. Vertical stress was calculated by averaging the vertical pressure measured above and below the sample. The sample was inundated from the base, thus during the wetting the wetting front moved from the sample base to the top. The vertical pressure cell on the chamber base will therefore be the first to respond to the effects of wetting. The horizontal pressures are taken at the sample mid-height; hence at a given
Figure 6. Vertical stress against time for un-engineered fill.
time two different mechanisms (i.e. wetting induced collapse or swelling) may be observed at sample mid height and the base. Figure 5 shows the variation of horizontal pressure during the wetting of un-engineered fill. The lateral pressure tended to increase to a peak value and then reduce. For example in the case of the sample wetted under 50 kPa of overburden pressure the horizontal stress increased from 43 kPa to 64 kPa within a period of 2 hours, then reduced until the pressure stabilised at 37 kPa. Figure 6 shows the average vertical pressure plotted against time. The vertical stress first increased to a peak value before decreasing as the inundation progressed. For example, in the case of 50 kPa
363
140
140
120
120
Horizontal Stress (kPa)
Horizontal Stress (kPa)
160
100kPa
100 80 60 25kPa 40
100 50kPa
80 60 40 20
20
0
0 0
10
20
30
40
0
50
10
30
40
50
Time (Hrs)
Time (Hrs)
Figure 9. Horizontal stress against time for engineered fill case 2.
Figure 7. Horizontal stress against time for engineered fill case 1.
80
140
70
Vertical Stress ( kPa)
100kPa
120
Vertical Stress ( kPa)
20
100 80 60 25kPa
40
50kPa
60 50 40 30 20
20
10 0
0 0
10
20 30 Time (Hrs)
40
0
50
10
20
30
40
50
Time (hrs)
Figure 8. Vertical stress against time for engineered fill case 1.
Figure 10. Vertical stress against time for engineered fill case 2.
of overburden pressure the average vertical pressure increased from 51 kPa to 67 kPa and subsequently reduced. The pattern of behaviour observed at different overburden pressures was the same, with the horizontal and vertical stresses increasing at the beginning of the wetting process as the overburden stress increased from 25 kPa to 100 kPa. The horizontal stress and the vertical stress against time are displayed in Figures 7 and 8 respectively for engineered fill case 1. The average horizontal stress initially increased to a peak value before reducing and stabilising as the inundation proceeded. For example under an overburden pressure of 100 kPa the lateral
pressure increased from 79 kPa to 132 kPa over a period of 4 hours, after which the horizontal pressure reduced and stabilised at 100 kPa. The vertical pressure increased as the wetting progressed to a peak value and then diminished to a final value. For example under an overburden pressure of 100 kPa the stress increased from 84 kPa to 119 kPa before falling to the final value of 110 kPa. One test simulating engineered fill case 2 was carried out under an overburden pressure of 50 kPa. Figures 9 and 10 display the horizontal stress and the vertical stress against time respectively. The lateral horizontal stress increased from 90 kPa to a peak
364
A Loading Collapse
Suction, s
Wetting
Yield Curve
Path B C
2µm
Net vertical stress, Figure 11. Scanning Electron Microscopy image of the bimodal pore size distribution of a compacted clay.
Figure 12.
1.5 25kPa
Displacement (mm)
value of 133 kPa before reducing to a stable value of 73 kPa as the inundation progressed. However the vertical pressure decreased from 67 kPa to 57 kPa as the inundation progressed. It appears that increasing the compaction pressure results in increasing lateral stresses. The lateral stresses in all three samples (i.e. unengineered fill, engineered fill case 1 and engineered fill case 2) increased significantly at the beginning of the wetting as a result of inundation. This can be explained using the bi-modal pore size distribution of unsaturated soils pictured in Figure 11. The aggregates are formed of particles, which are generally saturated (Thom et al. 2007). These particles are held together by suction. Inundation of the soil results in a reduced suction in the aggregates. This process can lead to an enlargement of the aggregates, resulting in an overall increase in sample volume. The reduction in suction can simultaneously weaken the stability of the inter-aggregate contacts, possibly leading to a collapse settlement (Matayas and Radhakrishna 1968, Alonso et al. 1990, and Wheeler et al. 2003). It is the combination of aggregate swelling and collapse settlement which controls the overall soil behaviour. The initial suction in the sample was measured using a thermocouple psychrometer and found to be approximately 850 kPa, this reduced to zero as the inundation progressed. Figure 12 shows a wetting path for a sample under a constant overburden pressure in the suction and net vertical stress plane. The loading collapse yield locus represents the significance of collapse settlement induced by wetting. During wetting from A to B aggregate swelling dominates the soil response, whereas from Point B to C collapse settlement controls the soil behaviour. Therefore it could be postulated that Path AB will be accompanied by an increase in horizontal pressures whereas Path BC will be accompanied by a significant reduction in
The wetting path of an unsaturated soil.
1
50kPa
0.5
0
0
10
20
30
-0.5
40
50
100kPa
-1 Time (Hrs) Figure 13. Displacement against time for un-engineered fill.
horizontal pressures. The initial increase in horizontal stresses shown in Figures 5, 7 and 9 can be taken as indicative of aggregate swelling at mid-height. The position of the LC yield locus shown in Figure 12 is controlled by the initial compaction effort. Figures 5, 7 and 9 show that the lateral pressures, after reaching a peak value, reduced as the inundation progressed regardless of the compaction effort applied. This suggests that another mechanism must have contributed to the reduction in lateral pressures as the wetting continued. This is further substantiated by the sample volume change behaviour. Figures 13, 14 and 15 show the vertical displacement of the sample top surface during the wetting. Collapse settlement is observed in the case of wetting of un-engineered fill at 100 kPa, however in all other cases sample
365
6 v
Displacement (mm)
5
25kPa
4
Side
Side
Friction
Friction
3 2
Vertical
100kPa
Pressure Cell
1 Figure 16. chamber.
0
0
10
20
30
40
Side friction acting in the consolidation
50
Time (Hrs) Figure 14. Displacement against time for engineered fill case 1.
4.5
Displacement (mm)
4 50kPa
3.5 3
Figure 17. (a) Initial aggregate orientation (b) Final aggregate orientation.
2.5 2 1.5 1 0.5 0
0
10
20 30 Time (hrs)
40
50
Figure 15. Displacement against time for engineered fill case 2.
swelling was observed as a result of the wetting. The swelling behaviour indicates that the wetting path remained inside the LC yield locus. The vertical pressure response will be examined alongside these observations. Figures 6, 8 and 10 show the average vertical pressure at the sample mid height. Vertical pressure increased at the beginning of the wetting process and then subsequently reduced as the inundation continued. The overburden pressure applied at the top of the sample was maintained at a constant value; hence the changes shown in Figures 6, 8 and 10 are caused by the increase/decrease in vertical pressure at
the bottom of the sample. Aggregate swelling will only result in a pressure increase when swelling is restricted. In the case of vertical pressure at the base, the restriction to aggregate swelling comes from the side friction between the sample and the chamber walls (Fig. 16). However in semi-infinite space such friction effects do not exist and the situation across the deposit can be considered to be ‘‘truly one dimensional’’. Therefore the vertical pressures presented in Figures 6, 8 and 10 are not a true representation of the stress regime that might have existed at the sample mid height. Based on the foregoing argument it is possible to explain the reduction in lateral pressures at the end of wetting though the sample swelled overall as result of inundation. At the start of wetting the lateral pressure rapidly increases and at one point it becomes the major principle stress and the vertical pressure the minor principle stress, assuming no frictional resistance between the sample and the consolidation chamber. Aggregates attempting to expand, triggered by the suction reduction, will orientate themselves in a minimum energy condition (Murray & Brown 2006). The vertical direction provides less resistance to swelling; hence the particles will expand in the vertical direction and not the horizontal direction, which is illustrated in Figure 17. The re-orientation of
366
particles is an important mechanism that can qualitatively explain some of the observed soils behaviour, though further research is necessary. 4
CONCLUSIONS
Experimental research inundating compacted clay fills in a laterally confined environment was conducted in a one dimensional loading chamber. This work simulated the behaviour behind a retaining structure. The horizontal and vertical pressures and surface displacements were recorded. The effect of varying the compaction effort and the overburden pressure during wetting was examined. A combination of high lateral stresses and sample swelling were observed during the wetting process. The results indicate reorientation of particles under one dimensional loading. These findings have important practical implications for the designers of retaining structures, when calculating the maximum possible stresses acting on a wall. Further advances in this research are essential.
REFERENCES Alonso, E.E., Gens, A. & Josa, A. (1990) A constitutive model for partially saturated soils. Géotechnique 40(3): 405–430. Bishop, A.W. (1958) Test requirements for measuring the coefficient of earth pressure at rest. Proc. Conf. on Earth Pressure Problems, Brussels (1): 2–14. Brooker, E.W. & Ireland, H.O. (1965) Earth pressures related to stress history. Canadian Geotechnical Journal 2(1): 1–15. Carder, D.R. (1988) Earth pressures on retaining walls and abutments. Ground Engineering 21(5): 7–10. Georgiadis, K., Potts, D.M. & Zdravkovic, L. (2003) The influence of partial soil saturation on pile behaviour. Géotechnique 53(1): 11–25. Habib, S.A.E-A. (1995) Lateral pressure of unsaturated expansive clay in looped stress path. Proc. 1st Intern. Conf. on Unsaturated Soils, Paris (1): 95–100. Jaky, J. (1948) Earth pressure: Pressure in silos. Proc. 2nd Intern. Conf. on Soil Mechanics and Foundation Engineering, Rotterdam (1): 103–108.
Lloret, A., Villar, M.V., Sánchez, M., Gens, A., Pintado, X. & Alonso, E.E. (2003) Mechanical behaviour of heavily compacted bentonite under high suction changes. Géotechnique 53(1): 27–40. Maine, P.W. & Kulhawy, F.H. (1982) K 0 -OCR relationships in soil. Journal of Soil Mechanics and Foundation Division. 108(GT6): 851–872. Matyas, E.L. & Radhakrishna, H.S. (1968) Volume change characteristics of partially saturated soils. Géotechnique, (18), 432–448. Murray, E.J. & Brown, J. (2006) Assumptions in equilibrium analysis and experimentation in unsaturated soil. Proc. 4th Int. Conf. on Unsaturated Soil, Arizona (2): 2401–2407. Navaneethan, T. (2003) Pre-yield characteristics and earth pressure coefficient of overconsolidated clays. PhD Thesis, Queen’s University Belfast, UK. Schmidt, B. (1966) Discussion: Earth pressure at rest related to stress history. Canadian Geotechnical Journal 3(4): 239–242. Sivakumar, R. (2005) Effects of anisotropy on the behaviour of unsaturated compacted clay. PhD Thesis, Queen’s University Belfast, UK. Sivakumar, R., Sivakumar, V., Blatz, J. & Vimalan, J. (2006) Twin-cell stress path apparatus for testing unsaturated soils. Geotechnical Testing Journal 29(2): 1–5. Sivakumar, V. (1993) A critical state framework for unsaturated soil. PhD Thesis, University of Sheffield, UK. Sivakumar, V. & Wheeler, S.J. (2000) Influence of compaction procedure on the mechanical behaviour of an unsaturated compacted clay Part 1: Wetting and isotropic compression. Géotechnique 50(4): 359–368. Sivakumar, V., Doran, I.G., Graham, J. & Navaneethan, T. (2002) Relationship between K0 and overconsolidation ratio—a theoretical approach. Géotechnique 52(3): 225–230. Springman, S.M., Jommi, C. & Teysseire, P. (2003) Instabilities on moraine slopes induced by loss of suction: a case history. Géotechnique 53(1): 3–10. Thom, R., Sivakumar, R., Sivakumar, V., Murray, E.J. & Mackinnon, P. (2007) Pore size distribution of unsaturated compacted kaolin: the initial states and final states following saturation. Géotechnique 57(5): 469–474. Wheeler, S.J., Sharma, R.S. & Buisson, M.S.R. (2003) Coupling hydraulic hysteresis and stress-strain behavior in unsaturated soils. Géotechnique, 53(1), 41–54. Wheeler, S.J. & Sivakumar, V. (1995) An elasto-plastic critical state framework for unsaturated soil. Géotechnique 45(1): 33–53.
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Compression-induced suction change in a compacted expansive clay A.M. Tang & Y.J. Cui Université Paris-Est, Institut Navier, ENPC-CERMES, Paris, France
N. Barnel Electricité de France, Département MMC, France
ABSTRACT: The present work aims at studying the coupling between mechanical stress, suction and degree of saturation on compacted expansive clays. Isotropic compression tests were performed on compacted MX80 clay under constant water content condition and with suction monitoring. The experimental results showed a decrease of suction when the isotropic total stress is increased. Moreover, when plotting the suction-degree of saturation relationships, together with that obtained from previous work, the hysteresis phenomenon and the effect of soil porosity were evident. Finally, the compression curves of these suction-monitored tests are compared with those of suction-controlled tests, showing the effect of suction on the mechanical behaviour.
1
INTRODUCTION
Compacted expansive clay is often considered as a possible engineered barrier in deep nuclear waste disposal. In order to study its hydro-mechanical behaviour, suction controlled oedometer tests are often carried out in laboratory. These tests provide most of the required mechanical parameters for numerical simulations using constitutive models such as BExM (Alonso et al., 1999). For the determination of hydraulic parameters, it is a common practice to establish the relationship between the hydraulic state of soil (degree of saturation) and soil suction through the water retention curve. From an experimental point of view, some studies on the coupling between mechanical stress, suction and degree of saturation have been performed on low-plastic soils (Tarantino & Tombolato, 2005); however, it has been rarely studied on compacted expansive clays. In the present work, three isotropic compression tests were performed on compacted MX80 expansive clay at constant water content condition with monitoring of total suction. These tests enable investigation of hydro-mechanical coupling in compacted expansive clays. 2
MATERIAL AND EXPERIMENTAL DEVICE
MX80 bentonite, a clay from Wyoming (USA), is one of the reference materials considered for the engineered barrier or sealing material in deep nuclear waste disposal. With its high content of montmorillonite
(82%), it has a liquid limit wL = 520%, a plastic limit wP = 46%. Its specific gravity Gs = 2.76 and its cation exchange capacity (CEC) is 76 meq/100 g. Prior to utilisation, the clay was sieved at 2 mm and dried at 44% relative humidity (RH ), corresponding to a total suction of 110 MPa (see Tang & Cui, 2005). At equilibrium, it had a water content of 10 ± 2%. After that, the clay powder was compacted in an isotropic cell under a static pressure of 40 MPa. The compacted specimens were then placed back in the chamber with relative humidity controlled at RH = 44%. This procedure allowed compacted soil specimens to be obtained with a dry density ρd = 1.78 ± 0.3 Mg/m3 , a void ratio e = 0.55 ± 0.03. The suction-temperature controlled isotropic cell presented in Tang et al. (2007b) has been modified and adapted to this study. The schematic diagram of the cell is presented in Figure 1. The soil specimen (10-mm high and 80-mm diameter) is sandwiched between two porous stones that are installed inside two metallic plates. Various small holes (2 mm diameter) are drilled in the lower plate to ensure moisture exchange between the soil specimen and the chamber below. A neoprene membrane of 1.2 mm thick covers the soil specimen and the metallic plates. A volume/pressure controller is used to control the water confining pressure as well as to monitor the volume change of the soil specimen. The total suction of the soil specimen is monitored using a relative humidity (RH ) sensor installed in the chamber beneath the lower plate. This design with protection of RH sensor was applied because the sensor can not stand high pressure. The salt solution cup used
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by Tang et al. (2007b) for suction control was replaced by a metallic block to reduce the air volume in the chamber. The cell was wholly immersed in a bath with temperature controlled at 25 ± 0.1◦ C. Three compacted specimens were initially put in three chambers with total suction controlled at 110 (test T01), 39 (test T03) and 20 MPa (test T02) using saturated salt solutions of K2 CO3 , NaCl and KCl, respectively. After reaching equilibrium, these specimens were installed in the isotropic cell as indicated previously. For each test, the confining pressure was increased step-by-step from 0.1 MPa to 0.2, 0.5, 1, 2, 5, 10, 20 and 50 MPa and then decreased equally stepby-step until 0.1 MPa. Each step was maintained until stabilisation of the soil volume change and the total suction change. Pressure and volume changes of the volume/pressure controller and the RH changes were recorded. The volume change of the soil specimen was calculated using the calibration results performed on metallic specimen (see Tang et al. 2007b).
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The results obtained from the three tests are presented in Figure 2. The confining pressure (Figure 2a) was controlled by the volume/pressure controller. The duration of the loading steps was changing, depending on the time required at each state for stabilisation of the volume change and the total suction. dV presented in Figure 2b corresponds to the volume change of water contained in the controller when pressure was changing. It corresponds to the sum of soil volume change and the deformation of the cell and the tubing system upon pressure change. A calibration curve was then required to determine the soil volume change. Total suction measured (s) is plotted versus time in Figures 2c, 2d and 2e for tests T01, T02 and T03 respectively. In general, it can be observed that s decreased when pressure was increasing. The fluctuation of ±2 MPa observed on the measurement corresponds to the fluctuation of the cell temperature (±0.1◦ C). More details on the effect of temperature
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fluctuation on the total suction can be found in Tang & Cui (2005). For Test T01, the suction decreased from 115 to 95 MPa when the pressure was increasing from 0.1 to 50 MPa; the suction increased from 95 to 112 MPa during the unloading path. For Test T02, loading from 0.1 to 50 MPa decreased the total suction from 18 to 9 MPa; the suction increased from 9 to 24 MPa during unloading. In the case of Test T03, the suction decreased from 30 to 9 MPa and then came back to 30 MPa during unloading. The total elapsed time was 750 h (31 days), 2400 h (100 days), and 2300 h (96 days) for Tests T01, T02, T03, respectively.
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The results obtained at the end of each loading step for test T01 are plotted in Figure 3. The initial state of the soil specimen was: e = 0.52, s = 110 (prepared using K2 CO3 solution), w = 8.4% and Sr = 45%. Note that the water content of the soil w was assumed to be constant during the test. For each loading step, e and Sr were calculated from the volume change of the soil specimen. The e-p plot shows that increasing pressure from 0.1 to 50 MPa decreased e from 0.52 to 0.40; during unloading, e returned to 0.46. The initial suction measured was s = 115 MPa (see s-p, e-s, and s-Sr plots). When p was increasing, s increased slightly until 120 MPa and then decreased with increasing p. For p ≥ 5 MPa, the s-p plot shows a unique and linear relationship. The following slope can be determined: ds/dp = −0.35. It can be observed in the s-Sr plot that s decreased when Sr was increasing. During the loading path (increases of p), s decreased from 115 to 95 MPa while Sr increased from 45 to 57%. Nevertheless, when suction was increasing during the unloading path, Sr initially remained almost constant until a suction of about 108 MPa and then reduced from 56 to 51% when suction increased up to 112 MPa. The e-s plot is similar to the s-Sr plot because e and Sr were all calculated from the volume change of the soil specimen. The results of test T02 are presented in Figure 4. When increasing the pressure from 0.1 to 50 MPa, the void ratio decreased from 0.90 to 0.57. After the unloading, the final value of void ratio was 0.60. The initial total suction in the soil was 18 MPa even though the imposed suction by KCl solution was 20 MPa. When the pressure was increasing, s increased slightly
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to 20 MPa and then reduced to 9 MPa at p = 50 MPa. During unloading, s increased to 24 MPa when p reduced to 0.2 MPa. The relationship between s and p on unloading can be correlated using a linear function with a slope ds/dp = −0.30. The initial degree of saturation was Sr = 55%. During the loading path, Sr increased to 87% corresponding to s = 9 MPa. During the unloading path, Sr reduced slightly to 83% while s increased significantly to 24 MPa. The results of test T03 are presented in Figure 5. During loading from 0.1 to 50 MPa and unloading to 0.2 MPa, the void ratio decreased from 0.82 to 0.48 and increased at the end to 0.49. The s-p plot shows a general decrease of suction when pressure was increasing and a linear correlation with a slope ds/dp = −0.46 can be determined. On the s-Sr plot, loading reduced slightly the total suction from 30 to 25 MPa (at p = 20 MPa); Sr was increased from 56 to 93%. After that, loading from 20 to 50 MPa decreased quickly s from 25 to 9 MPa while Sr increased slightly from 93 to 97%. During unloading from 50 to 0.2 MPa, s increased from 9 to 30 MPa while Sr decreased from 97 to 95%. In Figure 6, the total suction measured is plotted versus water content for all the tests. The results obtained from Tang & Cui (2005) and Delage et al. (2006) are also plotted. In the work of Tang & Cui (2005), MX80 clay was compacted at w = 8.5%, e = 0.67. After that, total suction was imposed on the soil under free-swell condition. On the other hand, in the work of Delage et al. (2006), MX80 clay was compacted at w = 8.2%, e = 0.57. The water retention curve was obtained by imposing total suction using saturated salt solutions under constant volume condition.
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It can be observed that the water retention curves obtained from different works are similar at high suction range (higher than 20 MPa). At low suction range, the results from the present work are different from that presented by Delage et al. (2006). For further analyses, the total suction is plotted versus degree of saturation in Figure 7 for all the tests of the present work and the test presented by Delage et al. (2006). It can be observed that the s-Sr plots obtained from different tests are different and no unique relationship exists even at the high suction range. In order to analyze the effect of suction changes on the compressibility of the soil, void ratio is plotted versus logarithm of suction for tests T02,
T03 in Figure 8. In this figure, the results of one test presented by Tang et al. (2007b) are also plotted. This concerns the compression curve of MX80 clay with a total suction controlled at 39 MPa. It can be observed that the results for the loading stage from 0.1 to 5 MPa in test T02 are similar to that from the test by Tang et al. (2007b). At higher pressure, the curves are different from each other: a linear relationship between e and log p can be observed for the test with suction control while for the tests at constant water content (suction monitored) condition, the slope of the curves starts to change when p is higher than 10 MPa. 4
DISCUSSION
The initial suction measured in the cell was found to be slightly different from the imposed values. This can
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be partly attributed to the accuracy of the suction controlled by vapour equilibrium technique or the suction measured by RH sensor. On the other hand, the initial air humidity in the gap between the lower base of the cell and the metallic block may also affect the initial suction measured. The matric suction change upon mechanical loading under undrained condition has been investigated under K0 conditions (Rahardjo & Fredlund, 2003; Tarantino & Tombolato, 2005; Delage et al. 2007) or isotropic pressure condition (Kawai et al., 2002). Suction has been found to monotonically decrease with increasing pressure following a linear function with a slope ds/dp = −0.1 to −0.8. Suction was limited to 1 MPa in these works. In the work of Blatz & Graham (2003), the total suction in a compacted sand/bentonite mixture was monitored using a psychrometer and the suction range measured was 0–8 MPa. Isotropic compression tests performed also showed a suction decrease when pressure was increasing with a linear function; the average value of the slope was ds/dp = −0.83. In the present work, total suction was monitored using a relative humidity sensor and the suction range measured was 9–120 MPa. During compression, a slight suction increase was observed at the beginning followed by a decrease in suction. For the decreasing part, a similar relationship between suction and pressure has been observed and the slope of the linear correlation is ds/dp = −0.30 to −0.46. The structure of compacted bentonite was described in different scales by Kröhn (2003): the clay particle (∼300 nm) corresponds to a stack of lamella; the clay grain (∼0.1 mm) corresponds to an assembly of particles. The pore size distribution of MX80 clay compacted at w = 8.2% and e = 0.65 has been observed by Delage et al. (2007) by using mercury intrusion porosimetry. A typical bimodal porosity was observed with entrance pore radii of about 0.02 μm for intra-aggregates pores and 2 μm for inter-aggregates pores. After Pusch & Yong (2003), water is absorbed in compacted bentonite by two mechanisms: absorption on exposed mineral surfaces, representing the osmotic suction; and storage in pore space, representing the matric suction. Even though utilisation of Laplace-Jurin’s law is incorrect for the description of the osmotic suction (as it is based on capillary phenomenon), for a global analysis, it can be used to estimate the pore radius that would separate the smaller water saturated pores from the larger unsaturated pores. Putting the initial suctions of tests T01 (115 MPa), T02 (18 MPa) and T03 (30 MPa) in the Laplace-Jurin equation by taking an air-water interfacial tension of 0.073 N/m and a zero contact angle, a separating radius of 0.001 μm was obtained for test T01, 0.008 μm for test 02 and 0.005 μm for test 03. All these values are smaller than
0.02 μm, identified by Delage et al. (2007) for intraaggregates pores. This means that the micropores of the tested three samples were initially not saturated. In this case, it was possible that with mechanical compression, the micropore size was decreased, resulting in an osmotic suction increase. When the size of micropore can not be changed anymore due to especially the increase in internal forces in the clay particles, the suction changes start to be governed by the degree of saturation changes in inter-aggregates macropores and common matric suction decrease with compression was observed. This would be what happened in the three tests conducted. Following this explanation, only a suction decrease would be obtained when compressing a soil sample having micropores that were initially saturated. Taking the value of 0.02 μm to represent the micropore size and applying Laplace-Jurin’s law, a corresponding suction of 7.3 MPa can be obtained. This means that all the tests on the samples with an initial suction higher than 7.3 MPa would present the phenomenon of suction increase followed by a suction decrease. In the s-Sr plot (Figure 7), the compression path corresponds to a wetting path of the water retention curve (increasing of Sr and decreasing of s). And vice versa, the unloading path corresponds to the drying path. The difference between these two curves represents the well-known hysteresis phenomenon. Works on the retention curves of deformable clays (Romero & Vaunat 2000) have shown that the log s-w curve is strongly dependent on stress, void ratio and hydraulic history at low suction range. That is in agreement with the results obtained in the present work (Figure 6): for a given value of water content, suction is lower in the soil having higher dry density (or lower void ratio). The deviation from the linear trend of the compression curves at high stresses in oedometer tests at constant water content was equally noted by Tang et al. (2007a), Perdok et al. (2002) among others. In the present work, these inflection point (Figure 8) corresponds to the inflection point obtained on the s-Sr curves (Figure 7). Regarding the change of the slope on the s-Sr plot, it is often explained by the air entry value of the water retention curve which is the limit of the saturated state and the unsaturated state (Rahardjo & Fredlund, 2003). The compression curve of Tang et al. (2007b) presented in Figure 8 was performed under suction controlled at 39 MPa. The initial total suction in the test T02 is 18 MPa. It can be observed that the compression curves of the two tests are similar during the loading path from 0.1 to 5 MPa. Lloret et al. (2003) performed suction-controlled oedometer tests on compacted FEBEX bentonite and observed a decrease of the apparent preconsolidation stress when suction is decreasing. In the work of Lloret et al. (2003), soil
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specimens were prepared at the same initial state and then conducted to various suction values prior to the compression tests. The soil samples having different suction value then had different values of void ratio: the lower the suction, the higher the value of void ratio. In the case of tests presented in Figure 8, the initial suction values are different, 18 MPa (for test T02) and 39 MPa (for test performed by Tang et al. 2007b). Nevertheless, their initial void ratio values are similar (0.90). As a result, it can be concluded that the effect of void ratio on the compressibility of compacted soil is more significant than the effect of suction in this range of suction. 5
CONCLUSION
Three isotropic compression tests at constant water content and with monitoring of the total suction were performed on compacted expansive MX80 clay. The results showed a slight increase in total suction (s) in the beginning followed by a decrease when the pressure (p) was increased. The initial suction increase would be explained by the non saturation of the micropores of the compacted samples: with mechanical compression, the micropore size was decreased, approaching the clay particles and thus resulting in an osmotic suction increase. For the suction decreasing part, a linear s-p relationship was observed with a slope ds/dp varying from −0.30 to −0.46. The water retention curves obtained (suction versus water content, and suction versus degree of saturation) were compared with the existing results from previous works on the same material. It was observed that the water retention curves are influenced by various aspects: hysteresis, void ratio, initial state, etc. The compressibility curves (void ratio versus logarithm of pressure) obtained at constant water content were compared with the existing curves performed at constant total suction. Similar results have been obtained in the low pressure range; but in the high pressure range (p > 5 MPa), it was observed that constant slope was kept in the case of controlled suction whereas the slope became smaller when the pressure was higher than 10 MPa in the case of constant water content. It was noted also that the effect of void ratio on the compressibility is more significant than the effect of suction. ACKNOWLEDGMENT The authors are grateful to Ecole Nationale des Ponts et Chaussées and French Electricity Company (EDF) for their financial support.
REFERENCES Alonso, E.E., Vaunat, J. & Gens, A. 1999. Modelling the mechanical behaviour of expansive clays. Engineering Geology 54(1–2), 173–183. Blatz, J.A. & Graham, J. 2003. Elastic-plastic modeling of unsaturated soil using results from a new triaxial test with controlled suction. Géotechnique 53(1), 113–122. Delage, P., Marcial, D., Cui, Y.J. & Ruiz, X. 2006. Ageing effects in a compacted bentonite: a microstructure approach. Géotechnique 56(5), 291–304. Delage, P., Le, T.T., Tang, A.M., Cui, Y.J. & Li, X.L. 2007. Suction effects in deep Boom Clay block samples. Géotechnique 57(1), 239–244. Kawai, K., Weichuan, W. & Ogawa, K. 2002. The behavior of unsaturated soil compressed isotropically under undrained condition. In Jucá, J.F.T., de Campos, T.M.P. & Marinho, F.A.M. (ed.), Unsaturated Soils. Proc. 3rd Int. Conf. on Unsaturated Soils (UNSAT 2002), Recife, Brazil, Vol. 2: 521–528. Lisse: Swets & Zeitlinger. Kröhn, K.P. 2003. New conceptual models for the resaturation of bentonite. Applied Clay Science 23, 25–33. Lloret, A., Villar, M.V., Sanchez, M., Gens, A., Pintado, X. & Alonso, E.E. 2003. Mechanical behaviour of heavily compacted bentonite under high suction changes. Géotechnique 53(1), 27–40. Perdok, U.D., Kroesbergen, B. & Hoogmoed, W.B. 2002. Possibilities for modeling the effect of compression on mechanical and physical properties of various Dutch soil types. Soil & Tillage Research 65, 61–75. Pusch, R. & Yong, R. 2003. Water saturation and retention of hydrophilic clay buffer—microstructural aspects. Applied Clay Science 23, 61–68. Rahardjo, H. & Fredlund, D.G. 2003. K0 -volume change characteristics of an unsaturated soil with respect to various loading paths. Geotechnical Testing Journal 26(1), 79–91. Romero, E. & Vaunat, J. 2000. Retention curves of deformable clays. In Tarantino & Mancuso (ed.), Experimental Evidence and Theorical Approaches in Unsaturated Soils: 91–106. Rotterdam: Balkema. Tang, A.M. & Cui, Y.J. 2005. Controlling suction by the vapour equilibrium technique at different temperatures and its application in determining the water retention properties of MX80 clay. Canadian Geotechnical Journal 42(1), 287–296. Tang, A.M., Cui, Y.J., Eslami, J. & Défossez, P. 2007a. Compressive behaviour of four agricultural soils from France under confined uniaxial test. In T. Schanz (ed.), Experimental Unsaturated Soil Mechanics; Springer Proceedings in Physics 112: 475–482. Tang, A.M., Cui, Y.J. & Barnel, N. 2007b. A new isotropic cell for studying the thermo-mechanical behavior of unsaturated expansive clays. Geotechnical Testing Journal 30(5), 341–348. Tarantino, A. & Tombolato, S. 2005. Coupling of hydraulic and mechanical behaviour in unsaturated compacted clay. Géotechnique 55(4), 307–317.
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Theoretical modelling of the compaction curve N. Kurucuk & J. Kodikara Department of Civil Engineering, Faculty of Engineering, Monash University, Clayton, VIC, Australia
D.G. Fredlund Golder Associates, Saskatoon, Saskatchewan, Canada
ABSTRACT: Soil compaction is one of the major activities in geotechnical engineering involving earthworks. The compaction curve is used to find the optimum water content that maximizes dry density. Since its introduction by Proctor in 1933, several researchers have provided qualitative explanations for the inverted parabolic shape of the compaction curve. However, fundamental research on the compaction process and the evolution of compaction characteristics are limited, particularly from a quantitative sense. In order to understand the driving mechanisms of soil compaction, this paper investigates the effect of soil suction, stiffness and pore air pressure on the shape of the compaction curve, from an unsaturated soil mechanics standpoint. This paper presents an approach to predict the soil compaction curve during undrained loading. Particular attention is focused on the derivation of the compressibility coefficient due to net stress. Model predictions of the compaction curve are compared with some experimental results from the literature.
1
INTRODUCTION
Soil compaction is widely used in geo-engineering and is important for the construction of roads, dams, landfills, airfields, foundations, hydraulic barriers, and ground improvements. Compaction is applied to the soil, with the purpose of finding optimum water content in order to maximize its dry density, and therefore, to decrease compressibility, increase shearing strength, and in some cases, to reduce permeability. Proper compaction of materials ensures the durability and stability of earthen constructions. A typical compaction curve presents different densification stages when the soil is compacted with the same apparent energy input but different water contents. The water content at the peak of the curve is called the optimum water content (OWC) and represents the water content at which dry density is at its maximum for a given compaction energy. Since Proctor’s pioneering work in 1933, many researchers have attempted to explain qualitatively the leading mechanisms in the densification stages, mainly on the dry side of optimum water content. The compaction curve was explained in terms of capillarity and lubrication (Proctor, 1933), viscous water (Hogentogler, 1936), pore pressure theory in unsaturated soils (Hilf, 1956), physico-chemical interactions (Lambe, 1960), and concepts of effective stress theory (Olson, 1963). More recently, Barden & Sides (1970) undertook experimental research on the relation between the
engineering performance of compacted unsaturated clay and microscopic observations of clay structure. In addition, Lee & Suedkamp (1972) conducted research on the shape of the compaction curve for different soils. Despite this research work, and the importance and high demand for the compaction process in engineering practice, the compaction of soil is quite complex and not well explained, particularly from a quantitative sense. Theoretical modelling of the soil compaction curve will provide a better understanding of the main parameters that affect the shape of the compaction curve, and understanding the behaviour of compacted materials. Therefore, there is need for research to be undertaken at a fundamental level to understand the compaction characteristics of soil and the inverted parabolic shape of the compaction curve. This paper presents a theoretical explanation of the compaction curve using unsaturated soil mechanics principles. Particular attention is focused on the prediction of the compressibility coefficient due to net stress. Likely predictions of the model are compared with the experimental results from literature. 2
THEORETICAL BACKGROUND FOR MODELLING
Theoretical concepts utilized for the development of soil compaction curves are presented in this section.
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Initially, Hilf ’s (1948) approach for pore pressure development is presented. This is continued with Fredlund & Morgenstern’s (1976) volume change theory for a compacted soil and the derivation of the dry density of soil. 2.1
Pore pressure development during static compaction
One of the main simulations for the generation of the compaction curve is that of pore pressure development. Hilf (1948) developed a relationship between pore pressure and applied stress, which is based on one-dimensional K 0 soil compression, Boyle’s law, and Henry’s law, and is expressed as follows: ua =
1 1+
(1−S0 +hS0 )n0 (ua0 +ua )mv
σy
(1)
where; ua = change in absolute pore air pressure, S0 = initial degree of saturation, h = coefficient of solubility, n0 = initial porosity, ua0 = initial absolute air pressure, mv = coefficient of volume change in saturated soil, and σy = change in applied vertical stress. Hilf (1948) developed this equation assuming that air and water phases are undrained, and volume reduction is due to air dissolving in the water and compression of free air. Both liquid and solid parts were considered to be volumetrically incompressible. Hilf also assumed that the change in pore air pressure is equal to the change in pore water pressure, and therefore, matric suction change was insignificant. Experimental results on suction change during compaction can be found in literature (e.g. Li 1995, Montanez 2002). It is shown that matric suction only decreases marginally with a density increase and may be approximated to be constant. Therefore, Hilf’s analysis assuming constant suction during compaction appears to be close to the real situation. Further justification for assuming constant matric suction during the compaction test is presented in Kurucuk et al. (2007). 2.2
3
MODELLING ASSUMPTIONS
Kurucuk et al. (2007) showed that the assumption of constant coefficients of compressibility during compaction does not produce a proper shape of the compaction curve especially on the dry side of the optimum water content. Their analysis showed that it is m1s that controls the volume changes during compaction because the associated change in suction may be neglected. The parameter m1s was represented as a function of saturation and decreases with decreasing saturation. However, the experimental results presented by Loret et al. (2003) showed that m1s decreased with both suction and net stress. Therefore, following the functional form suggested by Sheng et al. (2007), the volumetric strain, ignoring suction change, may be presented as: εv =
d (σnet − ua ) dV = λvp V (σnet − ua ) + s0
Vv = ms1 σy − ua + ms2 (ua − uw ) V
(2)
where; εv = volumetric strain, Vv = overall volume change of soil element, V = initial total volume of soil
(3)
where; εv = volumetric strain, (σnet − ua ) = mean net stress, ua = pore air pressure, s0 = suction, λvp = slope of the normal compression line (NCL) of the saturated soil, and V = initial total volume of the soil element. This gives m1s as:
Computation of volume change and dry density
The volume change constitutive relationship as applicable to K0 loading, which is defined in terms of two independent stress variables as proposed by Fredlund & Morgenstern (1976) for unsaturated soils, is used for the calculation of compaction curves: εv =
element, m1s = compressibility of soil particles with respect to net stress (σy − ua ), m2s = compressibility of soil particles referenced to matric suction (ua −uw ), (σy − ua ) = change in net stress, and (ua − uw ) = change in soil suction. Since soil particles are incompressible, it is accepted that deformation is primarily due to compression of the pore fluid (i.e., the air and air/water mixture). The independent stress state variable concept is utilized in the derivation; namely, net stress (σy − ua ) (causes a reduction in volume with compression), and matric suction stress (ua − uw ) (generally results in volume increase with compression). Once the overall volume change is computed, the corresponding dry density can be easily computed.
λvp σy − ua + s0
ms1 =
(4)
This assumption will be used and discussed further in the modelling of the compaction curve. It is reasonable to replace mv in Equation 1 by m1s . A numerical example of the variation of m1s during compaction process is given in the following section. Equations (1), (3) and (4) were used in incremental forms to compute the incremental and total volume change and the corresponding dry density values during compaction.
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4
NUMERICAL EXAMPLES
The performance of the proposed model is demonstrated by comparing the experimental results presented by Montanez (2002) and Kenai et al. (2006). Figures 1 and 2 show the compaction curves for sandbentonite mixture with bentonite content of 5% and 15% by weight. Montanez’s experimental data present values for the Standard Proctor Test (BS, external gross energy input = 637 kJ/m3 or kPa). In Figures 1 and 2, two model predictions are also shown. The curves shown by dashed lines represent the static compaction curve predicted by the model for undrained (air/water) loading up to external quasi-static pressure, σy , of 637 kPa. The curves shown by solid lines are for equal energy input, calculated by integrating the applied stress σy with respect to volumetric strain. The actual energy input into the soil was computed on the basis of the values applicable at the optimum water content, which were found to be 16 kJ/m3 and 18 kJ/m3 respectively.
Figure 3 shows an example of compaction curve for clay sandy soil (liquid limit = 39%, plasticity index = 15%) adopted from Kenai et al. (2006). Experimental results shown in figure are for static (σy = 2100 kPa) and dynamic (external gross energy input 3000 kJ/m3 ) compaction tests. Both predicted compaction curves are produced from quasi-static compaction up to external pressures, σy , of 2100 kPa and 4000 kPa respectively. Model parameters used for prediction of the above compaction curves are shown in Table 1, 2 and 3. Initial pore air pressure (ua0 ) is taken to be equal to atmospheric pressure (101.3 kPa). For a certain soil, a lower initial porosity was assumed and the computations were performed for a range of moisture contents which also define the values of initial degree of saturation (S0 ). The water solubility value is adopted from Fredlund & Rahardjo (1993). The values of λvp (slope of the NCL) are selected to best fit the experimental results and compared with the measured values from literature. These values are found to be generally in the range of experimentally measured values. Table 2 shows the initial equilibrium suctions measured for compacted specimens at different moisture contents given by Montanez (2002). They are presented as constant suction contours which are
Figure 1. Comparison of predicted and experimental compaction curves for well graded sand with 5% bentonite (after Montanez, 2002).
Figure 3. Comparison of predicted and experimental compaction curves for clay sandy soil (after Kenai et al., 2006). Table 1.
Figure 2. Comparison of predicted and experimental compaction curves for well graded sand with 15% bentonite (after Montanez, 2002).
Parameter values for the proposed model. Well graded sand with 5% bentonite
Well graded sand with 15% bentonite
Parameter
Value
Value
h∗ λvp n0 Gs
0.02 0.045 34 % 2.656
0.02 0.13 36 % 2.660
∗
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Water solubility
Table 2.
Initial matric suction (s0 ) values.
Well graded sand with 5% bentonite content
Well graded sand with 15% bentonite content
w (%)
s0 (kPa)
w (%)
s0 (kPa)
3.9 5.8 7.8 9.7 11.7 13.6 15.6 17.5
4630 1130 350 130 54 32 26 22
4.9 6.4 8.5 10.6 12.7 14.9 17.0 19.1
17800 11500 2550 1260 850 530 290 270
Table 3.
Figure 4. Variations of m1s with initial degree of saturation (S0 ) and during compaction for well graded sand with 5% bentonite.
Parameter values for the proposed model. Clay sandy soil
Parameter
Value
h∗
0.02 1.3 46 % 2.66
λvp n0 Gs
generally perpendicular to the water content axis giving approximately constant suction values for a given compaction water content. This ignores the curving of these contours close to saturation towards the left eventually becoming almost parallel to the full saturation line. Figures 1 and 2 show comparisons between experimental and predicted values of compaction curves for sand-bentonite mixtures. The experiments were performed under dynamic conditions (Proctor compaction), whereas model prediction assumed static undrained conditions for both air and water. Despite these differences, it is clear that reasonable predictions of the shape of the compaction curve can be obtained with the proposed approach. Figure 3 shows comparison between experimental and predicted values of the compaction curve for sandy clay soil. For this example, experiments were performed under both dynamic and static conditions. It should be noted that in this example, experimental results did not include the initial suction values. Therefore, initial suction values are assumed to be same as well graded sand with 15% bentonite (Table 2). Differences in the predicted and experimental behaviour can be traced to a number of sources. One possibility is the drainage of air, particularly on the dry side of the optimum, which can lead to higher dry densities. This analysis, however, shows that the
development of air pressure on the dry side is not very significant, but will depend on m1s . It can be seen that the predicted and experimental density difference on Figure 1 is higher than that of Figure 2. In addition to the likely influence of the other assumptions made in the analysis, this difference seems to indicate that the drainage of air may lead to higher densities in the dry side. It is likely that the pore sizes in well graded sand with 5% bentonite content is higher than the same sand with 15% bentonite. These issues will be further examined through future targeted experiments. Figure 4 shows the variation of m1s with initial degree of saturation (S0 ) and during compaction for the well graded sand with 5% bentonite content. It can be seen that coefficient of compressibility due to net stress (m1s ) decreases with decreasing initial degree of saturation (S0 ), as assumed previously by Kurucuk et al. (2007). However, during the compaction process, the degree of saturation increases from the initial value, but the coefficient of compressibility (m1s ) decreases. This decrease of compressibility happens owing to the increase of net stress as the compaction progresses. It is also apparent that much of the compaction takes place in the early part of the process where the soil compressibility decreases rapidly.
5
CONCLUSION
This paper presents theoretical concepts to predict the compaction curve for soil during undrained K0 or isotropic loading using unsaturated soil mechanics principles. It highlights the fact that the wellknown inverted parabolic shape of the compaction curve may be theoretically predicted using unsaturated soil mechanics principles, arguably for the first time in literature. This was demonstrated using published experimental results, but it was necessary to make some assumptions. The controlling parameter
378
governing the compaction process was identified as the coefficient of compressibility with respect to net stress or m1s . It was also identified that the variation in drainage conditions during compaction may influence the results. Future experiments will be targeted to develop a comprehensive set of data to examine the modelling assumptions and improve modelling capability. ACKNOWLEDGEMENTS Thanks are rendered to Monash University for providing a Monash Graduate Scholarship and financial assistance to the first author for her PhD candidature. REFERENCES Barden, L. & Sides, G.R. 1970. Engineering behaviour and structure of compacted clay. Journal Soil Mechanics and Foundations Division, ASCE, 96, No. SM4: 1171. Fredlund, D.G. & Rahardjo, H. 1993. Soil mechanics for unsaturated soils. John Wiley & Sons, Inc. Fredlund, D.G. & Morgenstern, N.R. 1976. Constitutive relations for volume change in unsaturated soils. Canadian Geotechnical Journal, 14, 3: 261–276. Hilf, J.W. 1948. Estimating construction pore pressures in rolled earth dams. Proceedings of 2nd International Conference in Soil Mechanics and Foundation Engineering, 3: 234–240. Rotterdam, The Netherlands. Hilf, J.W. 1956. An investigation of pore water pressures in compacted cohesive soils. Technical Memorandum 654, U.S. Department of the Interior, Bureau of Reclamation, Denver, Colorado.
Hogentogler, C.A. 1936. Essentials of soil compaction. Proceedings Highway Research Board, National Research Council, Washington, D.C., 309–316. Kenai, S., Bahar, R. & Benazzoug, M. 2006. Experimental analysis of the effect of some compaction methods on mechanical properties and durability of cement stabilized soil. Journal of Material Science, 41: 6956–6964. Kurucuk, N., Kodikara, J. & Fredlund, D.G. 2007. Prediction of compaction curves. 10th ANZ Conference on Geomechanics, 2: 115–119. Lambe, T.W. 1960. Structure of compacted clay. Transactions, ASCE, 125: 682–705. Lee, D.Y. & Suedkamp, R.J. 1972. Characteristics of irregularly shaped compaction curves of soil. Highway Research Board, 381: 1–9. Li, Z.M. 1995. Compressibility and collapsibility of compacted unsaturated loessial soils. Unsaturated Soils. Proc. 1st Int. Conf. on Unsaturated Soils (UNSAT 95), Paris, France (ed. Alonzo, E.E. and Delage, P.), Rotterdam: Balkema, Vol. 1: 139–144. Lloret, A., Villar, M.V., Sanchez, M., Gens, A., Pintado, X. & Alonso, E.E. 2003. Mechanical behaviour of heavily compacted bentonite under high suction changes. Géotechnique, 53(1): 27–40. Montanez, J.E.C. 2002. Suction and volume changes of compacted sand-bentonite mixtures. PhD thesis, University of London, Imperial College of Science, London, England. Olson, R.E. 1963. Effective stress theory of soil compaction. Journal Soil Mechanics and Foundations Division, ASCE, 89, No. SM2: 27–45. Proctor, R.R. 1933. Fundamental Principles of Soil Compaction, Engineering News-Record, 111: 286. Sheng, D., Fredlund, D.G. & Gens, A. 2007. A new modelling approach for unsaturated soils using independent stress state variables. Research Report No. 261.11.06, University of Newcastle, NSW 2308, Australia.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Prediction of the residual void ratio of clayey soils after drying based on their initial state, physical properties and structure M.E. Bardanis & M.J. Kavvadas National Technical University, Athens, Greece
ABSTRACT: Bardanis & Kavvadas (2006) proposed an empirical relation between residual void ratio er of clayey soils after drying and simple properties: initial void ratio eo , liquid limit wL and specific gravity Gs . Additional results are presented in this paper which support a new relation based on plastic limit wP , along with new results from undisturbed soil specimens, which indicate the possible effect of structure due to natural processes. A generalised relation therefore would predict er from eo , wP , Gs and an empirical parameter related to the structure of natural soils. However, the findings of this study indicate great scatter in correlations of er with soil index properties. Additionally, studies on undisturbed soils indicate considerable influence of soil stress history on er , thus complicating the development of a generalized relation for predictive purposes.
1
INTRODUCTION
Prediction of volume changes occurring with changes in suction is fundamental for the study of the mechanical behaviour of unsaturated soils. Constitutive models proposed for unsaturated soils predict volume changes by the corresponding parameters for elastic and plastic strains, κs and λs respectively (Alonso et al. 1990). As shown in Figure 1 (curve (a)) for changes in suction under zero total stress, specific volume υ(υ = 1 + e), and therefore void ratio e, vary linearly with suction (in logarithmic scale), according to parameter κs for suction values up to suction so (an arbitrary value of suction corresponding to yielding during drying, physically representing the maximum suction applied to the soil) and according to parameter λs for suction values past so . This type of formulation is in agreement with the formulation for the prediction of volume changes due to total stress changes under constant suction, according to parameters κ and λ(s). Such models predict realistic volume changes for suctions lower than that corresponding to residual water content, down to which shrinking during drying occurs. For suctions close to residual water content, or higher, this type of formulation overestimates volume change as it underestimates final specific volume/void ratio values. Numerous published test results (e.g. Fredlund & Rahardjo, 1993) and common experience with shrinkage tests have shown that total volume and void ratio during drying under zero total stress are expected to reach a limiting lower value er , which corresponds to residual water content and will be referred to as the residual void ratio. The value of er (or its
corresponding value of specific volume υr = 1 + er ) should be the lowest value predicted by constitutive models for unsaturated soils. Models have been proposed recently which introduce parameters limiting volume changes with increasing suction under constant total stress (e.g. Toll, 1995, Kohgo, 2004). Toll (1995) presented a conceptual model for the drying and wetting of soil which predicts the limiting of void ratio changes and therefore the calculated volume change up to the void ratio corresponding to shrinkage limit (curve (b) in Fig. 1). For this to be possible only one additional parameter is necessary. This is either the value of suction sr at which er is
e or
sO
sr
ln s
s
s
(b)
er (a)
Figure 1. Void ratio/Specific volume changes with increasing suction under zero total stress: a) without accounting for residual void ratio, and b) taking residual void ratio into account.
381
first achieved (second inflection point of curve (b) in Fig. 1) or simply er itself. Residual void ratio er therefore emerges as a critical parameter for constitutive modeling of deformable unsaturated soils.
0.8
er/eO
2
1.0
PREDICTION OF RESIDUAL VOID RATIO
0.6 0.4
Anticipating the advantages of using er rather than sr for use in constitutive modeling, Bardanis & Kavvadas (2006) proposed an empirical relation predicting er on the basis of tests on low to high plasticity clays and marls (Eq. 1). Residual void ratio er is predicted from the initial state of the soil, as expressed by initial void ratio when drying starts, eo , the physical properties of the soils, as expressed by their liquid limit wL and specific gravity Gs , and an empirical parameter m, found equal to 0.43. m · eo (1) er = eo 1 − wL · Gs Equation 1 was obtained from ten experimental points obtained for four materials. Residual void ratio values were measured on specimens left to dry in atmospheric conditions from a slurry condition or after being consolidated one-dimensionally and then unloaded to zero overburden stress. Since then experimental results from other soils have been collected and they are presented in Section 3. Index properties of the soils tested by Bardanis & Kavvadas (2006) are presented in Table 1, along with initial and residual void ratio values. The experimental results with the plot of Equation 1 are presented in Figure 2. Equation 1 Table 1. Index properties of the soils tested by Bardanis & Kavvadas (2006) along with eo and er values. Soil Chania clay
wL (%)
Ip –
Gs –
Condition1
eo –
0.2 0.0
9
2.68
0.5
1.0
1.5
2.0
2.5
eO/eL Figure 2. Normalised residual void ratio er /eo vs normalised initial void ratio eo /eL at the beginning of drying with the empirical relation proposed by Bardanis & Kavvadas (2006) and expected extensions (dashed lines).
obtained from the experimental results in Table 1 has 90% degree of correlation and passes through point {er /eo = 1, eo /eL = 0}. Equation 1 was derived from a small number of experimental points. Still the degree of correlation was very high, the best-fit equation passes through point {er /eo = 1, eo /eL = 0}, which is expected given the normalisations used, and the scatter of the points around the best-fit line is relatively small. For eo /eL tending to 0, er /eo is logically expected to tend to unity. Using eo to normalise er expresses essentially how much the total volume of an initially saturated specimen decreases due to drying, while using eL to normalise eo as correlation parameter expresses that the state relative to the nature of the soil (expressed by the void ratio at liquid limit, eL = Gs · wL ) is the determining correlating factor.
er –
3 24
0.0
Slurry Slurry 100 kPa 200 kPa 400 kPa 1600 kPa
1.05 1.04 0.59 0.52 0.51 0.43
0.35 0.34 0.33 0.31 0.34 0.31
Speswhite Kaolin Corinth Marl
64
32
2.61
Slurry
2.81
0.72
34
12
2.67
Slurry 800 kPa
1.27 0.66
0.51 0.51
Kifissia Marl
31
16
2.66
600 kPa
0.57
0.34
1 The stress reported in column ‘‘Condition’’ is the maximum stress applied one-dimensionally to a slurry of the soil and then removed before drying started.
ADDITIONAL EXPERIMENTAL RESULTS FOR RECONSTITUTED SOILS
Although small, the number of experimental points used by Bardanis & Kavvadas (2006) was sufficient to support a conceptual relation between er and the initial state and physical properties of reconstituted soil slurries as well as of reconstituted soils consolidated one-dimensionally and then unloaded. Still it was considered important that further experimental results were gathered in order to study residual void ratio and its correlation with the physical properties and the initial state of soil. In Table 2 additional experimental results obtained for two more soils tested at NTUA are presented and in Table 3 additional experimental results from various sources. With the experimental results presented in Tables 2 & 3 the total number of
382
Table 2. Index properties of additional soils tested along with eo and er values.
Ioannina lake silt Kifissia clay
wL (%)
Ip –
Gs –
Condition1
eo –
Bardanis & Kavvadas, 2006
0.8
er –
New data
24
1
2.55
100 kPa
0.69
0.58
41
21
2.67
600 kPa
0.70
0.34
eO/eL
Soil
1.0
0.6 0.4 0.2
1
The stress reported in column ‘‘Condition’’ is the maximum stress applied one-dimensionally to a slurry of the soil and then removed before drying started.
0.0 0.0
eo Condition1 –
er –
Soil
w L Ip (%) –
Fleureau et al. (1993) Sterrebeek loam
27
4
2.652 Slurry 200 31 9.5 2.652 Slurry 37 17.5 2.653 Slurry 61 30 2.673 Slurry 170 110 2.643 Slurry
0.78 0.61 1.23 1.26 2.00 7.40
64 74
32 45
2.61 2.64
200 200
1.15 0.76 1.12 0.42
95
48
2.652 200
1.27 0.80
35
16
2.71
Slurry
1.42 0.75
28
18
2.64
200
0.54 0.44
19
9
2.69
Slurry
0.77 0.35
75
50
2.65
6.2 kPa 400 kPa
3.00 0.45 1.40 0.45
130 97
2.65
Slurry
4.50 0.70
50
27
2.64
Slurry
1.98 0.51
32
15
2.71
Slurry
1.33 0.57
28.3 10.7 2.64
Slurry
0.53 0.44
Orly loam Jossigny loam White clay Montmorillonite Dineen (1997) Speswhite Kaolin London clay Melgarejo et al. (2002) Colluvium Fleureau et al. (2002) La Verne clay Cunningham et al. (2003) Silty clay Fleureau et al. (2004) Silty sand Fredlund (2004) Regina clay Agus & Schanz (2006) Bentonite/sand Abou-Bekr et al. (2006) Sikkak Peron et al. (2006) Bioley silt Pineda & Colmenares (2006) Clayey silt
1.0
1.5
2.0
2.5
eO/eL
Table 3. Index properties, initial void ratio and residual void ratio for soils from various sources. Gs –
0.5
0.61 0.52 0.39 0.46 0.88 0.95
Figure 3. Normalised residual void ratio er /eo vs normalised initial void ratio eo /eL with the empirical relation proposed by Bardanis & Kavvadas (2006), their experimental data and the new experimental data included.
Bardanis & Kavvadas (2006) and the empirical relation they proposed. As observed, the scatter of the sum of all data now is much larger, even though it seems evenly distributed on either side of the linear relation proposed. Regression analysis of the whole set of data shows that the equation describing the linear relation between er /eo and eo /eL does not change significantly but the degree of correlation drops from 90% to 44%. This picture of the whole set of data on the er /eo -eo /eL plot showed that an alternative relation should be investigated. Following the same line of thought regarding the parameters that should be used to express the relation of residual void ratio to physical properties and initial conditions, an alternative to eL was examined. In Figure 4 all the experimental data available are plotted but the void ratio at liquid limit has been substituted with the void ratio at plastic limit, eP (eP = Gs · wP ). As observed, the scatter of data decreases significantly and an exponential relation between er /eo and eo /eP appears as the best-fit curve. This is described by Equation 2. er eo = 1.108 · exp −0.42 · eo eP
1
The stress reported in column ‘‘Condition’’ is the maximum stress applied one-dimensionally to a slurry of the soil and then removed before drying started. 2 Assumed value. 3 Value derived from the slope of the full saturation line in the e-w plots presented by the authors.
experimental points rose to 30, obtained for 21 materials, ranging from pure high plasticity clays (even pure kaolinites and montmorillonites) to silty sands. In Figure 3, all the additional new data are plotted (empty circles) over the experimental points from
(2)
Equation 2 has 81% degree of correlation. The line described by Equation 2 does not pass through point {er /eo = 1, eo /eP = 0} as should theoretically be expected. If the best-fit line is forced to pass through point {er /eo = 1, eo /eP = 0} it is described by Equation 3 which has 80% degree of correlation. Equation 3 diverges only slightly from Equation 2 as shown by their comparison in Figure 4 (dashed and solid lines respectively).
383
1.0
1.4 +25%
0.8
Forced through 1
1.2
Best fit (exponential)
1.0
0.6
+50%
Predicted er
er/eO
Data
–25%
0.8
0.4
–40%
0.6 0.4
0.2
0.2 0.0 0.0
1.0
2.0
3.0
4.0
5.0
6.0
0.0 0.0
eO/eL Figure 4. Normalised residual void ratio er /eo vs normalised initial void ratio eo /eP with best fit (exponential) and if forced through point {er /eo = 1, eo /eP = 0}. 1.0
0.8
Outliers
er/eO
0.6
0.4
+35%
0.2
0.0 0.0
–35%
1.0
2.0
3.0
4.0
5.0
6.0
eO/eP Figure 5. Normalised residual void ratio er /eo vs normalised initial void ratio eo /eP with best fit (exponential) curve forced through point {er /eo = 1, eo /eP = 0} and curves defining ±35%. Outliers are marked by dashed circles.
eo er = exp −0.38 · eo eP
Outliers in Fig. 5 0.2
0.4
0.6
0.8
1.0
1.2
1.4
Measured er Figure 6.
Predicted values of er against measured values.
shown in Fig. 5) although it may overestimate it even up to 50%. Still only 4 experimental points lie above the +25% line (and below the +50% line). Therefore for 24 out of 30 experimental points predicted values of er from Equation 3 lie within a range of ±25% of the measured values, and for the whole set of experimental points predicted values lie within a range of +50%/−40% of the measured values. This scatter is very large, especially for the empirical relation expressed by Equation 3 to be used for predictive purposes. Still it is the belief of the authors that this scatter is sufficiently low to support the theoretical relation between the parameters used. It is also sufficiently low to justify the need for further experimental research on various soils in pursuit of this type of empirical relation. Soils used in this research should be left to dry after they have been consolidated and unloaded to various eo values, ranging from those corresponding to slurries to those corresponding to high stresses (in the order of MPa).
4
EXPERIMENTAL EVIDENCE FOR NATURAL SOILS
(3)
As may be observed in Figure 5, all experimental data (with the exception of two outliers) lie within a range of ±35% from the line described by Equation 3. Predicted values of residual void ratio have been plotted against measured values in Figure 6. As it is observed, Equation 3 does not underestimate residual void ratio by more than 25% (except for the outliers
Apart from the additional data for reconstituted soils left to dry from a slurry condition and reconstituted soils consolidated one-dimensionally to a maximum stress and then unloaded, a limited number of additional experimental data have been collected for natural soils with structure that were left to dry. The experimental results are presented in Table 4. One of the soils was undisturbed Corinth Marl and the other a natural colluvium reported by Melgarejo et al. (2006).
384
Table 4. Index properties of natural soils tested or found in the literature along with eo and er values. Soil
wL (%)
Ip –
Gs –
Initial suction
eo –
er –
Corinth Marl Colluvium2
34 95
12 48
2.67 2.65
9 kPa1 1000 kPa3
0.64 1.10
0.62 0.80
1.0
0.8
1 Average
value of suction measured in-situ with a Soil Moisture Quickdraw tensiometer. 2 Melgarejo et al. (2002). 3 Measured with calibrated filter papers.
er/eO
0.6
0.4
Bardanis & Kavvadas (2004) have presented a laboratory investigation of the virgin drying of the Corinth Marls. These naturally occurring marls are found in the greater area around the city of Corinth in Greece and especially along the 6.3 km long and 80 m high Corinth Canal. The excellent long-term stability of the canal’s steep slopes (the canal is 115 years old and its slopes have an inclination of 4.5:1 without any benches or berms) has driven the research in the engineering behaviour of the Corinth Marls, as their structure and partial saturation contribute greatly to the stability of the slopes. Being cemented, this natural material exhibits higher values of air-entry pressure and residual void ratio than when reconstituted and reconsolidated to the same void ratio as the natural material. Bardanis & Kavvadas (2004) have attributed this behaviour to the cementation of the undisturbed Corinth Marl, which does not exist in the reconstituted/reconsolidated specimens. This point seems to be the one more worthy of further investigation, as experimental results for unsaturated properties of marls (especially focusing on the effect of their cementation in their drying behaviour) are scarce, if any, in the literature. More information on the engineering behaviour of Corinth Marl and the role played by its cementation may be found in Kavvadas et al. (2003). Melgarejo et al. (2002) presented preliminary results from their investigation into the unsaturated properties of a colluvium from Brazil. What their results show is that although the natural structured soil has lower initial void ratio than the same soil reconstituted to a slurry condition, consolidated to 200 kPa and then unloaded, they both dry to the same value of residual void ratio. In Figure 7 all the experimental data are plotted along with these additional data for undisturbed specimens of natural soils which are indicated by arrows starting from the experimental points corresponding to the same soils reconstituted, reconsolidated and then unloaded. These data are very few. They indicate however that natural soils exhibit a higher er /eo ratio than that exhibited by the same soils when reconstituted, reconsolidated and unloaded. A general form
+35%
0.2
0.0 0.0
-35%
1.0
2.0
3.0
4.0
5.0
6.0
eO/eP Figure 7. Experimental points for slurries and overconsolidated samples with best-fit curve (exponential) forced through point {er /eo = 1, eo /eP = 0}, the lines defining ±35% from the best-fit curve and two points for soils with natural structure (empty circles with shade). The arrows start from points corresponding to the same material reconstituted and reconsolidated.
of an empirical equation predicting residual void ratio therefore would have the characteristics of Equation 4; a parameter me controlling the curvature of the exponential equation and a parameter Ms introducing the structure of natural soils. In this study me was found equal to −0.38. er eo = Ms · exp me · eo eP
(4)
Parameter Ms cannot be measured yet with the very limited data available so far and should be considered conceptual for the time being. Still its presence is evident from the differences observed between reconstituted /reconsolidated soils and natural soils. Parameter Ms must take such values that er /eo never becomes higher than unity. From Equation 4 therefore it is easily obtained that although Ms is higher than unity, it also has an upper bound found to be equal to { exp[me · eo /eP ]}−1 . It is here emphasized that the increasing factor Ms reflects the structure of natural materials rather than that created by loading history.
385
The effect of this type of structure created in reconstituted soils is already taken into account in the empirical relation by using as a correlating parameter the ratio eo /eP rather than initial void ratio eo by itself.
one-dimensional conditions) will exhibit if this conceptual formulation is sound. If it is, such analysis will also yield a relation between the empirical factor Ms and structure.
5
ACKNOWLEDGEMENTS
CONCLUSIONS
The initial empirical relation proposed by Bardanis & Kavvadas (2006) that relates residual void ratio er with initial void ratio eo , liquid limit wL and specific gravity Gs has been found valid for additional experimental data from new tests and test results collected from various publications. Although the scatter of the additional experimental points seems evenly distributed on either side of the linear relation proposed by Bardanis & Kavvadas (2006), it is so large and the degree of correlation has dropped so much that an alternative relation where wL has been substituted with wP is proposed as this exhibits higher degree of correlation. All experimental points but two (out of a total of 30) lie within a range of ±35% from the best-fit exponential equation. As far as actual values of er are concerned, for 24 out of 30 experimental points the predicted values lie within a range of ±25% of the measured values, and for the whole set of experimental points predicted values lie within a range of +50%/−40% of the measured values. These ranges are very large for the proposed equation to be used for predictive purposes. Still this scatter is sufficiently low to support a soundly based theoretical relation between the parameters used. It is also sufficiently low to justify the need for further experimental research on various soils in pursuit of this type of empirical relation. Despite these limitations of the proposed empirical relation, comparison of the experimental data for reconstituted/reconsolidated soils with the very few experimental points from tests on undisturbed samples of soils indicates that natural soils exhibit a higher er /eo ratio than that exhibited by the same soils when reconstituted, reconsolidated and unloaded. Although this latter observation cannot yet be quantified (especially given the very small number of experimental data available for soils with natural structure), it may be conceptually expressed by the formulation of Equation 4, which introduces an empirical factor increasing the value of residual void ratio predicted from eo , wP and Gs . This increasing factor is expected to be a function of the structure of natural soils. Additional experimental data for more natural soils with the accompanying data for the same soils after reconstitution and consolidation to a void ratio similar to that of the natural soils, along with measurement of the structure of these soils (for example by measuring the yield stress of both the undisturbed samples and the reconstituted samples—after a loading unloading loop to the in-situ vertical stress—under
Part of the research by M.E. Bardanis has been funded by the National Scholarship Foundation (IKY) of Greece. REFERENCES Abou-Bekr, N., Bendi-Ouis, A., Taibi, S. 2006. Characterization of the clay of Sikkak earth dam core (west of Algeria). In Miller et al (eds), Proc. 4th Int. Conf. on Unsaturated Soils, Carefree, Arizona, 2–5 April, 2006, 1607–1616, Reston, Virginia: ASCE Press. Agus, S.S., Schanz, T. 2006. Drying, wetting, and suction characteristic curves of a bentonite-sand mixture. In Miller et al. (eds), Proc. 4th Int. Conf. on Unsaturated Soils, Carefree, Arizona, 2–5 April, 2006, 1405–1414, Reston, Virginia: ASCE Press. Alonso, E.E., Gens, A., Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique 40(3): 405–430. Bardanis, M.E., Kavvadas, M.J. 2004. Laboratory investigation of the virgin drying of the Corinth Marls, in T. Schanz (ed.), Unsaturated Soils: Experimental Studies, Proc. of the Int. Conf. ‘‘From Experimental Evidence towards Numerical Modelling of Unsaturated Soils’’, Weimar, 17–18 September 2003, 421–432, Berlin: Springer. Bardanis, M., Kavvadas, M. 2006. Prediction of the limiting void ratio of clayey soils after drying. In Miller et al. (eds), Proc. 4th Int. Conf. on Unsaturated Soils, Carefree, Arizona, 2–5 April, 2006, 1085–1096, Reston, Virginia: ASCE Press. Cunningham, M.R., Ridley, A.M., Dineen, K., Burland, J.B. 2003. The mechanical behaviour of a reconstituted unsaturated silty clay. Géotechnique 53(2): 183–194. Dineen, K. 1997. The influence of soil suction on compressibility and swelling, PhD Thesis, Imperial College of Science, Technology and Medicine, University of London. Fleureau, J.M., Kheirbek-Saoud, S., Soemitro, R., Taibi, S. 1993. Behavior of clayey soils on drying-wetting paths. Can. Geotech. J. 30: 287–296. Fleureau, J.M., Hadiwardoyo, S., Kheirbek-Saoud, S. 2004. Simplified approach to the behavior of compacted soils on drying and wetting paths. In Jucá et al. (eds), Proc. 3rd Int. Conf. Unsaturated Soils, UNSAT 2002, 10–13 March 2002, Recife, Brazil 3: 1147–1154, Lisse: Swets & Zeitlinger. Fleureau, J.M., Verbrugge, J.C., Huergo, P.J., Correia, A.G., Kheirbek-Saoud, S. 2002. Aspects of the behaviour of compacted clayey soils on drying and wetting paths. Can. Geotech. J. 39(6): 1341–1357. Fredlund, D.G. 2004. Use of soil-water characteristic curves in the implementation of unsaturated soil mechanics. In Jucá et al. (eds), Proc. 3rd Int. Conf. Unsaturated Soils,
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UNSAT 2002, 10–13 March 2002, Recife, Brazil 3: 887–902, Lisse: Swets & Zeitlinger. Fredlund, D.G., Rahardjo, H. 1993. Soil Mechanics for Unsaturated Soils, New York: John Wiley & Sons, Inc. Kavvadas, M.J., Anagnostopoulos, A.G., Georgiannou, V.N., Bardanis, M.E. 2003. Characterisation and engineering properties of the Corinth Marl, in Tan et al. (eds.), Proc. Int. Workshop ‘Characterisation and Engineering Properties of Natural Soils’, Singapore, 2002, 2, 1435–1459, Lisse: Swets & Zeitlinger. Kohgo, Y. 2004. Elastoplastic models for unsaturated soils with two suction effects and unsaturated soil behavior. In Jucá et al. (eds), Proc. 3rd Int. Conf. Unsaturated Soils, UNSAT 2002, 10–13 March 2002, Recife, Brazil 3: 905–915, Lisse: Swets & Zeitlinger. Melgarejo, M.L., Ridley, A.M., Dineen, K. 2002. A comparison of the soil water characteristic curves for reconstituted and undisturbed samples of a colluvium
from Rio de Janeiro. In Juca, et al. (eds), Proc. 3rd Int. Conf. Unsaturated Soils, UNSAT 2002, 10–13 March 2002, Recife, Brazil 1: 313–316, Lisse: Swets & Zeitlinger. Péron, H., Laloui, L., Hueckel, T., Hu, L. 2006. Experimental study of dessication of soil. In Miller et al. (eds), Proc. 4th Int. Conf. on Unsaturated Soils, Carefree, Arizona, 2–5 April, 2006, 1073–1084, Reston, Virginia: ASCE Press. Pineda, J.A., Colmenares, J.E. 2006. Stress-strain-suction behaviour of two clayey materials under unconfined conditions. In Miller et al. (eds), Proc. 4th Int. Conf. on Unsaturated Soils, Carefree, Arizona, 2–5 April, 2006, 1109–1120, Reston, Virginia: ASCE Press. Toll, D.G. 1995. A conceptual model for the drying and wetting of soil. In Alonso & Delage (eds), Proc. 1st Int. Conf. Unsaturated Soils, Paris, 2: 805–810, Rotterdam: Balkema.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
An evaluation of soil suction measurements using the filter paper method and their use in volume change prediction J.M. Cumbers & J.D. Nelson Colorado State University & Tetra Tech, Inc., Fort Collins, CO, USA
K.C. Chao & D.D. Overton Tetra Tech, Inc., Fort Collins, CO, USA
ABSTRACT: An evaluation of swell prediction utilizing the filter paper test for measurement of soil suction was conducted in this investigation. Filter paper tests were conducted on four types of clay soils including claystone of the Denver and Pierre Shale Formations, from Colorado, USA, Black Cotton clay from Texas, USA and a sandy clay from Nunn, Colorado, USA. This paper presents the results of the filter paper calibration and measurement of suction values at low water contents for unsaturated soils and their use in predicting volume change. Total oven-dry suction values for the four soil types tested ranged from 6.32 pF to 6.51 pF. The calculation of the suction compression index, Ch , based on an oven-dry suction value of 6.25 pF rather than an oven-dry suction value of 6.4 pF results in an increase in Ch of 19.4% for the Denver formation and 16.0% for the Pierre Shale tested.
1
INTRODUCTION
At water contents greater than the shrinkage limit for a given soil, decreasing water contents have been shown to be directly related to increasing soil suction values. This phenomenon also results in decreasing void ratios as the water content increases. The slope of this relationship was determined to be linear for a silty clay above the shrinkage limit (Hamberg, 1985; Nelson and Miller, 1996) and because of that, the slope of the linear relation between water content and void ratio along the SWCC can be used to predict volume changes or free field heave. When suction values are used as a means for estimating the amount of volume change a soil will undergo due to changes in water content, the end points of the curve relating suction and water content are important. McKeen (1992) suggested that the typical range of suction values over which volume change will occur is between 9.8 kPa (2 pF) and 31,010 kPa (5.5 pF). The higher end of this suction range corresponds fairly well with the air-dry condition for the soil. The oven-dry intercept for a typical soil was found to exhibit a suction value of about 980,000 kPa (6.25 pF) and McKeen’s method for calculation of predicted heave uses that value to determine the slope of the suction versus water content relationship, or the dh/dw parameter.
One aspect of this relationship for which limited experimental data exists, is the soil suction values for very dry to oven-dry water contents. The soil suction characteristics of four different clay soils were observed by measuring the total and matric suction of the specimens using the filter paper test method. Filter paper tests were performed on remolded specimens prepared at very dry water contents to measure the suction potential of the soils in dry conditions.
2
EXPERIMENTAL PROCEDURES
Laboratory experiments were conducted on four different clay soil types: (1) a claystone from the Denver formation, (2) a sandy clay identified as Nunn clay, (3) a claystone from the upper Pierre Shale formation, and (4) a Texas Black Cotton soil. The first and third soils were collected at residential sites in Denver, Colorado and the second at a site near Nunn, Colorado. The Texas soil was from a residential development east of Austin, TX. The overall testing protocol included a series of index tests to characterize the four soils, a series of filter paper tests to measure the soil suction over a prescribed range of water contents, and oedometer tests to evaluate the potential for one-dimensional swell.
389
2.1
Specimen preparation
The clay soil specimens were prepared for the filter paper and oedometer testing using a modified moist tamping system at the optimum water content and 100% of the maximum dry density. The soils were initially allowed to air dry and were processed to pass through the number 4 (4.75 mm) sieve. The soil specimens were remolded and compacted into rings suitable for the oedometer tests. The sample preparation procedure is presented in a companion paper (Chao et al. 2008). 2.2
Filter paper calibration
The filter paper calibration curve for the batch of Whatman No. 42 filter papers used in these experiments was developed by Chao (2007) using a NaCl solution and molalities ranging from 0.001 to 2.70. The range of filter paper water contents evaluated based on this range of molalities was approximately 13% to 35%. The resulting filter paper calibration curve is shown in Figure 1. Because the suction measurements were being attempted for filter paper water contents below the minimum water content for the calibration data (Chao, 2007) that was being used, an effort was made to determine the total suction for filter paper with a water content below 13%. To do this, a digital hygrometer was sealed inside the lid of one of the filter paper containers. Three oven-dried filter papers were placed in the container and the container was sealed. Three other containers were also prepared each containing three oven-dry filter papers. This allowed simultaneous measurement of the relative humidity and temperature within the environment. The equilibrated water contents of the filter paper could then be related to the relative humidity and temperature of the test environment. The total suction was calculated using
7.0 Data from 3-Week Equilibration Period
6.0 (kPa) Log Total Suction,
Data from 2-Week Equilibration Period 5.0 4.0
Whatman No. 42 Filter Paper
3.0 log = 5.4634 – 0.0933 wf r2 = 0.991
2.0 1.0
log = 23.012 – 0.6389 wf r2 = 0.712
0.0 0
10
20 30 40 Filter Paper Water Content, wf (%)
50
60
Figure 1. Filter paper calibration curve for total suction measurement (Chao, 2007).
Kelvin’s equation and the measured relative humidity and temperature within the container. The filter papers were removed from the containers at intervals of 2 days, 4 days, 7 days and 11 days and weighed to determine the water contents. The calculated suction value was then correlated to the measured water content of the filter papers. 2.3 Filter paper tests The specimens for the filter paper tests were prepared in pairs. Each pair of brass rings were measured and weighed. Based on the volume of the ring, the mass of soil at optimum water content needed to fill the ring at 100% of the maximum density was calculated. This total mass was divided in fourths and compacted into layers in the brass rings. Once the specimen pairs had been compacted, they were placed in an oven at 110◦ C to reduce the water content. The objective volumetric water contents were 10%, 7.5%, 5%, 3%, 2%, 1% and 0% or fully oven-dried. To achieve this, the specimens were removed periodically from the oven, allowed to cool briefly, and weighed. Based on the initial optimum water content and the change in mass, the water content after drying was determined. Once the calculated water content had been reduced to near the target water content, the drying process was discontinued. The specimens were then allowed to cool for approximately one half-hour, and new measurements of diameter and height were taken to calculate the dried volume of the specimen. The specimens were also weighed individually prior to being placed in the sealed container for the filter paper test. The filter paper tests were performed according to ASTM D5298-03. Two sizes of Whatman No. 42 filter paper were used for the tests. The slightly larger diameters of papers were as placed on either side of the smaller diameter filter paper to provide protection from soil contamination. The filter papers were placed in the oven overnight to remove any existing moisture. They were then removed, handled only with tweezers and placed in a dessicator to cool for several minutes prior to being placed with the soil. Because of shrinkage during drying the soil specimens typically slid easily out of the brass rings in which they were compacted. Two pieces of measurement filter paper were sandwiched between the larger protective filter paper, and were placed on top of the bottom specimen. The upper specimen was then placed on top of the protective piece of filter paper. Electrical tape was wrapped gently around the pair to seal the filter papers in-place and maintain good contact between the top and bottom specimens. The combined pair of specimens was then lowered into a plastic container with a resealable lid. A piece of metal window screen, slightly larger than the diameter of the
390
specimens was placed on top of the upper soil specimen and three additional filter papers were rested on the screen. The lid was sealed and a piece of electrical tape was placed around the lid to provide an additional seal for the jar. The container was then placed within a climate-controlled box for 7 days at a temperature of approximately 23.0◦ C(73.4◦ F). After a seven-day equilibration period, the container was opened and the mass of water within the filter papers was determined. Five water content tins with lids were weighed empty and cool using an enclosed scale, capable of precision to 0.0001 grams. Once the mass of the containers was obtained, the plastic jar containing the soil specimens and filter papers was unsealed and opened. The upper filter papers being used for measuring total suction were quickly placed into individual tins with lids and weighed. The pair of specimens were then separated carefully to prevent any soil contamination of the inner measuring papers. The two matric suction papers were then individually weighed in covered moisture tins as well. The moisture tins were then propped open slightly, to allow moisture loss during drying, and then placed in the drying oven so that the water content of the filter papers could be determined. The soil specimens themselves were then weighed individually and placed in the drying oven in order to determine the soil water content for the suction values. The moisture content tins were handled with latex gloves to prevent oils from the skin from affecting the weights of the tins. The filter papers were left in the oven overnight to dry. The soil samples were oven dried for 48 hours. Each was weighed after that period to determine the oven-dry mass and the water contents.
Table 1.
3
Figures 3 and 4 show second and third-order polynomial equations that were fitted to the data. The matric suction calibration curve shown by the dashed line in the figures is the curve outlined in ASTM D5298-03. Compared to the linear curve fit, the correlation coefficients did not increase significantly for the second and third-order polynomial equations. Also as indicated by the very small magnitudes of the coefficients for the second and third-order terms, even the polynomial equations represent a near linear relationship.
3.1
RESULTS AND ANALYSES Filter paper calibration
Four sets of three filter papers were prepared in separate containers and the papers were weighed at 2, 4, 7 and 11 days. The water content of the filter papers did not vary between days 2 and 4 days but increased by about 0.5% between days 4 and 7 and then by 0.9% between days 7 and 11. Table 1 presents a summary of the measured temperatures, relative humidities and calculated suctions within the filter paper container over the 11-day period. The soil suction results were then calculated using the calibration curves shown in Figure 2 which depicts a bilinear interpolation of the calibration shown in Figure 1 with the additional points included. The additional points shown on the curve depict the measured water contents of the filter paper which ranged from 2.75% to 4.29% and the decreasing total suctions for the monitoring period from 204,488 kPa (6.32 pF) initially to 170,950 kPa (6.24pF) on day 11.
Test conditions for filter paper calibration.
Time
Temp. ◦C
Relative humidity %
avg. filter paper water content(1) %
Initial 2 Days 4 Days 7 Days 11 Days
23.4 23.4 23.3 22.9 23.2
22.3 23.8 23.3 26.7 28.5
– 2.75 2.73 3.39 4.29
(1) Average
of three filter papers.
Total suction kPa, (pF) 204,488 (6.32) 195,617 (6.30) 186,156 (6.28) 179,665 (6.26) 170,950 (6.24)
7.0 Measured Total Suction 6.0
Chao (2007) ASTM Matric Curve
5.0 4.0 3.0
R2 = 0.997
2.0 1.0 R2 = 0.713
0.0 0
10
20 30 40 Filter Paper Water Content, wf (%)
50
60
Figure 2. Bilinear filter paper calibration curve for whatman no. 42 filter paper (Modified from Chao, 2007 and ASTM).
3.2 Filter paper test results The results for the four soils tested using the filter paper method are summarized in Table 2. Each total suction point represents the average total suction calculated from the water content of three filter papers and each matric suction value represents the average matric suction calculated from the water content of
391
Table 2.
7.0
Summary of filter paper test results.
Measured Total Suction 6.0
Chao (2007) ASTM Matric Curve
5.0
Soil type
4.0 3.0 R2 = 0.997
2.0 1.0 R2 = 0.713
0.0 0
10
20 30 40 Filter Paper Water Content, wf (%)
50
60
Figure 3. 2nd-order polynomial filter paper calibration curve for Whatman no. 42 filter paper (Modified from Chao, 2007 and ASTM).
Matric
Osmotic
Denver 8.22 Formation 3.68 3.18 1.18 1.05 1.08 Oven-dry Oven-dry
158,928 216,294 232,198 264,867 263,371 274,736 238,293 254,014
118,903 142,713 153,475 171,405 160,226 160,635 168,242 163,126
40,025 73,580 78,723 93,462 103,145 114,101 70,051 90,888
Nunn Clay
10.59 7.18 4.84 3.58 2.73 Oven-dry Oven-dry Oven-dry
29,083 62,446 111,325 168,635 183,428 301,573 271,151 238,543
22,009 49,870 77,372 103,418 119,722 177,495 161,833 152,406
7,074 12,576 33,953 65,217 63,706 124,078 109,318 86,137
Pierre Shale
8.07 5.54 5.52 2.90 2.11 1.22 Oven-dry Oven-dry
121,940 135,810 164,372 213,318 234,039 261,906 253,711 263,967
93,096 120,125 120,125 135,604 146,608 165,895 161,041 167,516
28,845 15,685 44,247 77,714 87,431 96,011 92,670 96,451
Texas Black Cotton Clay
12.92 6.05 2.17 1.48 0.99 0.78 Oven-dry Oven-dry
90,001 187,292 236,817 241,297 238,598 277,190 271,039 288,347
64,800 121,900 152,737 161,113 164,686 175,333 167,577 162,567
25,201 65,392 84,079 80,185 73,912 101,857 103,463 125,780
Measured Total Suction Chao (2007) ASTM Matric Curve 5.0 4.0 3.0 2.0
2
R = 0.998
1.0 R2 = 0.713
0.0
0
10
20 30 40 Filter Paper Water Content, wf (%)
50
60
Figure 4. 3rd-order polynomial filter paper calibration curve for Whatman no. 42 filter paper (Modified from Chao, 2007 and ASTM).
two filter papers. The osmotic suction was calculated as the difference between the measured value of average total suction and the average measured value of matric suction. The Texas Black Cotton soil (which was less expansive) had higher values of suction at oven-dry conditions. However, the differences in values of total suction are most likely statistically insignificant. Two tests were run on oven-dried samples of each soil type. The average total suctions resulting for the four soils tested at oven-dry conditions are shown in Table 3. Table 3 presents the range of oven-dry total suction values measured along with the inundation pressures and the corresponding percent swell results for the consolidation-swell tests. The more expansive soils, Pierre Shale and Denver Formations have lower total suction values at oven-dry water contents than the Nunn Clay and the Texas Black Cotton clay.
Suction, kPa Total
7.0 6.0
Volumetric Water Content, %
4
DISCUSSION
Initially the filter paper test results were calculated using the calibration function developed by Chao (2007) which extended only to a filter paper water content of approximately 13%. However, after additional points were obtained for the curve, the test results were adjusted by using a new curve fitted to the combined set of data covering the broader range of filter paper water contents including the dry end of the curve. With this adjustment to the calibration curve, the importance of utilizing data points over the full range of soil suction measurements became evident. By adjusting the calibration curve for total suction to include three additional points over the range from oven-dry conditions to a water content of 13%, gravimetric water content for the
392
Table 3. Summary of oven-dry suction values and percent swell results.
7.10 7.00 Calculated Points Using Kelvin's Equation
6.90
Denver formation Nunn clay
Pierre Shale Texas Black Cotton
Percent swell, %
9.58 19.15 47.88 9.58 19.15 47.88 9.58 − 47.88 9.58 19.15 47.88
5.23 0.60 2.66 0.40 0.37 −0.14 5.30 − 4.18 2.59 2.35 −0.89
kPa 246,153
Total Suction, pF
Soil type
Inundation pressure, kPa
Overall average total suction(1) pF
270,422
6.44
P Po
6.50
258,839
6.42
279,693
6.46
6.20 0%
5%
10% 15% 20% Relative Humidity, %
25%
30%
Figure 5. Plot of Kelvin’s equation and calculated filter paper calibration points.
filter paper—the total suction values calculated using the curve from Chao (2007) without the extended range—increased in amounts up to 40%. The calibration curves for Whatman No. 42 filter paper are shown in Figures 2 through 4 along with the fitted trendline equations and the R2 values for each. Based on curve fitting of linear, second, and third-order polynomials, each provided a quality fit with R2 values that are essentially identical. However, because of the dramatic change in the test results by adding just three points to the initial data set, additional points along this calibration curve would likely result in one of the curve fitting techniques being identified as superior to the others. The overall shape of the calibration curve tends to favor the third-order polynomial (Leong and Rahardjo, 1997 and Fredlund and Xing, 1994). Figure 5 shows the total suction calculated from Kelvin’s equation. Kelvin’s equation is a function of relative humidity.
6.60
6.30
values based on a minimum of two tests per soil with three filter papers each.
RT ∗ ln ν
6.70
6.40
6.40
(1) Average
ht =
Calculated Points Used in Calibration Curve
6.80
(1)
From Figure 5, the total suction at a water content of zero is shown to be approximately 1,000,000 kPa (7.01 pF). A straight line drawn through the four points used in the calibration curve intersects the vertical axis at a suction value of approximately 6.60 pF while extrapolation of points plotted more within the range of relative humidities encountered in geotechnical engineering applications would intersect the vertical axis
at lower values. This would account for the value of 6.25 pF used by McKeen (1992) or the value of 6.40 pF calculated by Chao (2007). Two important issues are related to this topic. The first is that the lowest values of filter paper gravimetric water content measured for the oven-dry soil specimens were approximately 1% with an average total suction of 6.43 pF which means the filter paper method may not be capable of measuring suctions higher than that unless the relative humidity of the test environment is controlled at a more humid state to perform the test. Second, as the relative humidities decrease, the calibration curve should be based on a logarithmic function (as Kelvin’s equation is) rather than a linear interpolation extending to zero. This will also increase the value of the estimated oven-dry suction.
4.1 The oven dry water content intercept and Ch One of the primary objectives of this research was to evaluate the total soil suction values for the test soils at oven-dry water contents. Previous research has indicated that this point is located in the range of 6.0 pF to 7.0 pF. McKeen (1992) stated that at zero water content the total suction is equal to 6.25 pF while data from Chao (2007) for the Denver Formation and the Pierre Shale indicated an oven-dry intercept of approximately 6.4 pF. However, the calibration curve used for that data set likely caused a slight underestimation of those oven-dry results. Values measured for the Pierre Shale were 6.41 pF and 6.43 pF while values measured for the Denver Formation were 6.39 pF and 6.41 pF. The importance of this intercept is related to the prediction of volume change using the slope of the soil water characteristic curve (SWCC). The suction compression index, Ch (McKeen, 1992), which is used to calculate volume change for a soil, can be calculated
393
directly from the slope of the SWCC between the existing water content of a soil and the assumed oven-dry intercept. Because of this, as this value of the soil suction at an oven-dry condition decreases, the value of Ch is going to increase, thereby resulting in higher values of predicted volume change. Table 4 presents a summary of calculations of Ch assuming different values of total suction, pFo , at an oven-dry state. The value of Ch was calculated using water contents close to the average in-situ water contents for the Denver Formation and the Pierre Shale tested in this research. For the Denver Formation, a water content of 18.6% with a total suction of 4.63 pF was used and for the Pierre Shale a water content of 17.0% and a total suction of 4.31 pF was used. The calculated values are plotted in Figure 6. Calculating Ch based on an oven-dry suction value of 6.25 pF rather than an oven-dry suction value of 6.4 pF will result in an increase in Ch of 19.4% for the Denver formation and 16.0% for the Pierre Shale tested. Often the value of this oven-dry intercept is assumed to be a constant value for all soils when predicting volume change for a particular soil. For the soils tested, which generally cover an assorted range
of swell potentials, the oven-dry suction values varied over a range of 63,280 kPa (0.06 pF). This means that assuming the same suction value for the oven-dry water content of a non-expansive soil and an expansive soil may result in miscalculation of the swell potential for both soil types. However, the range in values of oven-dry suctions is quite small and the differences measured may be due to the difficulties in calibrating the filter papers at very low water contents. A statistical analysis was performed to evaluate the results obtained from the individual filter papers for the soil specimens prepared at oven-dry water contents. Tests for equal variances were carried out to determine if the total suction values at oven-dry water contents, for each soil, displayed normal distributions. Additionally, student T-tests were performed using varying sets of oven-dry data, both among soil types and combining soil types into groups to determine if the total suctions were statistically different for the four soil types. The statistical results indicate that there is no significant difference between the results obtained for the Denver Formation and those obtained for the Pierre Shale. The values obtained for the Nunn Clay and the Texas clay were found to be significantly statistically different from the claystones yet not significantly different from each other.
Table 4. Comparison of Ch values calculated using different oven-dry suctions.
5 Denver formation
CONCLUSIONS
Pierre Shale
Oven-dry suction pFo
Calculated values of Ch using equation by Perko (2000)
6.25 6.40 6.42 6.44 6.46 7.0
−0.279 −0.233 −0.228 −0.223 −0.218 −0.130
Total suction values at oven-dry water contents for the four soil types tested ranged from 206,060 kPa (6.32 pF) to 315,021 kPa (6.51 pF). The soil with the largest percentage of clay size particles, Texas Black Cotton clay, did exhibit the highest average suction value at oven-dry conditions and the Nunn Clay which has the largest range of particle sizes, and had the least plasticity, exhibited the largest range of oven-dry suction values. Using values of the oven-dry total suction within the range of values measured appears to have a significant effect on the calculated value of the suction compression index Ch .
−0.179 −0.154 −0.151 −0.149 −0.146 −0.093
0.00
Suction Compression Index, Ch
–0.05
REFERENCES
–0.10 –0.15 –0.20 –0.25 Denver –0.30
Pierre Shale
–0.35 –0.40 –0.45 6
6.1
6.2
6.3
6.4
6.5
6.6
6.7
6.8
6.9
7
Total Suction at Oven-Dry Conditions, pFo
Figure 6. Effect of oven-dry total suction on computed values of suction compression index, Ch .
ASTM D 5298–03. 1994. Standard Test Method for Measurement of Soil Potential (Suction) Using Filter Paper. 1996 Annual Book of ASTM Standards, Vol. 04.09, Soil and Rock, American Society for Testing and Materials, West Conshohocken, PA. Chao, K.C. 2007. Design Principles for Foundations on Expansive Soils. Dissertation, Colorado State University, Fort Collins, Colorado. Chao, K.C., Nelson, J.D., Overton, D.D. and Cumbers, J.M. 2008. Soil Water Characteristic Curves for Remolded Expansive Soils. First European Conference on Unsaturated Soils. Durham, United Kingdom.
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Cumbers, J.M. 2007. Soil Suction for Clay Soils at OvenDry Water Contents and the End of Swelling Conditions. Thesis. Colorado State University, Fort Collins, Colorado. Fredlund, D.G. and Xing, A. 1994. Equations for the soil-water characteristic curve. Canadian Geotechnical Journal, Vol. 31. pp. 521–532. Hamberg, D.J. 1985. A simplified method for predicting heave in expansive soils. M.S. thesis, Colorado State University, Fort Collins, CO. Leong, E.C. and Rahardjo, H. 1997. Review of Soil-Water Characteristic Curve Equations. Journal of Geotechnical and Geoenvironmental Engineering. pp. 1106–1117.
Nelson, J.D. and Miller, D.J. 1992. Expansive Soils: Problems and Practice in Foundation and Pavement Engineering, Wiley, New York. McKeen, R.G. 1992. A Model for Predicting Expansive Soil Behavior. 7th International Conference on Expansive Soils. Dallas, Texas, USA. pp. 1–6. Perko, H.A., Thompson, R.W., and Nelson, J.D. 2000. Suction Compression Index Based on CLOD Test Results. Geo-Denver 2000. pp. 393–408.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Validation of a swelling potential index for expansive soils J.L. Zheng, R. Zhang & H.P. Yang School of Highway Engineering, Changsha University of Science and Technology, Hunan, China
ABSTRACT: A new swelling potential index for expansive soils, the Standard Absorption Moisture Content (SAMC), was recommended in Chinese Specifications for Design of Highway Subgrades JTG D302004. In order to validate the index, sixteen soils were obtained from six typical areas where expansive soils exist in China. Extensive tests on soil properties indicative of swelling potential, such as Atterberg limits, free swelling ratio, clay content, SAMC, cation exchange capacity, specific surface area and montmorillonite content, were conducted. Correlations between the various indices were obtained and analyzed. The study shows that SAMC is more strongly correlated with the mineralogical and chemical properties, which determine swelling potential in nature, than other physical indices. Therefore, the new swelling potential index was validated to be reliable to identify and classify swelling potential of expansive soils.
1
INTRODUCTION
Soil property indices are the basis for identifying expansive soils and grading their swelling potential (Tan, 2007). Numerous studies have been carried out to obtain a suitable soil property index that can reflect and grade swelling potential of expansive soils. Karathanasis & Hajek (1985) found montmorillonite content (MC) as the only consistent soil property that significantly correlated with laboratory-measured shrink-swell potential. Ross (1978) concluded that swell potential of montmorillonitic soils were correlated with clay content (CC) and specific surface area (SSA). Gill & Reaves (1957) described cation exchange capacity (CEC), saturation moisture (SM) and plastic index (PI) as some of the most representative properties in the estimation of swelling potential having established them as highly correlated to the SSA. Snethen et al. (1977) evaluated 17 swelling indices and concluded that liquid limit (LL) and PI are the best indicators of potential swell and Parker et al. (1977) concluded swell index (SI) (Lambe 1960) and PI were superior to other indices. The free swelling ratio (FSR), defined as the volume increment of oven-dried soil passing 0.5 mm sieve and fully swelling in a graduated flask with distilled water expressed as a ratio of the initial volume of the soil (10 ml), is used as the sole swelling potential index in the Chinese Technical Code for Building in Expansive Soil Area (China Ministry of Construction
2003). The maximum linear shrinkage ratio, plastic limit (PL), the shrinkage limit, potential volume change index were also suggested and recommended by some researchers (Parker et al. 1977, Williams 1958). The indices used to characterize swelling potential of expansive soils can be classified into two types. The first type mainly involves mineralogical and chemical properties, such as MC, SSA, CEC, which determine the expansion of soils in nature (Mitchell 1976, Shi et al. 2002) and are reasonable to be used as swelling potential indices (Tan 2007). The second type involves physical properties, such as FSR, SI, Atterberg limit, swelling pressure, shear strength, and others, and are easily influenced by external environment and testing factors resulting in a wide range of values and misleading swelling potential grade. Thomas et al. (2000) suggested that shrinkswell behavior can best be predicted by examining a combination of physical and mineralogical properties. However, because the mineralogical and chemical properties are not easy to be measured, it is hard to apply them to grade swelling potential in engineering practice. In order to find a new swelling potential index, which would be easily measured and strongly correlated with the mineralogical and chemical properties of expansive soils, Yao et al. (2004) conducted many tests and put forward the standard absorption moisture content (SAMC). The index has been temporarily adopted as an index of the swelling potential rating
397
Table 1.
Swell potential rating system.
seal
Swell potential class
SAMC (%)
PI (%)
FSR (%)
Low Medium High
2.5–4.8 4.8–6.8 >6.8
15–28 28–40 >40
40–60 60–90 >90
glass container box soil sample porous plate saturated salt solution
system for expansive soils (Tab. 1) in the Chinese Specifications for Design of Highway Subgrades (China Ministry of Communications 2003). However, the index has been tested only for a small range of expansive soils, so the applicability to identify and classify expansive soils still needs further study. The objectives of this study was to validate and evaluate SAMC as a swelling potential index through (1) quantifying physical and mineralogical properties of 16 expansive soil samples in 6 areas in China, (2) examining and analyzing the correlation between SAMC and the mineralogical indexes, and (3) comparing the results of classifying swelling potential. It should be noted that the method has not yet been compared with direct measurements of swelling potential on undisturbed samples.
2 2.1
THE STANDARD ABSORPTION MOISTURE CONTENT Definition and physical meaning of SAMC
The standard absorption moisture content (SAMC) is the equilibrium water content when the soil is dried from its natural water content at (25 ± 2)◦ C and (60 ± 3)% relative humidity. The moisture absorbed on the surface (and in the interlayers) of montmorillonite mostly contributes to the amount of moisture absorption of the soil in this condition (Yao et al. 2005). The more montmorillonite the soil sample contains, the bigger SAMC is. Therefore, SAMC indirectly reflects the montmorillonite content of the soil.
Figure 1.
A glass container (Constant Humidity).
3. Desiccator, a glass container similar to the one shown in Figure 1, but with calcium chloride powder in the bottom instead of saturated salt solution. 4. Aluminum Box which is 1.5 cm in height and 6 cm in diameter and used to hold samples in the oven, desiccator or constant humidity container. 5. Electronic Balance with measurement precision of 0.001 g. The test procedure is as follows: 1. Weigh the oven dried aluminum box with the electronic balance, record the weight as W0 . 2. Cut undisturbed soil into slices, put 4 g of them into the box, weigh the aluminum box and soil sample together and record the weight as W1 . 3. Place the aluminum box holding the soil sample on the porous plate in the constant humidity container. Then seal the container and place it in a room with constant temperature of 25◦ C. 4. Take out and weigh the box holding the soil sample every day, then put it back into the container. Observe the change of weight till it changes little. Record the final weight as W2 . 5. Put the box holding soil sample into the oven and keep for 5 hours at 105–110◦ C. 6. Take the box out of the oven and put it into the desiccator. Keep for 1 hour to make its temperature reach the room temperature. Then, weigh the box holding soil sample as W3 . The SAMC can be calculated according to the following formula,
2.2 Test methods of SAMC The devices used to measure SAMC of expansive soils are as follows: 1. Constant Humidity Container, a glass container with 1000 ml saturated or oversaturated sodium bromide (NaBr) solution in the bottom, and it should be placed in a room at 25◦ C (Figure 1). 2. Oven where the temperature can be controlled at 105–110◦ C to dry samples.
wa =
W2 − W 3 W3 − W0
(1)
Where wa = SAMC (%); W2 −W3 = the maximum weight of absorbed moisture (0.001 g); and W3 −W0 = the weight of dry sample (0.001 g).
398
To ensure accuracy, parallel tests should be conducted. The permissible error is 0.2%, with regard the average. The average value is taken as the final result.
3 3.1
MATERIALS AND METHODS Sampling site selection
Sampling sites were carefully selected based on six physiographic zones described by Liao (1984). Undisturbed soil samples were obtained from Ningming basin and Nanning basin in the autonomous region of Guangxi Zhuangzu, Nanyang basin in Henan province, Hanzhong of Shanxi Province, and Zhaotong and Chuxiong of Yunnan province. These places are typical of areas in China that have widespread distributions of expansive soils. Sampling locations and description are summarized in Table 2. 3.2
Laboratory tests
Laboratory tests include measuring SAMC as well as Atterberg limits, free swelling ratio (FSR), particlesize distribution, CEC, SSA and mineralogical composition; these are usually used as swelling potential indices. The samples were sieved to remove coarse fragments >2 mm prior to analysis for the various indices. The Atterberg limits (PL, LL, PI), were measured according to JTJ-051-93: T0118-93 (China Ministry of Communications 1996). FSR was measured according to JTJ-051-93: T0124-93. The grain size analysis was conducted with the addition of (NaPO3 )6 as a dispersant to better determine the dispersive capability of the soil in its natural state. Then, the clay content (the percentage <0.002 mm) was obtained through the grain size analysis. The clay minerals were especially examined using X-ray diffractometry (XRD). To identify the clay minerals quantitatively, the specimens were treated to remove organic matter, carbonates and iron oxides, and oriented glass slides were prepared in three ways: normal, heated and glycolated (Al-Homoud et al. 1996). As a result, MC was obtained. The water-air adsorption balance method was used to examine specific surface area (SSA) of soil specimens. Total cation exchange Table 2.
capacity (TCEC) and exchangeable cations were determined by atomic absorption spectroscopy. It has been reported that air-dry samples and ovendry samples could also be used in the SAMC test (Xu et al. 2006). However the initial water content, microstructure of the sample and the change of moisture content in the test would be different so the measured SAMC would be less real. Therefore, undisturbed samples were still used in the SAMC test.
3.3
Statistical analysis
Correlation coefficients of the linear relationships between SAMC and MC, SSA, and CEC were used to validate SAMC as a swelling potential index for expansive soils. In addition, Pearson’s correlation coefficients of the relationships between the various physical properties indices and the obtained mineralogical soil properties were used to reevaluate the usual indices for rating swelling potential of Expansive Soils.
4
RESULTS AND ANALYSIS
The main laboratory test results are summarized in Table 3. According to the results, the linear relationship and the correlation coefficients between SAMC and MC, SSA, and CEC has been analyzed and is shown in Figures 2, 3 and 4 respectively. Figure 2 shows a strong linear correlation between SAMC and MC, the regression coefficient is 0.960. It can be explained as follows: expansive soils typically contain strongly hydrophilic clay minerals (montmorillonite and illite). Montmorillonite is the main mineral influencing the shrink-swell behavior of the expansive soils due to the high ability to absorb water on inner and outer surfaces of montmorillonite crystals. The adsorbability is 1013.3 to 2026.5 MPa. In the standard test condition (25◦ C in temperature and 60% in relative humidity), the absorbability is very stable. There is also illite, kaolinite and other clay mineral in expansive soils, but their ability to absorb water is much lower than montmorillonite’s. The water
Sampling locations and description.
Location
Origin
Source of materials
Geological times
Geomorphology unit
Sample no.
Ningming Naning Hanzhong Dengxian Zhaotong Chuxiong
Eluvial Lacustrine Pluvial Pluvial Eluvial Lacustrine
Claystone, shale Weathering of mudstone Weathering of metamorphic rock Weathering of marlite Weathering of claystone Weathering of marlite
N–Q1 Q3 –Q4 Q1 –Q2 Q2 –Q3 N2 –Q1 N2 –Q1
Hilly area Intermountain basin Basin and terrace ridge Basin and terrace ridge Intermountain basin Second terrace
1, 2, 3, 4, 5, 6 7, 8, 9 10, 11 12, 13 14, 15 16
399
Table 3.
Soil parameters for expansive soils. Depth
PL
LL
PI
FSR
CC
SAMC
CEC
SSA
MC
Sample no.
m
%
%
%
%
%
%
meq/1 kg
m2 /g
%
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
1.5 3.5 9.9 12.0 1.5 6.0 2.0 5.0 8.0 2.3 4.8 2.0 4.5 2.0 5.0 2.0
27.5 30.4 24.1 21.9 27.1 28.2 23.4 23.6 24.3 18.6 19.3 24.5 21.6 31.5 34.8 22
55.9 60.0 52.6 44.2 59.7 56.9 51.0 48.6 49.3 39.6 36.8 59.2 49.9 78 83.4 44.2
28.4 29.6 28.5 22.3 32.6 28.7 27.6 25.0 25.0 21.0 17.5 34.7 28.3 46.5 48.6 22.9
45 44 18 20 75 58 87 68 65 47 38 98 87 145 127 65
40.1 47.1 28.2 23.7 52.1 48.2 46.7 43.5 45.7 38.3 32.4 48.2 43.6 62.2 53.8 48.9
6.6 5.9 4.9 4.1 6.2 6.3 3.5 3.4 3.6 4.7 4.5 7.3 6.1 11.1 13.1 3.9
198.4 199.2 212.9 219.3 221.8 228.5 164.3 161.9 166.8 225.9 230.1 275.1 246.5 354.2 385 165.4
175.46 170.9 161.11 158.06 194.76 191.38 121.25 112.78 99.21 145.34 122.74 237.13 192.36 335.38 356.2 152.48
21.65 19.07 17.64 15.52 20.01 20.14 12.76 12.39 11.51 16.37 11.4 26.73 22.46 40.07 40.95 12.53
50
CEC (me/1kg)
40 MC (%)
400
MC = 3.275 SAMC + 0.612 2
R = 0.960
30 20 10
2
R = 0.883
300 250 200 150 100
0 2
4
6
8 10 SAMC (%)
12
2
14
Figure 2. Relationship between standard absorption moisture content and montmorillonite content.
SSA (m 2/g)
CEC = 22.09 SAMC + 97.32
350
400 350 300 250 200 150 100 50
SSA= 26.03 SAMC+ 28.23 2
R = 0.952
2
4
6
8 10 SAMC (%)
12
14
Figure 3. Relationship between standard absorption moisture content and specific surface area.
absorbed by montmorillonite accounts for a large percentage of the water in an expansive soil in this test condition. Therefore, SAMC reflects the degree of montmorillonite present, the more montmorillonite contained in expansive soils, the bigger the SAMC,
4
6
8 10 SAMC (%)
12
14
Figure 4. Relationship between standard absorption moisture content and cation exchange capacity.
and SAMC is strongly correlated with montmorillonite content (MC). Figure 3 and Figure 4 also show good linear relationships between SAMC and SSA and CEC. This is because the specific surface area of montmorillonite is larger than specific surface area of Illite and other clay minerals. Therefore, the larger the SSA, the bigger SAMC. It has been found that CEC is highly correlated with SSA (Gill & Reaves, 1957), so it is reasonable that a good linear relationship occurs between SAMC and CEC. In conclusion, SAMC is strongly correlated with the mineralogical soil properties. Montmorillonite is the main reason why an expansive soil undergoes appreciable volume following a change in moisture content. Cation exchange capacity reflects the adsorbability of the crystal lattice of expansive soil, the amount and type of cation are the extrinsic factors that influence the hydrophilicity and shrink-swell behavior of expansive
400
soils. Therefore, SAMC also reflects the basic properties of expansive soils, and it could be a swelling index for expansive soils. Table 4 gives the Pearson’s correlation coefficients (r) of the relationship between the various physical property indices and the mineralogical properties indices (MC, SEC, and SSA). It shows that the PI is also strongly correlated with the mineralogical indices. This is because PI not only represents the dispersibility of clay minerals of expansive soils due to exchangeable cations but also reflects the degree of absorbtion of water by osmosis which directly influences the shrink-swell ability of expansive soil. However, the other indices, PL, free swelling ratio (FSR) and clay content (CC) are not well correlated with the mineralogical indices. As for FSR, it cannot reflect the characteristic of expansive soils and the testing result is influenced by many extrinsic factors, as a result it gives a wide range of values. CC can not represent the swelling potential either, because the potential is mainly controlled by strongly hydrophilic clay mineral such as montmorillonite. If soil only contains most of weakly hydrophilic minerals such as kaolinite, even if the clay content is large, it would not mean that the soil possesses high swelling potential. In order to validate the applicability of the new index SAMC and the swelling potential rating system recommended in the Chinese Specifications for Design of Highway Subgrades, the swelling potential of expansive soil samples were classified according to Method 1, the rating system shown in Table 1, and Method 2, the rating system which mainly involves mineralogical and chemical properties indices and is shown in Table 5. The classification results are summarized in Table 6. The consistency between the results of the two methods shows that the recommended swelling potential rating system involving the new swell index SAMC may correctly identify and classify swelling potential of expansive soils. Table 4. Correlations between physical indices and mineralogical indices. r
PL
LL
PI
FSR
CC
SAMC
MC SSA CEC
0.759 0.585 0.745
0.912 0.781 0.901
0.940 0.927 0.818
0.748 0.666 0.738
0.580 0.414 0.580
0.979 0.940 0.975
Table 5. Swelling potential rating system (China Ministry of Railways, 2001). Swell potential class
MC (%)
CEC (meg/kg)
FSR (%)
Low Medium High
7–17 17–27 >27
100–190 190–360 >360
40–60 60–90 >90
Table 6.
Classification results.
Sample no.
Method 1
Method 2
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
moderate moderate moderate low moderate moderate low low low low low high moderate high high low
moderate moderate moderate low moderate moderate low low low low low moderate moderate high high low
5
CONCLUSIONS
Based on the above research results, the following conclusions can be drawn: 1. The swelling potential indices can be classified as physical properties indices and mineralogical properties indices. Mineralogical properties indices involve montmorillonite content, specific surface area and cation exchange capacity. These reflect and influence shrink-swell behavior of expansive soils in nature, and therefore they are reliable swelling potential indices. 2. The standard absorption moisture content is linearly correlated with mineralogical properties of expansive soils, it possesses clear physical meaning and reflects the characteristic of expansive soils, and therefore it can be used as a swelling index. 3. The classification results of the recommended swelling potential rating system involving of the new swell index SAMC are consistent with the rating system mainly involving of the mineralogical properties indices. It shows that swelling potential of expansive soils can be correctly identified and classified according to the recommended rating system. This suggests that SAMC can be used practically as a swelling index. However, it should be noted that the method has not yet been compared with direct measurements of swelling potential on undisturbed samples. REFERENCES Al-Homoud, A.S., Khoury, H. & Al-Omari, Y.A. 1996. Mineralogical and engineering properties of problematic expansive clayey beds causing landslides. Bulletin of the International Association of Engineering Geology, 54: 13–31. Paris.
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China Ministry of Communications. 2003. Specifications for Design of Highway Subgrades JTJ013-2002. Beijing: China communications Press, China. China Ministry of Communications. 1996. Test Methods of Soils for Highway Engineering JTJ051-93. Beijing: China Communications Press. China Ministry of Construction. 2003. Technical Code for Building in Expansive Soil Area GBJ112-87. Beijing: Chinese planning press. China Ministry of Railways. 2002. Code for Rock and Soil Classification of Railway Engineering TB 10077-2001. Beijing: China Railway Publishing House. Gill, W.R. & Reaves, C.A. 1957. Relationships of Atterberg limits and cation-exchange capacity to some physical properties of soil. Soil Sci. Soc. Am. Proc. 21: 491–494. Karathanasis, A.D. & Hajek, B.F. 1985. Shrink-swell potential of montmorillonitic soils in udic moisture regimes. Soil Sci. Soc. Am. J. 49:159–166. Lambe, T.W. 1960. The character and identification of expansive soils. Fed. Housing Admin. Rep. 701. U.S. Gov. Print. Office, Washington, DC. Liao, S.W. 1984. Expansive Soil and Railway Engineering. Beijing: Chinese Railway Publishing Press. Mitchell, J.K. 1976. Fundamentals of Soil Behavior. New York: John Wiley & Sons Inc. Parker, J.C., Amos, D.F. & Kaster, D.L. 1977. An evaluation of several methods of estimating soil volume change. Soil Soc. Am. J. 41: 1059–1064. Peck, R., Hanson, W. & Thornburg, T. 1974. Foundation Engineering. New York: John Wiley & Sons Inc. Ross, G.J. 1978. Relationships of specific surface area and clay content to shrink–swell potential of soils having
different clay mineralogical compositions. Can. J. Soil Sci. 58: 159–166. Shi, B., Jiang, H.T. & Liu, Z.B. 2002. Engineering geological characteristics of expansive soils in China. Engineering Geology 67: 63–71. Snethen, D.R., Johnson, L.D. & Patrick, D.M. 1977. An evaluation of expedient methodology for identification of potentially expansive soils. Soil and Pavements Laboratory, U.S. Army Eng. Waterway Exp. Sta., Vicksburg, MS, Rep. No. FHWA-RE-77-94, NTIS PB-289-164. Tan, L.R. 2007. Identification and Classification of Swellshrinking Soil. Soil Engineering and Foundation. 21(4): 85–88. Thomas, P.J., Baker, J.C. & Zelazny, L.W. 2000. An expansive soil index for predicting shrink-swell potential. Soil Sci. Soc. Am. J. 64: 268–274. Williams, A.B. 1958. Discussion of the prediction of total heave from double oedometer test. South African Institution of Civil Engineers, 5(6): 49–51. Xu, X.C., Chen, S.X. & Yu, F. 2006. Effect of different sampling methods on standard absorption water content. Chinese Journal of Rock Mechanics and Engineering. 25(10): 2135–2139. Yao, H.L., Yang, Y. & Cheng, P. 2004. Standard moisture absorption water content of soil and its testing standard. Rock and Soil Mechanics. 25(6): 856–859. Yao, H.L., Cheng, P., Yang Y., & Wu, W.P. 2005. Theory and practice concerning classification for expansive soils using standard moisture absorption water content. Science in China Ser. E. Engineering & Materials Science. 48(1): 31–40.
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Shear behaviour
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Effect of moisture content on tensile strength and fracture toughness of a silty soil M.R. Lakshmikantha, P.C. Prat, J. Tapia & A. Ledesma Technical University of Catalonia, Barcelona, Spain
ABSTRACT: Determination of fracture parameters (tensile strength, fracture toughness) is essential in determining the cracking behaviour of soils. In drying soils, a crack initiates when the tensile stresses exceed the soil strength. Crack propagation is considered to be governed by the stress state in the crack front and subsequent dissipation of fracture energy, for which Fracture Mechanics Theory can be used. In this context characterizing the soil for these two parameters require two different testing equipments. The tensile strength was determined using existing equipment (direct method) at the Soil Mechanics Laboratory of UPC whereas new equipment was designed for the fracture toughness determination. The results of tensile strength tests are consistent with published literature. Fracture toughness decreases as the moisture content increases; an attempt is made to explain this using the concept of Rate Process Theory and Activation Energy of soils.
1
soil densities, with average moisture content ranging from 12% to 30%.
INTRODUCTION
In a drying soil, a crack initiates when the tensile stresses exceed the soil strength. Crack propagation is considered to be governed by the stress state in the crack front and subsequent dissipation of fracture energy, for which Fracture Mechanics Theory can be used. In this context determination of fracture parameters (tensile strength, fracture toughness) is essential in determining the cracking behaviour. Characterizing the soil for these two parameters require two different testing equipments. The tensile strength was determined using existing equipment (direct method) at the Soil Mechanics Laboratory of UPC whereas new equipment was designed for the fracture toughness determination. To determine fracture toughness, two sizes (medium and big) of compact tension (CT) tests specimens were used. Originally there was another size (small) of CT test specimen, but due to the problems with sample preparation and handling the tests were not conducted with this size. Apart from the determination of fracture toughness, the effect of moisture content was also studied. Tensile strength of soils is an important indicator, as it depends on various other properties of soil. Until recently, determination of the soil’s tensile strength has not received the attention it deserves, mainly because of the difficulty of the experimental set-up. It is known that the tensile strength of soils varies with the degree of saturation (moisture content) as well as with the density, so, the tensile strength was determined for two
2 2.1
MATERIALS AND METHODS The soil
The soil used in the experiments is a Barcelona silty clay collected from a construction site near the laboratory at a depth of approximately 4 m below ground surface. This type of soil is commonly found in the area and has been extensively studied in the past in the laboratory, its geotechnical and hydro-mechanical properties being well known (Barrera 2002). Figure 1 shows typical grain size distribution and water retention curves for the soil used in the experiments. It is a fine grained soil, with 60.6% passing the No.200 sieve. Its main characteristics are: unit weight of soil particles γs = 27.1 kN/m3 ; liquid limit wL = 32%; plastic limit wP = 16%. According to the unified soil classification system, the soil can be classified as low plasticity clay (CL). 2.2
Compact tension tests
The equipment for the determination of fracture toughness (KIC ) was developed at the Soil Mechanics Laboratory of UPC, using the equipment design of Ávila (Ávila 2004). Test specimens of two different sizes were tested (Table 1) at different moisture content, with a constant density γ = 1.95 ± 0.05 kN/m3 . Figure 2 show the schematics of the equipment.
405
The dry soil was sieved through a mechanical sieve of 1.18 mm (sieve no. 16); the material passing was used for the test. Distilled water was added in required quantity to achieve the intended moisture content. Once a visibly homogeneous paste was obtained, its moisture content was determined before pouring it into the CT-moulds. Moisture content was determined again when the experiment was completed. The CTmould was filled with the prepared material in three layers in order to have a homogeneous density. Loading pins were inserted to the specimens after removing from the moulds and a Methacrylate plate was inserted between the specimen and the nuts of the loading pin in order to ensure the correct load transmission to the right fracture zone just below the initial crack. The load was applied manually, with a constant frequency. The fracture load was determined counting all the weights in the loading pan after the specimen failed. The procedure was repeated for all the specimens. The moisture contents of the test specimens were 16%, 18%, 19%, and 21%, with an initial crack length of 10, 15, and 20 mm for the medium and 20, 30, and 40 mm for the big specimen. For each size, moisture content and initial crack length, tests were repeated with a minimum of two specimens and in some cases with three. A total of 55 specimens were tested. Table 1 gives the details of the geometry of the test specimens, with length (L), width (B), and thickness (W). A circular hole of diameter (φ) was made form a distance (d) to the edge of the specimen for loading pins. Figure 1. a) Grain size distribution; b) typical water retention curves for different dry unit weights (Barrera 2002). Table 1.
KI =
P ˆ √ k(α) B D
(1)
KI2 (2) E Fracture toughness (K) was calculated by eq.1, where D is the characteristic dimension of the specimen (in the present case W = D); P is the fracture ˆ load; and B is the width of the specimen. k(α) is a function depending on the geometry of the specimen ˆ (α = a/W). k(α) was calculated using two different empirical formulas, given by Eq. 3 (ASTM-E399-83 1983) and Eq. 4 (Srawley 1976). The fracture energy (G) was calculated using Eq. 2, with υ = 0.3 and E = 4.2 MPa (Barrera 2002).
GIC = (1 − ν 2 )
Details of CT-test specimens.
Mould
L (mm)
B (mm)
W (mm)
d (mm)
φ (mm)
Medium Big
60 120
25 50
45 90
15 30
12 24
k(α) = (30.96α − 195.8α 2 + 730.6α 3 − 1186.3α 4 + 754.6α 5 )
(3)
k(α) = (2 + α) 0.886 + 4.64α − 13.32α 2 + 14.72α 3 − 5.6α 4 × (1 − α)3/2 Figure 2.
(4)
Schematic diagram of CT-test equipment.
406
Figure 3. Schematic diagram of direct tensile strength equipment.
2.3
Direct tensile strength test
Tensile strength was determined using an equipment designed by Rodríguez (Rodríguez 2002), the equipment is similar to the one explained by Mikulish and Gudeus (Mikulish and Gudeus 1995). The equipment is made up of 3 main parts, (see fig. 3): two pieces of trapezoidal shape, one fixed and another one freely movable on application of external force, and a central part that is removed just before the application of the load; this is the only part of the specimen which will be subjected to tension during the test. A total of 42 tests were conducted for two different densities (18 tests with γ = 16 kN/m3 , and 24 tests with γ = 19 kN/m3 ) with average moisture content ranging from 12% to 30%. For each density and moisture content the tests were repeated with a minimum of two specimens and in some cases three. The soil used and the preparation of the material was the same as explained earlier for the fracture toughness tests. The depth of the soil placed in the equipment was fixed and the weight of the soil was varied to obtain different densities. The tensile strength (σT ) was calculated directly by dividing the area of soil under tension by the total load applied.
3
variation of the tensile strength with moisture content for all tests carried out. The maximum tensile strength is obtained with a moisture content of about 16% to 17%. The OMC (Optimum Moisture Content) of the soil is around 13.5% with a degree of saturation of approximately 80%. According to Towner (Towner 1987), the tensile strength is a material property that depends in general on both suction and water content. Moreover the relationship also depends on the degree of inherent or induced anisotropy that may exist in the material. Several methods are available to determine the tensile strength of soils. Accuracy of the values depends on the test methods used and the equipment. The direct method is considered to be the most straightforward and reliable. In the present study, because of the trapezoidal shape of the equipment, the tension was applied only to the central zone. Figure 4 shows the variation of tensile strength with moisture content for two dry densities. A clear difference in the tensile strength for different densities on the dry-side is observed, whereas on the wet-side the difference is smaller. Similar behaviour has been observed by other authors (Favaretti 1996; Tamarakar, Toyosawa et al. 2005; Rodríguez 2006). 3.2
Fracture toughness
Figure 5a shows the variation of fracture load for the two specimen sizes (medium and big) at various moisture contents. As a common and well known trend, here also the fracture load increases with decrease in initial crack length (Lee, Lo et al. 1988; Nichols and Grismer
RESULTS AND DISCUSSIONS
3.1 Tensile strength The tensile strength was determined for two densities and at different moisture contents. Figure 4 shows the
Figure 4. content.
407
Variation of tensile strength with moisture
bond ruptures that constitute the mechanism of fracture are provoked by the energies of thermal vibrations (Cottrell 1964). This is valid for many materials: metals, glass, ceramics, rocks, concrete, etc. which can be considered as single phase and/or continuous medium. Soils, however are particulate media, and usually two-phase (solid particles and pore fluid when fully saturated) or three-phase systems (solidpore fluid-air when un-saturated). The most important characteristic of such materials is the behaviour of stress-strain relationship depending on the degree of saturation keeping aside the temperature effects. At a given temperature the variation in degree of saturation will affect the stress-strain behaviour. Therefore the fracture behaviour of soils depends largely on the variation of degree of saturation (suction and tensile strength) which affects the fracture toughness. Figure 6 shows the fracture toughness vs moisture content. The data points follow an exponential behaviour, with decreasing K values for increasing moisture content. Bazant and Prat (Bazant and Prat 1988) observed a similar behaviour on the fracture energy of concrete with temperature. Fracture energy decreased exponentially with increase in temperature. They used Rate Process Theory and Activation Energy to explain the behaviour, which generally follows a formula of the type a˙ = f (K) exp(−U /RT ) (Cherepanov 1979), where U = activation energy of bond rupture; R = universal gas constant; T = absolute temperature; K = stress intensity factor; and f (K) = empirical monotonically increasing function. Further studies are necessary to establish the applicability of the rate process theory and activation energy
Figure 5.
(a) Fracture load (b) Fracture energy.
1997) irrespective of specimen size and moisture content. Other observed important behaviour, particular to soils, is the effect of moisture content on the fracture load: fracture load decreases as the moisture content of the test specimens increases for both sizes’s tested. Figure 5b shows the variation of the fracture energy, G, with the initial crack length. The regression lines calculated with the ASTM and Srawley methods show that G is approximately constant (Lee, Lo et al. 1988) for a given moisture content, proving that G is a material constant (depending on moisture content for soils). 3.3
Activation energy
It is generally accepted that fracture is a thermally activated rate process. This means that the atomic
Figure 6. content.
408
Variation of fracture toughness with moisture
to explain the variation of fracture toughness with soil moisture change. 4
CONCLUSIONS
At lower moisture contents (drier moisture content to OMC), the effect of density is more pronounced on the tensile strength, whereas at moisture content wetter to OMC, there seems to be little effect of density and is almost negligible at saturation. Fracture toughness (Mode I) of Barcelona Silty soil significantly depends on the moisture content. It decreases monotonically with the increase in moisture content. The data points of fracture toughness vs moisture content follow an exponential curve. Similar behavior was observed for concrete with temperature. This prompts to check the applicability of Rate Process Theory and Activation Energy to explain such a behavior. ACKNOWLEDGEMENTS The research reported in this paper has been carried out within the framework of two research projects financed by the Spanish Ministry of Education and Science (BIA2003-03417 and CGL2006-09847). Their support is gratefully acknowledged. REFERENCES ASTM-E399-83. 1983. Standard test method for planestrain fracture toughness of metallic materials. American Society for Testing and Materials. Ávila, G. 2004. Estudio de la retracción y el agrietamiento de arcillas. Aplicación a la arcilla de Bogotá (In Spanish). Technical University of Catalonia.
Barrera, M.B. 2002. Estudio experimental del comportamiento hidro-mecánico de suelos colapsables (In Spanish). Technical University of Catalonia. Bazant, Z.P. and Prat, P.C. 1988. ‘‘Effect of temperature and humidity on fracture energy of concrete.’’ ACI Materials Journal (July–August): 262–271. Cottrell, A.H. 1964. The Mechanical Properties of Matter. New York, John Wiley & Sons. Cherepanov, G.P. 1979. Mechanics of brittle fracture. New York, McGraw-Hill Book Co. Favaretti, M. 1996. Tensile strength of compacted clays. State of the art in Unsaturated Soils, E.E. Alonso and P. Delage, eds, Rotterdam, Balkema. Lee, F.H., Lo, K.W. et al. 1988. Tension crack development in soils. ASCE J. Geotech. Engrg. 114(8): 915–929. Mikulish, W.A. and Gudeus, G. 1995. Uniaxial tension, biaxial loading and wetting tests on loess. First Int. Conf. on Unsaturated Soils, Paris, Balkema/Presses des Ponts et Chaussées. Nichols, J.R. and Grismer, M.E. 1997. Measurement of fracture mechanics parameters in silty-clay soils. Soil Science 162(5): 309–322. Rodríguez, R. 2006. Hydrogeotechnical characterization of a metallurgical waste. Canadian Geotechnical Journal 43: 1042–1060. Rodríguez, R.L. 2002. Estudio experimental de flujo y transporte de cromo, níquel y manganeso en residuos de la zona minera de Moa (Cuba): Influencia del comportamiento hidromecánico (In Spanish). Technical University of Catalonia. Srawley, J.E. 1976. Wide range stress intensity factor expressions for ASTM E-399 standard fracture toughness specimens. Int. J. Fracture 95: 475–476. Tamarakar, S.B., Toyosawa, Y. et al. 2005. Tensile strength of compacted and natural soils using newly developed tensile strength measuring apparatus. Soils and Foundations 45(6): 103–110. Towner, G.D. 1987. The mechanics of cracking of drying clay. J. Agric. Engrg. Res 36: 115–124.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Tensile strength of some compacted fine-grained soils A.J. Lutenegger & A. Rubin University of Massachusetts, Amherst, MA, USA
ABSTRACT: Compacted soils are generally unsaturated soils, at least initially after compaction, although they may become saturated over time as a result of rising water tables, surface water infiltration, etc. The tensile strength of compacted soils can be an important design parameter for earth dams and embankments and should be considered in the design and development of earthwork specifications. A laboratory study was performed to determine the tensile strength of four compacted soils representing a wide range of geologic materials including an alluvial clay from Mississippi, a Piedmont residual soil from Georgia, a loess soil from Nebraska and a lacustrine clay from Massachusetts. Proctor curves for each soil were developed using Reduced, Standard, and Modified compaction energy. Following compaction the tensile strength of each specimen was determined using the Double Punch Test. The results showed that the Double Punch Test is most reliable near the Optimum Water Content. The measured tensile strength for each water content in the range of OWC ±6% was normalized by the tensile strength at the Optimum Water Content for each level of compaction effort. The results showed a linear trend between Normalized Tensile Strength and the deviation from the Optimum Water Content.
1 1.1
INTRODUCTION AND BACKGROUND Tensile strength of compacted soils
The tensile strength of soils has received relatively minor attention in the past 40 years, perhaps because it is assumed that the tensile strength is a small quantity in comparison to compressive strength or perhaps because engineers have a poor understanding of tensile strength. Tensile failure of soils can occur in natural soils, such as in slope failures, landslides, or cuts or in compacted soils in slopes, embankments, dams, or clay liners. The development of tension cracks in soils is an indication that tensile strength may be important in various design situations. Compacted soils are by default unsaturated and they may remain unsaturated throughout their life or they may take on water as a result of water infiltration or water flow, as through an earth dam. The engineering properties of compacted soils are therefore dependent on a range of water content that the soil may have after compaction, but in some cases may be critical immediately after compaction has been completed. Previous studies on the tensile strength of compacted clays have used both Direct Tensile Tests (e.g., Tschebotarioff et al. 1953; Dash and Lovell 1972; Ramiah et al. 1977) and Indirect Tensile Tests (e.g., Narain and Rawai 1970; Fang and Chen 1971, 1972;
Satyanarayana and Satyanarayana Rao 1972; Fang and Fernandez 1981; Favaretti 1991, 1995) to evaluate tensile strength. By far, the majority of previous studies have used Indirect Tensile Tests, including: 1) the Split Tensile Test; 2) Bending Tests; and 3) the Double Punch Test. 1.2
The Double Punch Test
The Double Punch Test (DPT) was developed by Fang and Chen (1971, 1972) as an indirect method for determining the tensile strength of compacted soils. A schematic of the Double Punch Test is shown in Figure 1. The Double Punch Test is essentially an unconfined splitting test which is performed by first centering a standard cylindrical compaction specimen between two steel discs centered on the top and bottom of the specimen. A vertical load is then applied slowly on the discs until the specimen reaches failure. The tensile strength of the soil is then calculated from the maximum load using the theory of plasticity. Fang and Chen (1972) plotted the results of tensile strength as calculated by the Double Punch Test versus the Split Tensile Test and found an excellent comparison. The Double Punch Test is an attractive approach to determining tensile strength of compacted soils for a number of reasons; 1) the test is easy to perform and
411
clay from Mississippi; 2) Geo-Hydro (GH)—a Piedmont residual clay from Atlanta Georgia; 3) Nebraska Loess (NBL)—a Late Wisconsinan loess deposit from east-central Nebraska; 4) Connecticut Valley Varved Clay (CVVC)—a lacustrine clay and silt deposit from Amherst, Massachusetts. The soils represent a wide range of geologic materials. Standard engineering properties of the four soils are given in Table 1. 2.2
Figure 1.
Schematic of the Double Punch Test.
requires no particular special equipment aside from a loading frame and a set of steel punches; 2) the test may be performed in conjunction with a Proctor compaction test; 3) it appears that the tensile strength is not sensitive to the rate of strain within the range of 0.03 to 2.0 in per min.; 4) the test results appear to be very closely correlated to results from the Split Tension Test. However, the test is not without limitations: 1) the test procedure is not standardized; 2) Fang and Chen (1972) found that the punch size affects the tensile strength and recommend punch diameters between 12.5 mm and 37.5 mm to be used on Proctor compaction specimens; 3) homogeneity of the soil is assumed, but this is an unavoidable deviation from the ideal found in nearly all soil tests; 4) when very soft high water content clays (i.e., very wet of the Optimum Water Content) are placed on the bottom punch, they may slump or barrel out or the punches may simply penetrate into the ends of the specimen without creating a true tensile failure; 5) when soils compacted very dry of the Optimum Water Content are tested, the failure may not follow the idealized assumed tensile failure plane. Overall, for soils compacted slightly below and slightly above the Optimum Water Content, the test appears to provide very useful results. It is in this range of water content where the engineer is most interested for compacted works.
2 2.1
Test procedures
Test specimens were compacted using Standard Proctor (SP), Modified Proctor (MP) and Reduced compaction energies. Reduced compaction (RP) is identical to Standard Proctor except that each layer only receives 15 drops of the Standard hammer instead of 25 drops. After compaction, specimens were extruded from the compaction mold and Double Punch Tests were performed. Test specimens were carefully centered between the top and bottom loading stainless steel punches which had a diameter of 25 mm. Alignment of top and bottom punches was rechecked and zero readings were taken on an LVDT and electronic load cell connected to an automated data acquisition system. Specimens were loaded at a constant rate of vertical displacement of 0.5 mm per minute until peak load was reached. The tensile strength was calculated using the approach presented by Fang and Chen 1971; 1972) as: σt = P/(π(kbH − a2 )) where: σt = tensile strength P = maximum observed load k = tan(2α + ϕ) ≈ 1 a = radius of the punch b = radius of specimen H = height of specimen α = angle of the cone to the surface ϕ = friction angle of the soil The value of k in Equation 1 takes into account the friction angle of the soil, ϕ, the sample punch dimension Table 1.
Soil
INVESTIGATION Soils tested
Four fine-grained soils were selected for testing; 1) Buckshot Clay (BSC)—a high plasticity alluvial
(1)
BSC GH NBL CVVC
412
Summary of soil properties of soils tested. Liquid limit (%)
Plastic limit (%)
Shrinkage limit (%)
clay (%)
52.6 38.0 34.6 47.1
21.4 18.0 20.9 26.1
7.5 18.0 17.5 20.4
35.8 30.1 22.3 37.9
ratio bH/a2 , and the soil compression-tensile strength ratio qu /σt (Fang and Chen 1972). According to Fang and Chen (1972) the value of k for soils compacted in a Proctor mold is approximately 1. Favaretti (1995) suggested that using a k value of 0.9 would provide a better correlation between results from the Double Punch Test and the Brazilian Test.
3
RESULTS
Table 2 gives a summary of the Optimum Water Content (OWC) and the Maximum Dry Density (MDD) obtained for each level of compaction energy for each of the four soils. Results of all compaction and tensile strength tests are given in Table 3. Figures 2 and 3 show the variation in tensile strength with compaction water content and compacted dry density for all tests. The results are highly scattered and clearly show no apparent trend. This is generally to be expected as the soil specimens exhibit degrees of saturation from 60% to 90% along the compaction curves for each of the compaction energies. It should be expected however that for a given soil dry density the soil with the lower degree of saturation, will exhibit higher tensile strength. Some of the variation in Figures 2 and 3 may be related to problems in the testing procedure discussed in paragraph 1.2. This is particularly noticeable at very low and very high water content. At these extreme water contents, the soil dry densities are low and difficulties in performing the Double Punch Test are encountered. In particular, at very low water content, failure of the specimens is very abrupt and the specimen often does not fail along vertical failure planes as assumed; at very high water content, the end punches simply penetrate into the ends of the specimen without producing a tensile failure. Based on these observations, it appears that the DPT is likely to be most applicable within a relatively narrow range of water content near the Optimum Water Content where the soil behaves more plastic. Figure 4 shows the variation in tensile strength for the Buckshot Clay as a function of the compaction Table 2. Interpreted optimum water content and maximum dry density. Reduced
Standard
Modified
Soil
OWC MDD OWC MDD OWC MDD (%) (Mg/m3 ) (%) (Mg/m3 ) (%) (Mg/m3 )
BSC GH NBL CVVC
22.5 20.0 17.8 25.0
1.61 1.71 1.62 1.43
21.0 18.5 17.0 22.5
1.63 1.78 1.71 1.59
20.0 15.6 15.0 19.7
1.73 1.90 1.81 1.71
Table 3.
Summary of compaction and tensile strength tests.
Specimen
Water content (%)
Dry density (Mg/m3 )
Tensile strength (kPa)
Buckshot Clay 1R 2R 3R 4R 5R 1S 2S 3S 4S 5S 1M 2M 3M 4M 5M
10.7 16.8 19.1 21.9 24.1 10.3 15.4 18.1 21.6 24.5 10.7 15.4 18.0 20.7 23.8
1.42 1.40 1.43 1.55 1.45 1.54 1.48 1.60 1.61 1.60 1.64 1.68 1.64 1.70 1.64
3.8 10.8 10.4 10.0 5.4 11.3 16.5 18.1 15.6 8.3 21.6 38.2 33.1 17.6 11.0
Geo-Hydro 1R 2R 3R 4R 5R 1S 2S 3S 4S 5S 6S 1M 2M 3M 4M 5M
9.8 12.8 15.1 17.7 19.2 9.4 12.2 16.2 19.3 20.0 24.0 8.6 11.4 15.6 20.1 21.4
1.51 1.52 1.71 1.72 1.70 1.62 1.63 1.75 1.77 1.78 1.72 1.70 1.79 1.90 1.70 1.73
4.5 10.1 8.8 5.7 3.7 7.9 16.6 15.5 4.2 3.4 1.3 15.7 36.6 16.4 3.7 2.1
Nebraska Loess 1R 2R 3R 4R 5R 1S 2S 3S 4S 5S 1M 2M 3M 4M 5M
11.5 14.8 17.8 19.3 22.6 10.6 13.3 17.2 19.5 24.0 9.0 14.1 17.8 20.4 23.9
1.53 1.57 1.62 1.60 1.59 1.65 1.68 1.71 1.70 1.56 1.67 1.80 1.79 1.72 1.61
9.3 8.5 7.6 5.0 2.0 14.5 14.3 8.4 5.9 1.3 26.7 26.6 8.4 5.5 1.8
CVVC 1R 2R 3R 4R
8.1 12.3 15.9 19.8
1.41 1.41 1.38 1.41
1.9 2.9 3.8 6.0 (continued)
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Table 3.
(continued)
50 Buckshot Reduced
Specimen 5R 1S 2S 3S 4S 5S 1M 2M 3M 4M 5M
Dry density (Mg/m3 )
25.0 7.8 10.4 15.2 21.2 24.9 7.8 11.9 15.1 19.7 23.4
Tensile strength (kPa)
1.43 1.48 1.50 1.52 1.53 1.59 1.58 1.58 1.66 1.71 1.65
Buckshot Standard
40
Tensile Strength (kPa)
Water content (%)
6.5 4.6 5.7 10.6 11.9 7.5 18.3 19.5 24.3 19.3 3.7
Buckshot Modified 30
20
10
0 -6
-4
-2
0
2
4
6
Water Content Deviation from OWC (%)
Figure 4. Relationship between tensile strength and deviation from OWC. 50
Tensile Strength (kPa)
Table 4. content.
Buckshot GeoHydro Nebraska CVVC
40
Interpreted tensile strength at optimum water Tensile strength (kPa)
30
20
10
Soil
Reduced
Standard
Modified
BS GH NBL CVVC
8.0 3.0 7.2 6.0
15.0 7.5 9.0 10.5
22.5 20.0 17.5 15.5
0 6
8
10
12
14
16
18
20
22
24
26
Water Content (%)
Figure 2.
Variation in tensile strength with water content.
50 Buckshot GeoHydro Nebraska CVVC
Tensile Strength (kPa)
40
30
20
10
0 1.3
1.4
1.5
1.6
1.7
1.8
1.9
2.0
Dry Density (Mg/m3 )
Figure 3.
Variation in tensile strength with dry density.
water content deviation (both + and −) away from the Optimum Water Content. The data indicate a variation that is approximately linear over the range OWC ±6%. Since it is unlikely that a specimen will be compacted exactly at the OWC, the tensile strength at the OWC
may be estimated from the linear trends shown in Figure 4. The other three soils showed similar results. The interpreted tensile strength at the OWC for each level of compaction energy for all four soils is given in Table 4. The interpreted tensile strength at the OWC may be then used to calculate the ‘‘Normalized Tensile Strength’’, i.e. tensile strength at any water content divide by the tensile strength at OWC. As an example, the variation in Normalized Tensile Strength as a function of the deviation from the OWC for the Buckshot Clay is Figure 5. These results also show an approximate linear trend. The combined Normalized Tensile Strength results for all four soils are shown in Figure 6. Even though the soils represent a wide range in geologic and geographic origin and have different properties, there appears to be a unifying linear trend between the Normalized Tensile Strength and the deviation of water content from the OWC for all levels of compaction energy within the window of water contents just below and just above OWC. Some of the variability shown in Figure 6 may simply be related to the interpretation of the Optimum Water Content from the compaction curve for each soil. The water content deviation from the OWC shown in Figure 6 is actually quite large (±6%) and most
414
a project. The results appear to be insensitive to soil type, at least within the range of characteristics for the four soils tested.
Normalized Tensile Strength
3 Buckshot Reduced Buckshot Standard Buckshot Modified Regression Line
2
4 1
0 -6
-4
-2
0
2
4
6
Deviation from Optimum Water Content (%)
Figure 5. Variation in Normalized Tensile Strength with deviation from OWC for Buckshot Clay.
Normalized Tensile Strength
4 Buckshot GeoHydro Nebraska CVVC Trend Line
3
2
0 -4
-2
0
2
4
The tensile strength of four fine-grained soils was evaluated using the Double Punch Test for three different levels of compaction energy. The results suggest that the Double Punch Test can be used to reliably estimate the tensile strength of compacted soils and is most applicable at water contents near the OWC. At extreme water content both dry and wet of OWC there are difficulties with the test in determining the tensile strength of the soil. The results also show a general global linear trend between the Normalized Tensile Strength and the water content deviation away from the OWC, particularly in the range of OWC ±4%, which is a typical working range for many field compaction specifications.
REFERENCES
1
-6
CONCLUSIONS
6
Deviation from Optimum Water Content (%) Figure 6. Variation in Normalized Tensile Strength with deviation from OWC for all four soils.
likely somewhat unrealistic for an actual field application for compacted soil, considering typical compaction specifications. The data shown in Figure 6 still indicate considerable scatter at low water content. A more realistic range in water content for field compaction specifications would likely be on the order of OWC ±3 to 4% depending on other design criteria. The results shown in Figure 6 suggest that tensile strength of compacted fine-grained soils may be described using Normalized Tensile Strength relative to the deviation of compacted water content away from the OWC within the window of typical field compaction procedures. This is convenient since it is only necessary to determine the tensile strength at the OWC in order to predict the range in tensile strength of other conditions of water content and compacted density on
Dash, U. and Lovell, C.W., Jr. 1972. Tensile Strength of Clays. Proc. 3rd Southeast Asian Conference on Soil Engineering: 205–210. Fang, H.Y. and Chen, W.F. 1971. New Method for Determination of Tensile Strength of Soils. Highway Research Record (345): 62–68. Fang, H.Y. and Chen, W.F. 1972. Further Study of DoublePunch Test for Tensile Strength of Soils. Proc. 3rd Southeast Asian Conference on Soil Engineering. 211–215. Fang, H.Y. and Fernandez, J. 1981. Determination of Tensile Strength of Soils by Unconfined Penetration Test. ASTM STP 740: 130–144. Favaretti, M. 1991. Tensile Strength Tests on Cohesive Compacted Soils. Proc. 9th Asian Regional Conference on Soil Mechanics and Foundation Engineering, 1, 37–40. Favaretti, M. 1995. Tensile Strength of Compacted Clays. Proc. 1st International Conference on Unsaturated Soils, 1: 51–56. Narain, J. and Rawai, P.C. 1970. Tensile Strength of Compacted Soils. Journal of the Soil Mechanics and Foundations Division, ASCE, 96 (SM6): 2185–2190. Ramiah, B.K., Purusothsama Raj, P., Chickanagappa, L.S. and Raghunatth, S.P. 1977. Some Studies on the Tensile Strength of Soils. Proc. 5th S.E. Asian Conference on Soil Engineering: 327–337. Satyanarayana, B. and Satyanarayana Rao, K. 1972. Measurement of Tensile Strength of Compacted Soil. Geotechnical Engineering, 3: 61–66. Tschebotarioff, G.P., Ward, E.R. and DePhilippe, A.A. 1953. The Tensile Strength of Disturbed and Recompacted Soils. Proc. 3rd International Conference on Soil Mechanics and Foundation Engineering, 1: 207–210.
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Unsaturated characteristics of rammed earth P.A. Jaquin, C.E. Augarde & L. Legrand Durham University, Durham, UK
ABSTRACT: Rammed earth is both an ancient construction technique and the name for the material produced by the technique. Rammed earth is gaining in popularity around the world due to its ecological and sustainable attributes. Walls of rammed earth are formed by taking a graded mixture of (usually) locally-won soil and compacting the mixture between formwork in a similar manner to concrete. The formwork is then removed leaving a solid earth wall. There is little scientific understanding of the source of strength in rammed earth and design to date has used empirical approaches. In this paper we consider rammed earth as an unsaturated soil thus explaining one source of strength to be from suction. Laboratory tests have been carried out on rammed earth samples including unconfined compression and Brazilian tests (to measure strength) and filter paper tests (to determine the water retention properties). The tests all indicate that a source of strength in rammed earth derives from suction and conclusions are drawn as to their levels in ancient rammed earth structures.
1
INTRODUCTION
Rammed earth is both a material (a compacted mixture of sand, gravel and clay) and the name for the construction procedure whereby walls are built using this material rammed in layers between formwork. The technique has been used by man for thousands of years and many historic structures containing rammed earth features remain standing to this day. Examples include the Potala Palace in Lhasa, Tibet and the Alhambra in Granada, Spain (Guillaud et al. 2004). Historic rammed earth structures have been studied by engineers and archaeologists at Durham for a number of years (e.g. Jaquin et al. 2006). The use of rammed earth for building has to date relied on empirical rules developed from experience, and often linked to a particular location in the world. A large number of heritage rammed earth structures exist, some of considerable antiquity. They are most commonly located in a belt around the equator reaching as far north as the UK (Jaquin et al. 2007). The nature of the material is such that arid conditions are favourable for long term durability and there are now concerns for the future of some of these structures under the effects of climate change. Increased interest in rammed earth for new buildings is being seen in countries away from this traditional zone of past use. The reason for this is the inherent sustainability of the material (it can be re-used), the often local sourcing and the avoidance of the use of cement. An exception to the last of these is the material termed ‘‘stabilised’’ rammed earth, where
cement or another stabiliser is added to improve durability. In the tests described later in this paper we will be concerned only with unstabilised rammed earth. Rammed earth mix design is somewhat of a black art with advice varying according to location, soil type and occasionally cultural constraints. A typical mix is well-graded, containing particles in each of the four soil fractions: gravel, sand, silt and clay. Walker et al. (2005) indicate that the majority of modern rammed earth mixes lie in the following ranges of percentages by mass: sand and gravel, 45–80%; silt 10–30% and clay, 5–20%. The large size of these ranges provides further evidence of the empirical nature of rammed earth design. It is clear that a material which can be formed into vertical walls which stand for hundreds of years has some cohesive strength. The source for this could be cementation between particles; however, walls can also be built from plain unstabilised rammed earth where no cementation is present. The source of strength must then lie elsewhere and suction appears to be a prime candidate, although to our knowledge this has not been highlighted before. Few studies exist where rammed earth is characterized as an engineering material using rigorous testing procedures. One example is Lilley and Robinson (1995) who describe tests on rammed earth walls built at near full-size studying the effects of making (or forming) various openings. In this work the authors undertook rudimentary materials testing including cube tests (as for concrete) finding compressive strengths of 1.8–2.3 MPa. Another example
417
can be found in a series of papers by Hall (e.g. Hall and Djerbib, 2004) where the hydraulic behaviour is linked to particle size distribution through experimental and analytical work. However neither of these or the few other published studies make the link between suction and strength in rammed earth. Our contention is that rammed earth can be regarded as a compacted unsaturated soil. Modern rammed earth is usually prepared and compacted into place at optimum moisture content. With further drying, made easy by the large surface area of the walls, the material must reach a very low degree of saturation. This is likely to be even lower than the degree of saturation found in compacted soils with which geotechnical engineers are familiar. Therefore high suctions must be generated within the walls, hence providing some apparent cohesion. The purpose of the research described below is to begin to verify this theory. If rammed earth can be regarded as a manufactured unsaturated soil it is then possible to bring a greater degree of scientific rigour to the study of the material and to the development of economic design codes. Clearly this suction-induced increase of apparent cohesion with drying cannot be unlimited. A completely dry rammed earth mix would have no apparent cohesion due to suction as no water would be present. However this is both unrealistic (as rammed earth in a structure will never completely dry) and in the laboratory as, even at oven dry conditions (i.e. zero water content), adsorbed water will still be present on clay particles and will be available to generate suctions. Other studies (e.g. Toll and Ong, 2003) have shown that in soils similar to rammed earth the contribution to strength from suction reduces as the degree of saturation reduces, so although suction increases as the soil dries out, the contribution to strength reaches a peak and then drops away (Toll, 1990). The apparent cohesion in rammed earth is therefore expected to peak between the two limits of zero water content and saturation.
s=−
Suction and relative humidity
Rammed earth includes particles with a much greater range of sizes than in the unsaturated soils that are commonly studied. However, there is no reason why the presence of water in liquid bridges should not provide strength through established mechanisms. A liquid bridge exists in a soil pore where both air and water are present in the pore space. The surface tension acting at the interface of the water and air, combined with tension in the water, act to provide an attractive force across the pore, which provides an unsaturated soil with an apparent cohesion. This liquid bridge force between the soil particles was first idealised by considering the soil particles to be
ρw RT ln(RH ) wv
(1)
where R = the universal gas constant, T = absolute temperature, ρw = density of water and wv = the molecular mass of water vapour (Likos and Lu 2004). Equation 1 is plotted in Figure 1 for T = 20◦ C. The figure shows that small variations in RH between 100% and 95% lead to large changes in total suction up to around 1MPa. Small variations in RH below 95% then lead to relatively small changes in suction (although the actual values of suction are large). Such low values of RH are likely to be present in the arid parts of the world where heritage structures containing rammed earth can be found and thus supports the hypothesis that suction is the significant provider of strength in rammed earth. Structures existing in
Relative Humidity
1.1
spherical (Fisher 1926) assuming a wetting angle of zero. Developments of this theory towards realistic soils has progressed via the works of Gillespie and Settineri (1967) who extended to a finite liquid-solid contact angle, and Pietsch (1968) who took account of surface roughness of the particles by assuming a separation distance between idealised smooth spheres. Lian et al. (1993) provided a mathematical basis for the interactions between a liquid bridge and rough rigid spheres which were applied more recently by Molenkamp and Nazemi (2003). It is clear that further developments could begin to approach the pore structures likely to be present in rammed earth, with large particle size ranges, angularity and surface roughness. In addition, at the continuum level double-structure models for unsaturated soils (as reviewed recently in Gens et al. (2006)) could provide suitable frameworks for constitutive modelling of rammed earth materials. The effect of relative humidity (RH) is particularly important for rammed earth due to the large exposed surface areas. Total suction s (the sum of matric and osmotic suctions) is linked to the relative humidity of the pore air through Kelvin’s equation, which can be expressed as
100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 Suction (kPa)
Figure 1. suction.
418
Relation between relative humidity and total
regions in which RH is in the descending part of the curve of Figure 1 will experience relatively small changes in suction, thus leading to stability over time. Evaporation of pore water is affected by the relative humidity (RH ) of the pore air compared to that of the adjacent air outside the wall. In practice drying of the walls will continue until the pore air humidity equals the humidity of the surrounding air.
2
LABORATORY TESTING
The aim of the laboratory testing described below was to confirm a link between suction and strength in rammed earth and also to study the changes in water retention behaviour as changes are made to the mix constituents. Laboratory testing consisted of unconfined compression tests, Brazilian tests and filter paper tests. The basic rammed earth mixture used in this study was taken from a development site at Aykley Heads, Durham, which included a large rammed earth wall completed in 2006. The mixture used on site was blended from material dug from the site (alluvial sand), coarse aggregate and a powdered clay/silt mixed in proportions (0.25:0.60:0.15; aggregate:sand:clay) using a horizontal axis mixer. In the laboratory tests described here, this mixture was first sieved to remove material retained on a 14 mm sieve. This was necessary to enable testing on standard sized samples. The sieved basic mix constituents are given in Table 1. The basic mix was altered for the Brazilian and filter paper tests to include a 10% increase in sand (mix A) and a 10% increase in clay (mix B). The dry density/water content relationship for the basic mix was obtained using the vibrating hammer compaction test (BS1377:2, 1990) and showed an optimum water content of approximately 8–10%. The vibratinghammer was used as it was thought closer to the field compaction that would be used during wall construction and the method of sample preparation for the compression tests (in comparison to the standard Proctor test).
air-drying of the samples. A tensiometer was used in each test to measure suction during shearing. These instruments have been developed at Durham University for the measurement of high suctions up to the air entry value of the ceramic incorporated into these devices, in this case 1500 kPa (Lourenço et al. 2006). Cylindrical samples (200 × 100 mm dia.) were prepared using a Proctor split compaction mould, as outlined in Walker et al. (2005), with modifications following Horncastle (2006). Samples were compacted in 5 layers following which a screed of particles passing a 425 μm sieve was placed on the top surface of the cylinder. This screed served a dual purpose of producing both a flat loading surface and a fine particle paste on which to place the tensiometer. Immediately following application of this screed, the Proctor split mould was removed and the mass and height of the sample recorded. Dry densities of between 2017 and 2061 kg/m3 were achieved using the same compactive effort each time. Once samples had air dried to the required water content for testing they were wrapped in an impermeable sheath secured with rubber O-rings placed against steel loading plates at the top and bottom of the sample. The samples were then left for at least 7 days to allow suctions to equilibrate throughout the sample. When it was considered that the samples were ready for testing, the top plate was replaced with a loading plate drilled to accommodate a tensiometer. The samples were sheared under constant water content conditions in a triaxial testing rig. Displacement was controlled at a constant 0.1 mm/min and measurements of suction, load and axial displacement taken every 10 seconds using the logging software Triax (Toll 1999). Figure 2 shows plots of deviator stress against suction measured for the seven tests. The figure provides strong evidence of a link between starting water content and strength as indicated by the dotted envelope to the results. However, this can also be stated as a link between suction present in the sample at the start of testing and strength. 700
Unconfined compression tests
Deviator stress (kPa)
2.1
Seven unconfined compression tests at constant water content were carried out on the basic rammed earth mix at variable water contents achieved through Table 1.
% by mass
Passing
Size
Sand Silt Clay
21.5 52.3 26.2
D10 D30 D60
2.1 μm 85.9 μm 345.0 μm
500 400 300 200
100 10.2 0
Constituents for basic rammed earth mix.
Constituent
600
9.4
0
8.6
8.4
200
7.1
400 Suction (kPa)
5.5
600
800
Figure 2. Plots of deviator stress against suction for unconfined compression tests. Test water contents indicated against each test.
419
Another feature evident from this figure is the difference in the change in suction during shearing. In samples with initially high water contents, suction rises during the test. For the low water content samples the opposite is seen to happen. This is consistent with the concept of a unique water content to suction relationship at the Critical State as proposed by Toll (1990). It also complies with the framework including a Continuously Disturbed Line (CDL) for unsaturated soils proposed by Croney and Coleman (1954) and revisited recently by Tarantino (2007). Figure 3 shows plots of axial total stress against axial strain for the seven tests. Here it is notable that there is brittle behaviour for the low starting water content samples and ductile for high water content samples. Linking Figures 2 and 3 it is possible also to conclude that stiffness of a rammed earth sample is linked to suction. Further aspects of these tests are explored in more detail in Jaquin et al. (2007a). 2.2
Brazilian and filter paper tests
Following the unconfined compression tests described above the basic rammed earth mix was remixed to increase the coarse (sand) fraction (termed mix A) or to increase the fine (clay) fraction (termed mix B). What limited advice there is at present for the design of rammed earth mixes is based on mix proportions of the fractions. In this part of the study the aim therefore was to investigate the effects of changing the particle size distribution in a controlled way on the strength (and additionally) on the water retention properties. The filter paper test is an indirect method of measuring both matric and osmotic suction where filter papers are arranged adjacent to or sandwiched between, soil samples which are then left to equilibrate. The final water content of the filter paper provides the suction present in the soil sample via a calibration curve. In these tests the procedure described by Leong et al. (2002) was used. The advantage of 700 Deviator Stress (kPa)
600
5.5 500 400
7.1
300
8.4 8.6
200
10.2 9.4
100 0 0
1
2 3 Axial strain (%)
4
5
Figure 3. Plots of axial total stress against axial strain for the unconfined compression tests. Test water contents indicated against each test.
the filter paper method over the tensiometers used in the unconfined compression tests is that much higher suctions can be measured with the former. The filter paper specimens were prepared at 55 mm diameter with a height of 22 ± 2 mm from each of mixes A and B at a starting water content of 10%. Dynamic compaction of these specimens in an adapted Proctor apparatus proved difficult to control so these specimens were instead statically compacted in a triaxial rig to the required thickness maintaining the same target dry density of 2.05 Mg/m3 . Then a sandwich of three filter papers was inserted between two compacted samples and the joint wrapped with electrical tape. An additional filter paper was suspended above the soil sample and the whole system placed inside a closed sealed jar and left to equilibrate for two weeks inside a constant temperature container at 25 ± 1◦ C. By preparing a batch of samples and leaving them to dry to different moisture contents before filter paper testing it was possible to determine portions of the drying part of the soil water retention curve. Following the filter paper tests the same samples were then quickly tested using a modified Brazilian test. This test is widely employed to determine tensile strengths in rocks and involves compressive loading of a circular disc sample across a diameter to failure. An analytical solution exists (assuming elasticity) linking the tensile strength of the sample σt with the applied load P as follows: σt =
2P πdt
(2)
Where d = sample diameter and t = sample thickness. Clearly most soils are unsuitable for this type of test having little or no tensile strength and also often being too friable to withstand these conditions. For the rammed earth samples at low water contents no problems of this nature were experienced. The reuse of samples from the filter paper test for the subsequent Brazilian test proved successful although it was important to minimize the time between completing the filter paper test and starting the Brazilian test. Figure 4 shows the change in water content over time as samples air-dried. Note the scatter in the initial water contents. Although the mixes were prepared as a whole to uniform water content, the actual water content of each individual disc varied about this value. It is noticeable that mix B (clay added) dries to approximately the same water content in the first day as mix A (sand added) despite starting from a generally higher initial water content although the mechanism for this difference is not clear. The process of drying in rammed earth is complex. Knowledge of the particle size distribution does not provide sufficient information on the soil microstructure in the
420
6
12
5
Water content (%)
Water content (%)
14
10 8 6 4 2
Mix A Mix B
4 3 2 1
0 0
1
2
3 4 Time (days)
5
6
0
7
90
140
14
190 240 Tensile strength (kPa)
290
Water content (%)
12
Figure 6.
10
6 4 2 0 0
1
2
3 4 Time (days)
5
6
7
Figure 4. Drying of samples with time. Mix A (upper); Mix B (lower).
Water content (%)
Brazilian test results.
8
9 8 7 6 5 4 3 2 1 0
Mix A - total Mix A - matric Mix B - total Mix B - matric
0
10000
20000
30000
40000
Suction (kPa)
Figure 5. Soil-water retention curves for rammed earth mixes A and B.
two mixes, which has the greatest influence on drying. Rather it is the pore size distribution which must be critical, dependent on the former but also on compaction. From Equation 1 there is a direct link between suction and RH so it is natural that all samples dry to the same suction approximately. Figure 5 shows the drying portion of the soil-water retention curves for the two mixes A and B taken from the filter paper results. Both matric and total suctions are plotted showing that osmotic suction is of secondary importance in these samples, as might be expected from the nature of the pore water. The suctions rise to a high level at the very low water contents reached by the samples indicating again the need for the filter paper test in the determination of suctions. The coarser mix (A) appears to have a SWRC lying below that of the finer mix (B) thus having a lower water content for a given suction value. This
might be explained by consideration of the likely pore structures in these samples. The finer mix will have a more widespread network of smaller sized pores than the coarse mix. Therefore it is likely this mix will carry more of its pore water as bulk (funicular) water than the coarse sample. So for a given suction it will need more water as much will be trapped in the bulk masses, providing less potential than water in the pendular regime. This feature can also be linked to the theoretical analysis of Likos and Lu (2004) where theoretical soil-water retention curves for coarser materials lie below those for finer materials. Figure 6 shows the results of the Brazilian tests. The water content at the time of the test is plotted against tensile strength calculated from Equation 2. As water content reduces so tensile strength increases as expected if suction is a source of tensile strength. For a given tensile strength there is more water in mix B than in Mix A. Again this links to the idea that in mix B more water is held in the funicular regime, contributing less to strength than ‘‘equivalent’’ pendular water. The plot also shows that tensile strength increases rapidly at very low water contents as might be expected to occur in the surface of a rammed earth wall under prolonged dry conditions.
3
DISCUSSION
It seems obvious from these results that suction must provide a significant component of the strength of unstabilised rammed earth and therefore understanding of its evolution from compaction, through drying to long-term changes in relative humidity is important for the stability of a rammed earth structure. Considering that most walls are of considerable thickness (usually >300 mm and much greater in heritage structures) it can be surmised that a gradient of water content exists through the wall thickness. At the surface water content is low and suction is high. Permeability will also reduce as water content decreases in these locations. Thus the centre of a rammed earth wall
421
will be protected to some degree from water ingress, and will maintain a relatively constant level of suction and hence strength. This behaviour has been recorded in the laboratory by Hall and Djerbib (2004), referred to as the ‘‘Overcoat Effect’’. The high suctions present at the surface of a rammed earth wall will suck in impinging water. Surviving heritage structures often have design details that reduce impinging water, e.g. large overhanging eaves, features usually thought to aid longevity due to reduction in impact. The results above indicate that these features also serve to maintain surfaces at high suction and hence high strength. While knowledge of unstabilised rammed earth is vital to the conservation of existing structures it is accepted that it is unlikely to become widely used in temperate parts of the world for new-build due to its surface friability which, despite the discussion above, is inferior to concrete. It is stabilised rammed earth, however, that is likely to be the choice in these areas. For this material, in addition to suction there will be cementation between agglomerations of particles to add to the tensile strength. The interaction between the free water available in the material at time of compaction and the stabiliser (e.g. cement) is clearly important and much more difficult to study. The relative contributions to strength from cementation and from suction will depend on many variables, such as pore size distribution, proportions of stabiliser, curing conditions amongst others. This is an important area of future research.
4
CONCLUSIONS
This study is the first (to the authors’ knowledge) that has treated rammed earth as an unsaturated soil. The tests described above are intended to support this theory qualitatively and pave the way for further laboratory testing, which will be necessary if rammed earth materials are to be modelled in a modern geotechnical framework.
ACKNOWLEDGEMENTS The first author has been supported by an EPSRC DTA grant. The use of the rammed earth material from the Aykley Heads Site, Durham by Rivergreen Developments Ltd is gratefully acknowledged. The third author contributed through an ERASMUS placement at Durham University in 2007.
REFERENCES Croney, D. and Coleman, J.D. 1954. Soil Structure in Relation to Soil Suction (pF), J. Soil Science, 5(1), 75–84. Fisher, R.A. 1926. On the capillary forces in an ideal soil. Journal of Agricultural Science 16, 492–505.
Gens, A., Sanchez, M. & Sheng, D. 2006. On constitutive modelling of unsaturated soils. Acta Geotechnica, 1(3), 137–147. Gillespie, T. and Settineri, W.J. 1967. The effect of capillary liquid force on the force of adhesion between spherical solid particles. Journal of Colloid Interface Science 24, 199–202. Guillaud, H., Houben, H., Alva, A., Rodrigues, R., Pinto, F., Sastre, J.M., Shimotsuma, K. and Castellanos, C. 2004. Earthen Architectural Heritage on UNESCO’s ‘World Cultural Heritage List’. UNESCO, Paris, France. Hall, M. and Djerbib, Y. 2004. Moisture ingress in rammed earth: Part 1—The effect of soils particle size distribution on the rate of capillary suction. Constr. Bldg. Mats, 18(4), 269–281. Horncastle, T. 2006. Rammed earth construction. School of Engineering Durham University, MEng Dissertation. Jaquin, P.A., Augarde, C.E. and Gerrard, C.M. 2006. Analysis of historic rammed earth construction. Proc. 5th Int. Conf. Structural Analysis of Historical Constructions, Nov 6–8, New Delhi, India. Vol. 2, 1091–1098. Jaquin, P.A., Augarde, C.E. and Gerrard, C.M. 2007. Historic rammed earth distribution, International Journal of Architectural Heritage: Conservation, Analysis, and Restoration (submitted). Jaquin, P.A., Augarde, C.E., Gallipoli, D. and Toll, D.G. 2007a. The strength of rammed earth materials. Géotechnique (submitted). Leong, E.C., He, L. and Rahardjo, H. 2002. Factors affecting the filter paper method for total and matric suction measurements. Geotech. Test. J. 25(3): 322–333. Lian, G., Thornton, C. and Adams, M.J. 1993. A theoretical study of the liquid bridge forces between two rigid spherical bodies. Journal of Colloid Interface Science 161, 138–147. Lilley, D.M. and Robinson, J. 1995. Ultimate strength of rammed earth walls with openings, Proceedings—ICE: Structures & Buildings 110(3), 278–287. Likos, W.J. and Lu, N. 2004. Hysteresis of Capillary Stress in Unsaturated Granular Soil. Journal Engineering Mechanics ASCE 130(6): 646–655. Lourenço, S.D.N., Gallipoli, D., Toll, D.G. and Evans, F.D. 2006. Development of a Commercial Tensiometer for Triaxial Testing of Unsaturated Soils. 4th International Conference on Unsaturated Soils, April 2006 Phoenix, USA. Molenkamp, F. and Nazemi, A.H. 2003. Interactions between two rough spheres, water bridge and water vapour. Géotechnique 53(2): 255–264. Pietsch, W.B. 1968. Tensile strength of granular materials. Nature 217, 736–737. Tarantino, A. 2007. A possible critical state framework for unsaturated soils, Géotechnique 57, 385–389. Toll, D.G. 1990. A framework for unsaturated soil behaviour. Géotechnique 40(1): 31–44. Toll, D.G. 1999. A data acquisition and control system for geotechnical testing. Computing developments in civil and structural engineering, Edinburgh, Scotland. Toll, D.G. and Ong, B.H. 2003. Critical-state parameters for an unsaturated residual sandy clay, Géotechnique 53, 93–103. Walker, P., Keable, R., Martin, J. and Maniatidis, V. 2005. Rammed Earth, Design and Construction Guidelines. BRE Bookshop: Watford.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Experimental study of the influence of suction on the residual friction angle of clays V. Merchán, J. Vaunat, E. Romero & T. Meca Technical University of Catalonia, Barcelona, Spain
ABSTRACT: This paper presents a study on the effect of high suctions on the value of the residual strength of a high plasticity clay. Tests were carried out in a Bromhead ring shear apparatus adapted to allow for control of the relative humidity around the shear box during shearing. Data were obtained by testing samples of remolded FEBEX bentonite (wL = 102, IP = 53) prepared close to its plastic limit and further loaded and sheared under suctions ranging from 0 to 120 MPa. Experimental data shows evidence of a huge increase of the residual shear strength when the sample is sheared in unsaturated conditions. As a matter of fact, the shear strength envelope at a suction of 75 MPa is characterized by a null cohesion and a residual friction angle φrdry equal to 28◦ , that is 21◦ higher than the value in saturated conditions (7◦ ). Such a result extends to high plasticity clays the conclusions already obtained in previous studies on a low plastic silty clay (wL = 30, IP = 16, increment of φr between saturated and dry conditions equal to 5◦ ) and a medium plastic clay (wL = 55, IP = 28, increment of φr equal to 15◦ ). An explanation to such high changes in values of residual shear strength is finally discussed in the light of the process of clay aggregation during drying, whose existence is supported by visual observations (micrographs obtained in an Environmental Scanning Electron Microscope) and evidences of changes in the pore size distribution (measured by Microstructure Intrusion Porosimetry).
1
INTRODUCTION
It is well-known that clay materials present a decrease in shear strength when submitted to large relative displacements as a result of particle reorientation (Skempton, 1964). Factors affecting such a decrease have been the object of numerous experimental studies, which used different equipment such as direct or the annular shear devices (Bishop, 1971; Skempton, 1985; Bromhead, 1979). They indicated that the shear strength reaches a lower bound for very large displacements, characterized by a null cohesion and a residual friction angle. Value of the residual friction angle appears to be controlled by the level of normal stress (Skempton, 1985; Stark & Eid, 1994), soil grading (Skempton, 1964; Kenney, 1967; Lupini et al., 1981; Skempton, 1985), particle mineralogy (Mitchell, 1993), rate of shearing (Tika et al., 1996), pore water chemistry (Di Maio, 1996a, 1996b, Chighini et al., 2005). More recently, the effect of suction on the residual strength had been studied at low suctions by Sedano et al. (2007) and at high suctions with by Vaunat et al. (2006) and Vaunat et al. (2007). The latter results indicate that high values of suction (typically higher than 10 MPa) increase significantly the residual strength and that this effect becomes more important when the material is more plastic. As a matter of fact,
the increase in friction angle has been observed to be around 5◦ in Barcelona silt, a low plastic silty clay and 15◦ in Boom clay, a medium plastic clay. The main explanation for such an increase is similar to that put forward by Toll (1990) for the strength at critical state. It is due to a process of enhancement of material aggregation during drying that makes it behave in a more granular way. The present work deals with a continuation of the study and address the effect of high suctions on the residual strength of Febex bentonite, a high plasticity clay. The experimental programme is based on tests carried out in a Bromhead apparatus adapted to control the relative humidity in the shear box. In order to verify the hypothesis of clay aggregation, it is completed by observations carried out in a Environmental Scanning Electron Microscope and by determination of pore size distribution by Mercury Intrusion Porosimetry before and after the tests in the ring shear box.
2
MATERIALS AND TEST PROCEDURE
Table 1 presents the main properties of the FEBEX bentonite. The properties of the low and medium plasticity clay tested in previous studies (Vaunat et al.
423
Table 1.
Properties of the tested materials.
Property
BCN silty clay
Boom clay
FEBEX bentonite
30 16 2.66
55 28 2.7
102 53 2.7
15
40
68
Liquid limit (%) Plastic limit (%) Particle density, ρs (Mg/m3 ) Clay fraction < 2 μm (%)
2006; Vaunat et al., 2007) are reported in the same table. As in the previous studies, the material has been tested in a Bromhead ring shear apparatus adapted to control the relative humidity inside the shear box (Vaunat et al., 2007). A general scheme of the apparatus is presented in Figure 1. A glass cap placed around the shear box allows the sample to be isolated from the laboratory environment. The value of suction is imposed in the isolated chamber by means of a closed circuit of forced vapor convection connected to a vessel with controlled relative humidity (the relative humidity in the vessel is in equilibrium with a solution saturated in salts placed at its bottom). A hole perforated in the glass cap and further sealed with silicon allows for installing a hygrometer (Model HMT 100, ±%RH at [0–90%RH] and ±1.7%RH at [90–100%RH]) that measures the temperature and relative humidity actually applied inside the chamber during the test. Data is stored in real time on a computer through a USB device (NI9001). The general procedure involves: a. Preparation of a remolded sample close to its plastic limit. b. Consolidation of the sample under a given normal stress. c. Suction application through the vapor transfer technique. From that time, the evolution of relative humidity and temperature inside the chamber started to be registered. Also, the vertical displacement experienced by the sample (uv ) was measured by the LVDT. This stage is considered equilibrated when the relative change in vertical displacement δuv /uv reaches values lower than 1%. Because of the low permeability of the clay, the time to reach equilibrium has proved to be very long: 22 days have been necessary for a sample of 5 mm height to reach a suction of 75 MPa (in equilibrium with a relative humidity equal to 58% in the chamber). d. Shearing at a controlled displacement rate equal to 0.32 mm/min. Pilot tests performed on Boom clay have shown that this velocity is low enough for keeping ‘drained’ conditions during the shear.
Figure 1. General scheme of the Bromhead ring shear apparatus adapted to suction control.
Due to the high plasticity of the clay, displacements required to attain the full residual state are of the order of 80 mm. As a result of the long times involved during suction equilibration and shearing stages, only three tests, labeled Test I, II and III, have been performed. TEST I aimed at determining the residual strength envelope of the saturated material. It consists of a twostage shearing test performed under normal stresses equal to 300 and 450 kPa. The results indicate that the residual strength of saturated Febex bentonite is characterized by a null cohesion and a friction angle equal to 7.5◦ (see Fig. 3). Test II is a five-stage test that aimed at defining the residual shear strength envelope of the material at a suction of 75 MPa and after resaturation. The sample was first equilibrated under a relative humidity equal to 58% (suction equal to 75 MPa) and sheared consecutively under a normal stress equal to 100, 200 and 300 kPa. Afterwards, the system to control relative humidity was removed and the sample brought to saturated conditions by flooding. Material was then sheared in two steps under normal stresses equal to 100 and 200 kPa, respectively. The accumulated displacement applied during all the test is 2535 mm. Test III is a seven-stage test that aims at studying the residual strength envelope under suctions equal to 18 and 45 MPa and after resaturation. The sample was initially sheared at a suction equal to 18 MPa and three levels of stress: 100, 200 and 300 kPa. The sample was then brought to a suction of 45 MPa by changing the saline solution controlling the relative humidity inside the vessel and further sheared under normal stresses equal to 300, 200 and 100 kPa, respectively. Finally, the glass cap was removed and the sample flooded before applying two shearing stages under normal stresses equal to 100 and 200 kPa. The total displacement applied during this test is equal to 3873 mm.
424
SHEAR STRENGTH VS DISPLACEMENT CURVES
B5
120 B3 B6
80 (kPa)
Figure 2 shows the shear strength vs displacement curve obtained during Test III at a suction equal to 18 MPa for both the initial stage (prepared sample dried to a suction equal to 18 MPa and sheared) and after application of a suction of 45 MPa (prepared sample brought to a suction equal to 18 MPa, sheared, then brought to a suction equal to 45 MPa, sheared and then wetted down to a suction equal to 18 MPa and sheared). The stress-displacement curves obtained in both cases show very similar values after a displacement equal to 50 mm. This result gives, on the one hand, good feedback concerning the reliability of the test procedure and, on the other hand, provides clues to the fact that the residual shear strength is, in that case, independent of suction history. Before 50 mm of displacement, the curve corresponding to the first shearing (Stages B1, B2 and B3) presents an initial peak which disappears when shearing is applied on an already pre-sheared sample (stages B5, B6 and B7). Such a kind of response is reported in the literature for the case of saturated materials and is generally attributed to the effort required initially to reorient the particles in the direction of shearing. Points relating the shear strength at large displacements to the normal stress are reported in Figure 3. They evidence a linear relationship between both variables for the range of loads considered. Parameters controlling the shear strength envelope at a suction equal to 18 MPa are cr = 0 and φr = 20◦ . The same linear trend can be observed in Figure 3 for the test performed under a suction equal to 75 MPa. Values of cohesion and friction angles obtained in this case are cr = 0 and φr = 28.2◦ . The shear strength envelope in saturated conditions is moreover depicted in Figure 3. The data show the huge effect exerted by the suction on the value of the friction angle that increases by a value of 21◦ when the soil passes from saturated conditions to a suction equal to 75 MPa. Such an outcome extends, in an amplified manner, to the case of active clays results already observed on low and medium plastic clays (Vaunat et al. 2006; Vaunat et al. 2007). Figure 4 summarizes the variation of residual friction angles with suction as measured on samples of Barcelona silty clay (wL = 30, IP = 16), Boom clay (wL = 55, IP = 28) and Febex bentonite (wL = 102, IP = 53). The increase in residual friction angle increases generally with the plasticity of clay. As a matter of fact, the increase in friction angle between saturated conditions and a suction equal to 75 MPa is around to 2.5◦ for the low plastic silty clay, 15◦ for the medium plastic clay and 21◦ for the high plastic clay. Another observation coming out from the figure is the non linear variation of residual friction angle
100kPa 100kPa after suction change 200kPa 200kPa after suction change 300kPa 300kPa after suction change
B2 B7 40 B1
0 0
50
100 150 Displacement (mm)
200
250
Figure 2. Residual strength measured in the ring shear apparatus at a suction equal to 18 MPa. 180
s = 75 MPa r = 28.2º
160
Shear stress (kPa)
3
140
s = 18 MPa, unloading r = 22.5º
120
s = 18 MPa, loading r = 22.1º
100 80 60
s=0 r = 7.5º
40 20 0 0
100
200 300 Normal stress (kPa)
400
500
Figure 3. Shear strength envelope of FEBEX bentonite at different suctions.
with suction. Most of the increase in friction angle occurs between 0 and 100 MPa. Afterwards, the effect of suction on φr becomes significantly smaller and tends to an asymptotic value for a suction close to 300 MPa. Such an increase is interpreted as being due to the process of aggregation during drying, that makes the material essentially more granular at high suctions. In the case of the low and medium plasticity clay, this interpretation has been reinforced by observations about the dilatancy of the material during first shearing. The latter appeared indeed to increase
425
40 35
tan–1( r / )
30 25 20 15
BCN silty clay data Boom clay data Febex Bentonite data Boom clay (Hyperbolic aproximation) BCN silty clay (Hyperbolic aproximation) Febex Bentonite (Hyperbolic aproximation)
10 5 0 0
50
100 150 200 Total Suction, S (MPa)
250
300
Figure 4. Variation of the friction angle with suction for the low, medium and high plastic clays.
Figure 5. Sample of remolded FEBEX bentonite prepared at the liquid limit (magnification 200x).
drastically when the material is sheared under high suction. In the present work, more direct evidence of the aggregation process have been looked for through two techniques: 1. The direct observation of microstructural changes during drying by Environmental Scanning Electron Microscopy (ESEM); 2. The determination of the pore size distributions for the saturated and dry material by the Mercury Intrusion Porosimetry technique (MIP).
4
MICROSTRUCTURAL OBSERVATIONS
ESEM is a technique that consists of performing the Scanning Electron Microscopy under gas pressure, which allows for observing materials with liquid constituents. It is in particular possible to observe changes in soil structure during drying by controlling the temperature and the partial vapour pressure inside the observation chamber of the microscope. Figures 5, 6, 7 and 8 show four ESEM micrographs taken on samples of remolded FEBEX bentonite prepared respectively at the liquid (Figures 5 and 6) and plastic limits (Figures 7 and 8). The as-prepared structure of the material can be observed in Figures 5 and 7. Figures 6 and 8 show the structure of the material after applying a relative humidity equal to 7%. At the liquid limit, the material presents a relatively homogeneous structure characterized by stacks of clay particles of typically 10 μm size and few macro-voids (two of them can be observed in the upper part of the micrograph). After drying at 7% of relative humidity,
Figure 6. Sample of remolded FEBEX bentonite prepared at the liquid limit and dried under a relative humidity of 7% (magnification 215x).
an important increase can be observed in the existing macro-voids accompanied by a general enhancement of the inter-particle porosity that degenerates in many points in the creation of new macro-voids. Further connection between macro-voids leads to the build-up of isolated aggregates in the clay. An incipient formation of aggregated structure due to drying can be observed in Figure 6. The picture is slightly different for the sample prepared at the plastic limit. Material presents initially a more complex structure where stacks of clay particles, micro-voids (with some local enlargements) and macro-voids can be observed. After application of drying under a relative humidity equal to 28%
426
Initial state (remoulded at plastic limit) Final state (after consolidation, drying and shearing)
Pore size density function ( e/ log )
2.5
2
1.5
1
0.5
0 1
Figure 7. Sample of FEBEX bentonite prepared at the plastic limit (magnification 200x).
10
100 1000 10000 Entrance por size, d (nm)
100000 1000000
a) pore size density function Initial state (remoulded at plastic limit) Final state (after consolidation, drying and shearing) 1.2
Intruded void ratio
1 0.8 0.6 0.4 0.2 0 1
10
100 1000 10000 Entrance por size, d (nm)
100000 1000000
b) accumulated pore size distribution Figure 8. Sample of remolded FEBEX bentonite prepared at the plastic limit and dried under a relative humidity of 7% (magnification 200x).
(suction approximately equal to 170 MPa), the size of the macro-voids gently decreases at the expense of an enhancement in the inter-particle porosity but without significant changes in the general pattern of material structure. It seems thus that preparation of the material close to the plastic limit create a pre-aggregated structure that remains stable during suction application. Effect of drying will in this case essentially stiffen the pre-existing structure. More quantitative insights can be realized by analyzing the pore size distribution of Febex bentonite before and after being tested in the ring shear apparatus. Two pore size distributions have been determined by the MIP technique: one corresponding
Figure 9. Pore size distributions in a remolded sample of FEBEX bentonite before and after being sheared under a vertical stress equal to 100 kPa and a suction equal to 120 MPa (sample was initially prepared close to the plastic limit).
to a remolded sample prepared close to the plastic limit and the other to the same sample once loaded under a vertical stress equal to 100 kPa, subsequently dried at a suction equal to 120 MPa and finally sheared in the Bromhead shear apparatus. A comparison between both curves can be observed in Figure 9. The sample prepared close to the plastic limit presents a mono-modal pore size distribution with pore sizes concentrated between 0.3 and 3 μm, that is at the inter-particle level (the size of a particle is typically of the order of 1 μm (1000 nm)—see Figure 5).
427
This peak disappears completely after the combination of loading, drying and shearing and the curve splits into two parts. One part is associated with pore sizes between 10 and 20 nm and existing thus at the intraparticle level. The other part contains pores of size higher that 10 μm, indicating the existence of an interaggregate porosity. It is expected that a peak in the pore size distribution would have existed around the value of 10 μm at the end of drying and would have further been erased and distributed over a wider range of pore sizes during shearing. 5
CONCLUDING REMARKS
The paper reports on a study on the effect of high suction on the residual strength of FEBEX bentonite. Experimental results allow for completing conclusions already drawn for materials of lower plasticity (Barcelona silty clay and Boom clay). They are: • Strong drying increases strongly the residual strength at relatively low normal stress (below 300 kPa) I. • The increase is due only to an increase in friction angle and not in cohesion. • Most of the increase in friction angle takes place for suction below 100 MPa. For higher suctions, the friction angle reaches an asymptotic value. • The increase in friction angle is higher when the plasticity of the clay is higher. For a low plastic silty clay (wL = 30, IP = 16), the increase in friction angle for a suction between saturated conditions and a suction equal to 75 MPa is equal to 2.5◦ , for a medium plastic (wL = 55, IP = 28) clay to 15◦ and for a high plastic clay (wL = 102, IP = 53) to 21◦ . • Such an increase is explained by a process of clay aggregation or aggregation stiffening during strong drying that makes the material behave in a more granular way. Pictures taken in the Environmental Scanning Electron Microscopy evidence indeed the incipient formation of aggregates during drying when the clay is prepared at the liquid limit. When the clay is prepared at the plastic limit, micrographs evidence a pre-aggregated structure that remains essentially unchanged during drying. In that case, suction stiffens the aggregates of the material. ACKNOWLEDGMENTS Mr. Merchán wishes to thank Alβan Program, the EU program of high level scholarships for Latin America, scholarship N◦ E05D052296CO. The support of the European Commission through the Research and
Training Network MUSE (Mechanics of Unsaturated Soils for Engineering) is gratefully acknowledged. REFERENCES Bishop, A.W. 1971. Shear strength parameters for undisturbed and remolded soil specimens. In Proceedings of the Roscoe Memorial Symposium, Cambridge, Foulis. Bromhead, E.N. 1979. A simple ring shear apparatus. Ground Eng., vol. 12, pp. 40–44. Chighini, S., Lancellotta, R., Musso, G. and Romero, E. 2005. Mechanical behavior of Monastero Bormida clay: chemical and destructuration effects. In Bilsel and Nalbantoˇglu (eds), Proc. Int. Conf. on Problematic Soils, Vol. 1, 381–388. Famagusta: Eastern Mediterranean University. Di Maio, C. 1996a. The influence of pore fluid composition on the residual shear strength of some natural clayey soils. In K. Senneset (ed.), Proc. 7th Int. Conf. on Landslides, 2, 1189–1194. Rotterdam: Balkema. Di Maio, C. 1996b. Exposure of bentonite to salt solution: osmotic and mechanical effect. Géotechnique, 46 (4), 695–707. Kenney, T.C. 1967. The influence of mineral composition on the residual strength of natural soils. Proc. Geotech. Conf. on the Shear strength properties of natural soils and Rocks, 1, 123–129. Lupini, J.F., Skinner, A.E. and Vaughan, P.R. 1981. The drained residual strength of cohesive soils. Géotechnique, 31 (2), 181–213. Mitchell, J.K. 1993. Fundamentals of soil behaviour. 2nd edition, John Wiley & Sons, New York. Skempton, A.W. 1964. Long-term stability of clay slopes. Géotechnique, vol. 14, no. 2, pp. 77–102. Skempton, A.W. 1985. Residual strength of clays in landslides, folded strata ad the laboratory. Géotechnique, vol. 35, no. 1, pp. 3–18. Sedano, J.A.I., Vanapalli, S.K. and Garga, V.K. 2007. Modified ring shear apparatus for unsaturated soils testing. Geotechnical Testing Journal, vol. 30, no. 1, pp. 39–47. Stark, T.D. and Eid, H.T. 1994. Drained residual strength of cohesive soils. J. of Geotech. Engng., ASCE, 120 (5), 856–871. Tika, T.E., Vaughan, P. and Lemos, L.J.L.J. 1996. Fast shearing of pre-existing shear zones in soil. Géotechnique, 46 (2), 197–233. Toll, D.G. 1990. A framework for unsaturated soil behaviour. Géotechnique, 40 (1), 31–44. Vaunat, J., Amador, C., Romero, E. and Djeran-Maigre, I. 2006. Residual strength of low plasticity clay at high suctions. In Proceedings of the 4th International Conference on Unsaturated Soils, Phoenix, Arizona, USA, vol. 1, pp. 1279–1289. Vaunat J., Merchán, V., Romero, E. and Pineda, J. 2007. Residual strength of clays at high suctions. In Proceedings of the 2nd International Conference on Mechanics of Unsaturated Soils, Weimar, Germany, vol. 2, pp. 151–162.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Ultimate shear strength of unsaturated soils T.B. Hamid GeoConcepts Engineering Inc., Virginia, USA
ABSTRACT: This paper presents triaxial and direct shear tests results from literature conducted on soils under unsaturated conditions with measurement of matric suction (ua − uw ). The results of these tests indicate that matric suction has less influence on ultimate shear strength than on the peak shear strength. It is inferred from the test results that neglecting suction is appropriate for analyzing slopes that contain pre-existing surfaces or that have history of previous sliding. However, suction has a significant effect on the depth of tension cracks in unsaturated soils and this should be considered as it reduces the factor of safety.
1
INTRODUCTION
The ultimate and residual shear strength of overconsolidated clay is an important parameter in evaluating the stability of new and existing slopes that contain a pre-existing surface or that have history of previous sliding. Ultimate shear strength is achieved when soil exhibits no appreciable changes in stress or volume during shearing. This ultimate state is followed by residual state that is reached after a large shear deformation. In residual state, soil particles increase in parallel orientation in the direction of shear deformation. Many researchers have studied the effect of matric suction on the peak shear strength of unsaturated soils (e.g. Escario & Saez 1986). However, lacking in the available literature is treatment of ultimate and residual shear strength in unsaturated soils. The results of triaxial and direct shear tests results with measurement of matric suction from literature are presented in this paper. The test results indicate that the effect of matric suction on ultimate shear strength is less significant as compared to the effect of matric suction on peak shear strength. Slope stability analysis is generally required as part of site development in Washington, D.C., Maryland and Virginia. Both natural and construction related landslides have occurred in these areas, which are underlain by overconsolidated clays, locally known as ‘‘Marine Clay’’. The marine clay deposits are considered problematic soils in these areas and several landslides and surficial slope failures have occurred in marine clay deposits. Geotechnical engineers are required to determine the engineering properties of marine clay for slope stability analysis. The local practice is to use residual shear strength of marine clay for slope stability analysis.
Marine clay deposits have many surface fractures and water can fill these fractures in wet seasons. Even in the dry season, free flowing water can enter in these fractures. The depth of these fractures increases as the negative pore water pressure (matric suction) of the soil increases. This paper indicates that a factor of safety computed using ultimate or residual shear strength parameters can decrease considerably in the wet season due to the horizontal water force developing in the tension crack.
2
ULTIMATE SHEAR STRENGTH OF UNSATURATED SOILS
Fredlund & Rahardjo (1998) indicated that in cases where groundwater table is deep, slope stability analyses should be performed using the shear strength contribution from the matric suction. However, the author of this paper understands that the use of shear strength contribution from the matric suction should be limited to the analyses where peak shear strength controls the stability of slopes. The peak shear strength of cohesive soils is generally used in the analysis of slopes in residual soils and normally consolidated clays, and in soils that have not undergone previous sliding. However, there are situations where ultimate or residual shear strength of unsaturated soils controls the stability of slopes, such as the stability of new and existing slopes that contain a pre-existing surface or that have history of previous sliding. Based on suction controlled and constant water content test results reported in the literature, the effect of matric suction on the ultimate shear strength of unsaturated soils is studied in this paper.
429
140 u a - u w = 100 kPa
Shear stress (kPa)
Deviator Stress, kPa
120 100 80
u a - u w = 20 kPa
60 40
(a)
20 0 0
2
4
6
8
10
Volumetric Strain, %
Horizontal displacement (mm) -0.015 -0.01 u a - u w = 100 kPa
v/H0
-0.005 0
Axial Strain, %
0.005
Figure 1. Stress-strain and volume change curves at cell pressure = 50 kPa and various suctions (after Cui & Delage 1996).
u a - u w = 20 kPa
0.01
(b)
0.015 0
Cui & Delage (1996) have presented suction controlled triaxial test results of an Aeolian Silt (Liquid Limit (LL) = 37% and Plasticity Index (PI) = 18%) and are reproduced in Figures 1a and 1b. Figure 1a indicates that for a cell pressure of 50 kPa, when suction value increased from 200 kPa to 1500 kPa, peak shear strength increased from about 320 kPa to 750 kPa. Volume change curves (Fig. 1b) indicate typical behavior of overconsolidated clay, i. e. initial compression followed by the dilation. The volume change curves indicate that dilatancy increased as suction value increased. The shear strength and volumetric strain curves indicate a tendency to level off at axial strains of about 8%, suggesting that the ultimate strength is being approached. However, at matric suction value of 800 and 1500 kPa volumetric strain is still changing towards the end of the tests. Although a true ultimate state is never reached in the tests presented in Figures 1a and 1b, the rate of change of shear strength and volumetric strain reduce considerably except for 1500 kPa suction. The degree of saturation after shearing was 79% for 200 kPa, 75% for 400 kPa, 67% for 800 kPa, and 56% for 1500 kPa matric suction. Figures 2a and 2b indicate the results of suction controlled direct shear tests conducted on Minco Silt
2
4
6
8
10
Horizontal displacement (mm)
Figure 2. Shear stress (a) and volume change (b) against horizontal displacement at net normal stress = 105 kPa for two values of suctions (Hamid, 2005).
(LL = 28% and PI = 8%). For a net normal stress (σn − ua ) of 105 kPa, increasing suction resulted in an increase of peak shear strength and stiffness. Strain softening behavior and a pronounced peak are obvious only for 100 kPa suction, illustrating an increasing brittleness of the sample with increasing suction. Figure 2 shows that both shear stress and volumetric strain, v/H0 (where v = vertical displacement and H0 = specimen thickness) generally reached a steady state at horizontal displacement of about 4–6 mm, indicating an ultimate state is achieved. In Figure 2a, the ultimate shear stress of 100 kPa suction sample is approximately similar to the ultimate shear strength of the sample tested at 20 kPa matric suction. The degree of saturation after shearing was about 90% and 75% for 20 kPa and 100 kPa matric suction, respectively. A similar picture is seen for σn − ua = 155 kPa in Figures 3a and 3b.
430
200 u a - u w = 100 kPa
180 Shear stress (kPa)
160 140 120 100
u a - u w = 20 kPa
80 60 40 20
(a)
0 0
2
4
6
8
10
Horizontal displacement (mm)
-0.015 u a - u w = 100 kPa -0.01
v/H0
-0.005 0
Figure 4. Deviator stress and volume change against axial strain at confining stress = 50 kPa and various suctions. (Toll & Ong 2003).
0.005 0.01
u a - u w = 20 kPa (b)
0.015 0
2
4
6
8
10
Horizontal displacement (mm) Figure 3. Shear stress (a) and volume change (b) against horizontal displacement at net normal stress = 155 kPa for two values of suctions (Hamid, 2005).
Figure 4 shows constant water content test results reported by Toll & Ong (2003). These tests were conducted on Jurong residual soil (LL = 36% and PI = 15%). It can be seen that ultimate state is being approached by the end of the tests cw50-230 (1), cw50230 (2), cw50-300, and cw50-400. Further, the rate of change of deviator stress (q) and volumetric strain generally reduce considerably toward the end of the tests and an ultimate state can be reasonably assumed (Toll & Ong, 2003). The degree of saturation after shearing was 66% for 230 kPa, 63% for 300 kPa, and 72% for 400 kPa matric suction. The results of Figures 1 through 4 are plotted in Figure 5 as peak and ultimate strength envelopes. In order to plot the strength envelopes the test results for net normal stress of 210 kPa presented in Hamid (2005) were utilized but the plot of horizontal displacement against shear strength and volume strain are not
presented in this paper. Similarly, constant water content test results for confining stress of 150 and 250 kPa presented in Toll & Ong (2003) are presented in Figure 5 but the plots of deviator stress against axial strain are not presented in this paper. The slope of the best fit lines of strength envelopes represents the friction angle for suction (φ b ). The values of φ b calculated from best fit lines of Figure 5 are given in Table 1. It is evident from laboratory test results presented in Figures 1 through 5 and in Table 1 that the effect of matric suction is generally less significant for the ultimate friction angle for suction than the peak friction angle for suction. Particularly for low confining and net normal stress (e.g. 50 kPa) the effect of sucb tion on φult is small (Figure 5). This conclusion is also supported by Tarantino & Tombolato (2005) who concluded that water menisci have a negligible effect on the ultimate shear strength. A possible explanation of the effect of matric suction on the peak shear strength and ultimate shear strength is presented in the following paragraphs. In unsaturated soil, the meniscus around soil grains contact points tends to draw the particles together. This attractive force, called capillary force (Nc ), acts perpendicular to the grain contact surface. It has been shown that under certain conditions Nc increases with an increase of suction (Kohgo et al. 1993). Increase in Nc induces an increase of shear resistance between the soil particles. This inhibits the relative sliding between
431
Shear stress (kPa)
860
Table 1. Peak Ultimate
660 460 260
(a)
60 100
600
1100
1600
u a - u w (kPa) 220 Shear stress (kPa)
n
b ) Peak (φpeak
b ) Ultimate (φult
50∗ 50• 150• 250• 105† 155† 210†
15 47 64 68 22 28 30
3 26 62 59 2 9 23
180 n
by adding water to the system the column of grains will collapse. Test results presented in Figures 1 through 4 indicate strain softening behavior that suggests beginning of destruction of bonding between soil particles due to interlocking and due to meniscus. In the ultimate state particles slide over each other, i.e. interlocking bond has been destroyed and bonding due to meniscus has also been destroyed. Therefore the soil shows a stable ultimate state, i.e. no further reduction in shear strength. In other words, as opposed to the peak shear strength, in the ultimate state meniscus bonds do not exist and an increase in matric suction does not cause an increase in ultimate shear strength.
- u a = 155 kPa
140 100 n
(b)
- u a = 105 kPa
60 0
50
100
150
u a - u w (kPa)
860 Shear stress (kPa)
Confining/Net normal stress (kPa)
Note: ∗ Cui & Delage (1996); • Toll & Ong (2003); † Hamid (2005).
Peak Ultimate
- u a = 210 kPa
Peak and ultimate friction angles for suction.
Peak Ultimate
3
- u a = 250 kPa
660 460 3
- u a = 150 kPa
3
260 (c)
3
- u a = 50 kPa
60 100
200
300
400
500
u a - u w (kPa)
Figure 5. Peak and ultimate shear strength envelopes for test results reported by (a) Cui and Delage (1996), (b) Hamid (2005), and (c) Toll and Ong (2003).
the particles and the magnitude of shear resistance of soil increases. Kohgo et al. (1993) suggested that the contribution of shear resistance caused by the capillary force may be regarded as nominal cohesion. Burland & Ridley (1996) used a grain column analogy to show that the meniscus around the soil particles results in increase in stability of soil structure. They suggested that the contact menisci can be thought of as ‘bonds’ holding the grains together. This bonded system can sustain some externally applied load without collapsing. However, if these bonds are then removed
SLOPE STABILITY APPROACH
In geotechnical practice, for small size projects, generally residual direct shear testing is not performed and conservatively, a low residual friction angle value generally 6◦ to 12◦ and zero cohesion are selected as residual shear strength parameters. The groundwater level used in the design is generally the highest recorded during the soil investigation program. However, the effect of rainfall and surface runoff water is not considered in the slope stability analysis and the upper crust is treated as unsaturated soil characterized using residual friction angle. A factor of safety ranging from 1.2 to 1.5 is generally considered satisfactory for slope stability analysis. As indicated previously, residual friction angle and zero cohesion are used as shear strength parameters in the slope stability analysis in marine clay. Neglecting the cohesion is considered a conservative approach. There are instances where ignoring the value of cohesion may result in a non-conservative value of factor of safety. If shear strength parameters are back-calculated assuming no cohesion, the estimated shear strength parameters may be overestimated. Cohesion also plays
432
an important role in the development of tension cracks in the slope. Ignoring cohesion implies that tension cracks can not develop in the soil. Tension cracks are generally developed above the groundwater table in unsaturated clay and the effect of the matric suction should be considered in the determination of depth of tension cracks. 4
EFFECT OF MATRIC SUCTION ON THE DEPTH OF TENSION CRACKS
As indicated previously residual shear strength is used for the slope stability analysis. However, the effect of tension cracks that may fill with water in wet seasons is not considered in the slope stability analysis. Tension cracks generally develop in a highly desiccated crust of soil and their depths may be calculated using Equation 1 (Fredlund & Rahardjo 1998): yt = (2c /γ ) tan(45 + φ/2) + [2(ua − uw ) tan φ b /γ ] × tan(45 + φ/2)
(1)
where yt = depth of tension crack; c = effective cohesion; γ = unit weight; φ = effective angle of internal friction; (ua − ub ) = matric suction; φ b = friction angle for suction. Equation 1 is used to calculate the depth of tension cracks for various values of matric suction and the results are plotted in Figure 6. Figure 6 indicates that the depth of tension cracks increase with increase in matric suction. For example, for matric suction 200 kPa and φ b = 10◦ , the depth of tension crack is almost double the depth of tension crack corresponding to the zero matric suction. It should be noted that, as the depth of tension crack is gradually increased, the factor of safety will
Depth of tension crack (m)
35 30
b
= 15 0
25 20
b
=10 0
15 b
10
decrease first (as tensile stresses are eliminated first), and then increase (as compressive stresses are eliminated). Factor of safety for slope stability should be calculated considering the depth of tension crack given by Equation 1. Alternatively one can calculate the factor safety for an assumed range of crack depths, and the appropriate depth is that producing the minimum factor of safety. For higher suction values crack depths calculated using Equation 1 may be more than the slope height. In this case a maximum depth equal to the height of slope should be utilized. Figure 7 presents chart developed by Janbu (1968) and can be used to calculate the tension crack adjustment factor (μt ). The tension crack adjustment factor indicates the effect of tension crack depth on the factor of safety. For example, for a slope angle of 60◦ and for Ht /H from 0 to 0.5, μt varies from 1 to about 0.75. A value of μt = 1 indicates no effect of tension cracks on factor of safety, on the other hand a value of μt = 0.75 indicate about 25 percent reduction in factor of safety calculated without considering the depth of tension crack.
=50
5
5
0 0
500
1000
1500
u a - u b (kPa) Figure 6. crack.
Figure 7. Tension crack adjustment factor (after Janbu 1968 via. EM 11102–2-1902, 2003).
Effect of matric suction on the depth of tension
CONCLUSIONS
As opposed to the peak shear strength, the effect of matric suction appears to be less significant on ultimate shear strength. Based on the laboratory test results of unsaturated soils presented in this paper, it may be concluded that suction can be neglected for analyzing slopes that contain pre-existing surfaces or
433
that have history of previous sliding. However, the effect of matric suction should be considered while incorporating the presence of a tension crack in slope stability analysis. ACKNOWLEDGEMENTS The author wishes to extend a special thank to O. Ayodeji, Fairfax County, Department of Public Works, Virginia, USA for reviewing this manuscript. Valuable comments and suggestions made by anonymous reviewers also helped to improve the quality of this paper. This paper reflects the personal opinion of the author and not necessarily those of GeoConcepts Engineering, Inc. REFERENCES Bishop. A.W. 1955. The use of the slip circle in the stability analysis of slopes. Geotechnique. 5: 7–17. Escario, I. & Saez, J. 1986. The shear strength of partly saturated soils. Geotechnique. 36: 453–456.
Fredlund, D.G. & Rahardjo, H. 1993. Soil Mechanics for Unsaturated Soils. New York: John Wiley and Sons, Inc. Janbu, N. 1968. Slope stability computations. Via US army Corps of Engineer, EM 1110-2-1901. 2003. Hamid, T.B. 2005. Testing and modeling of unsaturated interfaces. Ph.D. dissertation submitted to Civil and Environmental Engineering department. University of Oklahoma, USA. Kohgo, Y., Nakano, M. & Miyazaki, T. 1993, Theoretical aspects of constitutive modelling for unsaturated soils. Soils and Foundations. 33(4): 49–63. Morgenstern, N.R. & Price, V.E. 1965. The analysis of the stability of general slip surfaces. Geotechnique. 15: 70–93. Spencer, E. 1967. A method of analysis of the stability of embankments assuming parallel inter-slice forces Geotechnique. 17: 11–26. Toll, D.G. & Ong, B.H. 2003. Critical-state parameters for an unsaturated residual sandy clay. Geotechnique. 53(1): 93–103. Tarantino, A. & Tombolato, S. 2005. Coupling of hydraulic and mechanical behaviour in unsaturated compacted clay. Geotechnique. 55 (4): 307–317. US Army Corps of Engineer. Slope Stability. EM 1110-21901. 2003.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Critical State conditions for an unsaturated artificially bonded soil D.G. Toll School of Engineering, Durham University, Durham, UK
Z. Ali Rahman Faculty of Sciences and Technology, National University of Malaysia (UKM), Selangor, Malaysia
D. Gallipoli Department of Civil Engineering, University of Glasgow, Glasgow, UK
ABSTRACT: This paper reports on a set of triaxial test data on an artificially bonded sand tested in unsaturated conditions. Tests were performed using the axis translation technique to measure suctions while shearing under constant water content conditions. The results at the Critical State are interpreted to obtain the variation in the stress ratios: Ma representing the net stress component and Mb representing the suction component. These are also presented as Critical State angles of friction, (φ a )c and (φ b )c . It is found that Ma is higher than the saturated critical state stress ratio, Ms (i.e. (φ a )c > φc ). This supports the observation that we should not always make the assumption that φ a = φ . The changes in Ma and Mb can be related to the different phases of water retention behaviour. The regions of behaviour seem to be (i) before the air entry value Ma = Mb = Ms (ii) in the desaturation stage Ma rises above Ms but Mb = Ms (iii) in the residual stage Ma remains constant and Mb starts to reduce.
1
INTRODUCTION
This paper reports on a set of triaxial test data on an artificially bonded sand tested in unsaturated conditions. The results are relevant to the understanding of tropical residual soils, since these are typically bonded in nature and frequently exist in an unsaturated state. The use of artificial specimens allows reproducibility of bond strength, which is difficult to achieve with naturally bonded soils, such as residual soil. Tests on an artificially bonded sand in saturated conditions have been reported by Toll & Malandraki (1993); Malandraki & Toll (2000); Malandraki & Toll (2001) and Toll et al (2006). Further testing on saturated specimens has been carried out by Ali Rahman (2008). Tests on the unsaturated specimens were performed under constant water content conditions while using the axis translation technique to measure suctions. Shearing was carried out at three values of radial net stress (50, 100 and 300 kPa) and the suctions ranged from 0 to 560 kPa. The test results on the unsaturated bonded soil are interpreted by considering separately the contributions from net stress and suction. Critical State stress ratios are interpreted for each stress component: Ma for the
net stress component and Mb for the suction component. These are also presented as Critical State angles of friction, (φ a )c and (φ b )c . 2
MATERIAL & TEST PROCEDURES
The artificial soil was produced by mixing sand and kaolin (87% sand: 13% kaolin) and then firing the mixture at 500◦ C in a furnace. This was a technique first used by Maccarini (1987). At this temperature the kaolin changes in nature, forming a bond between the sand particles. The bond formed is not time dependent, so this technique has many advantages over using cement or other bonding agents that require a curing period and show a change in strength with time. The sand used for making the samples was Leighton Buzzard sand, a uniform medium sand (Figure 1). The tests described in this paper were all on specimens prepared at the same initial void ratio (e = 0.6). Specimens for testing in unsaturated conditions were initially prepared in a saturated state and then allowed to air-dry in the laboratory until each achieved a required value of water content. Figure 2 shows the water retention curve for the artificial soil. The drying curve was obtained from
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The net stress was then increased to the desired value (50, 100 or 300 kPa) by reducing the pore air pressure at constant cell pressure under constant water content conditions (allowing volume change to occur due to air flow, but preventing any flow of water). The changes in pore-water pressure and volume were observed until consolidation was deemed to be complete. Specimens were then sheared under constant water content conditions with radial net stress held constant. Measurements of pore-water pressure and volume change were made during shearing.
3
Figure 1. Particle size distribution for the Leighton Buzzard sand used to make the bonded soil.
Degree of saturation, Sr: %
100
Fredlund et al (1978) gave the shear strength equation for unsaturated soils as:
Drying - Axis translation
80
SHEAR STRESS AT CRITICAL STATE IN UNSATURATED SOILS
τ = c + (σ − ua ) tan φ a + (ua − uw ) tan φ b
Wetting - Axis translation (Walker et al, 2005)
(1)
Wetting - Filter Paper (Walker et al, 2005)
60
where 40
τ σ ua uw c
20 0 0.1
Figure 2.
1
10 100 Matric suction (u a - uw): kPa
1000
φa
Water retention curve.
φb measurements of suction on different specimens following air drying from saturated conditions to a specific water content (or degree of saturation). It can be seen that the retention curve is very steep in the suction range 2–4 kPa, (with some scatter in the data, which is emphasised by the logarithmic scale) followed by an almost flat portion once the degree of saturation drops below 25%. This made the control of suction quite difficult. Nevertheless, it was possible to prepare specimens at a range of suction from <1 kPa to over 500 kPa. After drying to the required water content, specimens were then installed in a triaxial cell fitted with a 500 kPa high air entry base ceramic for measurement of pore-water pressure. The pore air pressure was controlled through an air line connected to a coarse filter at the top of specimen. The air pressure was slowly increased to 595 kPa while also increasing the cell pressure to 600 kPa in order to maintain a small net stress (σ − ua ) of 5 kPa. The specimen was allowed to equilibrate under this small net stress (and constant water content conditions) until a stable value of pore-water pressure was observed.
is shear strength is the total stress is the pore air pressure is the pore water pressure is the cohesion when the two stress variables (σ − ua ) and (ua − uw ) are zero is the friction angle with respect to net stress (σ − ua ) is the friction angle with respect to matric suction (ua − uw )
Fredlund et al (1978) went on to suggest that, when the matric suction is zero, the (σ − ua ) plane will have the same friction angle as the (σ − uw ) plane. Therefore, they suggested that φ a is the same as φ (the friction angle with respect to effective stress). Fredlund and Rahardjo (1993: p. 238) suggest that the friction angle φ a ‘‘appears to be essentially equal to the effective angle of internal friction obtained from shear strength tests on saturated soil specimens’’. Fredlund et al (1978) also suggested that c is the same as c (the effective cohesion). Therefore, making these two assumptions, equation [1] becomes the following: τ = c + (σ − ua ) tan φ + (ua − uw ) tan φ b
(2)
and it is this equation that is commonly quoted (eg Fredlund and Rahardjo, 1993). Toll (2000) has argued that φ a is not necessarily the same as φ and therefore we should use the general form of the equation represented by Eq. [1].
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For the particular conditions of the Critical State, equation [1] can be rewritten as: τc = (σ − ua ) tan(φ a )c + (ua − uw ) tan(φ b )c
Ma = (3)
is the critical state angle of friction with respect to (σ − ua ) is the critical state angle of friction with respect to (ua − uw )
(φ b )c
and taking the cohesion intercept to be zero for critical state conditions (Atkinson, 1993: p. 116). This has been expressed using more general stress variables by Toll (1990) and Toll & Ong (2003) as: q = Ma ( p − ua ) + Mb (ua − uw )
(4)
where q p Ma Mb
is the deviator stress (σ1 − σ3 ) is the mean total stress (σ1 + σ2 + σ3 )/3 is the critical state stress ratio with respect to net mean stress (p − ua ) is the critical state stress ratio with respect to matric suction (ua − uw )
Ma = Mb =
(7)
Ma = M
(5)
Mb = kM
(6)
The major difference is that BBM assumes that M and k are constant, while here it is taken that Ma and Mb change with of degree of saturation or fabric of the soil. Net stress component, Ma
To estimate the stress ratio due to net stress, Ma , tests at low suctions have been considered. Eight tests were carried out where the suction at the critical state was 6 kPa or less. For these tests, the Mb (ua − uw ) term in Eq. 4 becomes small and the controlling component will be
q q = (p − ua ) + (ua − uw ) (p − uw )
(8)
However, some of the degrees of saturation are less than 50% even for the tests at low suction. Therefore, this assumption may not be valid. A third possible assumption is to assume that the values of Mb would be equal to Ms (the saturated critical state ratio). This assumption would lead to: Ma =
For comparison with the Barcelona Basic Model (BBM) (Alonso et al, 1990), the BBM assumes that the contribution from net stress is constant and equal to the saturated critical state stress ratio, M . In the BBM the contribution from matric suction is represented as a decrease in the intercept of the Critical State Line (CSL) on the p−ua axis defined by a parameter k. Therefore the relationships in the BBM are:
3.1
q ( p − ua )
However, since the suction values are non-zero, the values could have a small effect (particularly at lower values of net stress). A second assumption could be that the values of Ma and Mb would be equal at high degrees of saturation (Toll, 1990). This assumption would lead to:
where (φ a )c
the Ma ( p − ua ) term. If the suction is zero then:
q − Ms (ua − uw ) ( p − ua )
(9)
All three assumptions have been used to calculate Ma in Table 1. The range of average values for Ma is 1.38 to 1.41. These values equate to an equivalent angle of friction of (φ a )c = 34−35◦ . The values of deviator stress, q, at the Critical State from saturated tests have been plotted against mean effective stress, p , in Figure 3. The values for the unsaturated (low suction) tests have been superimposed on the plot. It can be seen that value of Ma is higher than the saturated value of Ms = 1.23, which is equivalent to φ = 31◦ . This supports the observation by Toll (2000) that we should not always make the assumption that φ a = φ . The results for the bonded soil show a significant difference between the two values. Table 1. Critical State values of the state variables for low suction tests. q p − ua (kPa) (kPa)
ua − u w (kPa)
269 298 137 735 141 108 825 821
4.1 5.5 1.2 1.1 6.1 0.1 3.3 5.4
437
190 200 96 545 97 86 577 575
Sr (%)
77.4 75.7 70.7 48.4 47.9 46.6 40.3 31.1 Average:
Ma Ma Ma (Eq. 7) (Eq. 8) (Eq. 9) 1.42 1.50 1.44 1.35 1.46 1.25 1.43 1.43 1.41
1.39 1.45 1.42 1.34 1.37 1.25 1.42 1.41 1.38
1.39 1.46 1.42 1.34 1.38 1.25 1.42 1.42 1.39
Figure 3.
3.2
Comparison of Critical State stress ratios for saturated and unsaturated tests.
Suction component, Mb
The values of Mb have been calculated by re-arranging Eq [4] so that Mb is given by: q − Ma (p − ua ) Mb = (ua − uw )
(10)
From the previous discussion about Ma values, it seems sensible to take an average value of Ma = 1.39 (based on Eq. [9]). Therefore, for tests performed at higher suctions, Mb has been calculated from Eq. [10] by assuming a constant value of Ma = 1.39. One value of Ma has been adjusted slightly (1.36) as otherwise an apparent negative value of Mb would be obtained. For the lower suctions, the individual values of Ma calculated from Eq. [9] in the previous section have been used. The values of Ma and Mb calculated in this way are given in Table 2. The values in Table 2 are plotted against degree of saturation in Figure 4(a). It can be seen that Mb drops sharply at degrees of saturation below 30%. For comparison the soil water retention curve at Critical State conditions is plotted with Sr on the horizontal axis in Figure 4(b). It can be seen that there is a sharp increase in suction below 30%, showing a mirror image. The drop in Mb coincides with the sharp change in the water retention behaviour (the end of the desaturation zone). The same data is plotted in terms of variation with suction in Figure 5(a). The changes in Ma and Mb can
Table 2. tests.
Critical State values of the state variables for all
q (kPa)
p − ua (kPa)
ua − u w (kPa)
Sr (%)
Ma
Mb
285 213 210 217 205 348 355 211 230 282 328 753 991 313 821 825 108 141 735 137 298 269
196 121 121 122 118 216 219 121 127 194 209 552 631 155 575 577 86 97 545 96 200 190
492.0 403.6 385.9 479.7 119.0 260.5 392.1 498.7 168.8 100.7 104.0 245.4 300.4 87.7 5.4 3.3 0.1 6.1 1.1 1.2 5.5 4.1
16.9 18.1 18.2 18.9 19.6 19.6 19.9 19.9 20.7 21.8 21.8 21.9 22.6 24.2 31.1 40.3 46.6 47.9 48.4 70.7 75.7 77.4
1.39 1.39 1.39 1.39 1.39 1.39 1.39 1.39 1.39 1.39 1.39 1.36 1.39 1.39 1.42 1.42 1.25 1.38 1.34 1.42 1.46 1.39
0.02 0.11 0.11 0.10 0.34 0.18 0.13 0.08 0.32 0.12 0.35 0.00 0.38 1.12 1.23 1.23 1.23 1.23 1.23 1.23 1.23 1.23
be related to the different phases of water retention behaviour in Figure 5(b). The regions of behaviour seem to be (i) before the air entry value Ma = Mb = Ms (ii) in the desaturation stage Ma rises above Ms
438
35
1.0
25
Mb
20 15
0.5
0.0 20
40
60
80
15 10
(a)
5
0.0
0 0.1
1
10
100
1000
Matric suction (ua-uw): kPa 100
Degree of saturation, Sr: %
Residual zone
500 400 300 200
Desaturation zone
100
20
0.5
Degree of saturation, Sr: % 600
25
Mb
0 100
'
30
1.0
5
(a) 0
Ms Stress ratio, M
30
′ Angle of friction,
Stress ratio, M
Ms
10
Matric Suction (ua- u w): kPa
Ma
1.5
35
Angle of friction,
Ma
1.5
80 60
Residual zone
40 20
(b)
Desaturation zone
0
(b)
0.1
0
1
10
100
1000
Matric suction (u a - uw): kPa
0
20
40
60
80
100
Figure 5. (a) Variation in Critical State stress ratios with suction (b) Degree of saturation vs suction at Critical State.
Degree of saturation, Sr: %
Figure 4. (a) Variation in Critical State stress ratios with degree of saturation (b) Suction vs degree of saturation at Critical State.
but Mb = Ms (iii) in the residual stage Ma remains constant and equal to 1.39 while Mb starts to reduce. It does of course have to be noted that the conditions Mb = Ms in region (ii) and Ma = 1.39 in region (iii) have been explicitly imposed in the present model. Nevertheless, the possible range of values that satisfies the values of the state variables q, p − ua and ua − uw is not that large. It is particularly interesting that for this bonded material, the value of Mb seems to remains close to Ms even when the degree of saturation is significantly reducing. This is probably due to the uniform nature of the bonded sand. The desaturation process in this material probably represents a removal of ‘‘bulk’’ water and the development of ‘‘meniscus’’ water (Karube and Kawai, 2001) as opposed to emptying of pores. In more widely graded materials, the desaturation process will be more complex (involving a wider range of pore sizes) and it might be expected that Mb (and hence (φ b )c ) would drop within the desaturation zone (Vanipalli et al, 1996; Toll and Ong, 2003). Toll et al (2006) interpreted values of φ b at peak state conditions for this artificially bonded soil based on the assumption that φ a = φ . This led to apparently
anomalous results with values of φ b in excess of φ . The analysis here suggests that a value of φ a > φ should have been used, which would then give sensible values for φ b .
4
CONCLUSIONS
A set of triaxial test results performed on unsaturated specimens have been used to derive the variation in the Critical State stress ratios: Ma representing the net stress component and Mb representing the suction component. These are also presented as Critical State angles of friction, (φ a )c and (φ b )c . It is found that Ma is higher than the saturated critical state stress ratio, Ms (i.e. φ a > φ ). This supports the observation that we should not always make the assumption that φ a = φ . The changes in Ma and Mb can be related to the different phases of water retention behaviour. The regions of behaviour indicate that (i) before the air entry value Ma = Mb = Ms (ii) in the desaturation stage Ma rises above Ms but Mb = Ms (iii) in the residual stage Ma remains constant and Mb starts to reduce. This pattern of behaviour is probably explained by the narrow range of pore sizes in the uniform bonded sand.
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REFERENCES Atkinson, J.H. (1993). The Mechanics of Soils and Foundations, London: McGraw Hill. Ali Rahman, Z. (2008). The Engineering Behaviour of a Weakly Bonded Soil including the Unsaturated State. PhD Thesis, Durham University. Alonso, E.E., Gens, A. and Josa, (1990). A Constitutive Model for Partially Saturated Soils, Géotechnique 40(3): pp. 405–430. Fredlund, D.G., Morgenstern, N.R. and Widger, R.A. (1978). The Shear Strength of Unsaturated Soils, Canadian Geotechnicl Journal, 15: pp. 313–321. Fredlund, D.G. and Rahardjo, H. (1993). Soil Mechanics for Unsaturated Soils, New York: Wiley. Karube, D. and Kawai, K. (2001). The role of pore water in the mechanical behaviour of unsaturated soils. Geotechnical and Geological Engineering, 19: pp. 211–241. Maccarini, M. (1987). Laboratory Studies of a Weakly Bonded Artificial Soil. PhD thesis, University of London. Malandraki, V. and Toll, D. (2000). Drained Probing Triaxial Tests on a Weakly Bonded Artificial Soil. Géotechnique, 50(2): pp. 141–151. Malandraki, V. and Toll, D.G. (2001). Triaxial Tests on a Weakly Bonded Soil with Changes in Stress Path. Journal of Geotechnical and Geoenvironmental Engineering 127(2): pp. 282–291. Toll, D.G. (1990). A Framework for Unsaturated Soil Behaviour, Géotechnique, 40(1): pp. 31–44. Toll, D.G. (2000). The Influence of Fabric on the Shear Behaviour of Unsaturated Compacted Soils, In Shackleford, C., Houston, S.L. and Chang, N.Y. (eds.), Advances
in Unsaturated Soils, Geotechnical Special Publication No. 99, American Society of Civil Engineers, Reston: pp. 222–234. Toll, D.G., Ali Rahman, Z. and Gallipoli, D. (2007). Towards Understanding the Behaviour of Unsaturated Bonded Soils, Proc. 3rd Asian Conference on Unsaturated Soils, Nanjing, P.R. China, (eds. Yin, Z.Z., Yuan, J.P. and Chiu, A.C.F), Beijing: Science Press, pp. 139–142. Toll, D.G. and Malandraki, V. (1993). Stress Path Triaxial Testing of a Weakly Cemented Soil. In Anagnostopoulos, A., Schlosser, F., Kalteziotis, N. & Frank, R. (eds.), Geotechnical Engineering of Hard Soils—Soft Rocks, Rotterdam: Balkema, Vol.1: pp. 817–823. Toll, D.G., Malandraki, V., Ali Rahman, Z. and Gallipoli, D. (2006). Bonded Soils: Problematic or Predictable? Proc. 2nd International Conference on Problematic Soils, Malaysia, Singapore, CI-Premier: pp. 55–62. Toll, D.G. and Ong. B.H. (2003). Critical State Parameters for an Unsaturated Residual Sandy Clay, Géotechnique, 53(1): pp. 93–103. Vanapalli, S.K., Fredlund, D.G., Pufahl, D.E. and Clifton, A.W. (1996). Model for the Prediction of Shear Strength with Respect to Soil Suction, Canadian Geotechnical Journal, 33: pp. 379–392. Walker, S., Gallipoli, D. and Toll, D.G. (2005). The Effect of Structure on the Water Retention of Soil Tested using Different Methods of Suction Measurement. Proc. International Symposium on Advanced Experimental Unsaturated Soil Mechanics, Trento, Italy, London: Taylor & Francis, pp. 33–39.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Determination of the shear strength behavior of an unsaturated soil in the high suction range using the vapor pressure technique T. Nishimura Ashikaga Institute of Technology, Tochigi, Japan
H. Toyota Nagaoka University of Technology, Niigata, Japan
S.K. Vanapalli & Won Taek Oh University of Ottawa, Ottawa, Ontario, Canada
ABSTRACT: The shear strength behaviour of an unsaturated silty soil in the high suction range was determined from unconfined compression tests using specially designed shear testing equipment with a dual cylinder triaxial cell. The relative humidity conditions of the compacted specimens used for testing were controlled in desiccators in a temperature controlled chamber. The high suction values achieved in the compacted specimens were calculated using Kelvin’s equation. The stress-strain curve behaviour of the compacted soil specimens with high suctions following both the drying and wetting path were measured and presented in this paper. The peak values of shear strength for all the tested specimens were observed to occur at axial strains lower than 1%. The test results suggest that there is little difference in the measured shear strength values of the tested specimens at high suction values. These results also suggest that the shear strength envelope is horizontal in the high suction range for the soil tested.
1 1.1
INTRODUCTION Background
The shear strength of unsaturated soils in the matric suction range of 0 to 700 kPa (0 to 100 psi) are conventionally measured using modified triaxial or modified direct shear equipment using axis translation technique. Typically, soil specimens used for the determination of shear strength are initially in a saturated state. These specimens are subjected to desaturation by increasing the matric suction by varying the applied pore-air pressure, ua and pore-water pressure, uw using axis translation technique. The increase in the matric suction in the range of 0 to 700 kPa results in a decrease in the water content the soil specimens. In recent years, there has been a significant interest in understanding the mechanical behavior of unsaturated soils such as shear strength and volume change in the high suction range greater than 3,000 kPa, (Cui and Delage, 1996; Nishimura and Vanapalli, 2005). Changes in moisture content in unsaturated soil specimens at suctions greater than 3,000 kPa can be controlled using vapor phase equilibrium. It is convenient and as well safer to use osmotic control or vapour pressure technique to determine the shear strength and volume change
behaviour. The osmotic or vapour pressure technique has been commonly used in the literature for measurement of the soil-water characteristic curve (SWCC) behaviour in the high suction range (Fredlund and Rahardjo, 1993; Vanapalli et al. 1999). This technique is useful in achieving high suction values in soil specimens by controlling relative humidity conditions using different salt solutions in a temperature controlled environment. The soil specimens achieve equilibrium conditions with respect to their moisture content over a considerable period of time. Several investigators have used this technique to achieve high suction values in the specimens and studied the mechanical behavior of unsaturated soils (Cui and Delage, 1996; Blatz and Graham, 2000; Nishimura and Fredlund, 2003 and Nishimura and Vanapalli, 2005). Similar techniques with some modifications are used in this paper for determining shear strength behaviour of an unsaturated silty soil from unconfined compression tests through the use of specially designed equipment. 1.2
Purpose of this study
The study presented in this paper focuses on the determination of the shear strength behaviour of
441
compacted unsaturated soil specimens in the high suction range both along the drying and wetting path from unconfined compression tests. Predetermined relative humidity (RH ) conditions were achieved in the soil specimens by placing them in desiccators with different salt solutions in a temperature controlled environment. These specimens were then placed in specially designed triaxial testing equipment with a dual cylinder triaxial cell. The specimens were sheared without application of confining pressures. The unconfined compressive strengths of specimens with high suction values were determined and the stress versus strain relationships are presented and discussed.
specimens. The water content (10%) and dry density (13.73 kN/m3 ) used in the preparation of the specimens correspond to the dry side of optimum moisture content (17%) and maximum dry density value (15.1 kN/m3 ) determined from Proctors compaction curve (Table 1). The inner surface of the steel mould that was used for the preparation of the static compaction specimens was coated with acrylic to achieve negligible friction between the inner surface of the steel mould and lateral surface of the compacted soil specimen. This technique was useful in the removal of relatively non-plastic silty soil specimens after compaction with ease and without any disturbance. 2.3 Specimens with high soil suction values
2 2.1
MATERIAL AND METHODS Soil properties
The study presented in this paper was carried out on a relatively non-plastic silty soil. The properties of the soil are summarized in Table 1. Figures 1, 2 show grain size distribution and compaction curves respectively. 2.2
High suction values can be achieved by placing soil specimens in desiccators with different salt solutions which are capable of inducing different relative humidity (RH ) conditions in a temperature controlled environment (Fig. 3).
Soil specimen preparation
The soil specimens of 50 mm in diameter and 100 mm in height were prepared using static compaction technique. A steel mould of 50 mm in diameter and 300 mm in height was used for preparing the soil Table 1.
Properties of the soil used in this study.
Liquid Limit, wL (%) Plastic Limit, wP (%) Plasticity Index, Ip Specific gravity, Gs Max. dry density, γd(max) (kN/m3 ) Optimum moisture content, OMC (%)
24.7 22.8 1.9 2.65 15.1 17.0
Figure 2.
Compaction curve.
Temperature and Temperature Humidity controlled chamber
100
Percent finer (%)
80
60
40
Desiccator
20
Salt solution
0 0.001
0.01
0.1
Particle size (mm)
Figure 1.
Grain size distribution curve.
1
Figure 3. Compacted specimens placed in desiccators with different salt solutions to achieve high suction values in a temperature controlled chamber.
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The salt solutions such as Potassium Sulfate (K2 S04 ), Potassium Nitrate (KNO3 ), Ammonium Dihydrogenphosphate (NH4 H2 PO4 ), Sodium Chloride (NaCl), Magnesium Nitrate (Mg(NO3 )2 .6H2 O), Magnesium Chloride (MgCl2 .6H2 O) and Lithium Chloride (LiCl) are commonly used to achieve different relative humidity conditions (Oteo-Mazo et al. 1995; Delage et al. 1998). These salt solutions are capable of inducing RH in the range from 98% to 11% to the soil specimens in a controlled environmental chamber. In other words each of the salt solution is capable of inducing a different suction value to the soil specimens. The suction values that can be achieved in the specimens range from 2,830 kPa to 296,000 kPa for the RH values in the range of 98% to 11%. The value of soil suction at a temperature of 20◦ C can be calculated using Lord Kelvin’s equation (Eq. 1) by knowing the relative humidity (RH ). ψ = −135022 ln(RH )
(1)
ψ = soil suction or total suction (kPa)
(2)
RH = relative humidity (%)
(3) Figure 4.
2.4 New triaxial test apparatus for determining the mechanical behavior of unsaturated soils A new apparatus was designed for determining the mechanical behavior of unsaturated soils by modifying a conventional triaxial testing apparatus. A dual cylinder triaxial cell was used instead of conventional triaxial cell. Figure 4 shows the triaxial cell set up used in the study to perform unconfined compression tests with the measurement of volume change during shear stage. Figure 5 shows the schematic of the equipment set up providing all the key details. Several investigators have provided various techniques to reliably measure the volume change behaviour of unsaturated soils (Bishop and Donald, 1961; Cui and Delage, 1996; Ng et al. 2002; Infante Sedano et al. 2007). The volume changes of the soil specimen during the shearing stage in this study were measured using difference displacement gap sensor placed in the side chamber which is connected to inner cell of the triaxial cell made of transparent acrylic (Figs 4, 5). The volume change of the specimen in the inner cell is equal to the amount of water which moves into or out of the side chamber connected outside of the inner cell. A gap sensor facilitates in measuring the difference of the voltage due to the changes in the movement of water associated with volume changes. The volume change of the soil specimen can be calculated using a calibration curve between volume changes versus voltage, developed prior to testing (Fig. 6). This is a reliable technique for measurement of the volume change of both saturated and
Triaxial cell set up used in the study.
Figure 5. Schematic of the triaxial test apparatus set up used in the study.
unsaturated soil specimens. More details of the procedures could not be discussed in the paper due to space limitations. 2.5 Equilibrium time The procedure followed towards achieving predetermined RH in the soil specimens is explained in this section. For example, a soil specimen can be subjected to drying to achieve RH of 45% in the desiccator at a temperature of 20◦ C in the humidity chamber (Fig. 3).
443
14
R 2 = 0.998
12
Volume (cc)
minute. The axial deformation in the soil specimens along with their volume change behavior during the shearing stage was measured until failure conditions in the tested soil specimens.
Volume = 20.403 x Voltage
10 8 6
3
TEST RESULTS
4
3.1 Stress versus strain relationships
0 0.0
0.2
0.4
0.6
0.8
Voltage (V)
Figure 6. change.
Calibration curve for measuring specimen volume
The same specimen of RH of 45% can also be subjected to wetting by placing the specimen in a different desiccator to achieve, say for example a different RH of 60% by wetting process. The salt solutions used in the desiccators to achieve different relative humidity conditions were discussed in an earlier section of the paper. Several trial studies confirmed that equilibrium conditions with respect to different relative humidity conditions (i.e. suction values) can be achieved in the specimens by placing them in the humidity chamber for a period of 30 days. The mass of the soil specimens attains a constant value at equilibrium conditions.
70 RH 60% RH 70% RH 80%
60
Unconfined compression tests
50 40 30 20 10
The specimens were subjected to different relative humidity conditions to achieve high values of soil suctions. The RH conditions chosen for the present study were in the range of 80% to 40% with 10% differences (RH = 80%, 70%, 60%, 50% and 40%). This series of tests represent the drying path. Another series of tests were also conducted to determine the unconfined compressive strength of the specimens following the wetting path. The relative humidity of the specimens which were first subjected to 40% was increased in 10% stages to achieve RH values in the 40% to 80% range. The RH values chosen in the study result in suction values in the range of 2830 kPa to 296,000 kPa in the soil specimens. The prepared soil specimens were then placed in the test set up of the triaxial test apparatus shown in Figure 4. The specimen to be tested was covered with a rubber membrane in order to facilitate measurement of volume change behavior during the shearing stage. However, the influence of the rubber membrane on the shear strength and the variation of suction values during the shearing were not taken into account in this paper. Unconfined compression tests were conducted on the specimens using a shearing rate of 0.1% per
0 0
1
2
3
Axial strain (%)
Figure 7a. Stress-strain curve behavior of specimens following the drying path. 70 RH 40% RH 50%
60
Deviator stress (kPa)
2.6
Figure 7a, b show the stress versus strain relationships from unconfined compression tests conducted on specimens following the drying path. The test results from all the specimens show that the axial stress increases rapidly. All the specimens tested failed at axial strain values less than 1%. Figure 8a, b show the stress versus strain relationships from unconfined compression tests conducted on specimens following the wetting path. The stressstrain characteristics were similar to that of specimens
Deviator stress (kPa)
2
50 40 30 20 10 0 0
1
2
3
Axial strain (%)
Figure 7b. Stress-strain curve behavior of specimens following the drying path.
444
70
-1.0 RH 50% RH 60%
Deviator stress (kPa)
Deviator stress (kPa)
60 50 40 30 20
RH 40% RH 50% RH 60% RH 70% RH 80%
-0.5
0.0
0.5
10 1.0
0 0
1
2
0
3
2
3
Axial strain (%)
Axial strain (%)
Figure 9a. path.
Figure 8a. Stress-strain curve behavior of specimens following the wetting path.
Dilation at unconfined compression on drying
-2.0
70 RH 70% RH 80%
RH 50% RH 60% RH 70% RH 80%
-1.5
Volumetric change (%)
60
Deviator stress (kPa)
1
50 40 30 20
-1.0 -0.5 0.0 0.5
10 1.0
0 0
1
2
0
3
1
2
3
Axial strain (%)
Axial strain (%)
Figure 8b. Stress-strain curve behavior of specimens following the wetting path.
Figure 9b. path.
following the drying path. The peak values of stresses were reached in the specimens at axial strains less than 1%.
determined from stress versus strain relationships. The term deviator stress is used in the paper as there will be a little influence of the confining pressure due to the use of the rubber membrane. As discussed earlier, the influence on rubber membrane was not considered in this study. The soil suction values of the specimens were estimated using Equation 1 knowing the relative humidity. The entire soil-water characteristic curve (SWCC) in the suction range of 0 to 106 is shown in Figure 10. The test data suggest that the gravimetric water content of the tested soil is low (i.e., less than 2%) for the suction range in which the shear strength and volume change behavior was determined. The suction range studied in the present research program is mainly in the residual stage of saturation (Vanapalli et al. 1996). The water content in sands and silts at residual conditions can be low and may not transmit suction effectively to soil particle or aggregate contact. Thus, even large suction values will not contribute towards significant increases in shear strength.
3.2
Volume change behavior during shearing stage
Figure 9a, b show the volume change versus percentage axial strain relationships for specimens at various RH . While positive values indicate compression, negative values suggest expansion, i.e., dilation, in the specimens. All soil specimens undergo some compression during the initial stages of shearing. The specimen dilates during the later stages of shearing until the failure which typically occurs at axial strains lower than 1%. 3.3
SWCC and the shear strength versus suction relationship
The unconfined compressive strength i.e., the shear strength is half the maximum deviator stress
445
Dilation at unconfined compression on wetting
Figure 11a, b respectively. Numbers in parenthesis correspond to magnitude of relative humidity applied to soil specimen. The test results suggest that the shear strength increase is negligible with increasing soil suction in the range of RH from 40% to 60% (i.e., for the suction range of 130,000 to 70,000 kPa). In other words, for all practical purposes the shear strength envelope may be considered to be horizontal for the suction range (Fig. 11b). The results presented in this paper are consistent with the observations of Vanapalli et al. (1996) and Vanapalli & Fredlund (2000).
Gravimetric water content (%)
30 25 20 Residual stage of desaturation
15 10 5 0 1e-1
1e+0
1e+1
1e+2
1e+3
1e+4
1e+5
1e+6
Suction (kPa)
Figure 10.
4
SWCC of the compacted soil specimen.
The stress-strain curve behaviour of the compacted soil specimens with high suctions following both the drying and wetting path were measured from unconfined compression tests. High suction values were achieved in the specimens by controlling relative humidity. The unconfined compressive strength of the compacted specimens was determined under unconfined conditions using specially designed triaxial equipment with a dual cylinder triaxial cell. The peak shear strength values for all the tested specimens were observed to occur at axial strains lower than 1%. The variation of shear strength with respect to high soil suction values both for drying and wetting paths exhibited essentially horizontal shear strength envelope in the high suction range used in this study.
Gravimetric water content (%)
2.0 Drying process Wetting process
1.5
1.0 Suction range used for unconfined compression tests
0.5
0.0 1000
10000
100000
1000000
Soil suction (kPa)
Unconfined compressive strength (kPa)
Figure 11a. SWCC of the compacted soil specimens in the high suction range.
ACKNOWLEDGEMENTS This research work was supported by the Grantsin-Aid for Scientific Research (No.18206051) from Ministry of Education, Culture, Sports, Science and Technology, Japan.
100 (number) : RH
80 (50) (70)
60
CONCLUSIONS
(40)
(60)
(80)
REFERENCES
40 Drying process Wetting process
20
0 0
50000
100000
150000
Soil suction (kPa)
Figure 11b. Variation of unconfined compressive strength with respect to soil suction in the high suction range.
The SWCC and the relationship between unconfined compressive strength and suction from the two different series (drying path and wetting path) highlighting the high suction range are plotted in
Bishop, A.W. and Donald, I.B. 1961. The experimental study of partially saturated soil in triaxial apparatus, Proceedings of fifth International conference on Soil Mechanics and Foundation Engineering, 1: 3–21. Blatz, J.A. and Graham, J. 2000. A system for controlled suction in triaxial tests, Géotechnique, 50(4): 465–478. Cui, Y.J. and Delage, P. 1996. Yielding and plastic behavior of an unsaturated silt, Géotechnique, 46(2): 291–311. Delage, P., Howat, M.D. and Cui, Y.J. 1998. The relationship between suction and swelling properties in a heavily compacted unsaturated clay, Engineering Geology, 50: 31–48. Fredlund, D.G. and Rahardjo, H. 1993. Soil Mechanics for Unsaturated Soils, John Wiley & Sons, USA. Infante Sedano, J.A., Vanapalli, S.K. and Garga, V.K. 2007. Modified ring shear apparatus to determine the shear
446
strength of unsaturated soils testing, Geotechnical Testing Journal, 30(1): 1–9. Ng, C.W.W., Zhan, L.T. and Cui, Y.J. 2002. A new simple system for measuring volume changes in unsaturated soils, Comput. Graph. Image Process, 39: 757–764. Nishimura, T. and Fredlund, D.G. 2003. A new triaxial apparatus for high total suction using relative humidity control, 12th Asian Regional Conference on Soil Mechanics and Geotechnical Engineering, 65–68. Nishimura, T. and Vanapalli, S.K. 2005. Volume change and shear strength behavior of an unsaturated soil with high soil suction, 16th International Conference on Soil Mechanics and Geotechnical Engineering, 563–566.
Oteo-Mazo, C., Saez-Aunon, J. and Esteban, F. 1995. Laboratory tests and equipment with suction control, Proceedings of the 1st International Conference on Unsaturated Soils, Paris, 3: 509–1515. Vanapalli, S.K., Fredlund, D.G. and Pufahl, D.E. 1996. The relationship between the soil-water characteristic curve and the shear strength of a compacted glacial till. Geotechnical Testing Journal, GTJODJ 19(3): 259–268. Vanapalli, S.K. and Fredlund, D.G. 2000. Comparison of empirical procedures to predict the shear strength of unsaturated soils uses the soil-water characteristic curve. Geo-Denver 2000, ASCE, Special Publication 99: 195–209.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Effect of suction on compressibility and shear behaviour of unsaturated silty soil A.R. Estabragh Faculty of Soil and Water Engineering, University of Tehran, Iran
A.A. Javadi School of Engineering, Computer Science and Mathematics, University of Exeter, UK
ABSTRACT: This paper presents the results of an experimental study on the effect of suction on compressibility and shear behaviour of unsaturated silty soil under various types of loading. A series of laboratory experiments have been conducted in a double-walled triaxial cell on samples of a compacted silty soil. In the experiments the soil samples were subjected to isotropic consolidation followed by unloading and subsequent reloading under constant suction. The experimental results will be presented in the context of an elasto-plastic model for unsaturated soil. The effect of suction on mechanical behaviour of unsaturated silty soil will be presented and discussed. 1
INTRODUCTION
Unsaturated soil is a three phase material containing solid particles, water and air. The mechanical behaviour of unsaturated soil is strongly influences by both pore air pressure (ua ) and pore water pressure (uw ). The difference between ua and uw is defined as suction (s = ua − uw ). Early investigations of the mechanical behaviour of unsaturated soils focused on attempts to combine total stress, σ pore air pressure, ua and pore water pressure, uw within a single effective stress, σ as suggested by Bishop (1959): σ = σ − ua + χ(ua − uw )
(1)
where χ is a factor varying with the degree of saturation, Sr from zero for dry soil to unity for fully saturated conditions. Jenning and Burland (1962) were the first authors to challenge the validity of Bishop’s effective stress. They recognised that the mechanical behaviour of an unsaturated soil can not be described in term of a single stress state parameter because the suction within the pore water and external stress applied to the boundary of a soil element act in qualitatively different ways on the soil skeleton. Therefore this led to use of two stress state variables: net stress (σ − ua ) and suction (s). One of the application of the concept of two independent stress state variable is to explain the volume change behaviour of unsaturated soil. Matyas and Radhakrishna (1968) were amongst the first researchers to consider the two stress state variables as two independent stress state for describing the volume change
of unsaturated soil. Fredlund and Morgenstern (1977) proposed sets of constitutive equations to relate the volume change of unsaturated soil to two stress state variable. Another important contribution of two stress state variables was the development of a constitutive model for unsaturated soil behaviour by Fredlund et al. (1978) who suggested a relationship between the shear strength of unsaturated soil and two stress state variables as: τ = c + (σ − ua ) tan φ + (ua − uw ) tan φ b
(2)
where c and φ are the cohesive and friction angle (with respect to effective stress) at saturation condition and φ b is the angle of internal friction with respect to suction. In recent years researchers have been attempting to analyse unsaturated soil in terms of constitutive relations linking volume change; shear deformation and strength in the context of a single elasto-plastic model. Alonso et al. (1987) were among the first researcher to propose an integrated framework incorporating both the volumetric and shear behaviour of unsaturated soil. This proposed framework was based on the theory of elasto-plastic and was initially proposed in qualitative way, rather than with full mathematical development. A fully developed mathematical formulation for unsaturated soil was proposed by Alonso et al. (1990) in the form of critical state type model. This study focuses on the effect of suction on the consolidation and shear strength behaviour of unsaturated silty soil. In what follows the experimental program and results are presented and discussed.
449
EXPERIMENTAL PROCEDURES
1.75
s = 300 kPa
1.7
1.65
s = 100 kPa
s = 200 kPa
1.6
s = 0kPa
1.55
1.5 100
1000
Mean net stress, p′ : kP
Figure 2. suction.
Normal consolidation lines for different values of
0.12
0.1
s)
A series of suction controlled consolidation and triaxial tests were carried out on samples of compacted silty soil to investigate the influence of suction on mechanical behaviour of unsaturated soil. The silty soil used in this work consist of 5% sand, 90% silt and 5% clay. It had a liquid limit of 29% and plasticity index of 19%. All samples were prepared at a water content of 10% (4% below the optimum value from the standard proctor compaction test). The samples were compacted by static compaction in nine layers with each layer being subjected to a vertical stress 1600 kPa. The tests on unsaturated soil samples were conducted in a Bishop-Wesley hydraulic triaxial cell, modified to a double-walled cell by Estabragh et al. (2004). The suction in the samples was controlled by the axis translation technique. The samples were initially subjected to an equalization stage. Subsequently all samples were subjected to isotropic consolidation to the defined mean net stress. The next stage involved isotropic unloading to a predefined value and final step was shearing (reloading).
Specific volume,
2
0.08
3
TEST RESULTS
In consolidation tests the mean net stress was increased from 20 or 50 kPa to 550 kPa (target value) while holding suction constant (0, 100, 200 or 300 kPa). Typical variation of specific volume (v) with mean net stress (p ) during consolidation is shown in Figure 1. It is shown in this figure that the volume of soil decreased as mean net stress increased. A continuous increase in mean net stress caused the soil to start yielding at some point. The values of yield stresses were estimated by the method of intersection of two linear segments of the consolidation curve as suggested by Cui and Delage (1996). As expected the yield stresss increased with
Specific volume, v
1.82
s = 300 kPa
1.77
s = 200 kPa
1.72
s = 100 kPa
1.67 1.62
s = 0 kPa
1.57 1.52 10
100
1000
Mean net stress, p ′ : kPa Figure 1. Variation of specific volume during consolidation for different values of suction.
0.06
0.04 0
100
200
300
Suction, s : kPa
Figure 3.
Variation of λ(s) with suction.
increasing suction. When the yield stress at a particular value of suction was exceeded, the soil state falls on an isotropic normal consolidation line as shown in Figure 2. The slope of normal consolidation line (λ(s)) and its intercept (N (s)) were calculated from results. The variation of λ(s) with suction is shown in Figure 3. Drained shear tests were performed at the end of unloading stage at constant cell pressure and suction. In this work five cell pressures (50, 100, 200, 300 and 400 kPa), four suction (0, 100, 200 and 300 kPa) and a number of pre-defined value of OCR (overconsolidation ratio) were used. During the test the variation specific volume and water content were recorded. Typical results of the triaxial tests for s = 100 kPa are shown in Figure 4. Compression of a sample during shearing is expressed using a negative sign, and a positive sign is used for dilation of the sample in the graphs of volumetric strain versus axial strain.
450
1000
40 0
Deviator stress, q : kPa
800
= 400 kPa 3
600 400
3
200 3
3
= 50 kPa
Suction , s : kPa
3
= 300 kPa
= 200 kPa
= 100 kPa
30 0
20 0
10 0
0
0
0
5
10
15
Axial strain,
20
0
100
200
300
Mean net stress, p ′: kPa
a:%
(a)
Figure 5.
Loading-collapse (LC) yield curve.
3=
1 3=
-1
300 kPa
3 = 200 kPa
Deviator stress, q : kPa
Volume strain,
50 kPa 50 0
v:
%
3
-3 -5
3 = 100 kPa
-7
3=
400 kPa
-9 0
5
10
Axial strain,
15 a
20
40 0
30 0
20 0
:%
0
(b)
10 0
20 0
300
Suction, s : kPa
Figure 4. Stress-strain curves (a), volumetric–axial strain curve at s = 100 kPa under various cell pressures.
Figure 6. suction.
Variation of maximum deviator stress with
10 0
DISCUSSION
For the isotropic stress state, the intersection of the yield surface with q = 0 plane defines a loadingcollapse (LC) yield curve, with the isotropic yield stress increasing with increase in suction from the saturated value zero suction. The stresses on the LC yield curve correspond to virgin state, and the resulting values of specific volume lie on a unique isotropic normal compression surface in v − p – space s. This corresponds to a series of normal compression lines for different values of suction in the v − p plane. The LC yield curve was produced from the yield points obtained from the isotropic consolidation curves (Fig. 5). The shape of the LC yield curve is consistent with that proposed in the model of Alonso et al. (1990). It was found from the experimental results that λ(s) is a function of suction. The value of λ(s) decreased with increasing suction (for suction greater than 80 kPa) but λ(s) appeared to decrease sharply as the suction reduced to zero. This behaviour was not
Cohesion,c : kPa
4
50
0 0
10 0
20 0
30 0
Suction, s : kPa Figure 7.
Variation of cohesion with suction.
consistent with model of Alonso et al. (1990) who proposed that the slope of isotropic normal consolidation lines λ(s) decreases monotonically with increasing suction from saturation condition. The results of triaxial test at cell pressure of 50 kPa (Fig. 4) shows that the deviator stress first increased to a peak value of 250 kPa at about 2% axial strain
451
after which it became nearly constant. During shearing the volume of the sample increased after a slight initial contraction. In test with cell pressure of 100 kPa shearing continued up to an axial strain of about 18% as shown in Figure 4. The deviator stress increased to a peak value of about 370 kPa at axial strain of nearly 2% and then remained nearly constant while the volume of sample decreased. The shear tests for cell pressures of 200, 300 and 400 kPa were performed up to 12, 15 and 18% axial strains respectively. In these tests the deviator stress increased to a peak value and then remained nearly constant. In the tests with cell pressure of 50 kPa and suctions of 200 and 300 kPa the deviator stress first increased and then slightly decreased and during shearing the volume of these samples increased after a slight initial contraction. Therefore these samples with cell pressure of 50 kPa exhibited a relatively brittle behaviour during shearing. This behaviour can be attributed to the influence of suction on the stiffness, brittleness and dilatancy of the soil sample at low confining pressure. Figure 6 shows typical results of variation of maximum deviator stress with suction at constant cell pressure. This figure shows that the deviator stress increases with increasing suction. The brittleness of soil decreased with increasing confining pressure and the strength increases with increasing suction in a non linear fashion. Under constant suction the increase in cell pressure causes a progressive evolution from dilatancy to compression behaviour until the dilatancy completely disappears. Figure 7 presents another pattern of increase in cohesion intercept with increase in suction at the peak shear stress for all samples tested at different confining pressures.
5
CONCLUSION
An experimental program consisting of a series of controlled suction consolidation and drained triaxial tests were used to investigate the effect of suction on subsequent mechanical behaviour of unsaturated silty soil.
Based on the test results the following conclusion can be drawn: With increasing suction the yield stress increases but λ(s) generally decreases. The LC yield curve is consistent with the model of Alonso et al. (1990). Dilatancy in the sample depends on the value of suction: at a constant cell pressure, a greater suction causes more dilatancy. For a given cell pressure, the increase in soil stiffness depends on the value of suction. Both suction and confining pressure affect the shear strength behaviour of unsaturated soil and cohesion is also a function of suction in a non linear fashion. REFERENCES Alonso, E.E., Gens, A. and Hight, D.W. 1987. Special problem soils. General report. In proceedings of the 9th European Conference on Soil Mechanics and Foundation Engineer ing, Vol. 3, pp. 1087–1146. Alonso, E.E., Gens, A. and Josa, A. 1990. A constitutive for partially saturated soils. Géotechnique 40, No.3, 405–430. Bishop, A.W. (1959). The principle of effective stress. Teknisk Ukeblad 106, No.39, 859–863. Cui, Y, J., and Delage, P. 1996. Yielding and plastic behaveiour of an unsaturated compacted silt. Géotechnique, Vol. 46, No.2, 405–430. Estabragh, A.R., Javadi, A.A. and Boot, J.C. 2004. Effect of compaction pressure on consolidation behaviour of unsaturated silty soil. Canadian Geotechnical Journal, Vol. 41, No.3, 540–550. Fredlund, D.G., and Morgestern, N.R. 1977. Stress state variables for unsaturated soils. Journal of the Geotechnical Engineering, Division, ASCE, Vol. 15, No.3, 313–321. Fredlund, D.G., Rahardjo, H. and Gan, J.K.M. 1978. The shear strength of unsaturated soil, Canadian Geotechnical Journal, No.15, 313–321. Jenning, J.E.B. and Burland, J.B. 1962. Limitation to the use of effective stress in partially saturated soils, Géotechnique, 12, No.2, 125–144. Matyas, E.L. and Radhakrishna, H.S. 1968. Volume change characteristics of partially saturated soils. Géotechnique, Vol. 18, No.4, 432–448.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Mechanical behaviour of an unsaturated clayey sand A. Mirzaii & S.S. Yasrebi University of Tarbiat Modares, Tehran, Iran
B. Gatmiri University of Tehran, Iran Ecole Nationale des Ponts et Chausses, France
ABSTRACT: This paper presents the mechanical behaviour of an unsaturated clayey sand. 12 triaxial compression tests were performed on a sand-kaolinite mixture, including 3 saturated drained (CD), 3 saturated undrained (CU) and 6 unsaturated constant water content (CW) triaxial tests. Unsaturated constant water content tests were carried out with a double-walled triaxial cell and using the axis translation technique. The soil samples were remolded and brought to initial matrix suctions of 100 and 150 kPa. The soil specimens were consolidated and sheared under different values of net confining stress. Based on the results, the stress-strain and critical state behaviour of the soil are shown in terms of net stresses and suction. The water retention behaviour is presented as a surface relating degree of saturation to suction and specific volume.
1
INTRODUCTION
Bishop and Blight (1963) presented the principle of effective stress in unsaturated soils by using two independent stress variables of matrix suction (ua − uw ) and net normal stress (σ − ua ) as: σ = (σ − ua ) + χ(ua − uw )
(1)
where σ is the effective stress, σ is the total stress and ua , uw are pore air and water pressures respectively. χ is the effective stress parameter and has a value of zero for dry soils; while the soil is saturated it becomes equal to 1 and Equation 1 is similar to the principle of effective stress in saturated soils described by Terzaghi (1936). Fredlund, Morgenstern and Widger (1978) introduced the shear strength of unsaturated soils by using two stress variables of matrix suction and net normal stresses: τ = c + (σ − ua ) tan ϕ + (ua − uw ) tan ϕ b
(2)
where τ is the shear stress, ϕ is the effective angle of internal friction and ϕ b is the angle of internal friction with respect to matrix suction. The value of ϕ was assumed to be constant for all values of matrix suction and was taken to be equal to that measured in saturated conditions. Additional test data interpreted using Equation 2 were presented by Ho & Fredlund (1982). However the use of a linear relationship between τ and ua − uw was shown to be
in error by Escario & Saez (1986). This nonlinearity was confirmed by Fredlund, Rahardjo & Gan (1987) who assumed ϕ b varied as a function of matrix suction. Some attempts has also been made to use soilwater retention curves for predicting the mechanical behaviour such as models suggested by Fredlund et al. (1994) and Vanapalli et al. (1996) for predicting the shear strength of unsaturated soils by using the retention curves and saturated shear strength parameters. Shear strength equations formulated for saturated soils, within the context of critical state models have also been extended to unsaturated soils. Several models have been proposed (e.g. Toll 1990; Alonso et al. 1990; Wheeler and Sivakumar 1995) to describe the shear strength of an unsaturated soil under critical state condition. The previous proposed frameworks relate the stressstrain behaviour to the variation of net stresses and matrix suction and do not provide information on the variation of degree of saturation, Sr . In early attempts, changes in degree of saturation were related to the matrix suction by assuming either a unique water retention curve (or SWCC curve) or a unique ‘‘state surface’’ expression relating Sr to matrix suction and net stress. However the relationship between degree of saturation, Sr and matrix suction, s would be nonunique due to the changes of void ratio and ‘‘hydraulic hysteresis’’ (Gallipoli, Wheeler & Karstunen 2003). By neglecting the effect of hydraulic hysteresis, the relationship between matrix suction, s and degree of
453
saturation, Sr should be modified to take account of volume changes. The general hypothesis proposed by Gallipoli, Wheeler & Karstunen is: Sr = f (v, s)
(3)
where v is the specific volume. Considering Equation 3, Gallipoli, Wheeler & Karstunen proposed a unique relationship between matrix suction and degree of saturation incorporating the effect of changes in specific volume as: Sr =
1
m
n 1 + (v − 1)ψ · s
(4)
where , ψ, n, m are soil constants. Equation 4 describes a series of water-retention curves of Sr plotted against s each for a different value of v. As the specific volume decreases, the dimensions of voids would be expected to decrease, so that a higher value of suction would be required to produce a given degree of saturation, resulting in a corresponding shift of the water retention curves. This paper presents the results of an experimental programme including a series of 12 triaxial compression tests to study the mechanical behaviour and water retention behaviour of an unsaturated clayey sand.
The soil samples had a diameter of 49.5 mm and height of 100 mm and were compacted in 8 equal layers and brought to a dry density that was 84% of the maximum dry density achieved in the Standard Proctor compaction test. The physical properties of soil samples are given in Table 2. Table 1.
Classification properties of soil.
Soil type: (unified system) Liquid limit % Plastic limit % Plasticity index % Specific gravity (Gs ) Clay percent % Optimum water content∗ % Maximum dry unit weight∗ (kN/m3 ) ∗
SC 23.5 14 9.5 2.66 40 9.58 19.71
From standard proctor compaction test.
Table 2.
Physical properties of compacted soil samples.
Wet unit weight (kN/m3 ) Dry unit weight (kN/m3 ) Initial Sr % Moisture content % Void ratio Porosity
18.04 16.64 39.36 8.4 0.568 0.362
500
2
CD 200
TEST PROGRAMME & MATERIALS 400
Dev. Stress (kPa)
Constant water content triaxial tests were carried out on unsaturated soil samples of clayey sand. In addition consolidated drained (CD) and consolidated undrained (CU) triaxial compression tests were performed to define soil behaviour in the saturated condition. The soil tested was a mix of 60% sand and 40% kaolinite. The particle size distribution of the soil mixture is shown in Figure 1 and classification properties of the soil are given in Table 1.
300 CD 100 200 CD 50 100
0 0
5
10
15
20
25
Axial strain % (a) Axial strain %
100
0
5
10
15
20
25
0
80 Vol. Strain %
-1
Finer %
60 40
0.001
0.01
0.1
-2
-3
20
-4
0
-5
CD 50
CD 100
CD 200
(b)
1
Diameter (mm)
Figure 1.
Particle size distribution of soil.
Figure 2. Results for saturated CD tests plotted against axial strain: a) Deviator stress, q; b) Volume strain %.
454
Three drained triaxial compression tests (CD) were performed on saturated samples. The samples were isotropically consolidated to effective consolidation pressures of 50, 100 and 200 kPa and were sheared with an axial strain rate of 0.05%/min. The shearing stage was continued until the samples reached the critical states. The results are plotted in Figure 2. Three undrained triaxial compression tests (CU) were carried out on saturated samples at effective consolidation pressures of 50, 100 and 200 kPa, with
600 CW-S100-200
Dev. Stress (kPa)
450 CW-S100-100 300 CW-S100-50 150
0 0
5
10
15
20
25
Axial Strain %
(a) 200
Axial Strain % 0
CU 200
5
10
15
20
25
0 -1
100
CW-S100-50
-2
CU 100
Vol. Strain %
Dev. Stress ( kPa)
150
CU 50 50
-3 CW-S100-100 -4 -5 CW-S100-200
-6 -7
0 0
5
10
15
20
(b)
25
Axial strain % (a) CW-S100-50
160
160
Matrix suction ( kPa )
CU 200
P.W.P ( kPa)
120
80 CU 100
40
CU 50
120
80
40
0 0
5
10
15
20
25
30
Axial strain %
0 0
5
10
15
20
(c)
25
Axial strain % (b)
Figure 3. Results for saturated CU tests plotted against axial strain: a) Deviator stress, q; b) Changes in P.W.P.
5 S100 4
Vol. of water flow (cc)
CW-S100-200
CW-S100-100
3
S150
2 1 0 0
50
100
150
200
Time (hr)
Figure 4.
Wetting curves during equalization stage.
250
Figure 5. Results for constant water content tests at initial matrix suction of 100 kPa plotted against axial strain: a) Deviator stress, q; b) Volumetric strains; c) Matrix suction.
shearing at an axial strain rate of 0.5%/min. The shearing stage was continued until the pore water pressure of the specimen remained constant and the sample reached a critical state. The results are plotted in Figure 3. A series of constant water content triaxial tests were carried out on unsaturated soil samples with a suctioncontrolled doubled-wall triaxial cell, designed and built at the University of Tarbiat Modares. After compaction of the soil samples, they were brought to initial matrix suctions of 100 or 150 kPa using the method of wetting and axis translation technique. During this equalization stage an elevated air pressure of 300 kPa was applied to the top of the soil samples and water
455
in volume of the specimens were determined by measuring the volume of flow in or out of the inner acrylic triaxial cell and a correction was applied due to the downward movement of the loading ram. A constant axial strain rate of 0.009%/min was applied to the specimens to give consistent readings of matrix suction. The shearing stage continued until the sample reached a critical state. The results are shown in Figures 5 and 6.
750
CW-S150-200
Dev. Stress (kPa)
600
450
CW-S150-100 300
CW-S150-50 150
0 0
5
10
15
20
25
30
3
Axial Strain %
(a)
3.1
Axial Strain % 0
5
10
15
20
25
CW-S150-50
Vol. Strain %
-2
-4
CW-S150-100 -6
CW-S150-200 -8
-10
(b) 210 CW-S150-50 CW-S150-200
Matrix suction (kPa)
Saturated soil behaviour
The results of 6 saturated CD and CU tests are plotted in Figures 2 and 3 respectively. The saturated drained tests (CD50, CD100 and CD200) (Fig. 2) show that both the deviator stress and the volumetric strain leveled off at axial strains of 20–25% and the soil reached a critical state. In the saturated undrained tests (CU50, CU100 and CU200) (Fig. 3) the deviator stress and pore water pressure became constant at axial strains of 15–20% and similar to the drained tests the soil reached a critical state. The stress paths for saturated drained and undrained tests are plotted in Figure 7. The critical state and Mohr Coulomb parameters of the saturated soil are presented in Table 3 obtained from CD and CU tests. Due to the relative compaction of the soil, volumes of the specimens decreased during drained tests and pore water pressure increased in undrained tests.
30
0
CW-S150-100
RESULTS
170
130
3.2 90
Constant water content triaxial tests were continued until the deviator stress, volumetric strain and matrix suction tended to constant values. The test results are shown in Figures 5 and 6 for initial matrix suctions of 100 and 150 kPa respectively. Table 4 shows the values of stress state and phase state variables at the end of
50 0
5
10
15
20
25
Unsaturated soil behaviour
30
Axial strain %
(c)
Figure 6. Results for constant water content tests at initial matrix suction of 150 kPa plotted against axial strain: a) Deviator stress, q; b) Volumetric strains; c) Matrix suction.
500
CD 200
back pressure of 200 or 150 kPa was applied to the bottom of the specimen through a 5 bar high entry porous ceramic disk to reduce the initial matrix suction of the samples to 100 or 150 kPa. This stage continued until the volume of the water in the soil remained constant (6–8 days). The wetting curves during the equalization stage are plotted in Figure 4. After the equalization stage the soil samples were isotropically consolidated to a net confining pressure of 50, 100 or 200 kPa. The specimens were then sheared at constant water content by preventing any flow of water in or out of the specimen. The changes
Dev. Stress ( kPa)
400
300 CD 100
200
CU 200
CD 50 100
CU 100
CU 50
0 0
50
100
150
200
250
300
350
400
Mean effective stress (kPa)
Figure 7. tests.
456
Stress paths for saturated drained and undrained
Table 3. Critical state and Mohr Coulomb parameters obtained from saturated drained and undrained tests. c (kpa) ϕ (deg) M λ
3.8 30.7 1.30 −0.061 1.73
Table 4. Failure stress state and phase state variables at constant water triaxial tests. S100
S150
Test (σ3 − ua ) 50∗
100
200
(σ1 − σ3 )f 199.9 300 (ua − uw )f 152.5 153.7 (Sr )f % 49.5 53.7 (1 + e)f 1.53 1.48 3.81 c (kpa) ϕ (deg) 33.15 34.62 ϕ b (deg) 7.72 5.34 ∗
50
100
200
524 232.9 356 151 186.8 199.1 62.9 45.8 52.2 1.41 1.53 1.50 3.81 34.13 29.57 31.39 6.79 10.14 7.38
616 191 61.9 1.4
4
1
Degree of saturation,Sr
0.9 0.8 0.7 0.6 0.5 0.4
0
50
CONCLUSIONS
In this paper the mechanical behaviour of an unsaturated clayey sand was studied in terms of net stresses and matrix suction, s. In addition, water retention behavior was represented as a relationship between degree of saturation, matrix suction and specific volume. Based on the results as the initial matrix suctions of specimens increased the value of degree of saturation reduced and this caused an increase in the value of deviator stress during shearing. During constant water content shearing the reduction of void spaces caused an increase in the values of Sr and s. Based on the results, by relating mechanical behaviour to net stresses and suction and by assuming a relationship between matrix suction, s and degree of saturation, Sr incorporating the variations of specific volume, it is possible to represent both mechanical and water retention behaviour of the unsaturated soil.
30.8 9.216
Stress variables are in kPa.
Matrix Suction, s (kPa)
during the shearing stage. Considering Tables 3 and 4, the values obtained for ϕ from unsaturated constant water tests have good consistency with the value gained from saturated drained and undrained tests. The values obtained for ϕ b are lower than the values gained for ϕ from constant water tests. The variations of degree of saturation, Sr matrix suction, s and specific volume, v are plotted in Figure 8 by passing a three dimensional fitting curve through the data obtained from shearing stage. Considering Figure 8, the specimen air volume tends to decrease during axial loading and causes a decrease in the void spaces and particularly volume of the specimen. As the void ratio decreases, the specimens become denser and the values of degree of saturation and soil matrix suction increases.
2 100
1.8 150
1.6 1.4
Specifc Volume,v
ACKNOWLEDGEMENTS
Figure 8. Surface fitting experimental data obtained for shearing stage in constant water tests in (Sr , s, v) space.
each test. The values of the shear strength parameters proposed by Fredlund et al. (see Equation 2) are also calculated and presented in Table 4. Based on the results (Figs. 5 and 6) the volumetric strains in test group S150 are greater than in the tests carried out at an initial suction of 100 kPa (S100). As the initial volume of air in the void spaces increases, it causes a higher reduction in the total volume of the soil during shearing, explaining the greater volumetric strains in the samples of S150. The irregularities in the deviator stress diagrams (Figs. 5(a) and 6(a)) were probably due to the occurrence of shear zone failures
This research was funded by grants given by the University of Tarbiat Modares and performed under the supervision of Dr. S.S. Yasrebi. The authors are thankful for useful comments of Dr. D.G. Toll (University of Durham) and Prof. N. Khalili (University of New South Wales) during the project.
REFERENCES Alonso, E.E., Gens, A. & Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique 40(3): 405–430. Bishop, M.A. & Blight, G.E. 1963. Some aspects of effective stress in saturated and partly saturated soil. Geotechnique 13(3): 177–197.
457
Escario, V. & Saez, J. 1986. The shear strength of partly saturated soils. Some aspects of effective stress in saturated and partly saturated soil. Géotechnique 36(3): 453–456. Fredlund, D.G., Rahardjo, H. Gan, J.K.M. 1987. Nonlinearity of strength envelope for unsaturated soils. Proc. 6th Int. Conf. expansive soils. New Dehli, 49–54. Fredlund, D.G., Morgenstern, N.R. & Widger, R.A. 1978. The shear strength of unsatuarted soils. Can. Géotech. J. 15(3): 177–197, 313–321. Fredlund, D.G. & Xing, A. 1994. Equations for the soil-water characteristic curve. Can. Geotech. J., 31(4):533–546. Gallipoli, D., Wheeler, S.J. & Karstunen, M. 2003. Modelling the variation of degree of saturation in a deformable unsaturated soil. Géotechnique 53(1): 105–112. Ho, D.Y.F. Fredlund, D.G. 1982. Increase in strength due to suction for two Hong-Hong soils. Proc. Conf. Engng
and Construction in Tropical and residual soils, Honolulu, 263–295. Terzaghi, K. 1936. The shearing resistance of saturated soils and the angle between the planes of shear. Proc. 1st Int. Conf. Soil Mech. 1:54–56. Toll, D.G. 1990. A framework for unsaturated soil behaviour. Géotechnique 40(1): 31–44. Vanapalli, S.K., Fredlund, D.G., Pufahl, D.E& Clifton, A.W. 1996. Model for the prediction of shear strength with respect to soil suction. Can. Geotech. J. 33: 379–392. Wheeler, S.J. & Sivakumar, V. 1995. An elasto-plastic critical state framework for unsaturated soil. Géotechnique 45(1): 35–53.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Shear strength of unsaturated soil and its influence on slope stability O. Tomboy, V. Whenham & M. De Vos Belgian Building Research Institute, Belgium
R. Charlier Université de Liège, Belgium
J. Maertens Jan Maertens bvba & Katholieke Universiteit Leuven, Belgium
J.-C. Verbrugge Université Libre de Bruxelles, Belgium
ABSTRACT: Within the framework of a national project undertaken in Belgium (2003–2009), investigations on the stability of temporary trenches in unsaturated soil are carried out by means of theoretical and experimental approaches. It is well known that soil matric suction is an essential stress variable that influences the shear strength of unsaturated soil and consequently slope stability. In this contribution, the characterisation of the shear strength of a partially saturated quaternary loam is achieved by using simple unconfined compression tests. The derived shear strength is then used for numerical simulations of a 5 m depth full-scale experimental trench, executed and monitored in the unsaturated loam at the site of Belgian Building Research Institute (BBRI). Comparison of numerical investigations and practical observations reveals that the adopted procedure remains on the safe side. This paper includes descriptions of the laboratory investigations, full scale experiments and numerical simulations.
1
INTRODUCTION
At present, common design methods which are applied in Belgium for trench and slope stability do not take into account the suction which can be present in silty and sandy unsaturated soils. This suction is one of the reasons why steeply inclined slopes remain stable, but this stability can not be proven by common design rules. Because of the large occurrence of unsaturated loam and sand soils (possibly after groundwater lowering) during excavations, a research project on the stability of temporary trenches in unsaturated soil has been carried out in Belgium since 2003. The project aims at establishing guidelines for contractors and consultants to take into account the degree of saturation-dependent strength of soil for temporary trenches. To address this issue, the seasonal variations of suction in different soils typically encountered in Belgium are firstly investigated. Its influence on trench stability is then quantified thanks to the combination of laboratory tests and full scale experimental trenches. Complete hydro-mechanical modelling is known to be very complex. Simplifying assumptions are made
in this project since the concept of apparent cohesion is considered in order to take into account the influence of capillary forces or matric suction on slope stability. The apparent cohesion is derived from simple laboratory tests, i.e. unconfined compression tests and compared to traditional estimating methods. In this paper the results obtained on a quaternary loam found at the site of BBRI are presented. It includes descriptions of the laboratory investigations, full scale experiments and numerical simulations. 2
STRATEGY OF THE PROJECT
The actions undertaken to attain a better understanding of the stability of temporary trenches in unsaturated soils can be classified into three broad categories: (1) laboratory tests for characterising the unsaturated soils (mechanical and hydraulic behaviours), (2) monitoring of a full scale experimental trench, and (3) numerical investigations to validate the experimental results. It was decided to focus on soils commonly encountered in Belgium, i.e. mainly quaternary loam and Brusselian sand. Among others, the site of BBRI
459
Unconfined compression tests
Equation 1 proposed by Fredlund et al. (1978)
ca [kPa]
τf = c + (σ − ua ) tan ϕ + (ua − uw ) tan ϕ b
where c is the effective cohesion (kPa); σ is the total stress (kPa); ua is the pore air pressure (kPa); ϕ is the effective friction angle; uw is the pore water pressure and ϕ b is the friction angle taking into account the variations of matric suction. The difference (ua − uw ) is the matric suction. Compared to the shear strength of a dry soil, it can be stated that the apparent cohesion ca exhibited by an unsaturated soil is expressed as:
Ψ [kPa]
w [%] d
SWR C θ [%]
Figure 1.
ca = (ua − uw ) tan ϕ b
Relationship between the key parameters.
at Limelette where the subsoil consists of overlying quaternary loam was selected. At the site of BBRI, a total of nearly 80 tensiometers have been installed since 2003 in the unsaturated loam at different depths close to the full-scale experimental trench. Knowing the evolution of the matric suction in the soil, there is a great interest to adopt a methodology that allows the apparent cohesion to be related to the matric suction. Figure 1 illustrates the strategy adopted within this research concerning the determination of the apparent cohesion. It shows the relationship between the different key parameters, i.e. apparent cohesion ca , volumetric and gravimetric water contents θ and w, and matric suction . The strategy consists firstly in determining the relationship between the apparent cohesion and the gravimetric water content thanks to unconfined compression tests. The results of these laboratory tests, characterising the mechanical behaviour of the unsaturated quaternary loam, are presented in section 3. The hydraulic behaviour, defined by the soil water retention curve of the soil, has then been obtained using the Richards apparatus. The coupling of these characterisations leads us finally to the link between the matric suction and the apparent cohesion. It should be emphasised that the procedure adopted assumes that the effective friction angle is independent of the confining pressure of the specimen and that the matric suction remains relatively constant during the unconfined compression test.
3
(1)
(2)
Several authors suggested expressions for tan ϕ b , as e.g. Oberg & Salfors (1997) or Vanapalli et al. (1996). According to Oberg & Salfors (1997), tan ϕ b can be replaced as a first approximation by the degree of saturation Sr multiplied by tan ϕ . Vanapalli et al. (1996) suggested a similar expression but used the normalized volumetric water content = θ/θs (θ and θs are the volumetric water content, and that one at saturation, respectively) and a fitting factor k based on best fit of their equation to experimental data. Garven and Vanapalli (2006) suggested expression to estimate k as a function of the plasticity index Ip of the soil. These predicting approaches are listed in Table 1. In this contribution a simple experimental approach is adopted to determine the shear strength of an unsaturated soil. The approach proposed by Vanapalli et al. (1999) has been selected to that end. It consists in performing unconfined compression tests on unsaturated soil samples. At the failure, the stress state in the sample under simple compression may be represented by the traditional Mohr circle as shown in Figure 2. In this figure, the concept of apparent cohesion, reflecting the influence of the partly saturated state, is emphasised. Equation 3 expresses the apparent cohesion deduced from an unconfined compression test. In order to determine the apparent cohesion, only the saturated parameters are required, i.e. the effective cohesion and friction angle. ca =
σ1(a) − c 2 tan π4 + ϕ2
(3)
Table 1. Predicting approaches for estimating the shear strength of an unsaturated soil.
CHARACTERISATION OF SHEAR STRENGTH BASED ON LABORATORY EXPERIMENTS
Appr.
Within the concept of effective stress, the shear strength τf for an unsaturated soil may be given by
1 2
460
Equ. for tan ϕb . tan ϕ
Sr ( )k . tan ϕ
Reference Oberg & Sallfors (1997) Vanapalli et al. (1996)
(a) unsaturated soil (b) saturated soil
ca c'
'
' 1(b)
1(a)
,
'
Figure 2. Mohr circles at failure for an unconfined compression test.
4
8
qc (MPa) 12 16
20
24
0 0
2
2
4
4
z(m)
z(m)
0 0
6
Rf (%) 2 3
1
4
5
6
8
8
10
10
12
12
Figure 3.
Average CPT results at the site of BBRI.
a function of the depth of the specimen: the samples taken at a depth less than 2 m and those taken at a greater depth. The distinction may be argued by the heterogeneity of the ground. As revealed by the friction ratio plotted on Figure 3, the 2 first meters exhibit a more cohesive behaviour. If the data are grouped by depth, then it can be observed that the apparent cohesion increases as the water content in the specimen decreases, as would be expected. The determination of the SWRC has been made with Richards apparatus. These results are presented in Figure 5. An average of the experimental data and the interpolation of Fredlund & Xing (1994) are plotted. A different behaviour was also found for the samples taken at more and less than 2 m. Figure 6 depicts the apparent cohesion as a function of the matric suction for samples taken at depths greater and less than 2 m. This figure is obtained using the methodology proposed in Figure 1. In other words it consists of coupling Figures 4 and 5. As expected, the apparent cohesion increases as the matric suction increases due to the increase of capillary forces. The experimental data have been compared with prediction methods listed in Table 1. The degree of
Table 2. Mechanical properties of the quaternary loam for different periods of the year.
c ϕ
<2.25 m 8 2.25–3 m 0 3–7 m 0 >7 m 0 Safety factors
29.6 33.1 34.4 35
Dec. 2006
ca
ca
ca
30 25 30 –
20 0 10 18 14 40 – –
0 0 8 0 18 40 – –
0 0 18 –
1.14
<1
60
apparent cohesion (kPa)
Layer
Oct. 2006
Feb. 2007
<<1
Sample depth < 2 m 50
Sample depth > 2 m
40 30 20 10 0 16
17
18
19
20
21
22
23
24
25
26
gravimetric water content (%)
Figure 4. Results of the unconfined compression tests on the quaternary loam.
45 40
volumetric water content (%)
A series of 35 unconfined compression tests have been conducted on undisturbed specimens of quaternary loam with a natural gravimetric water content ranging from 17% to 25%. The specimens have been taken at several depths ranging from 0.5 m to 3.5 m. The quaternary loam was extensively investigated and described in Van Alboom & Whenham (2003). Figure 3 depicts average results of eight cone penetration tests performed at the site of BBRI. The plasticity index of the soil is found to be close to 10% for the 5 first meters and triaxial tests on saturated undisturbed specimen have been performed to determine the effective mechanical properties. The mechanical properties are given later in Table 2. Figure 4 depicts the deduced apparent cohesion of the loam as a function of the gravimetric water content. Two different behaviours can be distinguished as
35 30 25 20 15
exp. data : < 2m exp. data > 2m Fredlund & Xing : < 2m Fredlund & Xing : > 2m
10 5 0 1
Figure 5.
461
10
100 matric suction (kPa)
1000
10000
Soil water characteristic curves of the loam.
apparent cohesion (kPa)
60
exp. data : depth < 2m
50
Oberg & Salfors 1997
40
Vanapalli et al. 1996
30 20 10 0 0
10 20
30 40 50 60 70
80 90 100
apparent cohesion (kPa)
matric suction (kPa) 60
exp. data : depth > 2m
50
Oberg & Salfors 1997
40
Vanapalli et al. 1996
30 20 10 0 0
10
20 30
40 50 60
70 80
90 100
matric suction (kPa)
Figure 6. suction.
Apparent cohesion derived from the matric
saturation (Sr ) required for the estimating approach has been calculated based on the SWRC curves while the k value has been calculated based on the plasticity index Ip of the soil as proposed by Garven & Vanapalli (2006). The comparison reveals a relatively good agreement between the experimental data and the predictions which tend to be on the safe side.
4
FIELD EXPERIMENTS
Three experimental trenches have been excavated successively in the unsaturated loam of the site of BBRI between 2004 and 2006. The objective of these experiments was to visualise the influence of the seasonal variation of soil suction on the stability of full-scale trenches. The geometries of the trenches have been chosen in accordance with this objective, i.e. it should remain stable during the dry season due to apparent cohesion while it should collapse during winter (when the soil suction decreases). The experiments started each time in June during the dry period and took place during about one year. During the first experiment (June 2004–June 2005), the slope consisted of 3 m deep vertical walls. Failure occurred in January 2005 and emphasized the primordial effect of soil suction on the stability of a
vertical trench. The goal of the second experiment (June 2005–June 2006) was to provide insight on the beneficial effect of protection installed on a slope. The protection aims at minimizing the water infiltration and in turn the variations of soil suction with time. As a consequence, the slope remained stable for longer time. For the third experiment (June 2006–June 2007), an enlargement and deepening of the trench was executed (see further). The specific goal of that experiment was to analyze the effect of a change in trench geometries since inclination has been taken into account. In this contribution, the results of the third experimental trenches are presented. More details on the results obtained for the previous experiments may be found among others in De Vos & Whenham (2007), Whenham et al. (2007) and Tomboy et al. (2007). For the third experiment, a 20 m long and 5 m deep experimental trench has been executed in June 2006. The profile of the trench is depicted in Figure 7. A total of nearly 80 tensiometers were installed to monitor the soil suction. The investigated depths range from 0.5 m to 3.5 m. Figure 8 provides the matric suction measured (weekly readings) during the period June 2006–June 2007 in the quaternary loam at the site of BBRI, while Figure 9 presents the corresponding rain measurements. The water table is situated at a depth of 55 m, implying that it has no effect on the soil suction for the investigated depths. As a first approximation, changes in soil suction would result mainly from infiltration and/or evaporation. Figures 8–9 clearly point out that each decrease of soil suction value at shallow depths corresponds to a rain period. The influence of rainfall on soil suction appears mainly near the ground surface (0.5 m to 1.5 m depth). Moreover, it can be highlighted that during summer, the evaporation involves a relatively rapid increase of matric suction near the ground surface after a rain event. This observation is not valid in winter. On the other hand, it is clear from Figure 8 that the soil suction remains relatively constant for depths larger than 2 m. In other words, the matric suction has a more
11 m North
South 10˚
3m
5m 20˚ Figure 7.
462
Profile of the experimental trench.
2m
Average 0,5m Average 2,5m
Average 1,0m Average 3,5m
periods are given in Figure 10. It can be observed that no damage occurred till the middle of February. From December 2006 till February 2007, measurements reveal the soil suction value was about 0 near the ground surface (depth < 2 m) while it decreases from 20 kPa to nearly 0 kPa at 2.5 m depth (Fig. 8). On Figures 8–9, the failure period is represented by a vertical black line. It clearly points out that failure occurred when the matric suction at 2.5 m fell to nearly 0. A similar behaviour of the trench was already observed during the previous experiments (Whenham et al. 2007 and Tomboy et al. 2007).
Average 1,5m
0
Suction [kPa]
-10 -20 -30 -40 -50 -60 07-Jun
07-Aug
07-Oct
07-Dec
06-Feb
08-Apr
Figure 8. Average matric suction measurements around the experimental trench at the site of BBRI.
5
40
Numerical investigations using 2D plane strain finite element method has been conducted to simulate the trench corresponding to third full scale experiment presented above (Fig. 10). Based on the results of the cone penetration tests (Fig. 3) and the laboratory characterisation, it was decided to consider four layers to model the soil. The soil is modelled using elastoplasticity with a Mohr-Coulomb failure criterion. Three different periods have been chosen in order to investigate the effect of matric suction on the stability of the trench. Table 2 lists the three selected periods and the corresponding sets of soil suction and apparent cohesion. In Table 2, c , and ca are given in kPa and ϕ in ◦ . For the numerical calculations, the apparent cohesion has been added to the effective cohesion to obtain the total cohesion. The calculated safety factors based on the concept of ‘‘phi-c reduction’’ are also included in Table 2. The numerical investigations reveal that the apparent cohesion introduced in the model is not sufficient to assure the stability of the trench during the period of December while the practice proved that the trench remained stable during this period. That means that the adopted procedure kept the numerical estimations on the safe side.
Rainfall [l/m²j]
30
20
10
0 07-Jun
Figure 9.
a)
07-Aug
07-Oct
07-Dec
06-Feb
NUMERICAL APPLICATION
08-Apr
Rainfall measurement at the site of BBRI.
b)
c)
Figure 10. Views of the experimental trench: a) August 2006, b) 13th February 2007 and c) 26th February 2007.
global behaviour and it changes only if an accumulation of evaporation and/or infiltration occurred during a large period (as e.g. during the winter when the evaporation is very small and consequently the infiltration higher). A first collapse of the trench on the south side appeared on 26 February 2007 after an important rainfall. Some pictures of the south slope for different
6
3
2
8
9
18 4
17 7
5
14
10
15
y
0
x
Figure 11.
463
1
Numerical model of the slope.
6
CONCLUSION
This paper aims at giving insights on the stability of trenches in an unsaturated soil. To that end both laboratory and full-scale tests have been conducted. The investigated soil is a quaternary loam which has been characterised with laboratory tests. From a mechanical point of view, unconfined compression tests provided the variation of the apparent cohesion as a function of the water content. These results have been coupled with the SWRC of the soil (obtained with the Richards apparatus) in order to relate the apparent cohesion to the matric suction of the soil. These experimental results appear to be in good agreement with traditional prediction methods. An experimental trench has been constructed in order to analyse the influence of the matric suction on the stability of the trench at full scale. Measurements reveal that sliding occurred when suction at 2.5 m tend to 0 while the suction at higher depths remains more stable and the suction at lower depths equalled nearly 0 for several weeks. The numerical investigations show that the application of the apparent cohesion deduced from the characterisation of the soil is on the safe side since the failure of the trench is modelled for a period which has not been critical in practice. So, the use of the prediction method to evaluate the apparent cohesion appears to be on the safe side, at least for the studied case. REFERENCES BBRI—Research report. 2005. Stabilité des talus: Méthodes de calcul avec prise en compte du degré de saturation du sol, et déduction de règles pratiques pour l’exécution des tranchées et fouilles temporaires, biennale 2003–2005. De Vos, M. & Whenham, V. 2007. De stabiliteit van bouwputten in overzadigde gronden. Geotechniek, 2007 1: 50:55. Fredlund, D.G., Morgenstern, N.R. & Widger, R.A. 1978. The shear strength of unsaturated soils. Canadian Geotechnical Journal 15: 313–321.
Fredlund, D.G. & Xing, A. 1994. Equations for the soil-water characteristic curve. Canadian Geotechnical Journal 31: 521–532. Garven, E.A. & Vanapalli, S.K. 2006. ‘‘Evaluation of empirical procedures for predicting the shear strength of unsaturated soils’’, In Miller et al. (eds.) Proceedings of the 4th International Conference on Unsaturated Soils. 2–6 April 2006, Carefree, AZ. ASCE Geotechnical Special Publication no. 147. pp. 2570–2581. Leclercq, J. & Verbrugge, J.C. 1986. Moisture influence on the Cohesion of a Loam, Proceedings of the 8th DanubeEuropean Conference on Soil Mechanics and Foundation Engineering, Nuremberg, Fed. Rep. of Germany, September 24–26, 1986. Vol. 1: 147–149. Öberg, A.-L. & Salfors, G. 1997. Determination of shear strength parameters of unsaturated silts and sands based on the water retention curves. Geotechnical Testing Journal, Vol. 20, No. 1, pp. 40–48. Tomboy, O., Whenham, V., De Vos, M., Charlier, R., Maertens, J. & Verbrugge. 2007. Influence of soil suction on trench stability. XIV European Conference on Soils Mechanics and Geotechnical Engineering. Madrid, Spain, September 24–27, 2007. Vanapalli, S.K., Pufahl, D.E. & Fredlund, D.G. 1999. Interpretation of the shear strength of unsaturated soils in undrained loading conditions. Proceedings of the 52th Canadian Geotechnical Conference, Regina, Saskatchewan, October 24–27, 1999: 643–650. Vanapalli, D.G., Fredlund, D.E., Pufahl, D.E. & Clifton, A.W. 1996. Model for the prediction of shear strength with respect to soil suction. Canadian Geotechnical Journal 33: 379–392. Van Alboom, G. & Whenham, V. 2003. Soil investigation campaign at Limelette (Belgium): Results. In J. Maertens and N. Huybrechts (eds), Belgian Screw Pile Technology —design and recent developments; Proceedings of the 2nd symposium on screw piles, Brussels, Belgium, May 7, 2003. Vol. 1: 21–70. Rotterdam: A.A. Balkema. Whenham, V., De Vos, M., Legrand, C., Charlier, R., Maertens, J. & Verbrugge, J.-C. 2007. Influence of soil suction on trench stability. 2nd International Conference on Mechanics of unsaturated soils, Weimar, Germany, March 7–9, 2007.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Behaviour of a silt used in flood embankment construction in Indonesia G. McCloskey, M. Sanchez, M. Dyer & M. Kenny Department of Civil Engineering, University of Strathclyde, Glasgow, UK
ABSTRACT: Oedometer tests were carried out on a silt used in flood embankment construction in Indonesia. Three test series were carried out at dry-of-optimum, wet-of-optimum and prepared wet and then dried, initial conditions. Where collapse was observed, the collapse potential for the specimen was evaluated and severity of collapse determined. This material has been sampled from embankments in East Java, Indonesia where there is a recurrent history of geotechnical failures. These preliminary results show the importance of good compaction control at the site and help to explain some failures observed at the site.
1
INTRODUCTION
Many unsaturated soils may undergo a significant settlement when wetted under load. If water is readily available then this settlement can occur rapidly; this is known as collapse. There are four main conditions required for collapse to occur: (Barden et al. 1973, Mitchell 1976) (i) an open partly unstable, partly saturated fabric; (ii) high enough total stress that causes the structure to be metastable; (iii) a binding or cementing agent which stabilises the structure when dry and (iv) addition of water. Each of these must be present to produce a collapse phenomenon, the degree to which each is present influences the resulting collapse observed. Barden et al. (1973) postulated three types of bonding material or force: (i) simple capillary forces between silt-silt and silt-sand bonds; (ii) clay buttresses, where clay plates exist between sand or silt grains and (iii) chemical agents such as iron oxide, or calcium carbonate, often the bonding agent in loessial soils. However in many cases more than one of these types of bonding will be involved in stabilising the unsaturated soil. Lawton et al. (1989) carried out double oedometer tests using a moderately plastic soil. They reported that the soil exhibited both swelling and collapse depending on the overburden stress; that volume changes were inversely related to initial moisture content as was maximum collapse. Compacting the soil at a moisture content greater than optimum and to a level above a critical compaction value were suggested as two means of eliminating both collapse and swelling behaviour. Wetting-induced collapse is defined by Lawton et al. (1992) as the densification of a soil caused by the addition of water at a constant total vertical stress. Lawton et al. (1992) highlight the difference between the near surface collapse in naturally deposited soils
and the deep-seated collapse of compacted soils. Several case histories regarding the collapse of earth dams are discussed in Lawton et al. (1992), where it is indicated that damage or failure occurred soon after the initial filling of these reservoirs. More recent research in this area has focused on performing collapse tests using triaxial equipment (Lawton et al. 1991, Pereira & Fredlund 2000) and on the influence of cyclic wetting and drying (Rao & Revanasiddappa 2006). This paper presents a series of oedometer tests investigating the collapse behaviour of a silt used in flood embankment construction in Indonesia. It has been reported that tropical unsaturated soils have been typically less studied than soils from temperate climates (Futai & Almeida 2005). Flood embankments are constructed of compacted fills and interchange between the unsaturated and saturated states depending on the water table, flood levels and also infiltrated rainfall and precipitation. At the site under investigation a number of engineering works have been constructed to improve the stability of the embankments. However it is proposed here that these works provide the loading required, alongside the readily available access to water, low densities and moisture contents dry-of-optimum to produce conditions favouring collapse.
2
SITE DESCRIPTION
The soil investigated here was sampled from a site located along the flood defence embankments of the Bengawan Solo River, in the village of Kedunhardjo, East Java, Indonesia. The Bengawan Solo River is the longest river on the Island of Java at 540 km, with
465
the source located in central Java and entering the sea, north of Surabaya in East Java. The river level can vary as much as 10 m between the dry and wet seasons. The embankment is a 10 m high two-step embankment which is frequently overtopped in the rainy season. At this site the Bengawan Solo River is 100 m wide. Located to the landward side of the embankment is the village of Kedunhardjo. This village has to be evacuated each time overtopping of the embankments occur. This is a recurrent problem along the length of the Bengawan Solo River as Java is the most densely populated island in the world, with a population of 124 million. As a result many villages have to be relocated during periods of flooding. Not only are there immediate financial consequences but this repeated flooding has negative impacts on local agriculture, particularly reducing crop yields. Figure 1 highlights some of the geotechnical problems encountered along the embankments of the Bengawan Solo River. Figure 1a shows erosion of the natural embankment which runs along one side of the river at this section. It is this eroded material which has been removed from the river bed and used to construct the man-made embankment on the other side of the river. The material can therefore be considered a transported alluvial silt. As such, it is unlikely that a chemical agent provides the stabilising force in the unsaturated condition. Therefore according to Barden et al. (1973) it may be assumed that the bonding forces are due to simple capillary forces or clay buttresses. The natural embankment is in a continual state of erosion and failure; evidence of which was observed along the entire length of the natural embankment. Figure 1b shows a global slip failure which occurred on the gabion reinforced section of the embankment. This measure put in place by the Ministry for Public works, due to previous failure of the embankment at this location, was constructed during the dry season of 2005. The failure observed in Figure 1b occurred during the first wet season after this construction, in December 2005. This failure could be attributed to a deep-seated collapse of a compacted fill under heavy loading, after first wetting as described by Lawton et al. (1992). In another location, Figure 1c, the Ministry installed concrete slabs to act as protection to the slope of the embankment against erosion. Differential settlements and slippage of the slabs have been observed here. The site was visited at the beginning of May 2006, at the end of the wet season, one week previous, the embankments had been overtopped and the village flooded. Sand cone tests were carried out and low in-situ densities were found ranging from 1.18–1.36 Mg/m3 alongside high moisture contents ranging from 36–43%. Dr Ria Soemitro of ITS, Surabaya working in collaboration with the Ministry for Public Works has communicated to the authors that in-situ densities
(a)
(b)
(c) Figure 1. Failures along the Bengawan Solo Embankments: (a) erosion of natural embankments; (b) global failure of gabion reinforced embankments; (c) differential settlement under concrete protection slabs.
as low as 0.8–1.0 Mg/m3 have been found along these embankments. Shear vane tests were also carried out and the cohesion ranged from 20 kPa to 40 kPa, indicating a soft soil as classified in BS: 8004:1986.
3
LABORATORY TESTS
3.1 Material properties The material investigated here was sampled at a depth of 1–1.5 m from the crest of the step of the embankment at a location close to a site of previous
466
failure. Table 1 presents the material properties for the Bengawan Solo fill. Figure 2 shows the soil water retention curve for the Bengawan Solo fill material obtained using the filter paper method. Specimens were prepared at a dry density of 1.2 Mg/m3 and five different moisture contents. Whatman No. 42 filter paper was used and the samples were left for 7 days to allow equilibrium to be reached. At a moisture content of 20%, the material at this density has a suction of almost 1000 kPa.
1.2 1.0
e
0.8 0.6 0.4 0.2 0.0 0
1
10
100
1000
10000
Vertical Stress (kPa)
3.2
(a)
Oedometer tests
Oedometer tests were carried out on compacted specimens of particle size passing the 4.0 mm sieve. Of particular interest was the behaviour of the soil at a low dry density and dry-of-optimum water content. Under these conditions the material was found to be collapsible. Figure 3 presents oedometer tests carried out under (a) dry-of-optimum (Series A), (b) wet-of-optimum (Series B) and (c) prepared wet and dried to 20% (Series C) initial conditions. In Series A, specimens had an initial dry density of 1.16 Mg/m3 and a moisture content between 18 and 19%. A fully saturated and
1.1
1
e
0.9
0.8
0.7
0.6 0
1
10
100
1000
100
1000
Vertical Stress (kPa)
(b) 1
Table 1.
Soil properties. 0.9
Value
Liquid Limit (%) Plastic Limit (%) Plasticity Index Particle Density (Mg/m3 ) Sand Content (%) Silt Content (%) Clay Content (%) Mean Grain Size (mm) Coefficient of uniformity Max. dry density (Mg/m3 ) Optimum moisture content (%)
53 37 16 2.49 36 47 17 0.026 40 1.44 27
Gravimetric Moisture Content (%)
Property
0.8
e
0.7 0.6 0.5 0.4 0
1
10
Vertical Stress (kPa)
(c) Figure 3. Oedometer results: (a) dry of optimum, (b) wet of optimum, (c) prepared wet and then dried to 20% moisture content.
45 40 35 30 25 20 15 1
10
100
Matric Suction (kPa)
Figure 2.
Soil water retention curve.
1000
fully unsaturated test is shown alongside two wetting paths where water was added at 63 kPa and 127 kPa respectively. It can be seen that after inundation the collapse curves follow closely the behaviour of the fully saturated curve. The final reading of settlement for all the collapse conditions presented here was taken 60 mins after the addition of de-aired water. Oedometer tests were further carried out wetof-optimum (Series B) to highlight the importance of initial moisture content in producing collapse. These specimens were prepared at a dry density of 1.16–1.20 Mg/m3 and a moisture content close
467
to 36%. Under these conditions tests were carried out on a specimen soaked at the beginning of the test, an unsoaked specimen and a specimen soaked at 63 kPa. It is clear that under these wet conditions the addition of water does not result in collapse, in fact slight swelling was observed, Table 3. In Series C, the specimens were prepared at 36% moisture content and then dried to 20% moisture content; two different dry densities were tested: 1.26 and 1.38 Mg/m3 . It is evident here that the specimen at 1.26 Mg/m3 on wetting at 127 kPa resulted in significantly more collapse than the specimen of dry density 1.38 Mg/m3 wetted at the same vertical stress. Where collapse was observed the specimens were evaluated in terms of their collapse potential. The collapse potential was calculated from Equation (1) (after Jennings & Knight 1957): Collapse Potential =
−e × 100% 1 + eunsoaked
(1)
where e is the decrease in void ratio of the specimen on wetting under the desired pressure (63 kPa or 127 kPa); eunsoaked is the void ratio of the unsoaked specimen at that pressure. Where swell potentials (positive values) are presented in Table 3, they were calculated as in Equation (1), but with e equal to the increase in void ratio of the specimen on wetting. The collapse potential test as originally carried out by Jennings & Knight (1957) involved saturating the specimen after loading to 200 kPa. Here much lower values of vertical stress were used: 63 and 127 kPa; still significant collapse settlements were observed. Low pressures were chosen to identify if the collapse mechanism could be responsible for collapse under small loads such as those generated under the concrete protection slabs installed at the site (Fig. 1c). Table 2 presents a qualitative guide to understanding collapse potentials and the severity of the problem; this guide is primarily for use in relation to tropical residual soils, (Fookes 1990). In Table 3 the results of Series A highlight the influence of the loading pressure at which saturation occurs; under the same initial conditions doubling the vertical stress increased the collapse potential by more than Table 2. 1990).
Guidance for collapse potential (after Fookes
Collapse potential (%)
Likely severity of problem
<1 1–5 5–10 10–20 >20
No problem Moderate trouble Trouble Severe trouble Very severe trouble
Table 3.
Collapse potential and severity of collapse.
w Series (%) A B C
18.2 18.8 36.2 20.1 19.8 20.1
Vertical Collapse stress potential Severity ρd (Mg/m3 ) (kPa) (%) (Fookes 1990) 1.16 1.15 1.18 1.38 1.38 1.26
63 127 63 63 127 127
−9.9 −13.8 +0.004 +0.13 −3.3 −9.1
Trouble Severe Trouble Slight swelling Slight swelling Mod. Trouble Trouble
one third. This resulted in moving the severity from a Trouble scenario to a Severe Trouble scenario. Furthermore in Series C, an increase in loading pressure of saturation resulted in similar specimens changing from exhibiting slightly swelling behaviour (+0.13%) to exhibiting significant collapse behaviour (−3.3%). The overburden pressure is a key factor in producing a collapsible material. From Series B it is clear that no collapse occurred on saturating a sample already wet-of-optimum. However very slight swelling of negligible quantity occurred (Table 3). These results are in agreement with the suggestion by Lawton et al. (1989) that compacting wet-of-optimum can eliminate collapse behaviour. However this could not be implemented as a practical solution in Indonesia where flood embankment works can only be carried out during the dry season due to high river levels. Even if soil was compacted at a moisture content wet-of-optimum, the climate would ensure that the material dried quickly resulting in specimens not unlike those tested in Series C, where again collapse was observed. From the retention curve (Fig. 2), a specimen at 1.2 Mg/m3 dry density and 20% moisture content has a matric suction value close to 1000 kPa. For 36% moisture content at the same dry density, matric suction lies close to 30 kPa. It is clear that suction is playing an important role in stabilising the structure of the unsaturated soil and for this reason at higher moisture contents (i.e. wet-of-optimum) where suction is already low, no collapse has been observed. More work is planned to include for suction monitored tests to be carried out in the oedometer to further verify the role of suction as the bonding force for this material. The last two entries in Table 3, Series C highlight the influence of dry density on collapse potential. Both saturated at loading pressures of 127 kPa, a decrease in dry density of 8.5% from 1.38 Mg/m3 (96% ρdmax ) to 1.26 Mg/m3 (88% ρdmax ) almost trebled the collapse potential determined. The embankment under investigation was constructed at 80–85% optimum dry density; therefore the material as constructed
468
is at a dry density suitable for collapse conditions. Furthermore this result indicates that for this material a small reduction in dry density can have a significant impact on the collapse behaviour. For this reason good control of compaction on site during construction is of utmost importance. The results identify that the Bengawan Solo fill material is a collapsible material at low dry densities, similar to those found in-situ and at dry-of-optimum moisture contents. Collapse potentials as high as 13.8% have been determined indicating that there is a severe problem regarding collapse of the soil under these conditions. The loading induced by engineering works at the site, combined with low dry densities, dry-of-optimum moisture contents and wetting from the river may have resulted in fulfilling the conditions required to produce collapse. 4
CONCLUSIONS
Results found that increasing the vertical pressure at which saturation occurred, resulted in higher collapse potentials. Increasing the initial moisture content of the specimen to wet-of-optimum, effectively eliminated collapse behaviour. Small decreases in dry density were found to significantly increase collapse potentials. This result highlights the importance of good compaction control during construction of embankments using this material. The collapse behaviour is thought to have been one of the main mechanisms resulting in failure of the gabion reinforced embankment and the differential settlements under the protection slabs at the site. These preliminary results are part of an ongoing research being carried out at the University of Strathclyde on the Bengawan Solo fill material. Future work will include suction monitored and suction controlled experiments to further improve the understanding regarding the collapse behaviour of this material.
The help of Dr. Ria Soemitro and the technical staff of the Soil Mechanics Laboratory, ITS, Surabaya is also greatly appreciated. Travel to ITS and the site investigation carried out at the Bengawan Solo River was supported by a travel grant from the Carnegie Trust. REFERENCES Barden, L., McGown, A. and Collins, K. 1973. The collapse mechanism in partly saturated soil, Eng. Geol., 7, 49–60. Fookes, P.G. 1990. Tropical Residual Soils, Report of the Geological Society Engineering Group Working Party, Quarterly Journal of Engineering Geology, 23, 4–101 Futai, M.M. and Almeida, M.S.S. 2005. An experimental investigation of the mechanical behaviour of an unsaturated gneiss residual soil, Géotechnique 55, No. 3, 201–213. Jennings, J.E.B. and Knight, K. 1957. The additional settlement of foundations due to collapse of structure of sandy subsoil on wetting; Proc., 4th Int. Conf. on Soil Mech. and Found. Engrg., Vol. 1, 316–319. Lawton, E.C., Fragaszy, R.J. and Hardcastle, J.H. 1989. Collapse of compacted clayey soils, J. Geotech. Engrg., ASCE, 115, 1252–1267. Lawton, E.C., Fragaszy, R.J. and Hardcastle, J.H. 1991. Stress ratio effects on collapse of compacted clayey sand, J. Geotech. Engrg., ASCE, 117, 714–730. Lawton, E.C., Fragaszy, R.J. and Hetherington, M.D. 1992. Review of wetting induced collapse in compacted soil, J. Geotech. Engrg., ASCE, 118, 1376–1394. Mitchell, J.K. 1976. Fundamentals of soil behavior, Wiley, New York. Pereira, J.H.F. and Fredlund, D.G. 2000. Volume change behaviour of collapsible compacted gneiss soil, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 126, 907–916. Rao, S.M. and Revanasiddappa, K. 2006. The influence of cyclic wetting drying on collapse behaviour of compacted residual soil, Geotechnical and Geological Engineering, 24, 725–734.
ACKNOWLEDGEMENTS The authors would like to acknowledge the assistance of Andrew Galbraith and Pierre Cunat in carrying out some of the oedometer tests presented here.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Strength and yielding of unsaturated compacted silt from Beijing – Kowloon railway embankment J.K. Liu & L.Y. Peng School of Civil Engineering, Beijing Jiaotong University, Beijing, China
ABSTRACT: Consolidated Undrained (CU) triaxial tests under different water contents were conducted to study the strength and yielding character of unsaturated compacted silt used as fill material in the Beijing—Kowloon railway embankment. It was found that the silt compacted dry of the optimum water content exhibits a work softening character and has higher strength, while the silt compacted on the wet side of the optimum water content exhibits a work hardening character and has lower strength. Within the water content range under study (8.2%–29.2%), both the yield stress and strength decreases with the water content increase, suggesting a water softening effect on the soil behavior. It was also observed that the Critical State Lines (CSL) in q-p plane at different water content are linear parallel lines, meaning that the slope of the CSL was independent of the value of the water content. Nonlinear relationship exists between the apparent cohesive strength and water content, which shows the contribution of water content to shear strength. Besides, a simplified shear strength formula relating water content was proposed.
1
τf = c + (σ − ua )tgϕ + (ua − uw )tgϕ b
INTRODUCTION
Compacted soil can be encountered in nearly all areas of earthwork related engineering: railway, airport, highway embankment construction; earth dam erection; backfilling of pit foundations, retaining walls and barriers etc. Soils after compaction usually exhibit favourable engineering properties such as higher shear strength, lower permeability and less compressibility because of the reduction in volume of voids during compaction. A plastic flow rule of an unsaturated compacted silt was proposed by Cui (1998) by studying the relationship between the direction of the plastic strain increment and the stress ratio; Research on the behavior of a compacted silty sand during suction controlled testing was put forward by Rampino (1998); Yoshimura (1998) studied the effect of suction and moisture on strength and deformation of a compacted clay using an unconfined compression tests. Numerous shear strength tests of unsaturated soil have been conducted during the past 30 years. It is now widely accepted that the stress state for an unsaturated soil can be adequately described by two independent stress state variables: the net normal stress and the matric suction (Matyas and Radhakrishna, 1968). These two variables can be used to describe the shear strength of soil using a Mohr-Coulomb type equation with the following form (Fredlund and Rahardjo, 1993)
(1)
where: τf = shear strength on a failure plane, c = cohesion, σ is total stress normal to the failure plane, ua is pore air pressure, ϕ is angle of internal friction associated with the net normal stress, uw is pore water pressure and ϕ b is angle of internal friction associated with the matric suction. Note that for a saturated soil ua = uw and c and ϕ become effective stress strength parameters. Actually, due to the difficulty in measuring suction, equation (1) was not widely used in engineering practice. To simplify the unsaturated soil strength theory for practical use, several alternative forms of shear strength equations have been presented. A shear strength formula of unsaturated expansive soil linking the shear strength and expansive force was proposed by Lu (1997); On the basis of fractal microstructure, Xu (1998) studied the shear strength character of unsaturated expansive soil; Using multistage triaxial tests, a hyperbola model describing a characteristic of shear strength of unsaturated soil was put forward by Shen (1996) and Yu (1998). Based on micro analysis, Vanapalli and Fredlund (1996) adopted the soil water characteristic curve (SWCC) to predict the shear strength of unsaturated soil. Combined Bishop’s formula and Fredlund’s formula together, a shear strength expressions taking water content as parameters was proposed by Miao (1999).
471
300 250 Deviator stress q /kPa
Different from saturated soil, the yield points of unsaturated soil are distributed in the invariant stress space p (net mean press)—q (deviatoric stress)—s (suction) and the yielding was characterized by two curves: loading-collapse (LC) and suction-increase (SI), its hardening laws were controlled by the total plastic volumetric deformation (Alonso et al. 1990). The soil suction is directly related to water content, so the yielding of unsaturated soil with the change of moisture is as important as that of suction. This paper presents experimental study results on silt under unsaturated conditions, with emphasis on the influence of water content on the shear strength and yield characteristic, taking the water content as parameter which can be used easily in the engineering practical. Using traditional Bishop type strength equation, a simplified shear strength formula relating water content was proposed.
200 150 100 50 0 0
2
4
6
8
10
12
14
16
Figure 1. Stress-strain curves of compacted silt at different water content σ 3 = 100 kPa.
1.5
0
5
10
15
1
SHEAR STRENGTH OF UNSATURATED COMPACTED SILT
0.5 0
The silt in this study is from Beijing to Kowloon railway embankment. The physical properties of the soil are given in Table 1. The sample was prepared as close as possible to the embankment state. The procedure included mixing a dry soil with de-aired and de-mineralising water to obtain the required water content and compacting it by layers to get the required density. A series of compacted samples with different water content (8.2%, 10.4%, 12%, 18%, 29.2%) were consolidated at cell pressure of 100 kPa and then undrained triaxial tests were performed until they failed. Fig. 1 illustrates stress-strain behavior of samples sheared at different cell pressure. It is observed that strength increased with ω (water content) reduction and stress-strain curves exhibited peak strength followed by strain softening when compacted on the dry side of ωopt . (optimum water content), and exhibited strain hardening when compacted on the wet side of ωopt . The magnitude of strength reduction was different on the two sides of ωopt . Note that the strength at ωsat (saturated water content) only accounts for half of that at ωopt , but strength at ω = 8.2% is close to the strength at ωopt , so it can be concluded that samples compacted on the dry side of ωopt have more strength Table 1.
Main physical properties of the test soil. Fraction (mm) %
ωL %
ωP %
IP
0.25–0.075
0.075–0.005
<0.005
30.4
21.4
9.0
20.55
67.76
11.69
v /%
2
0.5 1 1.5 2 2.5 3 3.5
Figure 2. Volumetric vs axial strain curves of compacted silt at different water content (σ3 = 100 kPa).
than that compacted on the wet side of ωopt . Besides, the peak strength at ω = 8.2% and ω = 10.4% were similar to the strength at ωopt. with the strain of 15%, it means that further reduction of water content (less than 8.2%) would not have much influence on the strength. Silt with a large amount of fine grains will not be compacted very densely, even at ωopt and compacted to maximum dry density, there will be many void existing between grain particles. Due to this special fabric, silt exhibits stronger water sensitivity, so a small increase in moisture can cause substantial reduction of strength. Fig. 2(b) shows the relations of volumetric strain vs axial strain of compacted silt at different water content. It is found that when compacted at dry side of optimum water content, the silt sample will contract during shear at first then dilate (when volumetric strain is larger than 6%); when compacted on the wet side of optimum water content, the silt sample will shrink continuously. Under the same confining pressure, the more water content in compaction, the silt sample will
472
where: a, b, c, d are test parameters acquired from the curves of c − ω and φ − ω. By substituting ω = Sr e/Gs into the Eq. (4) a strength formula of unsaturated soil related to saturated degree, can be obtained as:
Total cohension/kPa
25 20 15 10 5
0
5
10
15
20
25
30
Sr e τf = a Gs
35
−b
Sr e −d + σ tg c Gs
(5)
Water content/% (a)
Water content/%
35
Taking water content or the degree of saturation as variables, equation (4) and (5) can be easily used in engineering practice without suction control and measurement.
30 25 20
3 15
0
10
20
30
40
Friction angle/° (b)
Figure 3. The curve of water content vs (a) total cohesion, (b) vs friction angle.
YIELDING CHARACTERISTIC OF UNSATURATED COMPACTED SILT
In the q-p plane, a critical state line equation of unsaturated soil at different matric suction was proposed by Wheeler (1995) in the following form: q = M (s)p + μ(s)
have more volumetric strain; Under the same water content in compaction, the higher confining pressure will produce more volumetric strain. As shown in Fig. 3(a) and Fig. 3(b) the cohesion and friction angle at different water content exhibited an exponent relationship, which can be expressed as follows: y = ax−b , where: a, b = test parameters. For Fig. 3(a), a = 87.349 b = 0.7441, For Fig. 3(b), a = 55.086 b = 0.2688. Using a Mohr-Coulomb type equation, for unsaturated expansive soil Miao (1999) gave the following form: τf = ctotal + σ tgϕtotal
(2)
where: ctotal and ϕtotal are no longer constant but functions of water content including the contribution of matric suction and structure of expansive soil which have great influence on shear strength. For the experimental data of the studied silt, after regression analysis we have: ctotal = aω−b ,
ϕtotal = cω−d
(3)
(6)
where: M (s) is the slope of the critical state line and μ(s) is the intercept of the critical state line on q axis, both of them are functions of matric suction. For the studied silt the critical state lines on the q-p plane at different water contents (8.2%, 10.4%, 12%, 18% and 29.2%) are given in Fig. 4. It is observed that the CSLs exhibit linear relationships at different water content and can be described by the same type of equation as Eq. (3), but coefficients M (ω) and μ(ω) will be the functions of water content. It can be found that the 5 CSL obtained in the tests are nearly parallel (Fig. 4), meaning their slopes are constant with water content. This agrees well with the results of Wheeler (1995) that M (s) was a constant with matric suction. Here M (ω) = 1.08 for the tested compacted silt. The intercept of CSL μ(ω) on the q axis reflects the contribution of water content to shear strength. As shown in Fig. 5, μ(ω) and water content have an exponential relationship, which can be expressed as μ(ω) = aω−b , here a = 197.86, b = −0.8174. By substituting M (ω) = cons, μ(ω) = aω−b into Eq. (6), a CSL equation of unsaturated soil related to water content, can be obtained as following:
Combining Eq. (2) and Eq. (3) together, the strength formula of unsaturated soil considering water content is expressed as follows:
q = cp + aω−b
τf = aω−b + σ tg(cω−d )
where: a, b, c are test parameters from the critical state lines in the q-p plane.
(4)
473
(7)
ACKNOWLEDGEMENT
375
Deviator stress q/kPa
325
This research is supported by National Natural Science Foundation of China (NSFC) under Grant No. 50678020 and Program for New Century Excellent Talents Plan funded by Ministry of Education of China under Grant NCET-05-0092.
275 225 175 125
REFERENCES
75 25 50
100
150
200
250
300
Mean net stress p/ kPa
Figure 4.
Yield loci in q-p plane at different water content.
60 50 40 30 20 10 0
0
Figure 5.
10
20
30
40
The curve of μ(ω) and water content.
From Fig. 4 with Fig. 5, it can be concluded that the yielding strength of unsaturated soil is influenced substantially by the water content. μ(ω) is not a constant but increases when water content decreases.
4
CONCLUSION
Stress-strain curves of unsaturated compacted silt from the Beijing—Kowloon railway embankment exhibited peak strength followed by strain softening when compacted on the dry side of ωopt , and exhibited strain hardening when compacted on the wet side of ωopt . Samples compacted dry side of ωopt are stronger than those compacted on the wet side of ωopt . The shear strength and yielding stress increase with reduction in water content. Taking water content or saturation degree as variables, the strength equation proposed in this paper can be used easily in practical engineering without measuring suction. The slope of the critical state line M (ω) is a constant with water content; the intercept of critical state line on qaxis μ(ω) reflects the contribution of water content to shear strength.
Alonso, E.E., Gens, A. and Josa, A. 1990. A constitutive model for partially saturated soils, Geotechnique, 40(3): 405–430. Cui, Y.J., Sultan, N. and Delage, P. 1998. Plastic flow of an unsaturated compacted silt. Proceedings of the Second International Conference on Unsaturated Soils: Beijing: International Academic Publishers. Lu Zhaojun, Wu Xiaoming and Sun Yuzhen. 1997. The application of expansive force in unsaturated soils strength theory. Chinese Journal of Geotechnical Engineering. 19(5): 20–27. Lu Zhaojun, Zhang Huiming, Chen Jianhua and Feng Man. 1992. Shear Strength and Swelling Pressure of Unsaturated Soil. Chinese Journal of Geotechnical Engineering, 14(3): 1–8. Matyas E.L. and Radhakrishna, H.S. 1968. Volume changes characteristics of partially saturated soils. Geotechnique, Vol. 18, No. 4, pp. 432–448. Miao Linchang, Zhong Xiaochen and Yin Zonze. 1999. The Relationship Between Strength and Water Content of Expansive Soil. Rock and Soil Mechanics. 20(2): 71–75. Rampino, C., Mancuso, C. and Vinale, F. 1998. Behavior of the compacted silty sand during suction controlled tests. Proceedings of the Second International Conference on Unsaturated Soils: Beijing: International Academic Publishers. Shen Zhujiang. 1996. Some Problems of Unsaturated Soil in Present Study. Conference of regional geotechnical engineering problem: Beijing Atomic Energy Publishers. Vanapalli, S.K., Fredlund, D.G., Pufahl, D.E. and Clifton, A.W. 1996. Model for the Prediction of Shear Strength with respect to Soil Suction, Can. Geotech. Jnl., Vol. 33. Wheeler, S.J. and Sivakumar, V. 1995. An elasto-plastic critical state framework for unsaturated soil. Geotechnique, 45(1): 35–53. Xu Yongfu, Gong Yongping and Ying Zongze. 1998. Fractal characteristic of shear strength of unsaturated expansive soils. Engineering Mechanics. 15(2): 76–81. Yoshimura, Y. and Kato, S. 1998. Effects of suction and soil moisture on strength and deformation of a compacted silty clay in unconfined compression test. Proceedings of the Second International Conference on Unsaturated Soils: Beijing: International Academic Publishers. Yu Shenggang, Ma Yongfeng and Wang Zhao. 1998. The feature of suction and hyperbola model for shear strength of unsaturated soil. Proceedings of the Second International Conference on Unsaturated Soils: Beijing: International Academic Publishers. Fredlund, D.G. and Rahardjo, H. 1993. Soil mechanics for unsaturated soils. John Wiley and Sons, New York.
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Estimation of the shear strength of lean clay based on empirical equations and a laboratory experiment on slope failure J.V. Vasquez & L.M. Salinas Laboratorio de Geotecnia, Universidad Mayor de San Simón, Cochabamba, Bolivia
ABSTRACT: A series of laboratory tests and experiments were conducted to obtain the shear-strength envelope of an unsaturated lean clay soil. It was estimated with the equations proposed by Vanapalli et al. (1996) and measured using the conventional direct shear apparatus following the procedure proposed by Vanapalli & Lane (2002). Additionally, a physical model was vertically loaded to failure and shear strength along the surface was calculated by back analysis. The Soil Water Retention Curve (SWRC) was estimated by means of the filter-paper method. The results show a good approximation between the shear strength estimated and the one back calculated from the physical model.
1
INTRODUCTION
Shear strength is an important engineering property in the design of numerous structures such as earth dams and retaining walls. Usually the mechanical properties of the soil are analyzed ignoring the unsaturated state of the soil, even though soils encountered in engineering practice are often unsaturated. To have a better approximation of the shear strength behaviour of the soil, it is necessary to take into account the unsaturated state of the soil, which is possible using unsaturated soil mechanics theory. The shear strength of an unsaturated soil can be determined using modified direct shear or triaxial shear equipment. However, experimental studies related to the determination of the shear strength of unsaturated soils are time consuming and require extensive laboratory facilities, which are costly. Due to these reasons, application of shear strength studies in engineering practice has been limited. Hence, the estimation methods and techniques for determining the unsaturated shear strength are useful to determine the unsaturated shear strength in an economical and practical way. Several semi-empirical shear strength functions were proposed to predict the unsaturated shear strength. The proposed procedures use the saturated shear strength parameters (i.e. c and φ ) along with the soil water retention curve (Vanapalli et al., 1996; Fredlund et al., 1996; Oberg & Salfors, 1997; Khallili & Khabbaz, 1998; Bao et al., 1998). The prediction method selected was the nonlinear function proposed by Vanapalli et al. (1996). This equation provides predictions using the entire soil water retention curve (i.e. 0 to 1,000,000 kPa)
and the saturated shear strength parameters. Furthermore, a simple experimental technique was used for determining the same shear strength envelope of the soil, following a procedure proposed by Vanapalli and Lane (2002). In this regard, the envelopes found using the nonlinear function proposed by Vanapalli et al. (1996) and the procedure proposed by Vanapalli & Lane (2002) were compared between each other. Later, both of them were also assessed with the shear-strength values found by the back analysis of the failure surface of the physical model.
2
MATERIAL AND METHODS
The soil is lean clay typical of that from Cochabamba, Bolivia which was separated through sieve No. 4 (i.e. 4.75 mm). Liquid and plastic limits have been measured following the standard-test method ASTM D4318. The liquid limit found was 31.1%, the plastic limit, 18%, and the plastic index, 13%. The samples of soil used in laboratory experiments were compacted using a reduced Proctor. Reduced Proctor follows the same specifications as the standard Proctor but with only 12 drops of the compactive ram per lift rather than 25 drops. The dry density of the soil is 16.0 kN/m3 with an initial water content of 12.4%. The saturated shear strength parameters have been measured from a direct shear test following the standard test method ASTM D3080-98. The cohesion found was 0 kPa and, the effective angle of internal friction, 29.3◦ .
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2.1
SWRC determination
The SWRC was determined following the standard test method ASTM D5298-94, and the filter paper used was Whatmann No. 42. The samples, compacted at the desired dry density, were shaped using plastic rings of 76.2 mm diameter and 30 mm height. The specimens were wrapped in paper and saturated by submerging the samples in water with the plastic rings for a period of 48 hours. The saturated samples were placed in a drying room with a constant temperature of 27◦ C. Several 59 mm diameter by 20 mm height soil specimens were extracted by forcing a ring cutter into the samples, each one with different water content. The calibration curve used was the bilinear equation proposed by Leong & Rahardjo (2002) (Equations 1 and 2). Logψ = 2.909 − 0.0299wf
wf > 47
(1)
Logψ = 4.945 − 0.0673wf
wf ≤ 47
(2)
Figure 1. Relationship between the fitting parameter, κ, and the plastic index (from Vanapalli and Fredlund 2000).
where wf = water content of filter paper; ψ = soil suction. The results found in the filter-paper test were fitted using the equation proposed by Fredlund and Xing (1994) (Equation 3). ⎤ ψ ln 1 + ⎢ hr ⎥ θw (ψ) = θs ⎢ ⎥ ⎣1 − 106 ⎦ ln 1 + hr ⎡ ⎡
Figure 2.
⎤
⎥ ⎢ 1 ×⎢ n ,m ⎥ ⎦ ⎣ ) ψ ln exp(1) + a
(3)
where ψ = soil suction; θs = saturated volumetric water content; θw = volumetric water content; hr = suction value for residual water content. 2.2 Predicting the shear strength The function used to predict the shear strength was the procedure proposed by Vanapalli et al. (1996). This function is the more general, non-linear function using the entire soil water retention curve (i.e. 0 to 1,000,000 kPa) and the saturated shear strength parameters (Equation 4).
τ = c + (σn − ua ) tan φ . /
+ (ua − uw ) ( κ )(tan φ )
(4)
Direct shear box.
where κ = fitting parameter used to obtain a best fit between the measured and predicted values; = normalized water content. The fitting parameter was obtained from the relationship between the fitting parameter, κ, and the plastic index (Fig. 1).
2.3
Direct test shear on unsaturated soil specimens
The samples were prepared following the same procedure used in the filter paper test. They were extracted using a 59 mm square by 20 mm height cutter. The procedure used in this investigation was the technique proposed by Vanapalli & Lane (2002). The soil specimen was subjected to consolidation in a conventional direct shear apparatus under an applied net normal stress of 27.6 kPa for a period of 24 hours (Fig. 2). The soil specimens were sheared at a strain rate of 1.25 mm/min. The specimens were sheared using a direct test shear (Fig. 2) in accordance with ASTM standard D3080-98. It is assumed that there was no significant change in suction of the soil specimen during the shearing stage.
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Figure 3.
View of the physical model.
Figure 5.
View of the hydraulic equipment.
were used to find the values of the shear strength. An angle of shearing resistance with respect to matric suction, φ b = 14◦ , was used, and the shear strength was calculated using the equation proposed by Fredlund et al. (1978) (Equation 5). Figure 4.
2.4
τ = c + (σn − ua ) tan φ + (ua − uw ) tan φ b
Slip surface.
(5)
where φ b = angle of shearing resistance with respect to matric suction; and (ua − uw ) = matric suction of the soil on the plane of failure.
Physical model
The physical model was built with the following dimensions: 1 m high by 1.5 m length by 0.4 m thick. The slope of the soil model was 64.1◦ , and the height of the slope 0.66 m. The soil used in the model was compacted at a dry density of 16 kN/m3 , with an initial water content of 12.4% (Fig. 3). The water-table level was maintained at the height of the toe of the slope. The slope was gradually vertically loaded until 215 kN/m2 , where the slope failed (Fig. 4). The vertical force was generated by hydraulic equipment (Fig. 5). Many soil samples were taken at different points in order to obtain the variation of suction with depth, and the distinct values of the physical model, such as the slip surface, were simulated using SLOPE/W. The equilibrium limit theory was used and the selected method was Morgenstern & Price (1965). The back analysis was aimed at finding the shear strength acting in the slip surface, which was subdivided into 30 slices. The values of net normal stress and suction of slices
3
RESULTS AND DISCUSSION
The results of the filter-paper test were fitted using the mathematical equation proposed by Fredlund and Xing (1994) (Equation 3). The obtained SWRC is presented in Figure 6, the model parameters used can be observed in Table 1; the correlation was of R 2 = 0.957. The estimated shear strength envelope was obtained using Vanapalli et al. (1996) criteria, and the measured shear strength envelope was obtained using the Vanapalli & Lane (2002) technique. Both are presented in Figure 7 for 0 to 100 kPa suction range, and Figure 8, for 0 to 10,000 kPa suction range. For a range of 0 to 100 kPa, a maximum variation of 30% was observed between the measured and the estimated values. For a range of 0 to 10,000 kPa, there is a reasonable correlation between the measured and the estimated envelopes.
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Gravimetric water content,w (%)
0.25 0.20 0.15 0.10 Fredlund and Xing (1996) fitting 0.05 Filter Paper test 0.00 0.1
1
10
100 1000 Suction (kPa)
10000 100000 1E+06
Figure 6. SWRC by means of filter-paper test and Fredlund & Xing (994) fitting.
Figure 8. Shear strength envelopes for a suction range from 0 to 10000 kPa. 80
Fredlund & Xing (1994) model parameters.
Parameters
Value
a (kPa) n m hr (kPa)
2500 0.323 2.799 94567
Shear strength (kN/m†)
Table 1.
70 60
Shear strength estimated using Vanapalli et al. (1996)
50
Shear strength in the physical model
40 30 20 10 0 5
10
Figure 9.
15
Slices
20
25
30
Shear strength values versus number of slices.
60
Shear strength (kN/m²)
50 40 30 Estimated envelope using Vanapalli et al. (1996) equation Measured envelope using Vanapalli and Lane (2002) technique Shear strength from the physical model at normal stress of 27.65 (kPa)
20 10 0 0
Figure 7. Shear strength envelopes for a suction range from 0 to 100 kPa.
The slope failure obtained from the back analysis has a factor of safety close to 1 (i.e. 0.98). The estimated and observed shear-strength values are shown in Figure 9. There is a good approximation between the estimated shear strength and the backanalysis-shear-strength results. Figure 10 shows the back calculated value of shear strength with a net normal stress of 27.6 kPa for comparison with the estimated envelopes. The calibration curve used was the bilinear equation proposed by Leong & Rahardjo (2002), which was proven to be satisfactory for the estimations used in the present paper.
10
20
30
40
50 60 Suction (kPa)
70
80
90
100
Figure 10. Comparison between both the estimated envelope (Vanapalli et al. 1996) and the measured envelope (Vanapalli and Lane, 2002) and the obtained shear strength from the physical model at a net normal stress of 27.65 kPa.
Vanapalli et al. (1996) and Vanapalli & Lane (2002) are methods that estimate the unsaturated envelope. Both of them provide similar results for the range 0 kPa to 10000 kPa (Fig. 8), although the magnitude of strength is larger using the first method in the range of suction of 0 to 4000 kPa and lower in the second part. The physical model used in the present research was a very important tool of validation instead of more costly tests (e.g. modified triaxial tests). Nevertheless, in future, a better system of suction measurement
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during shearing of the soil must be used to provide better values of shear strength at failure. The unsaturated direct shear experiments proposed by Vanapalli & Lane (2002) show a reasonable correlation for a net normal stress of 27.6 kPa. More experiments using different net normal stress and different dry density are required. 4
CONCLUSIONS
During the development of this research project, the methods used were found to be useful, practical, economic and efficient for predicting the shear strength envelope. Both Vanapalli et al. (1996) and Vanapalli & Lane (2002) provided reasonable results for unsaturated shear strength envelopes compared with actual shear strength values back-calculated from a slope failure surface. ACKNOWLEDGMENTS The authors gratefully acknowledge financial support from the IUC-UMSS program. REFERENCES ASTM Standard. 1997. D 5298-94: Standard test Method for the Measurement of Soil Potential (Suction) Using Filter Paper, annual Book of ASTM Standard, Vol. 04.09. ASTM Standard. 1999. D 3080-98: Standard test Method for Direct Shear Test of Soils Under Consolidated Drained
Conditions. Annual Book of ASTM Standard, ASTM. West Conshohocken, PA. Bao, C.G., Gong, B. & Zan, L. 1998. Properties of Unsaturated Soils and Slope Stability of Expansive Soils, Keynote Lecture, UNSAT 98, 2nd International Conference on Unsaturated Soils, Beijing. Fredlund, D.G. & Xing, A. 1994. Equations for the Soil-Water Characteristic Curve, Canadian Geotechnical Journal, Vol. 34 No. 4, pp. Fredlund, M.D. & Barbour, S.L. 1996. The Relationship of the Unsaturated Soil Shear Strength Function to the Soil-Water Characteristic Curve. Canadian Geotechnical Journal. Vol. 33, No. 3, pp. 440–448. Khalili, N. & Khabbaz, M.H. 1997. A unique relationship for x for the determination of the shear strength of unsaturated soils. Geotechnique, 48. No. 5, pp. 681–687. Oberg, A. & Salfours, G. 1997. Determination of shear strength parameters of unsaturated silts and sands based on the water retention curve. Geotechnical Testing Journal, GTJODJ, 20. pp. 40–48. Leong, E.C. & Rahardjo, H. 2002. Factors Affecting the Filter Paper Method for Total and Matric Suction Measurements. Geotechnical Testing, Sept, 2002, Vol. 25 No. 3. Vanapalli, S.K., Fredlund, D.G., Pufahl, D.E. & Clifton, A.W. 1996. Model for the Predicting of Shear Strength with Respect of Soil Suction. Canadian Geotechnical Journal, 33(3): 379–392. Vanapalli, S.K. & Fredlund, D.G. 2000. Comparison of different procedures to predict unsaturated soil shear strength. Department of Civil Engineering, University of Saskatchewan, SK, Canada, S7N 5A9. Vanapalli, S.K. & Lane, J.J. 2002. A simple technique for determining the shear strength of fine-grained unsaturated soils using the conventional direct shear apparatus. Lakehead University, Thunder Bay, Ontario, Canada, P7B 5E1.
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Effects of drying and wetting cycles on unsaturated shear strength E.Y.M. Tse & C.W.W. Ng Department of Civil Engineering, Hong Kong University of Science and Technology, Hong Kong SAR
ABSTRACT: In humid and subtropical regions, for instance, Hong Kong, slope stability is threatened by intense rainfall. Alternate rainfall infiltration and subsequent evaporation cause soil to be constantly subjected to drying and wetting cycles. Hysteresis observed in the soil water characteristics curve seems to imply hysteresis in unsaturated shear strength. Some attempts have been made in recent years to investigate changes of unsaturated shear strength only within the primary drying and wetting cycles but not beyond. Also, the suction history effects on shear strength are still unclear. In this study, re-compacted soil specimens of completely decomposed tuff are tested in a modified direct shear box, subjected to different suction histories but sheared at identical net normal stress as well as matric suction. 1
INTRODUCTION
The predominant failure mode of slide-debris flows that have occurred in Lantau Island, Hong Kong is a translational one which is usually located at a depth of 0.5–2 m (Fuchu et al., 1999) and well above the ground water table. The unsaturated soil within the vadose zone is naturally subjected to various suction histories caused by alternate rainfall precipitation and subsequent evaporation due to climatic changes. The shear strength variations of soil induced by the corresponding suction histories determine the slope stability. Some studies in the literature have demonstrated different shear strengths attained by soil specimens reaching the same net normal stress and matric suction via drying and wetting paths. Han et al. (1995) suggested higher shear strength of the soil on the drying path in comparison with that at wetting due to its higher water content. On the contrary, Gallage & Uchimura (2006) presented counter findings (higher shear strength on the wetting path) and explained this was attributed to the more contractive behavior exhibited by the specimen at wetting than that at drying. Further investigation is thus required to manifest how drying and wetting cycles actually influence unsaturated shear strength parameters and thereafter provide consistent explanations. According to Vanapalli et al. (1996), the shear strength of an unsaturated soil at a given value of suction can be given by: θ − θr τ = c + (σn − ua ) tan φ + (ua − uw ) tan φ θs − θr
(1)
where τ is the shear strength of an unsaturated soil; c is the effective cohesion of saturated soil; φ is the effective angle of shearing resistance for a saturated
soil; (σn − ua ) is the net normal stress; (ua − uw ) is the matric suction; θ is the volumetric water content; θr is the residual volumetric water content; and θs is the saturated volumetric water content. This prediction was based on the drying path of the primary drying-wetting cycle in soil water characteristics curves (SWCC), suggesting the dependency of shear strength on volumetric water content. Ng & Pang (2000) presented the hysteretic influences of drying and wetting cycles on SWCC of a completely decomposed volcanic, including the corresponding changes in volumetric water content, air-entry value, adsorption and desorption characteristics. The hydraulic hysteresis demonstrated by the soil in response to drying-wetting cycles seemingly signifies that according change would be induced in shear strength. Hence, two series of direct shear tests were designed to be sheared at identical net normal stress of 40 kPa but different matric suction values, 20 kPa and 400 kPa. The first two tests of series 1 and the two tests of series 2 were used to study how shear strengths deviate when attaining the desired suction along drying and wetting paths in the primary drying-wetting cycle. However, in test series 1 of this study, the direct shear tests were repeated for one more wetting-drying cycle beyond the primary one to investigate the hysteretic effects imposed by drying-wetting cycles on unsaturated shear strength.
2
EXPERIMENTAL PROGRAM
The soil investigated in this study is a completely decomposed tuff (CDT) from Tung Chung, Hong Kong. The detailed stress paths to which the specimens
481
were subjected prior to shearing are depicted in Figure 1 and Table 1. The specimen identity, Xi_Y denotes that the CDT specimen subjected to X (D = drying; W = wetting) in the ith wetting drying cycle was sheared at matric suction of Y kPa and net normal stress of 40 kPa. Taking D1_20 as an example, the specimen was subjected to drying path in the first wetting-drying cycle before being sheared at matric suction of 20 kPa and net normal stress of 40 kPa. Testing equipment
Matric Suction (kPa)
The direct shear tests were carried out in the modified direct shear box (Gan (1986), Gan et al. (1988), Zhan (2003)) as shown in Figure 2. Modifications to the conventional apparatus enable matric suction control as well as change of unsaturated soil specimen water content measurement. The two stress state variables, i.e. net normal stress and matric suction can be controlled independently. The net normal stress is applied by applying the required vertical weight onto the loading frame. Suction is applied to a soil specimen based on the axis-translation technique (Hilf, 1956) by maintaining a constant air and water pressure in the air chamber and the water compartment below the ceramic disk of 5 bar air entry value. The testing system consists of two LVDTs, a load cell, a differential pressure transducer and a diffused air volume indicator for horizontal as well as vertical F E
400
D
0.001
0.010
0.100
1.000
10.000
Particle size (mm)
Figure 3.
Particle size distribution of CDT.
2.2 Testing material and specimen preparation
100
A
C
0 0
Figure 1. Table 1.
10
B
20 30 40 Net Normal Stress (kPa)
50
Stress paths adopted in the tests. Test program.
Series Specimen identity Stress path 1 1 1 1 2 2
100 90 80 70 60 50 40 30 20 10 0
displacements, shear force, change of water content and diffused air volume monitoring respectively. All the electrical instruments are connected to a data logger for data acquisition. Zhan (2003) provides further details of the modified shear box.
300 200
Figure 2. Modified direct shear box at the Hong Kong University of Science and Technology.
Percentage passing (%)
2.1
D1_20 W1_20 D2_20 W2_20 D1_400 W1_400
A→B→C A→B→D→C A→B→D→B→C A→B→D→B→D→C A→B→E A→B→F→E
According to Unified Soil Classification System, the testing soil is classified as an inorganic silty clay of low to medium plasticity (CL). The grain-size distribution determined by sieve and hydrometer analyses (British Standards Institution, 1990) as shown in Figure 3 exhibits that the CDT consists of 25% sand, 60% silt and 15% clay. Some index properties of the soil are summarized in Table 2. Soil specimens for direct shear tests were cuboids with dimensions of 50 mm × 50 mm × 21 mm prepared by static compaction at gravimetric water content of 17.3%. The static compaction was conducted in three layers to achieve a uniform specimen with dry density, specific volume and degree of saturation of 1600 kg/m3 , 1.68 and 69% respectively. As measured by a small tip tensiometer, the initial suction of the compacted specimen was 54 kPa.
482
Table 2.
Specific gravity Maximum dry density (kg/m3 ) Optimum moisture content (%) Initial moisture content (%) Sand content (≤2 mm, %) Silt content (≤63 μm, %) Clay content (≤2 μm, %) Liquid limit (%) Plastic limit (%) Plasticity index (%)
2.3
Table 3. Summary of θw , e and S values prior to and post shearing for the six specimens.
Index properties of the CDT. 2.68 1777 17.2 17.3 25.0 60.0 15.0 34.2 20.2 14.0
Before shearing
Testing procedures
Each test was composed of three stages, namely consolidation, drying-wetting cycles and drained shearing at constant suction. Water pressure beneath the high air entry ceramic disk was maintained at atmospheric pressure throughout the tests, i.e. matric suction numerically equals applied air pressure in the chamber. After specimen preparation and setting up, the vertical stress of 40 kPa was applied progressively until flow of water into the specimen as well as vertical deformation ceased. Thereafter, the specimen was subjected to the desired suction history as listed in Table 1. Each suction equalization stage was considered to be completed when negligible specimen water volume change (<0.05 cm3 /day) was observed. Having reached the desired matric suction and net vertical stress as well as having experienced a predefined suction history, the soil specimen was sheared at a constant displacement rate of 0.003 mm/min till 10 mm horizontal displacement was achieved. During the drained shearing, variations of specimen water volume, shear force, horizontal as well as vertical displacements were recorded. Upon completion of shearing and after dismantling the set-up, water content of the specimen was then determined.
3
EXPERIEMENTAL RESULTS – SHEAR BEHAVIOR OF CDT
As summarized in Table 1, six direct shear tests were conducted on CDT specimens after undergoing six different suction histories. The volumetric water content (θw ), void ratio (e) and degree of saturation (S) prior to and post shearing of the specimens are listed in Table 3. Figure 4(a) shows the shear stress variations with horizontal displacement. As illustrated, shear strength and stiffness increase with suction. Peak shear strengths are observed with strain softening followed by leveling off around 4 mm and 2 mm respectively in the case of the two specimens sheared at suction of 400 kPa, i.e. D1_400 and W1_400. The former specimen which achieved suction of 400 kPa on the drying
After shearing
ID
θw (%) e
S
θw (%) e
S
D1_20 W1_20 D2_20 W2_20 D1_400 W1_400
31.0 27.8 28.3 28.1 25.2 23.9
0.794 0.700 0.713 0.708 0.639 0.615
31.8 29.6 29.8 29.8 22.8 21.0
0.781 0.735 0.736 0.734 0.542 0.486
0.663 0.657 0.657 0.657 0.649 0.634
0.669 0.673 0.680 0.683 0.725 0.757
path possesses a greater peak shear strength than the latter which attained the same suction along the wetting path, with respective magnitudes of 139 kPa and 109 kPa. On the contrary, shear stresses of the four specimens sheared at low suction, 20 kPa, increase monotonically with horizontal displacement and reach an ultimate value of approximately 30 kPa as illustrated in Figure 4(b). At low suction (20 kPa), though the discrepancies between the maximum shear strengths of the soil specimens are relatively insignificant, two trends are noted: 1. shear stress at drying is greater than that of the one at wetting within the same drying-wetting cycle; 2. shear stress given by specimen at drying in the primary drying-wetting cycle is greater than one in the second drying-wetting cycle. Whereas, a reverse trend is observed in specimens at wetting. The first observation is more drastic as indicated by the higher suction cases (D1_400, W1_400). This signifies the dependency of shear strength on suction history and suction level. Notwithstanding the similar shear stress variation with horizontal displacement, D1_20, W1_20, D2_20 and W2_20 dilate with increasing magnitudes as shown in Figure 4(c). Dilatancy δy/δx, is defined as the ratio of incremental vertical displacement, δy, to incremental horizontal displacement, δx. Negative sign denotes dilative behavior. Within the same drying-wetting cycle, the dilatancy curve given by a specimen at drying is always above that of the one at wetting, indicating less dilative behavior. Additionally, the optimum dilatancy increases with suction, i.e. more negative dilatancy. This is consistent with the results reported by Gan & Fredlund (1996), Ng & Zhou (2005) and Zhan & Ng (2006). Figure 4(d) illustrates the responses of volumetric water content to shearing. The increase in volumetric water content (θw ) observed in the four soil specimens sheared at low suction (20 kPa) is as a result of their dilative behavior. As a specimen dilates, the void ratio increases and so do the dimensions of voids
483
40
150
(b)
120
Shear stress (k Pa)
Shear stress (k Pa)
(a)
90 D1_20 W1_20 D2_20
60
W2_20 D1_400 W1_400
30
20 D1_20 W1_20 D2_20 W2_20
10
0
0 1
2 3 4 5 6 7 8 Horizontal displacement (mm)
9
0
10
Change of volumetric water content (%)
0
0.1 0.0 Dilatancy, y/ x
30
-0.1 D1_20 W1_20 D2_20 W2_20 D1_400 W1_400
-0.2 -0.3 -0.4
(c)
-0.5 0
1
2 3 4 5 6 7 8 Horizontal displacement (mm)
9
10
1
2
3 4 5 6 7 8 9 Horizontal displacement (mm)
10
2 1 0 D1_20 W1_20 D2_20
-1
W2_20 D1_400 W1_400
-2
(d) -3 0
1
2 3 4 5 6 7 8 Horizontal displacement (mm)
9
10
Figure 4. Results of direct shear tests on unsaturated re-compacted CDT specimens: (a) shear stress versus horizontal displacement of Series 1 & 2; (b) shear stress versus horizontal displacement of Series 1; (c) dilatancy versus horizontal displacement; (d) change in volumetric water content (θw ) versus horizontal displacement.
as well as the connecting channels among voids. Consequently, a higher value of volumetric water content is required to produce a given suction. D1_400 and W1_400 demonstrate greater dilatancies in comparison to the specimens in the first series of testing and thus a greater extent of increase in volumetric water content is expected. However, a counter response is given, i.e. the volumetric water contents of the two specimens sheared at high suction decreases progressively with horizontal displacement. At such a high suction, water exists mostly in the form of meniscus water at inter-particle contact points. As the soil specimen dilates at 400 kPa, the coordination number decreases, resulting in loss of meniscus water at the inter-particle contact points and hence reduction in volumetric water content.
4 4.1
DISCUSSION Effects of suction history on shear strength within the primary drying-wetting cycle
In the literature, studies like Han et al. (1995) and Gallage & Uchimura (2006) reported different stressstrain behavior exhibited by soil subjected to drying and wetting. From the experimental results obtained from D1_400 and W1_400, peak shear strength given
by the former is higher than the latter by 28%. This is consistent with Han et al. (1995) but contrary to Gallage & Uchimura (2006). The higher shear strength given by the specimen at drying in comparison to the one at wetting is attributed to the higher degree of saturation (Sr) prior to, during and after shearing as shown in Table 3 and Figure 4(d). There are two forms of liquid water in an unsaturated soil, namely the bulk and meniscus water. Bulk water provides tangential and normal forces at inter-particle contacts while meniscus water imposes stabilizing influence through normal inter-particle forces. According to Wheeler et al. (2003), inter-particular forces imposed by suction within bulk water is dependent on both suction value and degree of saturation. The additional interparticle normal force due to meniscus water can be assumed to be constant whenever a meniscus water lens exits. The overall stability of the soil skeleton is controlled by the number of inter-particle contacts influenced by the meniscus water lens. At a high suction of 400 kPa, in which plastic changes of Sr in response to emptying of voids with water occurred, the water phase is discontinuous and the water phase exists mostly in the form of meniscus lenses. Thus, the higher the Sr, the more is the number of contacts affected by meniscus water and thus normal forces stabilizing the soil particles. As a result, shear strength of D1_400 is greater than that of W1_400.
484
φ = φ crit + 0.8ψ
(2)
Also, according to Zhan and Ng (2006), τf = c +(σ−ua ) tan(φ + ψ)+(ua −uw )f tan φb
(3)
where σ is the total normal stress, ua is the pore-air pressure, uw is the pore-water pressure, ψ is the dilation angle, φb represents the effect of capillary force on frictional resistance, c is the true cohesion, and φ is the internal frictional angle. These suggested that the greater the dilatancy, the higher is the shear strength. Thus, it is expected that W2_400 should have higher shear strength when comparing to D1_400. However, obviously, the effect of the lower S outweighs the contribution of shear strength from the more dilative behavior in the case of W1_400. For the low suction cases, i.e. D1_20 and W1_20, the difference in shear strength magnitude is relatively less significant but the same trend (shear strength at drying is greater than that at wetting) is observed. W1_20 exhibits a more dilative behavior than D1_20 does due to lower pre-shearing void ratio associated with W1_20. Considering D1_20, the lesser extent of stabilizing power arisen from dilatancy is counterbalanced by that contributed by its greater Sr for the CDT specimen at drying sheared at suction of 20 kPa in the primary drying-wetting cycle, resulting in a net decrease in shear strength caused by drying-wetting cycle. Actually, shear strength achieved by a specimen at a given suction is always affected simultaneously by the two factors, degree of saturation and dilatancy. It is hence proposed that: τ = c + (σn − ua ) tan(φ + ψ) θ − θr + (ua − uw ) tan φ θs − θr
(4)
As discussed above, the influences induced by the two factors generally occurs in a counteracting manner. For a given specimen on the drying path, higher initial degree of saturation is associated with a less dilative behavior while the contrary case occurs in specimen on the wetting path. At the two suction values studied
in this study, the contribution to increment in shear strength by Sr outweighs that of dilatancy at a given suction and grows progressively with suction. Han et al. (1995) demonstrated (Figure 5) that soil specimens at drying attained higher peak shear strength than those at wetting did over the suction range beyond 60 kPa. And, below 60 kPa suction, a counter case with a discernible discrepancy associated exists. Thus, it may be probable that there is a watershed (I) beyond which shear strength of a specimen at wetting is lower than that at drying as a result of Sr decrement induced by the drying-wetting cycle. And, the counter case occurs below the suction at the watershed. This suction value may be dependent on the soil properties, like soil grain size distribution and soil-water characteristic curve. Referring to Table 4, it is hypothesized that the higher the proportion of fine grains, the higher is the suction at which curves of shear strength versus matric suction at drying and wetting intersect (intersections I1 and I2 in Figure 5). However, intersection I1 is deduced from the limited experimental results in this study. Further investigation and extra experiments are required to confirm this preliminary hypothesis. 4.2 Cyclic drying-wetting effects on shear strength At a suction of 20 kPa, the shear stresses given by the four specimens subjected to different drying-wetting 800 Peak Shear Strength (kPa)
Meanwhile, a more pronounced dilative behavior is associated with W1_400 as shown in Figure 4(c) due to the smaller void ratio caused by drying and subsequent wetting. In saturated soil mechanics, the peak friction angle can be considered as the sum of interparticle friction, rearrangement, crushing, and then the dilation contribution. Bolton (1986) proposed the flowing empirical equation that relates the mobilized friction angle φ at a given stress state to the critical state friction angle φ crit and dilation angle ψ:
Drying - this study Drying - Han et al. (1995) Wetting - this study Wetting - Han et al. (1995)
700 600 500
I2
400 300 200 I1 100 0 0
100
200 300 Matric suction (kPa)
400
Figure 5. Peak shear strength versus matric suction for the primary drying-wetting cycle.
Table 4. Summary of particle size distribution and suction (I) at which the curves of shear strength versus matric suction given by specimens at drying and wetting intersect.
Sand content Silt content Clay content Position of I
485
This study
Han et al. (1995)
25% 60% 15% 20 kPa
49% 25% 26% 60 kPa
histories attain nearly the same maximum (around 30 kPa) but at different increasing rates. The shear stress-displacement curve given by D1_20 is the highest among the four in test Series 1 with D2_20, W2_20 and then W1_20 lying below. This order of variation is in consistent with that of volumetric water content prior to shearing. In this case, dilatancy no longer diverts the trend in shear stress variation. 5
CONCLUSIONS
Two series of direct shear tests were conducted on CDT specimens subjected to six different suction histories to investigate the influences of drying-wetting cycles on unsaturated shear strength and corresponding volumetric behavior. The following conclusions can be drawn: i. strain softening is observed for soil specimens sheared at suction of 400 kPa while shear stresses monotonically increase with horizontal displacement for specimens sheared at low suction of 20 kPa regardless of the suction history; ii. within the primary drying-wetting cycle, peak shear strength attained by specimen at drying is higher than that at wetting for both of the high and low suction cases though the discrepancy in shear strength magnitudes is relatively less noticeable in the latter case; iii. dilatancy is more pronounced in the wetting path and in the second drying-wetting cycle which is attributed to the lower void ratio induced by drying-wetting cycles; iv. shear stress given by specimen at drying in the primary drying-wetting cycle is greater than that in the second drying-wetting cycle. However, a reverse trend is observed in specimens at wetting; v. both degree of saturation, Sr and dilatancy contributes to shear strength increment (see equation (4)). In this study, the increment of shear strength contributed by Sr outweighs that of dilatancy. ACKNOWLEGDEMENTS The authors express their gratitude towards the research grants offered by HKUST (CA-MG07/08. EG01) as well as Ove Arup and Partners Hong Kong Limited., Dr. Jack Pappin in particular. REFERENCES Alshihabi, O., Shahrour, I. & Mieussens, C. 2002. Experimental study of the influence of drying-wetting cycles on the resistance of a compacted soil. Proceedings of the
third international conference on unsaturated soils, Vol. 2, 491–494, Recife, Bazil. Bolton, M.D. 1986. The strength and dilatancy of sand. Geotechnique 36, No. 1, 65–78. BSI. 1990. BS1377: Methods of test for soils for civil engineering purposes. British Standards Institution. Fredlund, D.G. & Rahardjo, H. 1993. Soil mechanics for unsaturated soils. John Wiley & Sons, Inc., New York. pp. 227. Fuchu , D., Lee, C.F. & Wang, S. 1999. Analysis of rainstorm-induced slide-debris flows on natural terrain of Lautau Island, Hong Kong. Engineering Geology. 50: 279–290. Gallage, C.P.K. & Uchimura, T. 2006. Effects of wetting and drying on the unsaturated shear strength of a silty sand under low suction. Proc. of the 4th Int. Conf. on Unsaturated Soils. Vol. 1. Carefree, Arizona, USA. 1247–1258. Gan, J.K.M. 1986. Direct shear strength testing of unsaturated soils. M.Sc. Thesis; University of Sakatchewan, Saskatoon. Gan, J.K.M., Fredlund, D.G. & Rahardjo, H. 1988. Determintaion of shear strength parameters of an unsaturated soil using direct shear test. Can. Geotech. J., 25, No. 3, 500–510. Gan, J.K.M. & Fredlund, D.G. 1996. Shear strength characteristics of two saprolitic soils. Can. Geotech. J., Vol. 33, pp. 595–609. Han, K.K., Rahardjo, H. & Broms, B.B. 1995. Effects of hysteresis on the shear strength of a residual soil. E.E. Alonso & P. Delage (Eds), Unsaturated soils, 2, 499–504. Hilf, J.W. 1956. An investigation of pore water pressure in compacted cohesive soils. Technical Memo 654, Bureau of Reclamation, Denver. Huang, S.Y., Fredlund, D.G. & Barbour, S.L. 1995. Measurements of the coefficient of permeability of an unsaturated soil. E.E. Alonso & P. Delage (Eds), Unsaturated soils, 2, 505–511. Ng, C.W.W., & Pang, Y.W. 2000. Experimental investigations of the soil-water characteristics of a volcanic soil. Can. Geotech. J. 37: 1252–1264. Ng, C.W.W. & Zhou, R.Z.B. (2005) Effects of soil suction on dilatancy of an unsaturated soil. Proce. Of the 16th ICSMGE, 12–16 Sept. Osaka, Japna. Vol. 2, 559–562. Vanapalli, S.K., Fredlund, D.G., Pufahl, D.E., Clifton, A.W. 1996. Model for the prediction of shear strength with respect to sil suction. Can. Geotech. J. 33: 379–392. Wheeler, S.J., Sharma, R.J. & Buisson, M.S.R. 2003. Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils. Geotechnique 53., No. 1, 41–54. Zhan, L.T. 2003. Field and laboratory study of an unsaturated expansive soil associated with rain-induced slope stability. PhD Thesis. The Hong Kong University of Science and Technology, HKSAR. Zhan, L.T. & Ng, W.W. 2006. Shear strength characteristics of an unsaturated expansive clay. Can. Geotech. J. 43: 751–763.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Degradation of compacted marls due to suction changes R. Cardoso Instituto Superior Técnico, Lisbon, Portugal
E.E. Alonso Universitat Poltècnica de Catalunya, Barcelona, Spain
ABSTRACT: Marls are classified as hard-soils/ soft rocks and require special attention when used as construction materials since their mechanical and hydraulic properties change due to alternate wetting-drying cycles as well as to other weathering processes. This evolution of behaviour is characterized by crack opening and/or loss of bonding, having in general negative impact on the strength and compressibility of the material. Embankments made with marls and other soft clayey rocks result in an agglomerated structure of rock fragments. The grading of these materials evolves resulting in relevant modifications of the overall behaviour of the aggregate. Settlements and loss of strength are the main concerns in practice and require suitable constitutive and computational models to predict these phenomena. This paper presents a study where the evolution of Jurassic marls (Arruda dos Vinhos, Portugal) is simulated considering concepts of unsaturated soil mechanics. The mechanisms leading to the breakage and eventually the destructuration of rock particles are investigated. Numerical simulations of the behaviour of individual rock fragments under wetting were performed and the contribution of initial suction has been analysed. The results obtained provide an insight into the nature of degradation induced by wetting. They also help to explain the overall mechanical behaviour of aggregates (compacted material) observed in suction controlled oedometric tests presented in this paper.
1
INTRODUCTION
Marls are classified as hard-soils/soft rocks and exhibit evolution of behaviour mainly associated to crack opening and/or loss of bonding. These processes usually have negative impact on strength and compressibility. This paper examines the physical phenomena controlling the evolution of behaviour of hard-soils/soft rocks when compacted and used for embankment construction. Embankments made with marl and other soft clayey rocks result in an agglomerated structure of finite size particles (just as in a rockfill). However, these particles evolve and result in major changes of the overall behaviour of the aggregate. Common compaction practices do not avoid the consequences of the evolutive behaviour of the aggregates, since the fragment left after compaction still allows the development of settlements and the loss of strength with time. There is an increasing number of studies on the evolution of the mechanical behaviour of hard soils/soft rocks (shales, mudstones, claystones, calcarenites and weak limestones) (Leroueil and Vaughan, 1990, Gens
and Nova, 1993, Vaughan, 1997, Rouania and Muir Wood, 1998, Vaunat and Gens, 2003, Pinyol et al., 2007, among others). However, very few studies are known to exist concerning the behaviour of aggregates. The study of the evolutive behaviour of individual rock fragments can be used to understand the behaviour of aggregates of marl particles (compacted material). Wetting and drying cycles controlled by atmospheric changes, which result in strong changes in suction, are probably one of the main reasons for rock degradation. For this reason it was considered appropriate to introduce concepts associated with the mechanics of unsaturated soils to investigate the causes of degradation, mainly associated with particle breakage and disintegration. Mechanisms leading to the breakage and eventually to the destructuration of single rock fragments are analysed. In particular, wetting effects will be analysed in some detail. The results of the study presented for one single fragment of rock will help to describe the behaviour of aggregates of particles (compacted material) observed in suction controlled oedometric tests.
487
2
DEGRADATION MECHANISMS
The photographs of marl fragments before and after a wetting cycle, presented in Figure 1, show the degradation phenomena of an unconfined set of particles with uniform size (particle dimensions varying between 9 mm and 4.75 mm) subjected to one wetting-drying cycle in a laboratory environment (T = 20◦ C ± 5◦ C and RH = 45% ± 10%). The water content before wetting was 9% (it corresponds to a suction of 10 MPa, according to the water retention curve of the material). Similar behaviour was observed for materials with different initial water contents. The observed degradation was higher for drier fragments. A possible explanation of the degradation mechanisms of marl fragments is schematically presented in Figure 2. During wetting the particle boundary is first wetted and a suction gradient is created inside the rock fragment. This suction gradient induces water transfer and reduces in time until it reaches a zero value when full saturation is reached. As long as there are suction gradients, differential swelling deformations will be developed inside the rock fragment. The geometry and confinement of the fragment restrain swelling displacements and leads to tensile and shear stresses which eventually result in cracking and destructuration. This degradation mechanism will be controlled by suction gradients. In fact, it was
observed (Fig. 1) that the drier the fragments initially subjected to wetting, the more significant the degradation observed. It was decided to explore the nature of these phenomena through numerical simulations of the behaviour of individual rock fragments subjected to suction cycles. They can also be useful at a larger scale, when the mechanical behaviour of aggregates of particles is investigated
3
NUMERICAL MODEL AND TESTS PERFORMED FOR ITS CALIBRATION
The material under investigation comes from Abadia Formation (Upper Jurassic, Arruda dos Vinhos, Portugal). Mineralogy analysis showed the presence of chlorite and gypsum, besides quartz, CaCl2 and mica. Its basic identification properties are presented in Table 1. A coupled hydro-mechanical computational model (CODE_BRIGHT, Olivella et al. 1996) was used adopting the Barcelona Basic Model, BBM (Alonso et al., 1990), as the constitutive mechanical model. The code solves the balance of water in liquid and gas phases, adopting Darcy’s law and Fick’s law for the calculation of the flux of water inside the material. The intrinsic permeability was calculated by Kozeny’s model and for the definition of the water retention curve (WRC, in Fig. 3), Eq. (1) was used
Table 1.
Identification properties of Abadia marl.
Porosity
win situ
LL
PI
Solid unit weight, γs
37%
17%
47%
25%
27.4 kN/m3
Figure 1. Particle breakage and destructuration observed in uniform-size particles (9 mm ≥ D > 4.75 mm) during a wetting-drying cycle. 1000.00
Total suction (MPa)
differential deformation due to swelling (proportional to the differential of suction)
Wet zone (sinitial<s<0) Dry zone (suction=sinitial)
sinitial s=0 MPa
Drying _ Block Wetting _ Block WRC-Drying WRC-Wetting
100.00
10.00
1.00
(saturated in the border)
0.10 2 Tension development (cracking)
Figure 2.
Degradation mechanisms inside a rock fragment.
4
6
8
10
12
14
16
water content, w (%)
Figure 3.
488
Water retention curves of Abadia marl.
18
(Van Genuchten, 1980),
Se = 1 +
P g − Pl P
λ −λ 1−λ
(1)
where Se is the degree of saturation at the current liquid pressure, Pl . Pg is the gas pressure (assumed to be the atmospheric pressure, 0.1 MPa), P is the pressure associated with the air entry value and λ is a fitting parameter. Several experimental tests on marl samples were performed to calibrate the numerical model, namely: (i) swelling tests in oedometric conditions of rock samples under different vertical stresses and with different initial suctions, (ii) Brazilian splitting tests and unconfined compression tests in marl samples under different suctions and (iii) suction controlled compression tests on marl samples in oedometric cells. The intrinsic permeability coefficient of the marl was also measured. Table 2 presents representative mechanical and hydraulic parameters adopted in the model. 4
ANALYSIS OF WETTING
Numerical simulations of individual fragments of rock subjected to suction cycles were performed. Wetting Table 2.
was assumed to start in a uniform manner at the particle boundary. Boundary suction was reduced from the initial value to saturated conditions (s = 0) in 15 minutes. For simplification, a circular geometry (9 mm diameter) was adopted under plane strain conditions. Degradation mechanisms were investigated for the confinement conditions presented in Figure 4. Since particles in the granular structure are confined by the neighbouring rock fragments, in a complex and heterogeneous manner, more confinement cases were analysed. Cardoso and Alonso (2008) present a more detailed analysis and describe the effect of other cases analysed. Since fracture is not incorporated in the numerical model adopted, degradation will be identified by the pattern of tensile stresses developed in the fragment and by the pattern of plastic deviatoric deformation, δεsP , and of plastic volumetric deformation, δεvP . The constitutive model is defined in terms of net mean stress, calculated through p = p − max{patm ; pl }
where p is total mean stress, patm is the atmospheric pressure and pl is the liquid pressure. Plastic deformations and tensile stresses developed during wetting are presented in Figures 5a, b.
Constitutive parameters for Abadia marl. Value
Constitutive model Parameter Description BBM
λ(0) λ(S) r β κ κs p∗o pc M K c0 ν
WRC
(2)
Pg
Fragment
Stiffness parameter for changes in net mean stress for virgin states in saturated conditions Stiffness parameter for changes in net mean stress for virgin states Parameter defining maximum stiffness Parameter controlling the rate of stiffness increase with suction Elastic stiffness parameter for changes in net mean stress Elastic stiffness parameter for changes in suction Pre-consolidation stress for saturated conditions Reference stress Slope of the critical state lines Parameter describing the increase in cohesion with suction Tensile stress resistance for saturated conditions Poisson coefficient
Backfill III
0.027
0.104
λ(S) = λ(0) (1 − r)e−βs + r 0.65 0.05 MPa−1
0.20 0.05 MPa−1
0.007 0.020 1.0 MPa 0.27 MPa 1.0 0.007 0.4M Pa 0.25
0.007 0.0002 0.5 MPa 0.05 MPa 1.0 0.007 0.004 MPa 0.25
0.1 MPa
0.1 MPa 1 MPa
0.20 8 × 10−18 m2
P
Gas pressure (assumed to be equal to the atmospheric pressure) Pressure corresponding to the air entry value
λ
Fitting parameter
0.3 MPa (drying branch) 0.9 MPa (wetting branch) 0.20 (both branches)
Intrinsic permeability
8 × 10−21
Permeability k
489
m2
E C B A
C Compression Tensile stress
max. principal stress (kPa)
150
D
AE
100 50
B D
E D BD
0 AE –50 0.00 0.25 Not saturated
Figure 4. Confinement case considered and finite element discretization of one particle.
C
0.50
0.75
B A
C 1.00
Fully Saturated
time (hours)
Figure 6. Time evolution inside the fragment of the maximum principal stress, σI .
deformations, plotted also in Figure 5 show concentrated shear damage in the outer border of the particle. Stresses σI developed during wetting inside the fragment (points B, C and D, see Figure 4) are presented in Figure 6. The evolution of tensile stresses follows the explanation given before and helps to understand the development of cracking. However a complete analysis must also consider shear stress. The stress path in space (p, q, s) is presented in Figure 7 for the centre point C. It is a complex stress path, represented also in three auxiliary two-dimensional stress spaces for a better comprehension. The shear stress reaches a peak when the suction s = 200 kPa, in the proximity of full saturation. Critical state conditions are closely approached at the end of the simulation performed.
5
Figure 5.
Damage pattern identification.
Swelling progresses from the boundary towards the centre. Vectors corresponding to the maximum principal stress in the fragment for two time instants (Figure 5) allow understanding the cracking pattern due to tensile stress. Tensile stresses develop internally while a boundary annulus increases volume and detaches from the core of the particle. This mechanism leads to cracking interpreted as peripheral detachment. This is the case for instant 15 minutes after wetting (Figure 5a). When the water reaches the inner core it starts swelling, pushing out the outer layers. This mechanism corresponds to radial cracking (Figure 5b, 5 hours after wetting). The corresponding plastic shear
COMPACTED SAMPLES
Suction controlled tests on compacted aggregates of marl were performed in oedometer cells. All the samples tested were compacted in similar conditions, adopting uniform size of particles (9 mm ≥ D > 4.75 mm) in order to speed up the suction imposition by vapour equilibrium. The protocol followed for these tests included drying under a small vertical load (σv = 50 kPa) followed by a suction increase applied by standard salt solutions, loading and finally saturation at σv = 600 kPa. The results of these tests are presented in Figure 8 and Table 3. Tests results show that the virgin compressibility, Cc, of the compacted marl decreases with increasing suction (values shown in Table 3). A similar behaviour is exhibited by rockfills and can be explained by a crack propagation phenomenon, with cracking speed increasing with water content, as if water would act as a corrosive agent (Oldecop and Alonso, 2003).
490
q (kPa) 2500
deviatoric stress, q (kPa)
2000 1500 1000 yielding point
500 0 10
5
10
0
10
s (kPa)
-5
-1000
0
2000
1000
3000
4000
1000 900 800 700 600 500 400 300 200 100 0 10000
Yielding point
1000
100
10
1
0
suction, s (kPa)
p (kPa) 1800
10000
MCC curve (s=10MPa )
deviatoric stress, q (kPa)
suction, s (kPa)
1000 Yielding point
100 10 Tensile yield locus
1
LC (q=0 )
0
1200 Yielding point
600
0
net mean stress, p (kPa)
net mean stress, p (kPa)
Stress path for point C (in the centre of the fragment) in space (p, q, s) (sinitial = 10 MPa).
1.1
Table 3. Results of suction controlled oedometer tests of marl aggregates (e = 1.078 ± 0.005, w = 15% ± 2%).
1.0 0.9
Void ratio, e
MCC saturated curve
-60006001200
-60006001200
Figure 7.
CSL saturated
drying v=50kPa
0.8 0.7
s=230MPa
0.6
s=38MPa
full saturation v=600kPa
s=12MPa
0.5
s=3MPa
0.4
Saturated test
0.3 1
10
100
1000
Compres. index, Cc
Volume decrease due to drying (1)
Collapse due to full wetting (2)
230 38 12 3 Saturated
0.095 0.379 0.394 0.536 0.141
3.9 % 3.4 % 1.3 % – –
20.4 % 15.7 % 13.9 % 9.7 % –
10000
(1) initial suction s = 3 MPa, vertical stress, σv = 50 kPa. (2) after saturation (final s = 0 MPa), σv = 600 kPa.
vertical stress (kPa)
Figure 8. marls.
Initial suction (MPa)
Suction controlled oedometer tests of compacted
Test results also show that marl aggregates and rockfill have similar behaviour on the high suction range (deformation is mainly explained by particle breakage). However, as the suction decreases, the observed response becomes similar to a clayey soil. In fact,
the compressibility of the saturated marl aggregates (Cc = 0.141) is similar to the compressibility of a reconstituted sample prepared with a water content w = 1.35LL (Burland, 1990). This result indicates that wetting leads not only to particle breakage but also to strong destructuration. This is consistent with visual
491
SIMULATION OF OEDOMETRIC TESTS ON AGGREGATES OF FRAGMENTS
LC (Backfill III) 10
A
D
B
0
Backfill
0
500
C 1000
1500
2000
2500
p (kPa)
Figure 9. Numberical model for the marl aggregate, loading path followed and LC curves for the fragments and Backfill III.
Table 4.
The degradation mechanism analyzed does not explain the transition from rockfill behaviour (dry samples) to a clayey soil (fully saturated samples). Besides cracking phenomena, the global porosity changes due to wetting in a fully degraded material must also be taken into account to simulate this transition. The combined behaviour of aggregates of fragments was investigated against stress and suction paths (Fig. 9) which included full saturation for a given stress level: (i) path ABC—full saturation under vertical stress, followed by loading; and (ii) path ADC— loading under a constant initial suction, followed by full wetting at high vertical stress. The purpose of this model was to analyse the effect, in the global behaviour, of the degradation of the fragments when wetted. CODE_BRIGHT was also used. The numerical model, shown in Figure 9, includes circular fragments (diameters of 9 mm, 7 mm and 5 mm) and a backfill material. The fragments were arranged to obtain an initial void ratio of 1.082, similar to the one adopted for the oedometer tests previously presented. Material parameters are given in Table 2. The virgin saturated compressibility of the backfill (which represents de-structured fragments) was similar to the experimental value derived from the oedometer test on the saturated aggregate (Fig. 8). Several sensitivity tests of the backfill properties were performed so the collapse of this material when fully saturated would partially compensate the swelling contribution of the individual fragments. Three different cases were analyzed by Cardoso and Alonso, 2008 (Backfill I, II and III) through three different LC curves. This paper presents the results for only one case (Backfill III). As presented in Table 4 and Figure 10, swelling was calculated for wetting under low vertical stress (path AB). Collapse was found for wetting under high vertical stress (path AD). The driest sample shows the lowest overall compressibility (lower compressibility index, Cc ), which agrees, in a qualitative manner, with the experimental results from Table 3.
Stiff frame LC (Marl)
Results of the numerical model (Backfill III).
Path followed
Compressibility. Deformation index, Cc due to wetting
ABC (s = 0 MPa) ADC (s = 10 MPa)
0.088 0.057
1.06% (swelling) –0.58% (collapse)
1.10 B swelling due to wetting
1.09 void ratio, e
6
Fragments
s (MPa)
observations during the wetting-drying cycle of marl fragments (Fig. 2). The experimental results on compacted samples can be analysed considering the behaviour of the single fragments of marl: (i) global volume decrease caused by drying (higher for higher suctions applied) is due to volume decrease of each particle when dried; (ii) collapse with full saturation is explained by particle breakage and rearrangement of the broken fragments.
1.08
A
1.07
ADC (III) ABC (III)
D C C
collapse due to wetting
1.06 100
Figure 10.
1000 vertical stress (kPa)
10000
Numerical results for Backfill III.
Figure 10 presents the evolution of the void ratio in the fragments and in the backfill for loading paths ABC and ADC. Contrary to the predictions of a pure BBM model, the mixture III experiences different reduction in void ratio when comparing path ADC (first loading and then wetting), with path ABC. The initial void ratios adopted for the fragments (0.37) and for the backfill (0.54) were different. However, wetting and loading tend to produce a rather homogeneous mixture (uniform void ratio of 0.47), a behaviour observed in practice. Another interesting result was strains development in time in two time scales.
7
CONCLUSIONS
Numerical simulations of individual fragments of rock (a porous marl) were performed. They show the
492
development of definite patterns of tensile stress, shear stress and plastic deformation during wetting. These patterns allowed the identification of degradation mechanisms of fragments of marl. Suction gradients inside the fragment, developed during wetting, play a significant role. This gradient allows the development of differential swelling deformations, leading to tensile stress/shear development and consequently to cracking. The numerical results from individual rock fragments provided a mechanical explanation for the overall behaviour of aggregates (compacted material) observed in experimental tests. Cracking development due to saturation leads to fragment size reduction and the collapse observed results from the rearrangement of the broken fragments. Numerical simulation of oedometric tests on particle arrangements, where different properties were adopted for the fragments and for the backfill material, were also performed. The mixture behaves as a ‘‘double porosity’’ material as strains develops in time in two time scales. An interesting result of modelling was the observed trend towards a homogeneous distribution of porosity inside the mixture, a result which agrees with experimental observations.
ACKNOWLEDGEMENTS The authors would like to thank Professor Emanuel Maranha das Neves for his useful comments in the preparation of this paper. Acknowledgement is also due to the Portuguese Foundation for Science and Technology, FCT, for the financial support that allowed this study (SFRH/BD/ 25846/2005, POCTI/ECM/59320/2004).
REFERENCES Alonso, E.E., Gens, A. and Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique, 40 (3), pp. 405–430. Burland, J.B. 1990. On the compressibility and shear strength of natural clays. Géotechnique, 40 (3), pp. 329–378. Cardoso, R and Alonso, E.E., 2008, Degradation of compacted marls—a microstructural investigation. Soils and Foundations (in prep.). Gens, A. and Nova, R. 1993. Conceptual bases for a constitutive model for bonded soils and weak rocks. Symp on Geotechnical Eng. Hard Soils-Soft Rocks, vol. 1, pp. 485–494. Leroueil, S. and Vaughan, P. 1990. The general and congruent effects of the structure in natural soils and weak rocks. Géotechnique, vol. 40 (3), pp. 467–488. Oldecop, L. & Alonso, E.E. 2003. Suction effects on rockfill compressibility, Géotechnique, vol. 53 (2), pp. 153–164. Olivella, S., Gens, A., Carrera, J. and Alonso, E.E. 1996. Numerical formulation for simulator (CODE_BRIGHT) for coupled analysis of saline media. Eng. Computations, 13 (7), pp. 87–112. Pinyol, N.M., Alonso, E.E. Vaunat, J. 2007 A constitutive model for soft clayey rocks that includes weathering effects Géotechnique vol. 57 (2), pp. 137–151. Rouania, M. and Muir Wood, D. 1998. A kinematic hardening model for structured clays, The geotechnics of hard soils—soft rocks, Evangelista & Picarelli (eds), Balkema, Rotterdam, vol. 2, pp. 817–824. Van Genuchten, M.T. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44, pp. 892–898. Vaughan 1997. Engineering behaviour of weak rocks: Some answers and some questions. Geotechnical Engineering of Hard Soils-Soft Rocks. Balkema, pp. 1741–1765. Vaunat, J. and Gens, A. 2003. Bond degradation and irreversible strains in soft argillaceous rock. Proc. 12th Panamerican Conf. on Soil Mechanics and Geotechnical Engineering, vol. 1, pp. 479–484.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Multiaxial behavior of partially saturated sand at high stresses N. Massoudi Bechtel Power Corporation, Frederick, Maryland, USA
H.-Y. Ko & S. Sture University of Colorado, Boulder, Colorado, USA
ABSTRACT: Results of 60 experiments conducted on a well-graded, partially saturated sand at high stresses are presented. These include drained and undrained isotropic compression, triaxial, and strain-controlled experiments. A multiaxial cubical apparatus with a pressure capacity of 69 MPa (10,000 psi) was utilized. Results indicate that the presence of even a small volume of air significantly affects the generated pore pressures in undrained loading, and in turn influence the state of effective stress and strength of the soil. Additionally, high confining stresses result in the dense sand responding in stress-strain characteristics resembling that typically observed in loose sands. And finally, intermediate principal stresses highly affect the soils’ response and their strength. High confining stresses also result is particle crushing, impacting material properties.
1
INTRODUCTION
The behavior of partially saturated soils can be more conveniently examined experimentally than analytically or in the field. The advantage of performing laboratory tests is in its greater control over test conditions such as the degree of saturation. The natural ground is rarely fully saturated. In fact, the seasonal fluctuation in groundwater level can lead to entrapment of air bubbles and produce levels of saturation below 100%. The objective of the experiments described herein was to provide a general understanding on the behavior of partly saturated sands with the aim of producing results on the stress-strain-strength behavior of the tested sand. The factors studied were the influence of high pressures, intermediate principal stress, and the 1-D behavior at partial saturation. The behavior of partly saturated soils has been studied for several decades. A single compilation of such works resulted from the 1960 Conference on Pore Pressure and Suction in London. A more recent undertaking is reflected in results of the 4th International Conference on Unsaturated Soils in Arizona, in 2006. These studies concentrated on understanding the basics of unsaturated properties of soils. Casagrande & Hirschfeld (1960) studied the behavior of partially saturated compacted clay at different water contents under undrained hydrostatic and
proportional loading conditions. They used the test results to construct a relationship between pore pressure, water content, confining stress, and total major principal stress. Lee & Haley (1968) studied the influence of compaction methods on the stress-strain-strength characteristics of partly saturated compacted Kaolinite and silty clay at high pressures. They showed that the behavior of these soils when subjected to high stresses will no longer be controlled by their initial fabric and structure; rather, regardless of the particle arrangement, the soil response is ductile and large positive pore pressures will develop. For soils containing a single pore fluid the effective normal stress was given by Terzaghi (1936). Its success led researchers to define similar relationships for unsaturated soils. The case of partially saturated soils, however, calls for special treatments because the pores are occupied by more than one fluid, usually air and water. A tentative expression for such case was introduced by Bishop (1960) as σ = σ − ua + x(ua − uw )
(1)
The parameter x in Eq. (1) is a function of the degree of saturation, but affected by factors such as soil structure, cycles of wetting or drying, stress state, etc. A number of similar relationships have been introduced to define the effective stress in partly saturated
495
τf = c + (σn − ua ) tan φ + (ua − uw ) tan φb
σ 2 − σ3 σ1 − σ3
75
50
25
10
1
0.1
0 0.01
Grain Size - mm
Figure 2.
Grain size distribution of the test soil.
Figure 3.
The 3-dimensional stress space.
(2)
Measuring some of the terms in Eq. (2) is difficult. Some have attempted to simplify these using curve fitting (Rohm and Vilar, 1995 and Abramento and Carvalho, 1989) while others have resorted to methods such as fractal models (Xu, 2004). For experiments described in this paper, a multiaxial cubical device was used. The apparatus had a pressure capacity of 69 MPa (10,000 psi) and provided several advantages over other geotechnical testing devices. These include the ability to independently control the applied stresses, which permits reaching virtually any point in the stress space, and the fluid cushion type boundaries that tremendously reduce the boundary problems normally encountered in other soil testing devices. The device has been described in detail by Ko et al. (1984). A schematic of the apparatus is shown in Fig. 1. The relative magnitude of intermediate principal stress was assigned to parameter b (the principal stress ratio), defined as b=
100
Finer by Weight (%)
soils. Common to all is the effort to keep their appearance as close to that of Terzaghi’s, however, incorporating a parameter in the relationship which is a function of the degree of saturation and soil type. Despite the simple appearance of these equations, evaluation of the parameters is not as simple. More recent formulations include the works of Fredlund (1979) and Hasan & Fredlund (1980). Fredlund et al. (1978) introduced a relationship for shear strength of partly saturated soils that included terms for pore air, pore water, suction, and other effects, represented by
(3)
During sample preparation, the breaking of the individual particles due to large compaction efforts was clearly audible. The experimental schedule consisted of tests along different stress paths in the three-dimensional stress space that is shown in Fig. 3. In all triaxial experiments, the stress paths were maintained in the octahedral plane, i.e., Δσoct = 0, with the octahedral normal stress (or mean stress) defined as σoct = 1/3(σ1 + σ2 + σ3 )
(4)
The test soil was classified, using the Unified Soil Classification System, as a well-graded sand (SP-SC) with about 5% fines by weight and with a specific gravity of 2.61. The sand’s gradation is shown in Fig. 2.
2
Figure 1.
The degree of saturation was calculated based on the weight-volume relationships. A value of about 85% was common for the specimens. Skempton B-values of about 0.02 were commonly measured. To examine specimen air contents, the volume of expelled water was visually observed and recorded during drained hydrostatic compression tests in addition to the routine volumetric calculation as sum of the three principal strains. Any difference in volume measurements (due to the presence of air) would have manifested itself in the form of two different volumetric responses because the calculation technique
Cubical cell apparatus and cubical soil specimen.
496
NEAR SATURATION TECHNIQUE
Volumetric Strain (%)
Axial Strain (%) 0 0 5
1
2
3
4
5
Calculated Measured
10 15 20
Figure 4.
Calculated and measured volume changes.
provides an overall volume change (without separating for air and water), whereas the visual measurement only refers to the volume of expelled water. The results are shown in Fig. 4. It is noticed that the two responses were quite similar despite the fact that air bubbles were observed to leave the specimen. Such volumetric responses are expected of soils with high saturation, especially in dense soils, because all but a small fraction of the void phase is occupied by water.
3
Figure 5.
Undrained triaxial compression tests (b = 0).
Figure 6.
Undrained triaxial tests with varying b-value.
UNDRAINED TRIAXIAL EXPERIMENTS
The influence of confining stress on the stress-strainstrength of the test sand is shown in Fig. 5. The identifying numbers correspond to the confining total stress prior to the triaxial loading. Note that these stresses may equal ‘effective’ stresses depending on the pore pressure state of the specimen at commencement of shearing. The influence of intermediate principle stress is shown in Fig. 6 for confining stress of 6.9 MPa (1,000 psi). Several observations are made from the results: {i.} With increase in magnitude of effective confinement, the sand’s stiffness increases. This was true regardless of the b-value. {ii.} Under the experimental procedure described, the sand’s strength is a maximum at a confining stress of around 6.9 MPa (1,000 psi). With increase in total stress, though an initially stiffer response is produced due to greater effective confinement, the reaching of a sample to a state of full or near full saturation causes greater excess pore pressures thus reducing the overall strength. {iii.} Volumetric responses indicate that the sand dilates at low confinement. With increase in stress the tendency towards dilation decreases. Tests at confining stresses where the soil had reached full saturation indicate small volume change during shear. This could be the result of a combination of factors, such as compression of water, compression of solid particles, and the time-dependent dissolution of air bubbles. {iv.} No excess pore pressures are generated at low confining stresses, which implied that the air content was significantly affecting the results. With increase in confinement, however,
the rate and the magnitude of excess pore pressure at failure increase. {iv.} For isotropic total stress levels larger than 10.4 MPa (1,000 psi), the soil reached full saturation, the effective confining stress remained
497
essentially unchanged, and the subsequent response resembled that for fully saturated conditions. It must be noted that reaching of full saturation at 10.4 MPa (1,000 psi) is associated with the 85% saturation level for the test sand. At other saturation levels this pressure would be different. {v.} The influence of intermediate principal stress on the soil’s response does not depart from those that have been established for the fully saturated condition (Ko et al., 1984). {vi.} The largest volume change during shear is associated with larger b-values. This is regardless of the nature of volume change (expansion or contraction). {vii.} Any one experiment that produces the greatest volume change also produces the greatest pore pressure at failure. 4
STRENGTH CHARACTERISTICS
Strength of partially saturated soils, like that of fully saturated soils, is controlled by the effective stresses within that soil. The Mohr-Coulomb strength envelope obtained from the nearly saturated undrained triaxial compression (TC, b = 0) experiments is presented in terms of effective stress in Fig. 7. The one distinguishing aspect of this envelope in Fig. 7 (a) is its cohesive intercept which is thought to be due to capillary effects (apparent cohesion) because of the <100% saturation, the large overconsolidation of the compacted soil at low stresses, and the presence of some fines in the soil. The results are also plotted in terms of total stress, as shown in Fig. 7(b). They indicate two different angles of shearing resistance, each belonging to different states of saturation. A small cohesion intercept and a φ = 27 degrees belong to the partially saturated state, whereas a rather large cohesive intercept and φ = 0 manifest for the fully saturated state. In general, the φ = 0 concept does not apply to
Figure 7. stress.
partially saturated soils, but once the confining stress becomes large enough to cause full saturation, any further increase in total stress does not cause an increase in effective stress and from this point the φ = 0 concept does apply. In this case the undrained strength may be specified in terms of total stress parameters cu and φu . 5
INFLUENCE OF INTERMEDIATE PRINCIPAL STRESS ON STRENGTH
It is now widely accepted that the intermediate principal stress can exert a significant influence on the behavior of soils. The degree of such influence, however, can vary substantially. For instance, condition of failure defined by a state of stress σ2 = σ1 (triaxial extension, TE) or σ2 = σ3 (triaxial compression, TC) influences the magnitude of volume change or excess pore pressure whose reflections become visible on strength of the soils. The effective stress paths in triaxial plane representing conditions of TC (b = 0) and TE (b = 1) is shown in Fig. 8. The number identifying a particular stress path refers to the total confining stress that the specimen was subjected to before shear. It is noted that for the lower confinement levels, lack of excess pore water pressure made the total and effective stresses identical, and also the effective stress path was identical to the total stress path. With increase in confining stress a larger volume of the pore air is dissolved into the pore water, bringing the sample closer to a state of full saturation. Stress paths for other intermediate principal stresses (not shown here) suggest similar findings. Thus, depending on the magnitude of confinement and the volume of air in voids, a nearly saturated sample may respond as if it was 100% saturated and loaded under fully drained, partially drained and undrained, or fully undrained conditions. The influence of intermediate principal stress on the angle of shearing resistance is shown in Fig. 9.
Strength envelope (a) effective stress, (b) total Figure 8.
498
Strength envelopes in triaxial plane (b = 0 and 1).
the more widespread responses in the first approach. A noticeable trend in the representation of φ vs. bvalue for the two approaches is: (1) the rather similar shape of the two curves for identical magnitude of stress and (2) the rather insignificant influence of c on φ calculations at higher stresses.
6
Figure 9.
Angle of shearing resistance and b-value.
The angle of shearing resistance is represented in two forms. In the first approach, φ is defined by Eq. (5) and the strength component associated with cohesion is neglected. φ = sin−1
σ 1 − σ3 σ1 + σ3
(5)
In the second approach, φ is defined as φ = sin−1
σ1 − σ3 − 2c cos φ σ1 + σ3
(6)
In Eq. (6) the value of c was assumed to remain unchanged and at 275 kPa (40 psi) for different b-values. In solving this equation, a value of φ was assumed and a new value was calculated. The iteration continued until the two values converged. In Fig. 9, the lowest φ occurs at the condition of b = 0 and increases sharply to conditions 0.2 ≤ b ≤ 0.5, with subsequent increase or decrease in φ with change in b-value. The trend is noticeably similar to that observed for tests at full saturation. For case of Eq. (6) an overall reduction in the value of φ is observed compared to Eq. (5). Such reduction is in correspondence with the general representation of strength in the Mohr-Coulomb diagram where a flattening of the strength envelope will be noticed if the envelope was to include a cohesive intercept and still represent a strength at the same effective normal stress. This latter representation of φ results in a clustering of the curves for different stresses as opposed to
KO EXPERIMENTS
Five undrained uniaxial strain tests with different levels of effective confining stress were conducted on the nearly saturated sand. In spite of the flexible boundaries of the apparatus, lateral strains were controlled within small fractions of one percent. At no time during the Ko loading did the lateral strains exceed 0.01%. The experiments were typically terminated when the soil reached full saturation. A typical stress-strain response for these tests is shown in Fig. 10 in terms of both total and effective stress. The response indicates perfect Ko condition. The response of the soil in the axial (z) direction indicates an initial curvature which reduces with further straining. This curvature is related to the stress history of the specimen, is reduced with increasing confining stress, and disappears when the specimen preconsolidation pressure of 9 MPa (1,300 psi) is exceeded. Results indicate that there is practically no difference between the total and effective stressstrain relations until the soil goes into full saturation at which point further increase in total stress is negated by the generated pore pressures, resulting in no further straining of the material. The stress history of the soil can best be studied from the results of Ko tests plotted in terms of void ratio-log of effective stress, as shown in Fig. 11. From Fig. 11, the maximum past consolidation stress is estimated to be about 9 MPa (1,300 psi). This is somewhat near the 9.7 MPa (1,400 psi) pressure that the specimens were compacted to. The compression and expansion indices are calculated to be Cc = 0.19 and Ce = 0.01; they compare well with 0.2 and 0.02 values, respectively, obtained from isotropic
Figure 10.
499
Ko tests.
Figure 13.
Figure 11. tions.
Comparison of isotropic and Ko loading condi-
Figure 12.
Ko (a) total and (b) effective stress paths.
compression tests. Such values are usually associated with highly compressible soils. Other studies have also shown that sands subjected to high stresses could become as compressible as clays (Roberts and DeSouza, 1958). Fig. 11 also shows very close correspondence between the two Ko and isotropic loading cases, even though they were generated via different stress paths. It is for this reason that soils retrieved from a site are usually loaded isotropically in the laboratory in lieu of trying to mimic a 1–D compression as is the more probable stress state existing in the ground. The stress paths that were generated during the Ko experimentation are displayed in Fig. 12. In Fig. 12(a), each total stress path starts at the confining stress that the sample was subjected to before the 1-D loading. Though all tests started at different stresses with different slopes, of interest is the final destination which they all seem to be converging towards. The effective stress paths for the same experiments, shown in Fig. 12(b), are similarly pointing towards a unique direction and had it not been for the reaching of full saturation, they would have undoubtedly ended up along the same path as that in total stress space. In Fig. 12(b), the effective stress paths for the 1.4 MPa (200 psi) and 3.5 MPa (500 psi) experiments suggest that no increase in lateral stresses were needed
Evolution of Ko values with stress history.
along certain portions of the stress path (shown by vertical rise in σ1 ), indicating that when an increment of axial stress was applied, the deformation in lateral directions were so small that no increase in lateral stresses were required to maintain zero lateral deformations. It is believed that this behavior is associated with a combination of particle crushing and the stiff soil skeleton. The effect of the latter is evident in the response of the 9 MPa (1,300 psi) experiment where reduced lateral stresses rendered the stress path for this Ko experiment resembling a conventional triaxial compression (CTC) stress path. This is not at all a conclusion that the Ko and CTC stress paths are similar, rather a realization that a stiff soil skeleton can provide substantial resistance to lateral deformation even at large applied axial stresses. Ko values are known to vary with stress history. Similar trends are indicated in Fig. 13 for the tested soil. All experiments initially show large Ko values. With increase in stress, Ko values converge toward a constant value of about 0.45. With further increase in stress, there appears a slight increase in Ko values, approaching 0.50. The 9 MPa (1,300 psi) experiment basically exhibits a similar trend to others in the Ko evolution, with the exception that its Ko values are higher than those experiments with lower stresses. This is attributed to the crushing of particles which occur at high pressures, resulting in a reduction in φ and in turn an increase in the Ko values.
7
CONCLUSIONS
Behavior of a nearly saturated sand in undrained conditions followed an evolution resembling both drained and undrained loading depending on its initial moisture state and loading conditions. At low confining stresses, lack of generated pore pressures due to a highly compressible pore fluid resulted in the total and effective stresses being identical. With increase in stress, a greater volume of air was dissolved into the pore liquid and brought the sample closer to the state
500
of full saturation, dictating the stress-strain-strength characteristics were comparable with those at full saturation. The influence of intermediate principal stress on stress-strain and strength of nearly saturated sand did not significantly depart, in qualitative terms, from that for fully saturated conditions, i.e., the greatest volume change (dilative or contractive) seemed to be associated with the TE condition. Intermediate principal stresses, however, affected the angle of shearing resistance, such that φ for the TC condition is always lower than that for the TE case, although at very high stresses this difference is much less pronounced. The test sand, although very dense, indicated relatively high compressibility at high stresses, as often observed in normally consolidated soils. High stresses render even dense soils rather compressible. This is also observed in results of the Ko experiments, with Ko values approaching 0.5 or even higher at high stresses, which is partly impacted by particle crushing.
ACKNOWLEDGEMENT The research described in this paper was funded by the United States Army Corps of Engineers, Waterways Experiment Station, Geomechanics Division, Vicksburg, Mississippi. This support is greatly acknowledged.
REFERENCES Abramento, M. & Carvalho, C.S. 1989. Geotechnical Parameters for the Study of Natural Slopes Instablisation at
‘Serra do Mar’ Brazil. Proceedings, 12th Intl. Conf. on Soil Mech. & Found. Engrg., Rio de Janeiro: 1599–1602. Bishop, A.W. 1960. The Measurement of Pore Pressure in the Triaxial Test. Conference. on Pore Pressure and Suction in Soils, London: 38–46. Casagrande, A. & Hirschfeld, R.C. 1960. Stress-Deformation and Strength Characteristics of a Clay Compacted to a Constant Dry Unit Weight. ASCE Research Conf. on Shear Strength of Cohesive Soils, Boulder, Colorado: 359–417. Fredlund, D.G., Morgenstern, N.R. & Widger, R.A. 1978. The Shear Strength of Unsaturated Soils. Canadian Geotechnical Journal 15: 313–321. Fredlund, D.G. 1979. Appropriate Concepts and Technology for Unsaturated Soils. Canadian Geotechnical Journal 16: 121–139. Hasan, J.U. & Fredlund, D.G. 1980. Pore Pressure Parameters for Unsaturated Soils. Canadian Geotechnical Journal 17: 395–404. Ko, H-Y., Sture, S. & Janoo, V.C. 1984. Development of A 10,000 psi Multiaxial Cubical Cell for Soil Testing with Pore Pressure Measuring Facilities. Report Submitted to Corps of Engineers, Waterways Experiment Station, Vicksburg, Mississippi. Lee, K.L. & Haley, S.C. 1968. Strength of Compacted Clay at High Pressure. ASCE Geotechnical Journal 94(6): 1303–1332. Roberts, J.E. & De Souza, J.M. 1958. The Compressibility of Sands. Proceedings, 61th Annual Meeting of ASTM 58: 1269–1277. Rohm, S.A. & Vilar, O.M. 1995. Shear Strength of Unsaturated Sandy Soils. Proceedings, 1st Intl. Conf. on Unsaturated Soils, Paris, 189–193. Terzaghi, K. 1936. The Shearing Resistance of Saturated Soils. Proceedings, 1st International Conference on Soil Mechanics 1. Xu, Y.F. 2004. Fractal Approach to Unsaturated Shear Strength. Journal of Geotechnical and Geoenvir. Engrg. 130: 264–272.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A simple method for the prediction of modulus of elasticity for unsaturated sandy soils S.K. Vanapalli & Won Taek Oh Department of Civil Engineering, University of Ottawa, Ontario, Canada
A.J. Puppala Department of Civil Engineering, University of Texas at Arlington, Texas, USA
ABSTRACT: A simple method is proposed in this paper to predict the variation of modulus of elasticity with respect to matric suction in unsaturated sandy soils using the Soil-Water Retention Curve (SWRC) and modulus of elasticity values under saturated conditions. Comparisons are provided between the predicted and measured modulus of elasticity and settlement values from model footing test results on three different sands using this method. The results of this study are encouraging as there is a good agreement between the predicted and measured moduli of elasticity and settlement values. 1
INTRODUCTION
The design of a foundation is significantly influenced by the bearing capacity and settlement behavior of soils. In many cases, it is the settlement behavior which governs the design of a foundation in comparison to the bearing capacity. This is particularly true in the case of coarse-grained soils such as sands in which settlements are immediate in nature due to relatively high coefficient of permeability values. In sandy soils, settlement must be estimated or predicted reliably due to two main reasons. Firstly, the differential settlements in sandy soils are more predominant in comparison to clayey soils because sand deposits are typically heterogeneous in nature. Secondly, the settlements in sandy soils occur quickly and may cause significant damages to the superstructures (Maugeri et al. 1998). It is conventional engineering practice to design a foundation assuming the soil is typically in a saturated condition. The concepts of conventional soil mechanics used for saturated soils may not be valid in the estimation of immediate settlement of foundations in unsaturated soils. Some studies have been performed to study the contribution of matric suction towards bearing capacity of unsaturated sandy soils (Steensen-Bach et al. 1987; Mohamed and Vanapalli 2006). However, there is limited information in the literature particularly with respect to the estimation of the settlement behavior of foundations in sandy soils that are in an unsaturated condition. The key parameter used in the estimation of foundation settlements is the modulus of elasticity which is typically assumed to be constant both below and above
the ground water table in homogeneous deposits of sands. In other words, the influence of matric suction (i.e., unsaturated conditions) is not taken into account. A close examination of the experimental results of stress versus settlement relationships for model footing tests conducted on soils that are in an unsaturated condition show that the modulus of elasticity is significantly influenced by matric suction (Vanapalli and Mohamed 2007). In this paper, stress versus settlement relationships from model footing tests performed on three different sands under unsaturated conditions is presented. The variation of modulus of elasticity with respect to matric suction is derived from the above results and plotted along with their soil-water retention curve (SWRC) behavior. These plots show that there is a relationship between the SWRC and the elasticity behavior, which is similar to the relationship between the SWRC and the shear strength/bearing capacity of unsaturated soils. Using similar procedures that were followed for the prediction of the shear strength and bearing capacity in unsaturated soils, a simple method is developed and presented in this paper for predicting the variation of modulus of elasticity with respect to matric suction using the SWRC and the modulus of elasticity under saturated conditions (Esat ). Comparisons are provided between the predicted and measured moduli of elasticity values from model footing test results using the proposed method. The results show a good comparison between the measured and predicted values of moduli of elasticity and settlement for the three different sands studied in this paper.
503
2
BACKGROUND
2.1
Foundation settlement
The settlement of foundations consists of three components. δ = δi + δc + δs
(1)
where δ = total settlement, δi = immediate or elastic settlement, δc = consolidation settlement and δs = secondary settlement or creep. The immediate or elastic settlement in coarsegrained soils occur under drained conditions while in fine-grained soils they occur under undrained conditions without significant dissipation of excess pore pressures. The total settlement in sands is associated with immediate or elastic settlement as there will be relatively no consolidation or secondary settlement. The foundation settlement in sands is conventionally estimated based on the theory of elasticity using two soil parameters: modulus of elasticity, E and Poisson’s ratio, ν. According to the previous studies by Lade and Nelson (1987), Lade (1988) and Lancellotta (1995), the technique or the procedure used in the determination of E has a significant effect on the estimation of immediate or elastic settlement. In comparison to E value, the Poisson’s ratio, ν does not play an important role. For analysis purposes, these parameters may be assumed to be constant although they vary with time for undrained loading condition (ν = 0.5 for idealized undrained case) and drained loading condition (0.15 ≤ υ ≤ 0.35 for loose to dense sand). The modulus of elasticity, E can be estimated both from laboratory and field tests. In general, the modulus of elasticity for fine-grained soils from conventional triaxial tests can be underestimated due to sample disturbance caused by stress relief and other mechanical disturbance. To overcome this disadvantage, Davis and Poulos (1968) suggested the use of K0 -consolidation triaxial test results to derive modulus of elasticity values. According to the test results by Simons and Som (1970), the modulus of elasticity from K0 -consolidation triaxial tests are much higher than those determined from conventional undrained triaxial tests. Plate load tests, cone penetration tests, pressuremeter tests or geophysical methods (i.e., seismic method) are usually used to estimate in situ modulus of elasticity values. In case of plate load tests (or model footing tests), the modulus of elasticity can be calculated using the equation below (Timoshenko and Goodier 1951). E=
(1 − ν 2 ) δ qp
Bp Iw
(2)
where (δ/δqp ) = slope of settlement versus plate pressure, ν = Poisson’s ratio (a value of 0.3 was used for this study assuming drained loading conditions), Bp = width or diameter of plate, and Iw = influence factor (i.e., 0.79 for circular plate and 0.88 for square plate). This value of modulus of elasticity determined using Eq. (2) is representative of soil within a depth zone which is approximately 1.5Bp ∼2.0Bp . 2.2
The relationship between the SWRC and the shear strength/bearing capacity of unsaturated soils
Vanapalli et al. (1996) proposed a semi-empirical nonlinear function for predicting the shear strength of an unsaturated soil using the SWRC and the shear strength parameters under saturated conditions. The shear strength contribution due to matric suction from that relationship can be determined using the equation below: τus = (ua − uw )(S κ )(tan φ )
(3)
where τus = Shear strength contribution associated with matric suction, (ua − uw ), S = degree of saturation and κ = fitting parameter. According to the studies by Vanapalli and Fredlund (2000) and Garven and Vanapalli (2006), a fitting parameter κ = 1 is required for predicting the shear strength of unsaturated sandy soils (i.e., for soils with Ip = 0). The nonlinear variation of shear strength with respect to matric suction can be obtained by differentiating Eq. (3). dτus d(ua − uw ) = S κ + (ua − uw )
tan φ b =
d (S κ ) tan φ d(ua − uw )
(4)
It is of interest to notice that the net contribution of suction close to the residual state conditions causes a reduction in the shear strength of sandy soils since S is small and the value of [d(S κ )/[d(ua − uw )] is negative (see Fig. 1(a)). Vanapalli and Mohamed (2007) suggested an equation for predicting the bearing capacity of surface footings on unsaturated sandy soils as follows. qult = [c + (ua − uw )S ψ tan φ ]Nc ξc + 0.5γ BNγ ξγ (5) where qult = ultimate bearing capacity, c = effective cohesion, φ = effective internal friction angle, ψ = fitting parameter, B = width of footing, γ = soil unit
504
Degree of Saturation, S (%)
where Eunsat = modulus of elasticity under unsaturated condition, Esat = modulus of elasticity under saturated condition, S = degree of saturation, and α and β are fitting parameters. In Eq. (6), the terms, (S)β and α control the nonlinear variation of the modulus of elasticity. A value of β equal to 1 is used for providing comparisons between the measured and predicted modulus of elasticity values following the earlier concepts discussed for shear strength and bearing capacity of unsaturated sandy soils (i.e., Ip = 0). The differential form of Eq. (5) shown in Eq. (6) can be used for providing mathematical explanations with respect to the nonlinear behavior of modulus of elasticity under unsaturated conditions.
100
Air entry value (ua-uw)b
Residual suction value
0
Shear strength / Bearing capacity
bearing capacity
shear strength
β d Sβ dEunsat = Esat α S + (ua − uw ) d(ua − uw ) d(ua − uw )
Immediate settlement
Elastic modulus
(a)
(7)
It can be seen that Eq. (6) is similar in form to that of Eq. (3). In other words, the net contribution of matric suction towards increase in modulus of elasticity starts decreasing as matric suction approaches residual suction value in coarse-grained soils such as gravels and sands (Fig. 1(b)). More details with respect to settlement behavior are offered while analyzing experimental results.
(b) Matric Suction
Figure 1. SWRC and the variation of shear strength, bearing capacity, modulus of elasticity, and settlement behavior with respect to matric suction in sandy soils.
3
weight, Nc and Nγ = bearing capacity factors from Terzaghi (1943) and Kumbhokjar (1993) respectively and ξc , ξγ = shape factors from Vesi´c (1973). The results of the study by Vanapalli and Mohamed (2007) demonstrate that the variation of bearing capacity with respect to suction is nonlinear and has similar trends as the shear strength behavior (see Fig. 1(a)). Their studies have also shown that the fitting parameter ψ = 1 is required for sandy soils with Ip = 0 for predicting the bearing capacity of unsaturated sandy soils using Eq. (5).
The properties of the sandy soils analyzed in this paper are summarized in Table 1. The SWRCs for three sands are shown in Figure 2. It can be seen that at the same degree of saturation, Sollerod sand shows the highest suction value followed by Coarse-grained sand and Lund sand. The Lund sand offers less resistance to desaturation due to relatively low percentage of fines. In other words, the
2.3
TEST RESULTS
3.1 Summary of the properties of the three sands studied
Table 1.
Summary of the data of three different sands. Vanapalli and Mohamed (2006)
Estimation of modulus of elasticity in unsaturated sandy soils
A simple equation is proposed in this paper for predicting the variation of modulus of elasticity of unsaturated sandy soils using the SWRC and the modulus of elasticity under saturated conditions extending similar concepts described in section 2.2. In this equation, two fitting parameters, α and β are used. β
Eunsat = Esat + Esat α(ua − uw )(S) . / = Esat 1 + α(ua − uw )(S)β
(6)
Steensen-Bach et al. (1987)
Soil type
Coarse-grained Sollerod Lund
Shear failure
General shear failure
B(mm) × L(mm) 100 × 100 150 × 150 c (kPa) 0.6 35.3 φ (◦ ) 4.0 (ua − uw )∗b (kPa) ∗ Air-entry
505
value.
22 × 22 0.8 35.8 5.7
0.6 44 1.1
1000
80
900
(3)
60
BxL = 100x100 (mm)
40 (1) Lund sand (1) Coarse-grained sand (2) Sollerod sand (3)
20
0 0
2
4
6
8
10
Matric suction, (u a-uw) (kPa)
Figure 2. studied.
Coarse-grained Sand (Mohamed and Vanapalli 2006) (ua-uw) = 6 kPa
800
(2)
Applied stress (kPa)
Degree of saturation (%)
100
Soil-water retention curves of the three sands
700 600 4 kPa
500 400
2 kPa
300 200 100 0 kPa
pore spaces in Lund sand are relatively larger than the other two sands. 3.2
0 0
Coarse-grained sand
4.1
15
20
25
1000 Coarse-grained Sand (Mohamed and Vanapalli 2006)
900
BxL =150x150 (mm)
800
Applied stress (kPa)
(ua-uw) = 6 kPa
700
4 kPa 2 kPa
600 500 400 300 200
0 kPa
100
Sollerod and lund sand
Steensen-Bach et al. (1987) performed model footing (22 × 22 × 20 mm) tests using a circular steel test pit (0.2 m diameter × 0.12 m height). The variation of degree of saturation due to the drainage of water from a saturated sample or the imbibitions into an unsaturated sample was monitored by means of an electronic balance. The model footing tests results for Sollerod and Lund sand are shown in Figures 4 and 5 respectively. Sollerod sand shows relatively low values of modulus of elasticity in comparison to other sands studied. 4
10
Settlement (mm)
Mohamed and Vanapalli (2006) carried out model footing tests using two different footing sizes (i.e., 100 × 100 mm and 150 × 150 mm) in specially designed bearing capacity tank (0.9 × 0.9 × 0.75 m) which has provisions to simulate saturated and unsaturated conditions. The tests results for two footings with different matric suction values are shown in Figure 3. The matric suction value at the center of gravity of the matric suction distribution diagram from 0 to 1.5Bp depth region was considered as the average value of matric suction in the analysis of the results (Mohamed and Vanapalli, 2006 and Vanapalli and Mohamed, 2007). This is the zone of depth in which the stresses due to loading are predominant (Poulos and Davis 1974). 3.3
5
ANALYSIS OF THE TESTS RESULTS Coarse-grained sand
Figure 6 shows the SWRC and the variation of modulus of elasticity and settlement with respect to matric
0 0
5
10
15
20
25
Settlement (mm) Figure 3. The relationship between the applied stress versus settlement in Coarse-grained sand.
suction for two model footing tests conducted on Coarse-grained sand. The fitting parameter, α was estimated as 1.5 and 2.5 for 100 × 100 mm and 150 × 150 mm footings respectively. For all the three sands studied in this paper, comparisons are provided between the measured and predicted values of settlements for an applied stress of 40 kPa. At this stress value, all sands exhibit elastic behavior.
506
100
1000 900
Degree of saturateion, S (%)
Sollerod Sand (Steensen-Bach et al. 1987) BxL = 22x22 (mm)
800 (ua-uw) = 8.04 kPa
Applied stress (kPa)
700 600
1.96 kPa
500
Coase-grained sand Mohamed and Vanapalli (2006)
80
60 Measured from Tempe cell apparatus Measured from the test tank
40
20
0
Elastic modulus, E (kPa)
400 300 200 9.81 kPa
100 0 kPa
0 0
20
40
60
80
100
12x103
= 2.5
10x103
= 1.5
8x103 6x103 4x103 2x103
Settlement (mm) 0
Settlement (mm)
Figure 4. The relationship between the applied stress versus settlement in Sollerod sand. 600 Lund Sand (Steensen-Bach et al. 1987) BxL = 22x22 (mm)
Applied stress (kPa)
500
predicted (100x100 mm) measured (100x100 mm) predicted (150x150 mm) measured (150x150 mm)
3
2
1
400
0 0
(ua-uw) = 0.98 kPa
2
4
6
8
10
Matric suction, (ua-uw)(kPa)
300 1.96 kPa
200
Figure 6. SWRC, variation of modulus of elasticity and immediate settlement with matric suction from model footing tests in Coarse-grained sand (Mohamed and Vanapalli 2006).
0.49 kPa 0 kPa
moduli of elasticity are significantly lower than values which are commonly observed for sandy soils. This behavior may be attributed to the relatively small size of the model footings used for testing and hence the modulus of elasticity values calculated using Eq. (2) are also relatively low. The α values required for Sollerod sand and Lund sand are estimated as 2.5 and 1.5 respectively.
100
0 0
10
20
30
40
50
60
Settlement (mm) Figure 5. The relationship between the applied stresses versus settlement in Lund sand.
5 4.2
SUMMARY AND DISCUSSION
5.1 Fitting parameter α
Sollerod sand and lund sand
Figures 7 and 8 show the variation of modulus of elasticity and settlement with respect to matric suction from model footing tests on Sollerod sand and Lund sand respectively. It can be seen that the estimated
The parameter, α in Eq. (5) used for providing bestfit values with the experimental results for the three different sands studied in this research program are summarized in Table 2.
507
1000 Lund sand Steensen-Bach et al. (1987)
Sollerod sand Steensen-Bach et al. (1987)
500
Elastic modulus, E (kPa)
Elastic modulus, E (kPa)
600
α = 2.5
400
300
200
100
predicted measured
600
400
200
predicted measured
2.0
Settlement (mm)
20
Settlement (mm)
α = 1.5
0
0
15
10
5
1.5
1.0
0.5
0.0
0 0
2
4
6
8
0
10
Fitting parameter α for each test.
Soil Coarse-grained sand 100 mm × 100 mm 150 mm × 150 mm Sollerod sand 22 mm × 22 mm Lund sand 22 mm × 22 mm
2
3
Figure 8. The variation of modulus of elasticity and elastic settlement with matric suction from model footing tests in Lund sand (Steensen-Bach et al. 1987).
Figure 7. The variation of modulus of elasticity and immediate settlement with matric suction from model footing tests in Sollerod sand (Steensen-Bach et al. 1987).
Table 2.
1
Matric suction, (ua-uw)(kPa)
Matric suction, (ua-uw)(kPa)
5.2
800
iii. Residual zone: the modulus of elasticity nonlinearly decreases and approaches a constant value.
α 1.5 2.5
5.3 Variation of settlement with matric suction
2.5 1.5
The variation of modulus of elasticity with respect to matric suction
From Figures 6, 7 and 8, it can be seen that the moduli of elasticity behavior is different in the three stages of desaturation; that is boundary effect zone, transition zone and residual zone (Vanapalli et al., 1999). i. Boundary effect zone: the modulus of elasticity linearly increases up to air-entry value. ii. Transition zone: the modulus of elasticity nonlinearly increases up to a certain suction value then gradually decreases.
The settlements gradually decrease with an increase in the modulus of elasticity values as matric suction increases in the boundary effect zone. In the transition zone, settlements are still decreasing to some extent but gradually start increasing as the suction approaches the residual zone. The settlement behavior in the residual zone approximately corresponds to the saturated soil behavior for the Coarse-grained soil tested. This can be attributed to the fact that the modulus of elasticity at zero suction is almost the same as that at 10 kPa of matric suction (i.e., degree of saturation is close to zero) (Fig. 6). Sollerod and Lund sand (Figures 7 and 8 respectively) show relatively poor fit results in comparison to Coarse-grained sand (Figure 6) test results. However, the proposed function (Eq. (6)) is able to provide reasonable trends of measured values of both modulus of elasticity and settlement for all the three sandy soils in all the three zones of the SWRC.
508
6
CONCLUSIONS
The conclusions obtained from this study are as follows. 1. The predicted modulus of elasticity and settlement values using the proposed method are approximately the same as the measured values. 2. The fitting parameter value of α(=1.5) and β(=1) are expected to provide reasonable estimations of settlement behavior of unsaturated sandy soils in foundation engineering practice. However, more test results are necessary both in the laboratory and in situ conditions. 3. The modulus of elasticity start decreasing as suction approaches the transition zone. It is of interest to notice that the settlement behavior of foundations in saturated conditions is similar to that of residual zone for the Coarse-grained sand tested. REFERENCES Davis, E.H. & Poulos, H.G. 1968. The use of elastic theory for settlement prediction under three-dimensional conditions. Géotechnique 18(1): 67–91. Garven, E. & Vanapalli, S.K. 2006. Evaluation of empirical procedures for predicting the shear strength of unsaturated soils. Proc. of the Fourth Int. Conf. on Unsaturated Soils, Carefree, Arizona, ASCE Geotechnical Special Publication 147(2): 2570–2581. Kumbhokjar A.S. 1993. Numerical evaluation of Terzaghi’s Nγ . Journal of Geotechnical Engineering, American Society of Civil Engineers 119(3): 598–607. Lade, P.V. 1988. Model and parameters for the elastic behaviour of soils. Proc. Conf. on Numer. Methods in Geomech. Roterdam: Balkema. Lade, P.V. & Nelson, R.B. 1987. Modeling the elastic behaviour of granular materials. Int. J. Numer. and Analytical Methods in Geomech 11: 521–542. Lancelotta, R. 1995. Geotechnical Engineering. Rotterdam: Balkema.
Maugeri, M., Castelli, F., Massimino, M.R. & Verona, G. 1998. Observed and computed settlements of two shallow foundations on sand. Journal of Geotechnical and Geoenvironmental engineering 124(7): 595–605. Mohamed, F.M.O & Vanapalli, S.K. 2006. Laboratory investigations for the measurement of the bearing capacity of an unsaturated coarse-grained soil, Proceedings of the 59th Canadian Geotechnical Conference, Vancouver. (http://www.x-cd.com/SeatoSkyOnline/S1/ 0219-226.pdf). Poulos, H.G. & Davis E.H. 1974. Elastic solutions for soil and rock mechanics. New York: John Wiley and Sons. Simon, N.E. & Som, N.N. 1970. Settlement of structures on clay with particular emphasis on London clay. Constr. Industry Research Institute Assoc. Report 22, 51pp. Steensen-Bach, J.O., Foged, N. & Steenfelt. J.S. 1987. Capillary induced stresses—Fact or fiction? Proc. 9th European conference on soil mechanics and foundation engineering, Budapest, Hungary, 83–89. Terzaghi, K. 1943. Theoretical Soil Mechanics, John Wiley and Sons, New York, NY, USA. Timoshenko, S. & Goodier, J.N. 1951. Theory of Elasticity. New York: McGraw-Hill. Vanapalli, S.K., Fredlund, D.G. & Pufahl. 1999. Influence of soil structure and stress history on the soil-water characteristics of a compacted till. Géotechnique 49(2): 143–159. Vanapalli, S.K., Fredlund, D.G., Pufahl, D.E. & Clifton, A.W., 1996. Model for the prediction of shear strength with respect to soil suction. Canadian Geotechnical Journal 33(3): 379–392. Vanapalli, S.K. & Fredlund, D.G. 2000. Comparison of empirical procedures to predict the shear strength of unsaturated soils using the soil-water characteristic curve. GeoDenver 2000, ASCE, Special Publication 99: 195–209. Vanapalli, S.K. & Mohamed, F.M.O. 2007. Bearing capacity of model footings in unsaturated soils, Experimental Unsaturated Soil mechanics. New York: Springer. 483–493. Vesi´c A.B. 1973. Analysis of ultimate loads of shallow foundations, Journal of the Soil Mechanics and Foundation Division, ASCE 99 (SM1): 45–73.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Suction effects on the pre-failure behaviour of a compacted clayey soil J.A. Pineda & E.E. Romero Department of Geotechnical Engineering and Geosciences, Universitat Politècnica de Catalunya, Barcelona, Spain
J.E. Colmenares National University of Colombia, Arauca, Colombia
ABSTRACT: This paper explores the pre-failure behaviour of a compacted clayey soil, when subjected to shearing (axial compression) under undrained conditions. Specifically, the study focuses on the effect of the suction state on the undrained Young modulus. The experimental programme carried out in a controlled-suction triaxial cell involved two stages. In the first stage, samples were left to equalise at specified matrix suctions using the axis translation technique. Afterwards, undrained axial compression tests with pore-water pressure and sample deformation measurements were run at a relatively low constant displacement rate to allow for suction equalisation throughout the sample. Axial stiffness could be related to the initial matrix suction before the shearing stage. In this way, the evolution of the undrained Young’s modulus was tracked during shearing where different responses were observed. To the authors’ knowledge, available information concerning this aspect of unsaturated soil is very limited in spite of its practical relevance.
1
SOIL STIFFNESS
q=(
a
-
E Tan and E sec
)
r
Failure
qf
The influence of non-linear soil stiffness on the behaviour of geotechnical structures is a key aspect during the design and construction of any engineering project. Typical stiffness decay curves for soils have been presented, for instance, by Atkinson & Sallfors (1991) and Mair (1993) (see Figure 1). These are defined in terms of Young’s modulus Etan or Esec or shear modulus G, and can be obtained from typical stress-strain curves. Three different zones define a stiffness decay curve: (i) an initial zone of very small strains where moduli are ‘‘unchanged’’ with strain, (ii) an intermediate zone of small strains where the stiffness-strain curve presents a higher slope, and (iii) a final zone of large strains (conventional laboratory tests) where soil stiffness leads to a residual value (see Figure 1b). Two limit strain values define the three zones: the initial very small strain ε0 delimiting the zone where stiffness is still ‘‘constant’’, while the second limit value is defined for a strain value of 0.1% which has been shown to coincide with characteristic ground strains near to structures (Atkinson, 2000). This value is the lowest that can be measured in conventional tests. During a shear test, peak stress is located within the large strain zone at a strain value εf defining the material failure. Deviatoric peak stress qf , failure strain εf and the stiffness at very small strains E0 are parameters needed to calculate both rigidity and degree of
Eo
ETan Esec
Very Small strains small strains E sec E Tan
Large strains
Eo
0.1%
f
log
Figure 1. Schematic stress-strain and stiffness-strain curves for a natural soil (from Atkinson, 2000).
non-linearity of soils. These are two parameters are used to determine the stiffness decay curve of soils (Atkinson, 2000). Rigidity is defined as the ratio of stiffness to strength (E/qf = 1/εf ) while the degree of non-linearity can be defined as the ratio of failure strain to a reference strain εf /εr . Using these concepts Atkinson (2000) presented a simple non-linear stiffness-strain curve in terms of the tangent Young’s modulus Etan that is mathematically defined as: Etan = E0
1−
ε r f
ε r εf 1− ε0
(1)
where E0 is the Young modulus at very small strain for a strain ε0 , εf is the strain at the peak deviatoric stress and r is a soil parameter which includes the degree
511
of non-linearity. According to Atkinson (2000), for saturated conditions, r can vary from 0.1 to 0.5. In the following sections studies on the influence of matric suction on the stiffness decay curves for compacted kaolin samples is presented. The influence of matrix suction on the axial stiffness is analysed and interpreted, and test results presented and commented within a conceptual framework. In the last part of the paper, a simple model able to simulate the observed axial stiffness decay curves depending on the initial Young modulus, the current matrix suction, and the axial strain is proposed.
2
MATERIAL USED AND EXPERIMENTAL PROCEDURE
2.1 Compacted samples Commercial Kaolin (index properties shown in Table 1) was chosen as a soil to be tested. Dry powdered commercial kaolin was mixed with distilled water at a moisture content of 32% (3% less than the optimum from the standard Proctor compaction test, Herrera 2004). In order to allow hydration, the material was wrapped inside a self sealing polyethylene bag and stored for 48 hours. Triaxial samples, 50 mm in diameter and 100 mm high, were prepared by static compaction in ten layers using a compression frame at a fixed displacement rate of 1.5 mm/min. The total vertical total stress applied to the soil specimens was equal to 400 kPa. This resulted in a dry density of 1.22 Mg/m3 , a void ratio of 1.145 and a degree of saturation of 73%. The initial matrix suction of the sample was measured using the filter paper technique (Chandler et al. 1992) and was found to equal 550 kPa. 2.2
Determination of soil water retention curve (SWRC)
The suction-water content relationships under drying and wetting paths were obtained using the filter paper method where matrix suction of the soil can be related to the water content of the filter paper using the calibration of Chandler et al. (1992). At the same stage samples were weighed, and measured to determine their volumes. The final weight was used to establish Table 1.
the water content (wc), void ratio (e) and the degree of saturation (Sr ) of the sample at each stage of the test. 2.3 Shear tests Undrained compression tests with pore water pressure measurement were conducted using a conventional triaxial apparatus (Bishop & Henkel, 1957), modified by Pineda (2004) to test unsaturated samples using the axis translation technique (Hilf, 1956). Pore water pressure uw was applied or measured at the base of the sample through a ceramic disc with an air entry value of 500 kPa. Pore air pressure, ua was applied at the top of the sample through a porous filter with a low air entry value. Cell pressure σ 3 , pore water pressure uw and pore air pressure ua were each independently controlled, and simultaneously axial load, axial displacement and flow of water from the sample were measured. Global displacement measurements were made using conventional micrometers. The initial phase of each test consisted of a wetting stage during which the samples were brought to a matrix suction value of 25 kPa, 50 kPa, 100 kPa, 200 kPa, 300 kPa or 400 kPa. This was achieved by applying a water pressure of 50 kPa to the base of the sample using an air back-pressure of 75 kPa, 100 kPa, 150 kPa, 250 kPa, 350 kPa or 450 kPa to the top of the sample, and a cell pressure of 80 kPa, 105 kPa, 155 kPa, 255 kPa, 355 kPa or 455 kPa respectively. The wetting stage of each test was finished when no change in the flow of water into the sample was registered (typically after 4–30 days). Then, each sample was subjected to shearing in undrained conditions with measurement of pore water pressure. Shearing was conducted at a constant displacement rate equal to 0.05 mm/min. By measuring the excess pore water pressure and keeping constant the pore air pressure during shearing, it was possible to evaluate changes in matrix suction. 3
EXPERIMENTAL RESULTS
A comprehensive analysis of the influence of the matrix suction on the shear strength and volumetric behaviour of this material was presented by Pineda & Colmenares (2005a, 2005b and 2006), respectively. This paper focuses on the evaluation of the decay of the stiffness as a function of matrix suction.
Index and compaction properties of kaolin.
Liquid Limit (LL) Plastic Limit (PL) Plasticity Index (IP ) Gs Maximum dry density Optimum moisture content (OMC)
84% 46% 38% 2.61 1.24 Mg/m3 35%
3.1 Soil water retention curve (SWRC) Figure 2 shows the gravimetric water content-matric suction relationship for compacted commercial kaolin obtained during the drying process. Additionally, the SWRC of reconstituted commercial kaolin (consolidated to a total vertical stress of 200 kPa) obtained by
512
shows that although the macrofabrics are considerably different, the microfabrics are probably similar. Figure 2 also includes the final suction and water content values obtained at the end of the wetting stage (open circles) in which wetting path corresponds to a scanning curve due to fact that the initial unsaturated state of the samples (wc = 32% and s = 550 kPa) locates them between the main wetting and drying curves such as was reported by Pineda-Jaimes (2003).
45 Gravimetric water content (%)
40 35
Wetting path before shearing
30
Drying curve for reconstituted kaolin (Pineda-Jaimes, 2003)
Drying curve for compacted kaolin
25 20
Soil behaviour is controlled by the macrostructure
Soil behaviour is controlled by the microstructure
15 10 5 0 10
100
1000 Matric suction (kPa)
10000
100000
3.2 Figure 2. Soil water retention curve for compacted and reconstituted commercial kaolin.
Pineda-Jaimes (2003) is included. The drying curve for the compacted kaolin lies below that of the reconstituted kaolin but is more or less parallel up to a suction of about 1000 kPa. For a suction value of 1500 kPa the reconstituted kaolin curve merges with the compacted curve and for higher suctions both follow a similar path. The differences between both curves can be explained by the different fabrics obtained by the preparation process. For fine-grained unsaturated soils, compaction processes lead to different structures, which depend mainly on water content controlling the mechanical behaviour (Gens et al. 1995). Soils compacted at water contents dry of optimum generally show a flocculated structure where aggregates of soil particles with an inherent bimodal pore size distribution are developed. In this case, a microstructural level is referred to the intra-aggregate voids within the particle aggregates while the macrostructural level is referred to the inter-aggregate voids between the aggregates. It has been demonstrated experimentally using, for instance, MIP tests as reported by Thom et al. (2007) for compacted kaolin, and Romero et al. (1999) for compacted Boom clay. Romero et al. (1999) showed that for deformable clayey soils in the low range of water content (i.e. high range of suction) the behaviour of the SWRC is determined by the specific surface. They point out that the main wetting and drying paths indicate a delimiting zone in the water retention curve separating a region of intra-aggregate porosity from an inter-aggregate porosity adjoining area. In the intra-aggregate region, water-ratio is not dependent on void ratio and retention curve parameters are mainly dependent on specific surface. However, in the inter-aggregate region, water ratio depends on void ratio and is strongly coupled to mechanical actions. On the other hand, reconstituted soils have been recognized as consisting of a uniform arrangement of soil particles compressed to form a single mass. The high coherence between both compacted and reconstituted samples at suction values greater than 1500 kPa
Shear tests
The deviatoric stress-axial strain relationship obtained from the unconfined compression tests is presented in Figure 3. Both stiffness and strength increase with the initial matrix suction value before shearing is increased. This is due to the increment of the interparticle forces, which tends to stabilize the soil structure due to capillary effects (Burland & Ridley, 1996). Two different responses can be distinguished in Figure 3 depending on the initial suction value. Samples with lower initial suction values (s ≤ 100 kPa) showed a stress-strain behaviour similar to normally consolidated soils while samples with higher initial suction values (s > 100 kPa) showed a stress-strain response typical of overconsolidated samples (softening after peak). Similar results have been reported by Ridley et al. (1995) and Colmenares & Ridley (2002) for both reconstituted Speswhite kaolin and a reconstituted silty clay soil, respectively. On the other hand, strain at peak decreases as suction increases accompanied by a higher peak stress (see Figure 4). In this case, a linear relationship was obtained between the deviatoric stress and the axial strain at peak. Sample M(0) with an initial suction value of 25 kPa shows a strain value at peak of 10.2% while sample M(5) with a suction value of 400 kPa reached the stress peak at a strain value of 2.7%. This means that wetting process leads to an increase in the strain at failure (softening) of about 4.5 times between sample M(5) and M(0) (400 and 25 kPa). Using data presented in Figure 4, secant modulus at peak (Esec = qpeak /εpeak ) was obtained for each sample. Figure 5 shows the variation of secant Young’s modulus with the matrix suction at peak. It can be seen that secant modulus increases as the suction increases. A non-linear relationship is observed where a smaller variation of the secant modulus was obtained for samples with lower initial suction values (25, 50 and 100 kPa). On the other hand, samples with suction values greater than 100 kPa show an increase in secant modulus at peak without evidence of a limit value. Comparison of secant modulus at peak for samples M(0) and M(5) show an increase of about 14 times between them following a exponential relationship with the matrix suction at peak.
513
200 160 Sri = 77,1%
140
25
s=400 kPa s=300 kPa s=200 kPa s=100 kPa s=50 kPa s=25 kPa
Sri = 75,1%
Secant Modulus, Esec (MPa)
Deviatoric stress, q (kPa)
180
Sr i = 80,0%
120 100
Sri = 84,9%
80 60 40 0
Sri = 88,9%
Sri = 90,1%
20 0
2
4
6 8 Axial strain
10 a (%)
12
14
200
Deviatoric stress (kPa)
S i = 400kPa
S i = 300kPa S i = 200kPa
100 S i = 100kPa S i = 50kPa
50
S i = 25kPa
0 0
2
4
6 Axial strain (%)
8
10
12
Figure 4. Relationship between deviatoric stress and axial strain at peak for compacted commercial kaolin.
Secant Modulus, E sec (MPa)
8 7 6 5 4 3 2 1 0 0
0.1
0.2
0.3
0.4
0.5
Matric suction at peak (MPa)
Figure 5. Variation of the secant modulus at peak with the axial strain.
4 4.1
15
STIFFNESS DEGRADATION Experimental results
Using the experimental data contained in Figure 3, stiffness moduli (secant and tangent modulus) were calculated. Very-small and small-strain zones (zones 1 and 2 in Figure 1) were not determined due to the accuracy of the gauges used during shear tests. For this reason, stiffness moduli were evaluated only within the
s=400 kPa s=300 kPa s=200 kPa s=100 kPa s=50 kPa s=25 kPa
10 5 0 0.1
16
Figure 3. Stress-strain-suction curves for Commercial compacted kaolin.
150
Peak deviatoric stress
20
Figure 6.
1 log a (%)
10
Variation of Esec with axial strain during shearing.
large strain zone (zone 3 in Figure 1). Secant modulus Esec and tangent modulus were evaluated as Esec = qi /εi and Etan = dqi /dεi , where i describes the current strain value on shearing. Figure 6 and Figure 7 shows the variation of secant and tangent moduli with axial strain during shearing where strain has been is plotted on a log scale. A strong non-linearity in the stiffness-strain curves is observed in all samples. Different slopes of the stiffness decay curves were obtained for different initial suction values. Secant modulus showed higher values than tangent modulus but also a higher slope was observed as suction increases. Arrows in Figure 6 indicate the strain value at failure (εf ) which corresponds to a slope change in the stiffness curve (see Figure 6) and also with a value of tangent modulus of cero (Figure 7). Figure 8 shows a comparison between secant and tangent modulus for two kaolin samples with the extreme suction values tested here. Squares are used to describe the behaviour of the sample with a matrix suction of s = 400 kPa while circles are used to the sample with a suction value of 50 kPa. These matrix suction values correspond to initial degree of saturation values of 75.1% and 88.90%, respectively. Figure 8 clearly shows the influence of the matrix suction on the stiffness behaviour of compacted kaolin samples. Although at very small strains both secant and tangent modulus have to be the same E0 = Etan = Esec (which is not contained in Figure 8), for strain values greater than 0.1% secant and tangent moduli are very different. For instance, at 0.2% of axial strain, the stiffness moduli were about 5 times greater (25 MPa versus 5 MPa for Esec and 20 MPa versus 4 MPa for Etan ) in the sample with an initial suction of 400 kPa compared with the sample with the lower suction value (50 kPa). As the strain increases both tangent and secant modulus decrease. However, values of tangent modulus decrease more quickly compared with secant modulus which decreases slowly and tends to reach a ‘‘limit’’ value at large strain.
514
Tangent Modulus, E tan (MPa)
20
Table 2. s=400 kPa s=300 kPa s=200 kPa s=100 kPa s=50 kPa s=25 kPa
15
10
5
0 0.1
1
log
Sample
Initial matrix suction (kPa)
E0 (kPa)
ε0 (%)
εf (%)
M(0) M(1) M(2) M(3) M(4) M(5)
25 50 100 200 300 400
40100 43000 50250 64900 85000 110000
0.001 0.001 0.001 0.001 0.001 0.001
10.2 10.0 8.50 5.60 4.50 2.70
10
(%)
Variation of Etan with axial strain during shearing.
25 Tangent Modulus E tan (MPa)
Figure 7.
a
Esec, Etan (MPa)
20
15
Esec Esec Etan Etan
s=400 kPa s=50 kPa s=400 kPa s=50 kPa
10
5
0 0.01
Parameters required for Equation (5).
s=400 kPa s=300 kPa s=200 kPa s=100 kPa s=50 kPa s=25 kPa Model s=400 kPa Model s=300 kPa Model s=200 kPa Model s=100 kPa Model s=50 kPa Model s=25 kPa
20 15 10 5 0 0.1
1 Log
0.1
1
log
a
a
10 (%)
10
Figure 9. Comparison between experimental and simulated stiffness-decay curves (tangent modulus).
(%)
Figure 8. Comparison between secant and tangent modulus for two compacted kaolin samples with different initial suctions.
The analysis of the experimental behaviour of compacted kaolin samples indicates that although all initial stress states are inside the inter-aggregate region of the SWRC (s < 1500 kPa), which is mainly controlled by macrofabric, the ‘volumetrically-stiffer’ effect of matrix suction leads to different stiffness responses. 4.2 A simple model of stiffness degradation during shearing As described above, a simple non-linear stiffnessstrain behaviour can be represented in terms of rigidity and degree of non-linearity. These two concepts are defined by four soil parameters E0 and qf (which define the rigidity), and finally εf and εr (which define the degree of linearity, where εr is a reference strain). Equation (1) was used as a first attempt to describe the experimental behaviour of unsaturated compacted kaolin samples. According to Atkinson (2000) parameter r of Equation (1), which relates rigidity and degree of non-linearity, can vary from 0.1 to 0.5 for saturated conditions but there are no reported values for unsaturated samples. Young’s moduli at very small strains E0 were obtained from bender element tests carried out by
Pineda (2007) on a kaolin sample compacted under similar initial conditions to the triaxial samples. Table 2 shows the parameters used to model the experimental behaviour of samples with different initial suction values. Figure 9 shows the simulated stiffness decay curves in terms of tangent Young’s modulus Etan obtained using Equation (1). The parameter r was obtained by fitting the synthetic curves with the experimental data. Good agreement was obtained in all cases although some scatter is observed in samples with higher initial suction values (e.g. s = 400 kPa in Figure 9). This could be due to the brittle behaviour of this sample which is not characterized in a ‘perfect’ way by Equation (1). In order to improve the agreement with experimental data, Equation (1) was modified to incorporate the influence of the matrix suction as Etan = E0
1−
ε r(s) f
ε r(s) εf 1− ε0
(2)
where r(s) is a function of the initial matrix suction. To evaluate this relationship Figure 10 shows the variation of the parameter r with the initial matrix suction of each sample. A linear relationship was found
515
By comparison between fitted and calculated values of the parameter r, it was possible to evaluate the mean error in each case. The maximum error in the predicted value of r with respect to the fitted value was equal to 5.6% (sample M(4) s = 300 kPa) indicating that Equation (4) can be used to describe the variation of the r parameter with the matrix suction. In addition, results indicate that Equation (5) could reproduce in a realistic manner the stiffness response of compacted kaolin samples during shearing.
0.45 0.4
Parameter r
0.35
Experimental data
0.3 0.25 0.2 0.15 0.1 0.05 0 0
100
200
300
400
Initial matric suction (MPa)
Figure 10. Variation of the ‘‘r’’ parameter with the initial matrix suction.
to fit well with the experimental data which can be defined as: r(s) = r(0) + μ · s
(3)
where r (0) is the value of the r parameter for kaolin in a saturated condition, s is the initial matrix suction value (kPa) and μ is the slope of the linear relationship which depends of the type of material. Using a value of r for saturated conditions equal to 0.44 (a typical value for kaolin), the value of the slope μc an be mathematically expressed in terms of initial and final suction values as follows: μ=−
r(0)(smax − smin ) 2pref
Etan = E0
ε r(0)+μ·s f
ε r(0)+μ·s εf 1− ε0 ⎛
=
1−
ε r(0)−⎝ f
ε
1−
εf ε0
⎛
r(0)−⎝
CONCLUDING REMARKS
The influence of matrix suction on the pre-failure behaviour of compacted kaolin has been presented in this paper. The stiffness-decay curves show a clear dependence of the initial matrix suction. From experimental results it is clear that although all initial stress states are inside the inter-aggregate region of the SWRC (s < 1500 kPa), which is mainly controlled by macrofabric, the ‘volumetrically-stiffer’ effect of matrix suction leads to different stiffness responses. The influence of matrix suction has been incurporated in a conventional stiffness strain relationship (Equation 1) using a linear relationship for r (s) (Equation 3). Using the r parameter for saturated conditions (r (0)) the stiffness-decay curves of unsaturated samples can be determined. Good agreement between experimental and calculated stiffness-decay curves was obtained using Equation (5).
(4)
where pref is a reference pressure and is equal to 1 kPa, smax and smin are the maximum and minimum initial matrix suction values (in kPa). Using equations (3) and (4), equation (2) can be re-written as: 1−
5
⎞
r(0)(smax − smin ) ⎠·s 2pref ⎞
r(0)(smax − smin ) ⎠·s 2pref
(5)
Equation (5) defines a simple stiffness-strain relationship for compacted kaolin in terms of tangent Young’s modulus Etan .
REFERENCES Atkinson, J.H. & Sallfors, G. 1991. Experimental determination of soil properties. General report to Session 1. Proc. 10th ECSMFE, Florence 3, pp. 915–956. Atkinson, J.H. 2000. Non-linear soil stiffness in routine design. 40th Rankine Lecture, Geotèchnique 50 (5), pp. 487–508. Bishop, A.W. & Henkel, D.J. 1957. The measurement of Soil properties in the triaxial cell. Edward Arnold (Publishers) Ltd. London. Burland, J.B. & Ridley, A.M. 1996. The importance of suction in soil mechanics. Proc. 12th Southeast Asian Geotechnical Conference, May, Kuala Lumpur. Chandler, R.J., Crilly, M.S. & Montgomery-Smith, 1992. A low-cost method of assessing clay desiccation for lowrise buildings. Proc. Instn. Civ. Engng, 92;2; 82–89. Colmenares, J.E. & Ridley, A. 2002. Stress-strain and strength relationships for a reconstituted clayey silt. UNSAT 2002 (Brazil), pp. 481–484 Gens, A., Alonso, E.E., Suriol, J. & Lloret, A. 1995. Effect of structure on the volumetric behaviour of a compacted soil. Proc. Int. Conf. Unsaturated Soils, Paris, 83–88. Herrera, A.F. 2004. Estudio experimental del comportamiento volumétrico de muestras de caolín compactadas
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sometidas a proceso de humedecimiento. Bachelor Dissertation, National University of Colombia. Hilf, J.W. 1956. An investigation of pore water pressure in compacted cohesive soils. Tech. memo 654, U.S. Dept Interior. Mair, R.J. 1993. Developments in geotechnical engineering research: applications to tunnels and deep excavations. Unwin memorial Lecture 1992. Proc. Inst. Civ. Eng., 3, pp. 27–45. Pineda, J.A. 2004. Influence of matric suction on the shear strength of a compacted soil (in Spanish). MSc Thesis in Soil Mechanics, National University of Colombia, Bogotá, pp. 120. Pineda, J.A. & Colmenares, J.E. 2005a. Influence of suction on shear strength of a compacted soil under unconfined condition. Part 1: Experimental results. Int. Symp. EXPERUS2005, Trento, pp. 215–220. Balkema. Pineda, J.A. & Colmenares, J.E. 2005b. Influence of suction on shear strength of a compacted soil under unconfined condition. Part 2: Shear strength prediction. Int. Symp. EXPERUS2005, Trento, pp. 215–220. Balkema. Pineda, J.A. & Colmenares, J.E. 2006. Stress-strain-suction behaviour of two clayey materials under unconfined
conditions. Proc. UNSAT 2006, Phoenix Arizona, ASCE Geotechnical Special publication No 147, pp. 1109–1120. Pineda, J.A. 2007. Calibration and performance of bender/extender elements. Internal report, UPC. Pineda-Jaimes, J.A. 2003. An Experimental study of the volumetric behavior of a shallow clay from Bogotá basin following a drying path (in Spanish). MSc Thesis in Soil Mechanics, National University of Colombia, Bogotá. Ridley, A.M., Burland, J.B. & Monroe, A.S. 1995. Unconfined compression tests with pore pressure measurements. Proc. 11th African Regional Conference. SMFE. Cairo. Romero, E., Gens, A. & Lloret, A. 1999. Water permeability, water retention and microstructure of unsaturated compacted Boom clay. Engineering Geology, (54), 117–127. Thom, R., Sivakumar, R., Sivakumar, V., Murray, E.J. & Mackinnon, P. 2007. Pore size distribution of unsaturated compacted kaolin: the initial states and final states following saturation. Technical Note Gèotechnique 57 (5), pp. 469–474.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Influence of hydraulic paths on the low-strain shear modulus of a stiff clay J.A. Pineda, A. Lima & E. Romero Department of Geotechnical Engineering and Geosciences, Universitat Politècnica de Catalunya, Barcelona, Spain
ABSTRACT: This paper shows the results of an experimental programme aimed at evaluating the low-strain shear modulus of a stiff clay (Boom clay, Belgium) and its dependency on water content changes (or, alternatively, degree of saturation or suction) and hydraulic history. Resonant column and bender element tests were carried out at different hydraulic states. Drying and wetting paths were followed using the vapour equilibrium technique, in which samples were allowed to equalise in sealed chambers at controlled relative humidity (44% to 97%). Time domain technique has been used to determine the travel time in bender element tests. The evolution of the shear modulus was carefully monitored along these hydraulic paths. Shear moduli results and their dependence on water content (suction or degree of saturation) and stress/hydraulic history, are discussed and interpreted. In addition, discrepancies observed in the results between the two dynamic techniques are evaluated and discussed.
1
INTRODUCTION
Belgium investigates the design for disposal of its High Level Radioactive Waste in a deep clay formation, the ‘Boom clay’ (Mol, Belgium). To study this clay, an underground laboratory at 230 m depth was constructed (HADES, High Activity Disposal Experimental Site). This Tertiary clay is located between 190 and 210 m deep and belongs to the Lower Oligocene period. This formation is the subject of an extensive research programme dealing with all phenomena that may possibly affect the performance of this potential disposal site during gallery construction and final operation. Specifically, during excavation of the deep underground facility some de-saturation can be induced on the formation by ventilation in the galleries. On the one hand, it is necessary to examine more systematically partial saturation consequences on the hydro-mechanical response of natural Boom clay. On the other hand, the low-strain shear modulus is of great importance for geotechnical analysis due to the non-linear behaviour of soils. In addition to its well known dependence on strain level and confining stress, water content—or, alternatively, degree of saturation or suction—and temperature play an important role on this parameter, especially in water and heat sensitive geomaterials. Regarding these aspects, the study of the influence of wetting and drying paths on the evolution of the low-strain shear modulus is important to monitor degradation and stiffness loss due to cyclic geoenvironmental actions. This paper shows results of an experimental programme aimed at evaluating the low-strain shear
modulus of natural Boom clay and its dependency on water content changes and hydraulic history. The study was performed using two low-strain dynamic techniques, namely, resonant column equipment under torsional mode of vibration and pulse transmission/ detection technique using bender elements. In addition, it presents the detailed characterisation of the stiff clay (microstructural analysis and water retention properties). The results obtained are evaluated and discussed.
2 2.1
TESTED MATERIAL AND EXPERIMENTAL PROGRAMME Basic characterisation and porosimetry
Boom clay presents a clay fraction between 30% and 70% (average 55%). From this percentage, illite is the main mineral (50%), followed by smectite (30%), inter-stratification of illite-smectite and kaolinite (10%). Non-clayey fraction is composed of quartz (25%) and feldspar (Coll, 2005). Table 1 summarises the basic characterisation and the main volumetric and gravimetric properties of the natural material, which is slightly overconsolidated. A mercury intrusion porosimetry test was performed on an ‘AutoPore IV 9500—Micromeritics Instrument Corp.’ porosimeter to characterise the porosity network of a freeze-dried sample. Figure 1 presents the pore size density function plotted against the entrance pore size. The graphic shows one dominant pore mode at 90 nm, as expected for a matrix type microstructure.
519
Table 1.
1000
Main properties of natural Boom clay.
WP4 equipment
drying
Value
Density, ρ Dry density, ρd Gravimetric water content, w Initial total suction, Density of soil solids, ρs Void ratio, e Porosity, n Degree of saturation, Sr Liquid limit (SBCW), wL Plasticity index, PI
Total suction (MPa)
Property
1.99 to 2.05 Mg/m3 1.65 to 1.71 Mg/m3 21 to 25% 2–4 MPa 2.67 Mg/m3 0.560 to 0.618 0.358 to 0.382 91 to 100% (55.7 ± 0.9)% (26.9 ± 1.0)%
wetting
Vapour equilibrium technique (LiCl)
drying
100
wetting
10
1 0
Figure 2.
1.00
5
10 15 Water content, w (% )
20
25
Water retention curve for natural Boom clay.
Pore size density function, - e nw`/
Natural Boom Clay
by Cardoso et al. (2007). Figure 2 shows the drying and wetting branches of the water retention curve. A small hysteretic loop between drying and wetting paths for suction values higher than 20 MPa is observed.
0.80
0.60
0.40
2.3 Experimental programme to evaluate the shear modulus Gmax
0.20
The influence of hydraulic paths on the shear modulus was studied by using two different techniques. Resonant column and bender element tests were carried out on samples starting at different initial states. Besides evaluating the influence of relatively small total suction changes on shear stiffness, resonant column tests also allowed studying the influence of the stress state. On the other hand, the water content dependency on the shear modulus Gmax along a drying/wetting cycle was studied using bender element transducers on a sample that was subjected to a previous drying process. A relatively small sample size was chosen to ensure a faster equalisation along the hydraulic paths. The hydraulic cycle was applied using vapour equilibrium technique. The procedures and results will be described hereafter.
0.00 1
10
100
1000
10000
Entrance pore size, x (nm)
Figure 1.
2.2
Pore size density function of natural Boom clay.
Water retention properties
The soil water retention curve was obtained by a chilled-mirror dew-point psychrometer (WP4, Decagon Devices, Inc, USA) under unstressed conditions. This instrument measured the temperature at which condensation first appeared (dew-point temperature) of an environment in equilibrium with a sample (37 mm in diameter and 7 mm height). An air drying procedure was followed to induce suction increase. The wetting path was followed by adding small water drops to the sample. With this procedure, the range of total suction studied was between 4 MPa and 100 MPa. Higher suction data were obtained via vapour equilibrium technique (Delage et al, 1998; Romero, 2001). This technique is based on the control of the relative humidity inside a closed system, in which the soil is immersed. In our case, lithium chloride (LiCl) was used to apply a relative humidity of around 15%. Readings of total suction on WP4 were registered after 24 hours to ensure sample equalisation, and data corrected according to the calibration equation proposed
3 GMAX RESULTS USING RESONANT COLUMN Resonant column tests at constant water content were performed to obtain shear moduli variation on a wide range of small shear strains (≤10−3 %). The influence of degree of saturation was evaluated using two different samples that were previously equilibrated at different relative humidity values (corresponding to total suctions of 4 and 10 MPa). The description of the equipment is detailed in Suriol (1993). The main properties of samples used in resonant column tests are indicated in Table 2 where the
520
Table 2. Main properties of Boom clay samples tested in resonant column tests. Samples (n◦ )
ψ (MPa)
w0 (%)
e
1
4∗
21.35
0.58
2
10
15.21
0.62
∗
σ3 (kPa)
G (MPa)
200 700 200 700
300 340 360 420
Initial condition of Boom clay sample.
Low-strain s hear modulus, G (MPa)
500
40 0
30 0 20 0 Sample 1
total suction 10MPa (vertical): 0.2MPa 0.7MPa 100 Sample 2 natural state (vertical): 0.2MPa 0.7MPa 0 1E-005
3E-005
0.0001 0.0003 0.001 Shear strain (%)
0.003
0.01
Figure 3. Variation of shear modulus Gmax with stress level and suction changes.
confining stress values applied were 200 and 700 kPa. Samples were 38 mm in diameter and 76 mm in height. Figure 3 shows the low-strain shear modulus plotted against the shear strain. Test results are also summarised in Table 3. As observed, comparable increases in the shear stiffness were obtained when increasing confining stress and total suction. 4
to obtain the variation of water content, void ratio and degree of saturation. Moreover, relative humidity and temperature were monitored using a hygrometer installed inside the desiccator (refer to Figure 4). Shear modulus Gmax was evaluated by means of bender element transducers developed to determine the shear wave velocity of soils (Shirley & Hampton, 1978). In this technique, two polarised piezoceramic transducers (one transmitter and one receiver) are used to transmit and capture a dynamic signal which travels through the soil sample. The time delay (or travel time) between emitted and received signals is used to determine the shear wave velocity (Vs ) where the travel length has been commonly taken as the tip-totip distance between piezoceramics (e.g., Viggiani & Atkinson, 1995; Jovicic et al, 1996). Thus, the lowstrain shear modulus (Gmax ) can be obtained from the total density (ρt ) and the shear wave velocity (Gmax = ρt Vs2 ). In this study a pair of ‘bender-extender’ transducers (Lings & Greening, 2001) designed at Bristol University, UK, were used to determine the shear wave velocity of Boom clay samples. Travel time was obtained form the output signal by direct detection of the first significant deflection. To avoid masking the true travel time due to near field effects (SanchezSalinero et al, 1986) a sine pulse with a high frequency of 40 kHz (amplitude = 20Vpp ) was used as input signal. By using this high input frequency f , the wave number Rd = lf /Vs , where l is the travel distance, was higher than 1.5 as recommended by Arulnathan et al. (1998). Input signal was generated and emitted by a programmable function generator, while both input and output signals were acquired through a digital oscilloscope. Due to the good quality of the output signal further amplification was not necessary. Figure 4 shows the setup used during the application of hydraulic paths and bender element tests presented in this paper. Figure 5 shows the evolution of the shear wave velocity (Vs ) with the gravimetric water content (w)
GMAX RESULTS USING BENDER ELEMENTS
As described in section 2.3, sequential bender element tests were performed following a drying/wetting cycle on a sample (38 mm in diameter and 28 mm high) that was previously dried. This drying process originated some degradation of the sample, which ended in a slightly larger initial void ratio of e = 0.68. The starting water content was w = 19.5% (degree of saturation around 75%). An air drying process was followed at a relative humidity of the laboratory of 50% and T ≈ 20◦ C. Distilled water was used to transfer water vapour inside a desiccator and induce the progressive wetting of the sample. Volume and mass measurements were registered during the application of the hydraulic paths in order
Figure 4. Setup of bender element tests. Bender element tests during the application of hydraulic paths.
521
500 Micro-Cracks opening
400 300
Sample broken
Initial state
200 Drying Wetting
100 0 0
2
4
6
8
10
12
14
16
18
20
22
24
Gravimetric water content (%)
Figure 5. Variation of shear wave velocity with gravimetric water content along drying-wetting paths.
Shear wave velocity, Vs (m/s)
600
Drying Wetting
550 500 450 400 350
Cracks opening
INITIAL STATE
300 250 200 0,5
0,55
0,6
0,65
0,7
Void ratio (e)
Figure 6. Variation of shear wave velocity with void ratio along drying-wetting paths.
during the application of the drying and wetting paths. As complementary information, the Vs —void ratio (e) relationship is presented in Figure 6. The evolution of the shear wave velocity displays a hysteretic behaviour during the application of the hydraulic cycle. For the initial condition (w = 19.5%, e = 0.68) the measured shear wave velocity was equal to 326 m/s. From this point on, shear wave velocity shows a quasi-linear increase as water content decreases. On the other hand, as shown in Fig. 6, this increase in Vs is also associated with the decrease of void ratio observed during the shrinkage path. Once a void ratio of e = 0.55 is reached, a further increase in Vs is detected, which is only associated with the decrease in water content. It is assumed that for reductions in water content beyond 6%, in which no appreciable volume changes were detected (near the shrinkage limit), changes in Vs are a consequence of the changes in stiffness of the clay aggregations (microstructure scale). This statement is based on the assumption the water content is held within clay aggregations at these relatively high total suction values (around 100 MPa, as observed in Figure 2). During the first stage of the wetting path, Vs quickly reduced, as a consequence of crack opening that could be detected (see Figure 6). Subsequent wetting, led to a
faster decrease of the shear wave velocity compared to the drying path. Comparison of both drying and wetting paths demonstrate clearly the hysteretic behaviour of Vs for Boom clay subjected to hydraulic effects. Crack opening also evolved on progressive wetting, leading to sample breakage during the seventh wetting step (see Figure 5). It is assumed that these microcracks could also affect the observed response, due to the fact that Vs is transmitted trough the solid structure of the material. Final values before sample breakage were Vs = 289 m/s, w = 13.6% and e = 0.64. Figure 7 shows a comparison of the results using both techniques. Shear strains for resonant column were obtained directly from the torsional motion of the apparatus, while in the case of bender elements the determination of shear strain was based on the piezoceramic properties, bender size and sample size. Several authors have determined that strain applied for bender elements could be lower than 0.001% (e.g., Dyvik & Madhus, 1985). In our case, based on the ceramic porperties (PZT-5B piezoceramic; Vernitron, 1992) and the dimensions of the transducer (length, width and thickness) the strain generated by the transmitter elements was about 0.001% for an input voltage of 20Vpp . This value is in agreement with the upper limit suggested (e.g., Dyvik & Madhus, 1985; Sulkorat, 2007). In addition, it is also expected that deflections generated in receiver elements are always smaller due to signal attenuation through the soil sample. As shear strain in the receiver element is unknown, the strain used to compare resonant column results with bender element tests was the one obtained for the transmitter element (0.001%). As observed in Figure 7, shear moduli Gmax show a strong dependency on water content (the initial value of 200 MPa increases to a maximum of 524 MPa at the end of the drying path). As previously indicated, this increase in shear stiffness was also a consequence of the void ratio decrease observed on drying. On the other hand, the degradation induced on the wetting path on the unconfined sample, led 600
Shear modulus, G (MPa)
Shear wave velocity, Vs (m/s)
Stiffness dominated by smaller voids of claymicrostructure
600
End of drying : w = 4.8% ; e = 0.55, Sr ≈0.25
500
Wetting path
400 300 Drying path Initial state : w =19.5% ; e = 0.68, Sr≈0.75
200
Final state : w =13.60% ; e = 0.64, Sr≈0.55
100 0 1,E-05
Natural BC 200kPa Dried sampe BC 200kPa, S=10MPa Weathered BC Drying
1,E-04
Natural BC 700kPa Dried sample BC 700kPa, S=10MPa Weathered BC Wetting
1,E-03
1,E-02
1,E-01
Shear strain, (%)
Figure 7. Comparison between shear moduli Gmax obtained with resonant column and bender elements.
522
to a final shear modulus of 152 MPa, considerable lower than the obtained during the drying path at equivalent water content. Shear moduli results using both techniques compare well, despite the degradation problems detected on the unconfined sample.
the European Commission, EU Programme of High Level Scholarships for Latin America, id number E04D027285CO.
5
Arulnathan, R., Boulanger, R.W. & Riemer, M.F. (1998) Analysis of bender element tests. ASTM Geotechnical Testing Journal, vol XXI, n 2, pp. 120–131. Cardoso, R., Romero, E., Lima, A., Ferrari, A. (2007). A comparative study of soil suction measurement using two different hight-range psychrometers. Mechanics of unsaturated soils. Weimar. Coll, C. (2005) Endommagement des Roches Argileuses et Perméabilité Induite au Voisinage d’Ouvrages Souterrains, PhD Thesis, Université Joseph Fourier, Grenoble. Delage, P., Le, T.-T., Tang, A.-M., Cui, Y.-J. & Li, X.-L. (2007). Suction effects in deep Boom Clay block samples. Géotechnique 57, n 1, 239–244. Lings, M.L. & Greening, P.D. (2001) A novel bender/extender element for soil testing. Technical Note Geotechnique, 51, n 8, pp. 713–717. Romero, E.E. (2001) Controlled suction techniques. Proc. 4◦ Simposio Brasileiro de Solos Nao Saturados. Gehling and Schnaid Edits. Porto Alegre, Brasil, pp. 535–542. Sanchez-Salinero, I., Roesset, J.M. & Stokoe, K.H. (1986) Analytical studies of body wave propagation and attenuation. (Geotechnical Engineering Report N0. GR86-15) Civil Engineering Department, University of Texas at Austin. Shirley, D.J. & Hampton, L.D. (1978) Shear-wave measurements in laboratory sediments. J. Acoustical Soc. Am. 63, n 2, pp. 607–613. Sukolrat, J. (2007) Structure and destructuration of Bothkennar clay. PhD Thesis, University of Bristol, UK, 396p. Suriol, J. (1993). Medida de la deformabilidad de suelos mediante el equipo de columna resonante. Revista de Obras Públicas, n 3 (319) 140, pp. 57–66, Madrid. Vernitron (1992) Ceramic acoustic elements in bimorph and multibimorph, for pick up cartridges, microphones paging systems and other law frequency uses. Bulletin 66012/D. Viggiani, G. & Atkinson, J.H. (1995) Interpretation of Bender Element Tests. Geotechnique, 45, n 1, pp. 149–154.
SUMMARY AND DISCUSSION
The main properties of the material used in the experimental programme (natural Boom clay) were described in detail (initial state, water retention properties and pore size distribution). Shear stiffness results along drying and wetting paths were continuously monitored using bender elements installed inside a desiccator. The results were compared with resonant column data, in which total suction effects also induced higher shear stiffness. A quite good agreement was observed between the different techniques used, despite some degradation was detected in the unconfined sample with bender elements. The drying results showed an important dependency of the shear stiffness with water content and void ratio. At the ultimate drying stage, the stiffness increased only as a consequence of water content changes, due to the fact that no important volume changes were detected below w = 6% (near the shrinkage limit). This response was assumed to be associated with the increase in stiffness of the clay aggregations, where water is held at elevated total suctions (around a total suction of 100 MPa). ACKNOWLEDGEMENTS The work described has been financially supported by EIG-EURIDICE/SCK.CEN through a PhD collaboration with UPC, which is greatly acknowledged. The first author acknowledges the financial support provided by ALBAN PROGRAMME grants from
REFERENCES
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Drying and wetting effects on shear wave velocity of an unsaturated soil J. Xu, C.W.W. Ng & S.Y. Yung Department of Civil Engineering, The Hong Kong University of Science and Technology, HKSAR
ABSTRACT: Measurements of shear wave velocity provide a simple and direct way to determine the small strain shear modulus of a soil. Shear wave velocity of an unsaturated soil are influenced by many factors, such as the confining stresses in the plane of shear, void ratio and matric suction. The effects of confining pressure, void ratio and matric suction on shear wave velocity have been studied by many researchers. However, as far as the authors are aware, drying and wetting effects on shear wave velocity have rarely been studied. In this study, drying and wetting tests at constant net mean stress were conducted on an unsaturated Completely Decomposed Tuff (CDT) using a modified triaxial apparatus equipped with three pairs of bender elements. Drying and wetting effects on multidirectional shear wave velocities and degree of stiffness anisotropy are investigated.
1
INTRODUCTION
Shear waves provide a simple and direct way of determining the small strain shear modulus (G0 ) of a soil. The velocities of shear waves propagating in different planes and polarizations of a soil specimen (νs(ij) , where i is the direction of wave propagation and j is the direction of particle motion) can be measured by bender elements (Pennington et al. 2001, Ng et al. 2004). Previous studies found that the shear wave velocity propagating in a completely dry or saturated soil depends on the effective stresses in the directions of wave propagation and particle motion and that it is independent of the effect stress normal to the plane of shear (Roesler 1979, Stokoe et al. 1995, Jamiolkowski et al. 1995). Increasing the confining pressure increases shear wave velocity (Hardin & Richart 1963, Leong et al. 2004). In addition to confining stresses, void ratio also has an effect on the shear wave velocity. Different void ratio functions have been proposed to account for the influence of the void ratio on shear wave velocity in saturated soils (Hardin & Drnevich 1972, Shibuya et al. 1997). Considering all these factors, Ng & Leung (2007) proposed a semiempirical equation relating the shear wave velocity to the state of a soil. They also conducted series of tests on saturated intact samples of a completely decomposed tuff (CDT) to study the degrees of inherent and stress-induced stiffness anisotropy and to investigate the effect of void ratio on shear wave velocities. Other than confining stresses and void ratio, the shear wave velocity propagating in an unsaturated soil is also significantly influenced by matric suction. Marinho et al. (1995) measured G0 in compacted
unsaturated London clay under zero confining stress using bender elements. They found that there was an initial rapid increase in G0 with increasing suction, followed by a leveling off or decline in G0 . This finding was similar to that of Picornell & Nazarian (1998), who investigated the influence of matric suction on G0 in coarse sand, fine sand, silt and clay using bender elements fixed inside a pressure-plate extractor. Cabarkapa et al. (1999) measured shear wave velocity and shear modulus of moist tamped quartz silt during isotropic loading and unloading tests at constant suctions using bender elements. At a given net mean stress, the measured G0 increased with an increase in suction but at a reducing rate. Many other researchers (Vinale et al. 1999, Mancuso et al. 2000, Vassallo & Mancuso 2000, Mancuso et al. 2002, Kim et al. 2003) also studied effect of suction on small strain behaviour of soils. Ng & Yung (2008) conducted isotropic compression tests on recompacted CDT at constant suctions, and measured the multidirectional shear wave velocities of CDT using 3 pairs of bender elements. They found that shear wave velocities all increased non-linearly with an increase in net mean stress but at a reducing rate. At any given net mean stress, shear wave velocities also increased non-linearly with increasing matric suction. Though the influence of suction on shear wave velocity has been investigated by many researchers, they were mainly limited to one direction, except for Ng & Yung (2008). Moreover, as far as the authors are aware, drying and wetting effects on shear wave velocity have rarely been studied, with exception of Vassallo et al. (2006, 2007a, 2007b). In this study, wetting and drying tests are carried out on unsaturated CDT using a modified triaxial apparatus equipped
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with three pairs of bender elements, to investigate the drying and wetting effects on multidirectional shear wave velocities.
2
TESTING EQUIPMENT
Figure 1 shows a schematic diagram of the modified triaxial testing system for testing unsaturated soils used in this study. The axis translation technique (Hilf 1956) was employed to control matric suction, so that cavitation could be avoided. Air pressure was controlled through a coarse low air-entry value corundum disk placed on top of a soil specimen, while water pressure was controlled through a saturated high air-entry value (3 bars) ceramic disk sealed to the pedestal of the triaxial apparatus. The conventional base pedestal was modified so that both a high-entry value ceramic disk and a bender element could be embedded into it. A spiral-shaped drainage groove that was 3 mm wide and 3 mm deep connected to the water drainage system was carved on the surface of the modified pedestal. Air bubbles that may have been trapped or may have accumulated beneath the high air-entry value ceramic disk due to diffusion during long periods of unsaturated soil testing could be removed by flushing de-aerated water along the spiral-shaped drainage groove. More details of the modified triaxial testing system and base pedestal are given by Ng & Yung (2008). In addition to taking conventional external measurements of axial strain using a Linear Variable Differential Transformer (LVDT), the modified triaxial apparatus was equipped with two axial and one radial
Hall effect transducers (Clayton et al. 1989) for measuring the local axial and radial displacements of each soil specimen. As a result, the current tip-totip travelling distance of shear waves and the volume change of each soil specimen can be determined throughout each test. Three pairs of bender elements were mounted on each soil specimen to measure the velocities of the shear waves propagating in different planes with different polarizations. The shear wave velocity, νs(vh) , was determined by a pair of bender elements incorporated in the top cap and base pedestal. The shear wave velocities, νs(hv) and νs(hh) , were evaluated by making use of a pair of bender element probes inserted into the mid-height surface of each soil specimen. Details of the bender element probes are given by Ng et al. (2004). An HP3563A control system analyzer was used as the shear wave generating and measuring system for the bender elements. The input signal consists of a single sinusoidal pulse with a frequency of 4 to 10 kHz. The range of frequency was selected to obtain a clear signal and to minimize the near field effect (Sanchez-Salinero et al. 1986). The transmitted and received signals of the shear wave propagating in the soil specimen were captured by the HP3563A control systems analyser simultaneously. The arrival time of shear wave was determined by measuring the peak-to-peak time distance between the transmitted and received signals (Callisto & Rampello 2002, Ng & Yung 2008). The traveling distance was determined as the current tip-to-tip distance between the transmitter and receiver bender elements (Dyvik & Madshus 1985, Viggiani & Atkinson 1995). 3
Load cell LVDT
3.1 Testing material
Frictionless loading rod
The testing material in this research is a completely decomposed tuff (CDT) extracted from a deep excavation site in Hong Kong. Figure 2 shows
Coarse porous disk Bender element (vs(vh)) Bender element probe (vs(hh), vs(hv)) Bender element (vs(vh)) High air-entry value disk Cell pressure
100
80
Percentage passing (%)
Top cap Specimen Hall effect transducer (radial) Hall effect transducer (axial) Base pedestal Air pressure Water outlet
TESTING MATERIAL AND SPECIMEN PREPARATION
Water inlet
60
40
20
0 0.001
0.01
0.1
1
10
Particle size (mm)
Figure 1. Schematic diagram of the modified triaxial system for testing unsaturated soils (Ng & Yung 2008).
Figure 2. 2008).
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Particle size distribution of CDT (Ng & Yung
Specimen preparation
Triaxial specimens, 76 mm in diameter and 152 mm in height, were prepared by moist tamping method at the optimum water content of 16.3%. Each soil specimen was compacted dynamically in ten layers directly onto the base pedestal of the triaxial cell in order to avoid any disturbance caused by transportation and to improve the contact between the specimen and the ceramic disk. The under-compaction method proposed by Ladd (1978) was adopted to achieve a more uniform specimen. The middle four layers of each soil specimen were compacted at the desired dry density, while the top three layers were compacted to be 4% denser than the desired dry density and the bottom three layers 4% looser. After sample preparation, the initial matric suction of soil specimen measured by a small tip tensiometer was about 54 kPa.
4
TESTING PROGRAM AND PROCEDURES
To study the drying and wetting effects on shear wave velocities of CDT, two drying and wetting tests were conducted on recompacted specimens at constant net mean stresses of 110 and 300 kPa. Each soil specimen was firstly brought to the desired net mean stress and then left for equalization at zero suction. The equalization stage was considered to be terminated when the changing rate of water content was less than 0.04% per day (Fredlund & Rahardjo 1993), which corresponded to a water flow of about 0.5 cm3 per day. Shear wave velocities were measured at the end of the equalization stage, and then the matric suction was increased to the next desired value. The matric suction was varied by changing pore water pressure while keeping cell pressure and pore air pressure constant. After the matric suction was changed, the soil specimen was left for equalization again. Upon completion of the drying phase up to a matric suction of 250 kPa, each test proceeded to the wetting phase. The drying and wetting tests consisted of many equalization stages. Measurements of shear wave velocities were performed at the end of each equalization stage.
TEST RESULTS AND DISCUSSION
5.1 Stress-dependent soil water characteristic curves (SDSWCCs) The soil-water characteristic curve (SWCC) represents the water retention ability of an unsaturated soil. A stress-dependent soil-water characteristic curve (SDSWCC) considers both the net normal stress effect and volume change of a soil specimen. Ng & Pang (2000) investigated the SDSWCCs of a completely decomposed volcanic (CDV), and found that the specimen subjected to a higher net normal stress possessed a higher air-entry value, lower rates of desorption and adsorption and a smaller hysteresis loop. During the drying and wetting tests at constant net mean stresses of 110 and 300 kPa, in addition to the measurements of shear wave velocities, total volume change and water volume change of each soil specimen were also measured and recorded. Thus, the SDSWCCs of the two recompacted CDT specimens subjected to net mean stresses of 110 and 300 kPa can be determined, as shown in Figure 3. It can be seen from Figure 3 that net mean stress has a significant influence on the SDSWCCs. The soil specimen under a higher net mean stress tends to possess a higher air-entry value. In Figure 3, the air-entry values of CDT are estimated as 55 and 85 kPa at net mean stresses of 110 and 300 kPa, respectively. When suction increases beyond the air-entry values, the two specimens start to desaturate but at different rates. The specimen subjected to 300 kPa net mean stress shows a lower desorption rate than the one under 110 kPa net mean stress. The reason for the above observations is probably that the soil specimen under higher net mean stress has a smaller average pore-size distribution and thus a better water retention ability (Ng & Pang 2000). Upon completion of the drying phase up to a matric suction of 250 kPa, the tests proceed to the wetting phase. At net mean stresses of both 110 and 300 kPa, there is a marked hysteresis between the drying and
100
S r (%)
3.2
5
Degree of saturation,
the particle size distribution of the CDT determined by sieve and hydrometer analyses. The material is yellowish-brown, slightly plastic, with a very small percentage of fine and coarse sand. The specific gravity (Gs ) of the material is 2.73. The liquid limit and plasticity index of the fines portion (finer than 425 μm) are 43% and 14%, respectively. According to the Unified Soil Classification System, the CDT is described as clayey silt (ML).
80
60
40 p -u a =110kPa p -u a =300kPa 20 1
10
100
1000
Matric suction, u a -u w (kPa)
Figure 3. Stress-dependent soil-water characteristic curves (SDSWCCs) of CDT (Ng et al. 2008).
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wetting curves. The size of the hysteresis loop appears to be smaller at the higher net mean stress. This is probably because of a less pronounced ink-bottle effect (Hillel 1982) and a smaller difference in the receding and advancing contact angles due to a smaller pore size distribution at a higher net mean stress (Ng & Pang 2000). The ink-bottle effect and the difference in the receding and advancing contact angles are the major causes of the formation of hysteresis in SDSWCCs. As a result, the resultant hysteresis loop is smaller for the specimen subjected to 300 kPa net mean stress. As shown in Figure 3, the end point of the wetting curve corresponding to the net mean stress of 110 kPa is lower than the corresponding starting point of the drying curve. This may be due to air being trapped in the soil specimen. In contrast, the end point of wetting curve almost returns to the starting point of the drying curve when net mean stress is 300 kPa. This is probably because it is easier to displace the air trapped in the small pores by capillary force than to displace the air trapped in the large pores (Ng & Pang 2000).
Shear wave velocity, νs(vh) (m/s)
450
(a)
400
Wetting
350 300 250
Drying
150 0
50
100
150
200
250
300
Matric suction, u a -u w (kPa)
Shear wave velocity, νs(hv) (m/s)
450
(b) Wetting
400 350 300
Drying
250
-u a =110kPa p(r-dw-p110) -u a =300kPa p(r-dw-p300)
200 150 0
50
100
150
200
250
300
Matric suction, u a -u w (kPa)
Drying and wetting effects on shear wave velocities
450
The variations of the measured shear wave velocities with matric suction during the two drying and wetting tests are shown in Figure 4. It can be seen that the variations of the shear wave velocities, νs(vh) , νs(hv) and νs(hh) , with matric suction follow a similar trend. The shear wave velocities increase with an increase in matric suction in a non-linear fashion at a reducing rate. At early stages of the drying process, i.e. when matric suction is relatively low, bulk water effects dominate the soil stiffness. Any increase in suction is practically equivalent to an increase in the confining pressure (Mancuso et al. 2002, Ng & Yung 2008). Therefore, shear wave velocities increase with an increase in matric suction. When drying continues, meniscus water effects become dominative. The meniscus water induces a normal force holding the soil particles together, so the soil specimen is compressed and the shear wave velocities increase. However, the induced normal force can not increase infinitely, due to the progressive reduction in the meniscus radius as suction increases (Mancuso et al. 2002, Ng & Yung 2008). Thus, the increasing rate of shear wave velocities becomes smaller when suction is higher. After drying to the maximum suction of 250 kPa, matric suction is reduced for wetting a soil specimen. The shear wave velocities, νs(vh) , νs(hv) and νs(hh) , all decrease with decreasing matric suction at a similar rate as that during drying. Similar to the SDSWCCs (see Fig. 3), there is a hysteresis between the drying and wetting curves of the variations of shear wave velocities with matric suction. At a same suction, the shear wave velocities measured during wetting phase
Shear wave velocity, νs(hh) (m/s)
5.2
-u a =110kPa p(r-dw-p110) -u a =300kPa p(r-dw-p300)
200
(c)
Wetting
400 350 300
Drying
250
-u a =110kPa p(r-dw-p110) -u a =300kPa p(r-dw-p300)
200 150 0
50
100
150
200
250
300
Matric suction, u a -u w (kPa)
Figure 4. Variations of shear wave velocities with matric suction during drying and wetting tests: (a) νs(vh) , (b) νs(hv) , (c) νs(hh) .
are consistently higher than those obtained during drying process. This is probably due to the irrecoverable volume compression induced during the drying and wetting cycle (Ng et al. 2008). During the drying process, both elastic and plastic compression take place, while only elastic swelling is resulted in the wetting process. It is noted from figure 4 that the shear wave velocities of CDT at a net mean stress of 300 kPa are consistently higher than those at a net mean stress of 110 kPa. This is because when the applied net normal stress is higher, the total volume shrinkage is larger. Thus, the soil is stiffer and the shear wave velocities are higher. Besides, at higher net mean stress, the changing rate of shear wave velocities with respect to matric suction is lower. For example, at net mean stress of
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110 kPa, the shear wave velocities, vs(vh) , vs(hv) and νs(hh) , increase by 48%, 46% and 47% as suction increases from 0 to 250 kPa, respectively. While at net mean stress of 300 kPa, the shear wave velocities, νs(vh) , νs(hv) and νs(hh) , only increase by 26%, 29% and 30%, respectively, for the same suction change. The reason is probably that the specimen with higher stiffness at a higher net mean stress would have a higher resistance to volume change due to drying and wetting (Ng et al. 2008). In an ideal elastic continuum, νs(hν) should be equal to νs(νh) . However, the measured value of νs(hν) is consistently higher than νs(νh) , as shown in Figure 4. The discrepancy between νs(hν) and νs(νh) may be due to the preferred orientation of soil particles in horizontal plane (Jardine et al. 1999, Ng & Leung 2007) or the different boundary conditions of different bender elements (Pennington et al. 2001, Ng & Yung 2008). 5.3
Drying and wetting effects on degree of stiffness anisotropy
In this paper, the degree of stiffness anisotropy is expressed as G0(hh) /G0(hv) or (νs(hh) /νs(hν) )2 . νs(hh) and νs(hv) are chosen for determining stiffness anisotropy, because they had the same boundary conditions, frequency and travelling distance (Pennington et al. 2001, Ng et al. 2004). The variations of the degree of stiffness anisotropy with matric suction during the drying and wetting tests are shown in Figure 5. It can be seen from Figure 5 that the variations of the degrees of stiffness anisotropy with matric suction at different net mean stresses follow a similar trend. However, the degree of stiffness anisotropy at net mean stress of 300 kPa is consistently higher than that at net mean stress of 110 kPa by about 1%. Initially at zero suction, the degrees of stiffness anisotropy are 1.026 and 1.039 at net mean stresses of 110 and 300 kPa,
G0(hh) / G0(hv) or ( vs(hh) /vs(hv) )
2
1.06
Wetting 1.05
1.04
respectively. This stiffness anisotropy is probably the inherent stiffness anisotropy due to sample preparation, as discussed in Ng & Yung (2008). At a given net mean stress, when matric suction increases, the degree of stiffness anisotropy increases slightly at a gradually reducing rate, but the increase is smaller than 1%. Similar to the SDSWCCs (see Fig. 3), there is also a hysteresis between the drying and wetting curves. Though the changes in the degree of stiffness anisotropy and the size of hysteresis loop are very small, the trends are clear. Therefore, drying and wetting appear to have small effects on the degree of stiffness anisotropy.
6
CONCLUSIONS
Drying and wetting effects on the shear wave velocities of unsaturated CDT were studied by two drying and wetting tests at constant net mean stress. Three pairs of bender elements were used to measure the multidirectional shear wave velocities, νs(vh) , νs(hν) and νs(hh) . During the drying and wetting tests, the shear wave velocities increased with an increase in matric suction at a reducing rate. Moreover, the changing rate was lower at higher net mean stress. Similar to the SDSWCC, there was a hysteresis between the drying and wetting curves of the variations of shear wave velocities with matric suction. The shear wave velocities measured during the wetting phase are consistently higher than those obtained during the drying process, probably due to the irrecoverable volume shrinkage induced in the drying and wetting cycle. The degrees of inherent stiffness anisotropy of recompacted CDT specimens were 1.026 and 1.039 at net mean stresses of 110 and 300 kPa, respectively. The degree of stiffness anisotropy increased slightly with matric suction at a reducing rate during drying and wetting tests at constant net mean stress, but the increase was smaller than 1%. The degree of stiffness anisotropy also showed hysteretic characteristic during drying and wetting tests, though the size of hysteresis loop was very small. It can be concluded that drying and wetting seem to have small effects on the degree of stiffness anisotropy.
Drying
1.03
p -u a =110kPa (r-dw-p110) p -u a =300kPa (r-dw-p300)
ACKNOWLEDGEMENTS
1.02 0
50
100
150
200
250
300
Matric suction , u a -u w (kPa)
Figure 5. Variations of degree of stiffness anisotropy with matric suction during drying and wetting tests (Ng et al. 2008).
The authors would like to acknowledge the financial support from research grants CA-MG07/08.EG01 and DAG04/05.EG31 provided by the Hong Kong University of Science and Technology.
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REFERENCES Cabarkapa, Z., Cuccovillo, T. & Gunn, M. 1999. Some aspects of the pre-failure behavior of unsaturated soil. Proc. of II Int. Symp. On Prefailure Deformation Characteristics of Geomaterials 1: 159–165. Callisto, L. & Rampello, S. 2002. Shear strength and smallstrain stiffness of a natural clay under general stress conditions. Géotechnique 52(8): 547–560. Clayton, C.R.I., Khatrush, S.A., Bica, A.V.D. & Siddique, A. 1989. The use of Hall effect semiconductors in geotechnical engineering. Geotechnical Testing Journal 12(1): 69–76. Dyvik, R. & Madshus, C. 1985. Laboratory measurement of Gmax using bender elements. Proceedings of ASCE Annual convention: Advances in the Art of Testing Soils under Cyclic Condition: 186–196. Detroit. Fredlund, D.G. & Rahardjo, H. 1993. Soil mechanics for unsaturated soils. New york: Wiley-Interscience Publication. Hardin, B.O. & Richart, F.E. 1963. Elastic wave velocities in granular soils. Journal of the Soil Mechanics and Foundations Division, ASCE 89: 33–65. Hardin, B.O. & Drnrvich, V.P. 1972. Shear modulus and damping in soils: measurements and parameter effects. Journal of Soil Mechanics and Foundation Engineering, ASCE 98: 603–624. Hillel, D. 1982. Introduction to soil physics. San Diego, CA, USA: Acadamic Press. Jamiolkowski, M., Lancellotta, R. & Lo Presti, D.C.F. 1995. Remarks on the stiffness at small strains of six Italian clays. In S. Shibuya, T. Mitachi and S. Muira (eds.), Proceedings of International Symposium on Pre-failure Deformation of Geomaterials 2: 817–836. Jardine, R.J., Kuwano, R., Zdravkovic, L. & Thornton, C. 1999. Some fundamental aspects of the pre-failure behaviour of granular soils. Proc. Int. Symp. on Prefailure Deformation of Geomaterials 2: 1077–1111. Kim, D.S., Seo, W.S. & Kim, M.J. 2003. Deformation characteristics of soils with variations of capillary pressure and water content. Soils and Foundations 43(4): 71–79. Ladd, R.S. 1978. Preparing test specimens using undercompaction. Geotechnical Testing Journal, ASTM 1: 16–23. Leong, E.C., Yeo, S.H. & Rahardjo, H. 2004. Measurement of wave velocities and attenuation using an ultrasonic test system. Canadian Geotechnical Journal 41(5): 844–860. Mancuso, C., Vassallo, R. & d’Onofrio, A. 2000. Soil behaviour in suction controlled cyclic and dynamic torsional shear tests. Proc. of 1st Asian Regional Conference on Unsaturated Soils, Singapore: 539–544. Mancuso, C., Vassallo, R. & d’Onofrio, A. 2002. Small strain behavior of a silty sand in controlled-suction resonant column—torsional shear tests. Canadian Geotechnical Journal 39(1): 22–31. Marinho, E.A.M., Chandler, R.J. & Crilly, M.S. 1995. Stiffness measurements on an unsaturated high plasticity clay using bender elements. Proceedings of the 1st International Conference on Unsaturated Soils, UNSAT ’95, Paris, 2: 535–539. Ng, C.W.W. & Pang, Y.W. 2000. Experimental investigations of the soil-water characteristics of a volcanic soil. Canadian Geotechnical Journal 37(6): 1252–1264.
Ng, C.W.W., Leung, E.H.Y. & Lau, C.K. 2004. Inherent anisotropic stiffness of weathered geomaterial and its influence on ground deformations around deep excavations. Canadian Geotechnical Journal 41(1): 12–24. Ng, C.W.W. & Leung, E.H.Y. 2007. Determination of shear-wave velocities and shear moduli of completely decomposed tuff. Journal of Geotechnical and Geoenvironmental Engineering. ASCE 133(6): 630–640. Ng, C.W.W. & Yung, S.Y. 2008. Determination of the anisotropic shear stiffness of an unsaturated decomposed soil. Géotechnique 58(1): 23–35. Ng, C.W.W., Xu, J. & Yung, S.Y. 2008. Effects of wettingdrying and stress ratio on anisotropic small strain stiffness of an unsaturated soil. Submitted to Canadian Geotechnical Journal. Pennington, D.S., Nash, D.F.T. & Lings, M.L. 2001. Horizontally mounted bender elements for measuring anisotropic shear moduli in triaxial clay specimen. Geotechnical Testing Journal 24(2): 133–144. Picornell, M. & Nazarian, S. 1998. Effects of soil suction on the low-strain shear modulus of soils. Proceedings of the 2nd International Conference on Unsaturated Soils, UNSAT ’98, Beijing, China, 2: 102–107. Roesler, S.K. 1979. Anisotropic shear modulus due to stress anisotropy. J. Geotech. Eng. Div., Am. Soc. Civ. Eng. 105(7): 871–880. Sanchez-Salinero, I., Roesset, J.M. & Stokoe, K.H. 1986. Analytical studies of body wave propagation and attenuation. Report GR 86-15, University of Texas, Austin. Shibuya, S., Hwang, S.C. & Mitachi, T. 1997. Elastic shear modulus of soft clays from shear wave velocity measurement. Géotechnique 47(3): 593–601. Stokoe, K.H. II, Hwang, S.K., Lee, J.N.K. & Andrus, R.D. 1995. Effects of various parameters on the stiffness and damping of soils at small to medium strains. In S. Shibuya et al. (eds.), Proc., Int. Symp. on Pre-failure Deformation of Geomaterials 2: 785–816. Vassallo, R. & Mancuso, C. 2000. Soil behaviour in the small and the large strain range under controlled suction conditions. International Workshop on Experimental Evidence and Theoretical Approaches in Unsaturated Soils, Trento: 75–89. Vassallo, R., Mancuso, C. & Vinale, F. 2006. Effects of stressstrain history on the initial shear stiffness of an unsaturated compacted silt. Geotechnical Special Publication 147: 1145–1156. Vassallo, R., Mancuso, C. & Vinale, F. 2007a. Effects of net stress and suction history on the small strain stiffness of a compacted clayey silt. Canadian Geotechnical Journal 44 (4): 447–462. Vassallo, R., Mancuso, C. & Vinale, F. 2007b. Modelling the influence of stress-strain history on the initial shear stiffness of an unsaturated compacted silt. Canadian Geotechnical Journal 44(4): 463–472. Viggiani, G. & Atkinson, J.H. 1995. Interpretation of bender element tests. Géotechnique 45(1): 149–154. Vinale, F., D’Onofrio, A., Mancuso, C., Santucci de Magistris, F. & Tatsuoka, F. 1999. The pre-failure behaviour of soils as construction materials. Proc. of II Int. Symp. On Prefailure Deformation Characteristics of Geomaterials 2: 955–1007.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Effects of unsaturated soil state on the local seismic response of soil deposits F. D’Onza University of Glasgow, UK
A. d’Onofrio & C. Mancuso University of Naples Federico II, Italy
ABSTRACT: This work is part of a wider research program in progress for several years at the Dipartimento di Ingegneria Idraulica, Geotecnica e Ambientale (DIGA) of the Università degli Studi di Napoli Federico II in Naples, Italy focusing on the analysis of the effects of partial saturation on the seismic response of soil deposits. This study is particularly relevant to the relatively high seismicity area of Naples (Italy), where unsaturated soils are often encountered. The paper summarises a parametric study based on the experimental results obtained during a comprehensive laboratory program carried out using a Resonant Column Torsional Shear device under suction controlled conditions. A set of 1D linear analyses were carried out and interpreted in terms of a transfer function, in order to highlight the role played by the unsaturated condition on the amplification function. Finally a synthesis of the results is attempted in order to quantify the effect of partial saturation on subsoils characterized by different plasticity index values. Results clearly show significant effects of the unsaturated state on the local seismic response in terms of both amplification ratio and natural frequency. This could be particularly relevant to the local response of deposits of limited thickness.
1
INTRODUCTION
During a seismic event, a key role in the wave propagation is played by the shallowest deformable soil deposits above the bedrock. The shallow soils act as a filter and significantly change the amplitudes and frequency content of the reference input motion registered on outcropping bedrock. Therefore, for a proper ground surface motion determination the subsoil geometry, as well as the stiffness and dissipative properties of the soil above the bedrock should carefully be determined. The natural shallow soil deposits are often located above the water table in a partially saturated state. In spite of this, the effects of suction are often ignored in the determination of local seismic response, due to the experimental difficulties in measuring the stress-strain behaviour of unsaturated soils at small strains. The influence of unsaturated soil conditions on local seismic response has been demonstrated here to be very relevant and justifies further efforts to investigate these effects. 2
EXPERIMENTAL EVIDENCE
A wide experimental programme aimed at analysing the effects of suction on the mechanical behaviour of
soils has been carried out and is still underway at the Dipartimento di Ingegneria Idraulica, Geotecnica e Ambientale (DIGA) of the Università degli Studi di Napoli Federico II in Naples, Italy. The main goal is the investigation of the effects of mean net stress and suction on the initial shear stiffness (G0 ) and damping ratio (D0 ) of soils with different plasticity indices. Different soils, in terms of particle grading, index limits and fabric, have been tested. These include a clayey silt and a silty sand compacted at the optimum water content following the standard and modified Proctor procedures respectively as well as a pyroclastic silty sand prepared by air pluviation technique and then saturated at constant volume. The main characteristics of the tested soils are summarised in Table 1. The experimental program has been carried out using a Resonant Column Torsional Shear apparatus properly modified to perform tests in suction controlled condition, by means of the axis translation technique. Details of this device can be found in Mancuso et al. (2002). G0 and D0 have been measured almost continuously, by resonant column tests, along various isotropic stress paths, including compressions and drying/wetting single stages or cycles. The main purpose of the experimental work has been the investigation of the influence of the stress state and history, in terms of
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Average properties of tested materials.
Material
Plasticity index, PI %
Water content, w %
250
Degree of saturation, Sr %
200 G0 (MPa)
Table 1.
150
Metramo silty sand Magispo clayey silt Pyroclastic silty sand
13.7
9.5
86.9
17.9
23.1
92.5
100 (ua-uw)s = 0 k Pa (ua-uw)s= 100 k Pa (ua-uw)s= 200 k Pa (ua-uw)s= 400 k Pa
50
0
55.2
100
a) 0 0
200
400 (p-ua) kPa
600
800
5 (ua-uw)s = 0 kPa (ua-uw)s = 100 kPa (ua-uw)s = 200 kPa (ua-uw)s = 400 kPa
D0h(%) p (% )
4
3
2
b) 1 0
100
200
300
400 500 p-ua (kPa)
600
700
800
Figure 1. a) Initial shear modulus, and b) initial damping ratio versus mean net stress at different suction. 250
200
G0 (MPa)
both suction and mean net stress, on the small strain behaviour of the tested soils. The observed behaviour during compression stages at constant suction is qualitatively similar to that of saturated soils. In normally consolidated conditions, G0 increases less than linearly while D0 decreases as the mean net stress increases at constant suction. This is shown, for example, in Figure 1 where the initial shear stiffness and the damping ratio measured on Magispo clayey sand are reported as a function of the applied mean net stress, (p − ua ) at constant suction, s. On the other hand, at equal mean net stress and in normally consolidated conditions, G0 increases and D0 decreases as suction increases. In more detail, the initial shear modulus seems to be differently influenced by the suction level. As an example, G0 values measured on the Magispo clayey silt are plotted against suction in Figure 2, which refers to experimental data shown in Figure 1. This figure plots the shear modulus as a function of both mean net stress at null suction (left diagram) and suction under a mean net stress equal to 200 kPa (right diagram). An S-shaped trend can be observed, which complies with the different arrangement of water and air within the voids and the interaction between water, air and soil skeleton as described in the following. In a saturated soil, Terzaghi’s principle of effective stress is valid and, in the presence of a positive value of suction, a curved air-water interface will exist at the soil boundary as the pore water is subjected to a pressure smaller than the surrounding air pressure. In this situation, a variation in suction at constant net stress changes both normal and tangential forces at the contacts between particles as it is equivalent to a variation in mean effective stress p . Similarly, at high degrees of saturation, the mechanical response is essentially influenced by bulk-water and thus the effects of an increase of suction, s, are those of an equal increase of mean effective stress. As suction increases and the soil starts to desaturate, bulk water is progressively replaced by menisci-water in the form of water lenses at the inter-particle contacts
150
100
50 experimental data -- simulation 0 100 200 0 [(p-ua) + (ua-uw) (kPa)]
Figure 2.
100
200 300 (ua-uw s) (kPa)
400
Initial shear modulus vs. suction.
resulting in a cohesive pull holding particles together. At low degree of saturation, the effect of menisci-water starts to become dominant and the significance of such cohesive inter-particle pull increases accordingly.
532
This is simplified by the Fisher’s model (1926) (which refers to two spherical particles with a water meniscus in between them), and Gili (1988) (which refers to more complex particle configurations and meniscus shapes). Such behaviour has a corresponding influence on the curve G0 : s. The way in which a real soil moves from a behaviour dominated by bulk-water to a behaviour dominated by menisci-water depends on the soil grading curve, mineralogy and, for the same soil in normally consolidated conditions, on the applied mean net stress. In any case it is possible to identify a defined suction value, s∗ , corresponding to the transition from a behaviour dependent on bulk water to a behaviour dependent on menisci-water. Together with the data gathered by the Authors, a number of other measurements of G0 in unsaturated normally consolidated soils have been presented in the literature. A detailed report about soils, compaction procedures and testing conditions relevant to these measurements can be found in Mancuso et al. (2002). All these data confirm the above described trend in terms of G0 versus suction. Once the suction exceeds the value s∗ , the variation of G0 with suction can be predicted by the relationship proposed by Mancuso et al. (2002): G0 (s) ∗ = {[1 − r] · e−β·(s−s ) + r}; G0 sat
1.0 e+2 RCTS - Sr controlled tests bender element tests bender element tests in TX cell RCTS - suction controlled tests
values
1.0 e+0
1.0 e-2
a)
1.0 e-4 20
r values
15
10
5
(s − s∗ ) ≥ 0 (1)
b)
0 0
where G0 sat is the value of stiffness corresponding to a suction equal to s∗ , β is a parameter that controls the rate of increase of G0 with suction (i.e. a measure of the soil sensitivity to suction changes) and r is the ratio between shear stiffness at very large values of suction and the shear stiffness at suction equal to s∗ . The relatively good fit of Equation 1 to the experimental data shown in Figure 2 indicates that this equation can properly describe the experimentally observed trend even for relatively high suction values. Equation 1 has also been used to interpret other data reported in the literature and described in Mancuso et al. (2002). The results of such analyses are shown in Figure 3 where the corresponding values of r and β are related to the Plasticity Index (PI) of each soil. Despite the variety of preparation procedures, testing conditions and techniques, a general trend can be detected in Figure 3. In particular, β decreases by about two orders of magnitude moving from coarse to fine grained soils (Fig. 3a); on the contrary r seems to be rather constant at least for relatively low plasticity soils (Fig. 3b). Best fitting equations, of both β and r values versus plasticity index, can be expressed as follows:
β = 0.1552 · (1 − 0.0199) · e−0.1284·PI + 0.0199 (2)
20
40
60
80
plasticity index, PI (%)
Figure 3.
(a) β vs. PI and (b) r vs PI.
r = 1.4081 · e0.0246·PI
(3)
Note that PI is expressed as percentage in Equation 2. Figure 4 shows the relationship between the shear stiffness at a generic suction s, normalized by the shear stiffness at zero suction, G0 (s)/G0 (0) versus suction for constant confining stress. This relationship is given by Equation 1 where the additional simplifying assumption of s∗ equal to zero is introduced. Two curves are shown in Figure 4 corresponding to the two different values of the plasticity index of 0% and 10% respectively with different values of β and r calculated from Equations 2 and 3. Note that the simplifying assumption that s∗ coincides with zero introduces a slight overestimation of the shear modulus at low suction values. As shown in Figure 4, an equal value of the normalized shear modulus G0 (s)/G0 (0) corresponds to different values of suction, depending on the values of β and r. Given the value of the normalised shear modulus G0 (s)/G0 (0) corresponding to a particular suction s in a generic soil (with parameter values βgen , rgen and PIgen ), it is possible to evaluate
533
3
2.00
PARAMETRIC ANALYSIS
0(s) /Ga0(0) G0((u a -u G ))/G 0 (0,p-ua) w),(p-u
1.90 1.80 1.70 1.60 1.50 1.40 1.30 1.20
PI Ip=0% PI Ip=10%
1.10 1.00
s
0
10
20
30
40
s eq 50
60
(ua-uw)s (kPa)
Figure 4. G0 (s)/G0 (0) as a function of suction for different values of PI. 2.1 G0 ((u a -u wG ),(p-u 0(s) /G 0(0) 0 (0,p-u a ) a ))/G
2.0 1.9 1.8 1.7 1.6 1.5 1.4 1.3
Ip=0% PI Ip=5% PI PI Ip=10%
1.2 1.1 1.0 0
10
Figure 5.
20
30
40
50
60
(u a -u ws) / * (kPa)
70
80
90
100
Ratio G0 (s)/G0 (0) versus equivalent suction.
the equivalent suction seq corresponding to the same value of the normalized shear modulus in a reference soil (with parameter values βref , rref and PIref ). Such equivalent suction seq can be related to the suction s in the generic soil. For relatively low-medium PI values it is reasonable to assume a constant r index. In this case, the expression of the equivalent suction is obtained as follows: G0 (seq ) G0 (s) = (4) G0 (0) gen G0 (0) ref (1 − r) · e e
−βgen ·s
−βgen ·s
=e
⇒ seq = seq =
+ r = (1 − r) · e
−βref ·seq
+r
(5)
⇒ βgen · s = βref · seq
βgen ·s βref
βgen ·s βref
−βref ·seq
(6) (7)
Representing G0 (s)/G0 (0) versus seq , a unique curve for every PI value is obtained once a βref is fixed (Fig. 5). This curve allows easy evaluation of the shear stiffness ratio G0 (s)/G0 (0) corresponding to a given suction whatever the soil.
A set of dynamic analyses have been carried out to assess the effects of partial saturation on the local seismic response of subsoils of different plasticity. Input conditions have been simplified as much as possible to isolate the effects of partial saturation from other affecting factors. With this aim, a series of one dimensional ground response analysis have been carried out on fictitious subsoils, assuming horizontal soil layering and SH wave propagation. Each fictitious soil deposit consist of an homogeneous material lying on the bedrock and has been divided in a number of layers to account for the influence of different confining stresses acting at different depths. Each layer consists of a continuous homogeneous single-phase visco-elastic linear material characterised in terms of initial shear modulus and damping ratio as a function of mean net stress and suction. The assumption of a linear response ensures the independency of the analyses on the input motion characteristics. A 30 m depth and a shear wave velocity of 800 m/s was assumed for the bedrock. Constant profiles of suction with depth have been adopted since preliminary analyses demonstrate a negligible influence of suction variation with depth on the seismic response. To take into account the dependency of G0 on suction and stress state, it has been first necessary to model the variation of G0 with stress state in the saturated condition and then take into account the additional effect of suction through Equation 1. The dependency of shear modulus on confining stress in saturated conditions has been modelled using the relationship proposed by Rampello et al. (1994): G0 =S pr
p pr
n (8)
where pr is a reference pressure, here taken equal to 100 kPa and S and n are stiffness dimensionless parameters which describe respectively the initial stiffness evaluated at reference pressure, and the sensitivity of G0 on stress state. A relationship between the dimensionless parameters S and n of Equation 8 and the plasticity index has been proposed by d’Onofrio & Silvestri (2001) on the basis of a large number of data from literature, as reported in Figure 6. The initial shear stiffness profile corresponding to a given suction has been obtained combining the dependency of shear stiffness on confining stress in saturated conditions given by Equation 8 with the effect of suction under partly saturated conditions given by Equation 1 in which s∗ has been assumed equal to 0 kPa. The values of β and r corresponding
534
1500
1.5
fF1(s) /f1(0)/F 1(0) 1(ua-uw)
stiffness coefficient, S
fluvial clays
1000
S=217+805.84*exp(-Ip/18.94)
500
a)
1.4
marine clays
1.3 1.2 1.1
PI IP=0 PI IP=5 PI IP=10 PI IP=50
1 0.9 0.8
a
0
0 0
50
100
150
200
200
400
600
800
1000
(ua-uw), s((kPa)
plasticity index, PI (%)
1.2
1 b
/A1(0) A A1(ua-uw) 1(s) /A1(0)
stiffness index, n
0.8 0.6 n=0.68-0.162*exp (-Ip/23) 0.4 fluvial clays
0.2
PI IP=0 PI IP=5 PI IP=10 PI IP=50
1 0.8 0.6 0.4 0.2
b)
marine clays 0
0 0
50
100
150
200
0
200
plasticity index, PI (%)
400
600
800
1000
(ua-uw),s (kPa)
Figure 6. a) Stiffness coefficient and b) stiffness index variation with PI.
Figure 7. First peak frequency (a) and first peak amplification ratio (b) normalized by the corresponding values under zero suction.
to different plasticity indexes have been calculated by using Equations 2 and 3. Analyses have been carried out by EERA code, a Shake—like code, designed by Bardet at the Southern California University (Bardet et al. 2000), working in the frequency domain. Modelling the soil as a linear visco-elastic medium allows the evaluation of the results in terms of a transfer function (i.e. the ratio between the amplitude motion at surface and bedrock as a function of frequency) which is influenced by the geometrical and mechanical properties of the soil but is independent on the input motion. Analyses for each fictitious subsoil have been compared with a similar analysis corresponding to a null suction profile. The results were examined in terms of amplification ratio, comparing the response of the subsoil in the unsaturated state with that of the same subsoil under null suction condition. Figure 7 shows the two ratios between the first peak amplification A1(s) and the first frequency f1(s) in unsaturated conditions and the corresponding quantities A1(0) and f1(0) under a null value of suction for different values of the plasticity index. The natural frequencies increase while the amplification ratios decrease as the suction attains larger
values. This can be explained with reference to the simplified pattern of a homogeneous visco-elastic stratum (i.e. with a constant value of G0 with depth) with shear wave velocity Vs and thickness H lying on a deformable bedrock. In this case, it is possible to express the nth natural frequency fn and peak value of the amplification function An as a function of the mechanical and geometrical properties of the stratum: fn =
(2n − 1) · Vs ; 4H
An =
1 μ + (2n − 1) π2 D0
(9)
The natural frequencies increase because the overall value of the shear wave velocity increases with suction. As for the amplification ratio, it depends on both soil/bedrock impedence ratio, μ and internal damping, D0 . The first peak of amplification significantly reduces at increasing suction, because the decrease in the impedance contrast plays a major role. The damping decrease with suction mainly affects the amplitude ratios of the subsequent modes which also increase as suction increases. As it appears from Figure 7, in analogy to shear stiffness, an equal variation of amplification ratio and
535
1.5 1.4 /F 1(0) fF1(s) /f 1(0) 1(ua-uw)
If the unsaturated state is not taken into account, the error on amplification ratio reaches 48% and that on frequencies 38% for relatively high values of suction, depending on mechanical properties of the soil deposits. These results emphasize that the unsaturated state could be meaningful in the local response of deposits of limited thickness, as it is the case in the Neapolitan area. Therefore, for a proper prediction of the local seismic response of a particular site, it is important to take into account the unsaturated state of the soil deposit.
a)
1.3 1.2 1.1
PI IP=0 PI IP=5 PI IP=10 PI IP=50
1 0.9 0.8 0
200
400
600
(ua-uw)s
800
1000
1.2
REFERENCES
PI IP=0 PI IP=5 PI IP=10 PI IP=50
1 A1(ua-uw) /A A 1(s) /A 1(0)1(0)
1200
*, (kPa)
0.8 0.6 0.4 0.2
b) 0 0
200
400
600
(ua-uw)s
800
1000
1200
*, (kPa)
Figure 8. First peak frequency (a) and first peak amplification ratio (b) normalized by the corresponding values under zero suction versus equivalent suction.
peak frequency corresponds to different values of suction depending on PI values. It is then possible to plot the normalized values of the first peak amplification A1(s) and frequency f1(s) , evaluated in unsaturated condition, with respect to that corresponding to the same subsoil under a null suction condition (i.e. A1(0) , f1(0) ), as a function of the equivalent suction defined in the previous section. As expected the curves corresponding to different values of PI overlap (Fig. 8). It is then possible to evaluate the variation with suction of both first peak frequency and amplification of the transfer function for a homogeneous subsoil with a given plasticity index by knowing the results for a reference subsoil with the same geometric characteristics. 4
CONCLUSIONS
Results clearly show the effects of partial saturation on the local seismic response. Natural frequency values of a soil deposits significantly increase with suction. This effect is more evident for shallowest bedrocks. Maximum amplification ratios, in the field of earthquake motion characteristic frequencies, are substantially reduced.
Bardet, J.P., Ichii, K. & Lin, C.H. 2000. Eera a computer program for equivalent—linear earthquake site Response Analyses of Layered Soil Deposits. Software manual. University of Southern California, Los Angeles. d’Onofrio, A. & Silvestri, F. 2001. Influence of microstructure on small-strain stiffness and damping of fine grained soils and effects on local site response. Fourth international Conference on Recent Advances in Geotechnical Earthquake Engineering and soil Dynamics, San Diego. Fisher, R.A. 1926. On the capillary forces in an ideal soil, Journal Agr. Science, 16: 492–505. Gili, Y.Y. 1988. Modelo microestructural para medios granulares no saturados. Doctoral Thesis, Universitat Politècnica de Catalunya, Barcelona, Spain. Mancuso, C., Vassallo, R. & d’Onofrio, A. 2002. Small strain behaviour of soils in controlled suction conditions. Proceedings of the third international conference on unsaturated soils, Recife, Brazil. Rampello, S., Silvestri, F. & Viggiani, G. 1994. The dependence of small strain stiffness on stress state and history for fine-grained soils: the example of Vallericca clay. I Symp. Pre-failure Deformations of Geomaterials; 1: 273–279. Balkema. Schnabel, P.B., Lysmer, J. & Seed, H.B. 1972. SHAKE: A computer program for earthquake response analysis of horizontally layered sites. Report No. EERC 72-12, Earthquake Engineering Research Center, University of California, Berkeley. Vassallo, R., Mancuso, C. & Vinale, F. 2007. Modelling the influence of stress-strain history on the initial shear stiffness of an unsaturated compacted silt. Canadian Geotechnical Journal, April/March issue. Vassallo, R. & Mancuso, C. 2000. Soil behaviour in the small and the large strain range under controlled suction conditions. International Workshop on Experimental Evidence and Theoretical Approaches in Unsaturated Soils, Trento, Italy, 75–90, Tarantino & Mancuso Ed. Vinale, F., d’Onofrio, A., Mancuso, C., Santucci De Magistris, F. & Tatsuoka, F. 2001. The pre-failure behaviour of soils as construction materials. Prefailure Deformation Characteristics of geomaterials. Jamiolkowski, Lancellotta & Lo Presti Ed. Yang, J. & Sato, T. 2001. Analytical study of saturation effects on seismic vertical amplification of a soil layer. Géotechnique, 52: 161–165.
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Constitutive modelling
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Thermo-plasticity in unsaturated soils, a constitutive approach B. François & L. Laloui Soil Mechanics Laboratory, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
ABSTRACT: Research interest in the thermo-mechanical behaviour of unsaturated soils is growing as a result of an increasing number of geomechanical problems involving both thermal and unsaturated effects. A new constitutive model dealing with partially saturated soils under non-isothermal conditions is presented through a unified and highly coupled constitutive approach. In the context of the elasto-thermoplasticity and the critical state theory, the so-called ACMEG-TS model uses the concepts of multi-mechanism and bounding surface theory. The generalized effective stress framework is adopted to represent the stress state in the soil. This model brings advancements on the thermo-hydraulic couplings that directly affect the mechanical behaviour of the materials. The constitutive relations based on the evolutions of the two key parameters (the preconsolidation pressure and the air-entry suction) make it possible to reproduce the main features of the thermo-mechanical behaviour of unsaturated soils. Theoretical aspects of the paper are supported by comparisons between numerical simulations and experimental results extracted from literature.
1
INTRODUCTION
In recent decades, the effect of temperature and humidity variations on the mechanical behaviour of soils has become more widely investigated following the need to consider such non-conventional external loadings for many applications in the field of geomechanics (Vulliet et al. 2002). The engineering applications where such effects are to be considered are: highlevel nuclear waste disposal (Gens & Olivella 2001), geothermal structures (Laloui et al. 2006, Brandl 2006), petroleum drilling, injection and production activities (Dusseault et al. 1988) or zones around buried high-voltage cables (Anders & Radhakrishna 1988). All display challenges to understand and to reproduce complex processes in which temperature and relative humidity effects have a key role. Some relevant contributions have been made in the development of unsaturated constitutive relations in non-isothermal conditions. Such models combine the formalism of unsaturated soils and thermo-plasticity. Similar to isothermal models, the choice of stress framework remains a matter of discussion. Gens (1995) and Wu et al. (2004) founded their constitutive relations on the two independent stress variables (net stress, suction) based on the Barcelona Basic Model (Alonso et al. 1990). On the contrary, Khalili & Loret (2001) and Bolzon & Schrefler (2005) elaborated their mechanical frameworks on a unified averaged stress variable.
This paper describes a new constitutive model using the so-called generalized effective stress according to Nuth & Laloui (2007a). This model brings advances concerning the thermo-hydraulic couplings that directly affect the mechanical behaviour of the materials. Those improvements are achieved using two interconnected constitutive parts. The first deals with the stress-strain relationship including possible changes in thermal and retention states, while the second focuses on the relationship between degree of saturation and suction considering the effects of stress and temperature states (François et al. 2007). Based on experimental evidence, the thermo-hydromechanical (THM) features of behaviour considered in the present model are briefly presented. Then, the constitutive relations of both parts of the model are introduced focusing on the connections between them. Finally, some selected comparisons between model simulations and experimental results for different combinations of temperature, suction and stress paths are presented. 2
EXPERIMENTAL EVIDENCE
Figure 1 summarizes the THM interactions in unsaturated soils and divides them in three categories; each being addressed in the three following sections, respectively. Those interactions between thermal,
539
of the soils by changing the degree of saturation for the same suction value.
3
CONSTITUTIVE RELATIONS
3.1 Generalized effective stress In partially saturated media, when air and water phases coexist in pores, the difference of pressure between the two fluid phases induces an internal stress variable, the suction (s = pa − pw ). Aiming to derive a single stress to describe the mechanical behaviour, combinations between stress tensors and fluid pressures are assessed in the generalized effective stress approach (Nuth & Laloui 2007b):
Figure 1. Schematic overview of the THM interactions considered in the ACMEG-TS model.
σij = σij − pa δij + Sr (pa − pw ) δij
retention and mechanical parts are fully coupled within a unified approach in the constitutive relations. 2.1
Thermo-mechanical interactions
Under normally consolidated conditions, clay contracts when it is heated and a significant part of this deformation is irreversible upon cooling. This behaviour over the whole cycle is representative of thermal hardening. Also, it has been shown that the preconsolidation pressure decreases with increasing temperature (Laloui & Cekerevac 2003). 2.2
where σij , pa , pw , Sr are respectively the mechanical external stress, pore air pressure, pore water pressure and degree of saturation. δij is the Kronecker’s symbol. This expression follows from Bishop (1959) in which the effective stress parameter is equal to the degree of saturation, as suggested by Bishop & Blight (1963) and by Schrefler (1984). Since the retention capacity of the soil depends on THM conditions (e.g. the suction level, the followed hydraulic paths, the dry density and the temperature), the inclusion of product Sr s in the effective stress formulation itself includes a number of intrinsic THM connections.
Hydro-mechanical interactions
The interactions between the deformations of the solid skeleton and the retention response must be considered as a double-way coupling. First, the suction variations affect the stress state of the material and the preconsolidation pressure which notably increases upon desaturation, causing peculiar swelling and collapse behaviours to occur upon wetting. However, this increase of the isotropic yield limit is recognized as being activated solely for suctions higher than the air entry value se , which is when air begins to enter the pores (Nuth & Laloui 2007a). Secondly, the retention capacity of soils has proved to be enhanced with increasing dry density because of a reduction of pore dimensions (Gallipoli et al. 2003). 2.3
(1)
Thermo-hydraulic interactions
The main thermal effect on the retention behaviour concerns the diminishing retention capacity of soils with temperature increase, mainly because the interfacial tension between the water and the grains decreases under heating (Romero et al. 2001). This thermal effect indirectly influences the mechanical response
3.2 Mechanical constitutive part The ACMEG-TS model considers that the total strain dε is generated by a non-linear thermo-elasticity, inducing reversible strain dε e , coupled with a multidissipative thermo-plasticity, producing irrecoverable strain dεp . Due to the strain history dependence, the formulation is given in terms of infinitesimal increments. Reference is made here to strains and stresses in the small deformation domain. The elastic part of the deformation is expressed as following: 1 −1 dεije = Eijkl dσkl − βs dT δij 3
(2)
where compression is taken as positive. Eijkl is the mechanical elastic tensor and βs the volumetric thermal expansion coefficient of the solid skeleton. Elastic strain may be induced either by total stress, suction, saturation degree variation (first term of Equation 2), or by temperature change (second term of Equation 2). Eijkl is composed of the following hypo-elastic moduli
540
which are assumed independent of temperature and suction value: K = Kref
p pref
ne
G = Gref
p pref
ne (3)
critical pressure, pcr . M is the slope of the critical state line in the (q − p ) plane and may depend on temperature: M = M0 − g (T − T0 );
M0 =
6 sin φ0 3 − sin φ0
(6)
where Kref and Gref are the reference bulk and shear elastic moduli, respectively, at a reference pressure, pref ; ne is a material parameter. Using the concept of multi-mechanism plasticity (Mandel 1965), the total irreversible strain increment p dεij is induced by two coupled dissipative processes: an isotropic and a deviatoric plastic mechanism. Each p,iso p,dev produces plastic strain increments, dεij and dεij , respectively. The yield limits of each mechanism, restricting the elastic domain in the generalized effective stress space, take the following expressions (Fig. 2):
where φ0 is the friction angle at critical state at the reference temperature T0 and g is a material parameter. The preconsolidation pressure pc is shared by both yield limits which makes the two mechanisms coupled. Moreover, this parameter is the main hardening p variable and depends on volumetric plastic strain εv (in the sense of Cam-Clay model family according to Roscoe & Burland (1968)), on temperature and on suction. It has been shown that logarithmic relations of pc with temperature and suction are in good agreement with experimental observations (Salager et al. 2008). As a consequence, the evolution of pc with the THM variables is given by:
fiso = p − pc riso = 0 dp fdev = q − Mp 1 − b ln rdev = 0 pc
pc εvp , T , s p ⎧ ⎪ ⎨pc0 exp βεv {1 − γT log [T /T0 ]} if s ≤ se = pc0 exp βεvp {1 − γT log [T /T0 ]} ⎪ ⎩ if s ≥ se (7) × {1 + γs log [s/se ]}
(4) (5)
where q is the deviatoric stress. b is a material parameter and d the distance (in the logarithmic plane) between the preconsolidation pressure, pc , and the
where pc0 is the initial preconsolidation pressure (at initial temperature and under saturated conditions) and β the plastic compressibility modulus. γT and γs are material parameters. riso and rdev are the degree of plastification of the isotropic and deviatoric mechanisms, respectively. According to the bounding surface theory (Dafalias & Herrmann 1980), this enables a progressive evolution of the isotropic and deviatoric yield limits during loading following the next two equations, respectively (Hujeux 1979): p,iso
e riso = riso +
εv c+
p,iso εv
;
driso =
(1 − riso )2 p,iso dεv c (8)
e rdev = rdev +
Figure 2. work.
Yield limits for the THM elasto-plastic frame-
p εd
p;
a + εd
drdev =
(1 − rdev ) p dεd a 2
(9)
e where c and a are material parameters while riso and e rdev define the size of the elastic nuclei of the isotropic p and deviatoric mechanisms, respectively. εd is the p,iso deviatoric plastic strain and εv the volumetric plastic strain induced by the isotropic mechanism. The flow rule of the isotropic mechanism is associated, while the deviatoric one is not, and they are
541
assumed to take the following forms, respectively:
two successive retention limits, fdry and fwet , upon drying and wetting paths, respectively:
p
p,iso
dεii
p,dev
dεij
=
λiso 3 p
= λdev
(10) 1 Mp
q ∂q +α M − p ∂σij
1 δij 3
(11)
where α is a material parameter. The plastic multip p pliers, λiso and λdev , are determined using Prager’s consistency equation for multidissipative plasticity (Prager 1958, Rizzi et al. 1996). The two consistency conditions must be met simultaneously, leading to the solving of two equations with two unknowns: ⎧ ⎨dF = ∂F : dσ + ∂F · dT + ∂F · ∂π · λp ≤ 0 ∂T ∂π ∂λp ∂σ (12) ⎩ p λ ≥ 0; dF · λp ≥ 0 where σ is the generalized effective stress vector and p π the internal variable matrix (riso and εv for the p isotropic plastic mechanism and rdev and εv for the P deviatoric plastic mechanism). λ and F are the plastic multiplier and yield limit vectors, respectively. 3.3
Retention constitutive part
In terms of retention response, desaturation is also seen as a yielding phenomenon. As long as the soil is dried, suction increases and the degree of saturation, Sr , tends to decrease mainly when the air-entry suction se is reached. Thereby, se is here considered as a retention limit separating fully and partially saturated states. Under re-wetting, a hysteretic retention phenomenon occurs which is represented by a second limit (Fig. 3). Then a sorption-desorption cycle activates
fdry = s − sd = 0
(13)
fwet = sd shys − s = 0
(14)
where sd is the drying yield limit and shys a material parameter considering the size of the retention hysteresis. If the initial state is saturated, the initial retention drying limit sd0 is equal to air-entry suction se and increases when suction overtakes se as follows: sd = sd0 exp (−βh Sr )
(15)
where βh is the slope of the desaturation curve in the (Sr − ln s) plane (Fig. 3). Finally, because the air-entry suction of the materials depends on temperature and dry density, sd0 is a function of temperature and volumetric plastic strain (François & Laloui, 2007): sd = sd0 exp (−βh Sr ) × 1 − θT log [T /T0 ] − θe log 1 − εvp
(16)
where θT and θe are material parameters describing the logarithmic evolution of the air-entry suction with respect to temperature and volumetric plastic strain, respectively. Because this retention response is governed by yielding mechanisms, the processes must be controlled by evolution laws in agreement with consistency equations, in addition to yield functions. The two following equations describe the flow rules of the drying and wetting mechanisms, respectively: ∂fdry p = λdry ≤ 0 ∂s p ∂fwet p = −λwet ≥ 0 = λwet ∂s p
d Srdry = λdry
(17)
d Srwet
(18)
In contrast to the mechanical mechanisms, these two retention mechanisms cannot be active simultaneously because they are activated in two opposite directions of hydraulic loading. As a consequence, the two retenp p tion plastic multipliers (λdry and λwet ) are independent. Moreover, these plastic multipliers must be negative because an increase of suction tends to reduce Sr . Within this framework, the current degree of saturation is given by: Figure 3. Modelling of the water retention curve with its hysteresis. The air-entry suction depends on volumetric plastic strain and temperature.
Sr = Sr0 + Srdry + Srwet
542
(19)
where Sr0 is the initial degree of saturation. The consistency conditions impose that: ⎧ ⎪ dF = ⎪ ⎪ hyd ⎨
∂Fhyd ∂Fhyd ∂Fhyd p ∂F ∂s ds+ ∂T dT + ∂εvp dεv + ∂π hyd ∂π
p
× ∂λphyd · λhyd ≤ 0 ⎪ hyd ⎪ ⎪ ⎩ p p λhyd ≤ 0; dFhyd · λhyd ≥ 0
(20)
simulations are displayed in the net stress reference (σij,net = σij − pa ), although the model uses the generalized effective stress. Figure 4 compares the numerical simulations with experimental results of oedometric compression tests at different suctions and at ambient temperature. The initial strain observed at 0.1 MPa of net stress is due to the suction path from 127 MPa to the suction
where Fhyd is the retention yield function vector and π hyd , the internal variables vector. These retention mechanisms include only one internal variable, the p variation of degree of saturation Sr . λhyd is the retention plastic multiplier vector. For very high suctions, the retention conditions reach a residual state defined by the residual degree of saturation Sr,res . At this state, no more variation of degree of saturation is possible, even if the suction increases (Fig. 3).
4
Figure 5. Numerical simulations of oedometric compression tests of FEBEX bentonite at the hydroscopic suction and two different temperatures. Comparisons with experiments.
NUMERICAL SIMULATIONS
In this section, comparison between numerical simulations and experimental results on compacted FEBEX bentonite are presented. These materials have been tested along coupled suction, temperature and mechanical paths under oedometric conditions by Lloret et al. (2004) and Romero et al. (2004). A set of 13 tests have been simulated. All the tests start at an applied initial stress of 0.1 MPa and at a compaction suction of about 127 MPa. Among these tests, 6 tests ((1), (3), (6), (7), (9) and (10) in Figures 4 to 7) were used to calibrate parameters, as presented in Table 1, while the 7 other tests are blind simulations. Because no deviatoric tests are available, the deviatoric parameters are not considered in these simulations. All the results and numerical
Figure 6. Numerical simulation of retention curve of FEBEX bentonite at three different temperatures. Comparisons with experiments.
Figure 4. Numerical simulations of oedometric compression tests of FEBEX bentonite at different suctions. Comparisons with experiments.
Figure 7. Numerical simulation of retention curve of FEBEX bentonite at two different dry densities ρd . Comparisons with experiments.
543
of elastic swelling and plastic collapse predicted by ACMEG-TS. (v) Finally, the mechanical unloading takes place elastically.
Table 1. Material parameters of the FEBEX bentonite used in the numerical simulations. Elastic parameters Kref , n, βs
[MPa], [−], [◦ C−1 ] 16, 1, 6.67 10−4
Isotropic plastic mechanical parameters ela β, γs , γT , c, riso
5
[−], [−], [−], [−], [−]14.3, 16, 2.1, 0.02, 0.45
Retention parameters se0 , βh , θT , θe , shys [MPa], [−], [−], [−] 4, 8.64, 0.7, 10.8, 0.6
Figure 8. Numerical simulation of combined THM paths in oedometer on FEBEX bentonite. Comparisons with experiments.
applied during compression. The subsequent compression paths clearly show the enhancement of the elastic domain when suction increases. Figure 5 reproduces the numerical simulation of oedometric compression tests at two temperatures under 127 MPa of suction. The initial strain observed for path (6) is due to the temperature increase. Figure 6 underlines the effect of temperature on the retention curve as considered by the ACMEG-TS model and compares it with experiments. In the (Sr − ln s) plane, the shift of the wetting curve to the left when temperature increases is well reproduced by the model. Figure 7 brings to light the retention hysteresis in addition to the effect of density. Consequently, this means the denser the soil, the higher the degree of saturation for a same suction. The experimental paths followed in the results presented in Figure 8 may be separated in five steps (Romero et al. 2004). (i) The heating phase induces an elastic mechanical response of the bentonite (e.g dilation). (ii) The wetting from a suction of 127 MPa to 14 MPa produces swelling. (iii) The mechanical load from 0.1 MPa to 5 MPa of net vertical stress showing a progressive change of compression slope mirrors an elasto-plastic behaviour. (iv) The wetting until a suction of 0.1 MPa exhibits a combination
CONCLUSIONS
When a soil is simultaneously submitted to mechanical, hydraulic and thermal variations, several coupling effects are involved in its global THM response. Those interactions have been presented here based on experimental evidence and have been incorporated in a unified constitutive framework, so-called ACMEG-TS, including two interconnected aspects. A generalized effective stress expression is used as a unique stress so as to convert a complex multiphase, multi-stress medium into a single mechanical state. The advanced coupling between the air-entry suction, the temperature and the dry density provides further performance to the framework. In addition, the double way coupling between the mechanical and the retention responses including temperature effects brings substantial advances in the field of constitutive modelling of thermal effects in partially saturated materials. Moreover, this theoretical and constitutive approach has been compared with experimental results through a set of numerical predictions which tend to prove the accuracy of the developed model.
ACKNOWLEDGEMENTS This work was partly supported by the Swiss State Secretariat for Education and Research SER, Grants OFES C04.0021.
REFERENCES Alonso, E.E., Gens, A. & Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique, 40(3), 405–430. Anders, G. & Radhakrishna, H. 1988. Computation of temperature field and moisture content in the vicinity of current carrying underground power cables. IEE Proceedings, 51–62. Bishop, A.W. 1959. The principle of effective stress. Tecnisk Ukeblad, 39, 859–863. Bishop, A.W. & Blight, G.E. 1963. Some aspects of effective stress in saturated and unsaturated soils. Géotechnique, 13, 177–197. Bolzon, G. & Schrefler, B.A. 2005. Thermal effects in partially saturated soils: a constitutive model. International Journal for Numerical and Analytical Methods in Geomechanics, 29(9), 861–877. Brandl, H. 2006. Energy foundations and other thermo-active ground structures. Géotechnique, 56(2), 81–122.
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Dafalias, Y. & Herrmann, L. 1980. A bounding surface soil plasticity model. International Symposium on soils under Cyclic and Transient Loading, Swansea, 335–345. Dusseault, M.B., Wang, Y. & Simmons, J.V. 1988. Induced stresses near a fire flood front. AOSTRa Journal of research, 4, 153–170. François, B., Nuth, M. & Laloui, L. 2007. Mechanical constitutive framework for thermal effects on unsaturated soils. 10th International Symposium on Numerical Models in Geomechanics, NUMOG X, 9–13. François, B. & Laloui, L. 2007. A stress-strain framework for modelling the behaviour of unsaturated soils under nonisothermal conditions. Springer proceedings in Physics 113, 119–125. Gallipoli, D., Wheeler, S.J. & Karstunen, M. 2003. Modelling the variation of degree of saturation in a deformable unsaturated soil. Géotechnique, 53(1), 105–112. Gens, A. 1995. Constitutive laws. In Modern issues in nonsaturated soils, Springer, 129–158. Gens, A. & Olivella, S. 2001. Clay Barrier in radioactive waste disposal. R.F. Génie Civil, 5(6), 845–856. Hujeux, J.C. 1979. Calcul numérique de problèmes de consolidation élastoplastique. PhD Thesis, Ecole Centrale de Paris. Khalili, N. & Loret, B. 2001. An elasto-plastic model for non-isothermal analysis of flow and deformation in unsaturated porous media: formulation. International Journal of Solids and Structures, 38, 8305–8330. Laloui, L. & Cekerevac, C. 2003. Thermo-plasticity of clays: An isotropic yield mechanism. Computer and Geotechnics, 30, 649–660. Laloui, L., Nuth, M. & Vulliet, L. 2006. Experimental and numerical investigations of the behaviour of a heat exchanged pile. International Journal for Numerical and Analytical Methods in Geomechanics, 30, 763–781. Lloret, A., Romero, E. & Villar, M. 2004. FEBEX II Project: Final report on thermo-hydro-mechanical laboratory tests. Publicación técnica 10/2004, ENRESA. Mandel, W. 1965. Généralisation de la théorie de Koiter. International Journal of Solids and Structures, 1, 273–295.
Nuth, M. & Laloui, L. 2007a. New insight into the unified hydro-mechanical constitutive modeling of unsaturated soils. Proceeding of the 3rd Asian Conference on Unsaturated Soils, 109–126. Nuth, M. & Laloui, L. 2007b. Effective stress concept in unsaturated soils: Clarification and validation of a unified framework.’’ International Journal of Numerical and Analytical Methods in Geomechanics. In press. Prager, W. 1958. Non-isothermal plastic deformation. Koninkklijk-Nederland Akademie Van Wetenschappen Te Amsterdam—Proc. of the section of sciences-B, 61, 176–182. Rizzi, E., Maier, G. & Willam, K. 1996. On failure indicators in multi-dissipative materials. International Journal of Solids and Structures, 33(20–22), 3187–3214. Romero, E., Gens, A. & Lloret, A. 2001. Temperature effects on the hydraulic behaviour of an unsaturated clay. Geotechnical and Geological Engineering, 19, 311–332. Romero, E., Villar, M.V. & Lloret, A. 2004. Thermo-hydromechanical behaviour of two heavily overconsolidated clays. Engineering Geology, 81, 255–268. Roscoe, K.H. & Burland, J.B. 1968. On the generalized stress—strain behaviour of ‘‘wet’’ clay. In Engineering plasticity. Cambridge University Press, Cambridge, England, 535–609. Salager, S., François, B., El Youssoufi, M.S., Laloui, L. & Saix, C. 2008. Experimental investigations on temperature and suction effects on mechanical behaviour of a sandy silt. Soils and Foundations. Accepted for publication. Schrefler, B.A. 1984. The finite element method in soil consolidation (with applications to surface subsidence). Ph.D. Thesis, University College of Swansea, C/Ph/76/84. Vulliet, L., Laloui, L. & Schrefler, B.A. 2002. Environmental geomechanics, EPFL Press, Lausanne. Wu, W., Li, X., Charlier, R. & Collin, F. 2004. A thermohydro-mechanical constitutive model and its numerical modelling for unsaturated soils. Computer and Geotechnics, 31, 155–167.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A thermomechanical framework for modeling the response of unsaturated soils S. Samat, J. Vaunat & A. Gens Technical University of Catalonia UPC, Barcelona, Spain
ABSTRACT: Unsaturated soils present challenging aspects from constitutive modeling point of view because stress-strain relationship have to include variables associated to the effect of air and water phase and also to the interfaces between them. Most traditional constitutive models have considered the suction (difference between air and water pressure) as an additional parameter that affects soil properties, as does, for example a structuration parameter (Alonso et al. 1990). However there are now increasing evidence that suction cannot be treated only as a parameter and that a comprehensive modeling of unsaturated materials have to associate to it an extensive variable such that the product of this variable by suction enters as an additional term in the energy balance of the triphasic medium (Houlsby 1997). In this paper, a model is proposed to represent, in a thermomechanical approach the response of unsaturated soils under load and suction changes. Energy concepts in triphasic medium are first revised and controlling variables defined (Coussy 2004). They include strain ij , net stress σ defined as the difference of total stress and air pressure, change in volumetric water content w and suction s. Relationship between s and w integrates the hysteresis of the retention curve as a hydraulic elastoplastic mechanism. Particular attention is given to the thermomechanical consistency of the generalized potentials associated to the model, with the objective to propose a comprehensive and sound formulation of the effect of suction on the response of unsaturated materials. Keywords: hyperporoplasticity, poromaterial, unsaturated soils, interface energy, shift stress, dissipation, energy function.
1
INTRODUCTION
In the present work a theoretical framework based on thermodynamic principles is outlined as a general approach to analyze the constitutive behavior of triphasic media. The study of porous continua is still a theme of debate due to the variety and complexity of coupled physical phenomena that naturally appears. A very deep physical study of this class of media has been performed by (Coussy 2004; Coussy & Fleureau 2004), mainly based on the pioneer works (Biot 1941; Biot 1977). The framework developed establishes a separation concept of the phases solid-fluid, studying the open system as an skeleton with porous voids and the corresponding energies of interface. The study of constitutive equations for fluid infiltrated porous solids is performed based on thermodynamic principles combining the first and second laws of thermodynamics yields to the Clausius-Duhem inequality. The last one becomes very important allowing the determination of couple conjugate state variables which are energy conjugate, (Houlsby 1997; Coussy 2004). The approach presented here is to start with thermodynamics potential and develop the plasticity model from them. This
hyperplasticity approach has been initiated by (Ziegler 1977) and so far extended by (Houlsby 1981; Collins & Houlsby 1997; Puzrin & Houlsby 2001; Houlsby & Puzrin 2006). The formulation proposed here under the light of the previous mentioned is adequately called ‘‘hyperporoplasticity’’. The remaining part of the article is organized in three sections: first the notation used is established, secondly the thermodynamics basis for triphasic media are described and finally the well known model for unsaturated soils BMM, (Alonso et al. 1990), is derived from thermodynamic potential energy functions. 2
NOTATION AND TERMINOLOGY
Before continue further, the notation and terminology used is presented in table 1. 3
THERMODYNAMICS OF TRIPHASIC MEDIA
By triphasic media we understand a continuum formed by three components (porous skeleton, air and water) the porous space becomes filled with two fluids so
547
Table 1. u g f gs fs d σij , p
ij , φ mf T
s
αij , αp χij , χp ρij , ρp fy p
ij , φ p Eχ φo pl , pg φl , φg ϕl , ϕg Sg , Sl fm fI g fs
The Clausius-Duhem equality for an isothermal process can be written now using the energy function of the porous skeleton as
Terminology. : : : : : : : : : : : : : : : : : : : : : : : : :
specific internal energy function specific Gibbs energy function specific Helmholtz energy function Gibbs energy func. of the skeleton Helmholtz energy func. of the skeleton dissipation function stress tensor and pore pressure strain tensor and porosity fluids concentrations temperature entropy kinematic internal variables generalized stress tensors shift stress tensors yield function plastic strain and porosity tensors generalized poroelastic domain Lagrangian porosity liquid and gas fluid pressures liquid and gas current porosities liquid and gas lagrangian porosities saturation degree of gas and liquid phases Helmholtz energy of the solid matrix interface energy function energy function of unsat. soil skeleton
σij d ij + pl dφl + pg dφg − dfs = 0
(4)
where is important to notice that apart from the energy of the solid matrix, the energy corresponding to the interfaces, fluid-fluid and solid-fluid, is considered. The state equations obtained by derivation of eq. [4] are expressed as σij = ∂ ij fs ;
pl = ∂φl fs ;
pg = ∂φg fs
(5)
The Clausius-Duhem inequality is the cornerstone of any energy approach to the constitutive equations of materials allowing the determination of adequate conjugate variables (Houlsby 1997; Coussy 2004; Laloui et al. 2003) and can be expressed as σij d ij + pl dφl + pg dφg − dfs ≥ 0
(6)
Using the relations φl = φ0 Sl +ϕl , φg = φ0 Sg +ϕg , 1 = Sl + Sg , jj = ϕl + ϕg where φo stands for the initial porosity, and replacing them in eq. [6], after some algebraic steps, one arrives to (σij d ij + pg dϕg ) + pl dϕl − (pg − pl )φo dSl − dfs ≥ 0 (7)
that the material is said to be unsaturated. The internal energy of the porous continua admits as natural arguments ij , mfα , s, αij , αp , then we can write u = u( ij , mfα , s, αij , αp )
Considering the incompressibility of the solid matrix eq. [7] yields (σij + pl δij )d ij − (pg − pl )(Sl d jj − φo dSl ) − dfs ≥ 0 (8)
(1)
where ij is the strain tensor, mfα is the mass concentration of fluids, αij and αp are internal kinematic variables. In eq. [1] the thermohydromechanical couplings associated with the surface tension or energy related to each fluid-fluid or fluid-solid are introduced. The Helmholtz free energy of the porous continua f = u − T s becomes
The term Sl d jj − φo dSl = d w is called the hydraulic strain and is used when the net stress is adopted as state stress variable to model partially saturated soils. The last set of conjugate variables has been used by (Vaunat & Romero 2000) to develop a hydromechanical model based on BBM, (Alonso et al. 1990). For isothermal process and using the first and second laws of thermodynamics the increment of fs is dfs = σij d ij + pl dϕl + pg dϕg − Tdsi
f = f ( ij , mfα , T , αij , αp )
(2)
The porous skeleton Helmholtz energy function (Coussy 2004) obtained extracting the mass concentration of fluids fs = f − mfα gfα , becomes a function of the arguments fs = fs ( ij , φ, T , αij , αp )
(3)
(9)
where dsi is the irreversible part of the rate of entropy production within a material element. The last equation can be rearranged to give σij d ij + pl dϕl + pg dϕg = dfs + d
(10)
On the other hand, an evolution of the Helmholtz skeleton energy can be obtained differentiating eq. [3] with respect to its variables
548
p
dfs = ∂ ij fs d ij + ∂ϕl fs dϕl + ∂ϕg fs dϕg + ∂αij fs dαij + ∂αp fs dαp
(11)
gs = −[gm1 (σij ) + gc1 (σij , s) + φo gI1 (s)]
Now, comparing eq. [10] and eq. [11] we have
p
+(σij ij + s wp )
d = Tdsi = −∂αij fs dαij − ∂αp fs dαp = χij dαij + χp dαp
p
χp = −∂αp fs
(13)
For decoupled poromaterials the Helmholtz free energy of the skeleton fs ( ij , φ, αij , αp ) takes the form fs = fs1 ( ij − αij , φ − αp ) + fs2 (αij , αp )
For a porous material the stresses relating the generalized and true stresses are the back or shift stresses determined as ρij = σij − χij = ∂αij fs2 ;
ρp = p − χp = ∂αp fs2 (15)
4
INTERFACE ENERGY—SUCTION CURVE
Several kinds of curves representing the relationships between the water content and suction (pg − pl ) have been proposed. For the non-deformable and isothermal case ij = 0 and φ = φo and T = 0 the state equation reduces to s = ∂ w fs ( w ) = ∂ w fI ( w )
(17)
where gm correspond to the energy of the matrix, gI is the interface energy, gc correspond to the coupling energy and so is the hardening parameter of the suction curve.
5
(14)
p
−[gm2 ( ij ) + gc2 ( ij , so ) + φo gI2 (so )]
(12)
where χij and χp are called dissipative or generalized stresses and can be obtained as χij = −∂αij fs ;
p
function of the skeleton gs (σij , s, ij , w ) can be written as, (Collins & Houlsby 1997),
BARCELONA BASIC MODEL—BBM
5.1 Hyperporoelastic potential functions The performance of the model derived from hyperporoplastic principles is obtained starting with the proposed potential energy functions, which in general form is eq. [17]. Before continuing further the notation used is summarized in a table. where ICL and NCL are the isotropic compression line and normal compression line respectively. For the elastic case, the Gibbs free energy function of the skeleton gs1 (p, q, s) can be explicitly expressed as p s + pat ∗ gs1 = −κ ∗ p ln p ln − 1 − κ s pc pat −
q2 − gI1 (s) 6G
(18)
(16) Table 2.
where fI is the interface energy function. The relationship from eq. [16] shows clear hysteretic behavior under non-monotonic flow conditions. In fact when a sample of porous material is subjected to a wettingdrying cycle, a hysteresis loop is observed so that the link between suction and degree of saturation is not one-to-one. A model proposed by (Wheeler et al. 2003) for the suction curve approximate its smooth nature by two straight lines with slopes κω∗ for the elastic path and λ∗ω for the plastic one and will be used further. An advanced and more realistic assumption is to introduce explicitly a dependence of the suction curve on the porous volume, allowing to rewrite the interface energy function as fI = fI (Sl , φ). Coussy (2004) shows that the latter relation can be expressed after a dimensional and mathematical analysis as fI = 1 φ − 3 fI φ (Sl ). For the case of decoupled poromaterials and under isothermal conditions, the Gibbs free energy
p s q
v
w
s κ∗ κs∗ pc pat κω∗ G λ∗(s) λ∗s λ∗ω e LC fy So y f
549
Notation. : : : : : : : : : : : : : : : : : :
mean net stress suction deviatoric stress volumetric strain hydraulic strain deviatoric strain slope of ICL in plane v − ln (p) slope of elastic branch in plane w − ln (p) reference pressure atmospheric pressure slope of the scanning curves shear modulus slope of NCL at suction s inelastic branch in plane w − ln (p) main wett-dry curves plane w − ln (s) void ratio loading-collapse yield surface suction increase-decrease yield loci (o = I − D)
From eq. [18] the hydraulic strain w derived using the state equation w = −∂s gs1 will take the form
w = −∂s gs1 = κs∗
p + gI1 (s) s + pat
(19)
The interface energy function gI1 (s) can be defined explicitly using for example the model proposed by (Wheeler et al. 2003). The Gibbs energy function of the skeleton gs (p, q, s) which includes the interface energy gI (s) can be expressed as p s + pat ∗ p ln − 1 − κ gs1 = −κ ∗ p ln s pc pat 2 s + pat q − κω∗ (s + pat ) ln −1 − pat 6G (20) By differentiation of the eq. [20], the expressions for the strain state variables becomes p s + pat ∗ + κ ln
v = −∂p gs1 = κ ∗ ln s pat pc s + pat p + κω∗ ln
w = −∂s gs1 = κs∗ s + pat pat q (21)
s = −∂q gs1 = 3G The compliance modulus is obtained by double differentiation of eq. [20] as ⎡
κs∗
∗
κ ⎢ p ⎢ ⎢ ⎢ κs∗ gs D =⎢ ⎢ s + pat ⎢ ⎣ 0
s + pat −
κs∗ p κω∗ − 2 s + pat (s + pat ) 0
⎤
fsg1 = gs1 + p v + q s
(24)
and eliminating p and q through eq. [23] a more convenient energy function is obtained 3 v fsg1 = κ ∗ pc exp ∗s + G s2 − κω∗ (s + pat ) κ 2 s + pat × ln −1 pat
(25)
From eq. [25] the conjugate variables are obtained by using the corresponding state equations p = pc exp
w =
vs
κ∗
s + pat κs∗ pc v exp ∗s + κω∗ ln pat s + pat κ
q = 3G s
(26)
and the stiffness matrix modulus is derived by double differentiation of eq. [22] g
Cfs = pc exp ⎡
0
⎥ ⎥ ⎥ ⎥ 0 ⎥ ⎥ ⎥ ⎦ 1 3G (22)
From equation [21a], it is possible to extract the mean net stress and the deviatoric stress as ⎞ ⎛ at
v − κs∗ ln s+p p at ⎠ = pc exp vs p = pc exp ⎝ ∗ κ∗ κ q = 3G s
an appropriate potential energy function to tackle this phenomenon. The Legendre transformation becomes a central tool in hyperporoplastic approach, because it allows a great number of possibles formulations interchanging extensive variables by the intensive ones. Applying a partial Legendre transformation to eq. [20] for the case of isothermal poromaterial expressed as
⎢ ⎢ ×⎢ ⎣
vs
κ∗
1 κ∗ κs∗ κ ∗ (s + pat ) 0
κs∗ (s + pat ) κs∗ β (s + pat ) 0
κ∗
⎤ 0
⎥ ⎥ ⎥ 0 ⎦ 3G (27)
where β = κs∗ /(κ ∗ (s + pat )) + κω∗ /κs∗ . 5.2 Trapped energy—hardening plasticity
(23)
where vs = v − κs∗ ln((s + pat )/pat ). In unsaturated soils, an important issue that always makes the computations more complex is the mixed control that naturally arise from the suction control of the test. Because of this fact, it is of interest to obtain
The coupled behavior between the mechanical and the hydraulic phases in a partially saturated media extends over more than the elastic stage, providing a cross hardening of the corresponding loading surfaces LC S (f y O, f y ) once the plastic stage has been reached. p p p p These coupled plastic works, Wv w and Ww v are considered to contribute to the trapped (or stored) energy recoverable in a reversible loading process (not dissipative). The comprehension of this physical phenomena allows to write the energy function of the skeleton gs2 (po , so ) in the form
550
1 ∗ po − 1 λ(s) − κ ∗ po ln pc 2 so + pat − λ∗ω − κω∗ − λ∗s − κs∗ po ln pat so + pat −1 (28) × (so + pat ) ln pat
gs2 = −
As before, it is possible to obtain gs2 (po , so ) as fsg2 vp , so = −gs2 (po , so ) + po vp
g p fs2 ( v , so )
from where it is possible to extract po as p
vs c po = p exp λ∗(s) − κ ∗
from (29)
g
ρp = ∂ vp f2 ;
g
ρs = −∂so f2
(34)
that are written explicitly as p
vs 1 c ρp = p exp λ∗(s) − κ ∗ 2 so + pat ρs = −(λ∗ω − κω∗ ) ln pat p
vs 1 λ∗s − κs∗ c p exp + λ∗(s) − κ ∗ 2 so + pat
(35)
(30) g
where vs = v − (λ∗s − κs∗ ) ln((so + pat )/pat ). Replacing eq. [30] in eq. [29] the conjugate function g p fs2 ( v , so ) becomes p
vs g ∗ ∗ c fs2 = (λ(s) − κ )p exp ∗ + (λ∗ω − κω∗ ) λ(s) − κ ∗ so + pat −1 (31) × (so + pat ) ln pat p
Using the complementary state equations it is possible to derive the shift or back stresses as
p
The translation matrix modulus R fs giving the translation rule between the generalized stress space (χ -space) and the true stress space (σ -space) is g obtained by double differentiation of f2 and is written as g
R fs =
⎡ (s + p ) o at ⎢ 2(λ∗(s) − κ ∗ ) ⎢ ∗ ∗ ×⎢ ⎢ −(λs − κs ) ⎣ 2(λ∗ − κ ∗ ) (s) 0
g
Finally the energy function fs is expressed with all its terms as p 3
vs − v fsg = κ ∗ pc exp − gI1 (s) + G( s − sp )2 κ∗ 2 p
vs p ∗ ∗ c − s w + (λ(s) − κ )p exp ∗ + gI2 (so ) λ(s) − κ ∗
6
(32) where gI1 (s) and gI2 (so ) represents the parts of the g energy function fs corresponding to the interface energy. Explicitly eq. [32] becomes p
vs − v 3 fsg = κ ∗ pc exp + G( s − sp )2 κ∗ 2 s + pat − κω∗ (s + pat ) ln − 1 − s wp pat p
vs ∗ ∗ c + (λ(s) − κ )p exp ∗ λ(s) − κ ∗ so + pat −1 + (λ∗ω − κω∗ ) (so + pat ) ln pat (33)
po (so + pat )
⎤ −(λ∗s − κs∗ ) 0 ⎥ 2(λ∗(s) − κ ∗ ) ⎥ (λ∗s − κs∗ )2 ⎥ λ∗ω − κω∗ − 0⎥ po 2(λ∗(s) − κ ∗ )so ⎦ 0 0 (36)
DISSIPATION AND YIELD FUNCTION
The second required function to completely define the hydromechanical model for the fluid infiltrated porous material is the dissipation energy which is an homogeneous function on the rate of plasticstrains and also p p depends on the internal variables, d χπo , d v , d s . This function takes the form, (Moradessi et al. 1994; Houlsby 1981) d LC = χπo (s, vp )[(d vp )2 + M 2 (d sp )2 ]1/2
(37)
From eq. [37] the yield locus is obtain as a degenerate case of Legendre transformation, fy
LC
:
χπ2 χ2 + 2τ 2 = 1 2 χπ o M χπ o
(38)
when eq. [38] is transformed to true stress space by using the standard shift stresses the resulting yield condition is
551
Dissipative Stress Space
between the true stresses and the dissipative ones through the back or shift stresses. The latter is physically derived from the fact that not all plastic work is dissipated but trapped (or stored) as plastic energy. Finally a modified version of BBM has been derive within the framework of hyperporoplasticity.
True Stress Space
REFERENCES
Figure 1.
f
yLC
:
Yield surface transformation.
p 2 o − ps p− 2 + p 2 o
2
M2
q2 p 2 = 1 o
2 (39)
Eqs. [33] and [38] indicate that the plastic yielding at the suction changes does not contribute to the plastic dissipation but only to the plastic work (Sheng et al. 2004). This means that all plastic work associated with p a plastic increment of the hydraulic strain dw is stored and can be recovered during a reverse plastic increment of saturation. This fact confirms the yield loci S S fy D, fy I , fy
So
: = χs = w − ρs = 0 → o = I , D
(40)
The resulting elastic domain and the corresponding yield functions for the modified BBM are shown in fig. [1]. 7
CONCLUDING REMARKS
A thermomechanical approach to derive unsaturated soil models in agreement with thermodynamics principles has been presented. With regard to the mechanical behavior of porous material the existence of the interface energy between the components phases (solid, air, water) has been considered. Thus, starting by proposing potential energy functions, Gibbs or Helmholtz energy and the dissipation energy, a complete elastoplastic model can be derived. The hyperporoplastic approach gives rise to the fundamental relation
Alonso, E., Gens, A. & Josa, A. (1990). A constitutive model for partially saturated soils. Géotechnique 40, No.3, (405–430). Biot, M. (1941). General theory of three dimensional consolidation. Journal of applied physics, No. 12, 155–164. Biot, M. (1977). Variational Lagrangian-thermodynamics of non isothermal finite strain. Mechanics of porous solid and thermomolecular diffusion. International journal of solids and structures No. 12, 579–597. Collins, I. & Houlsby, G. (1997). Application of thermomechanical principles to the modelling of geotechnical materials. Proc. R. Soc. Lond. A 453, 1975–2001. Coussy, O. (2004). Poromechanics. John wiley & Sons, Ltd. Coussy, O. & Fleureau, J. (2004). Méchanique des sols non saturés. John wiley & Sons, Ltd. Houlsby, G. (1981). A study of plasticity theories and their applicability to soils. Cambridge University, PhD. Thesis. Houlsby, G. (1997). The work input for an unsaturated granular material. Géotechnique 47, No. 1, (193–196). Houlsby, G. & Puzrin, A. (2006). Principles of Hyperplasticity. Springer. Laloui, L., Klubertanz, G. & Vulliet, L. (2003). Solidliquidair coupling in multiphase porous media. International Journal of Numerical and Analytical Methods in Geomechanics, v27-3, (183–206). Moradessi, H., Laloui, L. & Aubry, D. (1994). Thermodynamical approach for camclay-family models with Roscoe-type dilatancy rules. Int. J. Num. Analyt. Meth. Geomech. 18, (133–138). Puzrin, A.M. & Houlsby, G.T. (2001). Fundamentals of kinematic hardening hyperplasticity. Int. J. Solids Struct. 38, (3771–3794). Sheng, D., Sloan, S.W. & Gens, A. (2004). A constitutive model for unsaturated soils: thermomechanical and comutational aspects. Computational Mechanics, (31–44). Vaunat, J. & Romero, E. (2000). An elastoplastic hydromechanical model for unsaturated soils. Proc. Int.Work. on Unsaturated Soils, Trento-Italy, (121–138). Wheeler, S., Sharma, R.S. & Buison, M.S.R. (2003). Coupling of hydraulic hysteresis and stress—strain behaviour in unsaturated soils. Géotechnique 53, No. 1, 41–54. Ziegler, H. (1977). An Introduction to Thermomechanics. North-Holland, Amsterdam.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Discussion on meta-stable equilibrium in unsaturated soils E.J. Murray Murray Rix Geotechnical, Warwickshire, UK
B.J. Murray School of Chemistry, University of Leeds, UK
V. Sivakumar Department of Civil Engineering, Queen’s University of Belfast, Northern Ireland
ABSTRACT: A discussion is presented on meta-stable equilibrium and the significance in interpreting the behaviour of unsaturated soils. The paper brings together examples of thermal, mechanical and chemical metastable conditions to illustrate the problem in terms of thermodynamics. The arguments are extended to describe collapse and hysteresis mechanisms in unsaturated soils and the critical state strength on the transition between unsaturated and saturated conditions. 1
THE THERMODYNAMIC POTENTIAL
The principles of thermodynamics can be used to examine many aspects of material behaviour. This includes equilibrium and meta-stable equilibrium, numerous examples of which can be found in chemistry or physics. Under meta-stable equilibrium a material or system is not at its lowest possible thermodynamic potential. The system is likely to change to a lower potential state following some perturbation and given sufficient time. The conditions necessary for a meta-stable state are: (i) there must be a lower potential state; and (ii) mechanisms through which this metastable state may relax to a more stable state must be inhibited. Changes of phase between solid, liquid and gas provide the most frequent examples of meta-stable states but the thermodynamic potential and its minimisation is not just dictated by thermal and chemical change. A standard presentation of the thermodynamic potential in terms of the internal energy U is given in Equation 1: U = TS − pV +
μi mi
where, T is absolute temperature S is entropy p is pressure V is volume μi is the chemical potential mi mass
(1)
The three conjugate paired intensive variables (T , p and μi ) and extensive variables (S, V and m) on the right of Equation 1 represent the heat, mechanical and chemical potentials respectively. The significance of the extensive variables is that they are additive. Thus the total volume of a multi-phase material, such as an unsaturated soil, may be written as the sum of the volumes of the individual phases. In unsaturated soils the total volume is given by addition of the volumes of the air, water and solid phases (if the volumes of the interactions such as the contractile skin are included within the phase volumes). The paired intensive and extensive variables in Equation 1 are also extensive quantities. Thus the total chemical potential is often represented, as in Equation 1, by the summed potentials of the individual chemical potentials. While other potentials such as electrical or magnetic potentials can exist, the discussion is restricted to those in Equation 1. The various additive components of the thermodynamic potential will each tend to minimise at ‘equilibrium’, whether this is a true minimum equilibrium condition or a meta-stable equilibrium condition. The temperature T , pressure p and chemical potential μi may be thought of as intensive ‘forces’, which drive changes in the extensive entropy S, volume V and chemical mass mi respectively. Thus a small incremental change in the energy of a thermodynamic system may be expressed as the sum of the products of the intensive ‘forces’ and the generalized extensive ‘displacements’. Imbalance in the ‘forces’ causes ‘displacement’ and the products of the conjugate pairs given in the following equation is the total energy
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transfer for the condition where S, V and mi are the variables of state. dU = TdS − pdV +
μi dmi
(2)
Equation 2 is the differential form of the thermodynamic potential Equation 1 for infinitesimal changes. 2
META-STABLE EQUILIBRIUM
There are physical and chemical phenomena where analogous behaviour can be used to explain the underlying concepts. A simple mechanical analogy of a potential and its minimization is illustrated in Figure 1 where a ball is shown rolling down a valley side. The ball at A has a tendency to reduce its potential energy to a minimum value, which within the defined system is at D in the valley bottom. The potential energy for a ball of given mass is dictated by its height above the valley floor. The significance of the minimization of the thermodynamic potential for a soil is that equilibrium conditions are established and the potential of the soil system comprising the particles, water and air achieves a minimum under this equilibrium state. However, achieving an absolute minimum potential is ‘easier said than done’. Conditions can arise where a meta-stable equilibrium is established where an absolute minimum potential is not achieved as can be explained by again examining Figure 1. As the ball rolls down the valley side it is possible that a ledge (Position B) prevents the ball rolling down to the valley bottom, without some other factor agitating the ball in order for it to pass over the lip of the ledge at Point C, to the more stable state at D. Point B represents a position of meta-stable equilibrium as a lower equilibrium potential exists within the system. The lip at C represents an ‘energy barrier’ preventing the ball from achieving a minimum potential state. The phase changes of water present readily appreciated meta-stable conditions. Consider the case where
Elevation
A decreasing potential C B
D
Figure 1.
Analogy of ball rolling down valley side.
water is contained in a beaker and heated in a microwave. The water may not change to vapour at its boiling point of 100◦ C if the water is ‘clean’ as nucleation of the vapour phase is inhibited. When water exists at ambient pressure but at a temperature above 100◦ C, it is said to be in a superheated state. If this meta-stable water is agitated, possibly by the introduction of a solid substance, such as coffee, nucleation to the vapour phase occurs and the liquid suddenly boils as the superheated liquid changes to a vapour phase. Accidental superheating of a liquid is best avoided for safety reasons (Erné, 2000). At the other extreme of freezing it is interesting to draw on the contents of a letter written by Joseph Black (Professor of Chemistry in Edinburgh) in 1775 to Sir John Pringle. In the letter the writer describes some crude experiments of the freezing of water: (i) of water initially boiled then cooled to room temperature; and (ii) of water thawed from snow to room temperature. Separate cups of boiled and unboiled water were placed outside under freezing conditions. The boiled water froze readily and the unboiled water remained fluid. However, on agitation with a toothpick, the unboiled water also froze. Drawing on earlier work by Fahrenheit, who found that boiled water placed in glass globes purged of air did not freeze at temperatures some degrees below the normal freezing point, he described how Fahrenheit found that the supercooled water suddenly froze on agitation or exposure to air. Black (1775) argued that since one effect of boiling water was to expel the air, which it naturally contained, then as soon as the water cooled it began to absorb air again over a period of time; and the air entering the boiled water provided sufficient agitation to the water to facilitate passing over the energy barrier and freezing. The examples of meta-stable superheated and supercooled water illustrate that the creation of a new phase involves an interface, which in many situations costs energy and gives rise to an energy barrier to the formation of the new phase, analogous to the energy barrier at Point C in Figure 1. The examples also illustrate that substances under meta-stable conditions can experience dramatic change if a mechanism for change exists. The phase changes of water are driven by heat and chemical potentials. But the thermodynamic potential of Equation 1 also includes a mechanical potential term (pV) and there is no reason to suppose that similar abrupt energy changes will not occur at the extremes of mechanical change in soils. Such behaviour is considered true of unsaturated soils at the extremes of near-saturation and very dry conditions. Some caution must however be exercised as the occurrence of meta-stable conditions may represent various degrees of stability. In fact, while stable conditions may be perceived to exist, gradual changes may actually be taking place. Consider the nucleation
554
of gas bubbles in water and their attachment to the sides of a container. The bubbles may be perceived as attaining meta-stable equilibrium and only with some other influencing factor is a lower potential achievable by agitation of the bubbles allowing them to rise through the liquid. However, the growth and decay of gas bubbles (Keller, 1964), particularly within the void spaces of soils, is complex (Murray, 2002) and the rate of expansion and decay of the volume of free air is likely to influence the perceived equilibrium conditions. Bardon and Sides (1967) concluded that in unsaturated soils there is evidence that equilibrium in terms of Henry’s law may require a considerable time interval, far greater than in the absence of soil particles.
experimental observation that some aqueous solutions of inorganic salts, when cooled rapidly, first deposited crystals of a less stable form than that which normally crystallises. Ostwald (1897) attempted to generalize this sort of behaviour by propounding a ‘rule of stages’ which Mullen states as:
3
This quote succinctly summarises the law of stages and also hints at a physical explanation for it. If the transitions to lower energy states are governed by energy barriers then the height of these energy barriers will necessarily govern the rate at which the new states form. Hence, the state that forms from a metastable state is governed not by thermodynamics, but by kinetics (the kinetic rate being defined as the rate of change from one state to another). In many circumstances the energy barrier will be much smaller, and kinetics faster, for the transition to some intermediate state that more closely resembles the initial state. A good example of this is the formation of ice crystals from cold supersaturated water vapour. In an elegant experiment, Huang and Bartell (1995) cooled water vapour very rapidly in a jet expansion and at 200 K clusters of molecules formed. At this low temperature the thermodynamically most stable phase of the clusters is ice, however they demonstrated that liquid water droplets initially formed and only at some finite time later did these droplets then relax to form crystalline ice. In fact, when ice did form it did so in a meta-stable cubic form rather than the more stable hexagonal form and only at some later stage did the cubic ice particles relaxed to hexagonal ice. It is worth noting that such phase transformations can take protracted periods of time and meta-stable states can appear to be the most stable state (Murray and Bertram, 2006; Murray et al. 2005). A similar cascade through a sequence of metastable states may occur as soils relax. For instance in soils that are subject to collapse, there are a number of interacting factors including the interparticle stresses, the re-orientation of soil particles (or aggregates of particles) and the movement of water and air within void spaces that are changing anisotropically. The interplay between these factors may lead to the formation of meta-stable states which form more readily that the most stable state. Only given enough time and sufficient disturbance may the most stable state be obtained.
MINIMISATION OF THE POTENTIAL
Enthalpy, H , acts as the potential for work for a system at constant pressure (Callen, 1965) and is given by: H = pV + U
(3)
The Enthalpy Minimum Principle means that the mechanical equilibrium of a specimen in the triaxial cell under constant pressure is controlled by the minimization of the enthalpy which acts as the thermodynamic potential. This is true not just for isotropic loading conditions. As shown by Murray and Brown (2006), under anisotropic stress condition p is the mean stress, which complies with the term pV being an extensive quantity. Consistent with the minimization of the total enthalpy of a soil system at equilibrium is the minimization of the individual components of the total enthalpy. This is the same as saying that the stresses and pressures within the soil system will adjust to achieve a minimum energy condition. A more complete statement would be ‘the stresses adjust to a minimum under the volumetric restrictions’ as it is necessary to allow for meta-stable equilibrium of the soil particle structure. There could be a lower thermodynamic potential and reduced stresses and pressures associated with a redistribution of the particles. The analogy of a ball on a ledge on the valley side may again be drawn on. The ball is in meta-stable equilibrium on the ‘ledge’ but could achieve a lower potential if it were to roll down the slope to the valley bottom. This might correspond to collapse of a soil structure. At the ledge, the components of the soil system minimise their potential within the confines of the system. 4
STAGED CHANGES
As discussed by Mullen (2001), in the early part of the 19th century several researchers made the
‘An unstable system does not necessarily change directly into the most stable state, but into one which most closely resembles its own, i.e. into another transient state whose formation from the original is accompanied by the smallest loss of free energy.’
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5
HYSTERESIS AND COLLAPSE IN SOILS
The dependence of soil behaviour on stress history is apparent in moisture characteristic curves obtained on wetting and drying. On desaturation of a fine-grained soil, an aggregated structure results as air begins to fill the larger void spaces, with water filling the smaller intra-aggregate pore spaces with a small amount of water remaining at the inter-aggregate contact points. The aggregated structure persists during subsequent wetting and drying. Only if the soil is wetted and sufficiently agitated would it be possible to restore a dispersed soil structure. Wheeler et al. (2003) describe the existence of bulk water within the water-filled voids and meniscus water at the inter-particle contacts around air-filled voids. The bulk water complies with the water retained within the smaller intra-aggregate pores of fine-grained soils and the meniscus water complies with the water at the points of contact between the aggregations. The suction within the bulk water influences the normal and tangential forces at particle contacts whereas the suction within the meniscus water influences only the normal forces at inter-particle or inter-aggregate contacts. Wheeler et al. (2003) link the irreversibility during wetting and drying, and the onset of plastic deformations at suctions below suction levels previously experienced, with hydraulic hysteresis forces arising from the bulk and meniscus water. This gives rise to not only hysteresis but a plastic creep phenomenon during repeated wetting and drying. It is interesting to re-examine the results of a suction-controlled oedometer test on highly expansive clay reported by Alonso et al. (1995). The results are presented as Figure 2. During the first wetting path C1 , initial swelling was followed by collapse compression as the suction was progressively reduced. The plot shows significant irreversible components of compression during subsequent drying-stages of wetting-drying cycles C2 to C5 . The phenomenon of
collapse is consistent with an abrupt energy change from a meta-stable to a more stable, lower potential state. The subsequent phenomenon of hysteresis and plastic irreversible strains are consistent with metastable conditions and the soil not necessarily changing directly into the most stable state. The soil exhibits a staged transition analogous to the transient meta-stable phases observed by Ostwald (1897). Mathematical models of soils must take into consideration these meta-stable states in addition to considering the most thermodynamically favourable state. 6
CRITICAL STATE STRENGTH OF UNSATURATED SOILS
For saturated soils the deviator stress, q, at critical state is given by: q = M (p − uw )
(4)
where M is the stress ratio parameter q = (σ1 − σ3 ) p = (σ1 + 2σ3 )/3 uw is the pore water pressure σ1 and σ3 are the axial and radial total stresses in a triaxial cell test This is based on the effective stress being the controlling stress state variable. However, in unsaturated soils it is necessary to take account of the dual stress regime. Murray (2002), Murray & Sivakumar (2005) and Murray & Sivakumar (2006) derive the following equation for the stress state in an unsaturated soil, based on enthalpy being an extensive thermodynamic variable: pc = (p − ua ) + s
vw v
(5)
where, pc is the mean coupling stress ua is the pore air pressure vw is the specific water volume v is the specific volume s = (ua − uw ) is the matric suction
Figure 2. Wetting-drying cycles performed on Boom clay under oedometer conditions (Alonso et al. 1995).
The results of triaxial shearing tests on unsaturated kaolin (LL 70%, PL 34%, clay content 80%) tested to the critical state (Wheeler & Sivakumar, 1995) are plotted in Figure 3. The critical state results lie close to a unique line given by the following equation: q p (6) = Ma c − 1 + s s ! ! where is the intercept on the q s axis at pc s = 1.
556
3.0 Ma Suction stress ratios Ma and Mb
Ma 2.5 2.0
1
q/s
M 1.5 1.0 M = 0.84 = 0.6 0.5
0.8 0.6 0.4 0.2
0.7
0 0
0.5
1
1.5
2 p'c/s
2.5
3
3.5
Ma Mb = 0.6
0.8
0.9
1
vw/v
4
Figure 4.
Plots of Ma and Mb against vw /v for kaolin.
pc /s
Figure 3. q/s against for unsaturated conditions and q against (p − uw ) for saturated conditions.
Substituting for pc from Eq. (5) gives q = Ma ( p − ua ) + Mb s where, Mb = Ma
"v
w
(7)
# −1 +
v Ma and Mb are the net stress and suction stress ratios respectively. Equation 7 is in a similar form to that suggested by Toll (1990) and Toll & Ong (2003). In their analysis it is assumed that there is a smooth transition of critical state strength from unsaturated to saturated conditions and accordingly Ma and Mb vary with suction with the condition Ma = Mb = M at saturation. The derivation given above of Equation 7 does not rely on this assumption and Ma is shown experimentally in Figure! 3 to be constant, with Mb varying linearly with vw v as in Fig. 4. Decreasing Mb is consistent with the water phase being drawn back into the finer pores in the soil aggregations. Toll (1990, 2003) suggested that the packets of aggregated particles in an unsaturated soil act like large particles that are maintained by the suction and are not easily broken down or destroyed even at shearing to the critical state. If an aggregated structure were to be maintained on saturation of a soil specimen, Equation 7 indicates that the deviator stress would be given by q = Ma (p − uw ). The value of Ma from Figure 3 is 0.86 which is greater than M = 0.82 for a saturated soil. The difference though small is important and reflects the difference in the particle structure or soil fabric. The aggregated particle structure gives rise to a greater stress ratio parameter. As suggested by Murray (2002), under shearing to the critical state the aggregated structure in unsaturated soils is only
likely to break down to a more dispersed structure at low values of suction and there is a discontinuity, or abrupt energy change, between saturated and unsaturated conditions. No obvious breakdown of the aggregate structure during shearing is indicated for suctions even below 100 kPa. Results of a large number of other tests and on a range of materials confirm the relationships. It is instructive to examine Equation 3 for enthalpy where the isotropic pressure p is replaced by the mean stress. The equation may be written as:
1 (σ1 + 2σ3 ) V + U 3 1 = (σ1 − σ3 ) V + σ3 V + U 3
H=
(8)
Thus for a givenσ3 , the potential given by H for a pressure controlled system is a minimum when q = (σ1 − σ3 ) is a minimum. If the suction is not sufficient to hold the aggregation of particles together under shearing, they are likely to break down to form a more dispersed structure and give a lower shearing resistance at critical state. The transition of critical state strength from unsaturated to saturated conditions is thus seen as exhibiting phenomenon consistent with meta-stable conditions previously discussed. There is an energy barrier which has to be overcome by shearing in order to break down the aggregated soil structure to the more stable lower potential, lower strength state, of a dispersed soil structure. It is not clear from available evidence whether this is in stages but further investigation at low values of suction would shed light on the behavioural trends.
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7
CONCLUSIONS
Unsaturated soils exhibit meta-stable conditions which can lead to abrupt changes such as collapse settlement. They also exhibit hysteresis in the moisture characteristic curves and plastic deformations below the previous maximum stress level consistent with a staged change to a lower potential. There are a number of interacting factors affecting the rate, magnitude and degree of change in any specific test. These including the interparticle stresses, the re-orientation of soil particles (or aggregates of particles) and the movement of water and air within void spaces. Stress history and anisotropy of the soil affect the starting conditions and will also play a major role. The transition of critical state strength from unsaturated to saturated conditions also exhibits abrupt changes as a result of soil fabric changes from an aggregated to a more dispersed soil structure, and the soil endeavouring to relax to a lower, more stable, potential state. It is argued that the suction acts as an ‘energy barrier’ to the changes. REFERENCES Alonso, E.E., Lloret, A., Gens, A. and Yang, D.Q. (1995). Experimental behaviour of highly expansive doublestructure clay. Proc. 1st Int. Conf. On Unsaturated Soil, Paris, 1, 11–16. Barden, L., and Sides, G.R. (1967). The diffusion of air through the pore water of soils. Proceedings of the 3rd Asian Regional Conference on Soil Mechanics and Foundation Engineering, Israel, Vol. 1, 135–138. Black, J. (1775). The supposed effect of boiling upon water, in disposing it to freeze more readily, ascertained by experiments. Letter to Sir John Pringle, Bart. P.R.S., in Philosophical Transactions (1683–1775) of the Royal Society, Vol. 65 (1775), 124–128. Callen, H.B. (1965). Thermodynamics. John Wiley and Sons, Inc. Erné, B.H. (2000). Thermodynamics of water superheated in the microwave oven. Jnl. of Chemical Education, Vol. 77, No. 10, 1309–1310. Huang, J.F. & Bartell, L.S. (1995). Kinetics of homogeneous nucleation in the freezing of large water clusters. J. Phys. Chem. 99, 3924–3931.
Keller, J.B. (1964). Growth and decay of gas bubbles in liquids. Proc. of the Symp. on Cavitation in Real Liquids. General Motors Research Laboratories, Warren, Michigan, 1962, Ed. Davies R., Elsevier Publishing Co.: Amsterdam—London—New York. Mullen, J.W. (2001). Crystallization. Fourth Edition, Elsevier Butterworth-Heinemann, ISBN 0 7506 4833 3. Murray, B.J. and Bertram, A.K. (2006). Formation and stability of cubic ice in water droplets. Phys. Chem. Chem. Phys., 8, 186–192. Murray, B.J., Knopf D.A. and Bertram A.K. (2005). The formation of cubic ice under conditions relevant to Earth’s atmosphere. Nature, 434, 202–205. Murray, E.J. (2002). An equation of state for unsaturated soils. Can. Geotech. J. 39, 125–140. Murray E.J. and Brown, J. (2006). Assumptions in equilibrium analysis and experimentation in unsaturated soils. Proc. 4th Int. Conf. on Unsaturated Soils, UNSAT 2006, Carefree, Arizona, ASCE Geotechnical Special Publication No 147, Ed. Miller, G.A., Zapata, C.E., Houston, S.L. and Fredlund, Vol. 2, 2401–2407. Murray, E.J. and Sivakumar, V. (2005). Stresses and conjugate strain-increments in plotting experimental data for unsaturated soils. International Symposium on Advanced Experimental Unsaturated Soil Mechanics, Trento, Italy, 27–29 June, Ed. Tarantino, A, Romero, E. and Cui, Y.J. Murray E.J. and Sivakumar, V. (2006). Equilibrium stress conditions in unsaturated soils. Proc. 4th Int. Conf. on Unsaturated Soils, UNSAT 2006, Carefree, Arizona, ASCE Geotechnical Special Publication No 147, Ed. Miller, G.A., Zapata, C.E., Houston, S.L. and Fredlund, Vol. 2, 2392–2400. Ostwald, W. (1897). Studien über die Bildung und Umwandlung fester Körper. Z. Phys. Chem. 22, 289–330. Toll, D.G. (1990). A framework for unsaturated soil behaviour. Geotechnique 40, No. 1, 31–44. Toll, D.G. (2003). On the shear strength of unsaturated soils. International Conference on Problematic Soil, Vol. 1, Nottingham, UK, 127–136. Toll, D.G. and Ong, B.H. (2003). Critical state parameters for an unsaturated residual sandy soil. Geotechnique 53, No. 1, 93–103. Wheeler, S.J. and Sivakumar, V. (1995). An elasto-plastic critical state framework for unsaturated soils. Geotechnique 45, No.1, 35–53. Wheeler, S.J., Sharma, R.S. and Buisson, M.S.R. (2003). Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils. Geotechnique 53, No.1, 41–54.
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Advanced hydro-mechanical coupling for unified constitutive modelling of unsaturated soils M. Nuth & L. Laloui Soil Mechanics Laboratory, Ecole Polytechnique Fédérale de Lausanne, Switzerland
ABSTRACT: A new unified constitutive hydro-mechanical model named ACMEG-s is formulated to improve modelling of unsaturated soils in free or constrained conditions. Indeed, due to particular mechanical and hydraulic boundary conditions, some natural and engineered fine grained soils are highly constrained. When submitted to in-situ wetting-drying cycles, such soils are prone either to collapsing or to generating swelling pressures. The proposed unified framework provides a direct explanation for complex confined behaviour of unsaturated soils. A sophisticated saturated model based on two coupled plastic mechanisms has been extended to deal with partially saturated states. The adopted stress framework includes a Bishop-type effective stress for the mechanical part and the matric suction for the hydraulic part. Some simplifications brought by the socalled generalised effective stress representation versus conventional net stress and suction representation are overviewed and related to the definition of the ‘Loading Collapse’ yield curve. Other implications of the unique mechanical stress associated with suction couplings are shown to be essential in prediction. The most pioneering results from the model validation by integration via a custom numerical tool are exposed. The combination of the advanced yet simple stress framework and the adapted yield locus is used for the prediction of oedometric and constant volume tests, leading to a straightforward interpretation of swelling pressure tests.
1
INTRODUCTION
The current knowledge of unsaturated soil behaviour has been established from laboratory tests that shall be termed here as ‘‘conventional’’. The volumetric information, namely the mechanical deformation and pore fluids distributions are expressed as functions of variations in mechanical load, or exterior stress, and water content changes, or matric suction. Cohesive soils commonly present a preconsolidation pressure that increases with suction, meanwhile the soil stiffness evolves with saturation. Lastly, the shear strength is usually observed to increase with dehydration. The laying down of natural soil layers in the field often induces particular mechanical and hydraulic boundary conditions that go beyond the conventional laboratory tests. In fact, swelling collapse behaviour, which is the most harmful feature of behaviour for any engineering work on unsaturated soils occurs under important mechanical loads. A further level of complexity is reached for deep underground layers, where the hydraulic and mechanical elasto-plastic response to wetting under fully confined conditions is hardly predictable at present.
Indeed, partial saturation in geomechanical problems raises the need for (i) an advanced elasto-plastic framework, (ii) the identification of hydro-mechanical state variables and (iii) the accounting for intrinsic hydromechanical couplings. It is proposed thus to extend a saturated elastoplastic model (Hujeux 1985) to partial saturation by using an adequate effective stress, a simplified reversible description of the water retention curve and accounting for the capillary effects on the mechanical stress-strain response. Judging on experimental results, the key parameter to be modified with suction is the preconsolidation pressure through an improved version of the Loading Collapse yield curve. Among the noticeable breakthroughs, it is shown that a single mechanical stress leads to a number of simplifications in the constitutive modelling. The model is integrated in order to simulate experimental results essentially from drying wetting cycles. Combination between imposed stresses, strains and suction are made possible in the numerical simulations. Whenever displacements are free to occur, the repartition of the elastic and plastic deformations as well as non-linearity are automatically accounted for by the model. Swelling pressures are also accurately generated within the proposed framework.
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2
BASIC IMPLICATIONS OF GENERALISED EFFECTIVE STRESS
1 106 8 10
e −1 dεije = Dijkl dσkl
Matric suction s (Pa)
The original concept of effective stress (Terzaghi 1936) intends reaching homogenization of a multi phase porous medium into a mechanically equivalent, single-phase, single-stress state continuum. Then, the deformations are linked to changes in the macroscopic stress quantity: (1)
where dεije is the elastic strain increment of the solid e is the mechanical elastic matrix, and skeleton, Dijkl dσkl the increment of effective stress. Among the possible forms of effective stress extended to unsaturated soils, that of Bishop-Schrefler’s (Bishop 1959, Schrefler 1984) is used: σij = (σij − pg δij ) + Sr (pg − pl )δij
(2)
where pg and pl define the gas and liquid pressures, respectively, with the assumption of two idealised homogenous fluid phases filling the porous space. σij is the external stress. Sr is the degree of saturation, used to scale down the fluids contributions to the effective stress proportionally to their respective volumetric fractions. Equation (2) defines the ‘generalised effective stress’. Following the discussion from Nuth and Laloui (2007), this effective stress constitutes a single mechanical stress variable to be used within advanced constitutive frameworks. However, if thermodynamic considerations (Hutter et al. 1999) do justify the choice of this mechanical effective stress, they also converge towards the need for a second stress variable to build an exhaustive stress and work conjugate strains hydro-mechanical framework, as written below:
σij = σnet ij + Sr sδij s = pg − pl
and
εij Sr
(3)
σnet ij = σij − pg δij is the net stress and εij the skeleton strain. Equation (2) reveals an implicit direct dependency of the effective stress on both the matric suction and the degree of saturation. The major contribution of the use of a single mechanical effective stress is thus perceptible at the constitutive modelling level. The generalised effective stress (Eq. 2) is non linearly incremented either by modifications in the external mechanical stress σij or in the matric suction s or a combination of both, the consequence of which is a generation of a skeleton strain ε. Its increment dε is decomposed into an elastic part and a plastic part (dε = dεe + dε p ). As the mechanical stress
Possible yield limits
Net stress interpretation
5
6 105 4 105 2 105 0 -2 105
Effective stress interpretation 0
4 104
8 104
1.2 105
Mean stress pnet or p' (Pa) Figure 1. Drying path in two interpretations on Sion silt, experimental data from Geiser et al. (2006).
is unique, it is easy to determine whether the stress state remains inside the elastic domain, on the basis of the value of effective stress and yield locus only. Consequently, a single mechanical yield surface is sufficient. Yielding is thus uniquely predictable upon conventional mechanical loading path as well as along wetting-drying processes. By opposition, if the number of mechanical stress variables is double (e.g. net stress and suction), the strain increment will be divided into two parts related to each stress variable, and the yield locus will be double. For instance in BBM type frameworks (Alonso et al. 1990) the only way to yield upon drying (Fig. 1) is to introduce the ‘Suction Increase’ yield curve in addition to the ‘Loading Collapse’ curve. As illustrated in Fig. 1, such a SI yield locus is no longer necessary when using generalised effective stress. In the following, the analysis of experimental results within the proposed framework provides a convincing justification for simplifying the yield locus as proposed. Other advantages of framework (3) such as simplification in shear strength modelling have been investigated by Nuth and Laloui (2007). 3
CONSTITUTIVE MODELLING
A new constitutive model for unsaturated soils was formulated to understand better the constrained behaviour under hydric cycles. The principle is first to take advantage of the generalised effective stress as a single mechanical stress replacing the conventional Terzaghi’s effective stress. Then, an advanced saturated elasto-plastic constitutive model (Hujeux 1985)
560
is used as a reference for the conventional mechanical behaviour (non linear elasticity, plastic mechanisms, hardening plasticity). The hydraulic behaviour of the partially saturated soil (soil water retention curve) is also added to the framework, and the reference model is modified to include the effects of suction on the mechanical behaviour. To summarize the formulation of the model ACMEG-s detailed in Laloui and Nuth (2005):
1.2
Degree of saturation Sr (-)
(a)
0.6
=
pc0
for 0 < s < se # 1 + γs log sse
"
0.4 0.2 Exp. Van Genuchten 0 100
for s > se (4)
8
10
D Wetting
107
s
C
e
106 Yielding zone
105 B 104 Drying
1000 A E 100 100
(b) 4
6
10
108
10
Mean effective pressure p' (Pa) (c) A 0
B
(-)
Exp. ACMEG-s
v
(5)
pCR0
where are respectively the actual and initial critical state pressures ( pc = d · pCR , d is a material parameter), and β the coefficient of compressibility. 3.1
10
Stress path Initial LC Final LC
108
Volumetric strain
pCR ,
D 6
109
pc0 is the initial preconsolidation pressure at zero suction, γs is a material parameter, and se is the air entry suction (that is the suction beyond which the degree of saturation becomes smaller than 1). Eq. (4) accounts for the effect of capillarity on the size of the elastic domain. The reference stress-strain relationship in the saturated model is basically given by equation (1) for the elastic behaviour. Irreversible behaviour of the soil p gives birth to a volumetric plastic strain εv follow- p ing the normal compression line in plane εv − ln p which slope is defined by that of the critical state line: p log CR = βεvp pCR0
10
4
Matric suction (Pa)
Matric suction s (Pa)
⎩p˜ c (s)
C
E
0.8
i. The skeleton strain is directly linked only to σ (Eq. 1). Secondary effects of suction on mechanical compressibility are featured within the constitutive relations. ii. The distribution of pore fluids is described via the degree of saturation. In conformity with framework (3), Sr is related to s by the soil water retention curve anytime. An elementary non-linear reversible model is used here (Van Genuchten 1980) for the hydraulic behaviour. iii. The mechanical yield surface depends on the level of suction and, in particular, the preconsolidation pressure pc , is directly dependent on suction. Equation (4) below defines an improved ‘Loading Collapse’ curve: ⎧ ⎨p˜ c (s) = pc0
1
B
A
-0.12
Drying
-0.24 E C
-0.36
D
Wetting -0.48
Isotropic stress paths
100
Figures 2a and 2c plot the laboratory experimental result of a wetting drying cycle on clay under free mechanical boundary conditions. The fine grained material, initially slightly overconsolidated, is free to deform. Plastic straining is observed up to the air entry
104
106 se
108
Matric suction (Pa) Figure 2. Simulation of volumetric response to hydric cycle under constant null net stress. Experimental points from tests on white clay (Fleureau et al. 1993).
561
10
6
(a)
Matric suction s (Pa)
A
Wetting
10
5
B Yielding zone
s
e
10
C Wetting path Initial LC Final LC
D
4
5
10
Mean effective pressure p' (Pa) 0.03 (b) B
Wetting
Volumetric strain
v
(-)
0.015
A
0 -0.015 D C
-0.03 -0.045
Wetting path Mech. path -0.06
5
10
Mean effective pressure p' (Pa) 0.02 (c) B
v
(-)
0.01
Volumetric strain
value of suction se , while for suctions greater than se the material volume tends to stabilize. According to the present constitutive interpretation, the change in mean effective stress is caused by changes in both suction s and degree of saturation Sr . The soil water retention curve (Fig. 2a) is therefore an important input to the model. The mobilisation of the isotropic plastic mechanism is shown in the s − p stress plane, along with the followed stress path (Fig. 2b). The volumetric response εv is plotted as a function of matric suction in Fig. 2c. Even though the matric suction is the only control variable in this experiment, the model predictions are the result of the mechanical relationship linking εv to variations in p . Consequently, the elastic and plastic behaviour depends on the effective stress state (Fig. 2b) being inside the elastic domain or on the yield locus. The advanced shape of the loading collapse curve (Fig. 2b), combining a straight vertical part and an upper non-linear outline, contributes to achieving a proper fit. In the saturated domain s < se ; Sr = 1 any change in suction is directly equivalent to a change in p (Eq. 3) like during an isotropic purely mechanical loading. When Sr = 1, the volumetric response is thus identical in both εv − ln p and (εv − ln s) representations, with standard unloading-reloading paths (path AB and CE) and elasto-plastic part (path BC). Once se is reached the preconsolidation pressure is imposed to increase with suction (Eq. 4), faster than the mean effective stress increases (Fig. 2b), resulting in recovering an elastic response (CD). The elastic linear path in εv − ln p whose slope is indicated in dotted line in Fig. 2c for a matter of comparison permits to estimate (via Eq. 2) the response in (εv −ln s) plane. The obtained solid line CD in Fig. 2c is non linear. The swelling collapse behaviour upon soaking is a second inbuilt feature of the model. It is widely observable experimentally (Fig. 3c) when wetting a material under a high initial net stress. Again, this behaviour justifies the use of the Loading Collapse curve for the constitutive framework, even though the stress path is non-linear in s − p plane. Starting from the experimental initial state A (Fig. 3a), pc decreases faster than the mean effective stress upon wetting (Eq. 4). Two volumetric responses are predicted (Figure 3b and c); (i) a fully reversible swelling upon effective stress relief along paths AB and CD and (ii) a plastic compression due to yielding on LC curve along path BC. The superposition of numerical and experimental results for kaolin shows discrepancies between the predicted suction levels for the activation of the plastic response, mostly attributable to possible inaccuracy in the LC curve determination, carried out on the basis of other isotropic loading tests at various levels of suction. However, the volumetric variations are fairly
A
0 Wetting
-0.01 D -0.02
Exp. 1 Exp. 2 Exp. 3 ACMEG-s
C -0.03 -0.04 0
5
2 10
5
4 10
Matric suction s (Pa) Figure 3. Prediction of wetting collapse. Experimental points from tests on kaolin (Sivakumar 1993).
562
well predicted and the qualitative trends for alternative swelling and collapse are reliable. Oedometric conditions
Matric suction s (Pa)
3.2
9
10
Although oedometric paths are hardly ever used in conventional validation processes, they have major importance in experimental characterisation of unsaturated soil behaviour, provided that unsaturated oedometric cells are more widespread in geotechnical laboratories than unsaturated triaxial or isotropic compression apparatuses. Basically, experimental results from oedometric tests (e.g. Fig. 4) are similar to those of unsaturated isotropic compression, with an apparent preconsolidation pressure shifted with suction and modifications in compressibility. However, only an advanced numerical integration of the model catering for zero lateral total strain condition enables to reproduce such paths. The stress paths (Lloret et al. 2004) simulated here include a hydraulic equalization to a given level of suction and an oedometric compression at a constant level of suction (Figure 4a). Simulation of the wetting or drying processes from an initial suction of 138 MPa shows the model to predict satisfactorily the trend and magnitude of volumetric strains (Fig. 4b). Even though the global swelling trend is observed upon wetting for all tests, punctual decrease in εv is attributed to (i) the occurrence of mechanical compression prior to or during equalization and (ii) seamless plastic episodes with initiation of wetting collapse. Subsequent oedometric compression tests (Fig. 4c) at constant suctions from 0 (test5) to 500 MPa (test1) are also remarkably well-predicted with the proposed framework.
(a)
Test 2
Initial point
8
10
Test 3 7
10
Test 4 106 Final point
5
10
Test 5
4
6
10
8
10
10
Vertical stress
v
(Pa)
(b)
0.32
Volumetric strain
v
(-)
Exp. test 1 ACMEG-s test 1 Exp. test 3 ACMEG-s test 3 Exp. test 5 ACMEG-s test 5
0.24
0.16
0.08
Initial point
0
Wetting 5
7
10
9
10
10
Matric suction s (Pa) 0.4
Swelling pressure
Exp. 1 Mod. 1 Exp. 2 Mod. 2 Exp. 3 Mod. 3 Exp. 4 Mod. 4 Exp. 5 Mod. 5
(c)
(-)
0.3 v
The experimental behaviour of fully confined samples submitted to a wetting path is plotted in Fig. 5b and 5c. During swelling pressure tests, the total strain is imposed to remain null whereas effective and net stresses are generated within the cell. As soil wetting provokes swelling or collapse under free displacement conditions, confined soaking generates stresses to prevent such straining. According to the initial state (level of suction), the maximum generated pressures are variable. Also, the generated vertical stress σv does not hold a linear dependency on matric suction, and its evolution trend even tends to reverse twice (Fig. 5b). Again, with the help of the LC yield curve and effective stress concept together, ACMEG-s provides a straightforward interpretation of the swelling pressure with a distinctive stress path in the planes record, s − p and (s − pnet ) (Fig. 5a). The deduced stress
Volumetric strain
3.3
Test 1
0.2
0.1
0
-0.1 4 10
5
10
6
7
10
Vertical net stress
10 v
8
10
(Pa)
Figure 4. Back prediction of hydro-mechanical tests under oedometric conditions (Lloret et al. 2004).
563
Effective stress Net stress
100
Matric suction (MPa)
plane (s − σv ) (Fig. 5b) also reflects three zones of interest, the repartition of which is linked to the shape of the LC curve. At the initiation of wetting, i.e. domain A, the process is fully reversible as the stress state remains within the elastic domain; only constitutive equation (1) is needed. The elastic deformation is null so the variation in effective stress must be null too. This requires an increase in net stress to compensate the reduction of suction (Figure 5b). This phenomenon is in agreement with the unified framework according to which the increment of net stress is deduced from generalised effective stress definition: σnet ij = σij − Sr sδij = − Sr sδij (6)
(a)
A 10 Yielding zone B 1 C Wetting 0.1 Initial LC Final LC
0.01
1
100
Mean stress p', p (MPa) net
Equation (6) also indicates that the soil water retention curve model controls the non linearity of stress response in (s − σv ) plane anytime. Then, wetting in zone B implies yielding on the LC curve. The total deformations remain null but a plastic deformation is generated, balancing the elastic part of the deformation. The occurrence of elasto-plastic strains provokes a release of the effective stress according to the elastoplastic constitutive model, and obviously a different trend for the evolution of the net stress. Once suction drops down to the air entry value, the ultimate zone C is entered. Due to the shape of LC curve, all deformations are elastic in this zone so that Eq. (1) only is needed, with the simplification Sr = 1.
1000 SP1 EXP SP2 EXP SP3 EXP SP4 EXP
100
SP1 MOD SP2 MOD SP3 MOD SP4 MOD
10
Wetting
Matric suction s (MPa)
(b)
1
0.1
-2
0
2
4
6
8
10
12
Vertical net stress σ (MPa)
4
v
1.2
A unified constitutive framework for unsaturated soils is proposed. It takes advantage of the generalised effective stress along with advanced couplings including capillary effects. The experimental behaviour under free swelling as well as constrained conditions justify the need for an improved shape of the LC yield curve. Also, during the wetting-drying cycles the water retention curve has a strong influence on the mechanical stress-strain response. The unified framework thus provides a straightforward interpretation of swelling pressure tests without introducing further complex concepts linked to expansive materials.
(c) 1
r
Degree of saturation S (-)
CONCLUSIONS
0.8 0.6 0.4 0.2 Exp. Van Genuchten 0 0.1
10
1000
ACKNOWLEDGEMENTS
Matric suction (MPa) Figure 5. (a) (b) Stress responses to swelling pressure tests (c) Soil Water Retention Curve. Experimental points: bentonite (Lloret et al. 2004).
This work was partly supported by Swiss Competence Center Environment and Sustainability, project ‘Triggering of Rapid Mass Movements in Steep Terrain’.
564
REFERENCES Alonso, E.E., Gens, A. & Josa, A. 1990. A Constitutive Model for Partially Saturated Soils. Geotechnique 40(3): 405–430. Bishop, A.W. 1959. The principle of effective stress. Tecnisk Ukeblad 39: 859–863. Fleureau, J.M., Kheirbeksaoud, S., Soemitro, R. & Taibi, S. 1993. Behavior of Clayey Soils on Drying Wetting Paths. Canadian Geotechnical Journal 30(2): 287–296. Geiser, F., Laloui, L. & Vulliet, L. 2006. Elasto-plasticity of unsaturated soils: laboratory test results on a remoulded silt. Soils and Foundations Journal 46(5): 545–566. Hujeux, J. 1985. Une loi de comportement pour le chargement cyclique des sols. In Génie Parasismique: 287–353. Paris, Les éditions de l’ENPC. Hutter, K., Laloui, L. & Vulliet, L. 1999. Thermodynamically based mixture models of saturated and unsaturated soils. Mechanics of cohesive-frictional materials 4: 295–338. Laloui, L., Nuth, M. 2005. An introduction to the constitutive modelling of unsaturated soils. European Journal of Civil Engineering, 9(5–6): 651–670.
Lloret, A., Romero, E. & Villar, M.V. 2004. FEBEX II Project: Final report on thermo-hydro-mechanical laboratory tests, ENRESA. Nuth, M. & Laloui, L. 2007. Effective stress concept in unsaturated soils: Clarification and validation of a unified framework. International journal for numerical and analytical methods in Geomechanics. DOI 10.1002/nag.645. Schrefler, B.A. 1984. The finite element method in soil consolidation (with applications to surface subsidence). PhD. Thesis. University College of Swansea. Sivakumar, V. 1993. A critical state framework for unsaturated soils. PhD. Thesis. Sheffield, University of Sheffield. Terzaghi, K. 1936. The shearing resistance of saturated soils and the angle between the planes of shear. International Conference on Soil Mechanics and Foundation Engineering: 54–56. Harvard University Press. Van Genuchten, M.T. 1980. A closed form of the equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal (44): 892–898.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Generalised elasto-plastic stress-strain relations of a fully coupled hydro-mechanical model M. Lloret, M. Sanchez & M. Karstunen University of Strathclyde, Glasgow, UK
S. Wheeler University of Glasgow, Glasgow, UK
ABSTRACT: Wheeler and co-workers have recently proposed an elasto-plastic framework involving the coupling of hydraulic and mechanical behaviour in unsaturated soils. A characteristic of the model is that it has been formulated in terms of Bishop’s stress and modified suction (i.e. suction multiplied by porosity). By using these new stress variables it is possible to predict the influence of the degree of saturation on the stress-strain behaviour. In particular, this new framework is able to represent the coupling between hydraulic and mechanical behaviour, allowing the prediction of influences of changes in the degree of saturation on the stress-strain behaviour and conversely, influences of volumetric strains on the water retention relationship. In this paper a 3D generalization of the stress-strain governing equations of this model is proposed based on concepts of multi-dissipative materials. This is a proper framework as in this model the coupled hydro-mechanical behaviour is described by three elasto-plastic mechanisms.
1 1.1
INTRODUCTION General
Recently, the interest for understanding the behaviour of unsaturated soils and for improving the knowledge of them has considerably increased. Reasons for that may be found by the fact that the unsaturated condition is observed in many engineering problems: construction of embankments, constructions near the ground surface and a wide range of geo-environmental problems. Moreover, the recently observed variability of climate, mainly in terms of dry-wet seasons (rainfalls, flooding, drought periods followed by wet season, etc.) may lead to the need of a better understanding of unsaturated soil behaviour. Constitutive models are very useful tools as they can be used as conceptual frameworks to improve our understanding by analysing the main mechanisms that underline the behaviour of unsaturated soils; and also, after the implementation of the models in computer codes, they can be used to solve actual problems involving unsaturated conditions. The Barcelona Basic Model, BBM (Alonso et al., 1990) is the most commonly used constitutive model for unsaturated soils. This is because the BBM is able to include, within the same framework, the main characteristics of unsaturated soil behaviour. However, some particular features of the unsaturated condition can not be fully described by this model. For
example, the model does not give complete information of the proportion of the void occupied by water; hence, mechanisms involving this variable, such as hydraulic hysteresis observed in wetting/drying paths, can not be completely described. In order to characterise these particular features, Wheeler et al. (2003) proposed a new framework of analysis involving the degree of saturation. In this work an extension to the 3D conditions of the isotropic model originally developed by Wheeler and co-workers is proposed.
2 2.1
MODEL FORMULATION Isotropic stress state
Due to space constraints only the main features of the coupled hydro-mechanical model are presented in this section. A more detailed description of it can be found in Wheeler et al. (2003). Considering the increment of work input per unit of unsaturated soil (Houlsby, 1997), the stress variables adopted in this work will be Bishop’s stress and modified suction (Wheeler et al., 2003). Particularly, for the isotropic stress state, the stress variables used can be expressed as: p∗ = p − Sr uw − (1 − Sr )ua
(1)
s∗ = ns = n(ua − uw )
(2)
567
Elastic volumetric strains can be expressed as: dεve =
κ dp∗ v p∗
(6)
where κ is the slope of an elastic swelling line in the (v, ln p ) plane for saturated conditions. When yielding only on the LC curve, plastic volumetric strains are given by: dεvp =
λ − κ dp∗0 v p∗0
(7)
where λ is the slope of the normal compression line for saturated conditions and p∗0 is the hardening parameter defining location of LC yield curve. The flow rule for the LC curve corresponds to:
Figure 1. LC, SD and SI yield curves for isotropic stress states (after Wheeler et al., 2003).
p
dSr p =0 dεv where p∗ is the mean Bishop’s stress, p is the mean stress, Sr is the degree of saturation, uw pore water pressure, ua is the pore air pressure, s is suction, n is the porosity and s∗ is the modified suction. Note that this choice implies that the Bishop’s stress tensor, σij∗ , is work-conjugate with dεij whereas modified suction, s∗ , is work conjugate with −dSr . Two elasto-plastic physical processes are considered within the model. One is the mechanical process of deformation of the soil skeleton under applied stresses and the second is the hydraulic process of water inflow and outflow to individual voids. The plastic mechanisms are described by three different yield surfaces (see Fig. 1). One is associated to the slippage at inter-particle or inter-packet contacts (Loading Collapse yield curve, LC) and the other two are associated to irrecoverable changes of Sr when drying (Suction Increase, SI ) or when wetting (Suction Decrease, SD). Yielding on LC curve causes plastic volumetric strain, which produces coupled upwards movements of SI and SD curves. Yielding on SI causes plastic decrease of Sr , which produce coupled upward movement of SD curve and outward movement of LC curve. Yielding on SD curve causes plastic increments of Sr , which produce coupled downward movement of the SI curve and inward of the LC curve. These curves can be expressed in the following form:
∗
p = s∗ = s∗ =
p∗0 sI∗ ∗ sD
Elastic increments of Sr can be expressed as dSre = −
(5)
κs ds∗ s∗
(9)
where κs is an additional elastic constant. When yielding only on the SI or SD yield curve, plastic changes of Sr are given by dSrp = −(λs − κs )
∗ dsI∗ dsD ∗ = −(λs − κs ) ∗ sI sD
(10)
Equations (9) and (10) predict the water retention behaviour showed in Fig. 2. As noted by Wheeler et al. (2003) the model of water retention behaviour shown in this figure is relatively crude, and refinement may be desirable. The flow rule for the SI and SD yield curves corresponds to: p
dεv p =0 dSr
(11)
When yielding only on SI or SD curves, coupled movements of the LC curve are given by: ∗ dsI∗ dsD dp∗0 = k = k 1 1 ∗ p∗0 sI∗ sD
(3) (4)
(8)
(12)
∗ where k1 is a coupling parameter and sD and sI∗ are the hardening parameters defining location of SD and SI curves respectively.
568
When yielding only on LC curve, coupled movements of the SI and SD curves are given by: ∗ dp∗0 dsI∗ dsD = = k 2 ∗ sI∗ sD p∗0
(13)
where k2 is the second coupling parameter. By considering these equations, the overall movement of the LC curve is given by: dp∗0 k1 dSr vdεv − = λ−κ λs − κs p∗0 p
p
(14)
And, similarly, the overall movement of the SI and SD curves is given by: ∗ dsD dsI∗ vdεv dSr + k2 ∗ = ∗ =− sI sD λs − κs λ−κ p
p
(15)
Figure 2. Model for water retention behaviour (After Wheeler et al., 2003).
Combining the last two equations a general expression for plastic volumetric strain increments and plastic changes of Sr can be obtained. ∗ ∗ dsD dp0 λ−κ − k (16) dεvp = 1 ∗ v(1 − k1 k2 ) p∗0 dsD ∗ dp∗0 dsD λs − κs − k (17) −dSrp = 2 ∗ ∗ (1 − k1 k2 ) dsD p0 2.2
3D generalisation
Based on the ideas collected from the 3D generalisation of the BBM (Alonso, 1993), a 3D extension of the model presented in Section 2.1 is proposed here. The model will be formulated in terms of the three stress invariants ( p∗ , J , θ ) and the modified suction (s∗ ). In addition, the concept of generalised stress and strain vectors proposed in Vaunat et al. (2000) is adopted here, being: ∗ ∗ ∗ T σ˜ ∗ = σxx , σyy , σzz , τxy , τyz , τxz , s∗ (18) T (19) ε˜ = εxx , εyy , εzz , γxy , γyz , γxz , −Sr The saturated model adopted as a limit condition is a version of the Modified Cam Clay model which is extended along the s∗ axis following the shape of the LC shown in Figure 1. Accordingly, it is proposed that the yield curve for a sample at constant s∗ will be described by an ellipse which exhibits an isotropic preconsolidation stress lying on the LC yield curve. The resulting shape of the yield surface in the ( p∗ , J , s∗ ) space is a half elliptic cylinder (see Fig. 2) extended ∗ from the plane s∗ = sD to the plane s∗ = sI∗ . In order to define the ellipse it is necessary to specify the failure states. A critical state line (CSL) for the unsaturated condition should be defined. In the BBM
Figure 3. Evolution of CSL with suction in ( p∗ , q) plane (data from Wheeler & Sivakumar (1995); after Khalili et al., 2004).
the increase of suction is represented by an increase in cohesion maintaining the slope M of the CSL for saturated conditions. In here, the same assumption about M is held and the increase of cohesion is implicitly considered by using p∗ and s∗ as stress variables. From the observed behaviour, the assumption of considering M constant in the plane ( p∗ , q) seems to be reasonable (see Fig. 3). In fact, as Khalili et al. (2004) showed using the triaxial experimental results of Wheeler & Sivakumar (1995), Cui & Delage (1996) and Maâtouk et al. (1995) re-plotted in the (p∗ , q) plane, that critical state is represented by a unique state line for different levels of suction (Laloui et al., 2005). From this assumption and considering the shape of the LC curve suggested by Wheeler et al. (2003), the yield surfaces can be represented as shown in Figure 4. A generalized version of the Modified Cam Clay in terms of (p∗ , J , θ, s∗ and p∗0 ) is proposed as follows: FLC =
569
1 J2 − ∗ p∗0 − p∗ = 0 g 2 (θ) p∗2 p
(20)
joint action of several mechanisms that can act simultaneously. Concepts of multi-dissipative materials introduced by Rizzi et al. (1996) have been considered to take into account that different mechanisms can induce plastic generalized deformations. To develop the governing equations, a procedure similar to the one presented in Sánchez et al. (2005) has been followed here. A first step is the assumption of an additive decomposition of the generalized strains into elastic and plastic components; so, the increment of total generalised strains can be expressed as: n=na
d ε˜ = d ε˜ e +
d ε˜ pn
(26)
n=1
Figure 4. Three dimensional view of the yield surface in ( p∗ , q, s∗ ) stress space.
where p∗ is the first invariant of the Bishop’s stress tensor: p∗ = 1/3(σ1∗ + σ2∗ + σ3∗ ); J2 is the second invariant of the deviatoric Bishop’s stress tensor (sij∗ = σij∗ − δij p∗ ), and g(θ) is a function of the Lode angle (equivalent to M in the (p∗ , q) space). Different expressions of g(θ) are given for different failure criteria (i.e. Alonso, 1993). The other two yield surfaces are the same of the isotropic conditions, equations (4) and (5), and are expressed in the following form: FSI = s∗ − sI∗ = 0 ∗
FSD = s −
∗ sD
(21)
=0
(22)
The generic expression introduced as follows will be used in this work: Fβ = s∗ − sβ∗ = 0
β = SI or SD
(23)
As a first approximation, associated plasticity is considered within this framework. Hence, the yield surfaces and plastic potentials are defined by the same equations. The hardening rules can be expressed as: dp∗0 = p∗0
p
p
k1 dSr vdεv − λ−κ λs − κs
p p dSr vdεv + k2 dsβ∗ = sβ∗ − λs − κs λ−κ
(24) β = SI or SD (25)
2.3
where na is the number of active plastic mechanisms that correspond to one subset of the total plastic possible mechanisms. The model has three inelastic mechanisms: LC, SD and SI. Two is the maximum number of simultaneous active plastic mechanisms i.e. LC plus SD or SI (see Section 2.1). In classical plasticity theory, it is assumed that the material behaves either in elastic or plastic fashion. The yield surface defines the transition from elasticity to plasticity, stress states inside the yield surface are considered as elastic (F < 0). When a loading process is inelastic, plastic strain rates are assumed to be governed by a flow rule. For the LC plastic mechanism, the generalized strain increment can be expressed as: d ε˜ p = χLC
∂FLC = χLC mLC ∂ σ˜ ∗
(27)
When the yielding is on the SI or SD surface, the generalized plastic strain increment can be obtained through:
d ε˜ p = χβ
∂Fβ = χβ mβ ∂ σ˜ ∗
(28)
In classical plasticity it is assumed that once yield occurs (that is F = 0), the stresses must remain on the yield surface during plastic deformation. This constraint is enforced by the consistency condition, which implies that dF = 0. The consistency conditions for the plastic mechanisms consider here are introduced as follows. Consistency condition: LC yield curve:
Governing equations
The behaviour of the soil described by the model introduced above can be regarded as the consequence of the
dFLC =
570
∂FLC ∗ ∂FLC ∗ d σ˜ + dp0 = 0 ∂ σ˜ ∗ ∂p∗0
(29)
Using equation (24), the consistency equation can be expressed as:
Introducing (39) and (40) in (37) and (38) the final expressions are obtained:
p ∂FLC ∗ ∂FLC ∗ v dSr ˜ + dεvp − k1 =0 ∗ dσ ∗ p0 λ−κ λs − κs ∂ σ˜ ∂p0
T mLC d σ˜ ∗ − HLC χLC − hβ χβ = 0
(43)
mβT d σ˜ ∗ − Hβ χβ − hLC χLC = 0
(44)
(30)
where HLC , Hβ , hLC , hβ are moduli related to the plastic mechanisms evaluated according to:
Consistency condition: SI/SD yield curves: dFβ =
∂Fβ ∗ ∂Fβ ∗ d σ˜ + ∗ dsβ = 0 ∂ σ˜ ∗ ∂sβ
(31)
Using the hardening rule for sβ (25), the following expression is obtained:
p −dSr
(32) The following expressions are adopted for the generalised moduli: ∂FLC ∗ v ∗ p0 ∂p0 λ−κ ∂FLC ∗ k1 H2 = p ∂p∗0 0 λs − κs ∂Fβ 1 H3 = ∗ sβ∗ λs − κs ∂sβ ∂Fβ v H4 = ∗ sβ∗ k2 ∂sβ λ−κ
(45)
hβ = H2 msT mβ
(46)
Hβ = H3 msT mβ
(47)
hLC =
∂Fβ ∗ ∂Fβ ∗ v d σ˜ + ∗ sβ + k2 dε p = 0 ∂ σ˜ ∗ ∂sβ λs − κs λ−κ v
H1 =
HLC = −H1 mεT mLC
(33)
(34)
(35)
(36)
(37)
mβT d σ˜ ∗ − H3 dSrp + H4 dεvp = 0
(38)
In this model the material behaviour is described by elasto-plastic mechanisms that can be activated during the loading process. The set of active plastic mechanisms is not known in advance. Therefore it is necessary to use an iterative procedure to find them (Simó & Hughes, 1998). A possibility is to assume that all the plastic mechanisms are initially active. Here it is assumed that both plastic mechanisms are initially active: LC and β (that is SD or SI ). The increment of generalised stress can be expressed in terms of the elastic operator and the elastic and total elastic generalised strain increment according to: d σ˜ ∗ = De d ε˜ − χLC mLC − χβ mβ ;
β = SI , SD (49)
where: ⎛ ⎜ ⎜ ⎜ ⎜ De = ⎜ ⎜ ⎜ ⎝
The plastic volumetric strain and the plastic change in degree of saturation are obtained as follows: dεvp = χLC mεT mLC
(48)
2.4 Elasto-plastic stress-strain relations
Using the notation introduced above the consistency equations (30) and (32) can be expressed as: T mLC d σ˜ ∗ + H1 dεvp − H2 dSrp = 0
−H4 mεT mLC
E11
E12 E22 sym
E13 E23 E33
0 0 0 E44
0 0 0 0 E55
0 0 0 0 0 E66
0 0 0 0 0 0 E77
⎞ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎟ ⎠
(39) and:
dSrp
=
χβ msT mβ
(40)
E11 E44 E12 E77
where the auxiliary vectors are as follows: mε = (1, 1, 1, 0, 0, 0, 0)T
(41)
ms = (0, 0, 0, 0, 0, 0, −1)
T
(42)
= E22 = E33 = K + 4/3G = (v/k)p∗ + 4/3G; = E55 = E66 = G; = E23 = E13 = K−2/3G and = K¯ = (1/ks )s∗
Substituting this equation into the ones obtained from the consistency condition in the previous section,
571
the following expressions are obtained: T mLC De d ε˜ − χLC mLC − χβ mβ − HLC χLC − hβ χβ = 0 d ε˜ − χLC mLC − χβ mβ
(50)
− Hβ χβ − hLC χLC = 0
(51)
mβT De
−1
Rearranging,
χ =H e
c
c χLC HLC + HLC + χβ hβ + hβ = eLC χβ Hβ + Hβc + χLC hLC + hcLC = eβ
(52) (53)
c where HLC , Hβc , hcLC , hcβ , are moduli related to the plastic mechanisms and eLC and eβ are variables linked to the increment of generalised strains. The system formed by Equations (52) and (53) can be written as:
& χLC H¯ LC + χβ h¯ β = eLC χβ H¯ β + χLC h¯ LC = eβ
(62)
The choice of the plastic mechanisms initially assumed active should be verified by checking that they are actually active (Simó & Hughes, 1998). If one of them is not active, in this model, the case becomes a single dissipative model. Finally, the generalized stress increment (49) can be expressed as: d σ˜ ∗ = De d ε˜ −
(54)
n=na
d ε˜ p
(63)
n=1
After some algebra the following general equation can be obtained:
where: T c H¯ LC = HLC + HLC De mLC = HLC + mLC
(55)
T De mβ h¯ β = hβ + hcβ = hβ + mLC
(56)
T eLC = mLC De d ε˜
(57)
H¯ β = Hβ +
Hβc
= Hβ +
mβT De mβ
(58)
h¯ LC = hLC + hcLC = hLC + mβT De mLC
(59)
eβ = mβT De d ε˜
(60)
where H = H + H c
d σ˜ ∗ = Dep d ε˜
(61)
The hardening modulus matrix (H) is symmetric when there is reciprocity in the hardening rules of both mechanisms (reciprocal hardening implies that Hij = Hji for i = j). This model has non-reciprocal hardening (as for the general case H12 = H21 ). There is a unique increment of ε for any increment of σ if, and only if, H is a P-matrix (Rizzi et al., 1996). When this condition is satisfied, the flow rule of the multidissipative materials exhibits hardening, otherwise it exhibits softening. Finally, for H = 0 the behaviour is perfectly plastic. For the general case of non-associative plasticity, there is a unique increment of σ for any increment of ε if, and only if, the effective hardening matrix H is a P-matrix. Hc is the critical softening matrix.
(64)
The form of Dep (64) will depend on the plastic mechanism(s) active during loading (i.e. only the LC plastic mechanism is active, or only a β mechanism is active, or both plastic mechanisms are active). The specific elasto-plastic operators for each case, and more details of the generalized model, can be found in Lloret (2007). 3
Equivalently the system (54) can be written in a compact form as: Hχ = e;
The assumption that H is a P-matrix implies that each diagonal element of the H matrix plus the corresponding diagonal element of the Hc matrix is greater c than zero (i.e. (HLC + HLC ) > 0 and (Hβ + Hβc ) > 0). Therefore, the condition of H¯ > 0 is satisfied for each plastic mechanism. The solution of the system (62) requires the inversion of the H matrix which is assumed to be a P-matrix, obtaining:
CONCLUSIONS
A generalisation of the isotropic elasto-plastic framework presented by Wheeler et al. (2003) has been proposed in this work. A characteristic of the model is the proposal of a number of plastic mechanisms for describing the coupled hydro-mechanical behaviour observed in unsaturated soils. A formal framework for multi-dissipative materials has been used in this work to formulate the 3D generalised stress-strain relation of this model. REFERENCES Alonso, E.E., Gens, A. & Josa, A. 1990. A constitutive model for partially saturated soils. Geotechnique (40)3: 405–430. Alonso, E. 1993. Unsaturated soils: recent developments and applications. Constitutive models of unsaturated soils.
572
Civil engineering European courses, UPC, Barcelona, Spain. Cui, Y.J. & Delage, P. 1996. Yielding and plastic behaviour of an unsaturated compacted silt. Geotechnique (46): 291–311. Houlsby, G.T. 1997. The work input to an unsaturated granular material. Geotechnique (47) 1: 193–196. Khalili, N., Geiser, F. & Blight, G.E. 2004. Effective stress in unsaturated soils: Critical review with new evidence. International Journal of Geomechanics. ASCE; 4(2): 115–126. Laloui, L. & Nuth, M. 2005. An introduction to the constitutive modelling of unsaturated soils. Multiphysics Geomechanics 651–669. Lloret, M. 2007. Numerical Modelling of Coupled Behaviour in Unsaturated Soils. PhD Progress Report, University of Strathclyde and University of Glasgow, UK. Maâtouk, A., Leroueil, S. & La Rochelle, P. 1995. Yielding and critical state of a collapsible unsaturated silty soil. Geotechnique (45): 465–477.
Rizzi, E., Giulio, M. & William, K. 1996. On failure indicators in multi-dissipative materials. International Journal of Solids and Structures. 33 (20–22): 3187–3214. Sánchez, M., Gens, A., Guimarães, L. & Olivella, S. 2005. A double structure generalized plasticity model for expansive materials. International Journal for Numerical and Analytical Methods in Geomechanics (29): 751–787. Simó, J. & Hughes, T. 1998. Computational Plasticity. Springer: New York. Vaunat, J., Cante, J., Ledesma, A. & Gens, A. 2000. A stress point algorithm for an elastoplastic model in unsaturated soils. International journal of plasticity (16): 121–141. Wheeler, S.J. & Sivakumar, V. 1995. An elastoplastic critical state framework for unsaturated soil. Geotechnique (45) 1: 35–53. Wheeler, S., Sharma, R.S. & Buisson, M.S.R. 2003. Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils. Geotechnique (53) 1: 41–54.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Effect of degree of saturation on mechanical behaviour of unsaturated soils A.R. Estabragh Faculty of Soil and Water Engineering, University of Tehran, Iran
A.A. Javadi School of Engineering, Computer Science and Mathematics, University of Exeter, Exeter, UK
ABSTRACT: The effect of the unsaturated condition in soils is commonly expressed through suction. It is generally accepted that the suction and degree of saturation have a significant effect on the mechanical behaviour of unsaturated soils. However, the effect of degree of saturation is generally not included in the majority of existing elasto-plastic constitutive models. It is believed that inclusion of degree of saturation in constitutive models for unsaturated soils could lead to significant simplification for practical purposes. This paper presents the results of an investigation into the effect of degree of saturation on the behaviour of unsaturated silty soil in the light of a comprehensive set of experiments. The variation of degree of saturation during loading/unloading, wetting/drying and reloading is studied. The results show that the degree of saturation has a direct effect on the behaviour of unsaturated silty soil. The applicability of degree of saturation in an elasto-plastic constitutive model proposed in the literature is examined in the light of the experimental data and a suggestion is made for possible improvement in modelling of unsaturated soils.
1
INTRODUCTION
Unsaturated soil is a three phase material, containing solid particles, water and air. The presence of air along with water in the soil voids leads to two types of pore pressure: pore air pressure, ua and pore water pressure, uw . The pore air pressure is generally higher than the pore water pressure because of surface tension effects. It is generally accepted that suction, s (ua −uw ) and degree of saturation, Sr have a significant effect on the mechanical behaviour of unsaturated soils (Gallipoli et al., 2003). In fact suction influences the mechanical response of unsaturated soil through two basic mechanisms: the perturbing action of the average stress state and the stabilising effect of the water menisci at inter particle contacts. These two mechanisms that result from effects of suction are influenced by the state of saturation of the soil. The hysteresis phenomenon is usually observed in the soil-water characteristic relationship that is expressed in term of degree of saturation, Sr and suction, s. Many factors such as non-uniform pore size distribution and presence of entrapped air in the soil are considered to be the main causes for hysteresis in the soil-water characteristic curve. The occurrence of hydraulic hysteresis in the soil-water characteristic curve during drying and wetting means that two samples of the same soil
subjected to the same values of suction can have significantly different values of Sr if one is on the drying path and the other is on the wetting path. It shows that the inter-particle contact forces transmitted through the soil skeleton would be different in the two cases. Wheeler et al. (2003) indicated that two elastic-plastic processes can be considered for unsaturated soils: the first is the mechanical process of straining of the soil skeleton under changes of applied load which consists of elastic strain due to the elastic deformation of soil particles and plastic strain due to slippage of particles at contacts. The second is the hydraulic process of water inflow and outflow to individual voids that provides elastic deformation by changing the interface position (menisci separating air and water). 2
ELASTO-PLASTIC MODELS
Two well-known classes of elasto-plastic models for unsaturated soils have been published in the past years. The first class of models were presented in terms of the mean net stress, p (the difference between total stress and pore air pressure) and suction, s (the difference between pore air pressure and pore water pressure) (Alonso et al., 1990; Josa et al., 1992; Wheeler and Sivakumar, 1995 and Cui and Delage, 1996). In this
575
class of models the unsaturated condition is expressed through suction without any direct influence of degree of saturation, Sr . Therefore, these models are not able to provide correct predictions when the influence of hydraulic hysteresis on mechanical behaviour is prevalent (e.g., when studying behaviour of a soil under cycles of drying and wetting). The second class of elasto-plastic models for unsaturated soils are expressed in terms of a different set of constitutive variables that include the degree of saturation in their definition (Bolzon et al., 1996; Karube et al., 1998 and Karube and Kawai, 2001). The stress variable in this class of models has the form of Bishop (1959) relationship given as: σij = σij − δij [ua − χ (ua − uw )]
(1)
where σij is the total stress, σij has been referred to as Bishop’s stress (Bolzon et al. (1996) and Gallipoli et al. (2003)) or average skeleton stress (Jommi, 2000). χ is a soil parameter depending on the degree of saturation and ranges between one (at saturation) and zero (dry condition), δij is Kronker’s delta and ua and uw are pore air pressure and pore water pressure respectively. Although this class of models introduced Sr into the definition of a soil variable, they have some limitations when predicting certain important aspects of unsaturated soil behaviour such as irreversible compression during the drying stages of wetting-drying cycle and the influence of a wettingdrying cycle on subsequent behaviour during isotropic loading. Recently Wheeler et al. (2003) presented a new model which involves coupling of hydraulic hysteresis and mechanical behaviour and is suitable for prediction of hydraulic response and mechanical response of unsaturated soils. They concluded from Houlsby’s theoretical analysis (Houlsby, 1997) of work input for granular unsaturated soils that another alternative choice of stress state variables for isotropic condition would be as: p∗ = p − Sr .uw − (1 − Sr )ua ∗
s = n(ua − uw )
of the elasto-plastic model of Wheeler et al. (2003) for unsaturated silty soil is also examined in the light of experimental evidence and a suggestion is presented for elasto-plastic modelling of unsaturated soils.
3
EXPERIMENTAL PROCEDURE
A set of experimental tests were performed on samples of a compacted silty soil following the procedure explained by Estabragh et al. (2004). Several isotropic compression tests involving loading to a virgin state and unloading to a predefined stress, suction change (wetting or drying) and subsequent reloading were carried out in this research program. During each stage of the tests the variations of specific volume and degree of saturation were measured. From the results of these experiments the values of slope and intercept of normal compression lines in the v−ln p space were calculated for different values of suction. Typical experiments results are shown in Figs. 1 and 2. Data from these experiments were used to examine the prediction capabilities of the model proposed by Wheeler et al. (2003).
(2) (3)
where p∗ is mean Bishop’s stress, n is porosity and s∗ is modified suction. p∗ in the above equation represents the influence of applied total stress, pore air pressure and pore water pressure within bulk water whereas s∗ represents the influence within meniscus water. Wheeler et al. (2003) stated the elastic region in this model is surrounded by LC (loading and collapse), SD (suction decrease) and SI (suction increase) yield curves. In this paper, the variation of specific volume and degree of saturation during loading/unloading, wetting/drying and reloading are studied. The application
Figure 1. Effect of wetting on subsequent soil behaviour during loading, initial s = 300 kPa, final s = 50 kPa; variation of (a) specific volume; (b) degree of saturation with mean net stress.
576
Figure 2. Effect of wetting on subsequent soil behaviour during loading, initial s = 50 kPa, final s = 300 kPa; variation of (a) specific volume; (b) degree of saturation with mean net stress.
4
EXPERIMENTAL RESULTS
Figs. 1 (a) and 2 (a) show the results of two typical tests involving an isotropic loading and unloading cycle ab-c at constant suctions of 300 and 50 kPa respectively; followed by a wetting (or drying) cycle cd and subsequent isotropic reloading de. The results for each of these two tests are presented in a conventional format consisting of two plots; in the first plot the stress path followed in the test is shown (Figs. 1 (a) and 2 (a)) while in the second plot the variation of degree of saturation is plotted against mean net stress, p (on a logarithmic scale). In the test, the mean net stress was increased from 20 kPa to 550 kPa during loading path ab and then it was reduced from 550 kPa to 50 kPa in the unloading path bc. During the unloading path, suction was held constant throughout the test at 300 and 50 kPa in the first and second test respectively. Fig. 1 (a) shows the results from a typical test involving an isotropic loading and unloading cycle a-b-c at a constant suction of 300 kPa, followed by a wetting cycle cd and a subsequent isotropic reloading de. During the wetting stage, swelling occurred in the sample (path cd in Fig. 1 (a). As shown in Fig. 2 (a) loading and unloading were done at suction of 50 kPa; the drying stage continued until s = 300 kPa and was followed by the subsequent reloading stage.
Inspection of Figs. 1 (a) and 2 (a) shows that there was a change in the slope of compression curve during loading stage ab, corresponding to a yield point on the LC yield curve. During isotropic loading (path ab) when large plastic reduction in void ratio occurred, a significant increase in the degree of saturation was observed. In contrast, during subsequent unloading (path bc), when only a very small elastic swelling occurred, the changes of degree of saturation were very small and irreversible changes of degree of saturation were observed. As the specific volume decreases, the dimensions of voids and the connecting passageways between the voids tend to decrease, so that a higher value of suction is needed to produce a given degree of saturation. Figs. 1 (b) and 2 (b) show that the main variation in degree of saturation occurred after the yield point, as the great proportion of deformation occurred after yielding when large changes of specific volume were occurring. Inspection of Figs 1 and 2 shows that the degree of saturation increased in the wetting path cd (Fig. 1 (b)) and decreased in the drying path cd (Fig. 2 (b)). It shows that the value of Sr was higher in the drying path (Fig. 2 (b)) than in the wetting path (Fig. 1 (b)) at any given value of suction. The occurrence of hydraulic hysteresis is obvious by comparing the results of these two tests. In the subsequent reloading a yield point was observed, but the value of the yield stress does not correspond to the maximum value of mean net stress that was previously applied; this was because of the change in the initial value of suction in the sample during wetting or drying. 5
MODEL PREDICTION
In order to show the capabilities of the model in predicting different types of stress path in isotropic conditions the following values of soil constants were obtained for the soil from the experimental results: λ (parameter for volumetric strain on LC curve) = 0.075 k (parameter for elastic volumetric strains) = 0.013 λs (parameter for change of degree of saturation on SI or SD curve) = 0.12 and ks (parameter for elastic changes of degree of saturation) = 0.032. The initial state of the soil sample for test 1 is: p = 20 kPa, s = 300 kPa, v = 1.7519, Sr = 0.798 and pc = 190 kPa. The initial state of soil sample for test 2 is: p = 20 kPa, s = 50 kPa, v = 1.7519, Sr = 0.798 and pc = 150 kPa.
577
The increments of p∗ and s∗ can be expressed by the following equations (Wheeler et al., 2003): dp∗ = d(p − ua ) + Sr ds + sdSr
(4)
ds∗ = nds − sdε/v
(5)
The experimental and predicted results are shown in Figs. 3 and 4. The resulting stress paths in the s∗ : p∗ plane are shown in Figs. 3 (b) and 4 (c). The first case involves loading, unloading, wetting (suction decrease from 300 to 50 kPa) and reloading whereas the second case involved loading, unloading, drying and reloading. As shown in Figs. 3 (b) and 4 (c) during initial section AB of the loading path the value of s∗ reduces very slightly because of small decrease of porosity n, caused by elastic volumetric strain resulting from increase in p∗ . The LC yield curve is reached at B when substantial plastic volumetric strain commences. Large plastic increase of Sr therefore occurs as the loading proceeds beyond point B. During unloading the behaviour is purely elastic. During wetting (suction decrease from 300 kPa to 50 kPa) in test 1 (Figs. 1 (a) and 1 (b)) the volume of the sample increases and Sr increases significantly and overall there is a reduction in p∗ and a large reduction in s∗ . When reduction in suction takes place at p = 50 kPa the stress path remains inside the LC yield curve throughout the wetting process and
Figure 4. Model prediction of isotropic loading, unloading at constant s = 50 kPa, drying and reloading at s = 300 kPa; (a) specific volume; (b) path in modified stress space.
Figure 3. Model prediction of isotropic loading, unloading at constant s = 300 kPa, wetting and reloading at s = 50 kPa; (a) specific volume; (b) path in modified stress space.
volumetric response consists of elastic swelling caused by reduction of p∗ . In the second test (Fig. 2 (a)) drying (suction increase from 50 to 300 kPa) occurs at p = 50 kPa. In this case, reduction is observed in both Sr and volume of the sample. Overall increases are observed in p∗ and s∗ as shown in Fig. 4 (c) During drying suction increases and degree of saturation decreases and the net effect is a significant reduction in p∗ . Throughout the drying stage yielding occurs on the SI yield curve causing significant plastic increase in Sr . Figs. 3 (b) and 4 (c) show the path of the reloading stages for suctions of 300 and 50 kPa respectively. Fig. 4 (c) shows that the soil yields at point I on the LC yield curve so the value of p is less than 550 kPa that was previously applied. From I to F yielding takes place on the LC yield curve leading to plastic volumetric strain. Figs. 3(a), 4(a) and 4(b) show the comparison between the model predictions and
578
the measured results. It is shown that although the model is able to predict qualitatively various aspects of the soil behaviour, quantitatively, there are differences between the measured results and model predictions. 6
CONCLUSIONS
The results show that significant variations occurred in Sr during isotropic loading. This can be attributed to the influence of volumetric strains, as the main part of changes of Sr coincides with the post yield sections of loading stages where large changes of v are occurring. The experimental results indicate the occurrence of hydraulic hysteresis in the drying and wetting stages. The model that was proposed by Wheeler et al. (2003) for unsaturated soils is a new model that includes coupling of hydraulic hysteresis and mechanical behaviour. The performance of the model was examined in the light of results of experiments on an unsaturated silty soil in order to evaluate the capabilities of the model in predicting some aspects of unsaturated soil behaviour during loading, unloading, drying, wetting and reloading. It is concluded from the comparison of estimated and measured results that the model is able to predict qualitatively various aspects of the soil behaviour. However, the model predictions for some conditions do not coincide with the experimental results and in some cases there are considerable differences between them. It may be that some of the mathematical expressions of the model should be improved and the model needs to be fully validated by experimental data including extension to triaxial stress states. The effect of meniscus water on mechanical behaviour is likely to be dominantly a function of degree of saturation, Sr rather than s∗ . An increase of Sr suggests a decrease in the stabilising effect of meniscus. Therefore for modelling the hysteresis effects, a model which includes a link between Sr and s∗ might be appropriate.
REFERENCES Alonso, E.E., Gens, A. and Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique, Vol. 40, No.3, 405–430. Bolzon, G., Schrefler, B.A. and Zienkiewiez, O.C. 1996. Elasto-plastic soil constitutive laws generalised to partially saturated state. Géotechnique, Vol. 46, No. 2, 279–289. Cui, Y.J. and Delage, P. 1996. Yielding and plastic behaviour of an unsaturated compacted silt. Géotechnique, Vol. 46, No. 2, 405–430. Bishop, A.W. 1959. The principle of effective stress. Teknisk Ukeblad 106, No. 39, 859–863. Estabragh, A.R., Javadi, A.A. and Boot, J.C. 2004. Effect of compaction pressure on consolidation behaviour of unsaturated silty soil. Canadian Geotechnical Journal No. 41: 540–550. Gallipoli, D., Gens, A., Sharma, R.S. and Vaunat, J. 2003. An elasto-plastic model for unsaturated soil incorporating the effect of suction and degree of saturation on mechanical behaviour. Géotechnique, Vol. 53, No. 1, 123–135. Houlsby, G.T. 1997. The work input to an unsaturated granular material. Géotechnique, Vol. 47, No. 1, 193–196. Jommi, C. 2000. Remarks on the constitutive modelling of unsaturated soils. In Proceedings of the International workshop on unsaturated soils. 139–153. Josa, A., Balmaceda, A. Gens, A. and Alonso, E.E. 1992. An elasto-plastic model for partially saturated soils exhibiting a maximum collapse. Proc. 3rd, Int. Conf. Computational plasticity, Barelona, 815–826. Karube, D., Kato, S., Honda, M. and Kawai, K. 1998. A constitutive model for unsaturated soil evaluating effects of soil moisture distribution. In Proceedings of 3rd Int. Conf. on Unsaturated soils, Beijing, 485–490. Karube, D. and Kawai, K. 2001. The role of pore water in the mechanical behaviour of unsaturated soils. Geotech. Geolog. Engineering, No.19, 211–241. Wheeler, S.J and Sivakumar, V. 1995. An elasto-plastic critical state framework for unsaturated soil. Géotechnique, Vol. 45, No. 1, 35–53. Wheeler, S.J., Sharma, R.S. and Buisson, M.S.R. 2003. Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils. Géotechnique, Vol. 53, No. 1, 41–54.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
An improved constitutive model for unsaturated and saturated soils K. Georgiadis Aristotle University of Thessaloniki, Thessaloniki, Greece
D.M. Potts & L. Zdravkovic Imperial College, London, UK
ABSTRACT: This paper presents a constitutive model for unsaturated and saturated soils based on the critical state framework. The model includes a versatile expression for yield and plastic potential surfaces, the option of linear or nonlinear increase of shear strength with suction and three options for the shape of the unsaturated isotropic compression lines. The latter feature is of particular importance as it controls the amount of potential collapse the soil can experience due to wetting. Depending on the type of boundary value problem analysed a linear, bi-linear or exponential relationship can be used. Two sets of finite element analyses are presented here which investigate the influence of the shape of the isotropic compression line on the behaviour of strip footings and axially loaded single piles.
1
INTRODUCTION
Most existing constitutive models for unsaturated soils are based on fully saturated models, and in particular on a critical state framework. The effects of partial saturation and suction within a three-dimensional constitutive model are taken into account by the introduction of suction or equivalent suction as an additional stress state variable. Many of these models assume a linear relationship for the variation of shear strength with suction (e.g. Alonso et al. 1990) and for the shape of the partially saturated isotropic compression lines (e.g. Alonso et al. 1990, Wheeler & Sivakumar 1995). Experimental evidence, however, suggests that these relationships are nonlinear. Of particular importance is the shape of the isotropic compression line for unsaturated conditions, as it is directly related to the amount of potential collapse that the soil will experience upon wetting. Experimental results indicate that the amount of potential collapse increases nonlinearly at low confining stresses, reaches a maximum at a certain value of the confining stress and decreases at high confining stresses (e.g. Booth 1975, Yudhbir 1982). This paper presents a number of refinements made to the existing critical state constitutive model for unsaturated soils presented by Georgiadis et al. (2003) and Georgiadis et al. (2005) that aid flexibility and applicability. These involve an exponential expression for unsaturated isotropic compression lines, a nonlinear expression for the variation of shear strength with suction, as well as a flexible function for the shapes
of the yield and plastic potential surfaces. The advantages of these improvements are demonstrated in the finite element analyses of a surface strip foundation and an axially loaded pile. 2 2.1
CONSTITUTIVE MODEL Stress invariants
Two independent stress variables are required to model unsaturated soil behaviour. A convenient choice of stress variables for partially saturated conditions is the pair of equivalent stress: σ˜ = σ¯ + sair
(1)
and equivalent suction: seq = s − sair
(2)
where σ¯ (= σ − ua ) is the net stress, s is the matrix suction and sair is the air entry value of suction. The constitutive model is formulated in four-dimensional stress space (J , p, θ, seq ), where J is the generalised three dimensional deviatoric stress, p˜ is the mean equivalent stress and θ is the Lode’s angle. 2.2 Yield function and plastic potential surface The following modified version of the Lagioia et al. (1996) expression is used for the yield function and plastic potential equations:
581
F G
'
1+
=
p˜ + k · seq − p˜ o + k · seq
1+
η K2 η K1
Kβ2
J
f
Kβ1 = 0 f
k = Sr
where p˜ o is the isotropic yield equivalent stress at the current value of suction, k controls the increase in apparent cohesion due to suction, K1 , K2 and βf are constants calculated from the model parameters αi and μi from the following expressions:
K1,2 =
μi (1 − αi ) 1± 2 (1 − μi )
( 1−
constant k
(3)
4αi (1 − μi ) μi (1 − αi )2
seq Figure 1. Linear and non-linear variation of apparent cohesion with equivalent suction.
(4) degree of saturation, Sr , to suction has been proposed by van Genuchten (1980):
βf = (1 − μi ) (K1 − K2 )
Sr =
(6)
where, ψ, m and n are fitting parameters, and Sro is the residual degree of saturation at very high values of suction.
where Mji is the ratio J/(˜p + f (seq )) at which either ∂F/∂ p˜ = 0 or ∂G/∂ p˜ = 0.Mji depends on the Lode’s angle θ and the model parameter Mi and is calculated from the Matsuoka—Nakai criterion (Matsuoka & Nakai 1974). The parameters αi , μi and Mi are equal to αf , μf and Mf when the yield surface is being calculated and equal to αg , μg and Mg when the plastic potential surface is being calculated. Mg is the gradient of the critical state line in the conventional q − p space, corresponding to triaxial compression (θ = −30◦ ). The parameters αf , μf and Mf and αg , μg and Mg control the shape of the yield and plastic potential surfaces, respectively. With appropriate choice of these parameters a wide range of surfaces can be achieved including most of the well-known yield and plastic potential surfaces. 2.3
Variation of apparent cohesion with suction
The parameter k in equation (3) controls the increase of apparent cohesion Jci with suction through the following expression: Jci = k · Mji · seq
m
(5)
and η is the normalised stress ratio: ! J p˜ + f seq η= Mji
1
(7)
A constant value of k is only realistic if the problem analysed involves small variations of suction. In other cases it must be a function of suction or the degree of saturation (Figure 1). An expression relating the
n 1 + seq · ψ
(1 − Sro ) + Sro
(8)
2.4 Isotropic compression line The isotropic yield equivalent stress, p˜ o , at the current value of suction depends on the shape of the isotropic compression line. Three different options are incorporated in the model. 2.4.1 Option 1—linear isotropic compression line This option is the same as that proposed by Alonso et al. (1990) in the Barcelona Basic model and has been adopted in many other models, such as the Bolzon et al. (1996), Cui & Delage (1995), Modaressi & Abou-Bekr (1994) models. The isotropic compression line for this option (Figure 2) is given by: v = v1 seq − λ seq ln p˜ o (9) where v1 (seq ) is the specific volume at unit pressure and the current value of equivalent suction and λ(seq ) is the partially saturated compressibility coefficient. λ(seq ) is given by the following empirical expression (Alonso et al. (1990)): (10) λ seq = λ(0) (1 − r) e−βseq + r where λ(0) is the fully saturated compressibility coefficient and β and r are model parameters which control the shape of the primary yield and plastic potential surfaces in the p˜ − seq plane. This assumption for the isotropic compression line leads, through the same calculations as those described
582
lnp
pm
p = 1kPa v1(0) v1(seq)
Option 1 1
(seq) ~
pc
1 1 Saturated
Figure 3. Variation of potential plastic reduction of specific volume due to wetting with isotropic yield stress.
Figure 2. Isotropic compression lines for options 1 (linear) and 2 (bi-linear).
for the yield surface in the isotropic yield equivalent stress—equivalent suction space becomes:
in Alonso et al. (1990), to the following expression relating the isotropic yield equivalent stress, p˜ o , to the equivalent fully saturated yield stress, p˜ ∗o : p˜ o = p˜ c ·
p˜ ∗o p˜ c
~
(0) (0) Option 2
p~m
1/b
(λ(0)−κ)!(λ(seq )−κ ) (11)
where p˜ c is the characteristic pressure defining the limiting lower value of the equivalent fully saturated yield stress, p˜ ∗o , for which the Loading-Collapse yield curve is a vertical line (initially introduced by Alonso et al. 1990) and κ is the compressibility coefficient along elastic paths and is assumed to be independent of suction. Equation (11) implies that the amount of potential collapse due to wetting (vertical distance between the fully and partially saturated lines in the v-ln˜p plane) increases linearly with the increase of the logarithm of the confining stress, p˜ . This is a realistic assumption for the low confining stresses at which many laboratory tests on partially saturated soils are performed, but may give unrealistically high values of the yield stress, p˜ o , and the wetting induced volumetric plastic strains, at high confining stresses. 2.4.2 Option 2—Bi-linear isotropic compression line The characteristic pressure p˜ c is an arbitrary parameter the value of which is selected such that the shape of the Loading-Collapse yield curve matches the experimental data, and is assumed to be constant and unique for a particular soil. However, to avoid inconsistencies at high stress levels it would appear that p˜ c must be stress level dependent. An alternative approach is to assume that the ratio p˜ ∗o /˜pc is constant for confining stress ranges higher than those at which the experiments where performed. Adopting this approach, the expression
!
(λ(0)−λ(seq )) (λ(seq )−κ ) p˜ o = p˜ ∗o · αc
(12)
where, αc = p˜ ∗o /˜pc is a model parameter. The partially saturated isotropic compression line for this option is bi-linear and is shown in Figure 2. At low confining stresses expression (11) is adopted giving a linear increase of the amount of collapse with stress, while at high confining stresses expression (12) is adopted giving a constant amount of collapse. The switch from expression (11) to expression (12) takes place when the two expressions are equal. It can be shown that the confining stress, p˜ m , at which this switch takes place, is given by: !
(λ(0)−κ)
p˜ m = p˜ c · αc
(λ(seq )−κ )
(13)
2.4.3 Option 3—Non-linear isotropic compression line The idealised relationship between the amount of potential plastic reduction of the specific volume, vp , due to wetting of a partially saturated soil lying on the isotropic compression line, and the isotropic yield stress, po , is given in Figure 3. A mathematical expression of this form is the following: vp = λm
p˜ o p˜ c
−b ln
p˜ o p˜ c
(14)
where λm and b are model parameters. The partially saturated isotropic compression line is shown in Figure 4 and is given by: v = v1 (0) − λ (0) ln p˜ + v
583
(15)
~
option is given by the following equation:
~
⎛
N(0) N(seq)
p˜ ∗o = p˜ c x
1
⎞
⎝1−
λm x−b ⎠ λ (0) − κ
,
where x =
1
Option 3
3
Saturated
p˜ o p˜ c
(21)
FINITE ELEMENT ANALYSES
3.1 General
Figure 4. Isotropic compression line for option 3 (non-linear).
Two boundary value problems analysed with the above constitutive model are presented in this paper. The analyses aim to highlight the influence of the shape of the isotropic compression line on the behaviour of shallow and deep foundations.
where 3.2 Surface strip footing
v = vp − ve −b seq + patm p˜ o p˜ o ln c − κs ln = λm p˜ c p˜ patm
The parameter λm is therefore a measure of the soil stiffness at low confining stresses and is dependent on equivalent suction. It can be assumed that the initial slope of the isotropic compression line, λin (seq ), is given by equation (10). λm is obtained from combination of Equations 10 and 18 as follows:
All analyses involved a 2 m wide rough rigid strip footing bearing on a uniform soil. The groundwater table was at −2 m with a hydrostatic pore pressure profile to the ground surface. An air entry suction value of zero was used and therefore the soil was treated as partially saturated from the water table to the ground surface. Two sets of analyses were performed. In the first set the footing was loaded to failure and in the second the footing was first loaded to a certain load with the water table at −2 m and subsequently the groundwater table was raised to the ground level at constant applied load. Three different loads were considered: 100 kN, 175 kN and 350 kN. Both sets of analyses outlined above were performed with options 1 (linear isotropic compression line) and 3 (non-linear isotropic compression line). The soil parameters used in the analyses are shown in Table 1. Three values of b were considered: 0.1, 0.226 and 0.472, which correspond to maximum potential collapse at a confining stresses, pm , of approximately 265 MPa, 1000 kPa and 100 kPa, respectively. A constant value with depth of 1.5 was assumed for the OCR throughout the soil. OCR in this case refers to the equivalent fully saturated state (seq = 0): OCR = p˜ ∗o /˜p.
λm = λ (0) (1 − r) 1 − e−βseq
Table 1.
(16)
The slope of the partially saturated compression line at any value of p˜ o is calculated as follows: λ seq = λ (0) − λm
p˜ o p˜ c
−b
1 − b ln
p˜ o p˜ c
(17)
The initial slope of the isotropic compression line, λin (seq ), is obtained by setting p˜ o = p˜ c in Equation 17: λin seq = λ (0) − λm
(18)
(19)
The value of p˜ o at which maximum collapse takes place is given by: p˜ m = p˜ c e1/b
(20)
The relationship between the partially saturated and the equivalent fully saturated isotropic yield stress which corresponds to the non-linear curves of this
αf μf Mf αg μg Mg pc λ(0) κ
584
Material properties for footing analyses. 0.4 0.9 1.2 0.4 0.9 1.2 12.0 kPa 0.066 0.0077
r β κs ν1 k μ sair Ko γ
0.35 0.0164 kPa−1 0.001 2.0 0.8 0.2 0.0 kPa 1.0 17.0 kN/m3
Load (kN)
500 450 400 350 300 250 200 150 100 50 0
For the lower load of 175 kN only small settlements take place, which initially increase linearly with the rise of the groundwater table but level off as the G.W.T. approaches the ground surface. For the higher load of 350 kN much larger settlements are predicted indicating failure. Unlike the predictions for the load-settlement curve, the shape of the isotropic compression line can be seen to greatly affect the behaviour of the footing due to wetting. The settlements reduce significantly with increasing b. For the lower load of 175 kN an increase of the parameter b from 0 (equivalent to the analysis with option 1) to 0.472 leads to a decrease of the final predicted settlement of approximately 73%. For the larger load of 350 kN the effect of the parameter b is even greater. At a rise of the G.W.T. from −2 m to −1 m the settlement predicted for b = 0 is 150% larger than that predicted for b = 0.472. For isotropic stress states it is only the relationship between the yield stress, p˜ ∗o , and the equivalent fully saturated yield stress, p˜ o , that controls the amount of wetting induced collapse. In any other case the change in apparent cohesion also affects the predicted amount of collapse, but generally to a much lesser extent.
Option model 11 b = 0.1 b = 0.226 b = 0.472 0
0.5
1
1.5
2
Rise of groundwater table (m) 0.5 1 1.5
2
Settlement (m)
Figure 5.
0
0
Load-settlement curves.
Settlement (m)
0.05 0.1 0.15 0.2 0.25
Option 1 (175kN) b = 0.1 (175kN) b = 0.226 (175kN) b = 0.472 (175kN) Option 1 (350kN) b = 0.1 (350kN) b = 0.226 (350kN) b = 0.472 (350kN)
Figure 6. Progression of vertical movement with rise of groundwater table—influence of the parameter b.
For simplicity and since the problem analysed does not involve high values of suction (s ≤ 39.24 kPa) a linear increase of the apparent cohesion with suction was assumed (k = const.). Finally, the same unit weight of 17 kN/m3 was assigned to the soil above and below the groundwater table for all analyses. The predicted load-settlement curves from the first set of analyses are plotted in Figure 5. It can be seen that the parameter b does not have any significant influence on the predicted curves. Consequently neither does the shape of the isotropic compression line nor the shape of the Loading-Collapse curve. It is evident from this that for the low suction levels of this particular problem it is the increase of apparent cohesion that controls the soil strength and not the value of the isotropic yield stress, po . At these low values of suction the value of the isotropic yield stress does not vary sufficiently enough to significantly affect the size of the primary yield surface. Figure 6 shows the progression of the settlement with the rise of the G.W.T. predicted by the second set of analyses (rise of the groundwater table at a constant load of 175 kN and 350 kN) The results are directly comparable as the initial stress-strain conditions at the beginning of wetting are very similar for the given loads. The settlements predicted with option 3 follow the same pattern as that observed in the option 1 analyses.
3.3
Single pile
The influence of the shape of the isotropic compression line on the behaviour of bored piles endbearing in partially saturated soil is investigated in this section. The analyses presented here are supplementary to the analyses of a pile in Canary Wharf, London presented by Georgiadis et al. (2003). The ground profile used in the finite element analyses comprised (from top to bottom) 10 m of fill, 3.8 m of Terrace Gravel, 3.9 m of Lambeth Group Clay, 6.5 m of Lambeth Group Sands, 12.8 m of Thanet Sands underlain by Chalk. The pile analysed was of 1.5 m diameter and 20.5 m length and was wished in place. Two sets of analyses are presented. The first set of analyses involves axial loading of the pile to failure with the ground water table at the initial level shown in Figure 7. The second set includes analyses in which the pile was loaded to a certain load and subsequently the groundwater table was raised to the final level, also shown on the same figure. The model parameters for the Lambeth sand and Thanet sand layers are given in Tables 2 and 3. Because of the large suctions involved in this problem the cohesion increase parameter, k, was set equal to the degree of saturation, Sr . The variation of the degree of saturation with suction was obtained from the particle size distribution curves of the materials using the Arya & Paris (1981) method. These were in turn fitted into the Van Genuchten (1980) expression for the soil water characteristic curve.
585
Table 4. Material properties for Terrace Gravel, Lambeth Clay and Chalk.
-5
-10 φ μ E
-15
Terrace Gravel
Lambeth Clay
Chalk
33◦ 0.2 30 MPa
29◦ 0.2 30 MPa
34◦ 0.2 1000 MPa
-20 Cessation of dewatering
-25
-30 Pile construction -35
-40 -20 -15 -10
Figure 7. profiles. Table 2.
-5 0 5 10 Piezometric Level
15
20
25
Canary Wharf pile analyses—Pore pressure
Material properties for Lambeth sand.
αf
0.08
β
0.02 kPa−1
μf Mf αg μg Mg αc λ(0) κ r
2.0 0.9 0.01 0.57 1.32 1.667 0.06 0.005 0.25
κs ν1 μ sair ψ m n Sro
0.001 1.826 0.2 15.0 kPa 0.03 kPa−1 0.35 4.5 0.15
Table 3. αf μf Mf αg μg Mg αc λ(0) κ r
Material properties for Thanet sand. 0.08 2.0 1.0 0.01 0.57 1.46 1.667 0.06 0.005 0.25
β κs ν1 μ sair ψ m n Sro
0.02 kPa−1 0.001 1.872 0.2 13.0 kPa 0.014 kPa−1 0.4 5.0 0.13
Three different values of the parameter b are investigated; b = 0.472 which corresponds to maximum potential collapse at pm = 100 kPa, b = 0.226 which corresponds to pm = 1000 kPa, and b = 0.1 for which
maximum potential collapse takes place at a very high confining stress pm ≈ 26000 kPa. The Terrace Gravel, Lambeth Clay and Chalk layers were modelled with the generalised Mohr-Coulomb model. The soil properties adopted for the analyses are shown in Table 4. A value of zero was set for the angle of dilation for these layers. The Lambeth Clay was assumed to behave undrained. The Ko values assigned to each soil layer were 0.5 for the Terrace Gravel, 1.15 for the Lambeth Clay, Lambeth Sands and Thanet Sands, and 1.0 for the Chalk. These values refer to the initial fully saturated conditions, prior to pile construction. The concrete pile behaviour was modelled as linear elastic. A Young’s modulus of 20 GPa and a Poisson’s ratio of 0.15 were used in the analyses. Figure 8 shows the load-displacement curves predicted with option 3 for the three different values of b. Unlike the footing case, where the parameter b did not affect the predicted ultimate load, the ultimate pile load increases with decreasing value of b, and consequently increasing isotropic yield stress p˜ o . In this case the suctions and stresses in the partially saturated zone are sufficiently high to produce p˜ o values much higher than the equivalent p˜ ∗o value, therefore affecting significantly the size of the primary yield surface. Plotted on the same figure is the load-displacement curve predicted with option 2. It can be seen that this curve is very close to and slightly lower than that predicted with option 3 for b = 0.226 (approximately 3% lower). This is due to the fact that the isotropic compression line for option 2 is very close to that corresponding to option 3 and b = 0.226 for the confining stress level relevant to this analysis (higher than 200 kPa). The progression of the vertical displacements of the pile with the rise of the groundwater table, at different constant loads, is shown in Figure 9, for option 2 and option 3 with b = 0.226. It can be seen that the results are in good agreement, with option 2 giving slightly lower displacements at the higher loads of 32 MN and 26 MN, and identical results at the low load of 19 MN. This is consistent with the results of the loading analyses discussed above, therefore confirming that the two models produce very similar results for the given αc and b values, and the stress and suction range under consideration.
586
Rise of water table (m) 0
50
0
40
10
Vertical Displacement (mm)
Load (MN)
60
30 Option 2 Option 3 - b=0.1 Option 3 - b=0.226 Option 3 - b=0.472
20 10 0 0
20
40
60
80
100
5
7.5
10
12.5
15
20 30 40 50 60 70
b=0.226 (d=14.2mm) b=0.472 (d=14.2mm) b=0.226 (d=20mm) b=0.472 (d=20mm) b=0.226 (d=30mm) b=0.472 (d=30mm)
80
Settlement (mm)
Figure 8.
2.5
Figure 10. Progression of vertical displacements for different values of b.
Load-settlement curves for different values of b.
Rise of water table (m) 0
2.5
5
7.5
10
12.5
they are not performed for the same load levels. However, close inspection of the load-displacement curves in Figure 8 shows that the b = 0.472 analysis starts closer to the ultimate pile load with the shaft friction fully mobilised and is therefore more likely to predict collapse. The difference between the analyses can therefore be attributed primarily to the value of the parameter b and the shape of the isotropic compression line.
15
Vertical Displacement (mm)
0 10 20 30 40 50 60
Op. 2 (L=19MN) Op. 3 - b=0.226 (L=19MN) Op. 2 (L=26MN) Op. 3 - b=0.226 (L=26MN) Op. 2 (L=32MN) Op. 3 - b=0.226 (L=32MN)
70 80
Figure 9. Progression of vertical displacements: comparison of option 2 and 3.
The influence of the parameter b on the pile response to wetting can be seen in Figure 10 which presents pile movements due to rise of the groundwater table for different values of b (0.226 and 0.472) and initial pile settlement (14.2 mm, 20 mm and 30 mm). It was chosen to make the comparison at the same values of initial settlement instead of the same load levels because the latter would have been meaningless, especially at high loads, where the settlements increase rapidly (see Figure 8). The pile loads which correspond to initial displacements of 14.2 mm, 20 mm and 30 mm are 19 MN, 26 MN and 32 MN for b = 0.226, and 19 MN, 25 MN and 28 MN for b = 0.472, respectively. For the lowest initial settlement of 14.2 mm the value of b has no influence on the pile response; both analyses give purely elastic heave. For 20 mm initial settlement the two analyses produce very close results, giving near-elastic heave. In contrast to them, for the large initial settlement of 30 mm the predictions are very different. The analysis with b = 0.226 predicts much larger settlements than the b = 0.472 analysis indicating failure of the pile. It is acknowledged that the two analyses are not directly comparable, as
4
CONCLUSIONS
A constitutive model is presented in this paper which provides three different options for the loading collapse yield surface. Option 1 gives a linear isotropic compression line leading to a constant increase of the amount of potential wetting induced collapse with the increase of the confining stress. Option 2 gives a bilinear compression line leading to a constant amount of potential collapse beyond a certain value of the confining stress. Finally, option 3 adopts an exponential expression, so that the amount of potential collapse increases with confining stress at low stresses, reaches a maximum value and then decreases to zero at very high confining stresses. The influence of the shape of the isotropic compression line was investigated for two common boundary value problems. The following conclusions can be drawn: • For the low suction and stress range involved in the strip footing analyses, the shape of the isotropic compression line does not affect the predicted loadsettlement curve (options 1 and 3 give similar results). This indicates that in this suction and stress range it is the variation of apparent cohesion with suction that controls the shear strength of the soil. The Canary Wharf pile analyses, however, showed that for higher stress levels, the shape of the isotropic
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compression line has a significant effect on the predicted load-settlement curve. • For the suction and stress ranges involved in the problems analysed (both footing and Canary Wharf pile analyses), the response to rising groundwater table significantly depended on the shape of the isotropic compression line. • The Canary Wharf pile analyses showed that when the model parameters α c (for option 2) and b (for option 3) are selected such as to give similar isotropic compression lines over the stress and suction range relevant to the problem analysed, the finite element predictions are also very similar. REFERENCES Alonso E.E., Gens A. & Josa A. 1990. A constitutive model for partially saturated soils. Geotechnique 40, No. 3, pp. 405–430. Arya L.M. & Paris J.F. 1981. A physicoempirical model to predict the soil moisture characteristic from particle-size distribution and bulk density data. Soil Sci. Soc. Am. J., pp. 1023–1031. Bolzon G., Schrefler B.A. & Zienkiewicz O.C. 1996. Elastoplastic soil constitutive laws generalised to partially saturated states. Geotechnique 46, No. 2, pp. 279–289. Booth A.R. 1975. The factors influencing collapse settlement in compacted soils. Proc. 6th Reg. Conf. For Africa on Soils Mech. And Found. Eng. Durban, pp. 57–63.
Cui Y.J., Delage P. & Sultan N. 2003. An elastoplastic model for compacted soils. 1 st Int. Conf. On Unsaturated Soils, Paris, 2, pp.703–709. Georgiadis K., Potts D.M. & Zdravkovic L. 2003. The influence of partial soil saturation on pile behaviour. Geotechnique 53, No. 1, pp. 11–25. Georgiadis K., Potts D.M. & Zdravkovic L. 2005. ThreeDimensional Constitutive Model for Partially and Fully Saturated Soils. International Journal of Geomechanics, Volume 5, Issue 3, pp. 244–255. Lagioia R., Puzrin A.M. & Potts D.M. 1996. A new versatile expression for yield and plastic potential surfaces. Computers and Geotechnics 19, No. 3, pp. 171–191. Matsuoka H. & Nakai T. 1974. Stress-deformation and strength characteristics of soil under three different principal stresses. Proc. Jap. Soc. Civ. Eng. 232, pp. 59–70. Modaressi A. & Abou-Bekr N. 1994. Constitutive model for unsaturated soils: validation on silty material. 3rd Eur. Conf. Num. Methods Geotech. Eng. Manchester, pp. 91–96. Van Genuchten M.T. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J., pp. 892–898. Wheeler S.J., & Sivakumar V. 1995. An elastoplastic critical state framework for unsaturated soil. Geotechnique 45, No. 1, pp. 35–53. Yudhbir 1982. Collapsing behaviour of residual soils. Proc. 7th Southeast Asia Geot. Conf. Hong Kong. Vol. 1, pp. 915–930.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Modifying the Barcelona Basic Model to account for residual void ratio and subsequent decrease of shear strength relative to suction M.E. Bardanis & M.J. Kavvadas National Technical University, Athens, Greece
ABSTRACT: The paper presents modifications to the Barcelona Basic Model to account for two aspects of unsaturated soil behaviour affecting the predictions for both fine-grained and granular soils: stabilisation of void ratio and different patterns of shear strength evolution with increasing suction. The first modification improves predictions of volume change at suctions close to the residual state. The second modification improves predictions of shear strength evolution with increasing suction for various types of soils. It is shown how the proper selection of values for the new parameters introduced allows the prediction of either continuously increasing shear strength, or stabilising shear strength, or even subsequently decreasing shear strength after an initial increase. The paper concludes with a presentation of the differences caused by these modifications in the shape of the yield surface in the p − q − s space and the possible shape of the boundary of plastic volumetric deformation in the p-s plane.
1
2
INTRODUCTION
The Barcelona Basic Model (BBM) introduced by Alonso et al. (1990) was the first complete constitutive model for non-expansive unsaturated soils to capture the fundamental aspects of unsaturated soil behaviour. Since then other models based on BBM have been proposed, which introduce more detail into the prediction of unsaturated soil behaviour. All these models are based on critical state theory extended to include suction as a separate stress parameter. While they succeed in predicting the general behaviour of unsaturated soils, such as the increase of shear strength with suction exhibited by clays and the volume changes with suction expected for the corresponding total stress magnitude, they cannot predict certain specific characteristics which have been experimentally established. The first is the prediction of the range of suction in which shrinkage actually takes place for relatively low total stress. The second is the possibility of subsequent stabilisation or decrease of shear strength after an initial increase up to the air-entry pressure, as alternatives to continuous increase of shear strength exhibited by BBM and other models. The modifications introduced predict volume decrease only up to the shrinkage limit and the possibility of any shear strength evolution scenario past the air-entry pressure of the soil, i.e. further increase of shear strength, stabilisation of shear strength or even decrease to a lower value or even zero.
BBM AND OTHER MODELS
BBM remains until today the reference constitutive model describing the mechanical behaviour of nonexpansive unsaturated soils. The model is formulated in the p-q-s space, where p = (σ1 + 2σ3 )/3 − ua , q = σ1 − σ3 and s = ua − uw (ua and uw are the pressures of the pore air phase and the pore water phase respectively, and σ1 , σ2 and σ3 are the principal total stresses). The yield locus in the p-q plane is described by Equation 1, where ps is the tensile strength developed by suction, as described by Equation 2, M is the slope of the critical state line, po the yield stress on the v-p plane (s = 0) and k the rate of the tensile strength increase with suction. f1 p, q, s, p∗0 = q2 − M2 (p + ps ) (p0 − p) = 0 (1) ps = ks
(2)
The yield stress po evolves with suction according to Equation 3 where p∗o is the yield stress on the v-p plane (s = 0), pc is a reference stress, κ and λ(0) the compression indices on the v-p plane (s = 0) and λ(s) the compression index for p > po (s = 0) as described by Equation 4, where r and β are empirical parameters. po = pc
p∗o pc
λ(0)−κ λ(s)−κ
λ(s) = λ(0) [(1 − r) exp(−βs) + r]
589
(3) (4)
The yield locus in the p-q-s space is supplemented by Equation 5, where so is the yield suction on the v-s plane. (5)
As can be seen from Equations 1 to 5 (and from Curve a in Fig. 1), BBM incorporates only 3 parameters describing volume change directly associated to a variation of suction: κs , λs & so . These parameters allow the prediction of an initial low volume decrease (determined by κs ) up to an essentially arbitrary value of suction so (which can be considered to describe physically the maximum suction applied to the soil) and then a further (and generally larger) value of volume decrease (determined by λs ). Although this formulation is adequate for the range of suction significantly below the shrinkage limit of the soil, with the additional advantage that it is analogous to the formulation for volume decrease under zero suction conditions, it does not include a boundary corresponding to the shrinkage limit (either in terms of suction or void ratio) up to which volume may decrease, as presented by Curve b in Figure 1. For suctions close to residual water content, or higher, this type of formulation overestimates volume change as it underestimates final specific volume/void ratio values. As far as shear strength is concerned, setting p = 0 into Equation 1, and replacing ps , po and λ(s) from Equations 2, 3 and 4 respectively yields Equation 6 which represents the intersection of the 3-dimensional yield surface with the q-s plane (for q > 0). Plotting Equation 6 in Figure 2 shows that BBM predicts continuous increase of shear strength with increasing suction. Although this is true for clays, it is not the case for sands, tuffs and sometimes silts, as shown by experimental results presented by Fredlund et al. (1995).
e or
300
q (kPa)
f2 (s, s0 ) = s − s0 = 0
400
so
sr
ln s
s
s
(b)
er (a)
Figure 1. Void ratio/Specific volume changes with increasing suction under zero total stress: Curve a does not account for residual void ratio, while Curve b takes residual void ratio into account.
200 100 0
0
200
400
600
800
1000
s (kPa) Figure 2. Shear strength evolution with increasing suction according to BBM (graphical representation of Eq. 6).
∗ 2·λ(0)[(1−r)·exp(−βs)+r]−2·κ √ √ ) po k · M · s · pc (6) pc λ(0)−κ
q=
The terms in Equation 6 have been placed in such a sequence, so as the different effect of each factor can be distinguished. k 1/2 expresses the effect of the evolution of tensile strength. M expresses the direct effect of the slope of the critical state line on unsaturated shear strength. s1/2 expresses the direct effect of suction increase on the increase of shear strength. The rest of the terms essentially express the effect of the loading history and the effect of drying-wetting cycles (indirect effect of suction on the evolution of shear strength). Despite the presence of numerous other factors however, none can alter the continuous increase of shear strength shown in Figure 2 (as was proven by extensive parameter analyses carried out). For comparison, the curve shown in Figure 2 has been obtained for the set of values used by Alonso et al. (1990) for the ‘reference soil’ they used for their predictions with BBM (λ(0) = 0.2, κ = 0.02, r = 0.75, β = 12.5 MPa−1 , pc = 0.1 MPa, p∗o = 0.6 MPa, M = 1, k = 0.6). Other constitutive models which do not incorporate a limiting value of void ratio change or alternative possibilities for shear strength evolution have been proposed (e.g. Wheeler & Sivakumar, 1995). Toll (1995) presented a conceptual model for the drying and wetting of soil which predicts the limiting of void ratio changes and therefore the calculated volume changes up to the void ratio corresponding to shrinkage limit. Kohgo et al. (1993a & b) and Kohgo (2004) have proposed models which have limiting parameters for volume change and the capability to model alternative patterns of shear strength evolution. Georgiadis et al. (2003) proposed among other modifications that parameter k can vary with suction by setting k equal to degree of saturation and therefore the evolution of
590
k with suction equal to the soil-water characteristic curve of the soil. This approach solves the problem for soils expected to exhibit an initial increase of shear strength with suction and then a subsequent decrease, like granular soils, but it does not provide a universally applicable equation for shear strength evolution, making it therefore necessary to switch between equations for k for each type of material. Other approaches in constitutive modelling of unsaturated soils have focused on combining LC and SI curves into one single surface. Delage & Graham (1996) proposed first that the two curves are probably one single locus in the p-s plane. Sivakumar & Doran (2000) presented first experimental evidence to support this, while Tang & Graham (2002) took the effort one step further by proposing a conceptual but complete constitutive model with one single continuous 3-dimensional yield surface in the p-q-s space. This constitutes a different approach towards incorporating the capability to model various scenarios of shear strength evolution. 3
THE MODIFICATIONS TO BBM
Common shrinkage limit tests and a large number of published drying curves indicate that clayey soils shrink to a minimum value of their void ratio during drying and then shrink no more, irrespective of how large the suction becomes. As shown by Curve a in Figure 1 therefore the specific volume-suction curve described by only 4 parameters (initial value N of specific volume at atmospheric pressure pat , κs , λs and so ) should be substituted by the idealised Curve b shown in Figure 1 with a flat final portion corresponding to the residual void ratio er (vr = 1 + er ). This curve needs only one additional parameter for its description, either the residual void ratio er , or the suction at which it is first achieved. Recently, Bardanis & Kavvadas (2006) proposed an empirical relation predicting the residual void ratio of low to medium plasticity clays and marls which have been consolidated to various stresses from a slurry condition and then unloaded and left to dry to residual water content in atmospheric conditions. The residual void ratio is predicted from the physical properties of the soil (wL , Gs ) and its initial state before drying, as expressed by initial void ratio before drying, eo , and an empirical parameter, m, found to be 0.43 for the soils tested by Bardanis & Kavvadas (2006). More recently Bardanis & Kavvadas (2008) proposed another empirical relation (derived from many more soils and test results) based on wp rather than wL and an empirical parameter, me , equal to −0.38, along with its conceptual generalisation for soils with structure by addition of another parameter, Ms . The proposed relations by Bardanis & Kavvadas (2006 & 2008) are represented by Equations 7 & 8 respectively for soils
without natural structure, and by Equation 9 for natural soils. m er = eo 1 − · eo (7) wL · Gs eo (8) er = eo · exp me · wP · Gs eo (9) er = Ms · eo · exp me · wP · Gs The set of Equations 7 to 9 allows the prediction of the residual void ratio and as a result the calculation of the residual specific volume for incorporation as a model parameter into BBM. The use of the residual void ratio in the formulation of the BBM allows more realistic predictions of volume changes due to suction increase under constant total mean stress during elastic or elasto-plastic loading. It allows for the derivation of a limiting line in the p-s plane up to which volume changes do actually occur due to suction changes for the same mean total stress magnitude. Past this line the only volume changes that may occur are due to mean stress p increase. This point is further discussed in Section 4. For the more accurate prediction of shear strength, the most suitable term from Equation 6 was selected. This was k and it was given such a form so as to predict either continuous increase of shear strength, or initial increase and then stabilisation, or finally initial increase and then decrease of the shear strength. In order for this to take place it is proposed that k may be described by a function of the degree of saturation which takes the form of Equation 10. k = ζk · Sηr k
(10)
In Equation 10, k is the factor giving tensile stress, Sr is the degree of saturation and ζk and ηk are empirical parameters. For ηk = 0 and arbitrary values of ζk , prediction of shear strength is essentially as in the BBM. For ηk = 1 and ζk = 1, k becomes equal to the degree of saturation as adopted by Georgiadis et al. (2003). For selected values of ηk and ζk the prediction of all scenarios of the evolution of shear strength with increasing suction is possible. In Figure 3 the effect of ηk for constant ζk is shown and in Figure 4 the effect of ζk for constant ηk is shown. In order to plot Figures 3 and 4 a soil-water characteristic curve was assumed for the material corresponding to the parameter values mentioned in Section 2. This soil-water characteristic curve was produced by use of the Fredlund & Xing (1994) equation assuming the following values for the empirical parameters of the equation: a = 600 kPa, n = 4, m = 2 and sr = 5000 kPa. For the set of values
591
the initial slope and subsequent position of the q-s curve.
800
600 q (kPa)
4 BBM, k=0.6
ηk=0.2
400 ηk=0.5 200
ηk=1 ηk=2
0
0
1000
2000
3000
s (kPa)
Figure 3. The effect of parameter ηk on the evolution of shear strength with suction. ζk is constant with a value of 0.6 and the rest of the parameter values are the same as those for the curve in Figure 2 (bold curve in this figure). 400 BBM, k=0.6
q (kPa)
300 ζk=1.0 200
ζk=0.6 ζk=0.3
100
0
0
200
400 600 s (kPa)
800
1000
Figure 4. The effect of parameter ζk on the evolution of shear strength with suction. ηk is constant with a value of 2 and the rest of the parameter values are the same as those for the curve in Figure 2 (bold curve in this figure).
selected to plot Figure 2 the same relation between q and s is predicted for ζk = k of BBM and ηk = 0. Continuous increase of shear strength is also exhibited for ηk = 0.2, but the increase is smaller, while for a value of ηk = 0.5 the strength practically stabilises after its initial increase, while for ηk = 1 and ηk = 2 rapid decrease occurs after the initial increase in strength. The parameter ηk can be used therefore for determining the evolution of the shear strength of unsaturated soils past the initial increase, whether that may be further increase, stabilisation, or decrease. As far as the parameter ζk is concerned, it determines
EFFECT ON THE SHAPE OF THE YIELD LOCUS
Apart from the direct effect on the predictions of volume change and shear strength evolution with increasing suction, the modifications introduced into BBM have a major effect on the shape of the yield surface in the p-q-s space. In Figure 5a the intersection of the 3-dimensional yield surface of the BBM with the p-s plane is presented. The increase in the size of the yield locus in the p-q plane (or its trace on the p-s plane) is continuous according to the tensile strength increase law on one side and the evolution of the LC curve with suction on the other. For a material exhibiting continuous increase of tensile/shear strength with suction, the shape of the intersection of the yield surface with the p-s plane for the modified BBM is expected to be the same as for BBM (Fig. 5a). For materials exhibiting shear strength stabilization or decrease after an initial increase of shear strength however, the shape of the intersection of the yield surface with the p-s plane is expected to change as shown in Figures 5b & 5c respectively. For a soil with continuously increasing shear strength with suction, the left point of the ellipse defining the yield locus will continuously move towards more negative values of total mean stress (Fig. 5a). For a soil with stabilizing shear strength after a certain value of suction, this point will stabilise in the p-q plane and the expansion of the yield locus will be only due to a mean total stress increase (Fig. 5b). Finally for a soil with initially increasing and subsequently decreasing shear strength with suction, this point of the ellipse on the p-q plane will tend to approach the origin of the plot of this plane and once again the expansion of the yield locus will be only due to a mean total stress increase (Fig. 5c). As already mentioned in Section 3, the use of the residual void ratio in the formulation of the BBM allows for the derivation of a limiting line in the p-s plane up to which volume changes do actually occur due to suction changes for the same mean total stress magnitude. Past this line the only volume changes that may occur are due to mean stress p increase. Using one of the Equations 7 to 9 residual void ratio may be predicted. The initial void ratio eo before drying needs to be specified first. Once the residual void ratio has been predicted, then using so and λs (already used parameters of BBM) the value of the suction at which the residual void ratio is achieved may be calculated. Introducing now the change in initial void ratio caused by κ for zero suction in the elastic region, then the evolution of the suction at which the residual void ratio is achieved for constant total
592
3.5
A 3.0
s (MPa)
2.5
B
2.0
1.5
1.0
0.5
0.0 0.00
po*=0.2MPa, so=0.3MPa
0.20
0.40
0.60
p (MPa)
Figure 6. p-s plane with SI and LC loci and the predicted curve limiting the region of possible states for volume change to occur due to shrinkage for p < po ∗ .
Figure 5. Intersection of the 3-dimensional yield surface with the p-s plane for a soil: a) with continuous increase of shear strength, b) with initial increase and then stabilisation of its shear strength, and c) with initial increase and subsequent decrease of its shear strength with suction.
stress suction paths (for p < p∗o ) is obtained. This is as shown by curve A-B in Figure 6 for the parameter values mentioned in Section 2 (assuming eo = 0.9 for p = 10 kPa, which yields er = 0.629 according to Eq. 8 for this value of net mean stress and e = 0.840 for κ = 0.02 at p = 200 kPa, which itself yields er = 0.601 according to Eq. 8). The space in the p-s plane between the SI locus and curve A-B constitutes the space where plastic volumetric strains (in the form of irrecoverable shrinking) due to suction increase will take place for p values in the elastic region of the fully saturated soil yield locus. For constant total stress suction paths corresponding to p values greater than p∗o (which means that plastic volumetric deformation has already occurred before drying commences) and more complex paths involving alternations between constant total stress paths and constant suction paths or simultaneous p and s change paths it is considered that Equations 7 to 9 are not appropriate for an estimation of the locus limiting volume changes due to constant total stress suction changes. This limiting line is strongly dependent on the value of κ as this parameter controls the values of initial void ratio in the elastic region of the fully saturated yield locus. Figure 7 shows the different lines defined for various values of κ ranging from 0 to 0.04. The limiting curves in Figure 7 do not start from the axis p = 0 because of the logarithmic nature of the elastic relation between void ratio and mean net stress. A value of
593
s (MPa)
4.0 3.5
κ=0
3.0
κ=0.01
2.5
κ=0.02
2.0
κ=0.04
1.5 1.0 0.5
so=0.3MPa
0.0 0.00
0.05
0.10
0.15
0.20
p (MPa) Figure 7. p-s plane with SI locus and the predicted curves limiting the region of possible states for volume change to occur due to shrinkage for various values of κ(p < p∗o ).
κ = 0 yields a limiting line parallel to the SI locus as no change to initial void ratio before drying can occur in the elastic region. As the value of κ becomes higher, then the value of the suction that residual void ratio is achieved becomes smaller with increasing p, greater than 1.5 MPa for the values selected for the rest of the parameters in Figure 7. For simplicity the p axis in Figure 7 has been limited to 0.2 MPa, which is the fully saturated yield total stress (shown also in Figure 6), so as not to show the different LC yield locus that is derived for each of the κ values used.
5
all types of materials, : maximum volume shrinkage limited by residual void ratio, and various scenarios of shear strength evolution with suction. Apart from achieving the goals for which these modifications were introduced, they also have a strong effect on the shape of the 3-dimensional yield locus in the p-q-s space as indicated by its intersections with the p-s plane in Figure 5. For a soil with continuously increasing shear strength with suction, the left point of the ellipse defining the yield locus will continuously move towards more negative values of total mean stress. For a soil with stabilizing shear strength after a certain value of suction, the distance of this point from the suction axis will stabilise and the expansion of the yield locus will be only due to a mean total stress increase. Finally for a soil with initially increasing and subsequently decreasing shear strength with suction, the distance of this point from the suction axis will tend to decrease to zero and once again the expansion of the yield locus will be only due to a mean total stress increase. As far as the effect of the residual void ratio is concerned, a line limiting the plastic strain due to constant total stress suction changes for total stress values lower than the yield stress of the fully saturated soil may be defined. The area between the SI curve of the BBM and this limiting line defines the area of possible plastic strains due to shrinkage in the p-s plane, for total stress values lower than the yield stress of the fully saturated soil.
ACKNOWLEDGEMENTS Part of the research by M.E. Bardanis has been funded by the National Scholarship Foundation (IKY) of Greece.
CONCLUSIONS
Most of the existing constitutive models cannot predict stabilization of void ratio as a result of attaining a minimum total volume during shrinkage. Also they do not incorporate the possibility to model various scenarios of shear strength evolution with suction increase (continuous increase, stabilization or decrease after an initial increase up to the air-entry pressure). Various approaches towards solving these two problems have been published but either they do not propose single equations predicting all types of response by controlling the values of parameters, or they have proceeded to totally different approaches in the treatment of the 3-dimensional yield surface; an approach that elevates constitutive modeling of unsaturated soils at another level of difficulty. The modifications proposed for BBM in this paper maintain the capability to work with a well-established and well-understood framework, while capturing important aspects of unsaturated soil behaviour by the use of one single equation, universally applicable for
REFERENCES Alonso, E.E., Gens, A., Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique 40(3): 405–430. Bardanis, M., Kavvadas, M. 2006. Prediction of the limiting void ratio of clayey soils after drying. In Miller et al (eds), Proc. 4th Int. Conf. on Unsaturated Soils, Carefree, Arizona, 2–5 April, 2006, 1085–1096, Reston, Virginia: ASCE Press. Bardanis, M., Kavvadas, M. 2008. Prediction of the residual void ratio of clayey soils after drying, from their initial state, physical properties and structure. Proc. 1st Eur. Conf. on Unsaturated Soils, Durham, UK, 2–4 July, 2008. Delage, P., Graham, J. 1996. Mechanical behaviour of unsaturated soils: Understanding the behaviour of unsaturated soils requires reliable conceptual models. In Alonso & Delage (eds), Proc. 1st Int. Conf. Unsaturated Soils, Paris, 3: 1223–1256, Rotterdam: Balkema.
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Fredlund, D.G., Xing, A., Fredlund, M.D., Barbour, S.L. 1995. The relationship of the unsaturated soil shear strength to the soil-water characteristic curve. Can. Geot. J. 32: 440–448. Fredlund, D.G., Xing, A. 1994. Equations for the soil-water characteristic curve. Can. Geot. J. 31: 521–532. Georgiadis, K., Potts, D.M., Zdravkovic, L. 2003. The influence of partial soil saturation on pile behaviour. Géotechnique 53(1): 11–25. Kohgo, Y. 2004. Elastoplastic models for unsaturated soils with two suction effects and unsaturated soil behavior. In Jucá et al. (eds), Proc. 3rd Int. Conf. Unsaturated Soils, 3: 905–915, Lisse: Swets & Zeitlinger. Kohgo, Y., Nakano, M., Miyazaki, T. 1993a. Theoretical aspects of constitutive modeling for unsaturated soils. Soils & Foundations 33(4): 49–63.
Kohgo, Y., Nakano, M., Miyazaki, T. 1993b. Verification of the generalized elastoplastic model unsaturated soils. Soils & Foundations 33(4): 64–73. Sivakumar, V., Doran, I.G. 2000. Yielding characteristics of unsaturated compacted soils. Mechanics of CohesiveFrictional Materials 5: 291–303. Tang, G.X., Graham, J. 2002. A possible elastic-plastic framework for unsaturated soils with high plasticity. Can. Geotech. J. 39 ( . . . ): 894–907. Toll, D.G. 1995. A conceptual model for the drying and wetting of soil. In Alonso & Delage (eds), Proc. 1st Int. Conf. Unsaturated Soils, Paris, 2: 805–810, Rotterdam: Balkema. Wheeler, S.J., Sivakumar, V. 1995. An elasto-plastic critical state framework for unsaturated soil. Géotechnique 45(1): 35–53.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A cap model for partially saturated soils R. Kohler, M. Hofmann & G. Hofstetter University of Innsbruck, Austria
ABSTRACT: An elastic-plastic constitutive model for partially saturated soils is presented. It is formulated in terms of two stress state variables, consisting of the effective stress tensor for partially saturated soils and matric suction. The yield surface consists of a shear failure surface and a strain hardening cap. The plastic strain rate is computed by means of non-associated flow rules for both yield surfaces. The capability of the developed constitutive model is demonstrated by the numerical simulation of a series of suction controlled tests. In addition, an extension of the model in order to account for swelling soil behavior is presented.
1
2
INTRODUCTION
Partially saturated soils are three-phase media consisting of a deformable soil skeleton and the two fluid phases water and air. The difference between the pressures in the water and the air phase, called capillary pressure or matric suction, has a considerable impact on the mechanical behavior of partially saturated soils. Experimental evidence shows that an increase in matric suction in general results in an increase of the shear strength, the preconsolidation pressure and the elasto-plastic stiffness of the soil. Furthermore, a decrease in matric suction, i.e. an increase of the degree of water saturation, under high values of external stress can result in an irreversible decrease of the soil volume, denoted as collapse on wetting. Several elastic-plastic material models for unsaturated soils have been proposed in recent years, see e.g. (Alonso et al., 1990; Wheeler et al., 1995; Bolzon et al., 1996; Geiser et al., 2000; Gallipoli et al., 2003; Tamagnini, 2004; Santagiuliana et al., 2006). Most of these material models adopt some type of Cam clay formulation. In this contribution, a cap model for partially saturated soils is presented. It is formulated in terms of the effective stress tensor for partially saturated soils and matric suction, the latter playing the role of a stress-like plastic internal variable. The model is validated by an extensive series of suction controlled tests, described in (Macari et al., 2001) and (Macari et al., 2003). In addition, lab tests for swelling soil behavior are simulated numerically. To this end, the cap model is extended by adopting ideas for modelling of swelling presented in (Gens et al., 1992) and further developed in (Sanchez et al., 2005).
CONSTITUTIVE MODEL
A basic assumption of the elastic-plastic constitutive model is the additive decomposition of the total strain tensor ε into an elastic part ε e and a plastic part εp : ε = εe + εp
(1)
From thermodynamic considerations (Houlsby, 1997; Schrefler, 2002; Borja, 2004) it follows that a material model for the soil skeleton of a partially saturated soil can be formulated in terms of the effective stress tensor for partially saturated soils (i.e., the Bishop stress with the Bishop parameter equal to the degree of water saturation) σ = σ − p a I + S w ( pa − p w ) I
(2)
and matric suction pc = pa − pw
(3)
σ denotes the total stress tensor, S w represents the degree of water saturation and pa and pw are the pressures of the fluid phases air and water; I denotes the second order unit tensor. In the present model pc plays the role of a stress-like plastic internal variable. Hence, the elastic strain tensor solely depends on the effective stress tensor and for the special case of linear elasticity the constitutive relations are given as σ = C : εe = C : ε − εp with C denoting the elasticity tensor.
597
(4)
The degree of water saturation S w is expressed as a function of matric suction by the approximation proposed in (Van Genuchten et al., 1985) c n −m p S w = Srw + (Ssw − Srw ) 1 + pcb
(5)
In (5) Ssw and Srw denote the maximum and residual degree of water saturation, respectively, and pcb is the air entry value; m and n are parameters to fit the empirical equation to experimental data. For many soils, use of n = 1/(1 − m) can be made. The functional form of the shear failure surface is defined as f1 σ , pc = L(ϑ) s − Fe I1 − Fs ( pc ) (6) with Fe I1 = α + θ I1
and Fs ( pc ) = k pc ,
(7)
where I1 and s denote the first invariant and the norm of the deviatoric part of σ , L(ϑ) accounts for the dependence of the yield surface on the Lode angle ϑ according to (de Borst et al.,) and α, θ and k are material parameters. The functional form of the strain hardening cap is given as f2 σ , κ( pc ), pc = Fc s , I1 , ϑ, κ( pc ) (8) − Fe κ( pc ) − Fs ( pc ) with κ( pc ) ≤ I1 ≤ X (κ( pc )) and
(
Fc s , I1 , ϑ, κ( pc ) = L2 (ϑ) s 2 +
I1 −κ( pc ) 2 , R (9)
where R is a material parameter, defining the ratio of the major to the minor axis of the elliptic cap, and κ( pc ) is a hardening parameter. X κ( pc ) = κ( pc ) + R Fe κ( pc ) + Fs ( pc ) (10)
Figure 1.
The hardening law for the cap surface is given as ε˙ vp = λ( pc )
κ( pc ) = κ(0) +
X (κ( pc )) − X (κ(0)) − RFs ( pc ) 1 + Rθ (11)
X˙ (κ( pc )) − 3 (S˙ w pc + S w p˙ c ) X (κ( pc )) − 3 S w pc
(12)
It is obtained from a logarithmic hardening law, formulated in terms of net stress, relating the plastic p volumetric strain rate ε˙ v to the hardening parameter c κ( p ), which is transformed to effective stress. Since X is related to the first invariant of the stress, it follows from (2) that the difference between effective stress and net stress is given as 3S w pc , which results in the terms related to S w in (12). In (12) λ pc = λ(0) (1 − r) exp(−βpc ) + r
(13)
is a scaling factor for the plastic volumetric strain rate. It is assumed to decrease from λ(0) at zero matric suction to λ(pc ) → r · λ(0) for pc → ∞ with β and r (with r < 1) as material parameters accounting for the increasing plastic stiffness under hydrostatic loading with matric suction (Alonso et al., 1990). The plastic potentials g1 and g2 for the nonassociated Koiter’s flow rule are obtained from the yield functions (6) and (8) by setting L(ϑ) = 1 and by replacing θ by ψ, which determines the amount of plastic dilation. For more information on the constitutive model refer to (Kohler, 2006; Kohler et al., 2007).
3 denotes the apex of the elliptical cap. The yield surface of the cap model is shown in Fig. 1. The hardening parameter κ( pc ) is obtained by calculating the intersection of the elliptical cap and the failure envelope (Fig. 1) by inserting (71 ) with I1 = κ( pc ) into (10) and making use of the so obtained relation also for the special case of pc = 0 as
Yield surface of the cap model.
NUMERICAL SIMULATION OF SUCTION CONTROLLED TESTS
The extended cap model was validated by the numerical simulation of a series of suction controlled tests (Macari et al., 2001; Macari et al., 2003), which were conducted on cubical specimens of a silty sand. The stress paths followed in the experiments included hydrostatic compression (HC) tests, consisting of loading and unloading at different values of matric suction, triaxial compression (TC) tests and conventional triaxial compression (CTC) tests as well as triaxial
598
extension (TE) tests and simple shear (SS) tests at different values of matric suction and different values of hydrostatic pressure, and a wetting path. The material parameters for the cap model, determined from the experimental data, are given in the second column of Table 1. In this table Xinit denotes the initial value for the apex of the cap at water saturated conditions. Since the relationship between the degree of water saturation and matric suction was not known from the tests, the hydraulic parameters of the
Table 1.
S w pc -relationship (5) were chosen according to values for silty sands given in the literature. Here, only comparisons of the predicted and measured constitutive response for the HC tests (Fig. 2) and the TC tests (Fig. 3 to Fig. 6) are shown. Results for the CTC tests, TE tests, the SS tests and the wetting test can be found in (Kohler, 2006; Kohler et al., 2007). Since the test data are given in terms of net stress, the numerical results are also shown in terms of net stress.
Material parameters.
Parameter
Silty sand
Swelling soil
Unit
K G α θ R λ(0) Xinit Xc r β k ω η
42440 8803 0 0.269 3.0 0.095 126.3 108.0 0.2 0.018 0.6 0.8 -0.1
41700 19200 0 1.0 2.0 0.03 100.0 10.0 0.78 0.005 1.0 0.8 -0.1
kPa kPa kPa – – – kPa kPa – kPa−1 – –
Srw Ssw pcb m
0.25 0.95 50.0 0.32
0.0 1.0 500.0 2.1
– – kPa –
Figure 3. Comparison of the measured (dotted lines) and the computed (continuous lines) q − εq response for TC tests at I1 = 150 kPa and 3 different values of matric suction.
Figure 2. Comparison of the measured (dotted lines) and the computed (continuous lines) response for HC stress paths at 3 different values of matric suction.
Figure 4. Comparison of the measured (dotted lines) and the computed (continuous lines) q − εq response for TC tests at I1 = 600 kPa and 3 different values of matric suction.
599
Figure 2 demonstrates the ability of the model to describe the stiffening effect due to matric suction under hydrostatic loading. Fig. 3 and Fig. 4 show the measured and computed relations between the deviatoric stress q and the shear strain εq for TC tests, conducted at two different values of I1" (i.e. the first invariant of net stress) and three different values of pc (i.e., pc = 50 kPa, pc = 100 kPa and pc = 200 kPa). For the same tests Fig. 5 and Fig. 6 show the measured
Figure 5. Comparison of the measured (dotted lines) and the computed (continuous lines) v − εq response for TC tests at I1 = 150 kPa and 3 different values of matric suction.
and computed relation between the specific volume v and the shear strain εq . It follows from the latter figures that both the increasing shear strength with increasing matric suction and the dependence of the volume change on matric suction can be well described by the cap model. 4
MODELLING OF SWELLING
The cap model, presented so far, predicts an increase of the specific volume upon wetting by the change of the effective stress (2) due to changes in matric suction. Hence, the increase of the volumetric strain due to wetting depends on the bulk modulus of the soil skeleton K and the employed S w pc -relationship (5). However, in argillaceous rocks considerably larger volume changes are observed due to stress relief and/or wetting. This swelling behavior of argillaceous soil and rock often poses severe problems to the design and construction of tunnels. Tunnel excavation causes a stress redistribution in the vicinity of the tunnel, resulting in stress relief above the crown and below the invert. Additionally, water plays an important role for swelling. Water may already be present or, at initially unsaturated conditions, seepage water from adjacent zones might reach expansive zones by flowing along or beneath the invert of the tunnel. In the context of the cap model swelling is modelled by adopting ideas sketched in (Gens et al., 1992) and further developed in (Sanchez et al., 2005). A basic idea is to consider a microstructural and a macrostructural level of an argillaceous soil or rock. The origin of swelling are physico-chemical reactions at the microstructural level resulting in volumetric strains at the microstructural level, which lead to deformations at the macrostructural level depending on interactions between both levels. According to (Sanchez et al., 2005) the volumetric strain at the microstructural level depends on an effective pressure pˆ , which is given as pˆ = p − pa + χ pc
(14)
with p = σii /3 and a constant χ > 0. For p˙ˆ < 0 the microstructural volume is increasing whereas for p˙ˆ > 0 the microstructural volume is decreasing. The respective microstructural volumetric strain is determined assuming an elastic constitutive response as ε˙ vm = Figure 6. Comparison of the measured (dotted lines) and the computed (continuous lines) v − εq response for TC tests at I1 = 600 kPa and 3 different values of matric suction.
p˙ˆ Km
(15)
with K m representing the microstructural bulk modulus. The swelling strains at the macrostructural level,
600
caused by the microstructural strains, are considered as irreversible strains. They are added to the plastic strains due to loading. According to (Gens et al., 1992) the volumetric swelling strain at the macrostructural level is obtained from the microstructural strain through an interaction function h(Xr , X ), yielding
of Xr /X close to 1. Consequently, different interaction functions are used for microstructural swelling and microstructural contraction (Sanchez et al., 2005). For the numerical simulation of the swelling tests, presented subsequently, the interaction functions for swelling and contraction, are chosen as
p ε˙ v,sw = h(Xr , X ) ε˙ vm
Xr 2 hs (Xr , X ) = 1 − X
(16)
The interaction function depends on the position of the cap for the current stress point, X , and on the position of a ‘‘reference cap’’, Xr , which contains the current stress point (Fig. 7). The ratio Xr /X ≤ 1 characterizes the preloading of the macrostructure. A small value of Xr /X indicates large previous preloading and, hence, a dense macrostructure of the soil. In this case a larger fraction of the microstructural swelling strain will be present as deformations at the macrostructural level. Conversely, a smaller fraction of the microstructural swelling strain will be present as swelling strains at the macrostructural level in the case of a looser macrostructure, which is characterized by values of Xr /X close to 1. On the other hand, microstructural contraction has a stronger impact on the deformations at the macrostructural level for values s
* and hc (Xr , X ) =
Xr X (17)
First, the swelling pressure test, described in (Romero, 1999) is simulated. In this test an initially unsaturated soil specimen was wetted at fully constraint deformations and subsequently dried. It can be
pc Fe (I1) + Fs(pc)
r
Figure 7.
Xr
I' 1 X
Definition of X and Xr .
Figure 8. Comparison of the computed soil response in a swelling pressure test (continuous line) with experimental results (crosses).
Figure 9. Comparison of the computed response in a free swelling test (dotted lines) and a Huder-Amberg test (continuous lines).
601
seen in Fig. 8 that the model allows to represent the development of the first invariant of net stress, I1 , due to wetting and subsequent drying quite well. An interesting feature of this test is the fact that the largest value of I1" , i.e. the largest swelling pressure, occurs before the specimen is fully saturated. This behavior is a consequence of the so-called collapse upon wetting, which is reproduced by the employed model (the two dotted lines in Fig. 8 represent the load collapse yield curve). Fig. 9 contains a comparison of the computed soil response between a free swelling test and a HuderAmberg swelling test. In a free swelling test the initially unsaturated soil specimen is wetted, which results in the soil response, shown in Fig. 9 by the dotted lines. In a Huder-Amberg test the soil specimen in an oedometer is loaded first in axial direction (part 1 of the continuous lines), followed by wetting (part 2 of the continuous lines) and, subsequently, the axial loading is reduced in several steps, in each step keeping the axial stress constant until no further increase of the deformations is observed (parts 3 to 5 of the continuous lines).
5
CONCLUSIONS
The proposed cap model allows to represent basic features of the behavior of partially saturated soils, e.g. the increase of the shear strength and of the elasto-plastic stiffness with increasing matric suction and an irreversible decrease of the soil volume, denoted as collapse on wetting, due to an increase of the degree of water saturation, under high values of external stress. For the extensive suction controlled tests conducted on a silty sand, documented in (Macari et al., 2001; Macari et al., 2003), the proposed cap model yields good agreement with the measured soil behavior. In addition, the cap model was extended to take into account swelling behavior of soils and it was shown that the soil behavior, observed in typical swelling tests, can be reproduced.
REFERENCES Alonso, E.E., Gens, A., and Josa, A. (1990). A constitutive model for partially saturated soils. Géotechnique 40(3):405–430. Bolzon, G., and Schrefler, B.A. (1996). Elastoplastic soil constitutive laws generalized to partially saturated states. Géotechnique, 46(2):279–289. Borja, R.I. (2004). Cam-clay plasticity. part V: A mathematical framework for three-phase deformation and strain localization analyses of partially saturated porous media. Computer Methods in Applied Mechanics and Engineering, 193:5301–5338.
de Borst, R., and Groen, A.E. (2000). Computational strategies for standard soil plasticity models. In Zaman, M., Booker, J., and Gioda, G., editors, Modeling in Geomechanics, John Wiley & Sons, Ltd. Gallipoli, D., Gens, A., Sharma, R., and Vaunat, J. (2003). An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour. Géotechnique, 53(1):123–135. Geiser, F., Laloui, L., and Vulliet, L. (2000). Modelling the behaviour of unsaturated silt. In Tarantino, A., and Mancuso, C., editors, Experimental Evidence and Theoretical Approaches in Unsaturated Soils, 155–176. 27:1079–1098. Gens, A., and Alonso, E.E. (1992). A framework for the behavior of unsaturated expansive clays. Canadian Geotechnical Journal, 29:1013–1032. Houlsby, G.T. (1997). The work input to an unsaturated granular material. Géotechnique, 47(1):193–196. Kohler, R. (2006). Numerical modelling of partially saturated soils in the context of a three-phase-FE-formulation. Dissertation, University of Innsbruck, Austria. Kohler, R., and Hofstetter, G. (2007). A Cap Model for Partially Saturated Soils. International Journal for Numerical and Analytical Methods in Geomechanics, in press. Macari, E.J., and Hoyos, L.R. (2001). Mechanical behavior of an unsaturated soil under multi-axial stress states. Geotechnical Testing Journal, 24(1):14–22. Macari, E.J., Hoyos, L.R., and Arduino, P. (2003). Constitutive modeling of unsaturated soil behaviour under axisymmetric stress states using a stress/suction-controlled cubical test cell. International Journal of Plasticity, 19:1481–1515. Romero, E. (1999). Characterisation and thermal-hydromechanical behavior of unsaturated Boom clay: an experimental study. Ph.D. Thesis, Technical University of Catalonia, Spain. Sánchez, M., Gens, A., Guimarães, L.d.N., and Olivella, S. (2005). A double structure generalized plasticity model for expansive materials. International Journal for Numerical and Analytical Methods in Geomechanics, 29:751–787. Santagiuliana, R., and Schrefler, B.A. (2006). Enhancing the Bolzon-Schrefler-Zienkiewicz Constitutive Model for Partially Saturated Soil. Transport in Porous Media, 65: 1–30. Schrefler, B.A. (2002). Mechanics and thermodynamics of saturated/unsaturated porous materials and quantitative solutions. Applied Mechanics Reviews, 55(4):351–387. Tamagnini, R. (2004). An extended Cam-Clay model for unsaturated soils with hydraulic hysteresis. Géotechnique, 54(3):223–228. Van Genuchten, M. Th., and Nielsen, D. R. (1985). On describing and predicting the hydraulic properties of unsaturated soils. Annales Geophysicae, 3(5): 615–628. Wheeler, S.J., and Sivakumar, V. (1995). An elasto-plastic critical state framework for unsaturated soils. Géotechnique, 45(1):35–53.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Boundary surfaces and yield loci in unsaturated compacted clay A. Tarantino & S. Tombolato Dipartimento di Ingegneria Meccanica e Strutturale, Università degli Studi di Trento, Italy
ABSTRACT: Water-undrained one-dimensional compression tests with suction monitoring using Trento highcapacity tensiometers were carried out. During the loading-unloading cycles, suction, total vertical stress, degree of saturation, and specific volume were measured. It was observed that water retention behaviour is coupled to mechanical behaviour through the specific volume and, in turn, mechanical behaviour is coupled to water retention behaviour through the degree of saturation. The average skeleton stress and modified suction were adopted as generalised stress variables to model coupled behaviour and derived a ‘virgin loading’ mechanical boundary surface in the space: average skeleton stress, modified suction, and specific volume and a ‘main wetting’ hydraulic boundary surface in the space: modified suction, degree of saturation, and specific volume. This made it possible to investigate the yield loci in the generalised stress plane and it was observed that their shape differs from those suggested in the literature.
1
INTRODUCTION
The degree of saturation has an independent role on the mechanical behaviour of unsaturated soils. At the same suction, the higher the degree of saturation, the stiffer the soil is in the net stress-void ratio plane during virgin loading (Gallipoli et al., 2003a), the lower is the yield point in the net stress-void ratio plane (Wheeler et al., 2003), the higher is the ultimate shear strength under the same normal net stress (Tarantino & Tombolato, 2005, Boso, 2005). To account for the effect of the degree of saturation, and more in general the coupling between mechanical and water retention behaviour, constitutive models have recently been proposed that incorporate the degree of saturation into the stress variables (Jommi, 2000; Wheeler et al., 2003; Gallipo li et al., 2003a; Tamagnini, 2004). In particular, the model by Wheeler et al. (2003) is formulated in terms of two generalised stress variables, the average skeleton stress and the modified suction, which can be written under one-dimensional conditions as follows: σv = σv + sSr s∗ = ns
(1)
where σv is the average skeleton stress, s∗ is the modified suction, σv is the total vertical stress, s is the suction, Sr is the degree of saturation, and n is the porosity. These stress variables can be extracted as workconjugate stress variables from the rate of work input
per unit volume of unsaturated soil (Houlsby, 1997). The advantages in using the average skeleton stress and the modified suction are discussed by Wheeler et al. (2003). The basic framework proposed by Wheeler et al. (2003) included simple water retention and mechanical constitutive relationships. These allowed complex forms of mechanical behaviour to be simulated though at a qualitative level. However, it is likely that more realistic water retention and mechanical constitutive relationships would be required to quantitatively reproduce observed unsaturated coupled behaviour. This paper presents an experimental study of onedimensional compression behaviour of non-active clay. Tests were carried out under water-undrained conditions with matric suction monitoring using Trento high-capacity tensiometers. During the loading-unloading cycles, the suction s, the total vertical stress σv , the degree of saturation Sr and the porosity n were monitored. As such, hydraulic and mechanical paths in terms of average skeleton stress and modified suction could be investigated. In particular, we could derive a ‘virgin loading’ mechanical boundary surface in the space: average skeleton stress, modified suction, and specific volume and a ‘main wetting’ hydraulic boundary surface in the space: modified suction, degree of saturation, and specific volume. We could also derive the mechanical and hydraulic reversible responses in the planes σv −v and the plane s∗ − Sr respectively. This made it possible to investigate the form of the yield loci in the generalised stress plane σv − s∗ .
603
2 2.1
EXPERIMENTAL EQUIPMENT Trento high-capacity tensiometer
The Trento high-capacity tensiometer was used to measure matric suction (Tarantino & Mongiovì, 2002). The tensiometer was calibrated in the positive range 0–1500 kPa with a measured standard deviation of accuracy of ±1.5 kPa. It was assumed that calibration could be extrapolated into the negative range according to Tarantino & Mongiovì (2003). 2.2
Oedometer cell for one-dimensional compression tests
The soil was one-dimensionally compressed in the apparatus shown in Figure 1 (Tarantino & De Col, 2008). It consists of an oedometer cell, a loading pad and a pneumatic actuator. The oedometer cell was made impermeable at its base by inserting a stainless steel sheet between the base and ring. Two holes were machined into the loading pad to install two tensiometers. An O-ring was positioned in the tensiometer hole to avoid evaporation of soil water from the measurement area. Tensiometers were kept in place by small caps (not shown in the figure) which were tightened to the pad by means of three screws. A membrane obtained by cutting and pasting nitrile elastomer Bellofram rolling diaphragms was used to seal the annular gap between the loading pad and the oedometer ring. The membrane attachment was designed to minimise the volume of air enclosed by the membrane. A sphere was interposed between the loading pad and the ram to ensure that no moments were transferred to the loading pad. The apparatus was equipped with a load cell for measuring the vertical force (2000 N capacity with a measured standard deviation of accuracy of ±3 N)
Figure 1. Schematic layout of the oedometer cell for onedimensional compression (Tarantino & De Col 2008).
and one potentiometer displacement transducer for measuring the vertical displacements (34 mm travel with measured standard deviation of accuracy of ±0.01 mm). An electrovalve connected to the laboratory air supply system was used to control air pressure in the pneumatic actuator. The oedometer ring had diameter of 100 mm and height of 40 mm. 3
MATERIAL AND SPECIMEN PREPARATION
Speswhite Kaolin with plastic limit, wP = 0.32 and liquid limit, wL = 0.64 was chosen for tests presented in this paper. The grain size distribution showed it to have 0.20 silt fraction, and 0.80 clay fraction. Samples were prepared according to the procedure described by Tarantino & Tombolato (2005). Dry powdered Kaolin was laid in a large plastic basin in layers of about 10 mm and each layer sprayed with demineralised water to reach the target water content. The moistened powder was hand-mixed and saturated lumps were cut using four spatulas attached together. The material was sieved through a 1 mm aperture sieve to reduce the aggregate size. This size was considered acceptable when compared to the 20–25 mm specimen height. The moistened powder was wrapped inside two sealed plastic bags, placed in a plastic container and stored in a high-humidity room for at least 7 days. For the one-dimensional compression tests, the powder was placed in the oedoemeter and then compressed at loading rate of 5 kPa/min. 4
EXPERIMENTAL PROCEDURE
The kaolin powder was placed in the oedometer ring up to its height (40 mm). After placing the loading pad on the powder, a vertical stress of 150 kPa was applied and the membrane was set in place. Tensiometers were installed after applying a soil paste to the porous ceramic and were allowed to equilibrate for typically 1–2 hours. Prior to measurement, tensiometers were conditioned according to the procedure described by Tarantino (2004). The loading path involved loading-unloading cycles to 300, 600, 900, and 1200 kPa (Figure 2). The total vertical stress σv was increased or decreased at the constant rate of 5 kPa/min and each applied vertical stress was maintained constant for 30 min. The states of the specimen under quasi-zero vertical stress (14 kPa) were assumed to correspond to the states referred to as ‘as-compacted’ in the literature. The loading rate was selected on the basis of preliminary tests carried out at loading rates of 20, 10, and 5 kPa/min (Tarantino & De Col, 2008). After applying 150 kPa vertical stress, a calliper having 0.02 mm resolution was used to measure the distance between the loading cap and a reference point.
604
3
11
d v/dt=5 kPa/min
1050 8
900
2.8
10
w=0.259 w=0.275 w=0.254 w=0.236 w=0.299 w=0.215 w=0.311
750 5
600
7 Specific volume, v
Vertical stress, v : kPa
1200
450 Tensiometer insertion 300 2 4 150
1
0 0
3 400
12
9
6 800
1200
1600
2.6
2.4
2.2
Time: min 2
Figure 2. Loading path in one-dimensional tests. Numbers indicate first loading (1, 2, 5, 8, 11), unloading (3, 6, 9, 12) and reloading (4, 7, 10) vertical stresses (Tarantino & De Col 2008).
1.8 1000 Average skeleton stress,
This made it possible to determine the initial height of the specimen. As the vertical displacement was monitored during the one-dimensional compression process, the void ratio and hence the degree of saturation could be back calculated at any stage of the test. As no drainage was provided during the test, water content remained constant during one-dimensional compression and was measured at the end of the test.
v
Figure 3. Mechanical paths in terms of average skeleton stress and specific volume. 1
0.8
EXPERIMENTAL RESULTS
One-dimensional compression tests with continuous suction monitoring were carried out at 7 different water contents: 0.215, 0.236, 0.254, 0.259, 0.275, 0.299, and 0.311. The mechanical paths are represented in terms of specific volume, v, versus vertical average skeleton stress, σv , in Figure 3. Irreversible virgin compression paths and ‘reversible’ unloading-reloading paths can be clearly recognised. After every unloadingreloading cycle, the specific volume recovers the virgin compression curve. The hydraulic paths are represented in terms of degree of saturation, Sr , versus modified suction s∗ in Figure 4. When the soil is ‘virgin’ compressed under constant water content, the soil experiences the highest degrees of saturation and is therefore subjected to ‘main wetting’. The implicit assumption throughout the paper is that an increase in saturation due to compression at constant water content is equivalent to an increase in water content at constant void ratio according to Tarantino & Tombolato (2005). When the soil is unloaded and reloaded, the degree of saturation moves along scanning curves. 6
Degree of saturation, Sr
5
0.6
0.2 0
To model ‘main wetting’ behaviour, data from the seven one-dimensional compression tests lying on the
200
400
600
800
Modified matric suction, s *: kPa
Figure 4. Hydraulic paths in terms of modified suction and degree of saturation.
main wetting paths (virgin compression) and having void ratios of 1.0, 1.2, 1.4, 1.6, and 1.8 were selected. These data were interpolated using an equation of the form suggested by Gallipoli et al. (2003a) for the main wetting surface: Sr =
BOUNDARY SURFACES
w=0.311 w=0.299 w=0.275 w=0.259 w=0.254 w=0.236 w=0.215
0.4
1 1 + (φvψ s∗ )n
m (2)
where v is the specific volume and φ, ψ, m and n are parameters determined by best-fitting using the least
605
1.6 Specific volume over 'saturated' specific volume, v/vs
Degree of saturation, Sr
1
0.8
0.6
0.4
1.4
1.2
1
0.2 100
1000
10000
0
100000
Figure 5.
Hydraulic ‘main wetting’ boundary surface.
Figure 6.
squares method. With respect to the equation originally proposed by Gallipoli et al. (2003b), the specific volume and modified suction now replace the void ratio and suction respectively. The main wetting surface given by Eq. 2 acts as lower boundary surface in the space (s∗ , v, Sr ) (Vaunat et al., 2000; Gallipoli et al., 2003a; Tarantino & Tombolato, 2005) and is associated with the suction decrease (SD) yield locus discussed by Wheeler et al. (2003). The capability of Eq. 2 to capture the effect of specific volume on degree of saturation is shown in Figure 5 where the degree of saturation is plotted against the modified suction normalized with respect to specific volume, vψ s∗ . To model ‘virgin loading’ behaviour, data from the seven one-dimensional compression tests lying on virgin compression curves and having void ratios of 1.0, 1.2, 1.4, 1.6, and 1.8 were selected. These data were interpolated using the following equation: ∗ b s v = vs · 1 + a (3) σv
0.8
1.2
1.6
(4)
where N1−D and λ are the saturated virgin loading parameters. The virgin loading surface given by Equation (3) acts as boundary surface in the space (σv , s∗ , v) and is associated with the load-collapse (LC) yield locus discussed by Wheeler et al. (2003). The capability of Eq. 3 to capture the effect of average skeleton stress and modified suction on specific volume is shown in Figure 6.
Mechanical ‘virgin loading’ boundary surface.
Within the boundary surfaces, the behaviour is reversible as shown in Figure 3 and Figure 4. In particular, reversible degree of saturation paths (scanning paths) appear to be independent of specific volume Figure 4 and can be described by the following equation: Sr = Sr0 − κs s∗
(5)
where κs is the slope of the scanning paths in the plane s ∗ − Sr . Reversible specific volume paths (unloladingreloading paths) appear to be independent of modified suction (Figure 3) and can be described by the following equation: v = vk − κ ln σv
(6)
where κ is the slope of the unloading-reloading paths in the plane ln (σv ) − v and vk is the specific volume at σv = 1 kPa. 7
where a and b are best-fit parameters and vs is the specific volume in saturated conditions at the same average skeleton stress. The saturated specific volume vs was derived from tests on saturated specimens (Tarantino & De Col 2008): vs = N1−D − λ ln σv
0.4
Modified matric suction over average skeleton stress s*/ "v: kPa
Normalised modified matric suction v s*: kPa
HARDENING LAWS
Wheeler et al. (2003) presented a constitutive model for isotropic stress states. Yield curves in the plane (p − s∗ ), with p being the mean average skeleton stress, were assumed to be as shown in Figure 7. The locations of the LC and SD curves are defined by p∗0 ∗ and sD and these are related to the plastic volumetric p deformations dεv and the plastic degree of saturation p change dSr by the following hardening laws:
606
p
dεv = p dSr
λ−κ v (1 − k1 k2 )
λs − κs =− (1 − k1 k2 )
∗ dsD dp∗0 ∗ − k1 ∗ p0 sD
∗ dp∗0 dsD ∗ − k2 ∗ sD p0
(7)
where λ and κ are the parameters of the mechanical model, λs and ks are the parameters of the water retention model, and k1 and k2 are coupling parameters. Let us assume that this constitutive model also applies to one-dimensional stress states with p replaced by σv . During the one-dimensional virgin compression, the soil contemporarily moves along the mechanical boundary surface (Eq. 3) and the water retention boundary surface (Eq. 2). The stress state is then located on the bottom-right corner of the elastic domain shown in Figure 7. As such, during virgin ∗ loading, s∗ ≡ sD and σv = σ0∗ . p The hardening law associated with dSr can then be derived by differentiating Eq. 2 and Eq. 5 and assuming that the specific volume is given by Eq. 3. The p hardening law associated with dεv can be derived by differentiating Eq. 3 and Eq. 6. The following hardening laws were thus obtained:
∗ dsD dσ0∗ B = (A+B−C) ∗ − ∗ σ0 A + B − C sD ∗ dsD ψ (A + B) dσ0∗ p − dSr = −DE ∗ σ0∗ sD E
p dεv
(8)
where: λ κ vsat A= ;C = ; ;B = b 1 − vsat v v
D = mnSr 1 −
1m Sr /
;
s∗ E = ψB + 1 − κs . D
(9)
This suggests that the yield loci SD and LC may not have the form proposed in Figure 7. 8
YIELD LOCI
The yield locus SD can be derived by the intersection of the ‘main wetting’ lower boundary surface (Eq. 2) with the elastic wall defined by Eq. 5. The specific volume that appears in Eq. 2 is the volume associated with an elastic path reaching the SD yield locus and this is given by Eq. 6. The yield locus SD is obtained in implicit form as follows: ⎧ ⎫m ⎪ ⎪ ⎨ ⎬ 1 " # Sr0 − ks s∗ = (10) n ⎪ ⎩ 1 + φ vk − k ln σv ψ s∗ ⎪ ⎭ The yield locus LC can be derived by the intersection of the ‘virgin loading’ boundary surface (Eq. 3) with the elastic wall defined by Eq. 6. The following implicit equation was obtained: ∗ b s vk − k ln σv = vs · 1 + a (11) σv The LC and SD yield loci derived from the water retention and mechanical boundary surfaces and their evolution with loading are plotted in Figure 8 for the compression test at w = 0.311. As expected, the LC and SD yield curve have a more complex shape than assumed by Wheeler et al. (2003) in their basic model.
If Eq. 8 is compared with Eq. 7, it can be observed that the coupling terms k1 and k2 are not recovered.
400
Modified suction, s *: kPa
300
Start of test
200
100
LC
SD 0 0
400
800
1200
1600
2000
Average skeleton stres, v" : kPa
Figure 7. LC, SI and SD yield curves for isotropic stress states according to the model by Wheeler et al. (2003).
Figure 8. LC and SD yield loci derived from the water retention and mechanical boundary surfaces for the compression test at w = 0.311.
607
9
CONCLUSIONS
The paper has presented water-undrained onedimensional compression tests with suction monitoring using Trento high-capacity tensiometers. Loading and water retention paths were investigated using two generalised stress variables, the average skeleton stress and the modified suction. We derived a ‘virgin loading’ mechanical boundary surface in the space: average skeleton stress, modified suction, and specific volume and a ‘main wetting’ hydraulic boundary surface in the space: modified suction, degree of saturation, and specific volume. In turn, these boundary surfaces were used to derive the yield loci in the generalised stress plane. It was observed that their shape differs from those suggested in the literature. Equations for the LC and SD yield loci were obtained in implicit form. Future work will involve defining simpler explicit equations for the yield loci and deriving suitable hardening laws. REFERENCES Boso, M. 2005. Shear strength behaviour of a reconstituted partially saturated clayey silt. PhD dissertation, Università degli Studi di Trento, Italy. Gallipoli, D., Gens, A., Sharma, R. & Vaunat, J. 2003a. An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour. Géotechnique 53 (1): 123–136. Gallipoli, D., Wheeler, S.J. & Karstunen, M. 2003b. Modelling the variation of degree of saturation in a deformable unsaturated soil. Géotechnique, 53 (1): 105–112.
Houlsby, G.T. 1997. The work input to an unsaturated granular material. Géotechnique 47 (1): 193–196. Jommi, C. 2000. Remarks on the constitutive modelling of unsaturated soils. In Experimental Evidence and Theoretical Approaches in Unsaturated Soils, Proceedings of an International Workshop (eds A. Tarantino and C. Mancuso), pp. 139–153. Rotterdam: A.A. Balkema. Tamagnini, R. 2004. An extended Cam-clay model for unsaturated soils with hydraulic hysteresis. Géotechnique 54 (3): 223–228. Tarantino, A. 2004. Panel report: Direct measurement of soil water tension. In Proceedings 3rd International Conference on Unsaturated Soils (eds J.F.T. Jucá, T.M.P. de Campos and F.A.M. Marinho), Recife, 3, pp. 1005–1017. Rotterdam: A.A. Balkema. Tarantino, A. & Mongiovì, L. 2002. Design and construction of a tensiometer for direct measurement of matric suction. In Proceedings 3rd International Conference on Unsaturated Soils (eds J.F.T. Jucá, T.M.P. de Campos and F.A.M. Marinho), Recife, 1, pp.319–324. Tarantino, A. & Mongiovì, L. 2003. Calibration of tensiometer for direct measurement of matric suction. Géotechnique, 53 (1): 137–141. Tarantino, A. & Tombolato, S. 2005. Coupling of hydraulic and mechanical behaviour in unsaturated compacted clay. Géotechnique 55 (4): 307–317. Tarantino, A. & De Col, E. 2008. Compaction behaviour of clay. Géotechnique, in press. Vaunat, J., Romero, E. & Jommi, C. 2000. An elastoplastic hydro-mechanical model for unsaturated soils. In Experimental Evidence and Theoretical Approaches in Unsaturated Soils, Proceedings of an International Workshop (eds A. Tarantino and C. Mancuso), pp. 121–138. Rotterdam: A.A. Balkema. Wheeler, S.J., Sharma, R.S. & Buisson, M.S.R. 2003. Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils. Géotechnique 53 (1): 41–54.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Application to a compacted soil of a Cam Clay model extended to unsaturated conditions F. Casini Università Roma ‘‘La Sapienza’’, Roma, Italy
R. Vassallo Università della Basilicata, Potenza, Italy
C. Mancuso Università ‘‘Federico II’’, Napoli, Italy
A. Desideri Università Roma ‘‘La Sapienza’’, Roma, Italy
ABSTRACT: This paper presents an interpretation of experimental results obtained at the Department of Geotechnical Engineering of the Università di Napoli Federico II. The results are part of an extensive program carried out to investigate the effects of partial saturation on the volumetric behaviour and on the initial shear stiffness of a compacted silt. Tests were performed using two suction-controlled devices, a triaxial cell and a Resonant Column Torsional Shear (RCTS) cell. The compatibility of experimental data with a Bishop Stress Model (BSM) is discussed in the paper. The BSM permits highlighting of the two main effects of suction on soil behaviour: the increase of the average stress acting on the soil skeleton and the hardening—cementing of the soil packing. Hydraulic hysteresis is included in the definition of the water retention curve so that its effects, such as the irreversible component of volume change recorded during drying paths, are automatically incorporated in the predictions of the model.
1
INTRODUCTION
An extensive experimental program was carried out at the Department of Geotechnical Engineering of the Università di Napoli Federico II to investigate the effects of partial saturation on the volumetric behaviour and on the initial shear stiffness, G0 , of a compacted clayey silt (Vassallo et al., 2007a). A first interpretation of the results was provided by Vassallo et al. (2007b), using an approach in terms of net stresses and suction in the framework of the Barcelona Basic Model. In this paper some of the experimental data are re-interpreted using a Modified Cam Clay Model extended to unsaturated conditions (Jommi, 2000; Tamagnini, 2004). A similar approach has already been used by Casini et al. (2007) in order to understand if the model could predict the general features of the experimental results on the clayey silt. The model predicts correctly the influence of Sr on compressibility. However, for the sake of simplicity, the hydraulic hysteresis of the water retention curve was neglected.
This work takes a step forward by accounting for hysteresis and its effects on soil behaviour. The focus is on tests which included a compression stage and, then, wetting-drying cycles. 1.1 Material properties, experimental program The tested soil is the Po silt: a clayey—slightly sandy silt representative of the materials used for the construction of embankments on the Po river (Italy). On average, the material has a liquid limit (wL ) of 50.4%, a plastic limit (wP ) of 32.5% and therefore a plasticity index (IP ) of 17.9%. According to the Casagrande chart, it is classified as inorganic silt of medium/high compressibility. The material was compacted at the optimum water content by using the Standard Proctor procedure (ASTM, 2005). Table 1 summarises the average properties of the silt after compaction. Fifteen suction controlled tests were performed using a triaxial cell (Vassallo et al., 2007a). Three of them consisted of isotropic compression with
609
where σij are total stresses, ua is the air pressure, uw is the water pressure, δij is the Kronecker delta, χ(Sr ) is a weighing parameter which can account for the effects of surface tension. In this work χ(Sr ) was assumed equal to Sr . It has been argued that expression (1), often called Bishop’s stress with χ(Sr ) = Sr , represents the average stress acting on the solid phase if one neglects the work of the air-water interface (Hassanizadeh & Gray, 1980; Lewis & Schrefler, 1987; Hutter et al., 1999). Starting from the modified Cam Clay model for saturated conditions (Roscoe & Burland, 1968) and using the conceptual framework proposed by Jommi (2000) and Tamagnini (2004), the model is formulated as follows. As in the original modified Cam-clay model, elastic behaviour is defined by:
Table 1. Average properties of the tested material after compaction. w (%)
γd (kN/m3 )
v
Sr (%)
23.1 ± 0.3
15.59 ± 0.08
1.731 ± 0.009
86.9 ± 1.9
Table 2.
Stress paths of tests mp05RC and mp07RC.
mp05RC
mp07RC
p − ua ;
ua − uw (kPa)
p − ua ;
ua − uw (kPa)
10 200 200 200 200 200 200
200 200 400 100 400 100 200
10 200 200 200 200 550 –
400 400 100 400 200 200 –
ε˙ ve =
unloading and reloading stages. In the other twelve tests, the samples were isotropically consolidated at constant suction and then sheared. Besides the fully saturated condition, suctions of 50, 100, 200 and 400 kPa were investigated. Twelve suction controlled tests were carried out using a Resonant Column Torsional Shear (RCTS) cell (Vassallo et al., 2007a). During seven of them, after a preliminary equalization stage, an isotropic consolidation stage was carried out (in three cases including both loading and unloading) measuring almost continuously the initial stiffness G0 . The remaining five tests included stages of compression and of drying and wetting at constant mean net stress (p−ua ), again with a continuous measure of the initial stiffness G0 . Overall, three levels of suction (100, 200, 400 kPa) and mean net stresses ranging from 25 to 700 kPa were investigated. This paper focuses on two out of the five tests which included stages of drying and wetting. Table 2 summarises the stress paths followed in these tests, in terms of (p − ua ) and matric suction (ua − uw ). The soil parameters used to model the volumetric behaviour observed during these two tests are obtained from the complete set of isotropic stage results (both equalization and compression). 2
ELASTO-PLASTIC MODEL
1 p˙ K
ε˙ de =
1 q˙ 3G
(2)
where p is the mean effective stress, q is the deviator stress, ε˙ ve and ε˙ de are the increments of elastic volumetric strain and elastic deviatoric strain, respectively, K is the bulk modulus and G is the shear modulus. The yield locus has the usual form: f = q2 + M 2 p · (p − p c )
(3)
where M is the slope of the critical state line in the p : q plane, and pc is the scalar internal variable (overconsolidation pressure) describing isotropic hardening. The evolution of pc is defined in terms of a double hardening mechanism: p˙ c = p˙ c sat + p˙ c unsat
(4)
where p˙ c sat =
vpc v ε˙ λ−κ p
(5)
describes the evolution of the yield function produced p by plastic volumetric strains ε˙ v as predicted in the original model for saturated soils. Parameter λ is the slope of the normal compression line, κ is the slope of unloading-reloading lines, and v is the specific volume. On the other hand, the expression: p˙ c unsat = −bpc S˙ r
(6)
2.1 Bishop stress model The classic Bishop equation for effective stress is adopted: σ ij = σij − ua + χ(S r )(ua − uw )δij
(1)
describes the evolution of the yield surface produced by changes in the degree of saturation, which may occur even if the current stress lies in the elastic domain. Parameter b is a constant soil property.
610
pc = pc sat · exp[b(1 − Sr )]
(7)
Thus, b controls the rate of change in pc caused by variations in Sr . Hardening has an irreversible component dependent on the development of plastic volumetric strains, related to the evolution of pc sat , and a reversible component related to changes in Sr . The model requires a hydraulic constitutive relationship describing the water storage mechanism, as shown in Figure 1. The retention curve θw = θw (s) obtained upon an imbibition process differs from that obtained upon drying (hysteresis). Equilibrium at a given suction may be obtained with different θw . The two main curves are linked by scanning curves that can be linear or not. The issue of the hydraulic component of constitutive models was first addressed by Wheeler (1996) and by Dangla et al. (1997). Probably, the first full attempt to couple hydraulic behaviour with a mechanical model for unsaturated soils was proposed by Vaunat et al. (2000). More recently, Wheeler et al. (2003) presented an elastoplastic constitutive model that also fully couples hydraulic hysteresis with mechanical behaviour of unsaturated soils. A comprehensive review of constitutive models for unsaturated soils, including those based on Bishop’s stress, was presented by Gens et al. (2006). In this study the equation proposed by Van Genuchten (1980): θw = θw sat
1 1 + (αs)n
m (8)
is used, where θw is the volumetric water content, θw sat is the volumetric water content under saturated conditions and s is matric suction.
The main drying and wetting curves are obtained assuming different values for the constitutive parameters α, n and m (Romero & Vaunat, 2000). Scanning curves are assumed linear in the θw : s plane: θ˙w = −ks s˙
(9)
in which the constitutive parameter ks is the slope of the scanning curves. Since different values of θw can correspond to the same value of s, as shown in Figure 1, the hardening parameter p c in Equation (7) results smaller along the main drying curve than along the main wetting curve for the same values of suction and porosity. The physical meaning of the assumptions above rests on the fact that lower degree of saturation implies a higher number of contact zones between the pore fluids (menisci) so that the bonding effect exerted by the menisci is higher along a wetting path than along a drying path (Tamagnini, 2004).
2.2 Modelling of experimental results Figure 2 reports, in the θw : s plane, the 26 experimental points relative to the end of the equalization stages for all triaxial and resonant column tests together with the adopted water retention relationship. The average suction of the tested soil after compaction is about 140 kPa (Vassallo et al., 2007a). Therefore, equalization at suction 200 and 400 kPa is a drying process while equalization at lower suction is a wetting process. Table 3 summarises the parameters chosen for the water retention curve. All the available experimental data from compression stages were analysed to obtain the parameters of Equations (5) and (6), reported in Table 4.
400
s
s (kPa)
300
main drying
drying
scanning curve
The integration of Equation (4) yields to:
wetting
200 main drying
100
scanning curve
0 30
main wetting
main wetting
35
40
45
w (%)
w
Figure 1. Constitutive relationships describing water storage mechanism.
Figure 2. Experimental results of equalization stages versus the adopted water retention relationship.
611
The performance of the model was verified for tests mp07RC and mp05RC, whose results are described in detail by Vassallo et al. (2007a). Figure 3a reports a comparison between model predictions and experimental results for test mp07RC. As reported in Table 2, this test consisted of a compression at constant suction s = 400 kPa, up to p ∼ = 510 kPa (path 0-1), followed by several wetting-drying stages to s = 100–400–200 kPa (path 1-2-3-4) and finally by compression to p ∼ = 710 kPa (path 4-5). Experimental data for drying and wetting stages show only two data points at the beginning and at the end of each stage. Since suction was applied immediately at the boundary of the specimen, then waiting for the achievement of equilibrium, only the initial and final specific volumes can be attributed to the imposed net stress and suction. Differently, a complete v : p curve was obtained for each stage by modelling. During the first wetting stage at s = 100 kPa (path 1-2) the material swells. During the following drying at s = 400 kPa (path 2-3) there is a small accumulation of irreversible deformations due to the increase in suction, as shown by the specific volume at point Table 3.
Drying Wetting
3 which is smaller than that at point 1. During the subsequent wetting at s = 200 kPa (path 3-4) the material swells. Then, in the final stage of compression, the material seems to reach a normally consolidated state at p ∼ = 490 kPa. Model predictions are also reported in Figures 3b and 3c in θw : s and p : (1 − Sr ) planes. An overconsolidated state is predicted at point 0 (beginning of compression). Points 0 and 1 lie on the main drying curve (Fig. 3b) as the imposed suction (400 kPa) is greater than the after compaction suction. Compression stage 0-1 does not affect the predicted value of θw (Fig. 3b). On the other hand, there is a change in Sr , and thus in variables (1 − Sr ) and p , due to the change in porosity (Fig. 3c). For this stage, the prediction in the p : v plane is satisfying. The model also predicts well soil behaviour for the wetting stage 1-2 from s = 400 kPa to s = 100 kPa, that lies completely in the elastic domain, and for the drying stage 2-3 from s = 100 kPa to s = 400 kPa, that represents an elasto-plastic path. In the first case the state path follows first a scanning curve and then reaches the main wetting curve; in the second case, the model predicts that the state path returns to the same value of θw of points 0-1. Furthermore, the model predicts some (slight) hardening in the p : (1 − Sr ) plane due to the different changes which both p and p c experience along paths 1-2 and 2-3 (Fig. 3c). The subsequent wetting 3-4 to s = 200 kPa only induces elastic strains, in good agreement with experimental data. The final compression stage is also well predicted by the model. Figure 4a compares experimental results to model predictions for test mp05RC. This test included a compression at constant suction s = 200 kPa, up to p − ua = 200 kPa (path 0-1), then several dryingwetting stages s = 400–100–400–100–200 kPa (path 1-2-3-4-5-6) (see Table 2).
Parameters describing soil water retention curve. α(kPa−1 )
n
m
θw sat (%)
ks (kPa−1 )
0.11 0.07
1.07 1.10
0.07 0.09
44 44
0.00256 0.00256
Table 4. Parameters describing soil compressibility and the evolution of the yield surface produced by changes in Sr . λ
κ
b
N (Sr = 1)
0.06
0.018
7
2.015
experimental data model predictions 300 4
1 3
4-5
w.
1.70 100
1000 p'=p–ua+Sr(ua–uw) (kPa)
Figure 3. plane (c).
in
100 5 30
5
0.1
3-4 1-2 Y.L. 0
40
w (%)
612
3
2
2
35
Test mp07RC. Experimental data versus predictions in p
1 4
5
s.c.
ma
1.72
0.2 1-S r
1.74
s.c.
.
2
0
d main
0
1.76
0.3
0-1-3
s (kPa)
1.78
v
(c)
(b)
(a)
10
100
1000
p' (kPa)
: v plane (a); predictions in θw : s plane (b) and p : (1−Sr )
(a)
(b)
(c)
experimental data model predictions
1.76
0.3
2-4
0
0-1
6 s.c.
100
w.
6mod
42 mod 24
3 5 0.1
1000
30
35 (%)
p'=p– ua+Sr(ua–uw) (kPa)
w
2-3
3-5 Y.L. 0
mod
1.68 100
1
1-S r
v
s (kPa)
6
5mod 3
s.c.
in ma
3mod 5
0
0.2
d.
1
1.72 1.70
main
300
1.74
40
10
2 4 6 4-5-6
1
100
1000
p' (kPa)
Figure 4. Test mp05RC. Experimental data versus predictions in p : v plane (a); predictions in θw : s plane (b) and p : (1−Sr ) plane (c).
The first drying at s = 400 kPa (path 1-2) induces irreversible deformations due to the increase in suction above its maximum past value (Vassallo et al. 2007ab). The irreversibility of previous volume changes is shown by the much smaller absolute value of the variation of v observed during the first wetting at s = 100 kPa (path 2-3). As expected, this wetting path induces swelling. The subsequent drying and wetting stages cause volume changes comparable to those of wetting 2-3 and smaller than those of drying 1-2. The material always swells along wetting paths and shrinks along drying paths. Substantially, all the experimental points, from 2 on, are very close to a single line in the p : v plane. Figures 4b and 4c show model predictions in the θw : s and p : (1 − Sr ) planes. The model predicts an overconsolidated state at the beginning of compression. Similarly to test mp07RC, the results of the first compression stage are well predicted. The model also predicts an irreversible reduction of v, quite close to the measured one, during the subsequent drying 1-2 to s = 400 kPa. For the model, the path 2-3 from s = 400 kPa to s = 100 kPa is elastic. The second drying 3-4 to s = 400 kPa is elasto-plastic like the first one, although predicted shrinkage is much smaller than for path 1-2. Irreversible strains along cycle 2-3-4 are due to the different changes which p and pc experience along path 2-3 and 3-4 (Fig. 4c), linked to the shape of the water retention relationship in the θw : s plane (Fig. 4b). The closed cycle in this plane does not correspond to a closed cycle in the Sr : s plane, which is relevant for model predictions. The second wetting 4-5 and the final drying 5-6 are elastic. It is worth noting that the measured value of v in point 2 is slightly smaller than that of point 4, i.e., the material accumulates a small swelling during a drying-wetting cycle. This cannot be easily explained from a physical point of view and could be due to incomplete equalization during some stages of
the test. More appropriately the model predicts a slight accumulation of shrinkage. However predictions are substantially in good agreement with measurements from point 2 to point 6. Points 0 and 1 in Figure 4b lie on a scanning curve because the imposed suction, s = 200 kPa, is just slightly higher than the after compaction suction. Similarly to test mp07RC, which was analyzed above, compression 0-1 does not influence the value of θw while it changes porosity and, thus, variables p and (1 − Sr ), as shown in Figure 4c. During the first drying 1-2, the main drying curve is reached and the yield locus is significantly shifted rightwards. This confirms that path 1-2 is elasto-plastic. During the wetting 2-3 a scanning curve is followed until the main wetting curve is reached; an elastic path is predicted in the plane p : (1 − Sr ). The same value of θw as at point 2 is reached after the second drying path 3-4. The model predicts a slight hardening, i.e., a slight further shift rightwards of the yield locus, linked to the different changes which both p and p c experience along paths 2-3 and 3-4 (Fig. 4c). The yield locus remains unvaried during the final wetting-drying stages 4-5-6. 2.3
Interpretation of stiffness measurements
Vassallo et al. (2007a-b) used the framework of the Barcelona Basic Model to interpret the measurements of initial shear stiffness G0 along both compression and wetting-drying paths. It was concluded that there is a significant influence of suction on stiffness, which generally increases as (ua − uw ) increases. Nevertheless, changes of suction may cause significant accumulation of irreversible changes of specific volume, accompanied by a further increase of G0 relative to a general stress state (p − ua ), (ua − uw ). In other words, there can be a significant effect of the stress history, expressed in terms of (p − ua ) and (ua − uw ), on the initial stiffness.
613
(a)
(c)
(b) mp05RC mp07RC
250
0.3
0.3
05-2
0
150 100
0
0.2 07-2
05-1
05-P
07-1
07-0
2 2
0.1 P
05-0
2 0.1
1
200
300
400
500
10
100
p' (kPa)
1-2
Y.L. 0
Y.L. 0 50
1
0.2
P1
1-Sr
G0 (MPa)
200
1000
p' (kPa)
10
100
1000
p' (kPa)
Figure 5. Measured initial stiffness G0 versus p for tests mp05RC and mp07RC (a); predictions in the p : (1 − Sr ) plane for tests mp05RC (b) and mp07RC (c).
As highlighted by Casini et al. (2007), an alternative approach is using Equation (1) and referring G0 measured values to corresponding p values. This way, the effects of partial saturation on the initial shear stiffness result similar to those ascribable to the structure of a natural soil compared to the same soil reconstituted (Rampello et al. 1994). In fact, as far as data collected during isotropic compression are concerned, moving from complete saturation to partial saturation induces a translation of experimental G0 : p curves. Figure 5a reports for tests mp05RC and mp07RC stiffness versus p , measured during the first compression stage and the subsequent first wetting or drying stage. Compression stage data belong to a narrow range centred on the dashed line plotted in the same figure. This proves that the stiffness of the unsaturated soil can be fundamentally interpreted by a single curve in the p : G0 plane. On the other hand, the stiffness measured after a drying or a wetting stage results significantly higher than the values on the dashed curve. Comparison can be made between points 05-2 and 07-1, characterized by the same (p−ua ) and (ua −uw ), and 05-P and 07-2, characterized by the same p . This suggests that there is also an effect of stress history in terms of Bishop’s stress. Figures 5b and 5c report model predictions in the plane p : (1 − Sr ) for the same tests. Point 2 of test mp05RC and point 1 of test mp07RC belong to different yield loci and have different (1 − Sr ) and p . The yield locus is more expanded for test mp05RC. As a consequence of different history, point P of test mp05RC is on the current yield locus while point 2 of test mp07RC is inside the yield locus. All this could justify the differences in measured stiffness. 3
CONCLUDING REMARKS
This paper verifies the possibility of interpreting some data from the comprehensive experimental study by
Vassallo et al. (2007a) within the framework of a Bishop Stress Model (BSM). Casini et al. (2007) had already confirmed that the BSM can interpret the progressive shift of normal consolidation lines as the degree of saturation decreases and, more in general, the influence that Sr has on compressibility. Herein, a step forward was taken in modelling, by accounting for the hysteresis of the water retention curve and for its effects on soil behaviour. This determines a hysteresis in the internal variable describing isotropic hardening (Tamagnini, 2004) and can justify the occurrence of irreversible deformations such as those induced by drying-wetting cycles. The predictions of the chosen model are in good qualitative and quantitative agreement with the experimental data in terms of specific volume changes plotted versus Bishop mean effective stress p . The representation of test paths and of yield loci in the plane p : (1 − Sr ) also seems quite useful to interpret the effects of stress state and stress history on the initial shear stiffness G0 . REFERENCES ASTM 2005. D0698-00 AE01 Test method for laboratory compaction characteristics of soil using standard effort (12, 400 ft · lbf /ft3 (600 kN · m/m3 )), ASTM Book of Standards, vol. 04.08, Philadelphia, USA. Casini F., Vassallo R., Mancuso C. & Desideri A. 2007. Interpretation of the behaviour of compacted soils using Cam-Clay extended to unsaturated conditions. Proceedings of the Second International Conference Mechanics of Unsaturated Soils, Weimar (Germany), 29–36. Dangla O.L., Malinsky L. & Coussy O. 1997. Plasticity and imbibition-drainage curves of unsaturated soils: a unified approach. 6th International Conference on numerical models in geomechanics, Montreal, 141–146. Gens A., Sanchez M. & Sheng D. 2006. On constitutive modelling of unsaturated soils. Acta Geotechnica, 1, 137–147.
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Hassanizadeh S.M. & Gray W.G. 1980. General conservation equations for multiphase systems: 3. Constitutive theory for porous media flow. Advanced Water Resource, 3, 25–40. Hutter K., Laloui L. & Vulliet L. 1999. Thermodynamically based mixture models for saturated and unsaturated soils. Mechanics of Cohesive-frictional Materials, 4, 295–338. Jommi C. 2000. Remarks on the constitutive modelling of unsaturated soils. Proceedings of the International Workshop Experimental Evidence and Theoretical Approaches in Unsaturated Soils, Trento (Italy), 139–153. Lewis R.W. & Schrefler B.A. 1987. The finite element method in the deformation and consolidation of porous media. Wiley, Chichester. Rampello S., Silvestri F. & Viggiani G. 1994. The dependence of small strain stiffness on stress state and history for fined grained soils: the example of Vallericca clay. Proceedings of the First International Symposium on Prefailure Deformation of Geomaterials, Sapporo (Japan), 273–278. Romero E. & Vaunat J. 2000. Retention curves of deformable clay. Proceedings of the International Workshop Experimental evidence and theoretical approaches in unsaturated soils, Trento (Italy), 91–106. Roscoe K.H. & Burland J.B. 1968. On the Generalized StressStrain Behavior of Wet Clay. Engineering Plasticity, Cambridge University Press, 535–609.
Tamagnini R. 2004. An extended Cam-clay model for unsaturated soils with hydraulic hysteresis. Géotechnique, 54, 223–228. Van Genuchten M.T. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 44, 892–898. Vassallo R., Mancuso C. & Vinale F. 2007a. Effects of net stress and suction history on the small strain stiffness of a compacted clayey silt. Canadian Geotechnical Journal, 44, 447–462. Vassallo R., Mancuso C. & Vinale F. 2007b. Modelling the influence of stress-strain history on the initial shear stiffness of an unsaturated compacted silt. Canadian Geotechnical Journal, 44, 463–472. Vaunat J., Romero E. & Jommi C. 2000. An elastoplastic hydro-mechanical model for unsaturated soils Proceedings of the International Workshop Experimental evidence and theoretical approaches in unsaturated soils, Trento (Italy), 121–138. Wheeler S.J. 1996. Inclusion of specific water volume within an elastoplastic model for unsaturated soil. Canadian Geotechnical Journal, 33, 42–57. Wheeler S.J., Sharma R.S. & Buisson M.S.R. 2003. Coupling of hydraulic hysteresis and stress strain behaviour in unsaturated soils. Géotechnique, 53, 41–54.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Mixed isotropic-rotational hardening to model the deformational response of unsaturated compacted soils C. Jommi Department of Structural Engineering, Politecnico di Milano, Milano, Italy
E. Romero Department of Geoengineering and Geoscience, Universitat Politècnica de Catalunya, Barcelona, Spain
ABSTRACT: The pattern of volumetric strains of unsaturated compacted soils along drying and wetting cycles have received considerable attention in the last years due to its practical implications during the service life of earth structures and backfills. Much attention has been devoted to the amount of collapse upon wetting as a function of suction and stress level. Oedometer test data are presented here to quantify the amount of collapse and shrinkage strains in wetting-drying-wetting cycles. Besides, results of an isotropic wetting test show that collapse is in general accompanied by distortional strains as a result of the initial anisotropy created during compaction. An elastic plastic model, in which the evolution of the soil structure is described by means of a mixed isotropic-rotational hardening, is presented. Coupling between hydraulic and mechanical behaviour is provided by a hysteretic retention curve. Comparison between model simulations and experimental data show that the model is able to reproduce correctly the whole irreversible strain path upon both wetting and drying.
1
INTRODUCTION
The deformational response of compacted soils under environmental actions is of paramount importance in the analysis of the service life of earth constructions such as dams, embankments, waste disposal facilities. Hydraulic loads, i.e. cyclic drying and wetting, besides changes in external loads, may condition to a large extent the overall behaviour of this class of structures. The abrupt volume reduction, termed collapse, that a compacted soil may undergo upon wetting, is considered to be the most problematic aspect of the deformational response of a compacted soil (e.g. Pereira & Fredlund 2000, Lim & Miller 2004). That soils compacted dry of optimum at low dry density undergo collapse when wetted under constant total stress is well known (Jennings & Burland 1962, Barden et al. 1973). More recent experimental results have shown that even soils compacted at optimum conditions or wet of optimum may experience collapsible behaviour at high stresses, if they undergo drying before wetting (Gens et al. 1995, Suriol et al. 1998). These experimental data suggest that the whole suction history, besides void ratio and suction, rules the overall deformational response of compacted soils. Less attention was paid in the past to irreversible volumetric strain experienced by compacted soils upon first drying, which are of the same sign as collapse
strains and may even be of comparable magnitude (e.g. Dif & Bluemel 1991, Fleureau et al. 1993). Besides, the role played by the initial anisotropic fabric created by the compaction procedures on the deformational response of compacted soils has not been studied in detail, although different researchers have highlighted the significant initial anisotropy developed under one-dimensional oedometer compaction (Zakaria et al. 1995, Cui & Delage 1996, Estabragh & Javadi 2006). Moreover, Zakaria et al. (1995) and Barrera et al. (2000) observed that a clear evolution of the anisotropic fabric occurs along the subsequent loading paths. In particular, Romero (1999) showed that, due to the initial anisotropic fabric, distortional strains may be appreciable along wetting paths under an external isotropic stress state. Shrinkage strains upon drying and collapse or swelling strains developed upon wetting are considered to be the result of different irreversible deformational mechanisms. Consequently, in the framework of elastoplasticity they are usually modelled with separate, although coupled, yield funcitons (e.g. Alonso et al. 1990, Wheeler et al. 2003, Sheng et al. 2004, Sun et al. 2007). A possible alternative unified view of the overall volumetric strains experienced by compacted soils along generalised hydraulic paths is suggested here. A rather simple elastic plastic constitutive model
617
is proposed, which exploits the hysteretic retention characteristics of compacted soils to describe both irreversible collapse upon wetting and irreversible shrinkage upon drying in a unified framework. A unique mixed isotropic-rotational hardening law describes the evolution of the soil fabric along generalised stress paths, allowing for irreversible shrinkage, irreversible collapse and anisotropy evolution to be taken into account at the same time. Relevant experimental results, coming from a wide investigation performed on compacted Boom clay (Romero, 1999) are presented and simulated numerically by means of the proposed model. Oedometer tests are exploited to analyse volumetric strains as a function of the stress level. A wetting-drying-wetting test under constant isotropic external load is then presented to highlight changes in the direction of plastic strain increments occurring along the hydraulic path. The latter test clearly shows the distortional effects caused by the initial anisotropic fabric and the evolution of fabric anisotropy, and allows a complete description of the general deformational response of the compacted soil.
2 2.1
CONSTITUTIVE FORMULATION Theoretical basis
Referring to axisymmetric test conditions, a full description of the soil state may be accomplished by adopting triaxial stress and strain variables. Total stress state will be described by total mean stress, p = (σa + 2σr )/3, deviator stress, q = (σa − σr ), and suction, s = (ua − uw ), where ua and uw are the air and the water pressures, respectively. As for the strain variables, volumetric strain, εv = εa + 2εr , and shear strain, εs = 2(εa − εr )/3, will be adopted. Subscripts a and r refer to axial and radial components, respectively. The amount of pore water will be described by both gravimetric water content, w, and degree of saturation, Sr . The average stress acting on the soil skeleton (‘‘skeleton stress’’ in the following) is adopted in the development of the constitutive formulation. With reference to axisymmetric conditions, mean skeleton stress, pˆ = [(p−ua )+Sr s] and deviator stress, q, describe the constitutive stress state. The modelling criteria suggested by Jommi & di Prisco (1994) are followed. Given an elastic plastic model conceived for soils in saturated conditions, its extension to unsaturated conditions may be simply conceived as follows. By substituting the skeleton stress for effective stress in the original constitutive equations, increase in the average stress acting on the soil skeleton due to suction may be taken into account. Besides, the ‘‘bonding’’ effect provided on the soil macrostructure by water menisci may be translated in
a generalisation of the hardening rules, by inserting a suitable dependence of the hardening parameters on suction or on degree of saturation. To keep the model as simple as possible, Modified Cam Clay with associated plastic potential is adopted herein as a reference for the saturated state. The formulation for unsaturated conditions is a rather simple extension of the works by Jommi (2000) and Tamagnini (2004). To complete the description of the soil behaviour a model for the retention curve is mandatory. Consistent advantages in modelling the deformational behaviour of unsaturated soils are provided if hysteresis in the soil water retention mechanism is taken into account, as previously discussed by Tamagnini (2004). To the latter aim, the hysteretic retention model proposed by Romero & Vaunat (2000) is introduced in the coupled hydro-mechanical model, and formulated as an additional constitutive law. 2.2
Mechanical model equations
Starting from Modified Cam Clay, a rotation of the axis of the yield surface and plastic potential can be introduced to allow for the description of an anisotropic response, following the proposal by Dafalias (1986): 2 f = q − Mα pˆ + M 2 − Mα2 pˆ pˆ − pˆ 0 = 0
(1)
where M describes critical state obliquity, which is assumed to be independent of suction. The internal variables pˆ 0 , describing the current preconsolidation pressure, and Mα , representing the inclination of the current rotated yield surface with respect to the pˆ axis, govern the isotropic and rotational hardening, respectively. The evolution of the two variables is ruled by both plastic strains and degree of saturation. The preconsolidation pressure in unsaturated conditions, pˆ 0 , is defined as the sum of the preconsolidation pressure in saturated conditions, p∗0 , depending on volumetric plastic strains, plus a term depending on degree of saturation, pˆ 0 = p∗0 {1 + b1 [exp [b2 (1 − Sr )] − 1]}
(2)
governed by parameters b1 and b2 . For p∗0 , the classical critical state evolution law is adopted: dp∗0 =
(1 + e) p∗0 p dεv λ−κ
(3)
where λ and κ are the elastic-plastic and elastic logarithmic volumetric compliances, e is the void ratio and p dεv the volumetric plastic strain increment.
618
Following Dafalias (1986), rotational hardening is assumed to be governed by the current angle between the obliquity, ηˆ = q/ˆp, and the inclination Mα of the yield surface:
Table 1. Parameters adopted in the simulation of compacted Boom clay.
. . dMα = c . dεvp . ηˆ − ξ Mα
κ G (MPa) λ M ξ b1 b2 c
0.014 40 0.125 0.87 1.484 0.11 8.2 136
Hydraulic parameter
Wetting
Drying
Scanning
a (MPa) α (MPa−1 ) n m l (MPa−1 )
300 19.3 1.12 0.20 –
400 1.4 0.95 0.41 –
– – – – 0.02
where c governs the rate of evolution of Mα , while ξ controls the target value of Mα for a given obliquity, hence dMα = 0 for ξ = η/M ˆ α. A constant shear modulus, G, completes the description of a classical hypoelastic behaviour. The model is defined in terms of eight material parameters. Four of them, M , λ, κ and G, describe the behaviour of the isotropic soil under saturated conditions, and may be calibrated on the basis of conventional laboratory tests performed on saturated samples. In principle, parameter c, ruling the velocity of rotational hardening, can be determined with reference to saturated samples too. Due to lack of information, in the present case, c was calibrated on the basis of the triaxial data on the unsaturated soil presented in the following. Parameter ξ can be calibrated from compaction data, assuming that at the end of compaction the direction of plastic strain increment were not changing any more. The initial values of the hardening parameters, pˆ 0in and Mαin can also be determined from the compaction data. Only the calibration of the two parameters b1 and b2 , governing the rate of evolution of the preconsolidation pressure with the degree of saturation, need experimental data from tests run on samples in unsaturated conditions. Here, they were calibrated in order to minimise the difference between experimental data and numerical simulation of volumetric plastic strain along the first wetting path of the isotropic test presented in Section 5. The complete set of parameters adopted is listed in Table 1. 2.3
1000
wetting: experimental data drying: experimental data drying: model wetting: model
100
Suction, s (MPa)
(4)
Mechanical parameter
10
1
0.1
0.01 0
Figure 1. model.
20
40 60 Degree of saturation, Sr (%)
80
100
Water retention curve: experimental data and
a function of suction, s (Romero & Vaunat 2000):
Hydraulic model equations
Literature data (e.g. Gallipoli et al. 2003, Tarantino & Tombolato 2005) show that irreversible strains undergone by a compacted soil along different hydromechanical stress paths affect its water retention properties. Nevertheless, a unique hysteretic retention curve in the suction-degree of saturation plane was chosen here, as a first approximation. Figure 1 shows the main wetting and drying branches of the water retention curve of Boom clay, based on experimental data obtained with both vapour equilibrium and axis translation techniques, for a constant void ratio of e0 = 0.93 characterising the as-compacted conditions (Romero 1999). The water retention data were fitted to a modified form of van Genuchten’s expression for degree of saturation, Sr , as
Sr = C(s)
1 1 + (α s)n
m ;
C(s) = 1 −
ln 1 + as . ln(2) (5)
Fitted parameters for the description of the retention curve are listed in Table 1. Parameters n, m and α are the same as used in van Genuchten’s expression. Parameter α is inversely associated with the air-entry value of the soil in the drying branch and with the air occlusion pressure in the wetting branch. The correction function C(s) is introduced to fit retention curve data for clayey soils at high suctions. The slope of the scanning curves, l, is given a constant value. It is worth noting that the hydraulic model
619
equation may be interpreted as a reversible-perfectly irreversible constitutive law, with no hardening.
-2
Volumetric strain, εv (%)
3
-4
MATERIAL AND EXPERIMENTAL TESTS
The experimental data refer to Boom clay from Mol (Belgium). The moderately swelling clay (20%–30% kaolinite, 20%–30% illite and 10%–20% smectite) has a liquid limit of wL = 56%, a plastic limit of wP = 29%, density of solid particles ρs = 2.70 Mg/m3 and a clay fraction CF = 50%. The samples were prepared by static oedometer compaction, on the dry side of optimum, at constant water content w = 15% to a dry density ρd = 1.40 Mg/m3 . Initial void ratio, e0 = 0.93, and degree of saturation, Sr0 = 0.44, are not far from the optimum standard Proctor value. The loading path to fabricate the soil and the following unloading path prior to testing were performed at an approximately constant suction, s = 1.9 MPa, which was determined from psychrometer readings. Maximum fabrication net vertical and horizontal stress were around 1.2 MPa and 0.44 MPa, respectively. After preparation, some samples were reloaded at constant water content in a controlled-suction oedometer up to four different net vertical stresses, namely 0.085, 0.30, 0.60 and 1.2 MPa. Wetting was then carried out using axis translation technique with four equalisation stages (s = 0.45, 0.20, 0.06 and 0.01 MPa). Afterwards, a multi-step drying, up to s = 0.45 MPa, and a subsequent wetting path were performed at the same net vertical stresses, following the same equalisation stages. Air pressure was maintained constant at 0.5 MPa throughout the wetting-drying-wetting process. The soil sample tested in the triaxial cell was removed from the oedometer ring after unloading and the lateral stress was released. Afterwards, the sample was mounted in the triaxial cell and subjected to an isotropic loading path at constant water content. At p = 0.6 MPa, the sample underwent a wettingdrying-wetting cycle, with the same four equalisation stages as before, by means of axis translation technique applied to both ends of the sample.
2 4 6
net vertical stress 0.085 MPa experimental numerical with rotational hardening numerical isotropic
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0
OEDOMETER TESTS
0 2 4 6 8 10
In Figure 2 the experimental data of the oedometer tests performed at constant net vertical stress, ranging from 0.085 MPa and 1.2 MPa are presented together with the numerical results. Numerical simulations run with the mixed isotropic-rotational hardening model presented herein are compared with the prediction of a
12 0.01
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Figure 2. Oedometer tests: experimental data and numerical simulations.
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rotational model) evolves differently in wetting and drying paths, hence allowing for irreversible strains to be correctly predicted in both cases. This model feature was highlighted by Tamagnini (2004). Here, its quantitative reliability is verified against data spanning over a wide stress range. 5
ISOTROPIC TRIAXIAL TEST
The advantages provided by the possibility of reproducing an anisotropic response by means of rotational hardening can be appreciated much better with reference to the experimental data presented in the following. Figures 3–4 show the whole strain path experienced by the initially anisotropic sample, reloaded to the isotropic pressure, p = 0.6 MPa, and then subjected to a hydraulic cycle. Figure 3 shows the axial and the radial strain data. In Figure 4, the evolution of volumetric and distortional strains with suction are shown, to highlight the influence of the initial anisotropic fabric and its evolution on the overall deformational response of the soil sample. Along the first wetting stage, distortional strain, due to anisotropy, accompanies the plastic volume collapse. Accumulated plastic strains eventually erase initial anisotropy. Starting from a suction value of 0.2 MPa, in the last wetting stages and in the following drying-wetting cycle the behaviour of the sample is isotropic. As in the previous oedometer tests, the following drying path induces a small, but irreversible, volume reduction. Distortional strains are negligible in the drying-wetting cycle, and the deformational response is fully isotropic. The numerical simulations of the triaxial test data, presented in Figure 3, show that the axial strain evolution is well predicted by both models. Rotational hardening does not seem to influence this strain component to a large extent. Differences are observed in numerical with rotational hardening numerical isotropic experimental
0.0
a
(%)
1.0 2.0 3.0 0.0
(%)
1.0 r
conventional isotropic hardening model (Jommi 2000, Tamagnini 2004). The influence of stress level on the volumetric strain experienced by the soil in the first wetting path, as well as in the following drying and wetting paths, may be clearly appreciated by comparison of the experimental data presented in the figures. During the first wetting stages, the competing deformational mechanisms, unloading of the aggregates (possibly accompanied by swelling of the aggregates themselves) and collapse of the macrostructure, may result in a net increase or a net decrease of volume, as a function of the applied vertical net stress. In any case, the volumetric strain experienced during the whole first wetting stage is almost irreversible, as the data for the following drying stage clearly show. In the first drying path, the soil experiences again a considerable irreversible volume reduction. At low stress levels shrinkage can be comparable to, or even higher than, the amount of collapse previously due to wetting. The ratio between the amount of collapse during first wetting and shrinkage during first drying increases with the stress level, as expected. The last wetting path induces a moderate elastic swelling, and further drying-wetting cycles, not shown here, are almost completely reversible (Romero 1999). Comparison between experimental data and numerical simulations show that the constitutive model with rotational hardening is able to capture all the relevant features of the experimental behaviour in the hydraulic cycle. The numerical simulations run with a simpler isotropic model are worse for low stress levels, while for the higher stress levels they are very similar to the previous ones. The differences at the lower stress levels are mostly due to a wider elastic domain predicted by the isotropic model with respect to the anisotropic one. If the isotropic model is adopted, for a net vertical stress of 0.0085 MPa the whole first wetting path lies inside the elastic domain, which overestimates the overall swelling. In any case, the volumetric strains predicted by the two models at the end of each whole hydraulic cycle do not differ much, which is consistent with the dependence of the hardening function on volumetric plastic strains only. In fact, some literature data seem to substantiate this choice (e.g. Lawton et al. 1992). It is worth noting that, in the elastic plastic models in which hardening is ruled by suction, two distinct yield functions, usually termed loading-collapse (LC) and suction increase (SI) yield functions, must be introduced in order to describe irreversible collapse upon first wetting and irreversible shrinkage upon first drying. On the contrary, if the hardening laws are ruled by degree of saturation (Eqs. 2,4), and hysteresis is explicitly taken into account, the preconsolidation pressure (and the direction of the yield surface axis for the
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Figure 3. Isotropic test (0.6 MPa): axial and radial strain evolution: experimental data and numerical simulations.
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(%)
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Rotational hardening, describing the evolution of the anisotropic fabric of a compacted soil along its mechanical and hydraulic history, could be easily introduced thanks to advanced experimental data allowing for calibration of the evolution laws. Extension of the model to general stress and strain paths, accomplished following literature suggestions, may provide a useful tool for engineering purposes.
numerical with rotational hardening numerical isotropic experimental
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ACKNOWLEDGEMENTS
20 15 0.01
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Figure 4. Isotropic test (0.6 MPa): distortional strain, volumetric strain, and water content evolution: experimental data and numerical simulations.
The financial support of the Spanish Ministry of Science (CGL2005-03677/BTE: Advances in Unsaturated Soil Mechanics: Behaviour under Generalised Stress States) is gratefully acknowledged. REFERENCES
the prediction of the radial strain component. While the model with rotational hardening allows for different values to be predicted, axial and radial strain components are obviously equal if an isotropic model is adopted. Advantages coming from rotational hardening appear clearly if attention is focused on the distortional strain, which cannot be reproduced by the isotropic model (Fig. 4). As a result, the total volumetric collapse is a little underestimated by the isotropic model. Experimental data in Figure 4 show that water content changes in the drying-wetting cycle following collapse are almost reversible. This observation confirms that plastic strains affect the retention properties of the soil too. Although the numerical predictions are still good quantitatively, the latter feature is not reproduced by the present model, in which a fixed retention curve in the suction-degree of saturation plane is assumed. 6
CONCLUDING REMARKS
The results presented show that the evolution of a compacted soil fabric may be correctly reproduced with simple, but coupled, elastic plastic models, by adopting the average stress acting on the soil skeleton to reproduce the confining stress increment due to suction, taking into account the hysteretic and irreversible water retention properties of the soil, and ruling hardening via both plastic strains and degree of saturation. The latter choice appears crucial in the interpretation and in the description of the overall deformational response. Lack of information on the evolution of hydraulic properties complicates the interpretation of the behaviour of unsaturated soils, which may be greatly simplified if a complete description of the hydraulic state evolution, besides stresses and strains, is provided.
Alonso, E.E., Gens, A. & Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique 40(3): 405–430. Barden, L., McGown, A. & Collins, K. 1973. The collapse mechanism in partly saturated soil. Engrg. Geol. 7: 49–60. Barrera, M., Romero, E., Lloret, A. & Gens, A. 2000. Collapse test on isotropic and anisotropic compacted soils. In A. Tarantino and C. Mancuso (eds.). Experimental Evidence and Theoretical Approaches in Unsaturated Soils: 33–45. Rotterdam: Balkema. Cui, Y.J. & Delage, P. 1996. Yielding and plastic behaviour of an unsaturated compacted silt. Géotechnique 46: 291–311. Dafalias Y.F. 1986. An anisotropic critical state soil plasticity model. Mech. Res. Comm., 13(6): 341–347. Dif, A.E. & Bluemel, W.F. 1991. Expansive soils under cyclic drying and wetting. Geot. Testing J., 14(1): 96–102. Estabragh, A.R. & Javadi, A.A. 2006. Yielding of unsaturated compacted silty soil under anisotropic conditions. In G.A. Miller, C.E. Zapata, S.L. Houston and D.G. Fredlund (eds.). Unsaturated Soils 2006, 1: 1259–1266. Virginia: ASCE. Fleureau, J.-M., Kheirbek-Saoud, S., Soemitro, R. & Taibi, S. 1993. Behaviour of clayey soils on drying-wetting paths. Can. Geotech. J., 30: 287–296. Gallipoli, D., Wheeler, S.J. & Karstunen., M. 2003. Modelling the variation of degree of saturation in a deformable unsaturated soil. Géotechnique 53(1): 105–112. Gens, A., Alonso, E.E., Suriol, J. & Lloret, A. 1995. Effect of structure on the volumetric behaviour of a compacted soil. In E.E. Alonso and P. Delage (eds.), Unsaturated Soils, 1: 83–88, Rotterdam, Balkema. Jennings, J.E. & Burland, J.B. 1962. Limitations to the use of effective stresses in partly saturated soils. Géotechnique 12(2): 125–144. Jommi, C. 2000. Remarks on the constitutive modelling of unsaturated soils. In A. Tarantino and C. Mancuso (eds.). Experimental Evidence and Theoretical Approaches in Unsaturated Soils: 139–153. Rotterdam: Balkema. Jommi, C. & di Prisco, C. 1994. A simple theoretical approach to model the mechanical behaviour of partially
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saturated granular soils (in Italian). Proc. of Italian Conf. Role of fluids in Geotechnical engineering. Mondovì, 1(II): 167–188. Lawton, E.C., Fragaszy, R.J. & Herington, M.D. 1992. Review of wetting-induced collapse in compacted soil. J. Geotech. Engrg. ASCE, 118(9): 1376–1394. Lim, Y.Y. & Miller, G.A. 2004. Wetting-induced compression of compacted Oklahoma soils. J. Geotech. Geoenv. Engng. 130(10): 1014–1023. Pereira, J.H.F. & Fredlund, D.G. 2000. Volume change behaviour of collapsible compacted gneiss soil. J. Geotech. Geoenv. Engng. 126(10): 907–916. Romero, E. 1999. Characterisation and thermo-hydromechanical behaviour of unsaturated Boom clay: an experimental study. PhD Thesis, UPC, Barcelona. Romero, E. & Vaunat, J. 2000. Retention curves of deformable clays. In A. Tarantino and C. Mancuso (eds.). Experimental Evidence and Theoretical Approaches in Unsaturated Soils: 91–106. Rotterdam: Balkema. Sheng, D., Sloan, S.W. & Gens, A. 2004. A constitutive model for unsaturated soils: thermomechanical and computational aspects. Computational Mechanics, 33: 453–465.
Sun, D.A., Sheng, D.C., Cui, H.B. & Sloan, S.W. 2007. A density-dependent elastoplastic hydro-mechanical model for unsaturated compacted soils. Int. J. Numer. Anal. Meth. Geomech., 31: 1257–1279. Suriol, J., Gens, A. & Alonso, E.E. 1998. Behaviour of compacted soils in suction-controlled oedometer. In Proc. 2nd Int. Conf. on Unsaturated Soils. Beijing, China, 1: 438–443. Beijing: International Academic Publishers. Tamagnini, R. 2004. An extended Cam-clay model for unsaturated soils with hydraulic hysteresis. Géotechnique, 54(3): 223–228. Tarantino, A. & Tombolato, S. 2005. Coupling of hydraulic and mechanical behaviour in unsaturated compacted clay. Géotechnique, 55 (4): 307–317. Wheeler, S.J., Sharma, R.S. & Buisoon, M.S.R. 2003. Coupling hydraulic hysteresis and stress-strain behaviour in unsaturated soils. Géotechnique, 53(2): 41–54. Zakaria, I., Wheeler, S.J. & Anderson, W.F. 1995. Yielding of unsaturated compacted kaolin. In E.E. Alonso and P. Delage (eds.), Unsaturated Soils, 1: 223–228, Rotterdam: Balkema.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
An anisotropic elasto-plastic model for unsaturated soils K. Stropeit & S.J. Wheeler University of Glasgow, Glasgow, UK
Y.J. Cui Ecole Nationale des Ponts et Chaussées, Paris, France
ABSTRACT: A new anisotropic elasto-plastic constitutive model for unsaturated soils (ABBM) has been developed, by combining features of the conventional Barcelona Basic Model (BBM) for unsaturated soils and the anisotropic S-CLAY1 model for saturated soils. In addition, the possibility of a non-linear variation of cohesion intercept with suction is introduced for both the BBM and the ABBM. Simulations with the ABBM and the BBM have been compared with experimental data from tests on compacted Jossigny silt reported by Cui & Delage (1996). The ABBM is able to provide a much better match than the BBM to the observed shape and size of the yield surface produced by one-dimensional compaction. In addition, the ABBM is able to provide improved predictions of yield stresses and volumetric strains during constant suction shearing, particularly if a non-linear variation of cohesion intercept with suction is incorporated. The current version of the ABBM can, however, sometimes result in unrealistic predictions of immediate post-yield softening, and further work is required to refine and fully validate the model.
1
2
INTRODUCTION
Many soils display anisotropy of mechanical behaviour, as a consequence of anisotropy of the soil fabric (e.g. Graham et al. 1983, Cui & Delage 1996). This anisotropy of fabric may be initiated during formation of the soil (e.g. deposition of natural soils or placement and compaction of fills), but it can be altered subsequently by plastic straining, which can produce re-arrangement of the fabric. Many anisotropic elasto-plastic constitutive models for saturated soils have been published in the literature. One of these anisotropic saturated models is S-CLAY 1, presented by Wheeler et al. (2003), which has a rotational hardening law (describing the development of anisotropy during plastic straining) that has now been extensively validated by experimental programmes on several soft saturated clays. Little, however, has been published on development of anisotropic elasto-plastic constitutive models for unsaturated soils. This paper presents a new anisotropic unsaturated elasto-plastic constitutive model (ABBM), in which the modelling of anisotropy from SCLAY1 is used to enhance the conventional Barcelona Basic Model (BBM) of Alonso et al. (1990).
ABBM MODEL
The new anisotropic elasto-plastic model for unsaturated soils (ABBM) is presented here for the simplified stress space of the triaxial test, in terms of mean net stress p, deviator stress q and suction s. Generalization of the model to three-dimensional stress states, including the possibility of rotation of principal stress directions, can be achieved by following the same logic as presented by Wheeler et al. (2003) for the saturated model S-CLAY 1. Modelling of elastic anisotropy that can change with plastic straining would be extremely complex (see Wheeler et al. 2003). In the interest of simplicity, therefore, the ABBM (like S-CLAY 1) assumes isotropic elastic behaviour. The elastic increments of volumetric strain and deviatoric strain are given by the same expressions as in the BBM. 2.1
Yield surface
Constant suction cross-sections of the ABBM yield surface take the form of geometrically sheared ellipses in the q: pf plane: 3 (q − αp)2 = (M2 − α 2 ) p + f (s) ( pm (s) − p) 2 (1)
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where M is the saturated critical state stress ratio. The parameters α and pm (s) define the inclination and size respectively of the yield curve (see Fig. 1), with the magnitude of α representing a measure of the current degree of plastic anisotropy. The value of α can change during plastic straining (as anisotropy changes), but it is assumed that cross-sections of the yield surface at different suctions all have the same inclination α (see Fig. 1). This assumption appears reasonably consistent with the experimental yield curves presented by Cui & Delage (1996). The yield curve for a given suction s has vertical tangents at two points, A and B, both falling on a line of gradient α through the origin, with point A having a coordinate p = −3f (s)/2 and point B having a coordinate p = pm (s) (see Fig. 1). f (s) is a function of suction (see later) which has a value of zero at s = 0. The yield curve for s = 0 corresponds to the S-CLAY1 anisotropic model for saturated soils. With α = 0 (isotropic behaviour) and a linear variation of f (s) with suction, Equation 1 gives the BBM yield curve expression. A single value of M can be used for the entire yield curve, or alternatively a lower triaxial extension value of M can be used for the section of yield curve below the vertical tangent points A and B (a possibility introduced in S-CLAY 1 by Wheeler et al. 2003). The size of the yield curve pm (s) is assumed to vary with suction according to the LC yield curve expression of the BBM: pm (s) = pc
pm (0) pc
2.2 Flow rule and hardening laws The ABBM employs an associated flow rule, which can be expressed as: p
2 (ηα − α) dεs p = M2 − ηα2 dεv
(3)
where ηα is the gradient of the line in the q: p plot from the vertical tangent point A (see Figure 1) to the current stress point: ηα =
! q + α · 3 2 f (s) ! p + 3 2 f (s)
(4)
Equation 3 reverts to the flow rule of the S-CLAY 1 model for the case s = 0. Wheeler et al. (2003) showed that, for saturated soils, an associated flow rule combined with the inclined S-CLAY 1 yield curve gives a reasonable match to observed patterns of behaviour, in contrast to the isotropic Modified Cam Clay model, where a non-associated flow rule generally gives improved predictions. Similarly, Alonso et al. (1990) suggested the use of a non-associated flow rule in the isotropic BBM. The ABBM incorporates two hardening laws. The first hardening law takes a similar form to the BBM hardening law and relates the change of size of the yield surface to the plastic volumetric strain:
λ(0)−κ λ(s)−κ
p
dpm (0) v · dεv = pm (0) λ(0) − κ
(2)
where pm (0) gives the size of the yield curve at s = 0 (see Fig. 1) and pc is a reference pressure (a soil constant). The variation of λ(s) with suction follows the same expression as in the BBM.
(5)
The second hardening law gives the change of yield surface inclination α produced by plastic straining: dα = μ
. η . / 0 3ηα α − α · dεvp + b − α · .dεsp . 4 3 (6)
where μ and b are two soil constants. For the case s = 0 (when ηα is replaced by the conventional stress ratio η), Equation 6 corresponds to the rotational hardening law of the S-CLAY 1 model. This saturated version of Equation 6 has now been extensively validated in experimental test programmes on several soft saturated clays, but there has been no validation for unsaturated conditions. An explanation of the rotational hardening law is given by Wheeler et al. (2003). 2.3 Critical states Figure 1.
Constant suction cross-sections of yield surface.
Equation 3 indicates that critical states are reached when ηα = M . Inspection of Equation 6 then shows
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that the ABBM (like S-CLAY1) predicts a unique critical state value of yield curve inclination αcs : αcs =
M 3
(7)
For each value of suction there is a unique critical state line in the q:p plane, defined by: q = Mp + Mf (s)
(9)
where k is a soil constant. With this assumption, the critical state line defined by Equation 8 coincides with the BBM critical state line expression. In the second version of the model, a non-linear variation of cohesion intercept with suction is assumed: s f (s) = a 1 − exp − a
(10)
where a is a soil constant. Equation 10 gives a nonlinear increase of shear strength with suction, as reported by many authors (e.g. Gan et al. 1988), with f (s) reaching a limiting value, of magnitude a, as suction tends to infinity. The form of Equation 10 ensures that a plot of f (s) against s has an initial gradient of unity at s = 0, thus satisfying the saturated effective stress requirement as s tends to zero. The non-linear cohesion intercept expression of Equation 10 can be used in the BBM as well as in the ABBM. 3
G κ κs pc λ (0) N (0) r
19.0 MPa 0.0047 0.004 2.0 kPa 0.064 1.9 0.8
β M k a μ b
0.004 kPa−1 1.1 0.29 352.0 kPa 187.5 1.0
(8)
i.e. critical state lines for different values of suction all have the same gradient M , with an intercept on the p axis at—f (s) (see Fig. 1). When α reaches the critical state value given by Equation 7, the vertical tangent point A falls on the extension of the critical state line defined by Equation 8 (see Fig. 1). As a consequence, when α = αcs the horizontal tangent point on the yield curve coincides with the intersection of the yield curve with the critical state line. This is not true for other values of α, except for the case s = 0. Two different forms have been assumed for the variation of f (s) with suction. The first version involves a linear variation of cohesion intercept with suction: f (s) = ks
Table 1. BBM and ABBM parameter values for compacted Jossigny silt.
INVESTIGATION OF MODEL VALIDITY
Experimental data from controlled-suction triaxial tests on unsaturated compacted Jossigny silt reported by Cui & Delage (1996) have been used to evaluate the ability of the ABBM to reproduce observed behaviour. Tests were performed at four different values of constant suction: 200, 400, 800 and 1500 kPa, and the
programme involved isotropic loading tests, proportional (constant η) loading tests and conventional shear tests (with radial net stress held constant). Simulations were performed at a stress point level with both the new ABBM and with the conventional BBM. In both cases, two versions of the model were employed, with either a linear or a non-linear variation of cohesion intercept with suction (Eqs. 9 and 10 respectively). For the ABBM simulations the associated flow rule of Equation 3 was employed, whereas the non-associated flow rule suggested by Alonso et al. (1990) was used in the BBM simulations. Parameter values employed in the simulations were selected using all the experimental data from Cui & Delage (1996) and are presented in Table 1. For the ABBM, the value of the parameter μ was determined using the empirical method suggested by Wheeler et al. (2003). In the absence of direct evidence on the value of the parameter b, a value of unity was selected (rather than using the indirect procedure for selecting a value for b suggested by Wheeler et al. 2003). The simulations presented here focus on two issues: the ability of the models to match the shape and size of the yield surface produced by one-dimensional compaction and the prediction of stress-strain behaviour during constant suction shearing. 3.1 Yield surface prediction from compaction procedure The samples of Jossigny silt were one-dimensionally compacted in a mould under an average vertical net stress of 840 kPa (the value varied slightly between samples). The suction after removal of the compaction load was measured at 200 kPa. Experience on other compacted soils suggests that the suction probably changed very little during removal of compaction load, and it was therefore assumed that the same suction of 200 kPa was present when the vertical compaction stress was applied. To calculate the values of mean net stress p and deviator stress q applied during compaction, it was necessary to estimate the value of horizontal net
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stress induced during compaction. For the ABBM simulations, the value of horizontal net stress was estimated by assuming that the value of ηα during one-dimensional compaction (at a suction of 200 kPa) was the same as the saturated normally consolidated K0 value of stress ratio η (calculated by assuming K0 = 1 − sinφ = (6 − 2M )/(6 + M )). For the BBM simulations an equivalent assumption was made. This resulted in slightly different sets of estimated p and q values during compaction for the different simulations, depending on the model used and on the assumed value of α in the ABBM simulations (see below). Knowing the values of p and q applied during compaction, it was possible to fit the ABBM yield curve expression of Equation 1 through the compaction stress point and hence calculate a value of yield curve size pm (s) at a suction of 200 kPa. To do this, a value had to be assumed for the yield curve inclination α induced by the one-dimensional compaction process. Wheeler et al. (2003) presented a method for calculating the value of αK0 , produced by K0 consolidation of a saturated clay under normally consolidated conditions. This procedure has now been well validated for a range of soft saturated clays, but it is unlikely to be valid for one-dimensional compaction under unsaturated conditions, because the ABBM predicts that the resulting value of α would also be affected by any change of suction occurring during the application of compaction load. Different values of α were tried, in order to examine the fit with the experimental yield curve data. The value that was selected as giving the best match (α = 0.75) is much higher than the value of saturated αK0 = 0.42 calculated according to the method proposed by Wheeler et al. (2003). Having calculated the value of pm (s) at a suction of 200 kPa, it was then possible to use the LC yield curve expression of Equation 2 to calculate the sizes of yield curves at different values of suction and hence the complete form of the yield surface. An equivalent procedure was used with the BBM. Figure 2a shows the predicted BBM yield curves (assuming a conventional linear variation of cohesion intercept with suction) for the four experimental values of suction. Also shown are the corresponding experimental yield points, as reported by Cui & Delage (1996). The experimental yield points were taken from isotropic loading, constant η and conventional shear tests. Interpretation of yield points from experimental data generally involves significant subjectivity, and therefore all experimental yield data should be viewed with a degree of caution. It is, however, clear from Figure 2a that, as expected, the isotropic BBM is unable to provide a good match to the experimentally observed yield curves. Figure 2b shows the predicted ABBM yield curves (assuming a non-linear variation of cohesion intercept
Figure 2. Comparison of yield surface model predictions with experimental yield points: (a) BBM; (b) ABBM with α = 0.75.
with suction) for the case α = 0.75. This provides a significantly better match to the experimental yield points than the BBM model, although yield stresses still appear to be over-predicted by the ABBM. The experimental yield points measured during isotropic loading were probably the most reliable. Figure 3 therefore examines the ability of the two models to match these isotropic yield points. The BBM (curve (a)) grossly overpredicts the yield points observed during isotropic loading (see also Fig. 2a). The ABBM with α = 0.75 (curve (c)) predicts substantially lower isotropic yield stresses (the effect is less marked with α = αK0 = 0.42, see curve (b)). Even with α = 0.75, however, the ABBM still overpredicts the experimentally observed isotropic yield stresses (see also Fig. 2b). The final curve in Figure 3 (curve (d)) shows the ABBM prediction with α = 0.75 but with a lower value of critical state stress ratio Me = 0.9 assumed in triaxial extension. This lower value Me has been used in the yield curve expression for the part of the yield curves below the vertical tangent points A and B (see Fig. 1), as suggested by
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Figure 3. Comparison of model predictions with experimental yield points measured during isotropic loading; dashed lines linear cohesion intercept, solid lines non-linear intercept.
Figure 5. Variation of specific volume with mean net stress during constant suction shearing: (a) s = 200 kPa; (b) s = 800 kPa.
shows that the combination of a lower Me value and α = 0.75 allows the ABBM to provide an excellent match to the experimentally observed isotropic yield stresses.
3.2
Figure 4. Variation of deviator stress with shear strain during constant suction shearing: (a) s = 200 kPa; (b) s = 800 kPa.
Wheeler et al. (2003), whereas the triaxial compression value Mc = 1.1 has been retained for the upper part of the yield curves, above the vertical tangent points. Use of a lower value of M in triaxial extension than in triaxial compression is consistent with expected behaviour for all soils. Inspection of Figure 3
Predicted behaviour during shearing
All constant suction shear tests reported by Cui & Delage (1996) have been simulated with the ABBM and the BBM. Two tests are shown here as examples. Both tests were conducted at a constant net radial stress of 200 kPa, with the first test at a suction of 200 kPa and the second at a suction of 800 kPa. For the ABBM simulations an initial yield curve inclination of α = 0.75 was assumed, and a single value of M = 1.1 was used for the entire yield surface. The initial value of po (0) (for the BBM) or pm (0) (for the ABBM) was selected to provide a best fit to the measured isotropic yield stresses at the 4 values of suction. This would be a common practice in selecting an appropriate initial state for numerical simulations. Figure 4 shows the variation of deviator stress with shear strain for the two example tests. Inspection of Figures 4a and 4b shows that the use of a non-linear variation of cohesion intercept with suction provides a
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simulations, in terms of both the yield stress and the final magnitude of the change of v during shearing. Again, however, the form of immediate post-yield behaviour predicted by the ABBM is unrealistic, as a consequence of the initial softening described in the previous paragraph. Figure 6 shows plots of volumetric strain against shear strain for the two example shear tests. The best match to the experimental results is produced by the ABBM with a non-linear variation of cohesion intercept with suction.
4
Figure 6. Variation of volumetric strain with shear strain during constant suction shearing: (a) s = 200 kPa; (b) s = 800 kPa.
significant improvement in the prediction of the final critical state values of deviator stress. In Figures 4a and 4b the yield stresses predicted by the ABBM are significantly higher than those predicted by the BBM, and this provides a better match to the observed behaviour, which is relatively stiff up to high values of q. The ABBM predictions of immediate post-yield behaviour are however a poor match to observed behaviour. In particular, the ABBM simulations at a suction of 800 kPa (Fig. 4b) show a small drop of deviator stress immediately post-yield, which is not seen in the experimental results. The unrealistic immediate post-yield softening in some of the ABBM simulations is mainly a consequence of the selection of an initial value of α much higher than the final critical state value αcs . The precise form of the yield curve expression of Equation 1 together with the flow rule of Equation 3 and the rotational hardening law of Equation 6 also contribute to the unrealistic prediction of immediate post-yield softening, and the validity of all three requires further investigation for unsaturated conditions. Figure 5 shows the variation of specific volume v with mean net stress p during the shearing stages of the two example tests. Inspection of Figures 5a and 5b shows that the ABBM simulations provide a better match to the experimental results than the BBM
CONCLUSIONS
Simulations with the new ABBM and the conventional BBM have been compared with experimental data from tests on compacted Jossigny silt reported by Cui and Delage (1996). The comparisons show that the ABBM is able to provide a much better match than the BBM to the observed shape and size of the yield surface produced by one-dimensional compaction. To provide a good match, the compaction-induced value of yield curve inclination α used in the ABBM must be much greater than would be predicted for K0 consolidated saturated samples of the same soil. Using a high value of α and different values of critical state stress ratio M in triaxial compression and triaxial extension, the ABBM is able to provide an excellent match to the values of yield stress observed during subsequent isotropic loading, whereas the isotropic yield stresses are grossly overpredicted by the BBM. Simulations of constant suction shear tests generally show better predictions from the ABBM than from the BBM. Final critical state values of deviator stress are best predicted by assuming a non-linear variation of cohesion intercept with suction (this feature can be incorporated in either the ABBM or the BBM). Yield stresses during shearing are better predicted by the ABBM than the BBM, and the magnitudes of volumetric strain during shearing are best predicted by the ABBM with a non-linear variation of cohesion intercept with suction. ABBM simulations of constant suction shearing sometimes show unrealistic softening in the immediate post-yield response. Final recommendations on the best forms for the ABBM yield curve expression, the flow rule and the rotational hardening law, which could address this problem, will require comparisons with experimental data from other unsaturated soils. Overall, the results presented here suggest that incorporation of anisotropy in elasto-plastic constitutive models for unsaturated soils may result in significantly improved predictions, but further work is required to finalise aspects of a fully realistic model.
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ACKNOWLEDGEMENTS The support of the European Commission via ‘MarieCurie’ Research Training Network contract number MRTN-CT-2004-506861 is gratefully acknowledged. REFERENCES Alonso, E.E., Gens, A., Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique 40(3): 405–430.
Cui, Y.-J., Delage, P. 1996. Yielding and plastic behaviour of an unsaturated compacted silt. Géotechnique 46(2): 291–311. Gan, J.K.M., Fredlund, D.G., Rahardjo, H. 1988. Determination of the shear strength parameters of an unsaturated soil using the direct shear test. Can. Geotech. J. 25(3): 500–510. Graham, J., Noonan, M.L. and Lew, K.V. 1983. Yield states and stress-strain relations in natural plastic clay. Can. Geotech. J. 20: 502–516. Wheeler, S.J., Näätänen, A., Karstunen, M., Lojander, M. 2003. An anisotropic elastoplastic model for soft clays. Can. Geotech. J. 40: 403–418.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
An elasto-viscoplastic model for chalk including suction effects F. Collin Université de Liège (FNRS, Department ARGENCO), Belgium
V. De Gennaro & P. Delage Ecole des Ponts, Paris (Université Paris-Est, Navier Institute – CERMES), France
G. Priol Arcadis, Paris, France
ABSTRACT: During the six years long Pasachalk project devoted to the mechanical behaviour of high porosity chalks from North Sea oilfields, the constitutive model Pasachalk (Collin et al., 2002) was proposed based on the Barcelona Basic Model (BBM) (Alonso et al., 1990). The approach was based on the similarities found between the oil-water interactions (oil and water being the non wetting and wetting fluid respectively) in oil reservoir chalk and the air-water interactions in unsaturated soils. This approach appeared to be relevant to interpret the subsidence of the seafloor during waterflooding operations for enhanced oil recovery that has been observed in North Sea oilfields (e.g. Ekofisk oilfield). Another important component of subsidence was then related to the creep behaviour of the multiphase chalk (De Gennaro et al., 2003). A modified Pasachalk model was proposed to account for time effects using the framework of Perzyna’s viscoplasticity (1964) but without considering suction effects. Based on available experimental results (Priol et al., 2007), a modified version of the viscoplastic Pasachalk model including suction effects is proposed in this paper.
1
INTRODUCTION
The mechanical behaviour of chalk has been extensively studied since the early eighties, in particular with regard to the behaviour of oil reservoir chalks in the North Sea (Ekofisk oilfield, see Hermansen et al., 2000, Nagel 2001). More recently, the risk assessment of the long-term stability of chalk pillars in mineworkings has been considered. In both situations, two poorly miscible pore fluids of different wettabilities are contained by chalk: water and oil in reservoir chalks and water and air in continental chalks from mines and quarries. In multiphase chalks, the partial saturation can change with time. The water saturation in oil reservoir chalks can increase due to reservoir enhanced exploitation by waterflooding (e.g. Ekofisk oilfield). Water saturation changes in mine chalks can be a consequence of the combined effects of changes in water table and in the hygrometry of the mine. Like in unsaturated soils, it has been showed that changes in partial saturation have an influence on the mechanical response of chalk, the higher the degree of water saturation, the higher the compressibility and the lower the strength (water weakening effect). In oil reservoirs, mines and quarries, the overburden formations apply long term hydro-mechanical loadings,
resulting in creep, a behaviour feature particularly pronounced in chalks. Some recent experimental and theoretical approaches carried out on partially saturated chalks have confirmed the relevance of some concepts of the mechanics of unsaturated soils to multiphase chalk behaviour, as suggested by Delage et al. (1996). Collin et al. (2002) proposed a modified version of the Barcelona Basic Model (BBM, Alonso et al., 1990) called Pasachalk model to model the behaviour of oil reservoir chalks. This model was extended to include viscoplastic behaviour of reservoir chalk but this latter model did not take implicitly the suction effect into account (De Gennaro et al., 2003). The effects of the oil-water suction on the time dependent behaviour of reservoir chalks has only been partially explored up to now. In this regard, recent findings (Priol, 2005; Priol et al., 2007) from oedometer tests carried out on chalk samples seem to suggest that the delayed strain of chalk is well correlated with the over-stress ratio (i.e. the ratio between the actual stress and the yield stress). Based on these findings and on other available results, a modified version of the viscoplastic Pasachalk model including oil-water suction effects is proposed in this paper.
633
2
EXPERIMENTAL EVIDENCE OF CREEP IN CHALK
Priol (2005) and Priol et al. (2007) reported results of oedometer compression tests carried out on Lixhe chalk (an outcrop chalk from Belgium) saturated with oil, with water, partially saturated and dry (Fig. 1). By analyzing the evolution of the creep curves obtained during multiple step loading tests, it was suggested to consider the following rheological law to fit the experimental data: e = βi t −αcr eoi
(1)
where e is the void ratio, eoi the initial void ratio, t the time, βi a coefficient accounting for the instantaneous
NORMALISED VOID RATIO e/eo
1
0.9
settlement and αcr for the time dependent settlement. The evolution of αcr is directly related to the creep behaviour of chalk (Fig. 2). One can observe that the amount of creep is both stress and suction dependent, the higher the wettability of chalk, the larger the amount of creep.
3
MODEL FORMULATION
Perzyna’s viscoplastic approach (Perzyna, 1964) has been adopted because it is based on a framework similar to that of elastoplasticity, facilitating further time-dependent developments of the elastoplastic Pasachalk model. Various viscoplastic models have been formulated adopting the Bjerrum’s notion of equivalent (or reference) time (e.g. Bjerrum, 1967; Borja & Kavazanjian, 1985; Hickman & Gutierrez, 2007). Other models have used the concept of the Non Stationary Flow Surface (NSFS) theory (e.g. Nova, 1982; Liingaard et al., 2004). A recent review of the literature is given by Liingaard et al., (2004). The Pasachalk model (Collin et al., 2002) is a cap model with a yield surface composed of three components: (i) Cam-Clay pore collapse model The Cam-Clay yield surface is adopted at low stress inclinations, with the following expression: 3c(s) f1 ≡ IIσˆ2 + m2 Iσ + (Iσ − 3p0 ) = 0 tan φC
0.8
DRY SAMPLE OIL SATURATED SAMPLE s = 200 kPa WATER SATURATED SAMPLE 0.7 100
1000
10000
100000
VERTICAL STRESS (kPa)
Figure 1. Oedometer compression tests on Lixhe chalk at various saturation states (Priol et al., 2007).
where Iσ and II σ are the first and second stress invariants, c is the cohesion, φC is the friction angle in compression path, p0 is the apparent pre-consolidation pressure that defines the size of the yield surface and m is a coefficient taking into account the effect of the Lode angle β. The coefficient m is defined by: m = a (1 + b sin 3β)n
0.02
B 0.016
WATER SATURATED
WATER SATURATED S S = 200 kPa OIL SATURATED SAM SAMPLE sDRY = 200 kPa
Water infiltration 0.008
0.004
(3)
where parameters a, b and n must verify some convexity conditions (Van Eekelen, 1980). Assuming associated plastic flow, the apparent preconsolidation pressure p0 is related to the volumetric plastic strain dεvp following the kinematic equation:
0.012
A
(2)
OIL SATURATED
dp0 =
1+e p0 dεvp λ−κ
(4)
DRY
0 0
10000
20000
30000
VERTICAL STRESS (kPa)
Figure 2. Influence of stress level and suction on the creep coefficient αcr (Priol et al., 2007).
where λ is the compression coefficient and κ is the elastic coefficient. Expression (4) allows both hardening or softening behaviour to be accounted for according to the sign of the volumetric plastic strain. However the softening zone will not be considered here. It can also be
634
noted that the irreversible volumetric strain includes the coupled effect of mechanical and suction changes. (ii) Internal friction model In order to formulate a friction model based on a MohrCoulomb type failure criterion with a smoothed plastic surface, Van Eekelen’s (1980) formulation has been adopted. It is based on a modification of DruckerPrager’s failure cone by introducing a dependence on Lode’s angle β, leading to the following expression of the failure criterion: 3c(s) f2 ≡ IIσˆ − m Iσ + =0 (5) tan φC An associated plasticity is considered also for the friction mechanism. (iii) Suction effect on yield surface (BBM model) Several phenomena are typical of unsaturated soils: – The yield stress p0 and the material stiffness increase with suction. In BBM this is described by the LC curve, the formulation of which has been adapted for chalk as follows: p0 (s) = p0 (0) + p0
s s + s∗
(6)
where p0 (0) is the yield stress for s = 0, p0 is the variation of p0 between water and oil saturated sample and s∗ is a parameter controlling the shape of the LC curve. – Cohesion increases with suction. This is modelled using Eq. (7). c(s) = c(0) + k s
(7)
where k is a material constant, c (0) is the cohesion at water saturated state. Note that in chalk, experiments showed that the friction angle is independent of the saturating fluid. Mechanical elastoviscoplastic model Viscous effects in chalk may be observed in triaxial tests performed at various stress rates and/or involving creep stages (Pasachalk2, 2004). The timedependent behaviour of chalk is introduced here based on the elastoviscoplastic approach proposed by Perzyna (1964). Hence, strains are divided into reversible and irreversible parts (related mechanical and suction loading): m,vp
ε˙ ij = ε˙ ijm,e + ε˙ ijs,e + ε˙ ij
s,p
+ ε˙ ij
time-dependent. The following relationship is taken [Alonso et al., 1990]: ε˙ ijs,e =
κs s˙ δij = heij s˙ (1 + e) (s + pat )
(9)
The stress increment can thus be expressed as follows: σ˙ = C e (s) (˙ε − ε˙ s,e − ε˙ m,vp )
(10)
Since only the irreversible behaviour is timedependent, the elastic moduli of the Pasachalk model can be kept. The values of the moduli defining Hooke’s law are recalled in Table 1. The elastic parameters are suction dependent. The following linear expressions (Pasachalk 2, 2004) have been chosen for the volumetric and shear moduli as a function of suction: K(s) = K(0) + ks · s
(11)
G(s) = G(0) + gs · s
(12)
where K(0) and G(0) are the elastic moduli for a nul suction (water saturated condition), ks and gs are equal to 38 and 66.7 respectively to model the increase of stiffness with the suction. The irreversible strain may be described as normal to some potential g: ε˙ m,vp = γ φ(f )
∂g ∂σ
(13)
This formulation is similar to the elastoplastic one, but it is not based on the consistency condition. The amount of strain rate is described with respect to a reference surface f , similar to the yield surface. Then, one may define two irreversible mechanisms, one dedicated to the pore collapse mechanism named fc , the second one to friction failure named fd . The reference surfacefc has the same equation as f1 in the Pasachalk model. The reference surface actually represents the elastoplastic yield surface defined based on a hypothetical experiment with an infinitely low strain rate. The function fc may help to define the overstress, as a measure of the amount of the stress state going outside the reference surface. Table 1.
Elastic parameters (Collin et al., 2002). Water
Oil
612 500 1180 0.18
726 700 1590 0.14
(8)
It has been observed that suction variations do not evolve permanent strains. Moreover, it is assumed that reversible strains related to suction are not
K [MPa] G [MPa] E [MPa] ν [−]
635
Concerning the pore collapse mechanism, the creep potential is based on the following equations: φc (fc ) =
Table 3.
αc
pd0 vp − 1 p0
(14)
and (Shao et al., 1993): γ =ω
Iσ pa
Pre-consolidation Parameter αc Parameter ω Parameter ι
vp p0
[MPa]
Water
Oil
2 5 5.1 10−9 0,0
5 5 5.1 10−9 0,0
ι (15)
where the viscous parameters are: γ , the fluidity parameter, ω, pa and ι, the parameters defining the influence of stress on the fluidity parameter and αc , the exponent of the visco-plastic strain relation (14). The parameters defining the yield surface of the elastoplastic model for a stress rate of 10−3 MPa/s are given in the Table 2. The viscous parameters concern mainly the pore collapse mechanism because the failure criterion is assumed to be time-independent. Hence, only the viscous parameters γ (fluidity parameter), the reference surface fc and the exponent αc of visco-plastic strain relation have to be determined. As shear failure is assumed to be time independent, the reference surface fc related to pore collapse only depends on the apparent viscoplastic prevp consolidation pressure p0 . Experiments have shown that the pre-consolidation pressure depended directly on the stress-rate. This relation is not defined directly in the model: the effect of rate dependence comes as a result of the chosen visco-plastic formulation. vp The p0 value and the other viscous parameters have been determined by trial and error process in order to fit isotropic compression tests on saturated chalk (oil and water), with loading rate ranging between 5 × 10−5 and 10−2 MPa/s (Pasachalk 2, 2004). Within the assumed loading rate range the final values of all parameters are given in Table 3. Note that, in agreement with the notion of overstress, it is not necessary to chose different values of viscous parameters (α, ω, ι) for oil or water saturated samples, as the influence of suction is taken into account through the apparent pre-consolidation pressure. For intermediate degrees of saturation, the LC curve adopted is similar to that used in the elastoplastic vp vp model, using Eq. (6) with p0 = 3 MPa, p0 (0) = 2 Table 2. model.
Viscous parameters of the model.
Yield surface parameters of the elastoplastic
Friction angle φ [◦ ] Cohesion c [MPa] Pre-consolidation p0 [MPa] Compressibility index λ
Water
Oil
22 1.5 10 0.195
22 2.0 21 0.195
MPa et s∗ = 0.2 MPa. It is important to notice that the same value of the compressibility index λ has been used for the definition of the hardening law of the viscoplastic model.
4
ASSESSMENT OF THE VISCOUS PARAMETERS
One of the major shortcomings associated with Perzyna’s approach is the definition of the viscous parameters and of the reference surfaces, which are usually found by a trial and error process and not directly experimentally determined. In order to link more directly the parameters to experimental measurement the results of CRS (Constant Rate of Strain) oedometer compression tests at different strain rates and suction (water or oil saturated, 200 kPa suction and dry samples) are first analysed (Priol, 2005; Priol et al., 2007). It was observed that for a given suction the yield limit (i.e. apparent pre-consolidation pressure) is a function of the imposed strain rate, as already shown in clays by Leroueil et al. (1985). The following relationship coupling the yield limit and the strain rate proposed by Leroueil appeared to fit reasonably data obtained on Lixhe chalk: log10 (σp ) = A +
1 log10 (˙ε1 ) m
(16)
where σp is the yield limit, ε˙ 1 is the strain rate and A and m two material parameters. Table 4 summarizes the values of A and m obtained for Lixhe chalk. Equation (16) describes a linear relationship between yield limit and strain rate in a log10 (σp ) : log10 (˙ε1 ) plot. It is worth noting that values of m depends now also on suction (Tab. 4). In other words the slope of the linear relationship (16) increases when suction decreases. This is a new further coupling which extends the original Leroueil’s relationship. Equation (16) gives the opportunity to define the size of the reference surface defined as the elastoplastic yield surface based on a hypothetical experiment with an infinitely low strain rate. Considering an extremely low strain rate (10–13 s−1 ), the yield stress of the reference surface
636
Table 4.
0.020
Material parameters of Leroueil’s law.
0.018
A
m
4,462 4,516 4,451 4,499
9,25 10,9 16,66 22,2
0.016 0.014 0.012 αcr [-]
Water s = 200 kPa Oil Dry
Water
0.010
Oil
0.008
Suction 0.006
Dry
0.004 0.002 3.5
0.000 0
3
2
4
6 8 Normalized stress [-]
10
12
14
Suction [MPa]
2.5
Figure 4. Influence of ‘‘normalized’’ stress level and suction on the creep coefficient αcr (Priol et al. 2007).
Experimental data
2
LC curve
1.5
Table 5. Viscous parameters of the model for unsaturated conditions.
1 0.5
Water
0 0
1
2
pvp 0
Figure 3.
3
4
5
[MPa]
vp
LC curve of the reference surface.
for the different suction conditions could be defined, together with the LC curve of the viscous reference surface (Fig. 3). Viscous parameters should now to be linked to the βi and αcr parameters of equation (1). Figure 2 shows a first discrepancy between the evolution of αcr and the viscous parameters of the model. Indeed Figure 2 does not show a unique relation between αcr and the stress state for the different saturation conditions. On the other hand, it is not necessary to chose different values of viscous parameters for oil or water saturated samples. The influence of suction is only taken into account through the LC curve. The apparent contradiction can be explained by inspecting Figure 2. One can observe that the creep parameter αcr remains very low up to a threshold that depends on the saturation conditions. Above the threshold, parameters follow a more or less linear relationship with slopes also depending on the saturation conditions. However, if the stress value is normalized with the apparent pre-consolidation pressure of each test as presented in Figure 4, the observed behaviour becomes reasonably independent of the saturation conditions. It would be interesting to find a direct relationship between the αcr and βi parameters of equation (1) and the ω and αc parameters of the viscous model (Equation 13). Unfortunately, it was not possible to find such a relationship analytically. The main reason is that equation (1) defines the total creep strain and the viscous strain rate is modelled through equation (13). Moreover, the analytical integration of the
Pre-consolidation p0 [MPa] at s = 0 MPa vp Parameter p0 [MPa] Parameter s∗ [MPa] Parameter αc Parameter ω
1,143 4 0.5 5 5,1 10−9
viscous model is not possible for any values of the material parameters. It was thus decided to keep the first estimation of the two viscous parameters for the modelling of the multi-stage loading tests.
5
NUMERICAL MODELLING
Some experimental results obtained by Priol (2005) by running creep oedometer tests under different suction conditions (water saturated, oil saturated and suction equal to 200 kPa) are reported in Figure 5 in terms of strain versus time curves. One can clearly see in the figure the various loading steps and the creep deformations under different applied stresses. With the single set of parameters and the proposed visco-plastic model, the three tests have been modelled. Figures 6–8 show satisfactory agreement between experimental data and numerical predictions. It should be emphasised that, besides creep tests, the collapse experiment can also be modelled by the proposed constitutive law. Indeed, during waterflooding, the suction is decreasing as well as the pre-consolidation pressure following the LC curve. This means that the overstress is growing during waterflooding, leading to an increase of the viscous creep deformation.
637
0.14
0.02 0.018
0.12
0.016 0.014
0.08
Strain [-]
Strain [-]
0.1
Water Oil Suction
0.06
0.012 0.01 0.008
Step 6 Modelling (6) Step 7 Modelling (7) Step 8 Modelling (8)
0.006
0.04
0.004 0.02
0.002 0 0
500
1000
1500
2000
2500
3000
3500
4000
0 0.0E+00
4500
2.0E+05
4.0E+05
6.0E+05
Time [hour]
Figure 5. Multiple stage loading tests for different saturation conditions (Priol, 2005).
0.05 0.045 0.04 0.035 Strain [-]
8.0E+05
1.0E+06
1.2E+06
1.4E+06
Time [s]
0.03 Step 13
0.025
Modelling (13) 0.02
Step 12
0.015
Modelling (12)
0.01 0.005 0
0.0E+00 1.0E+06 2.0E+06 3.0E+06 4.0E+06 5.0E+06 6.0E+06 7.0E+06 8.0E+06 9.0E+06 1.0E+07
Time [s]
Figure 6. Numerical modeling of creep phase for water saturated chalk samples.
0.04 0.035 0.03
Figure 8. Numerical modeling of creep phase for unsaturated chalk samples (s = 200 kPa).
significant creep deformations. The Pasachalk elastoplastic model (Collin et al., 2002) derived from the Barcelona Basic Model for multiphase reservoir chalk has been extended to account for time effects and creep behaviour as a function of suction. Some experimental results of multiple stage loading tests carried out on Lixhe chalk under different suction conditions showed that the results obtained under various suctions could be summarized into a single normalized curve. The relevant viscous parameters of the model were determined based on these experimental results, without using a trial and error method. This has only been possible for the definition of the viscous reference surface. We did not succeed to find an analytical relationship between the parameters of the viscous model and the constitutive law. By using one single set of parameters, different creep experiments under various suction conditions were simulated, with a satisfactory agreement between experimental data and numerical predictions.
Strain [-]
0.025 Step 7 0.02
Modelling (7)
ACKNOWLEDGMENTS
Step 8
0.015
Modelling (8) Step 10
0.01
The authors thank the FNRS for its financial support during the stay of the first author in CERMES.
Modelling (10)
0.005 0 0.0E+00
1.0E+06
2.0E+06
3.0E+06
4.0E+06
5.0E+06
6.0E+0
Time [s]
REFERENCES
Figure 7. Numerical modeling of creep phase for oil saturated chalk samples.
6
CONCLUSIONS
High porosity chalks have a complex mechanical behaviour that depends on chalk porosity, mineralogy, pore fluids, of temperature and of time with
Alonso, E.E., Gens A. and Josa A. 1990. A constitutive model for partially saturated soils. Géotechnique 40 (3): 405–430. Bjerrum, L. (1967): Engineering geology of Norwegian normally-consolidated marine clays as related to settlement of buildings. Géotechnique, 17: 81–118. Borja, R.I., Kavazanjian, E. 1985. A constitutive model for the stress—strain-time behaviour of wet clays. Géotechnique, 35 (3): 283–298.
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Collin F., Cui Y.J., Schroeder C. and Charlier R. 2002. Mechanical behaviour of Lixhe chalk partly saturated by oil and water: experiment and modelling. J. Num. Analytical Meth. In Geomechanics, 26, 897–924. De Gennaro V., Delage P., Cui Y.C., Schroeder Ch. & Collin F. 2003. Time-dependent behaviour of oil reservoir chalk: a multiphase approach. Soils and Foundations, 43 (4), 131–148. Delage P., Schroeder C. & Cui Y.J. 1996. Subsidence and capillary effects in chalks. Proc. EUROCK’96 Conf., vol. 2, 1291–1298, Torino, Italy. Hermansen H., Landa G.H., Sylte J.E. & Thomas L.K. 2000. Experiences after 10 years of waterflooding the Ekofisk field, Norway. J. of Petroleum Science and Eng., 26, 11–18. Hickman, R.J. & Gutierrez, M.S. 2007. Formulation of a three-dimensional rate-dependent constitutive model for chalk and porous rocks. Int. J. of Numerical and Anal. Meth. in Geomechanics, 31 (4): 583–605. Leroueil S., Kabbaj M., Tavenas, F. and Bouchard, R. 1985: Stress-strain-strain rate relation for compressibility of sensitive natural clays. Géotechnique 35 (2): 159–180. Liingaard M., Augustesen P. & Lade P.V. 2004. Characterization of Models for Time-Dependent Behavior of Soils. Int. J. of Geomechanics ASCE, 4 (3): 157–177. Nagel N. 2001. Ekofisk geomechanics monitoring, Int. Workshop on Geomechanics in Reservoir Simulation, IFP, Reuil-Malmaison, France.
Nova, R. 1982. A viscoplastic constitutive model for normally consolidated clays. Proc. IUTAM Conf. on Def. and failure of Granular Materials, Delft 1982: 287–295. Pasachalk2. 2004. Mechanical Behaviour of PArtially and Multiphase SAturated CHALKs Fluid-skeleton Interaction : Main Factor of Chalk Oil Reservoirs Compaction and Related Subsidence, Part 2, Publishable Final report, European contract N˚ ENK6-CT2000-0008, Brussels. Perzyna, P. 1964. The constitutive equations for rate sensitive plastic materials. Quart. Appl. Mech., 20, 321–332. Priol G. 2005. Comportement mécanique d’une craie pétrolifère—comportement différé et mouillabilité. PhD Thesis, Ecole des ponts, Paris. Priol G., De Gennaro V., Delage P. and Servant T. 2007. Experimental investigation on the time dependent behaviour of a multiphase chalk. Experimental Unsaturated Soil Mechanics, Proc. Physics 112, Springer, T. Schanz (ed.), 161–167. Shao J.F., Bederiat M. and Schroeder C. 1993. A viscoplastic theory for soft rock behaviour and application. Proc. Geotech. Eng. Hard Soils—Soft Rocks Conf., Balkema. Van Eekelen H.A.M. 1980. Isotropic yield surfaces in three dimensions for use in soil mechanics. Int. J. Num. and Anal. Meth. in Geomechanics, 4, 98–101.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
New basis for constitutive modelling of unsaturated aggregated soil with structure degradation A. Koliji, L. Vulliet & L. Laloui Soil Mechanics Laboratory, Ecole polytechnique fédérale de Lausanne (EPFL), Switzerland
ABSTRACT: The paper deals with the unsaturated aggregated state of soils, a commonly occurring state in natural and engineered materials. These soils are characterized by a double porosity fabric and exhibit a strong interaction between the fabric and inter-particle bonding in their structure. A new baseline for a hardening elasto-plastic constitutive model for these materials is proposed which incorporates the combined effects of soil structure (fabric and inter-particle bonding) and partial saturation. It uses a generalized effective stress and the critical state concept in unsaturated soils. Based on multi-scale experimental evidences, a state parameter is introduced to quantify the soil structure. An expression of apparent preconsolidation pressure is presented with respect to the combined effects of soil structure and partial saturation that describes the extension of the yield limit in unsaturated aggregated soil compared with the corresponding saturated reconstituted soil. 1 1.1
INTRODUCTION Background
Aggregation of particles is a commonly observed phenomenon in natural and agricultural soils (Horn 2003), compacted clays at dry side of optimum water (Sridharan et al. 1971, Collins & McGown 1974) and compacted expansive clays (Lloret et al. 2003). However, size of aggregates in expansive and compacted clays are some orders of magnitude smaller than aggregates in natural or agricultural soils. Aggregated soils, in general, are characterized by a fabric with two dominant pore sizes corresponding to micro (intra-aggregate) and macro (inter-aggregate) pores. The presence of the aggregated structure and double porosity fabric was found to have a major influence on the water retention properties and hydraulic behaviour of both agricultural (Coppola 2000) and compacted clays (Romero et al. 1999). Moreover, the mechanical behaviour of the soil is reported to be significantly influenced by the inter-particle bonding effects (e.g., Leroueil and Vaughan 1990). When dealing with unsaturated soils in a hydromechanical process, the coupling between the mechanical and hydraulic behaviour of unsaturated soils as well as the factors influencing this behaviour are of significant importance, specially, if the constitutive stress of the model depends on the degree of saturation. An appropriate constitutive model for unsaturated aggregated soil, therefore, should
incorporate the combined effects of soil structure (fabric and inter-particle bonding) and partial saturation on the hydro-mechanical behaviour of the material. Increasing interest in understanding and modelling of the influence of soil structure on the mechanical behaviour of unsaturated soils, in particular expansive soils, has led to development of new constitutive models. The proposed models are aimed to describe the material behaviour with respect to the microstructure and double porosity fabric (Alonso et al. 1999, Sanchez et al. 2005). In these models, however, soil structure effects are considered only through the fabric effects and the interparticle bonding and its degradation are not essentially considered. Alternatively and in line with the experimental observations revealing the importance of soil structure effects on the mechanical behaviour of natural structured soils, improvements to constitutive models for these materials have been proposed by making explicit consideration of soil structure and its degradation (Rouainia & Wood 2000, Gens & Nova 1993, among others). Although many natural structured soils are unsaturated, few studies have considered the combined effect of partial saturation and inter-particle bonding on soil behaviour (Alonso & Gens 1994, Leroueil & Barbosa 2000). It is reported in these works that suction in bonded soils has two effects corresponding to capillary effects on soil matrix and strengthening of inter-particle bonds.
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1.2
2
Modelling approach
In aggregated soils, there is a strong interaction between the soil structure components, namely, soil fabric and inter-particle bonding. The macropores are retained by an aggregated structure and the openness of fabric depends on the size and strength of aggregated particle assemblages which are formed as a result of inter-particle bonding. The aim of this paper is to propose a baseline for a constitutive model capable of describing the behaviour of aggregated soils over a wide range of saturation conditions with explicit consideration of soil structure evolution. Based on multi-scale experimental evidences, the model is expected to unify the effects of inter-particle bonding, fabric and partial saturation in a single framework. The model is based on the framework of strain hardening elasto-plasticity. For the constitutive stresses the model adopts the matric suction, s, and a generalized effective stress which is the Bishop’s effective stress (Bishop 1959) with the Bishop’s parameter being equal to the degree of saturation, Sr . Accordingly, the relation between the so-called general effective stress tensor, σ , and the total stress tensor, σ , reads: σ = (σ − pa I) + Sr sI
(1)
where pa is the air pressure and I is the second order identity tensor. Although the representation of stress paths in this stress framework is rather complex, the transition from the saturated to the unsaturated state is smooth and straightforward. The critical state concept for unsaturated soils has been evaluated by different authors (Alonso et al.1990, among others). Khalili et al. 2004 successfully investigated the uniqueness of the critical state line (CSL) in the q−p plane (deviatoric stress versus mean effective pressure) for unsaturated soils with different suctions. They used the Bishop’s effective stress with a particular expression for the Bishop’s parameter. Uniqueness of the CSL in terms of generalized effective stress has been further evaluated by Nuth & Laloui (2007b). These authors reported the unification of the CSL in the stress space of q−p for unsaturated soils regardless of the suction level. Adopting the generalized effective stress as the constitutive stress, the general incremental stress-strain constitutive relation reads: dσ = Dep : dε
FEATURES OF BEHAVIOUR
An extensive oedometric testing programme has been carried out by the authors to evaluate the mechanical behaviour of aggregated silts at different saturation conditions. The main features of this behaviour are outlined here. Figure 1 shows the oedometric compression of an aggregated silt sample (average aggregate size of about 2 mm) and a sample of the corresponding reconstituted soil of the same mineralogy, both tested under the constant matric suction of 1500 kPa. The aggregated sample was initially in a normal consolidation state. However, an initial stiff behaviour followed by yielding was observed in the oedometric compression of this sample. The yield limit is here referred to as apparent preconsolidation stress, which is a function not only of stress state and stress history but also of soil structure. At a given value of applied stress, a sample of aggregated soil has a higher void ratio than reconstituted soil and the compression curve of aggregated soil is located to the right side of the reconstituted compression curve at the same suction. The compression curves of aggregated and reconstituted soils at the same suction tend to converge at higher values of applied effective stress. The main effect of suction in reconstituted samples was found to be the increase of effective apparent preconsolidation stress with suction. In structured samples, however, a combined effect of suction and soil structure was observed. In these samples, similar to reconstituted samples, a higher matric suction results in higher values of effective apparent preconsolidation stress. This is linked to the capillary effects. In addition to this
(2)
where ε is the strain tensor and Dep is the elastoplastic constitutive matrix. In this equation, symbol ‘:’ denotes the inner product of tensors with double contraction and d(.) denotes the incremental value.
Figure 1. Oedometric response of unsaturated aggregated (average aggregate size 2 mm) and reconstituted silt.
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structure and its degradation requires an internal parameter capable of representing the state of the material in relation to its initial intact condition. Accordingly, a state parameter called degree of soil structure is here introduced as the ratio of the current macro void ratio, to its initial value at intact state. On the basis of the pore-scale experimental observations, the evolution of the degree of soil structure has been found to be reasonably reproduced by a decreasing exponential function of plastic strain (Koliji et al. 2007): R = exp(−ωεD ) Figure 2. 3D neutron tomography volume of an aggregated silt sample (sample size 35 mm in height & 80 mm in diameter).
effect, the horizontal separation between the compression curve of structured soils and normal consolidation line of reconstituted soil in the oedometric compression space was found to increase with suction. This evidence shows that suction has a hardening effect on the inter-particle bonding in the soil structure. In addition to the macro scale experiments, the behaviour of the material and the soil structure at the pore-scale has been evaluated using a combination of different methods. Results of mercury intrusion porosimetry showed that unsaturated aggregated samples initially exhibit a multi-modal PSD with at least two dominant pore radii corresponding to micro- and macropores. At the same condition, a corresponding reconstituted soil exhibits a uni-modal PSD with the dominant pore radius coinciding with the micropores in structured samples. During a wetting or mechanical loading, however, aggregated samples undergo structure degradation and they end up with a structure identical to that of reconstituted soil. On the other hand, the advanced method of neutron tomography was employed for a 3-dimensional evaluation of soil structure modifications during the oedometric testing (Fig. 2). Results of these tests showed that changes in macroporosity are associated mainly with plastic strain. This important experimental finding has a major impact on the modelling of this phenomenon. 3 3.1
CONSTITUTIVE FRAMEWORK Degree of soil structure
At a given state for an aggregated soil, the macro void ratio (ratio of macropore volume over the solid volume) could represent the actual state of the soil structure with respect to its initial state and a fully reconstituted state. However, quantification of soil
(3)
where R is the degree of soil structure, εD is a combination of volumetric and deviatoric plastic strains, and ω is the parameter controlling the rate of structure degradation. The expression of the degree of soil structure given by Equation 3 provides an experimentally based relation which establishes a link between the pore-scale structure of the soil and the macroscopic behaviour of the material. 3.2
ACMEG-2S constitutive framework
The constitutive model ACMEG-2S, (Advanced Constitutive Model for Environmental Geomechanics, extension for unsaturated structured soils) is an elastoplastic model based on the critical state concept. It uses non-linear elasticity and two plastic mechanisms: one isotropic and one deviatoric. The plastic mechanisms are coupled through the volumetric plastic strain. The model adopts an isotropic plastic strain hardening with the volumetric plastic strain being the hardening parameter. The flow rule is associated for isotropic mechanism and could be associated or non-associated for the deviatoric mechanism. The limit of elasticity and the onset of plastic deformations in each mechanism are determined by the yield criterion corresponding to that mechanism: fiso = p − pc riso = 0 p d fdev = q − Mp 1 − b ln rdev = 0 pc
(4) (5)
In these equations, riso and rdev are degrees of mobilization of the isotropic and deviatoric plastic mechanisms and are hyperbolic functions of the plastic volumetric strain provoked by the isotropic mechanism and of the plastic deviatoric strain respectively. M , b and d are material parameters directly inherited from the saturated reconstituted soil and pc is the apparent effective preconsolidation pressure. The elastic region
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apparent preconsolidation suction effects: ⎧ ⎨ 1; ψs = 1 + γs log(s/se1 ); ⎩ 1 + γs log (s/se );
pressure due to primary if 0 < s < s1e if s1e ≤ s < sref if s ≥ sref
(8)
in which s1e and se are the air entry value suction of micropores and reconstituted soil respectively; and, γs and γs are two dependent material parameters. The relation between the two parameters γs and γs is derived from the second and third expression in Equation 8: Figure 3. model.
Yield surfaces and elastic region in ACMEG-2S
γs =
given by Equations (4) and (5) in the q − p plane is depicted in Figure 3. Detailed description of the model formulation will be presented elsewhere. Here attention is given to the evaluation of the apparent preconsolidation pressure and its evolution. Combining the effects of suction and soil structure, a general expression for the apparent preconsolidation pressure in unsaturated structured soils is: ∗
pc = ψ st ψ s pc0
(6)
∗
where pc0 is the reference effective preconsolidation pressure in saturated reconstituted soil, and, ψ st and ψ s are two functions which incorporate the effects of soil structure and of suction respectively. The preconsolidation pressure of saturated recon∗ stituted soil, pc0 , evolves according to a plastic strain hardening rule similar to the Cam-clay model (Roscoe & Schofield 1963): ∗
dpc0 =
ν ∗ p dεp λ∗ − k c0 ν p
(7)
where εν is the plastic volumetric strain, ν is the specific volume, and, λ∗ and k are material parameters for reconstituted soil. The primary effects of suction on the increase of effective preconsolidation pressure are of the same nature in reconstituted and aggregated soils and are taken into account by ψ s . These effects are linked to the capillary effects and depend on the geometry of the pores and the air entry value of the system of the pores. Adopting an approach similar to that presented by Nuth and Laloui (2007b), a reversible function is proposed to quantify the evolution of
log (sref /se1 ) γ log (sref /se ) s
(9)
In the expression of apparent preconsolidation pressure (Eq. 6), ψ st is a function of degree of soil structure and it controls the extension of yield limit with respect to the reconstituted reference state. At constant suction, the following evolution rule has been derived for this variable (Koliji et al. 2007): ψ st = exp[R ln ψist ]
(10)
where the subscript i designates the initial value. In the presence of suction variation, however, secondary effects of suction on soil structure should be considered in ψ st . The following relation is proposed to account for the additional effects of suction: s + pat nst st , ψist = 1 (11) ψ st = ψref sref + pat st is the value at the reference suction in which ψref sref and the exponent nst is a material parameter. The atmospheric pressure pat in the denominator is added to avoid infinite values when the saturated state (zero suction) is the reference state. The condition ψist = 1 limits the validity of this equation to the structured soils, in which the initial yield limit is basically influenced by the inter-particle bonding effects. Figure 4 plots the prediction of the proposed equation (bold line) and the experimental values of ψist for three unsaturated aggregated silt and the corresponding reconstituted samples (dots). With a reference suction of 500 kPa and nst = 0.375, this relation appears to successfully reproduce the experimental data. Double effects of suction on the apparent preconsolidation pressure in structured soils are illustrated in Figure 5. In this figure, the abscissa is the ratio of apparent preconsolidation pressure over the saturated preconsolidation pressure in reconstituted sate ∗ (pc /pc0 ). The increase of apparent preconsolidation
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Figure 4. Influence of suction on the soil structure parameter.
combined effects of partial saturation and soil structure, have been reviewed on the basis of multi-scale experimental evidences. The constitutive framework, ACMEG-2S, based on the critical state concept was presented within the framework of strain hardening elasto-plasticity. The model adopts the generalized effective stress to describe the material behaviour in different conditions of saturation. A new state parameter called degree of soil structure is introduced to quantify the soil structure and its evolution. This parameter establishes the pore-scale information of the soil to the macroscopic response in terms of plastic strains. The apparent preconsolidation pressure, as the main parameter controlling the yield limit, was formulated with respect to the combined effects of partial saturation and soil structure. The proposed modelling approach provides a logical unification of the effects of inter-particle bonding, fabric and partial saturation in a single framework.
REFERENCES
Figure 5. Combined effects of suction and soil structure on the apparent isotropic preconsolidation pressure.
pressure due to intrinsic suction effect ( ψ1 ) is represented by curve a. Multiplication of this curve with a st reference soil structure function ψref gives the curve b which represents the increase in the apparent preconsolidation pressure due to intrinsic suction ( ψ1 ) and pure soil structure effects ( ψ2 ) without considering the suction-hardening of soil structure. Accounting for this latter effect by Equation 11, the final evolution of apparent preconsolidation pressure with suction in structured soils is represented by curve c. The gray area between curve b and c ( ψ3 ) corresponds to the effects of suction on the soil structure given by Equation 11. This effect is a hardening effect for suctions beyond sref and a softening effect for suction below this suction.
4
CONCLUSIONS
The main features of the mechanical behaviour of unsaturated aggregated soils, stemming from the
Alonso, E. and Gens, A. 1994. Keynote lecture: on the mechanical behaviour of arid soils. In Conference on Engineering Characteristics of Arid soils. London, pp. 173–205. Alonso, E.E., Gens, A. and Josa, A. 1990. A constitutive model for partially saturated soil. Géotechnique 40(3): 405–430. Alonso, E.E., Vaunat, J. and Gens, A. 1999. Modelling the mechanical behaviour of expansive clays. Engineering Geology 54: 173–183. Bishop, A.W. 1959. The principle of effective stress. Tecknish Ukeblad 106: 859–863. Collins, K. and McGown, A. 1974. The form and function of microfabric features in a variety of natural soils. Géotechnique 24(2): 223–254. Coppola, A. 2000. Unimodal and bimodal descriptions of hydraulic properties for aggregated soils. Soil Science Society of America Journal, 64(4): 1252–1262. Gens, A. and Nova, R. 1993. Conceptual bases for a constitutive model for bonded soils and weak rocks. In A. Anagnostopoulos, F. Schlosser, N. Kalteziotis & R. Frank (eds), Geotechnical Engineering of Hard Soils— Soft Rocks: 485–495. Rotterdam: Balkema. Horn, R. 1993. Mechanical properties of structured unsaturated soils. Soil Technology 6: 47–75. Khalili, N., Geiser, F. and Blight, G.E. 2004. Effective stress in unsaturated soils: Review with new evidence. International Journal of Geomechanics 4(2): 115–126. Koliji, A., Vulliet, L. and Laloui, L. 2007. Soil structure evolution: Experimental and constitutive consideration. In Edited by G.N. Pande & S. Pietruszczak (eds), Numerical models in geomechanics, NUMOG X: 133–138. Balkema. Leroueil, S. and Vaughan, P.R. 1990. The general and congruent effects of structure in natural soils and weak rocks. Géotechnique 40(3): 467–488.
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Leroueil, S. and Barbosa, A. 2000. Combined effect of fabric, bonding and partial saturation on yielding of soils. In Asian Conference on Unsaturated Soils: 527–532. Lloret, A., Villar, M.V., Sanchez, M., Gens, A., Pintado, X. and Alonso, E.E. 2003. Mechanical behaviour of heavily compacted bentonite under high suction changes. Géotechnique 53(1): 27–40. Nuth, M. and Laloui, L. 2007a. Implications of a generalized effective stress on the constitutive modelling of unsaturated soils. In T. Schanz (ed.), Theoretical and Numerical Unsaturated Soil Mechanics: 75–82. Springer. Nuth, M. and Laloui, L. 2007b. New insight into the unified hydro-mechanical constitutive modelling of unsaturated soils. In Z. Yin, J. Yuan & A.C.F. Chiu (eds), The 3rd Asian Conference on Unsaturated Soils: 109–126. China: Science Press. Romero, E., Gens, A. and Lloret, A. 1999. Water permeability, water retention and microstructure of unsaturated compacted Boom clay. Engineering Geology 54(1–2): 117–127.
Roscoe, K.H. and Schofield, A.N. 1963. Mechanical behaviour of an idealised wet clay. In European Conference on Soil Mechanics and Foundation Engineering Vol.1: 47–54. Rouainia, M. and Wood, D.M. 2000. A kinematic hardening constitutive model for natural clays with loss of structure. Géotechnique 50(2): 153–164. Sanchez, M., Gens, A., Guimarães, L.N. and Olivella, S. 2005. A double structure generalized plasticity model for expansive materials. International Journal for Numerical and Analytical Methods in Geomechanics 29: 751–787. Sridharan, A., Altaschaeffl, A.G. and Diamon, S. 1971. Poresize distribution studies. Journal of the Soil Mechanics and Foundation Division ASCE 97: 771–787.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A damage model for unsaturated natural loess submitted to cyclic loading J.M. Pereira, A.N. Ta, Y.J. Cui & J.P. Karam Université Paris-Est, UMR Navier, Ecole des Ponts – CERMES, Marne-la-Vallée, France
H.Y. Chai Chinese Academy of Sciences, Institute of Rock and Soil Mechanics, Wuhan, China
ABSTRACT: High speed railway from Northern France has encountered several stability problems in zones where loessic soils are present. Important sinkholes have been observed and were mainly due to the collapse susceptibility of the encountered loess when submitted to the cyclic loadings imposed by the passage of the high speed trains. This collapse susceptibility seems to be related to the degradation of the cemented bonds and to either the collapse under wetting at constant applied load or liquefaction depending on the natural water content of the soil. In this paper, a constitutive model is developed to gain insight into cyclic behaviour of theses soils. This model is an extension of a model previously proposed by the authors for modelling degradation of bonds and liquefaction potential of natural cemented soils under saturated states. The platform model, from which the extension is carried out, is based from one hand on the bounding surface plasticity theory for the description of the cyclic response of the soil and is inspired on the other hand from the work of Vaunat & Gens (2003) concerning bond degradation modelling. Influence of non-saturation effects is introduced following an approach similar to that of the Barcelona Basic Model (Alonso et al. 1990). The developed model is thus capable to describe the mechanical behaviour of unsaturated bonded soils under cyclic loading.
1
INTRODUCTION
High speed railway from Northern France crosses areas characterized by important loess deposits (aeolian sediments) which may reach some meters in thickness. In that region, sinkholes have been observed along the railway thus showing an important collapse risk for this kind of soils. Loessic soils are composed of a solid matrix made of sand grains which are cemented by various materials such as calcium carbonate, clay and silica. Figure 1 shows a schematic representation of loess in an unsaturated state. Due to the mode of deposition of these sediments, loessis soils present a high porosity which may lead in some cases to significant collapse deformations. Among the possible physical explanations at the origin of these phenomena, degradation of soil structure can be cited. As for other cemented geomaterials such as soft argillaceous rocks, stiff clays, aged sands, residual soils etc., the overall mechanical behaviour of loess is largely influenced by the presence of these bonds in terms of stiffness, yield locus and strength. Under mechanical loadings, the bonding between matrix grains may be affected by damage. Furthermore, since this degradation may lead to significant volumetric deformations and thus to large increases in pore water
Figure 1. Schematic representation of loess in an unsaturated state.
pressures, these soils present a risk of liquefaction when loaded from an initial saturated state or even near to it. A precise description of bond damage is thus of first importance in order to obtain a satisfactory constitutive model able to simulate the cyclic behaviour of loess and its liquefaction potential. For this purpose, a model has been proposed in Chai (2005) and Chai et al. (2007). Besides damage and liquefaction potential, environmental loadings imposed by rainfalls or flooding
647
may induce collapse due to wetting if the soil is non-saturated, this phenomenon being well known in unsaturated soil mechanics. Of course, observed collapses along the high speed railway may originate from bond degradation, wetting and more probably from couplings between these two phenomena. For instance, bond degradation will facilitate collapse under wetting or wetting could reduce the strength of bonds. Furthermore, a collapse under wetting may be followed by a liquefaction of the soil if cyclic loadings are subsequently applied to wetting. Due to the complexity of possible phenomena and couplings between them, this paper aims at presenting a constitutive model in order to assess the collapsibility of loess under cyclic and environmental loadings, from the point of view of unsaturated soil mechanics. After a concise description of the platform model, its extension to unsaturated states is presented. The paper ends with simulations of laboratory tests in order to demonstrate the capabilities of the proposed model.
stresses in the triaxial stress space. The indices m and b respectively refer to the matrix and to the bond material. Strains of the bonds εvb and εqb are defined over the bond phase (volume Vb ) and their apparent expressions (i.e. defined over total volume Vt ) are the following, after having defined the bond concentration β = Vb /Vt : βεvb ;
βεqb
(2)
Similarly, apparent strains of the matrix which are defined over voids Vv and solid matrix Vm volumes write as follows: (1 − β)εvm ;
(1 − β)εqm
(3)
A relation between total strain and strains in the matrix and bond phases can then be derived: dεv = (1 − β)dεvm + βdεvb
2
dεq = (1 − β)dεqm + βdεqb
CONSTITUTIVE MODEL
The proposed model consists in the extension of a model developed for saturated loess under cyclic loading (Chai 2005, Chai et al. 2007). This platform model is based on the theory of bounding surface plasticity (Dafalias 1986) to simulate cyclic behaviour of loess. To account for the possibility of damage of the soil structure, modelling of bond degradation follows the work of Vaunat & Gens (2003). The extension to unsaturated states of the platform model is dealt with by following the framework introduced in the Barcelona Basic Model from Alonso et al. (1990). Net stress (excess of total stress over gas pressure, pg ) and matric suction (s = pg − pw where pw stand for water pressure) are used as independent stress state variables and yield limit is assumed to be dependent of suction in order to simulate collapse under wetting according to the loading-collapse (LC) equivalence principle. Before going deeper in the unsaturated damage model for loessic soils, the bases of the saturated version from which it is extended are recalled. Interested readers may find further details in (Chai 2005, Chai et al. 2007). 2.1
Cementation effects
A partition of the total effective stress between matrix and bond contributions is assumed as follows: pm = p − pb ;
qm = q − qb
(1)
where p and q are respectively the total (apparent and saturated) effective isotropic and deviatoric
(4)
Elastic relations with respect to the different strains previously introduced are assumed as follows: e dεvm =
dpm ; Km
e dεqm =
e = dεvb
dpb ; Kb
e dεqb =
dq 3Gm dqb 3Gb
(5) (6)
where Km , Gm are the elastic moduli of the matrix and Kb , Gb are those related to the bonding phase under current state of degradation. Using Equations (4), (5) and (6) together with (1) provides total elastic strain increments: dp Kb e + β − (1 − β) dεvb Km Km dq Gb e dεqe = (1 − β) + β − (1 − β) dεqb 3Gm Gm dεve = (1 − β)
(7)
Since pb and qb are unknown, elastic strain increments of bonds remain to be computed. Following Vaunat & Gens (2003), the ratios of elastic strains of e e bonds dεvb , dεqb to total elastic strains dεve , dεqe are assumed constant before damage and depending on this latter afterwards: e dεvb /dεve = χ0 ;
e dεqb /dεqe = χ1
(8)
where χ0 and χ1 are positive scalars lower than 1. For simplicity, it will be assumed that χ0 = χ1 .
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2.2
Description of damage of bonds
Following basic elastic damage theory, it is supposed that bonds are submitted to elastic strains only. Beyond a certain level of energy elastically stored, a degradation of their mechanical properties is assumed. A damage scalar variable D varying from 0 to 1 can classically be introduced (Lemaître & Chaboche, 1985). However, as previously done by Carol et al. (2001), a rescaled counterpart L (varying from 0 and infinity) of the damage variable D is preferred in what follows. It is defined by: L = ln
1 1−D
The yield function and plastic potential are inspirited from (Pastor et al. 1985). After modifications to account for interparticle bonding and its damage, they both read as follows: αf 1 p¯ F(σ , p0 ) = q¯ − Mf p¯ 1 + 1− αf p¯ 0 1 p¯ αg 1− G(σ , pg ) = q¯ − Mg p¯ 1 + αg p¯ 0g (15)
(9)
Expressions (8) can then be rewritten to account for the damage state of bonds: e /dεve = χ0 e
; dεvb
e dεqb /dεqe = χ1 e (10)
where L0 is associated to the energy level at which degradation effectively starts and <x> represents the positive part of x. The evolution of L is assumed to depend on both volumetric and shear strains as follows: 1 1 . . L(ε) = kv ξv + kq ξq ; ξv = |dεv |; ξq = .dεq . (11)
where σ = ( p , q)T and Mf , αf , Mg , αg are parameters to determine and p¯ 0g is related to the size of the plastic potential. As in (Pastor et al. 1985), the bounding and yield surfaces are assumed to coincide. On the bounding surface, the plastic strain increment is defined by the following flow rule: dε p = (dεvp , dεqp )T =
Constitutive model for the matrix
A model based on bounding surface plasticity theory (Dafalias, 1986) has been rimentally simulate observed accumulation of irreversible strains even if the loading cycles are small compared to the yield limit estimated from monotonous tests. Bonding effects are introduced in the plastic potential and the yield function by defining the following changes of variable: p¯ = p + χpbc ;
q¯ = q + χqbc
(12)
where pbc and qbc are material constants to be determined and: χ = χ0 e
∂F ∂σ
T · dσ +
∂F ∂p0
∂p0 ∂εp
T · dε p +
∂F dL = 0 ∂L (17)
Inside the domain delimited by the bounding surface, the following mapping rule, inspired by the works presented in (Zienkiewicz et al. 1985, Pastor et al. 1985), is used to link the hardening modulus of the current stress point HL/U to that of the conjugate stress point cs HL/U : HL/U = cs HL/U
δ0 δ
γ0 (18)
where γ0 is a material parameter. Following the theory of bounding surface plasticity, HL/U is then used to classically compute the plastic strain increment inside the elastic domain. Figure 2 presents schematic representation of this mapping rule.
(13) 2.4 Extension to unsaturated states
The hardening parameter pc is also modified in the following way: p¯ 0 = (1 + χ)p0
(16)
with ngL/U and n the normal tensors to respectively the plastic potential surface during loading or unloading cs and the bounding surface and HL/U , the plastic modulus during loading or unloading. This latter can be computed using the consistency condition:
where kv and kq are materials constants to be determined. 2.3
ngL/U (nT · dσ ) cs HL/U
(14)
The extension to unsaturated states is implemented following the framework of the Barcelona Basic model (BBM) from Alonso et al. (1990).
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The energy-linked threshold L0 can be assumed to be dependent on the suction value. Concerning the modification of the yield surface, it is directly inspired from the Barcelona Basic Model (Alonso et al. 1990) so that: F(σ, p0 , L, s) Figure 2. Schematic representation of the mapping rule used to link plastic moduli at actual and conjugate stress points.
The main part of the saturated model presented here before remains valid. The effective stress p only has to be replaced by the net stress. The other modifications that are required to define the unsaturated model are now presented. By analogy to the mechanical behaviour, total elastic strains associated to suction variations are given by: dεvse =
1−β β + s s Km Kb
αf 1 p¯ 1− (24) = q¯ − Mf (¯p + ps ) 1 + p¯ 0 αf
with p¯ = p + eL0 −L pbc ; p¯ s = k0 s;
Kbs = Kb
(20)
After some derivations, it can be shown that the variations of the stress in the bond are given by:
p0 = pc
(27)
p∗0 pc
λ(0)−κ λ(s)−κ
(28)
λ(s) = λ(0) ((1 − r) exp(−bs) + r)
(29)
where p∗0 corresponds to the saturated yield limit introduced in Equations (14) and (15). The plastic potential is chosen as: G(σ , p0 , L, s)
αg 1 p¯ 1− (30) = q¯ − Mg (¯p + ps ) 1 + αg p¯ 0
and the plastic strain increment formally given in the saturated case by (16) and (18) remains the same. The hardening law is given by: dp∗0 1+e ∂ξ dεvp + β0 β1 e−β0 ξ p dεqp (31) ∗ = p0 λ(0) − κ ∂εq
(21) L0 −L
dqb = Gb0 χ11 e " # × dεqe − εqe (−1)n kv dεv + (−1)m kq dεq
∂F ∂σ +
(22)
T
∂F · dσ + ∗ ∂p0
∂F ds = 0 ∂s
(23)
∂p∗0 ∂εp
T · dε p +
∂F dL ∂L (32)
The suction increase yield locus (SI) introduced in BBM that is: SI (s, s0 ) = s − s0
and, in the matrix, by: dqm = dq − dqb
(26)
The consistency condition now takes into account suction changes and writes as follows:
dpb = Kb0 χ00 eL0 −L " # × dεve − εpe (−1)n kv dεv + (−1)m kq dεq
dpm = dp − dpb ;
(25)
The so-called LC curve is defined by:
(19)
where Kms and Kbs are the bulk moduli associated to suction variations of, respectively, the matrix and the bonds. Interparticle bonding being constituted of clay and calcite, it will be assumed further on that the air entry value of the bond material is larger than usual values of suction to which the soil is submitted. Since in that case the bonding material remains saturated, Terzaghi’s effective stress remains valid. With this assumption, the following simplification can be added to the previous equation:
p¯ 0 = (1 + χ)p0
χ = χ00 exp(L0 _L)
ds
q¯ = q + eL0 −L qbc
(33)
is not considered in this study due to a lack of experimental data justifying its existence. In other words,
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the suction value s0 which corresponds to the highest value at which the soil as ever been submitted is assumed to be larger than usual values encountered in the applications here considered. Concerning the hydraulic behaviour, van Genuchten’s equation (van Genuchten 1980) is considered for the water retention curve modelling so that:
Sr (s) =
1 1 + (Bs)n
Shear stress (kPa)
700 600 500 400 300 200 s=25 kPa s=1 kPa
100
m
0 0
(34)
where B, m and n are material parameters. Another choice is also considered, following Brooks & Corey’s proposal (1964): Sr (s) =
800
2
4
6
8
Figure 4. Influence of suction on monotonous triaxial tests performed at constant suction.
700 600
s α e
(35)
s
where se and α are material parameters.
500 400 300 200 100
s=1 kPa s=25 kPa
0 0
3
10
Axial strain (%)
Shear stress (kPa)
900
2
4
6
8
10
Axial strain (%)
PRELIMINARY RESULTS
Preliminary results are now presented. They aim at presenting the possibilities of the model to simulate the behaviour of unsaturated cemented materials. All simulation use van Genuchten’s equation to model the water retention curve of loess. The initial void ratio e is 0.83 and the initial stress is isotropic and close to zero since isotropic consolidation stages are simulated before starting triaxial tests. Figure 3 presents the water retention curves of the loess studied in this work obtained experimentally by Karam (2006) and simulated using Equations (34) and (35).
Figure 5. Influence of suction of cyclic triaxial tests performed at constant suction.
3.1 Monotonous triaxial tests Monotonous triaxial tests are simulated at two imposed suctions. They were performed after an isotropic compression stage. Results are presented in Figure 4 and show as expected an increase of the stiffness and the yield limit of the material when suction is increased. 3.2 Cyclic triaxial tests
1200 Experimental data van Genuchten Brooks & Corey
Suction (kPa)
1000 800 600 400 200 0 0.30
0.39
0.45
0.48
0.55
0.68
0.73
Degree of saturation
Figure 3. Experimental and simulated water retention curves of loess from Northern France (experimental data from (Karam 2006); simulated data using van Genuchten’s and Brooks & Corey’s models).
Finally, in order to illustrate the effects of bond degradation on the performance of the unsaturated model proposed in this paper, a cyclic triaxial test is simulated at two imposed suctions. These tests consist in imposing a given number of shear stress cycles after an isotropic consolidation stage. The results are presented in Figure 5. The influence of a suction increase is characterised by the reduction of axial strain at the end of a given cycle. Concerning the modelling of damage, it appears that the first cycles (for both suction values) present higher stiffness, higher yield limits and larger irreversible strains than the last cycles. This observation can be explained easily by considering that the first cycles involve a lowly damaged material which tends to increasingly degrade during the loading process.
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Table 1.
REFERENCES
Material parameters of bonds.
χ00 = χ11
β
kα = kβ
Kb (kPa)
νb
pbc (kPa)
0.35
0.35
2.0
5000
0.25
10
β0
β1
Table 2. λ1
Material parameters of matrix.
κ
ν
Mg
Mf
αg
αf
γ
0.17 0.012 0.25 1.35 0.58 0.45 0.45 4.3 0.23 1.4
Table 3. Material parameters of unsaturated extension and water retention curve (van Genuchten’s model). r
b
pr (kPa)
k
κs
n
m
B
0.75
0.01
25
0.02
0.01
0.5
1
5 × 10−5
3.3
Material parameters
The materials parameters used in the simulations are summarized in the Tables 1–3. Mechanical parameters (of bonding material and matrix, see Tables 1–2) were determined by curve fitting from experimental data in (Chai 2005). Unsaturated parameters were estimated from experimental results on similar soils and van Genuchten’s parameters were determined by curve fitting (see Figure 3 and Table 3). 4
CONCLUSIONS
A model that aims at assessing the collapsibility of loessic soils encountered along the high speed railway in Northern France has been presented. Theses soils are submitted to cyclic mechanical loadings and to environmental loadings which may lead to important collapse deformations. This model is able to simulate the effects of degradation of bonds and non-saturation on the behaviour of natural cemented soils. Preliminary results have been presented and show the good capabilities of the model.
Alonso, E.E., Gens, A. & Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique 40(3): 405–430. Brooks, R. & Corey, A. 1964. Hydraulic properties of porous media, Colorado State University Hydrology Paper 3: 27 pp. Carol, I., Rizzi, E. & Willam, K. 2001. On the formulation of anisotropic elastic degradation. I. Theory based on a pseudo-logarithmic damage tensor rate. International Journal of Solids and Structures 38(4): 491–518. Chai, H.Y. 2005. Modelling of the Mechanical Behaviour of Loessic soils under cyclic loadings. Research report. ENPC. Chai, H.Y., Pereira, J.M., Cui, Y.J. & Karam, J.P. 2007. Modelling loess behaviour under cyclic loadings using a damage model. International Journal for Numerical and Analytical Methods in Geomechanics (submitted). Dafalias, Y.H. 1986. Bounding surface plasticity: I. Mathematical foundation and hypoplasticity. Journal of Engineering Mechanics (ASCE) 112(9): 966–987. van Genuchten, M.T. 1980. Closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Science Society of America Journal 44(5): 892–898. Karam, J.P. 2006. Étude de la rhéologie des loess du Nord de la France. Application à l’évaluation de leur risque de liquéfaction. PhD Thesis, Ecole Nationale des Ponts et Chaussées, Paris, France. Pastor, M., Zienkiewicz, O. & Chan, A.H.C. 1990. Generalized plasticity and the modelling of soil behaviour. International Journal for Numerical and Analytical Methods in Geomechanics 14(3): 151–190. Pastor, M., Zienkiewicz, O.C. & Leung, K.H. 1985. Simple model for transient soil loading in earthquake analysis. II. Non-associative models for sands. International Journal for Numerical and Analytical Methods in Geomechanics 9: 477–498. Ta, A.N. 2006. Prise en compte de la non-saturation dans un modèle élastoplastique avec endommagement. MSc Thesis, Ecole Nationale des Ponts et Chaussées, Paris, France. Vaunat, J. & Gens, A. 2003. Bond degradation and irreversible strains in soft argillaceous rock. In Proc. of the 12th Panamerican Conference on Soil Mechanics and Geotechnical Engineering: 479–484. Zienkiewicz, O.C., Leung, K.H. & Pastor, M. 1985. Simple model for transient soil loading in earthquake analysis. I. Basic model and its application. International Journal for Numerical and Analytical Methods in Geomechanics 9: 453–476.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Desiccation shrinkage of unconstrained soil in the saturated phase L.B. Hu & T. Hueckel Duke University, Durham, North Carolina, USA
H. Peron & L. Laloui EPFL, Lausanne, Switzerland
ABSTRACT: Analysis of macroscopic desiccation shrinkage experiments indicates that most of the shrinkage occurs during drying while soil is still 100% wet. When air starts penetrating the soil, shrinkage practically ceases, while the water content is still above 20%. The remaining drying process occurs with a much-reduced shrinkage. In this context we look at the data of pore space evolution during saturated phase of drying as obtained via porosimetry. The observed behavior is modeled at a microscale using Poiseuille flow in capillary vessels with deformable walls driven by evaporation flux at the external boundary. A macroscopic model using Biot and Darcy theories for the continuum were recently presented by the authors.
1
INTRODUCTION
Desiccation phenomena in soils have been investigated for decades bringing progressively a better understanding of the mechanisms and physics involved (Abu-Hajleh & Znidarcic 1995, Kodikara et al. 1999, Konrad & Ayad 1997, Miller et al. 1998). Recent desiccation experiments (Peron et al. 2006) on initially saturated soils near liquid limit point out to the conclusion that most of the shrinkage occurs during saturated phase of the process. This is in agreement with a general perception that unsaturated soil has a much higher stiffness than saturated soil. This is quite a universal behavior independently of the type of soil and type of pore fluid, as shown by Hu et al. 2007 (Fig. 1). That includes shrinkage of soil permeated with ethanol solution, which has surface tension coefficient that is less than a half of that of water. When soil becomes unsaturated, shrinkage practically stops, while the water content is still above 20%. The remaining drying process occurs with a muchreduced deformation. Hu et al. 2007 have also shown that the amount of deformation during the saturated drying and the shrinkage limit in terms of void ratio depend on the compressibility of the solid, but seems to be independent of surface tension and/or fluid saturation vapor pressure which characterizes evaporation process, or finally, from fluid viscosity. However, the rate of fluid loss and rate of shrinking are controlled by the evaporative and hydraulic conductivity properties, thus, those of the fluid. As it is generally agreed that capillary effects are caused by the fluid surface
Figure 1. Void ratio evolution during drying versus the volumetric fluid content change in clayey silt [Bioley silt] (left) and a granite powder (right) filled with water, water/ethanol 50–50 mixture and water-ethylene glycol 65–35 mixture (see Peron et al. 2007 for details).
tension, it is postulated that the saturated phase of drying is largely independent from capillary effects, and shrinkage is due to the fluid removal from the pore space via Darcian flow, while fluid-gas interface is confined to the external soil mass boundary, where all the phase transition takes place. Furthermore, possible capillary effects at the boundary appear to play a minor role in deformation, and hence the so-called ‘‘skin effect’’ is a negligible factor in deformation analysis. A microscopic model of pore system deformation and transport is proposed to corroborate this hypothesis in relationship to the actual data on the evolution of the pore space. A macroscopic counterpart model has been recently developed using Biot and Darcy theories by Hu et al. 2007.
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2 2.1
PORE SPACE EVOLUTION Pore size distribution
Pore size distribution was obtained for Bioley clayey silt filled with water using Mercury Intrusion Porosimetry. The measurements were conducted at three stages of unconstrained desiccation: at the value of the water content of 33.1%, 24.8% and at 0.8%. These instants correspond to the initial state, near the shrinkage limit, and after the completion of the process. Figure 2 visualizes the volume fraction for each instant. The evolution of the pore space can be summarized as follows: (1) the initial pore size is visibly bi-modal, with Large Pores (LP), ranging between 0.6 μm and 3 μm occupying initially 17% of the volumes of the medium, and Small Pores (SP), ranging between 0.09 μm and 0.6 μm occupying initially 21% of the volume of the medium. There are also minor volumes of peripheral size pores outside of the range of MIP, including those of clayey fraction (see Peron 2008 for details). (2) At near shrinkage limit the LP take less than 5% of the volume of the medium, whereas the SP amount to 29%. Finally at near the completion of drying, the LP take less than 0.5% of the volume of the medium, whereas the SP still amount to 27%. 2.2
Assessment of the pore space evolution during drying
This result is very significant, as it indicates that during the entire process the Small Pores do not decrease significantly, neither in size nor in total volume they occupy. To the contrary, at near shrinkage limit, they probably include the volume of former LP. The LP themselves practically all close during the saturated phase of drying and disappear at completion of the process. Similar results were recently obtained by
Figure 2. Pore size distribution evolution during drying of Bioley silt.
Cuisinier & Laloui (2004) and Koliji et al. (2006) during suction induced desaturation process. Interestingly, it has been known for sometime that in bi-modal porosity soils, the SP remain virtually unchanged during consolidation process, whereas all volume changes are accommodated by LP (Delage & Lefebre 1984). In reference to the desiccation process such evolution of the pore space implies that only the water volume contained in the LP is subject to evacuation during the saturated phase, and only that water volume produces the observed shrinkage.
3
MICROSCOPIC MODEL OF PORE SPACE EVOLUTION
3.1 Formulation The above observations will be framed into a model of an evolving microscopic structure, based on the following specific postulates. It is recognized that the pore system of soil is made of sectors of straight tubes of two initial sizes: small (ST) and large (LT), with their internal diameters coinciding with the average values of the pore modes, identified in the preceding Section as 0.5 μm and 1 μm. The total initial volumes of the pores are set as equal to the initial value of the pore space of the corresponding modal volumes. The external radii of the tubes are not connected to any physical currently used characteristics of soils, except that the total volume of the solids of all the tubes must be representative of the total volume of the solids. Hence its value is determined as 2.5 μm. The grain size distribution data could provide some help, but not without a more extensive study. To begin with we consider a representative elementary volume (REV) in a form of a single cylindrical deformable tube around a single cylindrical Large Pore located centrally and a series of parallel cylindrical Small Pores, all filled with water, and connected at their extremities to the atmosphere with which they can exchange gas and fluid. The tube representation is shown in Figure 3(a). The solid of the tube represents a granular material, hence deforming irreversibly. The macroscopic
Figure 3. Schematics of a pore system in a cylindrical REV (a) and a BVP for a Small (b) eventually approximated via (d) and for a Large Pore (c).
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experiments (Peron et al. 2006) indicate that drying shrinkage strain is largely irreversible, while in the unsaturated phase the deformation is reversible to the state of the onset of desaturation, upon the removal of suction or re-wetting. The behavior of the solid material surrounding the pores will be considered as plastic, however it will be approximated via a linearly elastic law during loading and considered as perfectly rigid during an unloading. The adoption of a linear deformation law allows one to use a principle of superposition and hence represent the pore system of Figure 3(a) as a superposition of effects of a LP and multiple SPs. Eventually, for the reasons of simplicity, SPs will all be located centrally as well. Hence, the problem is reduced to that of a single tube with a single cylindrical pore. The tube is considered as symmetric along and around its axis, loaded with a negative pore fluid pressure at the ends. It is assumed that a tube is completely filled with water during the considered phase (saturated). Water undergoes a viscous (Poiseuille) flow, i.e. an incompressible Newtonian fluid through a cylindrical tube. For the external boundary conditions for the fluid one can envision either a known (negative) water pressure history, or an imposed flux, resulting from the evaporation flux. The removal of water from the tube implies that its volume is compensated by the deformation of the tube. The time evolution of the negative pressure applied is reconstructed from the experiment (Peron et al. 2005, 2006) and shown in Figure 4. At the axis of the symmetry at the tube half-length the no-flow condition is imposed. Water transport in the tube is a viscous nonfrictional (Poiseuille) flow with the externally applied negative pressure, which is evaporation-driven. ∂p 8μ 8μ = − 4Q = − 2 F ∂x πa a
(1)
Q is the volume-flow rate, F is the volume flux, p is water pressure, μ is viscosity and a is the inner radius of the tube. We assume that the flow is solely attributed to the loss of volume of the inner conduit, i.e. due to the change in a, thus the volume change of an infinitesimal tube element per unit volume is ∂v 2πa ∂a 2 ∂a = = ∂t πa2 ∂t a ∂t And the mass conservation requires (in 1D) ∂F ∂v =− ∂t ∂x
(3)
Thus substituting the flux into Equation 3, an approximate Poiseuille’s equation for the collapsing tube is obtained ∂ 2 p 2 ∂a ∂p 16μ ∂a = + a3 ∂t ∂x2 a ∂x ∂x
(4)
It should be pointed out that a similar equation can also be obtained from Equation 1 by replacing the volume flow rate with the total volume loss of tube. 1
x
Q=− 0
2πa ·
∂a (x, t) dx ∂t
(5)
In reality the tube radius a varies with x because of the elastic deformation in response to the variable (negative) pressure. A classical tube expansion/compression solution provides such a relationship. To further simplify the mathematical solution Fung (1984) expresses the change in radius as a function of the inner pressure by ignoring the radial strain a0 p(x) −1 a(x) = a0 1 − Eh
Figure 4. The negative pore pressure function imposed at the boundary x = L (from the experimental data).
(2)
(6)
E is the Young’s modulus, a0 is the initial value of the inner radius a, h is the thickness of the tube. Fung has shown that the latter approximation is very good, especially for low values of Poisson coefficient. As indicated in the subsequent context, the simulated deformation appears to be rather large, hence, a finite strain configuration may become a better approach. However, as our current priority in this paper is to examine the idea of using a deformable pore model to simulate the shrinkage, the mathematical merit of employing large deformation will be pursued in future work.
655
Substituting Equation 6 into the original Equation 4 produces a partial differential equation for pore pressure p. 2a0 ∂ 2p + ∂x2 Eh 1 −
pa0 Eh
∂p ∂x
2 =
pa 16μ 1 − Eh0 ∂p a0 Eh ∂t (7)
The initial condition is: at t = 0, p = p0 = 0. The boundary conditions are as follows: x = 0, ∂p/∂x = 0 and x = ±L, p = p (t), see Figure 4. Equation 7 is a parabolic PDE. Its solution has been obtained using Mathlab© .
3.2
Figure 5(a). Evolution of radii in LP at x = L, x = L/2, and x = L/4.
Results
The solutions are obtained numerically for large and small pores separately. The numerical value of the deformability modulus E = 50 KPa, and water viscosity chosen the same for the analyses of the LP and the SPs. The length of the tubes is 15 cm, taken as the length of the macroscopic experiments (see Peron et al. 2005). Both types of pores are subjected to the same external negative pressure evolution, as resulting from the same flux of water vapor (see Hu et al. 2007). The most significant difference between the two types of pores is in the amount of closure of the inner cavity: in 5 hours needed for reaching the shrinkage limit, the SP closes over 0.08 μm from the original 0.5 μm at the external boundary, whereas the LP closure amounts to 0.33 μm from 1 μm. This reflects correctly the porosimetry observation that the Large Pores convert into 0.6 μm (or nearly Small Pore types) in that period of time. The evolution of radii for selected cross sections of the tube proceeds similarly, but with a small but marked delay, as seen in Figures 5(a) and (b). The profiles of the opening along the axis for each pore type are shown in Figure 6. The results also indicate a different efficiency of SPs and LPs in transport of water toward the evaporating boundary. Figure 7 shows water flux evolution at the boundary for both types of pore relative to their cross section surface area. A single LP provides more than twice of water than a SP after 5 hours. Notably, as the areas of the individual tubes decrease in a significantly different manner, the volume flow rates per single tube yield a different picture (Fig. 8). Indeed, because of a large reduction of the cross section area of the large pore tube, it appears that the latter reaches a maximum of the water output at about two hours from the onset of the process of drying. It may be expected that the small tubes reach a similar maximum at a later moment.
Figure 5(b). Evolution of radii in SP at x = L, x = L/2, and x = L/4.
Figure 6. Radius profile for small and large pore after 5 hours of drying.
Hence, the outflow from the system stabilizes and then gradually decreases, driven by the tube constriction. Whether this remains within the range of validity of the presented model remains an open question. The cumulative volume loss via single LP and SP from
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Figure 7. Water flux evolution at the external boundary for individual LP and SP.
Figure 10. Small pore tube: evolution of the pressure profile along the tube axis.
Figure 8.
Volume flow rate evolution per single tube.
Figure 11. Large pore tube: evolution of the pressure profile along the tube axis.
Figure 9.
Cumulative volume output per single tube.
the onset of evaporation is shown in Figure 9. On the mechanics side of the problem it is interesting to note that because of the common value of the externally applied negative pressure, both types of tubes are exposed to very similar pressure throughout almost the entire history of the drying process in the saturated range. Figures 10 and 11 present the evolution of such pressure along respectively LP and SP, indicating indeed very limited differences. It has to be realized however, that the two types of tubes have drastically different stiffness because of the differences in their thickness. This indeed produces such a dramatically different response in terms of the deformation of the tubes. Finally, it is also seen that for selected
Figure 12. Evolution of pressure in LP at x = L/2 and x = L/4. For comparison also the boundary pressure is shown.
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cross sections of the tube the negative pressure evolves similarly, but with a marked delay, as visible in Figure 12. In fact the pressure evolution mimics that of the radius of the pore as may be expected from the form of Equation 6. 4
DISCUSSION AND CONCLUSIONS
The presented highly idealized microscopic model and numerical simulations of the drying process in its saturation phase indicate a series of characteristics that agree qualitatively with the experimental findings. The centerpiece of the model is transport of water toward the perimeter of the drying body producing the collapsing of the vessels. The model is largely based on the evolution of the pore system, idealized as bimodal. In particular, a significant reduction in diameter of large pores is seen, compared to that of smaller mode pores that is attributed to the difference in their deformability due to size difference. Transport of water is characterized by an initial phase (two hours) when the discharge increases via large pores to stabilize at start to gently decrease after about four hours. An open question remains whether the aforementioned decrease remains within the range of the model validity. Several simplifications and assumptions require further investigations, to start with the deformation modulus of the medium that comprises (only) smaller pores. An obvious limit of the validity of the model is the air entry moment. However, a microscopic criterion for this occurrence is still a point of discussion. ACKNOWLEDGEMENTS This work is funded by a cooperation between the Swiss National Science Foundation, grant 200020109661 and the US National Science Foundation, grant # 0324543.
Delage, P. & Lefebre, G., 1984, Study of the structure of the sensitive Champlain Clay and of its evolution during consolidation, Canadian Geotechnical J., 21 (1): 21–35. Fung, Y.C. 1984. Biodynamics: Circulation. New York: Springer. Hu, L.B., Peron, H., Hueckel, T. & Laloui, L. 2006. Numerical and phenomenological study of desiccation of soil. In N. Lu, L.R. Hoyos and L. Reddi (eds.), ASCE Geotechnical Special Publication: Advances in Unsaturated Soil, Seepage, and Environmental Geotechnics, 166–177. Hu, L.B., Peron, H., Hueckel, T. & Laloui, L. 2007. Drying shrinkage of deformable porous media: mechanisms induced by the fluid removal. In H.W. Olson (ed.), ASCE Geotechnical Special Publication 157: Geo-Denver 2007, New Peaks in Geotechnics. 10 pages, CD-ROM. Kodikara, J., Barbour, S.L. & Fredlund, D.G. 1999. ‘‘Changes in clay structure and behaviour due to wetting and drying.’’ Proceedings of the eighth Australia New Zealand Conference on Geomechanics, Hobart, 1: 179–185. Koliji, A., Laloui, L. Cuisinier, O. & Vulliet, L. 2006, Suction Induced Effects on the Fabric of a Structured Soil, Transport in Porous Media 64: 261–278. Konrad, J.M. & Ayad, R. 1997. An idealized framework for the analysis of cohesive soils undergoing desiccation. Canadian Geotechnical Journal 34: 477–488. Miller, C.J., Mi H. & Yesiller, N. 1998. Experimental analysis of desiccation crack propagation in clay liners. Journal of the American Water Resources Association 34 (3): 677–686. Peron, H. 2008. Ph. D. Thesis, Ecole Polytechnique Federal de Lausanne, ENAC, Lausanne, Switzerland, in preparation. Peron, H., Laloui, L. & Hueckel, T. 2005. An experimental Evidence in Desiccation Cracking in Sandy Silt, in Tarantino, Romero and Cui (eds.), Advanced Experimental Unsaturated Soil Mechanics, Proceeding of Conference, Trento, Italy, April 2005, Taylor and Francis Group, London, 475–480. Peron, H., Laloui, L., Hueckel, T. & Hu, L.B. 2006. Experimental study of desiccation of soil. In G.A. Miller, C.E. Zapata, S.L. Houston and D.G. Fredlund (eds.), ASCE Geotechnical Special Publication 147: Unsaturated Soils 2006, 1073–1084. Peron, H., Hu, L.B., Hueckel, T. & Laloui, L. 2007. The influence of the pore fluid on desiccation of a deformable porous material. In T. Schanz (ed.), Springer Proceedings in Physics, Experimental Unsaturated Soil Mechanics, 413–420.
REFERENCES Abu-Hajleh, A.N. & Znidarcic D. 1995, Desiccation theory for soft cohesive soils, J. Geotech. Eng. 121 (6): 492–502. Cuisinier, O. & Laloui, L. 2004, Fabric evolution during hydromechanical loading of a compacted silt, Int. J. for Numerical and Analytical Methods in Geomechanics 28: 483–499.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Modelling of the collapsible behaviour of unsaturated soils in hypoplasticity D. Mašín Charles University, Prague, Czech Republic
N. Khalili University of New South Wales, Sydney, Australia
ABSTRACT: The paper presents a recently developed constitutive model for unsaturated soils, based on the theory of hypoplasticity and the effective stress principle. The mathematical formulation of the model is outlined and the required state variables and parameters are described. The model is, among other features of unsaturated soil behaviour, capable of predicting collapse upon wetting, a phenomenon that could not be modelled with earlier hypoplastic models. Predictions of wetting-induced collapse agree well with experimental data on statically compacted Pearl clay.
1
INTRODUCTION
Hypoplasticity, a particular class of incrementally nonlinear constitutive models, has undergone a notable development during last two decades. Recently, hypoplastic models cover a wide range of geomaterials, such as granular materials, soils with a low friction angle and clays. Procedures to incorporate anisotropy, viscosity, structure and the elastic behaviour in the very small strain range and the effects of recent history are available. To date, however, most contributions on the constitutive modelling of soils using the theory of hypoplasticity have been in the domain of saturated soils. Extension of this class of constitutive models to unsaturated soils is presented in this contribution. Mašín and Khalili (2007) have recently developed a new hypoplastic model for unsaturated soils. The model is based on the hypoplastic model for clays by Mašín (2005). It is thus, as other advanced hypoplastic models, characterised by the following rate form: T˚ = fs (L : D + fd N D )
(1)
˚ is the objective rate of Cauchy stress tensor, where T D is Euler stretching tensor, L and N are two constitutive tensors and fs and fd are two scalar factors (named barotropy and pyknotropy factors respectively) that incorporate the influence of mean stress and void ratio. The model by Mašín (2005) is characterised by a low number of parameters and a simple calibration procedure. This advantageous property of the basic model is naturally shared also by its extension for unsaturated soils.
The aim of this contribution is to outline mathematical formulation and basic features of the hypoplastic model for unsaturated soils. The model is then evaluated with respect to experimental data on one characteristic feature of the unsaturated soil behaviour—collapse of the structure caused by wetting. More detailed description and evaluation of the model may be found in Mašín and Khalili (2007). Throughout this paper, sign conversion of continuum mechanics is considered, i.e. compression is taken as negative.
2
STRESS STATE VARIABLES
Central to the framework presented here is the concept of effective stress which can be defined in the following general form, subject to the solid grains incompressibility constraint (e.g., Bishop 1959) T = Tnet + 1χs
(2)
Stress variables without any superscript (T) denote the effective stress, Tnet is the net stress defined as Tnet = Ttot − 1ua and s = ua − uw is the matric suction. Ttot is the total stress, ua is the pore air pressure and uw is the pore water pressure. A simple formulation for the effective stress tensor T based on Eq. (2), which is sufficient for many practical applications, has been put forward by Khalili and Khabbaz (1998) and further evaluated by Khalili et al. (2004). On the basis of an extensive
659
is controlled by the isotropic virgin compression line with the formulation according to Butterfield (1979)
evaluation of experimental data they proposed the following empirical formulation for χ: χ=
& 1 s γ e
s
for s ≥ se for
s < se
(3)
where se is the suction value separating saturated from unsaturated states. It is equal to the air entry value for drying processes and the air expulsion value for wetting processes. γ is a material parameter, and it has been shown that for a broad range of different soils it is sufficient to assign γ = 0.55 (Khalili and Khabbaz 1998). For suctions lower than se the effective stress parameter χ is equal to 1, i.e. the soil is saturated and Eq. (2) reduces to the Terzaghi effective stress definition. Time differentiation of Eq. (2), with the use of (3) and taking into account rigid body rotations, imply the following formulation of the objective rate of the effective stress ˚ = T˚ net + 1(1 − γ )χ s˙ T
(4)
In addition to the effective stress tensor T, suction s is considered as a state variable that quantifies the stiffening effect of the water menisci. 3
HYPOPLASTIC MODEL FOR UNSATURATED SOILS
In this section, the hypoplastic model for unsaturated soils proposed recently by Mašín and Khalili (2007) will be presented. The basic aim of the derivations in this section is to demonstrate a conceptual way to incorporate the behaviour of unsaturated soils into hypoplasticity. The particular formulation adopted is very simple, but it may be readily modified by using the general rules outlined in this section. 3.1 Model for constant suction The overall mechanical response of a soil element is controlled by the effective stress tensor. Suction influences the effective stress and, in addition, it increases normal forces at interparticle contacts and thus acts as a quantity that increases the overall stability of the soil structure. In terms of the critical state soil mechanics, it increases the size of the state boundary surface (SBS), in a similar manner to bonding between soil particles in saturated cemented materials. State boundary surface is defined as a boundary of all possible states of a soil element in the stress vs. void ratio space. The incorporation of structure into hypoplastic model has been discussed in detail by Mašín (2007). In this context, the size of the SBS for unsaturated soils
ln(1 + e) = N (s) − λ∗ (s) ln
p pr
(5)
where e is the void ratio, which is considered as a state variable, and pr = 1 kPa is a reference stress. Quantities N (s) and λ∗ (s) define the position and the slope of the isotropic virgin compression line in the ln(p/pr ) vs. ln(1 + e) plane for given suction s. For the evaluation of model predictions through this paper, we assume for ln(s/se ) > 0 (unsaturated state) the following simple logarithmic dependency of N (s) and λ∗ (s) on s: s N (s) = N + n ln (6) se s (7) λ∗ (s) = λ∗ + l ln se where the quantities n and l represent two additional soil parameters. For ln(s/se ) < 0 (saturated state) N (s) = N and λ∗ (s) = λ∗ . It is, however, emphasized that the general formulation of the model can accommodate any other more complex relationships between N (s), λ∗ (s) and s. Mašín (2007) demonstrated that incorporation of variable virgin compressibility and the intercept N (s) into the hypoplastic model requires a modification of both barotropy and pyknotropy factors fs and fd in (1), which are now calculated in terms of N (s) and λ∗ (s). The respective expressions are given in Mašín and Khalili (2007). 3.2 Incorporation of wetting-induced collapse at normally consolidated states When an unsaturated soil with an initially open structure is subjected to a decreasing suction, the reduction in the normal forces acting at the inter-particle contacts may result in a situation in which the structure, for the given effective stress T and void ratio e, is no longer stable, and thus it collapses. This phenomenon, referred to as a wetting-induced collapse, cannot be modelled with the model for structured clays Mašín ˚ = 0 implies D = 0 (see Eq. (1)), i.e. no 2007), as T deformation of the soil skeleton can be predicted for variable suction with constant effective stress. In the context of the critical state soil mechanics, all admissible states of a soil element are bounded by the SBS. As the hypoplastic model from Sec. 3.1 predicts constant void ratio sections through the SBS of the same shape (see Mašín and Herle (2005)), it is advantageous to study collapse due to wetting in the stress space normalised by the size of the SBS
660
for current e. This size is quantified by the Hvorslev equivalent pressure pe , implied by Eq. (5). Mašín and Khalili (2007) have shown, that normalisation with respect to pe allows us to derive the following expression that ensures consistency of the model predictions with the SBS of suction-dependent size:
1
m=1 m=2 m=5 m=10 m=100
0.8
fu
0.6
˚ = fs (L : D + fd N D ) + H T
0.4
(8)
0.2
where H is a new term given by H=
T ∂pe s˙ pe ∂s
3.3
0.2
0.4
0.6
0.8
1
Figure 1. The influence of the parameter m on the value of suction hardening pyknotropy factor fu .
(10)
The following expression for the factor fu satisfying these requirements is proposed:
Model for any state of overconsolidation
The model from Sec. 3.2 may be used for constant value of suction (˙s = 0) and for wetting at normally consolidated states (states at the SBS). The following assumptions are utilised to extend Eq. (8) for arbitrary (physically admissible, i.e. inside the SBS) states and arbitrary loading conditions: 1. As suction controls stability of inter-particle contacts, increasing suction under constant effective stress imposes no deformation of soil skeleton. 2. The more open the soil structure, the larger the inter-particle contact shear forces and therefore the greater the number of inter-particle contact slips under wetting at constant effective stress. To reflect these two assumptions, the rate formulation of the model is written as ˚ = fs (L : D + fd N D ) + fu H T
0
p/pSBS
From the expression for the Hvorslev equivalent pressure pe follows T ∂N (s) ∂λ(s) pe − ln s˙ H= λ(s) ∂s ∂s pr
0
(9)
(11)
fu =
p
m (13)
pSBS
where pSBS is the effective mean stress at the SBS corresponding to the current stress state T/ tr T and current void ratio e and m is a model parameter controlling the influence of overconsolidation on the wetting-induced collapse. Eq. (13) is demonstrated graphically in Fig. 1. Clearly, value of the parameter m controlls dependency between collapse of structure and distance of the current state from the SBS. Note that basic elasto-plastic models based on suction hardening concept imply m → ∞ (collapse at the yield surface only). It may be shown from the definition of the pyknotropy factor fd of the basic hypoplastic model and using rules derived by Mašín and Herle (2005) that m/α fu = fd fs A−1 : N
(14)
with H=
T ∂N (s) ∂λ(s) pe − ln ˙s λ(s) ∂s ∂s pr
where the fourth-order tensor A is given by (12) A = fs L −
where the operator x denotes positive part of any scalar function x and fu is a new pyknotropy factor controlling tendency of the soil structure to collapse upon wetting. The factor fu must be equal to unity for states at the SBS (in that case the structure is as open as possible and collapse is controlled by H only) and fu → 0 for OCR → ∞ (no wetting-induced inter-particle slippage occurs in highly overconsolidated soil).
4
1 λ∗ (s)
T⊗1
(15)
WETTING-INDUCED STRAIN RATE
Wetting of normally consolidated soil at anisotropic stress state causes in addition to volumetric collapse development of shear strains (Sun et al. 2004, 2007). Eq. (8) allows us to derive an expression for the direction of stretching implied by wetting at constant
661
0.05
experiment m=1 m=2 m=5 m=10 m=100
0.6 0.04 0.4 0.03 εv [-]
q/p*e, dεs
0.2 0 – 0.2
0.02 0.01
– 0.4
0
– 0.6 0
0.2
0.4
0.6
0.8
–0.01
1
0
20
40
60
p/p*e, dεv
Figure 2. Direction of strain rate tensor induced by wetting at constant effective stress for Pearl clay parameters.
ϕc
λ∗
0.05
κ∗
0.005
100
120
140
Figure 3. s vs. v relationship for wetting of slightly overconsolidated soil at constant net stress.
Table 1. Parameters of the hypoplastic model for Pearl clay (calibrated using data from Sun et al. (2004)). 29◦
80 s [kPa]
N 1.003
0.86 0.84 0.82
r 0.5
0.8
l 0.024
m2
se [kPa] -15
ln (1+e)
n 0.164
0.78 0.76 0.74
effective stress for states at the SBS (see Mašín and Khalili (2007)). −1 =− A :N D A−1 : N
0.72 0.7 0.68
NCLs 3
(16)
3.5
4
4.5
5
5.5
6
6.5
5.5
6
6.5
ln (p/pref) 0.86
where the fourth-order tensor A is given by Eq. (15). Eq. (16) implies purely deviatoric strain rate at the critical state and purely volumetric strain rate at the isotropic stress state. Direction of the strain increment vector for different stress obliquities is graphically demonstrated in Fig. 2, together with the shape of the bounding surface for Pearl clay parameters (Tab. 1), evaluated by Mašín and Khalili (2007). It is clear that the strain increment vector is not perpendicular to the SBS (in terms of elasto-plasticity, neglecting the effects of elastic strains, this would be implied by a non-associated flow rule).
0.84 0.82
ln (1+e)
0.8 0.78 0.76 0.74 0.72 0.7 0.68
NCLs 3
3.5
4
4.5
5
ln (p/pref)
5
Figure 4. Isotropic compression tests at constant suction and wetting tests at constant net stress by Sun et al. (2007) replotted in the effective stress space (top) and predictions by the proposed model (bottom).
PREDICTING THE COLLAPSIBLE BEHAVIOUR OF UNSATURATED SOILS
Thorough evaluation of the hypoplastic model for unsaturated soils is presented in Mašín and Khalili (2007). It contains response to drying and wetting paths of soil specimens at isotropic and anisotropic stress states and response to constant suction shear tests and isotropic loading tests at different suction levels. Tests on five different soils performed in different
soil mechanics laboratories are used for evaluation. Due to the limited space, in this paper we restrict the model evaluation to tests at the isotropic and anisotropic stress state under constant and decreasing suction. The response to wetting paths is with respect
662
3
0.06
pnet=20 kPa pnet=49 kPa pnet=98 kPa net p =196 kPa net p =392 kPa pnet=588 kPa
0.05
2.5
0.03
R [-]
εv [-]
0.04
calib. m
2
0.02 1.5
0.01
R=1.5 R=2 R=2.5
0 1 – 0.01
0
20
40
60
80
100
120
0
140
0.02
0.04
0.06
0.1
0.12
0.14
0.16
0.18
0.16
0.18
εa [-]
– s [kPa] 3
0.06
pnet=20 kPa pnet=49 kPa pnet=98 kPa pnet=196 kPa pnet=392 kPa pnet=588 kPa
0.04
2.5
R [-]
0.05
εv [-]
0.08
0.03 calib. m
2
0.02 1.5
0.01
R=1.5 R=2 R=2.5
0 1 – 0.01
0
20
40
60
80
100
120
140
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
εa [-]
– s [kPa]
Figure 5. Wetting tests at constant isotropic net stress by Sun et al. (2007) plotted in s vs. v plane (top) and predictions by the proposed model (bottom).
to hypoplastic modelling the most important to study, as in this case the new terms H and fu are activated. The model is evaluated by means of experimental data on statically compacted Pearl clay by Sun et al. (2004, 2007). Pearl clay is a moderate plasticity soil with very little expansive clay minerals. The first set of experimental data consist of tests on soil specimens that have been isotropically compressed at constant suction −147 kPa to different mean net stress levels (49, 98, 196, 392 and 588 kPa). At this stage, the specimens were wetted at constant net stress and suction was decreased to zero. Some of the specimens were further compressed at zero suction to the mean net stress 588 kPa. Figure 3 shows response to wetting tests at the highest apparent overconsolidation ratio (the test where wetting took place at pnet = 49 kPa) and predictions by the model with different values of the parameter m from Eq. (14). The higher the value of m, the closer to the SBS the volumetric collapse takes place. The value of m = 2 has been considered as a suitable value to represent Pearl clay behaviour. Calibration of all other model parameters for Pearl clay (Tab. 1) is detailed in Mašín and Khalili (2007).
Figure 6. Constant net mean stress shear tests and constant R wetting tests by Sun et al. (2007) plotted in a vs. R = Ta /Tr plane (top) and predictions by the proposed model (bottom).
Figure 4 shows graphs of the constant suction isotropic compression tests and constant net stress wetting tests replotted in the effective stress space. Predictions are in a good agreement with the experimental results, the model predicts correctly both the constant suction and wetting parts of the experiments. In the wetting tests at the lower net mean stresses, the experiments show the initial decrease of the effective stress with very small change of void ratio. This aspect of the observed soil behaviour, which is progressively less pronounced with decreasing apparent OCR, can be modelled correctly by the proposed model thanks to the new pyknotropy factor fu . Results of the wetting parts of the experiments from Fig. 4 are plotted in the suction vs. volumetric strain plane in Fig. 5. The model predicts correctly the qualitative influence of the net mean stress on the volumetric behaviour. When the soil is wetted at low net mean stress (49 kPa), it first swells and only after the state gets closer to the state boundary surface the structure starts to collapse. On the other hand, specimens wetted at higher net mean stresses (i.e. at lower apparent OCRs) collapse since the beginning of the wetting test. This aspect of the soil behaviour is predicted correctly thanks to the proposed formulation for the
663
radial net stresses. At this stage, suction was decreased to zero under constant net stress, and finally the shear test continued under constant mean net stress and s = 0 kPa to failure. The specimens had approximately equal initial void ratios (initial apparent OCRs) and they were wetted at different values of the ratio R (1.5, 2 and 2.5). Figure 6 shows the results of the three constant net mean stress shear tests in the axial strain vs. principal net stress ratio plane. The corresponding radial strains are in Fig. 7. Correct predictions of the constant suction parts of the tests demonstrate the predictive capabilities of the basic hypoplastic model, which predicts the non-linear soil behaviour with gradual decrease of the shear stiffness. In the wetting parts of the tests, the model predicts significant increase of the collapse axial strains and of the negative radial strains at higher ratios R. The good quantitative agreement for both a and r demonstrates adequate modelling of the wetting-induced collapse strain rate direction. The analytical expression for this direction has been (for constant effective stress) derived in Sec. 4, see Fig. 2 for Pearl clay parameters.
3
R [-]
2.5
2
1.5 R=1.5 R=2 R=2.5
1 –0.07 –0.06 –0.05 –0.04 –0.03 –0.02 –0.01
0
0.01
0
0.01
εr [-] 3
R [-]
2.5
2
1.5 R=1.5 R=2 R=2.5 1 –0.07 –0.06 –0.05 –0.04 –0.03 –0.02 –0.01
6
εr [-]
Figure 7. Constant net mean stress shear tests and constant R wetting tests by Sun et al. (2007) plotted in a vs. r plane (top) and predictions by the proposed model (bottom).
factor fu . The experiments show the lowest collapsible strains for the wetting at the highest net mean stress (588 kPa). Correct predictions of the final value of the volumetric strains after collapse are achieved thanks to the converging normal compression lines of the saturated and unsaturated soils (Fig. 4), i.e. thanks to l > 0 (Eq. (6)). The predicted shape of the wetting path in the s vs. v plane is controlled by the factor fu (for the initially apparently overconsolidated specimens) and by the interpolation function for the quantities N (s) and λ∗ (s) (Eq. (6)). Good agreement between experimental data and model predictions also for wetting at higher net mean stresses (where the factor fu takes a constant value equal to 1) suggests that the logarithmic interpolation adopted is suitable to represent the actual soil behaviour. The second set of experimental data allows us to investigate the influence of the stress anisotropy on the wetting-induced collapse behaviour. The specimens were, after isotropic compression at constant suction s = −147 kPa to mean net stress pnet = 196 kPa, subjected to constant suction and constant net mean stress shear tests up to a target principal net stress ratio R = Tanet /Trnet , where Tanet and Trnet are the axial and
CONCLUDING REMARKS
A recently developed constitutive model for unsaturated soils is presented in the paper. The model is based on the theory of hypoplasticity, it is thus capable of predicting pre- and post-peak non-linear deformation behaviour of unsaturated soils, and the variation of the soil stiffness with loading direction—important aspects absent from many of the current constitutive models proposed for the behaviour of unsaturated soils. A specific feature of unsaturated soil behaviour— collapse of the structure induced by wetting—can be predicted thanks to the factors H and fu , novel to hypoplasticity. Predictions of the wetting-induced collapse, presented in this paper, agree well with experimentally observed behaviour.
ACKNOWLEDGEMENT The first author acknowledges the financial support by the research grants GAAV IAA200710605, GACR 103/07/0678 and MSM0021620855.
REFERENCES Bishop, A.W. (1959). The principle of effective stress. Teknisk Ukeblad 106(39), 859–863. Butterfield, R. (1979). A natural compression law for soils. Géotechnique 29(4), 469–480.
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Khalili, N., F. Geiser, and G.E. Blight (2004). Effective stress in unsaturated soils: Review with new evidence. International Journal of Geomechanics 4(2), 115– 126. Khalili, N. and M.H. Khabbaz (1998). A unique relationship for χ for the determination of the shear strength of unsaturated soils. Géotechnique 48(2), 1–7. Mašín, D. (2005). A hypoplastic constitutive model for clays. International Journal for Numerical and Analytical Methods in Geomechanics 29(4), 311–336. Mašín, D. (2007). A hypoplastic constitutive model for clays with meta-stable structure. Canadian Geotechnical Journal 44(3), 363–375.
Mašín, D. and I. Herle (2005). State boundary surface of a hypoplastic model for clays. Computers and Geotechnics 32(6), 400–410. Mašín, D. and N. Khalili (2007). A hypoplastic model for mechanical response of unsaturated soils. International Journal for Numerical and Analytical Methods in Geomechanics (submitted). Sun, D.A., H. Matsuoka, and Y.F. Xu (2004). Collapse behaviour of compacted clays in suction-controlled triaxial tests. Geotechnical Testing Journal 27(4), 362–370. Sun, D.A., D. Sheng, and Y.F. Xu (2007). Collapse behaviour of unsaturated compacted soil with different initial densities. Canadian Geotechnical Journal 44(6), 673–686.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Swelling pressure in compacted bentonite: Laboratory tests and modelling M. Sanchez University of Strathclyde, Glasgow, UK
M.V. Villar & R. Gómez-Espina CIEMAT, Madrid, Spain
A. Lloret & A. Gens UPC, Barcelona, Spain
ABSTRACT: The aim of this work is to extend an existent double structure model for expansive clays (Sanchez et al., 2005) to include the thermal effects in the analysis. Experimental results obtained in the context of the NF-PRO project have been used to extend the constitutive law. A fundamental characteristic of the double structure framework is the explicit distinction of two actual structural levels existent within the material: the macrostructural level, which accounts for the larger scale structure of the material and the microstructural level, associated with the active clay responsible for the swelling behaviour. In addition, the model considers the interaction between the two structural levels. In this paper the dependence of the swelling behaviour on temperature has been directly included in the constitutive law that describes the microstructural behaviour. This is the natural way to consider the thermal effects in expansive clays, as their swelling behaviour is controlled mainly by the clay minerals (microstructure).
1
INTRODUCTION
This research has been carried out in the context of projects concerning the engineered clay barrier of deep geological radioactive waste repositories. This barrier, made of compacted bentonite (a highly swelling material), will be placed between the waste canisters and the host rock, and will be saturated by the groundwater while it is subjected to high temperatures due to the radioactive decay of the wastes. These temperature changes affect the hydraulic and mechanical response of the bentonite, what has important implications on the design and performance of the repository. The behaviour of expansive soils is potentially very complex owing to the interaction between the volume change of aggregates made up of highly expansive clay minerals (microstructure) and the rearrangement of the granular-like skeleton formed by the aggregates (macrostructure). The BBM (Barcelona Basic Model), developed by Alonso et al. (1990) is able to deal with the main features of unsaturated soils but it is not able to describe the behaviour of expansive soils. The aim of this work is to extend an existent double structure model, specially developed for expansive clays (Sanchez et al., 2005), to include (in a consistent way) the influence of temperature on the expansive
clay behaviour. A basic feature of the model is the explicit distinction of two actual structural levels existent within the material: the macrostructure and the microstructure. The macrostructure accounts for the larger scale structure of the material and it is described using the BBM. The inclusion of the microstructural level (associated with the active clay particles) in the analysis allows the consideration of the physicochemical phenomena occurring at particle level. In addition, the model considers the interaction between the two structural levels. This is a key mechanism to describe the behaviour of swelling clays. The constitutive laws incorporate key aspects to model the complex behaviour of highly expansive material, such as, large swelling under wetting, yielding, stress path dependency, clay-fabric changes, among others. Even though the model is general, it has been mainly applied to explain and reproduce the behaviour of expansive clays used as engineered barrier to isolate high level radioactive waste (HLW). Figure 1 shows a typical scheme adopted in the design of clay barriers for HLW. In field conditions the clay barrier will be hydrated (due to the water coming from the host rock) under confined conditions and will also undergo heating (induced by the heatemitting waste) up to a maximum of 100◦ C (according
667
Rock Compacted bentonite Nuclear waste
Container
Figure 1. Scheme of an engineered barrier made up of compacted clay for a high level radioactive waste repository.
to the Spanish concept for the disposal of HLW). To understand and reproduce satisfactorily the behaviour of such kind of barriers it is crucial to validate a mechanical constitutive model able to reproduce the main trends of the expansive clays behaviour when are submitted to complex Thermo-Hydro-Mechanical (THM) paths. An extensive experimental campaign carried out on compacted FEBEX bentonite, which combined suction and load changes, has been used to validate the hydro-mechanical behaviour of the double structure model (Lloret et al., 2003). In the context of the ongoing NF-PRO project a research program is being carried out to advance the knowledge of the thermal behaviour of expansive clays. Results of saturation under load and swelling pressure tests at temperatures ranging from 30 to 80◦ C have been used in this work (Villar & Gómez-Espina 2006). For the material considered in this work, the FEBEX bentonite, a decrease of swelling capacity and swelling pressure with temperature has been observed. The upgrade of the model proposed in this work has been based on this experimental evidence. This work is organized as follows; firstly the main aspects of the experimental program are introduced. Then, the mechanical constitutive model for expansive soils is briefly presented. After that, the inclusion of the thermal effects in the analysis and the main results are discussed. Finally, the main conclusions of the work are presented.
2
EXPERIMENTAL WORK
The determination of the swelling pressure and permeability as a function of temperature was performed in high-pressure oedometer equipment. Granulated clay was compacted uniaxially and statically at room temperature in the oedometer ring, which had an inner diameter of 5.0 cm, the length of the resulting specimen being 1.2 cm. Nominal dry densities of 1.50 and 1.60 Mg/m3 were reached by applying vertical stresses of 11 and 16 ± 2 MPa, respectively.
Figure 2. Schematic representation of the oedometer cell for tests at high temperature.
The oedometer assemblage was placed inside a silicone oil thermostatic bath that kept target temperature. Once the temperature stabilised, the sample, confined between porous stainless steel sinters, was hydrated at constant volume through the bottom face with deionised water injected at a pressure of 0.01 MPa, while the upper outlet remained open to atmosphere. At the same time, a load cell installed in the loading frame measured the swelling pressure exerted by the clay. The small vertical deformation of the specimen, due mainly to load cell and frame deformability, was measured by two LVDTs. An automatic volume change apparatus measured the water exchange of the specimen. The values of load, strain and water exchange were automatically recorded. Figure 2 presents a schematic representation of the device used in the experimental program. Once the sample was completely saturated (which was assumed by the stabilisation of water intake and swelling pressure development), the injection of water was stopped, and the pressure registered was considered the swelling pressure value for the dry density attained. The actual density may differ slightly from the nominal one due to the small displacement allowed by the equipment (about 10 μm when a vertical stress of 2.2 MPa is applied). The main results of the swelling pressure tests are presented in Section 4.
3
DOUBLE STRUCTURE MODEL
Expansive clays generally present a clear double structure, made up from clay aggregates and large
668
Figure 3. Distributions of incremental pore volume obtained using MIP technique (Lloret et al., 2003) and schematic representation of the two structural levels considered.
macrostructural pores (e.g. Pusch, 1982). As an example, the mercury intrusion porosimetry tests preformed to examine the pore size distribution of the statically compacted samples of FEBEX bentonite are presented in Figure 3. This figure shows the measured incremental pore volume for two samples compacted to very different values of dry density (ρd ), 1.5 Mg/m3 and 1.8 Mg/m3 . It can be observed that the pore size distribution is clearly bimodal. The dominant values are 10 nm that would correspond to the pores inside clay aggregates and a larger pore size that depends on the compaction dry density and ranges from 10 μm (for ρd = 1.8 Mg/m3 ) to 40 μm (for ρd = 1.5 Mg/m3 ). These larger voids would correspond to the inter-aggregate pores. The boundary between the two pore size families can be seen to be around 0.13 μm, as pores smaller than this size do not appear to be affected by the magnitude of the compaction load. The pore space inside the aggregates is constituted by voids of a much smaller size. The two dominant pores size could be associated with two basic structural levels (Figure 3): • The macrostructural level, which accounts for the larger scale structure of the material. • The microstructural level, associated with the active clay responsible for the swelling behaviour. Only these two basic structural levels identified above are considered herein. The approach is open enough and it could be extended to include more structural levels in the analysis, if it deemed relevant. The soil fabric plays a crucial role to understand and to reproduce the behaviour of expansive clays. In this model, the inclusion of the clay fabric in the analysis is considered in the definition of laws for: 1) the macrostructural level, 2) the microstructural level, and 3) for the interaction between both structural levels.
Figure 4. a) BBM yield surface. b) Microstructural load directions on the p-s plane.
3.1 Macrostructural model The inclusion of this structural level in the analysis allows the consideration of phenomena that affect the skeleton of the material, for instance deformations due to loading and collapse. The BBM (Barcelona Basic Model) has been adopted to describe the macrostructural behavior (Alonso et al., 1990). The BBM considers two independent stress variables to model the unsaturated behaviour: the net stress (σ ) computed as the excess of the total stresses over the gas pressure, and the matric suction (s), computed as the difference between gas pressure and liquid pressure (pg − pl ). Figure 4a shows the BBM yield surface (FLC ), defined as: FLC = 3J 2 −
g(θ) g(−30◦ )
2 M 2 (p + ps )(p0 − p) = 0 (1)
where M is the slope of the critical state, po is the apparent unsaturated isotropic pre-consolidation pressure, g(θ) is a function of the Lode angle and ps considers the dependence of shear stress on suction
669
•
p∗0 = p∗0
(1 + e) • p ε (λ(0) − κ) v
(2) •
p
where e is the void index, εv is the volumetric plastic strain, κ is the elastic compression index for changes in p and λ(0) is the stiffness parameter for changes in p for virgin states of the soil in saturated conditions. In additions, the model is able to describe the reduction of the size of the yield surface and the strength of the material with the increase of temperature, according to the model suggested in Gens (1995). The Appendix contains the main model equations. 3.2
Microstructural model
The microstructure is the seat of the basic physicochemical phenomena occurring at clay particle level. The strains arising from microstructural phenomena are considered elastic and volumetric (Gens & Alonso, 1992). The microstructural effective stress is defined as: pˆ = p + χs
(3)
It is assumed that the total suction is equal to the matric suction (s), because the effect of the osmotic suction is not considered in this work. χ is a constant. It is also assumed hydraulic equilibrium between the water potentials of both structural levels. A more general formulation with non-equilibrium between water potentials is presented in Sanchez (2004). The increment of microstructural strains is expressed as: •
•
εv1 =
•
3.3 Interaction between macro and micro structure In expansive soils there are other mechanisms in addition to the ones included in the BBM which induce plastic strains. This irreversible behaviour is ascribed to the interaction between the macro and micro structures (Gens & Alonso 1992). It is assumed that the microstructural mechanical behaviour is not affected by the macrostructure but the opposite is not true. An assumption of the model is that the irreversible deformations of the macrostructure are proportional to the microstructural strains according to interaction functions f . The plastic macrostructural strains are evaluated by the following expression: (5)
p
4
EFFECT OF TEMPERATURE ON SWELLING
The swelling pressure results for the two dry densities tested are plotted in Figure 5. Deformations induced in the experimental device due to thermal effects have been calibrated and deducted from the informed results. The dispersion of data can be mostly attributed to the variations in dry density (whose average values were in fact 1.58 and 1.49 Mg/m3 ). This is caused by the small displacement allowed by the
(4)
where the subscript 1 refers to the microstructural level, the subscript v refers to the volumetric component of the strains and K1 is the microstructural bulk modulus. The Neutral Line (NL) corresponds to constant pˆ and no microstructural deformation occurs when the stress path moves on the NL (Figure 4b). The NL divides the p-s plane into two parts, defining two main generalized stress paths, which are identified as: MC (microstructural contraction) and MS (microstructural swelling).
•
where εvLC is the plastic strains induced by the yielding of the macrostructure (BBM). In fact the coupling is given by p∗o , hardening variable of the macrostructure (Figure 4a), which depends on the total plastic volumetric strain (Equation 2). In this way it is considered that the microstructural processes can affect the global arrangements of aggregates. More details can be found in Sánchez et al. (2005).
•
p s pˆ = +χ K1 K1 K1
• p
•
εvp = εvLC + f εv1
Swelling pressure (MPa)
and temperature. A basic point of the model is that the size of the yield surface increases with matric suction. The trace of the yield function on the isotropic p-s plane is called the LC (Loading-Collapse) yield curve, because it represents the locus of activation of irreversible deformations due to loading increments or collapse. The position of the LC curve is given by the pre-consolidation yield stress of the saturated state, p∗o (hardening variable), according to:
Error bars obtained from values of tests performed at laboratory
6
3
temperature (1.6Mg/m )
4
2
Dry density (Mg/m3) 1.5 1.6 Test Test Model Model
Error bars obtained from values of tests performed at laboratory temperature (1.5 Mg/m3)
0 20
30
40
50
60
70
80
Temperature (°C)
Figure 5. Swelling pressure as a function of temperature for saturated FEBEX clay compacted to different nominal dry densities. Experimental and modelling data.
670
K1 =
e−αm pˆ βm
(6)
where αm and βm are model parameters. The extension suggested here is to include a dependence of the parameter βm on temperature. The following expression is proposed: βm
βm = e
τ
T Tref
(7)
100.0
(p+s) (MPa)
equipment, as the swelling pressure value is very sensitive to small density changes. The error bars shown in the figure were obtained from values measured in tests performed at laboratory temperature (Lloret et al., 2003). A decrease of swelling pressure as a function of temperature is observed. This would be in accordance with the results obtained in soaking under load tests, which predict a decrease in swelling capacity with temperature (Villar & Gómez-Espina, 2006). The extrapolation towards higher temperatures would indicate that swelling pressures higher than 1 MPa would be developed even for temperatures of 100◦ C. Lingnau et al. (1996) also observed a reduction in swelling pressure with temperature for a sand/bentonite mixture, although it did not show any loss in the self-healing capability of the material, even for temperatures of up to 100◦ C. In order to represent more closely the behaviour of expansive clays it is important to consider the influence of temperature on swelling. With this aim the model presented in Section 3 has been extended to include thermal effects. In the constitutive law presented above, the large swelling of the material is modelled (mainly), through the microstructural law (Section 3.2). This has a strong physical sense because the expansive behaviour of soils is due to the wetting of the active clay minerals, which constitute the microstructure of expansive clays. So, the aim here is to include at this level the change in the swelling capacity of expansive clays due to thermal effects. The mechanical behaviour at microstructural level is represented by a non-lineal elastic model, because it is assumed that the expansion is controlled by physico-chemical effects occurring at clay particle level (microstructure) that are basically reversible. In this law (Equation 4) the expansion of the material depends on the microstructural effective stress (Equation 3) through a microstructural bulk modulus (K1 ). A first attempt to model the thermal effect is to include a dependence of K1 on temperature. The expression used to validate the expansive model with data of FEBEX bentonite (Lloret et al., 2003) is presented as follows:
ΔT (°C) τ : 0.12 0 20 40 60
10.0
1.0
0.1 1000
1500
2000
2500
3000
3500
K1 (MPa)
Figure 6. Changes in micro-structural stiffness with temperature.
where T is the temperature difference, that is the actual temperature minus Tref , a reference temperature (i.e. 20◦ C), and τ is a new parameter that may be obtained from experiments. In this analysis τ has been obtained by back-analysing the experiments. Figure 6 shows how the change of temperature affects the microstructural bulk modulus according to the suggested law. An increase in the microstructural stiffness with temperature is predicted with this law. This means lower expansion when tests are conducted at higher temperature. In order to check the capabilities of the extended constitutive law a series of analysis has been carried out in order to describe the dependence of swelling on temperature observed experimentally. Swelling pressure tests at constant temperature have been modelled (Figure 5). The initial suction has been determined from the retention curve. No major effects of temperature on retention behaviour of FEBEX bentonite have been observed, at least for the range of temperature analysed herein (FEBEX, 2006). The rest of initial and boundary conditions have been adopted to reproduce closely the conditions observed during the test (Villar & Gómez-Espina, 2006). As has been already mentioned, for the FEBEX bentonite, the main parameters of the constitutive law were previously obtained during the validation of the constitutive law (Lloret et al., 2003). In this work, the only parameters adjusted are the ones related to the new microstructural law. The main model parameters used in the analysis are presented in Table 1. In this model, the dependence of swelling on initial density is taken into account in a consistent way through the parameter p∗0 (Gens & Alonso, 1992). As can be observed from Figure 5, the model is able to reproduce quite well the dependence of swelling pressure on temperature for the two dry densities analysed.
671
Table 1.
Mechanical constitutive law parameters.
Parameters defining the BBM (macrostructure) κ
κs
λ(o)
r
ζ (MPa−1 )
p∗o (MPa)
α0 (◦ C−1 )
5−3
1−3
8−2
9−1
1.
(∗1 )
1.−5
Parameters defining microstructural behaviour (emicro = 0.46) αm (MPa−1 ) = 5.0 e−2
βm (MPa−1 ) = 7.8 e−4
τ = 0.12
χ=1
Interactions functions fC = 1 + 0.9 tan h (20 (pr /po ) − 0.25)
5
fS = 0.8 − 1.1 tan h (20 (pr /po ) − 0.25)
(∗1 ) dry density 1.6 (Mg/m3 ) p∗o = 7.0 (MPa)
e macro = 0.228
(∗1 ) dry density 1.5 (Mg/m3 ) p∗o = 4.5 (MPa)
e macro = 0.340
CONCLUSIONS
A double structure model, based on the general framework for expansive materials proposed by Gens & Alonso (1990) has been presented. In order to be closer to the typical fabric of expansive materials, the existence of two pore structures has been explicitly included in the formulation. The distinction between the macrostructure and microstructure provides the opportunity to take into account the dominant phenomena that affect the behaviour of each structure in a consistent way. The major advantage of this model is that it incorporates in a natural way the key aspects that control the behaviour of expansive clays, indicated as follows: the swelling features of clay minerals are explicitly considered through a microstructural law; the relevant effects of the granular-like skeleton are contemplated through the macrostructural law and the model also considers the interaction between both structural levels. In this paper the double structure model (Sanchez et al., 2005) has been extended to consider the effect of temperature on swelling. As the clay particles are mainly responsible for the expansive behaviour of clays a dependence of the microstructural law on temperature has been suggested in this work. It has been observed that the model is able to capture the main trends observed in the tests.
Gens, A. 1995. Constitutive Laws. In A. Gens P. Jouanna & B. Schrefler Modern issues in non-saturated soils: 129–158. Wien New York: Springer-Verlag. Gens, A. & Alonso, E.E. 1992. A framework for the behavior of unsaturated expansive clays. Can. Geotech. Jnl. 29:1013–1032. Lingnau, B.E., Graham, J., Yarechewski, D., Tanaka, N. & Gray, M.N. 1996. Effects of temperature on strength and compressibility of sand-bentonite buffer. Eng. Geol. 41 1–4: 103–115. Lloret, A., Villar, M.V., Sánchez, M., Gens, A., Pintado, X. & Alonso, E. 2003. Mechanical behaviour of heavily compacted bentonite under high suction changes. Géotechnique, 53(1): 27–40. Pusch, R. 1982. Mineral water-interaction and their influence on the physical behaviour of highly compacted Na bentonite. Can. Geotech. Jnl., 19: 381–387. Sánchez, M. 2004. Thermo-hydro-mechanical coupled analysis in low permeability media. Ph. D. Thesis, Technical University of Catalonia. Barcelona. Sánchez, M., Gens, A., Guimarães, L. & Olivella, S. 2005. A double structure generalized plasticity model for expansive materials. Int. Jnl. Num. Anal. Meth. in Geom. 29: 751–787. Villar, M.V. & Gómez-Espina, R. 2006. Deliverable 3.2.9: Progress report on laboratory tests performed by CIEMAT (WP3.2 NF-PRO Report). Madrid. EC.
APPENDIX The BBM plastic potential (G) is expressed as:
REFERENCES
Alonso, E., Gens, A. & Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique, 40(3): 405–430. FEBEX Report. 2006. Full-scale Engineered Barriers Experiment. Updated Final Report 1994–2004. Publicación Técnica ENRESA 05-0/2006. 590 pp. Madrid.
G = α3J 2 −
g(θ) g(−30◦ )
2 M 2 (p + ps ) (p0 − p) = 0 (A1)
where α is determined according to Alonso et al. (1990). The dependence of the tensile strength on
672
suction and temperature is given by: ps = ks e−ρ T
(A2)
where k and ρ are model parameters. The dependence of p0 on suction is given by: p0 = pc
p∗0T pc
−κ λλ(0)−κ (s)
;
p∗0T = p∗0 + 2(α1 T + α3 T | T | )
(A3)
where pc is a reference stress, α1 and α3 are model parameters. λ(s) is the compressibility parameter for changes in net mean stress for virgin states of the soil; which depends on suction according to: λ(s) = λ(0) [r + (1 − r) exp (−ζ s)]
(A4)
where r is a parameter which defines the minimum soil compressibility. ζ is a parameter that controls the rate of decrease of soil compressibility with suction.
673
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Modelling water retention characteristic of unsaturated soils Y. Wang Institute for Materials Research, School of Computing, Science and Engineering, University of Salford, Manchester, UK
G. Wu Department of Civil Engineering, Shanghai Jiao Tong University, Shanghai, P.R. China
S.M. Grove Advanced Composites Manufacture Centre, School of Engineering, University of Plymouth, Plymouth, UK
M.G. Anderson School of Geographical Sciences, University of Bristol, Bristol, UK
ABSTRACT: The water retention characteristic or Water Retention Curve (WRC) is an important constitutive feature of soils. Previous experiments have indicated that specific surface area has effects on the WRC. It has also been observed that a linear relationship generally exists between the air-water interface area and the pore saturation in unsaturated soils. However it seems that no study on their internal linkage with the WRC has been reported yet. This paper tries to explain the water retention curve according to the physical and chemical behaviours of the phases involved in unsaturated soils. Using the capillary, interfacial surface theories and averaging theorem, a deterministic formula which represents the water retention characteristic is derived. This formula demonstrates the internal linkage of the WRC to the specific surface area of porosities. It shows agreement with experimental observations. Based on this formula, a fitting model is proposed for the WRC of soils. Finally, this model is tested to fit the WRCs of a wide range of soils, and compared with other main models. 1
INTRODUCTION
The water retention characteristic or water retention curve (WRC) is an important constitutive feature of soils. It is an indispensable requirement in hydraulic transport modelling. Due to its great interest, a large number of research studies have been conducted and many models were proposed for the WRCs of soils. In general, these models could be classified into two groups, they are: the phenomenological or empirical models, and the conceptual or physical models. In the first group, van Genuchten’s model (van Genuchten 1980) could be the most popular one. But previous practice has shown it usually fails at low water content (Ippisch et al. 2006). Most conceptual models use a bundle of cylindrical capillaries (BCC) to represent the pore space geometry. They assume that the soil particle size distribution (PSD) due to the fragmentation processes decides the void/pore size distribution (VSD). It is the VSD that decides the WRC according to Laplace’s equation in capillary law. Different PSD models have been proposed, including power
functions (Assouline et al. 1998), which has been backed by the single fractal models (Xu & Dong 2004), and log-normal functions according to the probability of fragmentation theory (Tuli et al. 2001, Hwang & Choi 2006). A key issue of these models is that the relationship between VSD and PSD is not determinate, which could be linear or nonlinear (Assouline et al. 1998). Recently, a liquid configuration-based model was proposed to take account of the effect of the adsorption of solid surface (Tuller et al. 1999). But it has been pointed out that its representative unit cell cannot generally represent the irregular pore space in actual soils (Chertkov 2004). Precisely, all of these preceding models were proposed to model the WRC under static conditions, which do not take account of dynamic effects, such as the fluid in flowing processes, the viscous and/or gravity effects (Beliaev & Hassanizadeh 2001). The dynamic effects on WRC are very important. Some researchers ever studied the dynamic capillary pressure according to the thermodynamic behaviour of the fluids in multiphase flowing processes within porous media (Gray
675
and Hassanizadeh 1998). This paper, however, still only discusses the WRC under static conditions. Previous experiments have shown that unsaturated soils present a linear relationship between air-water interfacial area and the pore saturation. Petersen et al. (1996) found that water retention characteristic was significantly connected with the specific surface area of the soil (Bachmann & van der Ploeg 2002). This paper tries to investigate the internal relations between the WRCs and these observations. A traditional BCC model is employed to represent capillary pore geometry, meanwhile interfacial surface theory is used to describe the individual behaviour of the coexisting water and vapour phases in unsaturated porous media. Finally volume averaging analysis generates a determinate formula for water retention characteristic. Based on the formula, a simplified WRC model is proposed. The model is tested on different soils and compared with other models. 2
THEORY
In unsaturated soils, the curved meniscus is only a small part of the water-vapour interface. Because, at the start of a wetting or the end of a draining process, a thin uniform water film which coats the whole pore surface has been formed, the water-vapour interfacial area should decrease with water content once the meniscus is formed, and becomes zero at full saturation (Costanza-Robinson & Brusseau 2002). Modern interfacial science suggests that surface forces modify the properties and chemical potential of the interfacial region relative to their free bulk phase values (Tuller et al. 1999). Due to their surface interactions with the solid phase, the water and vapour phases in unsaturated soils have their individual pressures. Under equilibrium, the pressure difference of the two phases is balanced by the capillary pressure due to the meniscus, which follows the Young-Laplace equation (Dullien 1991): Pc = Pw − Pv =
2σvs 2σws − r r
meniscus. In another word, it could be said that, under equilibrium, the position of the meniscus just balances the pressure difference between the water and vapour phases. It is this mechanism that decides the WRCs of soils. It has been suggested that the chemical potential change caused by surface adsorption can be evaluated using Kelvin’s equation (Tuller et al. 1999): uf = RT ln
(2)
where uf is the molar chemical potential change of the adsorbed fluid on the substrate surface; R is the gas constant; T is temperature; and P/P0 is the relative pressure of the equilibrium vapour surrounding the adsorbed fluid. According to the mechanical equilibrium, the absolute pressure of the adsorbed fluid equals to its surrounding vapour pressure plus the chemical potential change due to adsorption, i.e.: Pfad
uf uf = + P0 exp Vf RT
(3)
where Vf is the molar volume of the fluid; Logically, Eq. (3) is applicable to both water and vapour phases in unsaturated soils. When the atmospheric pressure is set as reference, the individual absolute pressures of the two phases can be expressed as: Pw =
uw uw + P0 exp Vw RT
uv uv Pv = + P0 exp Vv RT
(4a)
(4b)
where the subscript w and v indicate the water and vapour phases, respectively. Substituting Eq. (4) into (1) yields:
(1) Pc =
where Pc is the capillary pressure; Pw and Pv are the absolute pressures of the water and vapour phases, respectively; σws is the interfacial tension between water and solid phases; σvs is the interfacial tension due to the molecular interaction between vapour and solid phases via a thin intervening water film (Iwamatsu & Horii 1996); r is the local pore size at the position of meniscus. Eq. (1) could be understood to mean that the pressures of the water and vapour phase in unsaturated soils are caused by their respective interactions with the solid phase, and related to the position of the
P P0
uv uw uw uv − + P0 exp − P0 exp Vw RT Vv RT (5)
Eq. (5) describes the phase equilibrium at microscopic pore scale. Using volume averaging theorem the macroscopic average of Pc is defined as: Pc =
676
=
1 Vpore 1 Vpore
1 Pc dV Vpore
1 Vpore
uw uw dV + P0 exp Vw RT
uv uv dV + P0 exp Vpore Vpore Vv RT 1 1 uw uw = + P0 exp dV Vpore Vwater Vw RT 1 uv uv 1 + P0 exp dV − Vpore Vvapour Vv RT 1
1
−
to the bulk volume of the porous material), the molar chemical potential changes of the water and vapour phases in unsaturated soils can be related to the specific surface areas of the two distinctive parts which are occupied by the water and vapour phases, respectively, i.e.: (6) 2 s 3 e uw = Am w Vw s¯ ws + Aw Vw s¯ ws + Aw Vw s¯ ws
where Vpore represents the total pore volume with an representative elementary volume (REV) of porous media; Vwater is water volume; Vvapour is vapour volume. Because the discussion is under the assumption of static/equilibrium states, when the local Pw and Pv are either constant (an intrinsic phase average) at any place where they occupy, respectively, or zero otherwise, Eq. (6) can be further developed as:
uw uw ds + P0 exp Vw RT 0 1 1−S uv uv d(1 − s) + P0 exp − RT Vv 0
1 Pc =
S
uv =
1 Vpore 1 Vpore
1 uw dV
(8a)
Vwater
1
uv dV
(8b)
Vvapour
According to Iwamatsu and Horii (1996) and Tuller et al. (1999), the molar chemical potential of an adsorbed fluid is related to the fluid thickness h on the substrate surface, and consists of several components, i.e.: uf (h) = Vf m (h) + e (h) + s (h) + a (h)
+ Asv Vv s¯vs
(10a) (10b)
s¯ws =
Sws Vbulk S
(11a)
s¯vs =
Svs Vbulk (1 − S)
(11b)
where Sws is the water-solid interfacial area; Svs is the vapour-solid interfacial area; Vbulk is the bulk volume of the porous material. Because a thin water film intervenes between all of the vapour-solid interfaces, it can be approximated that Svs ∼ = Svw by ignoring the extremely small cross section of the throats which connect pores, where Svw is the vapour-water interfacial area. Published experiments (Karkare & Fort 1996, Kim & Rao 1997, Costanza-Robinson & Brusseau 2002) and modelling works (Cary 1994, Bradford & 1997, Nordhaug et al. 2003) have generally demonstrated a linear relationship between vapour-water interfacial area and water saturation degree in unsaturated soils, i.e.: Svs ∼ Svw = s¯ (1 − S) = Vbulk Vbulk
(9)
where m (h) originates from van der Waals molecular interaction which is proportional to 1/h3 ; e (h) is the electrostatic component proportional to 1/h2 ; s (h) is the structural component proportional to 1/h; a (h) is a component due to non-uniform concentrations in the film which will be ignored in the following discussion. Using a BCC geometric model, the thickness h of the adsorbed fluid could be understood as the radius of the representing capillary. Under the rule of the same in pore surface area, the BCC model could be further equivalent to a single capillary with a ‘hydraulic radius’ which is defined as the ratio of the pore volume to the pore surface area (Dullien 1991). Because ‘hydraulic radius’ is inversely proportional to ‘specific surface area’ (the ratio of pore surface area
2 + Aev Vv s¯vs
where the subscript w and v indicate the water and vapour phases, respectively; A is constant; V is molar volume; s¯ws is the specific surface area of the waterfilled part of porosity, and s¯vs is the specific surface area of the vapour filled part of porosity, they are defined as:
(7)
where S is water saturation, uw and uv are the intrinsic average molar chemical potential changes of the water and vapour phases due to the adsorption effect of pore surfaces, which is defined as: uw =
uv =
3 Am v Vv s¯ vs
(12)
where s¯ is the specific surface area of the bulk porous material, which is defined as: s¯ =
Svs + Sws Vbulk
(13)
Substituting Eq. (12) into (13) yields: Sws = s¯ S Vbulk
(14)
Substituting Eqs. (12) and (13) into (11) yields that s¯ws = s¯vs = s¯ . So Eq. (10) represents two constants
which depend on the specific surface area of a porosity.
677
As a result, Eq. (8) can be rewritten as: uw = uw0 + uw S
(15a)
uv = uv0 + uv (1 − S)
(15b)
where uw0 and uv0 are initial chemical potential changes due to the formation of an initial water molecular film on pore surfaces before water and vapour phases start to accumulate within pore spaces. Substituting Eq. (15) into (7), then the integral produces: ⎡ 0 ⎢ uw
Pc = ⎣
Vw
S+
uw 2 S 2Vw
+
P0 exp
0 uw RT
exp
uw RT
uw S RT
⎤
⎥ −1 ⎦
3
0 uv ⎢ u − ⎣ v (1 − S) + (1 − S)2 Vv 2Vv
P0 exp
uv0 RT
uv RT
⎤ uv (1 − S) ⎥ −1 ⎦ exp RT (16)
If we set: 0 2 uw uw ; Pw0 = P0 exp RT RT 02 uv uv ; Pv0 = P0 exp RT RT φ0 = −
Pc = φ0 + P0 exp(αSe ) − exp(β(1 − Se ))
uv0 uv − + Pv0 − Pw0 ; Vv 2Vv
φ1 =
uw0 uv0 uv + + ; Vv Vv Vw
φ2 =
uw uv uw uv − ; αw = ; αv = , 2Vw 2Vv RT RT
Eq. (16) can be written as: Pc = φ0 + φ1 S + φ2 S 2 + Pw0 exp(αw S) − Pv0 exp(αv (1 − S))
(18)
where φ0 , P0 , α and β are four redefined fitting parameters. In the following, Eq. (18) will be compared with other models to fit the measurements of the WRCs of a wide range of soils.
⎡
+
Se = (S − Sr )/(Ss − Sr ) due to inaccessible pore spaces, where Sr is the remaining saturation and Ss is the saturated saturation. All of the constants, φ0 , φ1 , φ2 , Pw0 , Pv0 , αw and αv , are related to the specific surface area of the porous material. However, Eq. (17) is not convenient in practice. There are too many parameters and they are related to each other. To overcome this disadvantage, we propose to use the following model to fit WRCs (a detailed discussion on the reason to choose such form will be discussed elsewhere (Wang et al. 2008)):
(17)
Theoretically, Eq. (17) represents the water retention characteristic of porous media. The saturation S need to be replaced using the effective saturation
EXAMPLES
Figure 1 shows the fitting results for five soil samples and the comparison with van Genuchten model. The fitting parameters are listed in Table 1. As we can see, good fitting results have been obtained by both models, but a further improvement at the two ends can be observed in the case of Beit Netofa Clay when using the proposed model. An inflection point is seen in most cases, except for Beit Netofa Clay. If the measurements of Beit Netofa Clay are carefully studied, it can be noticed that its WRC is not continuous but presents an irregular concave shape in the middle of the curve. This is similar to an experimental result of dual-porosity soils (Kohne & Gerke 2002). That means two differently scaled pore systems could co-exist in the Beit Netofa Clay at the same time, for example, the clay sample could have fractures (a structured porosity) within it. According to the dual-porosity theory, the two different porosities have different ‘specific surface area’, and as a result the two different porosities have their individual WRCs which could be fitted using Eq. (16), respectively. A detailed study on the application on the multiporosity problems is underway. Figure 2 shows a comparison with a fractal model which is in a power-law form. It can be seen that the proposed model presents a much better result, particularly relating to the shape of the WRC. It demonstrates an inflection point which is in agreement with the experimental measurements. Figure 3 shows a comparison with two lognormal PSD models which assume a linear and nonlinear relation between PSD and VSD, respectively. It can be seen that the proposed model is even better than the original nonlinear model in the two cases, in particular on
678
Table 1.
Fitting Parameters for the Soil Sample in Fig. 1.
Hygiene Sandstone Touchet Silt Loam Silt Loam Beit Netofa Clay Guelph Loam (drying)
φ0 (cm)
P0 (cm) α
β
−127.8
0.2289 5.07
5.715 0.15
−209.8 −255.5
0.2342 6.227 6.745 0.18 0.47 2.048 4.728 7.223 0.131 0.396
Sr
Ss 0.25
−5.375e-5 1489
0.13
−98.69
3.166 5.726 0.218 0.52
3.673
5.342 0.0
0.446
(a) Fitting results use the proposed model
(b) Original data and modelling Figure 2. 2004).
Figure 1.
WRCs for soils (van Genuchten 1980).
Comparison with a fractal model (Xu & Dong P.
the side of low saturation where the accuracy improvement is more significant. Because the pressure head is presented in lognormal form, the fitting improvement at the low saturation (high pressure head) side will enhance the total accuracy significantly. Figure 4 shows a comparison with the configurationbased unit cell model. It can be seen that the proposed
679
volume averaging theorem, generates a deterministic formula for the water retention characteristic of unsaturated porous media. This formula demonstrates the internal linkage between the WRCs and the ‘specific surface area’. Based on this formula, a simplified fitting model has been proposed for the WRCs. Compared with other main models, it has been shown that this model is more accurate, particularly at the side of low saturation or high pressure head.
REFERENCES
Figure 3. Comparison with a lognormal PSD model (Hwang & Choi 2006).
(a) Fitting results using the proposed model
(b) Original data and modelling
Figure 4. 2002).
Comparison with a unit cell model (Tuller & Or
model works very well on both of the soil samples. The fitted WRCs present a very good shape and accuracy against the measurements.
4
CONCLUSIONS
This paper tried to explain the water retention characteristic according to the physical and chemical behaviours of the phases involved. The analysis, which follows the capillary, interfacial surface theories and
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Kohne, J.M. & Gerke, H.H. 2002. Estimating the hydraulic functions of dual-permeability models from bulk soil data. Water Resources Research 38: 26.1–26.11. Nordhaug, H.F. Celia, M. & Dahle, H.K. 2003. A pore network model for calculation of interfacial velocities. Advances in Water Resources 26: 1061–1074. Petersen, L.W. Moldrup, P. Jacobsen, O.H. & Rolston, D.E. 1996. Relations between specific surface area and soil physical and chemical properties. Soil Science 161: 9–12. Tuli, A. Kosugi, K. & Hopmans, J.W. 2001. Simultaneous scaling of soil water retention and unsaturated hydraulic conductivity functions assuming lognormal pore-size distribution. Advances in Water Resources 24: 677–688. Tuller, M. & Or, D. 2002. Unsaturated hydraulic conductivity of structured porous media: A review of liquid configuration-based models. Vadose Zone Journal 1: 14–37.
Tuller, M. Or, D. & Dudley L.M. 1999. Adsorption and capillary condensation in porous media: Liquid retention and interfacial configuration in angular pores. Water Resources Research 35(7): 1949–1964. van Genuchten, M.T. 1980. A close-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Soc. Am. J. 44: 892–898. Wang, Y. Grove, S.M. & Anderson, M.G. 2008. A physicalchemical model for the static water retention characteristic of unsaturated porous media, Advances in Water Resources (in press). Xu, Y.F. & Dong, P. 2004. Fractal approach to hydraulic properties in unsaturated porous media. Chaos Solutions & Fractals 19: 327–337.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Temperature effect on hydric behaviour for unsaturated deformable soils S. Salager, M.S. El Youssoufi & C. Saix Laboratoire de Mécanique et Génie Civil, Université Montpellier 2, France
ABSTRACT: Considering an unsaturated soil with pure water, the suction can be expressed with respect to three independent variables: water content, void ratio, and temperature. From the expression of the total differential of the suction, we propose a constitutive relation which links variations of suction, water content, void ratio, and temperature. This relation allows the analysis of several particular cases. At constant temperature, this relation could be represented by a characteristic surface in the parameter space (water content, suction, void ratio). This surface, which reflects the hydro-mechanical couplings in soils, can be considered as a generalization of the classical Soil Water Characteristic Curve (SWCC). At constant suction, the constitutive relation allows to predict the water content variations due to temperature changes. Thus, from a SWCC obtained at a given temperature, the model can predict this curve for other temperatures. This model has been successfully tested by the authors on experiments performed on two different materials.
1
INTRODUCTION
The relationship between suction and soil water content is generally presented through the Soil Water Characteristic Curve (SWCC); it is a fundamental relation used to describe the hydric behaviour of unsaturated soils. The SWCC was widely studied during the last decades: (i) fitting equation (Fredlund and Xing 1994), (ii) influence of soil compaction conditions (Sugii et al. 2002); (Verbrugge and Fleureau 2001); (Tarantino and Tombolato 2005); (iii) hysteresis modelling (Pham et al. 2005) (iv) temperature influence (Salager et al. 2006). Most of these authors present the SWCC using the saturation degree or the water content, but despite void ratio measurements in some cases, very few models taking into account volume changes have been proposed (Gallipoli et al. 2003); (Salager 2007). In the thermo-hydro-mechanical framework, a complete characterization of the hydric behaviour needs to use more complex tools than SWCC to take into account hydro-mechanical and hydro-thermal couplings. In this respect, this paper presents the development of constitutive relations which lead to provide a basis for analyzing the hydric behaviour of soil in a thermo-hydro-mechanical framework. At constant temperature, the constitutive relations define the characteristic surface which reflects the hydric behaviour of a soil taking into account hydromechanical couplings. The equation of this surface has been established in the case of a clayey silty sand from 250 experimental measurements. At constant suction, the constitutive relations lead to a thermo-hydric
model allowing to predict the effect of temperature on the SWCC. This model has been successfully tested by the authors on experiments performed on two different materials.
2
CONSTITUTIVE RELATIONS
To describe the evolution of the thermodynamic state of an unsaturated soil, the most frequently used variables are volume strain εv = tr(ε), water content w and temperature T . The volume strain, as usually in soil mechanics, will be linked to the void ratio variations e through the relation e = −(1 + e0 )tr(ε). The water content w could be substituted by the water volume fraction θ, or the degree of saturation Sr . The evolution of the thermodynamic state of a partially saturated soil could be, consequently, described by means of one of the three following sets of state variables: − water volume fraction θ, temperature T and void ratio e, − water content w, temperature T and void ratio e, − degree of saturation Sr , temperature T and void ratio e. The following theoretical developments are based on the different expressions of the suction differential with respect to the three variables of each set proposed above. In addition, only monotonic drying hydric paths are considered, permitting thus to avoid hysteresis phenomena.
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Suction differential with respect to θ , T , e
2.1
The suction differential with respect to the set of variables θ , T , e can be written: ∂s ∂s ∂s dθ + dT + de (1) ds = ∂θ T ,e ∂T θ ,e ∂e θ ,T In addition, the water volume fraction can be written as a function of the density of the solid phase ρs , the density of the liquid phase ρe , the water content w, and the void ratio: ρs w ρe (1 + e)
θ=
(2)
By introducing the volumetric thermal expansion coefe ficient of water βe = − ρ1e dρ dT and of the solid phase s − ρ1s dρ dT , the infinitesimal variation of θ
βs = written : dθ =
could be
ρs w ρs dw + (βe − βs )dT ρe (1 + e) ρe (1 + e) ρs w de − ρe (1 + e)2
(3)
Equation (2) also allows to write:
∂s ∂θ
ρe (1 + e) ρs
= T ,e
∂s ∂w
2σs cos φ r
∂s ∂T
θ ,e
=
(5)
∂φ ∂σs − s tan φ ∂T θ ,e ∂T θ ,e s ∂r − r ∂T θ ,e s σs
(6)
The surface tension of pure water depends mainly on the temperature. Thus, it comes:
∂σs ∂T
θ ,e
=
dσs dT
By introducing equations (3), (4) and (9) in equation (1), the final form of the suction differential is obtained: ∂s dw ds = ∂w T ,e s dσs dφ ∂s w(βe −βs )+ −s tan φ dT + ∂w T ,e σs dT dT ∂s w ∂s de (10) − + ∂e θ,T ∂w T ,e (1 + e) 2.2
Equation 5 allows to write :
The last term of equation (6) is the variation of the mean pore radius due to the temperature. The water volume fraction and the void ratio remaining constant, this term is equal to zero. Finally, equation (6) is reduced to: dφ s dσs ∂s − s tan φ (9) = ∂T θ,e σs dT dT
(4) T ,e
In pendular and funicular domains, water is in a capillary state, it is so justified to use Jurin’s law. This law expresses the suction s as a function of the surface tension of water σs , the mean pore radius r, and the contact angle φ. s=
the lack of information available in literature on this parameter, it is assumed that the contact angle is only a function of the temperature. This leads to: ∂φ dφ (8) = ∂T θ,e dT
(7)
The contact angle depends mainly on surface roughness of solid phase, temperature, and meaning evolution of the hydric state (wetting or drying). Given
Suction differential with respect to w, T , e and with respect to Sr , T , e
In the same way, the suction differential could be expressed with respect to the set of variables w, T , e: ∂s dw ds = ∂w T ,e dφ s ∂r s dσs − s tan φ − dT + σs dT dT r ∂T w,e ∂s de (11) + ∂e w,T and with respect to the set of variables Sr , T , e. The final form obtained is always written with the same set of variables than equations (10) and (11): ∂s dw ds = ∂w T ,e dφ s ∂r s dσs − s tan φ − dT + σs dT dT r ∂T w,e ∂s w ∂s de (12) − + ∂e Sr ,T ∂w T ,e e
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2.3
One can introduce in the three final equations obtained from each of the three previous developments the notations below: ∂s ∂s ; FT = ; Fw = ∂w T ,e ∂T w,e ∂s (13) Fe = ∂e T ,w
1. Fw =
∂s ∂w
(14) T ,e
Fw is a function associated with the suction variation due to the water content variation at constant temperature and void ratio. For an undeformable media, this term is the inverse of the SWCC slope. This function is negative because an increase of water content induces a decrease of suction. 2. FT = Fw w(βe − βs ) +
dφ s dσs − s tan φ σs dT dT
dφ s s dσs FT = − s tan φ − σs dT dT r
∂r ∂T
(15)
∂r ∂T
∂s ∂e
w Fe = − Fw (1 + e) θ,T w ∂s = − Fw e ∂e Sr ,T
=
∂s ∂e
T ,w
(18)
The sets of variables which involves the water content w is certainly the most appropriate for a comparison with experimental results. It is in connection with the easy determination of w which requires only mass measurements, in opposition to water volume fraction θ and degree of saturation Sr which require volume measurements. Nevertheless, ∂r one can note the ∂s difficulty to access the terms ∂T and ∂e . w,e θ,T Consequently to these two reasons, the following final form will be retained for the suction differential expression: ds = Fw dw dφ s dσs − s tan φ dT + Fw w(βe − βs ) + σs dT dT + Fe de
(16) w,e
= Fw w(βe − βs )
One can deduce from equations (15) and (16), a relation which links the volumetric thermal expansion coefficients of water and solid phase to meniscus radius as well as its variation with temperature. s r
3.
Fe is the function associated with the suction variation due to the void ratio variation at constant temperature and water content.
The identification between these three equations (equations (10),(11), and (12)) leads to make explicit the state functions Fw , FT , and Fe .
−
angle variation at constant water content and void ratio.
Parallel between the three developments
(17)
w,e
From the equation (15), one can also define three functions: − FT β = Fw w (βe − βs ) : which is the function associated with the suction variation due to the thermal expansion of liquid and solid phases at constant water content and void ratio, s − FT σ = σss dσ dT : which is the function associated with the suction variation due to surface tension variation at constant water content and void ratio, − FT φ = −s tan φ dφ dT : which is the function associated with the suction variation due to contact
(19)
Equation (19) defines an expression of the thermodynamic state evolution which links suction, water content, temperature, and void ratio variations in the general case. This expression will be used in the following in different particular cases. 2.4 Analysis of elementary cases Relation (19) can be used in the analysis of some elementary cases. This analysis, which allows the consistency of the proposed expression to be confirm, is based on the negative or positive sign of the three functions Fw , FT and Fe . Accounting for the SWCC shape, the function Fw is negative. The derivative of the surface tension with respect to temperature is negative, and therefore the function FT is negative. To determine the variation of the function Fe , in a first approximation, one can consider a physical model composed by two grains linked by a water meniscus. This function is determined at constant water content and temperature. The meniscus water volume is constant. If the grains are pulled aside to increase the void ratio, the meniscus hollow increases leading a decrease of the radius of curvature, and using the Jurin’s law, an increase of suction. Function Fe appears to be positive. Of course
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a variation of void ratio induces in the soil more complex phenomena but the characteristic surface that will be presented later confirms the results obtains with this simple physical model. Six cases where two of the four variables s, T , w, and e remain constant are presented here: – Case 1, e and T constant: in this case, equation (19) comes ds = Fw dw. Allowing that the function Fw is negative, a water content increase leads to a suction decrease. This is a classical result on the variations of water content and suction in the case of SWCC. – Case 2, w and T constant: in this case, it comes ds = Fe de. The function Fe is positive, and therefore void ratio increase leads to a suction increase. This result is also consistent because a void ratio increase at constant water content leads to a decrease of the degree of saturation Sr = Gs we and consequently a suction increase. – Case 3, e and w constant: in this case, it comes ds = FT dT . The function FT being negative, a temperature increase leads to a suction decrease. This means that the temperature and suction vary in opposite directions if the other variables are held constant. – Case 4, s and T constant: in this case, it comes Fw dw + Fe de = 0. The function Fw being negative and Fe positive, it is possible to infer that the void ratio and the water content vary in the same direction if the other variables remain constant. It means that a void ratio increase should be concomitant with a water content increase and vice versa. – Case 5, e and s constant: in this case, it comes Fw dw + FT dT = 0. The functions being negative, it is possible to infer that a temperature increase should be concomitant with a water content decrease if the other variables remain constant. – Case 6, w and s constant: in this case, it comes Fe de + FT dT = 0. The function Fe being positive and FT negative, it is possible to conclude that void ratio and temperature vary in the same direction; it means that a temperature increase should be concomitant with a void ratio increase if the other variables remain constant.
3
CONCEPT OF CHARACTERISTIC SURFACE
function could be represented by a surface in the space defined by the three variables. This surface which gives the retention capacity of the soil for any void ratio value could be named the Soil Water Characteristic Surface (SWCS). This surface has been established on a clayey silty sand in the case of monotonic drying hydric paths. This soil is classified as SC-CL according to the USCS. The liquid and plastic limits are respectively 25% and 14.5%. Sand, silt, and clay fraction are 72%, 18%, and 10% respectively. The clay fraction consists mainly of smectite, chlorite, and phyllite. Triplets (s, w, e) have been measured all along five drying paths corresponding to five initial void ratios. Each of these paths leads to 16 or 18 measurements (s, w, e). Each measurement itself is the average of the measurements done on three samples. Thus, the whole measurements are related to a total of 150 samples. These experimental results can be fitted to an analytical form of the characteristic surface which can be written (Salager et al. 2007): if w ≤ e/Gs ⇒ f = w − a · e − b · (1 − a · Gs ) = 0 e =0 (21) if w ≥ e/Gs ⇒ f = w − Gs where a and b are characteristic functions of the soil which depend on suction (a = a(s) and b = b(s)). These functions could be modeled by means of relations derived from the following expression (Fredlund and Xing 1994): ⎞ ln 1 + ssr x(0) ⎠ x(s) = ⎝1 − n m 106 ln 1 + sr ln exp(1) + ss ⎛
i
(22) where x(0) is the value of the function at saturation, sr , si , n and m are parameters adjusted from experimental results. The characteristic surface of the clayey silty sand is given in figure 1. The characteristic surface equation allows to proposed explicit expressions of the functions Fw and Fe : Fw =
At constant temperature, equation (19) leads to: ds = Fw dw + Fe de
(20)
This equation shows, that at a temperature T0 , there exists a function f which links the variations of suction, water content, and void ratio: f (s, w, e) = 0. This
Fe =
1 ∂a ∂s ∂a ∂s
(e − bGs ) + w a
−
b a
∂b ∂s
(1 − aGs )
−a +
∂b ∂s
(1 − aGs )
(23) (24)
Figure 2 represents the function Fw with respect to suction and void ratio; Figure 3 represents the function Fe with respect to suction and water content.
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To extract an equation of thermo-hydric evolution from the equation 19, one can consider, in the case of hydric loading path, a specified suction (s = cst, ds = 0). During a thermo-hydric process, the void ratio varies with suction and temperature. But it is already established that temperature has only a negligible effect on void ratio, compared to the suction effect (Francois et al 2007). In this case, specifying a suction implies specifying the void ratio too. In this condition, equation (19) could be reduced to a relation between water content and temperature variations. dw = − Figure 1.
Characteristic surface of the clayey silty sand.
FT dT Fw
(25)
In addition, there are few literature results concerning contact angle but it is known that, in natural soil, this angle and its variation versus temperature are very limited (Bachmann et al. 2000). Thus, it will not be taken into account. Futhermore, the volumetric thermal expansion coefficient of the solid phase is supposed to be negligible, compared with volumetric thermal expansion coefficient of water. It comes a simplified expression of the function FT and the explicit expression of the equation of thermo-hydric evolution could be written:
Figure 2. Fw evolution versus suction for different void ratios.
Figure 3. Fe evolution versus suction for different water contents.
4
PREDICTIVE EQUATION FOR TEMPERATURE EFFECT ON SWCC
Several mechanisms can be proposed to explain the influence of temperature on the unsaturated soil hydric behaviour: thermal expansion of liquid and solid phases, surface tension of water, and contact angle variations (Bachmann and van der Ploeg 2002). The equation of the thermodynamic state evolution (19) takes into account all these phenomena.
s dσs dw = − wβe + Fw σs dT
dT
(26)
βe and σs are water characteristics. Consequently, the equation of thermo-hydric evolution (26) needs only the knowledge of the function Fw . In the case of undeformable media, this function simply correspond to the inverse of the slope of the SWCC obtained at a reference temperature. In the general case, Fw depends on the suction and the void ratio. Consequently, its determination needs the knowledge of the derivative of the suction with respect to water content for each void ratio value. In this case, a reference SWCC is not sufficient. The approriate tool is the SWCS (Salager et al. 2007). The first media used to test the validity of the equation of thermo-hydric evolution is a ceramic. Its SWCC has been determinated experimentally for two temperature: 20 and 60◦ C. The SWCC obtained at 20◦ C is taken as reference. The function Fw is calculated from this curve. Using this function, equation (26) allows to predict the SWCC at 60◦ C. Figure 4 shows the SWCC obtained for the ceramic. The solid line represents the results corresponding to 20◦ C and the dashed line reprensents the ones corresponding to 60◦ C. These curves are modelled from experimental data using the fitting function of Fredlund and Xing (Fredlund and Xing 1994). The line with circle represents the SWCC corresponding to 60◦ C calculated
687
5
Figure 4. SWCC for the ceramic; experiments and modelling.
CONCLUSIONS
This paper proposed a constitutive relation which leads to a basis for the analyzis of the hydric behaviour of soil in a thermo-hydro-mechanical framework. In particular, this relation introduces the concept of soil water characteristic surface which appears to be relevant to model volume changes in deformable unsaturated soils. An example of soil water characteristic surface was presented in the case of monotonic drying paths for a clayey silty sand. This relation makes it possible to define a predictive equation on temperature effect on SWCC. This equation has been tested with success on two materials. REFERENCES
Figure 5. SWCC for the clayey silty sand; experiments and modelling.
from the predictive model. In spite of a little deviation around the slope changing of the curve, the results coming from the experiments and from the model are in good agreement for this material and validate the predictive function (26) for undeformable media. Like it has been done for the ceramic, two series of tests have been performed to determine the SWCC corresponding to 20 and 60◦ C of the clayey silty sand. This soil is deformable under hydric loading. Consequently, hydro-mecanical couplings have to be taken into account. The function Fw is calculated from its SWCS established beforehand and presented in Figure 1. Figure 5 shows the SWCC obtained for the clayey silty sand. The graphic guidelines is the same as for the ceramic. Concerning low suctions, the predictive model overestimates the temperature effect. However, for the rest of the suction range, the predictive model permits a good prediction of the SWCC at 60◦ C. This result validates the predictive function (26) for deformable media.
Bachmann, J., R. Horton, R. van der Ploeg, and S. Woche (2000). Modified sessile drop method for assessing initial soil-water contact angle of sandy soil. Soil Science Society of America Journal 64, 564–567. Bachmann, J. and R. van der Ploeg (2001). A review on recent developments in soil water retention theory: interfacial tension and temperature effects. Journal of Plant Nutrition Soil Science 165, 468–478. Francois, B., S. Salager, M. El Youssoufi, D. Ubals Picanyol, L. Laloui, and C. Saix (2007). Compression tests on a sandy silt at different suction and temperature level. In CDrom, 10 pages, Denver. GeoDenver. Fredlund, D. and A. Xing (1994). Equations for the soil-water characteristic curve. Canadian Geotechnical Journal 31(3), 521–532. Gallipoli, D., S. Wheeler, and M. Karstunen (2003). Modelling the variation of degree of saturation in a deformable unsaturated soil. Geotechnique 53(1), 105–112. Pham, H., Fredlund, D. and Barbour, S. (2005). A study of hysteresis models for soil-water characteristic curves. Canadian Geotechnical Journal 42, 1548–1568. Salager, S. (2007). Etude de la rétention déau et de la consolidation des sols dans un cadre thermo-hydro-mécanique. Ph. D. thesis, Université Montpellier 2. Salager, S., M. El Youssoufi, and C. Saix (2007). Experimental study of the water retention curve as a function of void ratio. In CDrom, Denver, pp. 10. GeoDenver. Salager, S., F. Jamin, M. El Youssoufi, and C. Saix (2006). Influence de la température sur la courbe de rétention d’eau. C.R. Mécanique 334, 393–398. Sugii, T., K. Yamada, and T. Kondou (2002). Relationship between soil-water characteristic curve and void ratio. Volume 1, pp. 209–214. 3rd International Conference on Unsaturated Soils: Swets and Zeitlinger. Tarantino, A. and S. Tombolato (2005). Coupling of hydraulic and mechanical behaviour in unsaturated compacted clay. Geotechnique 55(4), 307–317. Verbrugge, J. and J. Fleureau (2002). Bases expérimentales du comportement des sols non satur´es. In O. Coussy and J. Fleureau (Eds.), Mécanique des sols non saturés, pp. 69–112. Hermes.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A study of applied pressure on the Soil Water Characteristic Curve J. Zhou Geotechnical Engineering Institute, Civil Engineering Department, Zhejiang University, China
ABSTRACT: In order to study the influence of applied pressure on the Soil Water Characteristic Curve (SWCC), samples with different initial void ratio/density were tested in a triaxial apparatus for unsaturated soil. This paper focuses on the influence of pressure on SWCC and hydraulic hysteresis by analyzing the data reported in the literature. Results show that the higher the pressure, the higher the saturation and the air-entry value. The size of hysteresis loop becomes smaller with the applied pressure, which indicates that the effect of hydraulic hysteresis on soil behavior gets smaller. Based on the study, the SWCC under different applied pressure can be easily modeled since the same mathematical expression can be used due to little change in the shape. The findings described in this paper can also be used as a proof of coupled effect of pressure and suction.
1
INTRODUCTION
The soil-water characteristic curve (SWCC) plays a very important role in the behaviour of partially saturated soils. A number of properties of a partially saturated soil can be obtained from the SWCC, such as the coefficient of permeability, shear strength and volume strain, pore size distribution, the amount of water contained in the pores at any suction. Due to the enormous potential in application, many researchers have proposed general mathematical expressions for SWCC, which suit various soil types and have only a few parameters with clear physical meaning. Models such as that of Gardner (1956), Brooks & Corey (1964), Brutsaert (1966), van Genuchten (1980), McKee & Bumb (1987), Burdine (1953), Mualem (1976), Kosugi (1994), Fredlund & Xing (1994) are widely used. However, studies on this subject are still carried out, because various factors influencing the SWCC have not received much attention. Of those the applied pressure is a crucial one. In the field, due to its depositional history, soil normally experiences a certain stress, which is recognized to have some influence on SWCC (Fredlund & Rahardjo, 1993). The suction probe and the filter paper technique are often used for determining a SWCC from unconfined soil samples. Models based on these techniques cannot consider the effect of applied pressure. However, preparing sample with different initial void ratio/density or using modified triaxial tests can be an alternative method. In fact it is neither possible nor necessary to conduct tests under every condition, since tests of SWCC are very time-consuming. Regarding this, it is meaningful and worthwhile to study
the effect of applied pressures on SWCC through the existing data. Hydraulic hysteresis is a significant characteristic for partially saturated soil. When a soil is saturated or de-saturated, the corresponding soil water characteristic curve is different. This means that there is two different degrees of saturation corresponding to the same predetermined suction; one is on the drying path and the other on the wetting path. How the pressure affects hydraulic hysteresis is considered, as well as its influence on a single drying/wetting curve. A modified mathematical expression is proposed to easily simulate SWCC under different pressures. 2
EFFECT ON A SINGLE DRYING/WETTING CURVE
As mentioned before, many current techniques for determining SWCC are incapable of applying vertical pressure on unsaturated soil. Some alternative methods can be used; among which preparing specimen with different initial void ratio is one of the indirect ways. 2.1
Effect of initial void ratio
Kawai et al. (2000) used a silty clay to study the effect of initial void ratio on the SWCC by oedometer apparatus, in which suction was applied by means of pressure plate method. How air-entry value (AEV) changes with void ratio is shown in Fig. 1. The AEV (denoted SA in Fig. 1) reflects the magnitude of the capillary saturation zone in a soil. The larger the bulk pore sizes, the smaller the AEV. It can be seen that the smaller the
689
Figure 3. Soil-water characteristics for specimens compacted at optimum water content (Vanapalli, Fredlund & Pufahl, 1999).
Figure 1. Relationship between void ratio and AEV (Kawai et al., 2000).
the results of two series of samples, namely 7–10 and 5–10. The properties of the samples and the test procedures can be referred to the original thesis. All the samples in each series have nearly the same moisture content, but different void ratio, as shown in the legend in Fig. 2. It is clear from the test results in Fig. 2 that, as the void ratio becomes smaller, the hysteresis loops tend to move to higher suctions on the Sr -suction plot. This indicates the hysteresis loops should be dependent on void ratio. 2.2 Effect of stress state
Figure 2. SWCC for series 7–10 and 5–10 during first drying and wetting (Jotisankasa, 2005).
initial void ratio (i.e. the denser the soil), the higher the air-entry value, and the higher the residual degree of saturation as well. The air-entry value and the residual degree of saturation Sr0 can be expressed in terms of void ratio e using empirical relationships. The AEV is an important parameter for partially saturated soils since the degree of saturation starts to drop rapidly when the suction exceeds the AEV. There is a large range of AEVs corresponding to different void ratio values, as shown in Fig. 1. The denser the soil the higher the AEV, which implies that for soils with low void ratio values, if only small changes in degree of saturation occurred at low suctions, the soil can be simplified as fully saturated. This is a helpful assumption when dealing with soils from different depths. Jotisankasa (2005) also investigated the influence of initial void ratio on SWCC. The soil was artificial silty clay compacted dry of optimum. Fig. 2 shows
Vanapalli et al. (1996; 1998 and 1999) studied the influence of total stress state on the SWCC of a compacted fine-grained soil indirectly by pressure plate apparatus. The concept of equivalent pressure was used to represent different stress state. The SWCCs for the specimens compacted at optimum water content and with equivalent pressures of 25, 35, 80 and 200 kPa are shown in Fig. 3. It clearly shows that the air-entry value of specimens increases with increasing equivalent pressure. Specimens subjected to higher equivalent pressure correspond to higher saturation. The same conclusion can be drawn from the results of different equivalent pressures dry of optimum water content and wet of optimum water contents. So as the pressure increases, SWCCs move towards the right hand side with an increased value of AEV (the air-entry value).
3
EFFECT ON HYDRAULIC HYSTERESIS
In the constitutive model considering hydraulic hysteresis proposed by Wheeler et al. (2003), the coupled effect of stress and hydraulic hysteresis was simplified, as shown in Fig. 4. The increased plastic volume strain,
690
Figure 6. Figure 4. Influence of plastic volumetric strain on primary drying and primary wetting curve (Wheeler et al., 2003).
0.44
0.42
Volumetric water content
0.40
0.38
0.36
CDV-N1 (0kPa) CDV-N2 (40kPa)
0.34
CDV-N3 (80kPa)
0.32
0.30 0.1
Figure 5.
1
10 Matric suction (kPa)
100
1000
Effect of stress state on SWCCs (Ng et al., 2000b).
which was induced by stress, caused the primary drying and wetting curves to shift from the position shown by the solid lines to that of chain-dotted lines. In other words, the soil subjected to higher stresses will have higher saturation. But no detail was presented about how the stress influences the hysteresis loop itself, i.e. will the loop change its size when subjected to different stress. To investigate this phenomenon, Ng and Pang (2000) studied the influence of stress state on the SWCC of an ‘‘undisturbed’’ or natural, completely decomposed volcanic soil. A conventional volumetric pressure plate extractor and a modified one were used together. The SWCCs under different net normal stress from their research are shown in Fig. 5. It can be seen that soil specimens loaded to higher net normal stress exhibit lower initial volumetric water contents. The result implies that as matric suction increases, the volumetric water content of the specimen decreases, but at a different rate. The higher the
Results of bentonite/kaolin (Sharma, 1998).
applied load, the lower the rate of reduction in volumetric water content. In the end all three wetting curves shift to the positions lower than the original. Fig. 5 also shows that the size of these loops becomes smaller with stresses. The point where the volumetric water content starts to decrease significantly indicates the air-entry value. A general tendency that soil specimens subjected to higher stress exhibits higher air-entry values, which is related to the presence of a smaller average pore sizes distribution in soil specimens under higher load, can be observed. Testing data reveal that stress history or applied stresses seem to have little effect on the shape of SWCC. This is good news for mathematical modeling. Sharma (1998) conducted suction tests on bentonite/kaolin samples with the same maximum suction 400 kPa under different compaction pressures of 400 kPa, 800 kPa and 3200 kPa. Results are shown in Fig. 6. Results demonstrate that with the increase of the compaction pressure, the size of hysteresis loop gets smaller. Since the sample is expansive soil, its behavior is expected to be a little different from nonexpansive soil. However the general tendency shows that the degree of saturation gets higher with pressure. This conclusion agrees with what Vanapalli et al. (1999) gained for a single drying/wetting path and Ng et al. (2000b) for drying-wetting cycle. 4
MATHEMATICAL EXPRESSION
From the above results, the shape of SWCC can be assumed not significantly affected by pressure. Hence the same mathematical expression for zero pressure can be chosen while using different parameters. For example if using the van Genuchten model, a different set of parameters can be used for the drying curve and the wetting curve to simulate hydraulic hysteresis. If considering the effect of pressure on SWCC, a simple modification can be made by either relating
691
Figure 7. SWCC changing with applied pressure (only m changing with pressure).
the m parameter, or m and a parameters to the pressure, while keeping the remnant unchanged, since m is related to the asymmetry of the curve and a shifts the curve towards the higher or lower suction regions of the plot, but does not affect the curve shape. If only considering the m parameter changing with pressure, the following modification can be used: m = m[(1 − r) exp(−βp) + r]
(1)
where m is the original parameter in van Genuchten’s model and m is the modified parameter. r and β are best-fitting parameters for a certain soil. p is the applied pressure. Assuming m = 1, n = 1.5, a = 0.00013, r = 0.26 and β = 0.0164 and only considering modified parameter m changing with pressure, results in Fig. 7 show that the influence of pressure is significant at lower values and becomes smaller at higher values. At lower pressure values the gradient of the change in degree of saturation is significant, while it reduces with the increase of pressure. The air-entry value is increased with pressure. This is consistent with what was observed for non-expansive soils. As for expansive soil, different modifications may be preferred since the soil behaves in a different way. In modeling hydraulic hysteresis, parameters in two sets (one for drying curve and another for wetting curve) both need to be modified. Following the same concept, other models can also be modified. 5
Figure 8. Illustration of SWCC changing with different applied pressure.
change, as illustrated in Fig. 8. With the increase of applied pressures, a) the size of the hysteresis loop becomes smaller; b) the slope of SWCC becomes flatter; c) the degree of saturation gets higher. Results here clearly demonstrate that the coupled movement of SWCC and the volumetric stain, shown in Fig. 4, need to be modified. The shape of SWCC is not strongly influenced by the applied pressure, so the same mathematical expression can be applied after modifying the parameters. This provides a convenient way for modeling. A simple expression of relating m parameter with applied pressure by using van Genuchten’s model is presented. More tests on different soils and with large stress range are necessary. Further numerical analyses to verify the conclusions are also needed. Conclusions obtained in this paper are not only useful for mathematical modeling of SWCC under different pressure, but also helpful for the validation of coupled effect of suction and applied pressure when dealing with hydraulic hysteresis in constitutive modeling.
ACKNOWLEDGEMENTS Financial support from China Scholarship Council through Grant No.22833012 and from Chinese Education Ministry for overseas scholars is gratefully acknowledged. The author also acknowledges the New Star Project of Zhejiang University for its support, as well as the support and help from the host Imperial College, London, and in particular Prof. David M. Potts & Dr. Lidija Zdravkovic.
CONCLUSIONS
The influence of applied pressure on SWCC was investigated from existing published data. Single drying/wetting curves and hysteresis loops were both studied. It can be seen that a higher pressure leads to a high air-entry value and a high degree of saturation. When applying different pressures p1 , p2 and p3 , the primary drying and wetting curves will shift and
REFERENCES Brooks, R. & Corey, A. 1964. Hydraulic Properties of Porous Media, Hydrology Paper No.3. Colorado State University, Fort Collins, CO. Brutsaert, W. 1966. Probability laws for pore size distribution. Soil Science, 101:85–92.
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Fredlund, D.G. & Rahardjo, H. 1993. Soil Mechanics for Unsaturated Soils. New York: Wiley. Fredlund, D.G. & Xing, A. 1994. Equations for the soil-water characteristic curve. Canadian Geotechnical Journal 31: 521–532. Gardner, W. 1956. Mathematics of isothermal water condition in unsaturated Soils. Highway research board special report 40 international symposium on physico-chemical phenomenon in soils: 78–87. Washington D.C. Jotisankasa, A. 2005. Collapse behaviour of a compacted silty clay. PhD thesis, Imperial college, London. Kawai, K., Karube, D. & Kato, S. 2000. The model of water retention curve considering effects of void ratio. In: Rahardjo, H., Toll, D.G. & Leong, E.C. (Eds.), Unsaturated Soils for Asia: 329–334. Rotterdam: Balkema. McKee, C. & Bumb, A. 1987. Flow-testing coalbed methane production wells in the presence of water and gas. SPE Formation Evaluation 10: 599–608. Mualem, Y. 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research 12: 593–622. Ng, C.W.W. & Pang, Y.W. 2000. Influence of stress state on soil-water characteristics and slope stability. Journal of Geotechnical and Geoenvironmental Engineering 126 (2): 157–166.
Sillers, W.S., Fredlund, D.G. & Zakerzadeh, N. 2001, Mathematical attributes of some soil-water characteristic curve models. Geotechnical and Geological Engineering 19: 243–283. Vanapalli, S.K., Fredlund, D.G., Pufahl, D.E. & Clifton, A.W. 1996. Model for the prediction of shear strength with respect to soil suction. Canadian Geotechnical Journal 33: 379–392. Vanapalli, S.K., Pufahl, D.E. & Fredlund, D.G. 1998. The meaning and relevance of residual water content to unsaturated soils. Proceedings of 51st Canadian Geotechnical Conference: 101–108, Edmonton, AB. Vanapalli, S.K., Pufahl, D.E. & Fredlund, D.G. 1999. The influence of soil structure and stress history on the soilwater characteristic of a compacted till. Geotechnique 49 (2): 143–159. van Genuchten, M.T. 1980. A closed form equation predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44: 892–898. Wheeler, S.J., Sharama, R.J. & Buisson, M.S.R. 2003. Coupling of hydraulic hysteresis and stress-strain behavior in unsaturated soils. Geotechnique 53(1): 41–54.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Outline of the modelling of the excavated damaged zone in geological barriers C. Arson CERMES, Ecole Nationale des Ponts et Chaussées, France
B. Gatmiri University of Tehran, Tehran, Iran CERMES, Ecole Nationale des Ponts et Chaussées, France
ABSTRACT: This paper deals with the modelling of the massif neighbouring a nuclear waste repository before waste disposal. The main features of micromechanical and phenomenological damage modelling are reviewed. Flow computation tools provided by fracture network representations are also presented. A mixed damage model is developed for unsaturated porous media in isothermal conditions. It is formulated in independent state variables (net stress and suction), in order to be implemented in -Stock finite element software. 1
INTRODUCTION
Damage in unsaturated media is generally tackled either through purely mechanical theories or merely hydraulic flow representations. In the unsaturated Excavation Damaged Zone (EDZ) surrounding an empty nuclear waste repository, suction effects are combined with mechanical loading and fracturing. This induces complex coupled behaviour laws. It is thus necessary to combine Continuum Damage Mechanics concepts and fracture flow data in order to achieve a good representation of the EDZ. A relevant mechanical damage model has to be extended from dry to unsaturated materials, and damage has to be introduced in the formulas quantifying the flow in a porous medium. Firstly, the principles of micromechanical and phenomenological damage theories are reviewed. Secondly, the main highlights provided by hydraulic flow models are presented. Lastly, a damage model is proposed to extend the model of unsaturated soil programmed in -Stock software (Gatmiri 1997, Jenab-Vossoughi 2000) to fractured unsaturated porous materials.
2 2.1
is assumed that stresses are redistributed due to a decrease of the effective material area. Stress-strain relationships are thus written in terms of effective (or damaged) variables. The stress that develops in the fictive undamaged counterpart of the system is named the damaged stress σˆ , and is usually defined by means of a specific damaged stress operator M( ): σˆ = M( ) : σ
(1)
where is the damage variable, which may be a tensor. The damaged stress concept is often combined to the Principle of Equivalent Elastic Energy (PEEE) to compute the damaged rigidity tensor De ( ). As recalled in Hansen & Schreyer (1994), this approach consists in postulating that the elastic energy of the intact material submitted to the damaged stress σˆ is equal to the elastic energy of the damaged material submitted to the real stress σ : We (σˆ , = 0) = We (σ , )
(2)
which results in:
CONTINUUM-BASED DAMAGE THEORIES
De ( ) = M( )−1 : D0e : M( )−T
Micromechanical concepts
Micromechanical damage theories consist in modelling the influence of local damage on the macro-mechanical behaviour. Damage variables have a physical meaning related to the degradation of elastic properties or to the characteristics of the fracture network. It
(3)
D0e denotes the intact rigidity tensor. The definition of a damaged stress provides a framework to determine the damaged mechanical properties of the material.
695
However, damage remains an abstract notion, represented by its influence on behaviour laws. That is why in some models, damage is also given a physical meaning, generally related to fracturing. Cracks of close orientations are often gathered in ‘‘families’’ (Swoboda & Yang, 1999, Shao et al., 2005a). Supposing for example that the material is fractured in three principal directions, ni , the damage variable can be written as a diagonal tensor whose eigenvalues di represent crack densities: 3
=
di ni ⊗ ni
(4)
i=1
Adopting the definition 4 implies that damage can be quantified by three fictive homogenized fractures characterized by a normal vector ni and a relative volume di . 2.2 Phenomenological frames Energy considerations are particularly suited to model dissipative phenomena such as damage and plasticity. Thermodynamic potentials are given specific forms. The resolution of the problem of maximum dissipation makes it possible to deduce the behaviour, flowing and hardening/softening laws. The model is thus automatically thermodynamically consistent. Moreover, the manipulation of huge quantities of microscopic parameters is avoided, which accelerates numerical computations. In many models, the expression of the free energy is chosen depending on the expected behaviour law (Svedberg & Runesson, 1997; HomandEtienne et al., 1998; Menzel & Steinmann, 2001; Shao et al., 2005a,b). Formulations starting from the Principle of Virtual Power (Frémond & Nedjar, 1995; Pires-Domingues et al., 1998; Nedjar, 2001; Zhao et al., 2005) can encompass an enrichment of the material’s structure, implying the definition of higher-order stresses and specific boundary conditions. In phenomenological damage models, dissipation variables νi (x) are generally assumed to have the dimension of strains. In this case, it is possible to define stress-like variables conjugated to νi (x) through the free energy. The evolution laws of the dissipation variables νi (x) are then deduced from the derivation of a given dissipation potential, relatively to the stress-like conjugates of the νi (x). Alternatively, yield functions (fd ) have to be defined. If flow rules are non-associated, additional damage potentials have to be expressed. The damage multiplier increment (λ˙ d ) is computed by means of the consistency equation. The complementary conditions of Kuhn-Tucker have also to be met: λ˙ d ≥ 0,
fd ≤ 0,
λ˙ d fd = 0
(5)
Some conditions on the form of the internal power density may be set before assuming the expression of the free energy. By doing so, it is possible to change the global form of the Principle of Virtual Power, which influences the formulation of the balance equations. Moreover, the model of the material structure may be affected by the introduction of gradient variables in the expression of the internal power. For example, Frémond (Frémond & Nedjar, 1996) enriched the structure of the medium by introducing the gradient of damage in the expression of the internal power of the system. The gradient of damage plays the same role as the gradient of macrodeformations in the theory of Germain (Germain, 1973). Its introduction requires the definition of higher-order terms in the application of the Principle of Virtual Power. Other researchers followed the same reasoning, like Pires-Domingues (Pires-Domingues et al., 1998), who studied nonlinear elastic brittle materials, and Nedjar (Nedjar, 2001), who coupled the damage model of Frémond to an elastoplastic theory. Zhao and his co-workers (Zhao et al., 2005) based their model of coupled plasticity and damage on a second gradient theory, including the gradient of deformations in the internal power and the gradient of the hardening variable in the expression of the free energy.
3
HYDRAULIC PROPERTIES OF AN INTACT POROUS MEDIUM
Many flow theories are based on the van GenuchtenMualem model (van Genuchten, 1980). Originally, the purpose of this model was to give a framework to determine the hydraulic retention and conductivity properties of an unsaturated medium of heterogeneous porosity. Van Genuchten thus considered that a single porous network drove the flow. In multimodal or multi-continua models, each porous system is characterized by a set of hydraulic relations, which may be chosen similar to van Genuchten’s. But to represent the global hydraulic behaviour of the Representative Volume Element (RVE), an equivalent medium has to be defined. The equivalent hydraulic properties of the RVE are deduced from a homogenisation technique. Using the van Genuchten-Mualem model to study a fractured porous medium amounts to considering that cracks and matrix pores are all connected and form a unique network, of space-variable pore size. Moreover, a Bell-type relation is assumed between the adimensional water content (h) and pressure head h: −m (h) = 1 + (αh)n
696
(6)
in which the adimensional water content is defined as: (h) =
θw (h) − θwr θws − θwr
(7)
θwr and θws are the residual and saturated water contents respectively. α is the pore size for which pore density is maximal. The α parameter thus gives an idea of the more frequent pore size characterizing the material. m and n control the distribution extent towards a fine or coarse medium. Resorting to Mualem’s integral formula, the relative water permeability is defined as: ⎤2 ⎡3 (h) 1 dx 0 h(x) ⎦ kR ( (h)) = [ (h)]1/2 ⎣ 3 1 (8) 1 dx 0 h(x) The integration scheme imposes that: m =1−
1 , n
0<m <1
(9)
" m #2 kR ( (h)) = [ (h)]1/2 1 − 1 − [ (h)]1/m (10) HYDROMECHANICAL COUPLINGS IN A FRACTURED POROUS MEDIUM
Continuum Damage Mechanics describes the degraded mechanical behaviour of the rock mass. Flow network theories predict water transfers, considering only hydraulic parameters. The main issue in modelling the EDZ is thus to combine hydromechanical and damage concepts in a single theory. A fully thermohydro-mechanical coupled model for unsaturated soils has been implemented in the finite element software -Stock. The integrated formulation is based on the use of independent variables (suction and net stress) and on the introduction of state surfaces for the void ratio and the saturation degree. The elasto-plastic Barcelona model (Alonso et al., 1990) has been modified to include temperature effects (Gatmiri & Delage, 1995: Gatmiri, 1997: Gatmiri & Delage, 1997: JenabVossoughi, 2000). The aim of the following section is to propose a fully coupled hydromechanical damage model, which would conform to the formulation adopted in -Stock. 4.1
K abs (ε, , ) = k rel ( )k int (ε, )
Introducing damage in hydraulic properties
Some damage models introduce a damage dependency in the expression of permeability (Yang et al., 2007,
(11)
The relative permeability k rel ( ) is only related to interstitial fluids, and does not depend on damage. The intrinsic permeability k int (ε, ) characterizes the damaged solid part of the medium, and takes irreversible fracturing and path orientation into account. In -Stock, the strain dependency reduces to a porosity (n) dependency. For an undamaged unsaturated material subjected to isothermal conditions, the intrinsic permeability is defined as: k int (n, = 0) = k0 · 10αk ·e Id
Taking the inverse of relation 6 leads to:
4
Shao et al., 2005b). But the given formulas generally involve mechanical parameters only. In fact, the computed permeability reduces to the intrinsic component of absolute permeability. It is possible to define the absolute permeability of an unsaturated damaged medium as the product of a damaged intrinsic permeability with a van Genuchten-Mualem type relative permeability (van Genuchten 1980):
(12)
k0 is a reference permeability and αk is a material parameter. e is the void ratio, defined by a state surface depending on stress and suction (Gatmiri & Delage, 1995). To extend the model to a damaged unsaturated material, it is proposed to split the intrinsic permeability as follows: k int n, = k1 nrev , + k2 nfrac ,
(13)
nrev represents the reversible evolution of volumetric deformations, including crack closing. As the damage model induces a dependency between strains and damage, the reversible component of the intrinsic permeability k1 depends not only on reversible porosity nrev , but also on damage . By analogy with the formulas adopted in -Stock, the following expression is chosen: rev k1 nrev , = k0 · 10αk ·e Id
(14)
erev is the void ratio deduced from the computation of reversible deformations. nfrac refers to the porosity generated by fracturing. Damage is defined by means of a formula similar to expression 4. It is thus assumed that three main families of cracks damage the RVE chosen to study the massif. Following the reasoning of Shao and his co-workers (Shao et al., 2005b), it is supposed that
697
cracks are penny-shaped planes of radius rk , of opening ek and of normal direction nk , in which the interstitial liquid flows in the direction parallel to the plane. Applying the Navier-Stokes formulas to compute the celerity of the flow in the fracture network frac (vw ) provides: vfrac w = −
π 1 · · 12μw a3
3
rk · ek · δ − nk ⊗ nk 2
3
· ∇pw
k=1
(15) μw is the dynamic viscosity of the interstitial liquid, a is the characteristic dimension of the RVE, and pw is the interstitial liquid pressure. Like in the other behaviour models programmed in -Stock, the liquid transfer is assumed to be diffusive, and the Darcy law is adopted: vfrac w
= −k2
(16)
in which γw is the volumetric weight of the interstitial liquid, and z denotes the vertical coordinate, oriented positively upward. Equations 15 and 16 result in the following expression for the irreversible component of the intrinsic permeability: k2 nfrac ,
4.2
3
rk · ek · δ − nk ⊗ nk 2
3
(17)
Damage modelling in unsaturated materials is frequently based on Biot’s theory. Most approaches combine a micromechanical definition of damage with a postulate on the expression of the free energy F(ε, ) (Shao et al., 2005a). The constitutive relation
dσ = d ⎝
∂ε
ω is a scalar (isotropic) damage variable supposed to depend on suction s and deviatoric strains εs : dω = L1 (εs , s) : dε + L2 (εv , s) ds
(20)
εv refers to volumetric strains. Contrary to a mere effective stress concept, the damaged regions of the material are still submitted to stresses, even if these ‘‘damaged stresses’’ σd do not follow the same stress/strain relations than the ‘‘undamaged stresses’’ σi . The damage threshold is supposed to be reached
dσi = De : dε + Dse ds
(21)
dσd = Dep : dε + Dsep ds
(22)
De and Dep are respectively the elastic and elastoplas-
has the following general expression: ∂F(ε, )
(19)
before the plastic threshold. Accordingly, Lu affected a non-linear elastic behaviour law to the intact stresses and an elasto-plastic Barcelone-like behaviour law to the damaged stresses:
k=1
Extending damage models to unsaturated materials
⎛
σd and a relatively intact part σi : σa = (1 − ω)σi + ωσd
pw frac +z n , · ∇ γw
γw π = · · 12μw a3
effects in the constitutive stress relation. Capillarity effects on deformation are neglected. Damage growth is still synonymous with fracturing increase. Defect initiation or crack aperture generates a rise of pore size at the scale of the global network of the equivalent medium. Bigger pores induce smaller capillarity effects, and consequently, a weaker rigidity (Gatmiri, 1997). Conversely, suction is work-conjugated to the quantity nSw (Houlsby, 1997), which originates hydraulic effects in the mechanical behaviour. That is why a formulation based on net stress and suction might be more satisfying from a conceptual point of view. To the authors’ knowledge, formulations based on net stress and suction for damage models of unsaturated media do not exist in the current literature. Lu and his co-workers (Lu et al., 2006) proposed splitting total stresses σa into a relatively damaged part
tic mechanical rigidity tensors, and Dse and Dsep are
⎞
⎠ − b Sw dpw + (1 − Sw ) dpg · Id
respectively the elastic and elastoplastic suction rigidity tensors. Considering equation 19, the evolution of total stresses would be written:
(18) b is Biot’s hydromechanical coupling parameter, pg is the gas pressure, and Sw denotes the liquid saturation degree. Adopting such a representation of stress makes it possible to uncouple poromechanical and damage
dσa = (1 − ω)dσi + ωdσd + σr dω
(23)
in which the stress difference σr = σd − σi represents the transition between relatively intact and
698
relatively broken states. The increment of total stress is determined by combining equations 23, 21, 22 and 20. Supposing that strain and suction change consistently during loading in the relatively intact and relatively damaged regions, it is possible to simplify the constitutive relation into a general expression of the type: dσa = Dedmg : dε + Dsdmg ds
(24)
are The reversible strains associated with suction εrev s calculated by an energy method. The free energy of the skeleton contained in the RVE is split: ⎧ ⎪ ⎪ F ε, s, = Fed ε , + Fpe εrev , s, ⎪ ⎨ M dε = dεrev + dεd (28) ⎪ M M ⎪ ⎪ ⎩ dεrev = dεrev + dεrev M
S
Dedmg and Dsdmg denote the elastoplasticity damage rigidity tensors associated with strain and suction respectively. The model of Lu and his co-workers (Lu et al., 2006) can easily be extended to anisotropic damage. However, the approach is merely micromechanical and thermodynamic requirements are not considered. In -Stock, the behaviour laws of unsaturated media are formulated in net stress σ = σ − pg · Id and suction s = pg − pw . Corresponding to the chosen stress state variables, strain components are defined as follows (Gatmiri 1997, Gatmiri & Delage 1997): ⎧ dε = dε + dε ⎪ ⎪ M S ⎪ ⎨ dε = D−1 e : dσ M ⎪ ⎪ ⎪ ⎩ dε = D−1 s · ds
(25)
sponds to the poroelastic aspect of the model. A partial Legendre transform of Fpe εrev , s, gives: ⎛ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎜ ⎝
Fpe εrev , s, + Gpe σ , s, = σ : εrev ∂Fpe εrev , s, σ = ∂εrev ∂Gpe σ , s, εrev = ∂σ
(29)
Equation 28 shows that εrev can be deduced from S
εrev and εrev . εrev is known by applying the PEEE to
S
M
De is the standard stiffness tensor, and Ds is defined as a rigidity associated to suction. An irreversible deformation εd related to damage is added, and it is assumed that the reversible strains also depend on damage: ⎧ dε = dεrev + dεrev + dεd ⎪ ⎪ M ⎪ ⎪ S−1 ⎨ rev dε = De : dσ M ⎪ ⎪ −1 ⎪ ⎪ ⎩ dεrev = Ds · ds
Fed ε , is related to the degraded mechanical M behaviour of the material, and Fpe εrev , s, corre-
M
a Cordebois-Sidoroff type damage model (equations 26, 3 and 27). εrev can be computed by derivation of a given poroelastic Gibbs free energy Gpe (σ , s, ) (equation 29). Following the reasoning usually adopted in the models programmed in -Stock, it is assumed that the deformation related to suction εrev S
is isotropic (Gatmiri, 1997, Jenab-Vossoughi, 2000). It is expressed as: (26)
−1 dεrev = βs s, · Id · ds
(30)
S
S
Assuming the existence of a damage yield function fd , the irreversible strain increment dεd is computed
The rigidity associated to suction Ds ( ) is thus repre-
by means of an associative flow rule. The damaged rigidity tensor De ( ) is determined by applying the
edge of the volumetric part (εrev S )v of the deformations related to suction is needed to complete the behaviour laws:
PEEE (equation 3). The classical Cordebois-Sidoroff damaged stress operator M( ) is adopted: −1/2 −1/2 · σ · Id − σˆ = M : σ = Id −
sented by a scalar modulus βs (s, ). Only the knowl-
1 · d εrev S v · Id 3 1 = · d εrev v − d εrev M v · Id 3
dεrev =
(27)
699
S
(31)
rev d εrev M v can be deduced from ε . The resulting M
expression is of the following type (Gatmiri 1997): −1 d εrev dp M v = K σ ,
(32)
in which K(σ , ) is the degraded compressive modulus and p is the mean net stress. The requirements on the poroelastic Gibbs free energy Gpe (σ , s, ) reduce to a relation of the form: ⎛
⎞ pe , s, p ∂G ⎜ ⎟ d εrev v = d ⎝ ⎠ ∂p
(33)
By analogy with the model presented by Jenab (JenabVossoughi 2000), the following formula is proposed: ∂Gpe p , s, ∂p
1 = +
−1 K σ , dp ks sˆ + patm · ln 1 + e0 sˆg + patm
(34)
ks is a compression modulus associated to suction effects in the reversible domain, e0 is the initial void ratio, and patm refers to the atmospheric pressure. A damaged suction sˆ is defined, in the same way as damaged stresses (equation 1). sˆg is the biggest damaged suction ever submitted to the material. It is the equivalent of a consolidation stress. Equations 28, 32, 33 and 34 lead to: ∂ sˆ s, rev ks 1 d εS v = · ds (35) · · 1 + e0 sˆ + patm ∂s As explained before, the expression of the damaged suction sˆ(s, ) can be deduced from a relation of the type of equation 1, which enables the full calculation of expression 35. Equations 26, 31 and 35 sum up the hydromechanical damage model proposed here for -Stock software in unsaturated and isothermal conditions. Water transfers are also coupled to damage (equations 11, 10, 13, 14, 17). 5
CONCLUSIONS
A representation of damage is required to predict the evolution of fracturing in the neighbourhood of excavated galleries. Micromechanical models are based on effective mechanical concepts, crack characteristics and fracturing criteria. Phenomenological approaches
start from a postulate about the expression of the free energy of the medium. Saturation variations around galleries hugely influence the Excavation Damaged Zone. That is why damage has to be included in hydraulic transfer models and mechanical damage theories have to be extended to unsaturated porous media. Most of the hydro-mechanical models of damage are based on a Biot’s representation of stresses, defined for saturated soils. This theoretical frame cannot represent the effect of damage on suction rigidity, as is done in the -Stock software. A fully coupled formulation based on net stress and suction state variables may give a more complete description of damage in the EDZ. That is why, in the continuity of the works of Gatmiri’s research team, a model based on an additive breakdown of strains is proposed, to extend the behaviour laws existing for intact unsaturated soils to fractured unsaturated porous media. Water transfers are also made dependent on damage by a double split of permeability. The intrinsic permeability, representing the solid contribution, is written as the sum of a reversible component and an irreversible component, both related to damage. The main difficulty of such an approach lies in the evaluation of suction rigidity, the definition of which remains rather abstract. ACKNOWLEDGEMENTS This work is supported by the European project TIMODAZ (Thermal Impact On the Damaged Zone around nuclear waste disposals in clay host rocks), launched by EURATOM. REFERENCES Alonso, Gens & Josa. 1990. A constitutive model for partially saturated soils. Géotechnique, 40, 3, 405–430. Frémond & Nedjar. 1996. Damage, gradient of damage and principle of virtual power. Int. J. Solids Structures, 33, 8, 1083–1103. Gatmiri. 1997. Analysis of fully coupled behaviour of unsaturated porous media under stress, suction and temperature gradient. In: CERMES final report, 58p. Gatmiri & Delage. 1995. Nouvelle formulation de la surface d’état en indice des vides pour un modèle non linéaire élastique des sols non saturés—Code U-Dam. In: Alonso & Delage (eds), Proc. Unsaturated Soils: 1049–1056 (in French). Gatmiri & Delage. 1997. A formulation of fully coupled thermal-hydraulic-mechanical behaviour of saturated porous media—numerical approach. Int. J. for Numerical and Analytical Methods in Geomechanics, 21, 3, 199–225. Germain. 1973. La méthode des puissances virtuelles en mécanique des milieux continus. Première partie: Théorie du second gradient. Journal de mécanique, 12, 2, 235–274 (in French).
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Hansen & Schreyer. 1994. A thermodynamically consistent framework for theories of elastoplasticity coupled with damage. Int. J. Solids Structures, 31, 3, 359–389. Homand-Etienne, Hoxha & Shao. 1998. A continuum damage constitutive law for brittle rocks. Computers and Geotechnics, 22, 2, 135–151. Houlsby. 1997. The work input to an unsaturated granular material. Technical Note. Géotechnique, 47, 1, 193–196. Jenab-Vossoughi. 2000. Etude numérique de la modélisation thermo-élasto-plastique des sols non saturés. PhD dissertation, Ecole Nationale des Ponts et Chaussées, Paris. (in French). Lu, Chen, Fang, Guo & Zhou. 2006. Structural damage model of unsaturated expansive soil and its application in multi-field couple analysis on expansive soil slope. Applied Mathematics and Mechanics (English edition), 27, 7, 891–900. Menzel & Steinmann. 2001. A theoretical and computational framework for anisotropic continuum damage mechanics at large strains. International Journal of Solids and Structures, 38, 9505–9523. Nedjar. 2001. Elastoplastic-damage modeling including the gradient of damage: formulation and computational aspects. Int. J. Solids and Struct., 38, 5421–5451. Pires-Domingues, Costa-Mattos & Rochinha. 1998. Modelling of nonlinear damage on elastic brittle materials. Mechanics Research Communications, 25, 2, 147–153
Shao, Ata & Ozanam. 2005a. Study of desaturation and resaturation in brittle rock with anisotropic damage. Engineering Geology, 81, 341–352. Shao, Zhou & Chau. 2005b. Coupling between anisotropic damage and permeability variation in brittle rocks. International Journal for Numerical and Analytical Methods in Geomechanics, 29, 1231–1247. Svedberg & Runesson. 1997. A thermodynamically consistent theory of gradient-regularized plasticity coupled to damage. Int. J. of Plasticity, 13, 6–7, 669–696. Swoboda & Yang. 1999. An energy-based damage model of geomaterials. II. Deduction of damage evolution laws. Int. J. Solids and Struct., 36, 1735–1755. van Genuchten. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 44, 892–898. Yang, Liu, Zhu, Elsworth, Tham & Tang. 2007. A coupled flow-stress-damage model for groundwater outbursts from an underlying aquifer into mining excavations. Int. J. Rock Mech. And Min. Sci., 44, 87–97. Zhao, Sheng & Zhou. 2005. Shear banding analysis of geomaterials by strain gradient enhanced damage model. Int. J. Solids and Struct., 42, 5335–5355.
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Numerical modelling
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Stress path dependency and non-convexity of unsaturated soil models D.C. Sheng, D. Pedroso & A.J. Abbo Centre for Geotechnical and Material Modelling, University of Newcastle, NSW, Australia
ABSTRACT: Yield surfaces for unsaturated soils are inevitably non-convex if the size of the yield surface has to increase with increasing suction. An expanding yield surface with increasing suction is crucial for modelling the volume collapse due to wetting. The non-convexity always exists at the transition between saturated and unsaturated states, irrespective of the stress variables used in the model. Some recent models for unsaturated soils also possess a stress path dependent hardening law. The non-convexity and stress-path dependency of the constitutive model make the implementation into finite element codes very challenging. This paper discusses aspects of stress integration schemes for non-convex and stress-path dependent models for unsaturated soils.
1
INTRODUCTION
Constitutive models for unsaturated soils usually adopt a yield surface that expands with increasing suction, in order to model the volume collapse during wetting. The non-convexity of the yield surface thus exists at the transition between saturated and unsaturated states, irrespective of the stress variables used in the model (see Figure 1 below). The only exception is the model by Wheeler et al. (2003), where the size of the yield surface does not change with the modified suction. Another feature of unsaturated soil models is the stress-path dependent hardening law. Such a feature is present in a recent model by Sheng et al. (2006) and
s
is illustrated in Figure 2. If a slurry soil is dried from point A to B, the yield surface expands from p¯ 0 to p¯ yB , with its shape remaining unchanged. If the unsaturated soil at point B is then compressed to point C, the yield surface expands and its shape changes as well (denoted by the solid curve p¯ yC ) . However, if the slurry soil at point A is first compressed to point D and then dried to C, the yield surface would take a different shape (denoted by the dashed curve p¯ yC ). The essential reason for this stress path dependency is that a change in suction has a different effect on the plastic volumetric strain than a change in mean stress when the soil becomes unsaturated.
s
s
p
p yB
p0
unsaturated
45°
C
B
Elastic zone
Elastic zone
pyC
p yC
ssa
p′ saturated
A (a) net stress
45°
D
p
(b) effective stress
Figure 1. Non-Convexity of unsaturated soil models (¯p: net mean stress; p : effective mean stress; s: suction).
Figure 2. Stress path dependency of the model by Sheng et al. (2006), Ssa : saturation suction.
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The non-convexity and stress-path dependent hardening laws of unsaturated soil models present difficulties in the implementation of these soil models into finite element codes, particularly regarding the stress integration. tr
2
f= 0
NON-CONVEX YIELD SURFACE
For given strain and suction increments, the current stress state and internal variables must be updated in accordance with the constitutive law. This update is generally carried out using numerical stress integration schemes. Both implicit and explicit schemes have been used to integrate elastoplastic models. Implicit schemes, where all gradients are estimated at an advanced stress state, cannot be used for elastoplastic models with non-convex yield surfaces, because the extrapolated gradients cannot be determined due to the uncertainty of whether an advanced position is inside or outside the yield surface. On the other hand, explicit schemes can proceed in an incremental fashion, but require the intersection between the current yield surface and an elastic trial stress path to be determined. A key issue in integrating the incremental stressstrain relationships using an explicit method is thus to find the intersection between the elastic trial stress and the current yield surface. Figure 3 illustrates some possible situations. The most complicated situation occurs when the yield surface is crossed three times. However, it is not possible to know a priori how many times the yield surface is crossed, because the size of the yield surface will change after the first intersection due to hardening. Therefore, for non-convex yield surfaces, the key task is to find the very first intersection for any possible path. In order to determine whether the yield surface is crossed, a secant trial stress increment is computed, based on an elastic stress-suction-strain relationship. This elastic trial stress is given as follows: σ tr = De : ε + W e s
(1)
where the stress is either the net stress or effective stress (depending on the model), De is the fourth order elastic stiffness tensor and W e is a second order tensor defined according to a specific law for unsaturated soils; for example, the equations presented in Sheng et al. (2003, 2004, 2006) may be adopted. For models of saturated soils, the term W e s depends on the stress variables used. If the effective stress is used, the term W e s becomes zero and can be disregarded. On the other hand, if the net stress is used, the term W e s becomes −I uw , where I is the second order identity tensor and uw the pore water pressure.
Figure 3. Intersections between non-convex yield surface and elastic trial stress path.
In equation (1), ε is the strain increment provided from the finite element routines prior to the computation of the residuals between internal and external forces. For unsaturated soils, the increment of suction s is also input for the stress-update algorithm. If the elastic modulus is linear, i.e. it is independent of the stresses, suction and internal variables, it is trivial to compute the elastic trial increment. Otherwise, for some non-linear relations, a secant analytical modulus may be considered. Finding the intersection between the elastic trial stress increment and the current yield surface can be cast into the problem of finding multiple roots of a nonlinear equation. fα (α) = 0. The roots (α) must be computed inside the interval [0, 1]. As this function involves the evaluation of the yield function along the strain and suction paths, it is given as fα (α) = f (σα , sα , zk )
(2)
where f (σ , s, zk ) is the yield function, zk indicates a set of internal variables and the intermediate stresssuction states σα and sα are calculated according to σα = σcurrent + ασ tr
and
sα = scurrent + αs (3)
in which σcurrent and scurrent are the current stress and suction states. Note that in equation (2) the internal variables zk are kept constant during the solution for the intersection. These variables only change during hardening/softening when a portion of the trial stresssuction path is located outside the yield surface. The technique proposed here follows the KroneckerPicard (KP) formula for the determination of the
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number of roots of a nonlinear equation (Kavvadias et al., 1999). This formula, given by −γ N = π
b a
fα (x)hα (x) − g(x)2 dx fα (x)2 + γ 2 gα (x)2
γ ([fα (a)gα (b) − fα (b)gα (a)]) 1 + arctan π fα (a)fα (b) + γ 2 gα (a)gα (b) (4) requires that fα (α) must be continuously or piecewise differentiable to the second order for values of α from a to b. In equation (4), gα and hα represent the first and second derivatives of the function fα with respect to α, respectively, and γ is a small positive constant which does not affect the results computed with the KP formula (Kavvadias et al., 1999). The first and second derivative of fα with respect to α can be directly determined as follows: ∂fα dσα ∂fα dsα ∂fα = + : ∂α ∂σα dα ∂sα dα ∂f ∂f tr : σ + s = ∂σ ∂s
gα (α) =
α
hα (α) =
(5)
α
∂ 2 fα ∂ 2 f tr = σ : : σ tr ∂α 2 ∂σ ∂σ α ∂ 2 f ∂ 2 f + 2σ tr : s + s2 ∂σ ∂s α ∂s2 α
it does not constrain the solution to lie within specified bounds. Therefore, more advanced methods can be used here. For example, the Pegasus method used in Sloan et al. (2001) is very robust and competitively fast. The method by Brent (1971) provides another attractive alternative here. The Brent method does not use any derivative, does not require initial guesses and guarantees the convergence as long as the values of the function are computable within a given region containing a root. This characteristic of the Brent method is due to the combination of the bisection method, the secant method and inverse quadratic interpolation. Therefore, it has the reliability of the bisection method and the efficiency of the less reliable secant method or inverse quadratic interpolation. The evaluation of the integral in equation (4) with the KP formula is generally not trivial and so a numerical integration or quadrature technique has to be used. For example, the Gauss-Legendre method (Forsythe et al., 1990) can be used here. In addition, for highly non-linear yield functions, an adaptive integration scheme may also have to be used. In the numerical examples presented in this paper, the adaptive integration scheme explained in Piessens et al. (1983), implemented in the QAGS routines, is used. These routines which are based on the QUADPACK library, available at www. netlib. org, can efficiently perform the numerical integration even for functions with singularities. 3
(6)
The number of roots estimated according to equation (4) is used to divide the interval of α into subintervals until each subinterval contains at most one root. First, N is computed for the interval [a, b]. If N is larger than one, the interval [a, b] is divided into two equal subintervals, [a, (a + b)/2] and [(a + b)/2, b]. The number of roots for each subinterval is then computed and any subinterval that contains more than one root is further divided into two equal sub- subintervals. This process continues until each subinterval contains at most one root. As shown by Kavvadias et al. (1999), the usage of equal-size intervals (equiprobable parts) is not much worse than an algorithm which would consider the statistical distribution of the roots inside [a, b], such as the algorithm presented in Kavvadias et al. (1999). Once the roots are bracket, the solution of each root can be found by using existing numerical methods such as the Newton-Raphson method. It should be noted that the Newton-Raphson method, although fast, may not converge in some circumstances because
STRESS PATH DEPENDENCY
The discussion in this section is limited to the SFG model by Sheng et al. (2006). In this model, the yield function is written as f = q2 − M 2 (¯p − p0 (s))(py (s, z0 , z1 ) − p¯ ) = 0
(7)
where q is the deviatoric stress, M is the slope of the critical state line, z0 and z1 are internal variables and p0 and py are yield stresses given as follows:
k(s) if s > ssa −s otherwise z0 z0 − s + [s + k(s)] z1 py (s, z0 , z1 ) = z0 − s
p0 (s) =
if s > ssa otherwise (8)
where k(s) = −ssa − (1 + ssa ) ln
1+s 1 + ssa
(9)
Internal variable z0 corresponds to the size of the yield surface for saturated conditions. The other internal
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variable z1 is an auxiliary measure to the solution (integration) of the SFG model, and may be interpreted as a control on the shape of the yield surface. When it is smaller than z0 , the yield surface may be non-convex and the collapse due to wetting can be simulated. The evolution for z0 defines the hardening of the model. An isotropic hardening similar to the one used by the Cam Clay model (Schofield & Wroth, 1967) is adopted. The evolution of z1 is determined according to the stress-path, which is an interesting feature of SFG model, which leads to a stress path dependent hardening law. For elastoplastic behaviour, the suction-stress path can be measured according to the following expression: β = arctan
| d p¯ | ds
(10)
z0 p ε˙ λ−κ v
˙ e: σ˙ = De : ε˙ − D
∂f + W e s˙ ∂σ
(14)
and ˙ k z˙k = H
(k = 0 or 1)
(15)
where ˙ =
∂f ∂σ ∂f ∂σ
: De : ε˙ + : De :
∂f ∂σ
∂f ∂σ
−
: We +
∂f ∂z0 H0
−
∂f ∂s
s˙ (16)
∂f ∂z1 H1
and H0 =
The evolution for z0 is given by z˙0 =
The stress-strain relationship may be derived from the above equations (Sheng et al. 2006), leading to:
z0 λ−κ
∂f ∂f ∂f + + ∂σ11 ∂σ22 ∂σ33
H1 = cpath H0
, (17)
(11)
The rate of change of the internal variable z1 is given as a function of the rate of change of z0 :
De and W e can be found in Sheng et al. (2006). Equations (14) and (15) are used in the stress-update algorithm. For the implementation in a FEM code, the following equation is required as well:
z˙1 = cpath × z˙0
σ˙ = Dep : ε˙ + W ep s˙
(12)
where cpath is a parameter reflecting the pathdependent hardening law. The basic requirements for the hardening law (11) are: • if s > ssa
if s˙ > 0 and p˙¯ = 0, z1 must change at the same rate as z0 else, z1 changes at a rate proportional to z0 that z1 /z0 stays constant
• otherwise, ◦ the ratio z1 /z0 stays constant In this way the behaviour of both normally consolidated and compacted materials can be captured by the system of equations. Any expression for cpath satisfying these requirements can be adopted. Here, we introduce the following expression:
z1 β cpath = (1 − sin β) 1 − 1 − z0 π
where Dep and W ep are tangent modulus and are also presented in Sheng et al. (2006).
4
◦ if p˙¯ > 0 and s˙ = 0, the auxiliary internal variable z1 must stay unchanged ◦ otherwise,
(13)
(18)
SIMULATIONS
We first demonstrate the numerical solutions of the intersection and the stress updates for specific stresssuction paths. Figures 4 and 5 show two examples where the initial stress/suction state is inside the yield surface and an intersection must be determined. In these two cases, only the first intersections are needed. The second intersection actually never happens due to hardening (inside the updated yield surface) and hence is irrelevant. The final yield surfaces are tangent to the stress paths. The material properties are listed in Table 1. It may be concluded that the algorithm performs very well in finding the appropriate intersection points. Four different stress/suction paths are studied here, to demonstrate the effectiveness of the proposed algorithms in tackling the stress path dependency and the non-convexity problems. These paths are denoted as ABB CD, ABCD, ADCD and AFD and are shown in Figure 6–9, respectively. The material parameters are given in Table 1.
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suction [kPa] 100 150 200 250 300 0
C
s
50
80
100 60 40
B′
B
A
D 50
100 p [kPa]
150
200
A
0
20
40
60
80
v 1.60
0
1.65
20
1.70
0
100
B B′
1.55
p
Figure 4. Yield surface of SFG model and a stress-suction path with increasing suction. The initial state is inside the initial yield surface. After the first intersection, hardening takes place and the yield surface advances to the new position as shown.
1.50
C D 50
100
150 200 suction [kPa]
250
A
300
FEM
B
B′
1.55
v 1.60
1.65
1.70
0
1.50
C D 0
Figure 6.
Figure 5. Yield surface of SFG model and a stress-suction path with decreasing suction. Table 1. λ
κ
Parameters used in simulation. #v o
(ABB CD)
0.1 0.02 1.7 3 (others) #
φ
G, kPa ssa , kPa
25◦
100
10 (ABB CD) 100 (others)
Initial specific volume at initial mean stress and suction.
1
2
3 ln(p) [kPa]
4
5
Results for stress path ABB CD.
Test ABB CD represents an over consolidated clay subjected to an increase in suction, followed by an increase of mean stress and decrease of suction. Tests ABCD and ADCD represent a slurry soil and are useful to check the stress/suction path dependency predicted by the SFG model. In test ABCD, the suction is increased firstly and then the mean stress is increased, followed by a decrease in suction. Test ADCD does the opposite: increase mean stress first and then increase (and decrease) the suction. Therefore, comparing the results between ABCD and ADCD tests, it is possible to observe that the predicted behaviour is different, according to the path, due to the different shapes that the yield surface can exhibit, even thought the initial and final states are the same.
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1000
1000
C
suction [kPa] 400 600
200
200
D 200
400
600
800
0
0
A 0
1000
A
D
0
p [kPa]
200
400
600
800
1000
400 600 suction [kPa]
800
1000
3.0
p [kPa]
A
A
2.0 200
400 600 suction [kPa]
800
1000
A
D
C
0
FEM
200
A
FEM
2.0
2.0
v
v
2.5
2.5
3.0
0
1.5
B C
D
3.0
1.5
2.0
v
v
2.5
2.5
3.0
C
suction [kPa] 400 600 800
800
B
B
0
Figure 7.
1
2
3 4 ln(p) [kPa]
5
6
1.5
1.5
C D 7
D C 0
Results for stress path ABCD.
Figure 8.
The test AFD is useful to check the behaviour predicted by the SFG model, considering the path dependent hardening introduced here. In this case, the intermediate values calculated with equation (13) are used, since this test is set for combined increments of mean net stress and suction. Figures 6–9 present the results of the simulations. In each figure, three plots are presented: the suction/mean net stress path and the corresponding yield surface evolution; the specific volume—suction relationship; and the specific volume—net mean stress relationship. From these figures, it is possible to conclude that the methods proposed here can reasonably deal with the stress-path dependency and
1
2
3 4 ln(p) [kPa]
5
6
7
Results for stress path ADCD.
the non-convexity problems in the unsaturated soil models. 5
CONCLUSIONS
A simple method to account for the stress-path dependency during the stress update of an unsaturated soil model has been introduced. The method is based on the incorporation of a trial stress/suction increment into a second order explicit scheme. The non-convexity of the yield surface has also been considered by means of an explicit stress integration algorithm. This algorithm uses a recursive scheme to find all intersections
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1000
REFERENCES
F
0
200
suction [kPa] 400 600 800
Brent, R.P. (1971), An algorithm with guaranteed convergence for finding a zero of a function, The Computer Journal, 14:422–425. Forsythe, G., Malcolm, M. & Moler, C. (1990), Computer Methods for Mathematical Computations, Mir Ed., Moscou, Russia. Kavvadias, D.J., Makri, F.S. & Vrahatis, M.N. (1999), Locating and computing arbitrarily distributed zeros, SIAM Journal on Scientific Computing, 21(3):954–969. Piessens, R., Doncker-Kapenga, E.D., Uberhuber, C. & Kahaner, D. (1983), Quadpack: a Subroutine Package for Automatic Integration, Springer Verlag. Schofield, A.N. & Wroth, C.P. (1968), Critical State Soil Mechanics, McGraw-Hill, London, 1968. Sheng, D., Fredlund, D.G. & Gens, A. (2006), A new modelling approach for unsaturated soils using independent stress variables, Canadian Geotechnical Journal, 45(4), 2008 (in press. A short version of the report was published in the Proceedings of 3rd Asian Conference on Unsaturated Soils, Nanjing, April 19–22, 2007, Science Press, pp. 405–413). Sheng, D., Sloan, S.W., Gens, A. & Smith, D.W. (2003), Finite element formulation and algorithms for unsaturated soils. Part I: Theory, International Journal for Numerical and Analytical Methods in Geomechanics, 27:745–765. Sheng, D., Sloan, S.W. & Gens, A. (2004), ‘A constitutive model for unsaturated soils: thermomechanical and computational aspects’, Computational Mechanics, 33(6), 453–465. Sloan, S.W., Abbo, A.J. & Sheng, D. (2001), Refined explicit integration of elastoplastic models with automatic error control, Engineering Computations, 18:121–154. Wheeler, S.J., Sharma, R.S. & Buisson, M.S.R. (2003), ‘Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils’, Geotechnique, 53(1), 41–54.
A
D 200
400
p [kPa]
600
800
1000
A
1.5
2.0
v
2.5
3.0
0
F D 200
400 600 suction [kPa]
800
1000
A
FEM
2.0
v
2.5
3.0
0
1.5
F D 0
Figure 9.
1
2
3 4 ln(p) [kPa]
5
6
7
Results for stress path AFD.
that may arise during the stress update. The key step is the computation of the number of roots, which is done with the aid of the Kronecker-Picard formula. The only requirement for this method is that the yield function must be piecewise differentiable to the second order along the stress/suction secant path.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Implicit integration of an extended Cam-clay model for unsaturated soils R. Tamagnini & V. De Gennaro ENPC (Université Paris-Est, Navier Institute – Cermes), Paris, France
ABSTRACT: Recent developments in the field of constitutive modelling of partially saturated soils have shown the relevancy of the following two constitutive assumptions: (i) the use of an averaged stress similar to the so-called Bishop stress as an alternative stress component and (ii) the introduction of a hardening rule enabling the effect of changes in the degree of water saturation on the plastic yield function to be accounted for. This paper deals with the numerical integration of a constitutive model for partially saturated soils based on an extension of the Modified Cam Clay model for saturated soils (Tamagnini 2004). The proposed elastic-plastic stress-strain-saturation relationship is obtained following the two above mentioned constitutive assumptions. The rate constitutive equation is integrated adopting a return mapping scheme similar to that developed for saturated material, but modifying the elastic predictor stage. In particular, the dimension of the trial elastic domain is modified by the changes in the degree of saturation, independently of the state of stress existing at the beginning of the integration step. This mathematical feature follows from the hypothesis that the hardening variable which defines the initial size of the plastic yield function and its evolution during plastic loading is a function of the saturation degree. The derivation of the consistent tangent operators is then presented and some numerical applications discussed.
1
INTRODUCTION
In the last decades the mechanics of multiphase materials has been increasingly investigated and many advances in both the theoretical and experimental aspects have been obtained. Contrary to the mechanics of saturated geomaterials, in a three-phase geomaterial, where air and water interact with the soil skeleton, the basic constitutive assumptions are not so straightforward. In particular, the definition of the independent state variables and the corresponding state equations, or the hardening variables controlling the mechanical behaviour of the solid phase is not direct and the experimental verification not obvious. This is due to the complex interaction between the fluid phases and the effects of this interaction on the behaviour of the solid skeleton. It is well-known that the presence of two different fluids (a wetting and a non-wetting phase) implies the presence of interfaces into which the capillary forces act; this physical property strongly affects the mechanical response of the material. It is now well accepted that a thermodynamic consistent framework for unsaturated soils based on the theory of multiphase mixtures involves an ‘‘effective’’ stress as an independent stress variable, energy conjugate with the skeleton strains and a capillary stress as a second stress variables, energy conjugate to the water saturation degree (Coussy 1995, Coussy 2003,
Houlsby 1997, Lewis & Schrefler 1998). The aim of this paper is to present the numerical integration of a constitutive model for partially saturated soils (Tamagnini 2004) developed within the previously outlined theoretical framework. The rate equations are integrated adopting a return mapping scheme that allows for a fully implicit integration (Borja and Lee, 1990). The key role played by the water saturation degree in the soil modelling is discussed by means of some numerical simulations. The coupling arising between the water retention properties (modelled by the water retention curve WRC) and the mechanical response during saturation time evolution is highlighted. The constitutive framework and the adopted numerical scheme are the base for the definition of a more accurate constitutive equation for three-phase porous material and its numerical integration. 2
CONSTITUTIVE EQUATIONS
Tamagnini (2000, 2003, 2004) proposed an extension of the modified Cam-clay model (Roscoe & Burland, 1968) for the description of the behaviour of partially saturated soils. Moving from a thermodynamic based approach for multiphase mixtures the definition of an ‘‘effective’’ stress state variable, some times called improperly the Bishop’s stress, was introduced.
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The hardening law is formulated according to the proposal of Jommi & di Prisco (1994) and it includes the degree of saturation as a hidden variable. This variable is used to model the bonding exerted by capillary forces and it will be shown that this assumption can overcome the limitation of a single ‘‘effective’’ stress approach in modelling the collapse upon wetting. The Cam-clay ellipse is used to describe soil behaviour during deviator stress paths and in the sake of simplicity an associative flow rule is adopted. The constitutive equation of the model is defined in the space of the following stress tensor:
with the decrease of Sr . In order to define the plastic part of the constitutive model the plastic flow is introduced as:
σij = σij − ua δij + Sr (ua − uw )δij
1 dλ = H
(1)
This stress variable is similar to the Bishop’s stress (Bishop, 1959) that was defined experimentally and in which Sr is replaced by χ that is a function of the saturation degree. In equation (1) ua and uw are the pore air and water pressures, respectively. Their difference is termed suction, s; σij is the total stress tensor. In the following, the mean effective stress p and the deviator stress invariant q will be used and these are defined as: p =
1 σ 3 ii
q=
3 ||ξii || 2
1 ξij = σij − σii 3
vpc dε p − pc bdSr λ−κ v
(5)
in which λ is the plastic multiplier and it can be obtained by the consistency:
H =−
∂f ∂f ∂f dq − pc bdSr dp + ∂p ∂q ∂pc
(6)
∂f vpc ∂f ∂pc λ − k ∂p
Starting from the expression:
∂f e dσij = Dijkl dεkl − dλ ∂σkl
(7)
e is the fourth order elastic constitutive in which Dijkl tensor and the following relations:
(3)
in which M is the slope of the critical state line. The preconsolidation pressure pc describes the evolution of the ellipse dimension and it is defined in the rate form as proposed by Jommy Jommi & di Prisco (1994): dpc =
∂f ∂σij
(2)
The yield surface is represented by the ellipse: f = q2 + M 2 p (p − pc ) = 0
p
dεij = dλ
(4)
the first term is the classic isotropic strain hardening rule in which λ and k are the elatoplastic and elastic volumetric stiffness and it is defined for the saturated case; the second one introduces the effects of capillarity bonding, b is a constitutive parameter and it controls the sensitivity of the solid matrix to the effects of the intergranular forces exerted by interfaces. It has to be noticed that the increase of the yield surface dimension can occur even if the current Bishop stress is not on the yield surface and this kind of hardening can be reversed during suction cycles. The mechanical effects of wetting-drying cycles have been discussed by Tamagnini (2004) and they are not treated in this paper. Equation (4) states that capillarity hardening is an exponential function of the saturation degree (Tamagnini, 2000), and it increases monotonically
Hs =
∂f bp ∂pc c
K =
v p k
G =
3K (1 − 2ν) 2(1 + ν)
(8)
The constitutive equation is obtained in its incremental form as follows: ⎛ e dσij = ⎝Dijkl −
+
∂f e ∂σcd Dcdkl ∂f e ∂f ∂σij Dijkl ∂σkl
∂f e Dijab ∂σab ⊗
H+ e Dijkl
Hs−1 H +
∂f De ∂f ∂σij ijkl ∂σkl
⎞ ⎠ dεkl
∂f dSr ∂σkl
(9)
Note that in equation (9) the second right hand side term in which the saturation degree rate appears has the role of a stress rate. It means that soil behaviour is controlled by the changes in the Bishop stress, which depends on the saturation degree, but also by the changes in the capillary forces. In other words, the rate of Sr in (9) describes the variation in the content of interfaces within the representative volume and this is consistent with the hypothesis of the phase energy separation proposed by Coussy (2003).
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From the discrete Khun-Tucker condition results:
Equation (9) can be rewritten in the following form: dσij − dσij∗
⎛
e = ⎝Dijkl −
∂f e ∂σcd Dcdkl ∂f e ∂f ∂σij Dijkl ∂σkl
∂f e Dijab ∂σab ⊗
H+
f (σn+1 ; qn+1 ) = 0 λ˙ n+1 ≥ 0
⎞ ⎠ dεkl
The aim of the plastic corrector is the definition of the plastic multiplier at time tn+1 and then to compute the stress through the equations:
(10) From this expression it is clear that the stress rate exerted by the interfaces, σij∗ , is added to the averaged macroscopic fluids pressures introduced in equation (1). The role of dσ ∗ in (10) will be discussed based on the results of some numerical simulation that are obtained with the numerical algorithm developed in the next section.
3
IMPLICIT INTEGRATION OF THE CAM-CLAY MODEL FOR UNSATURATED SOILS
⎧ pk e ⎪ − Dijkl εkl σijkn+1 = σijtriial ⎪ n+1 n ⎪ ⎪ ⎨ pk pkcn+1 = ptrial cn exp(−θn εkl ) ⎪ ⎪ ⎪ ⎪ ⎩ k k k fn+1 = f (pkl n+1 ; qn+1 ; pcn+1 )
(11)
(13)
The rate of the equilibrium condition can be formulated as follow: k f int (σn+1 ) − f ext +
An extensive study on the numerical methods for the consolidation analyses of multiphase porous material can be found in Lewis and Schrefler (1998). As regards the use of a so-called Bishop stress in the vector of internal forces, Tamagnini (2003) has discussed an implicit integration scheme with an elasto-plastic single tangent matrix for the extended Cam-clay. The Cam Clay is integrated enhancing the return mapping scheme proposed by Borja and Lee (1990) for the saturated Cam Clay. The improvement is based on two points: the modification of the elastic trial step and the derivation of a second consistent tangent matrix that describes the variation of the ‘‘effective’’ stress due to changes in the degree of saturation (or better in the number of the interfaces between fluids). At time tn , in the equilibrium condition at the general iteration k, the increments: that can be written as εijk n+1 ; Srkn+1 are known and the trial state variables can be written as: ⎧ trial e ⎪ σijn+1 = σijn + Dijkl εklk n+1 ⎪ n ⎪ ⎪ ⎨ k ptrial cn+1 = pcn exp(−bSrn+1 ) ⎪ ⎪ ⎪ ⎪ ⎩ f trial = f (ptrial ; qtrial ; ptrial ) n+1 n+1 n+1 cn+1
(12)
+
k ) ∂f int (σn+1
k ) ∂f int (σn+1
∂(ukn+1 )
ukn+1
∂(Swk n+1 )
∂(Swk n+1 ) ∂(pkan+1 − pkan+1 )
(pkan+1 −pkwn+1 )
=0
(14) The first derivative in (14) is the classic consistent tangent matrix. The second group of derivatives in parentheses represents the variation of the internal forces due to the changes in suction (or degree of saturation). The coupling matrices are included in the vector of the external forces. Note that during the iterative solution, the equilibrium and then the internal forces vector can be perturbed by the variation in capillary forces, this implies a direct dependency of the displacement vector on degree of saturation (or suction). This mathematical feature is fundamental for the modelling of collapse upon wetting. The first consistent tangent operator can be obtained adapting the work of Borja and Lee (1990) for the unsaturated case. The second consistent tangent matrix is obtained, for constant strain, as follows:
Csrk n+1 =
∂σijkn+1 ∂Srkn+1
Aksn+1 ;
Aksn+1 =
∂Srkn+1 ∂(pa − pw )kn+1 (15)
The hardening rule is integrated in closed form and split by adopting Lie’s formula (Tamagnini 2000); this is a modification of the standard implicit scheme. The plastic corrector uses the trial stress and trial hardening as the initial condition and through a return mapping computes the stress and plastic strains.
and then: Csrk n+1
715
=
∂pkn+1 1+ ∂Srkn+1
k 2 ∂qn+1 n Aksn+1 3 ∂Srkn+1
(16)
the derivatives of the invariants and the preconsolidation pressure are: ∂λkn+1 ∂pkn+1 = −K (2pkn+1 − pkcn+1 ) n ∂Srkn+1 ∂Srkk+1 ∂pkcn+1 2∂pkn+1 k − k (17) +λn+1 ∂Srkn+1 ∂Sr n+1 ∂pkcn+1 ∂Srkn+1
= pkcn+1 θn
c8 = c3 c6 + c5
k ∂λkn+1 ∂qn+1 = c 10 ∂Srkn+1 ∂Srkk+1
Equations (17) and (18) can be written as:
c5 =
c11 =
∂λkn+1 ∂Srkn+1
= − Kn λnk+1 + 2Kn λkn+1 )
c2 = −
Kn (2pnk+1 (1 +
− pkcn+1 ) 2Kn λkn+1 )
pkcn+1 θn (2pkn+1 − pkcn+1 ) (1 + θn pcn+1 λkn+1 )
(2pn+1 − pkcn+1 )c6 + pn+1 c8 2qn+1 c M 2 10
+ (2pn+1 − pcn+1 )c7 − pn+1 c9
(26)
2pkcn+1 θn λnk+1 (1 + θn pcn+1 λkn+1 )
Substituting (20), (22), (24) and (26) in (16) the consistent tangent matrix can be obtained: (20)
Csrk n+1 = (c6 + c7 c11 )1 +
2 c10 n Aksn+1 3
(27)
−bpkcn+1 (1 + θn pcn+1 λkn+1 )
∂pkn+1 ∂Srkn+1
=
∂λkn+1 c7 ∂Srkk+1
4
+ c6
and: c6 =
M 2 + 6μλkn+1
k k ∂λkn+1 2qn+1 ∂fn+1 = c + (2pkn+1 − pkcn+1 ) 10 M2 ∂Srkn+1 ∂Srkn+1 ∂λkn+1 ∂λkn+1 k × c 6 + c7 − pn+1 c8 + c9 =0 ∂Srkn+1 ∂Srkn+1 (25)
with:
c4 =
k 6μqn+1
The plastic multiplier results:
∂pk ∂λkn+1 ∂pkn+1 = c1 c3 n+1 + (c2 c4 + c2 ) + c1 c5 k k ∂Srn+1 nSrkk+1 ∂Srn+1 f (19)
c3 =
c10 = −
The derivative of the plastic multiplier with respect to the saturation degree can be obtained from the consistency condition:
− pkcn+1 )
(18)
(1
(23)
For the deviatoric stress component:
λkn+1
c1 =
c9 = c3 c7 + c4
(24) ∂λkn+1 (2pkn+1 ∂Srkk+1
∂pkcn+1 2∂pkn+1 − k − bpkcn+1 + ∂Sr n+1 ∂Srkn+1 k k ∂qn+1 ∂qn+1 6μn ∂λkn+1 k k =− 2 q + λn+1 k ∂Srkn+1 M ∂Srkk+1 n+1 ∂Srn+1
with:
c1 c5 (1 − c1 c3 )
c7 =
(c1 c4 + c2 ) (1 − c1 c3 )
(21)
The derivative of the preconsolidation pressure can be defined as: ∂pkcn+1 ∂Srkn+1
= c9
∂λkn+1 + c8 ∂Srkk+1
(22)
NUMERICAL SIMULATIONS
In order to verify the proposed numerical integration of the model two numerical tests have been produced. Both are intended to check the hydro-mechanical coupling between the water retention properties of the materials and the mechanical equations. The first numerical test consisted in the simulation of an isotropic wetting process under isochoric (constant volume) condition (referred to the solid matter) and constant applied mean net stress. The isochoric boundary condition is the same as the experimental results of Romero (1999) reported in Figure 1. However, it must be noted that the assumption of constant net mean stress during isochoric conditions is
716
the saturation degree, that is the driving force for the numerical tests. The correspondent suction value is obtained directly from equation (26) as: dsn+1 =
dσ ∗ − sn dSr Srn
(29)
Material constitutive parameters are: k = 0.028; λ = 0.1; M = 1.0; ν = 0.3, b = 5.0. The initial values of the state variables are: Sr = 0.36; s = 2500 (these are not dimensional values but could be referred to kPa); v = 2.0 (specific volume); pc0 = 1000 corresponding to an initial mean net stress of 100. Figure 2 shows the computed water retention curve and it shows 10000
1000
Figure 1. (1999).
suction
100
Wetting test at constant volume after Romero
10
dσij = sdSr + Sr ds = tr ⎛ ⎜ ×⎜ ⎝
e Dijkl
Hs−1 H +
∂f De ∂f ∂σij ijkl ∂σkl
1
0.1 0.2
0.4
0.6
0.8
1
Sr
Figure 2. tion.
Water retention curve obtained by the computa-
4000
Applied total stress
3000
σ = 100 σ = 160
suction
only valid for part of the wetting test (when wetting from 400 kPa to 0.01 kPa). Also Romero’s data is for one-dimensional loading in an oedometer, rather than isotropic conditions. In this test the Bishop stress (1) and the yield surface are reduced by saturation. For the sake of simplicity the influence of hysteresis in the WRC is not considered as it would require a more detailed thermodynamic discussion and numerical considerations and only a monotonic wetting path is simulated. Since saturation induces changes in the capillary forces, the second left hand side term −dσ ∗ in equation (10) results in a compressive stress during saturation, the rate of stress dσ is negative (unloading) in order to contrast the compressive rate −dσ ∗ and this ensure the overall isochoric condition (i.e. dσ − dσ ∗ = 0). In order to obtain the hydraulic part of the constitutive model and imposing null strains (isochoric condition), the equation (10) can be written as: ⎞
2000
1000
∂f ⎟ ⎟ dSr = dσ ∗ ∂σkl ⎠ 0
(28)
0.2
The term dσ ∗ is then computed numerically during the simulation, starting from the increment dSr in
0.4
0.6
0.8
1
Sr
Figure 3.
717
Different WRC at different applied mean stress.
suction (KPa)
1000
100
10
q (KPa)
0
0
400
p' (KPa)
800
1200
100
200
300
Figure 6. Stress paths during the stress relaxation (Data redrawn from Romero 1999). Figure 4. volume.
Test by Romero (1999) at constant skeleton
1000
suction (KPa)
100
10
1 0.5
0.6
0.7
0.8
0.9
1
Sr
Figure 5. Simulation of the constant skeleton volume wetting (dots are experimental data).
qualitatively a good agreement with the usual experimental data in which a water entry value is recorded (e.g. Romero, 1999). In Figure 3 the ideal WRC of the first analysis (dashed line) is compared with the WRC (solid line) obtained for another isochoric condition
with the following initial stress: Sr = 0.36; s = 4000; pc0 = 1600 corresponding to an initial mean net stress of 160, the remaining constitutive parameters are the same of the previous analysis. The results plotted in Figure 3 clearly show that the increase in the applied mean net stress implies the upward translation of the WRC. This feature agrees with the experimental data for example by Ng and Pang (2000). The results plotted in Figure 3 shows that an increase of the mean net stress (p − ua ) at fixed suction and isochoric condition implies a higher saturation degree. This implies that the number of interfaces is lower and provides a possible explanation to the tensile nature of the capillary stress and the compressive effects arising during the equalization stages of the wetting path when the effective stress in (10) is reduced. In other words, in order to equilibrate the elastic swelling produced by the Bishop stress the induced collapse due to the capillary stress has to be smaller if the net applied stress is higher; this feature agrees with the experimental results of Romero (1999). Figure 1 shows that for lower applied net stress at the same suction value the applied net stress has to be reduced to obtain the isochoric condition (it is also true that the two tests have different densities). It is also interesting to observe that in a free strain condition a higher applied total stress implies a larger collapse. Indeed in this case the stored energy represented in the hydraulic plane Sr :s of the WRC is
718
greater, and for a fixed value of Sr the increase in the mean net stress implies an increase of the interfaces energy. Many other authors have studied the effects of the void ratio in the water retention properties; in this paper the effects of the total or net stress are discussed. The evolution of the mean Bishop stress of the test reported in Figure 1 is reported in Figure 4, (Romero, 1999) with the parameter χ = Sr . Figures 5–6 report the back analysis of the experimental data at high density packing with γd equal to 16.7 kN/m3 . In Figure 6 the evolution of the mean Bishop stress and the deviator stress are reported, the simulation starts from the suction value of 400 kPa when the collapse at constant mean applied stress takes place. The obtained parameters are: k = 0.065; λ = 0.12; M = 1.0; ν = 0.25, b = 4.283. The initial values of the state variables are: Sr = 0.8; s = 400 kPa the resulting initial Bishop stress tensor components are σ = (920; 1070; 1070; 0; 0; 0) kPa. Figure 5 reports the obtained WRC.
REFERENCES Bishop A.W. 1959. The principle of effective stress, Teknisk Ukeblad, 106(39); 859–863. Borja R.I. and Lee S.R. 1990, Cam-Clay plasticity, Part I: Implicit integration of elasto-plastic constitutive relations, Comp. Meth. Appl. Mech. Eng., 78 49–72.
Coussy O. 1995. Mechanics of Porous Continua, Ed. J. Wiley & Sons. Coussy O. 2003, Poro-mechanics, Ed. J. Wiley & Sons Houlsby G.T. 1997. The work input to an unsaturated granular material, Géotechnique 47(1), 193–196. Jommi C. and di Prisco C. 1994. A simple theoretical approach for modelling the mechanical behaviour of unsaturated granular soils (in Italian), Conf. Il ruolo dei fluidi nei problemi di ingegneria geotecnica, Mondovi, 1994, pp.167–188. Lewis R.W. and Schrefler B.A. 1998. The finite element method in the static and dynamic deformation and consolidation of porous media, J. Wiley & Sons. Ng C.W.W. and Pang Y.W. 2000. Influence of stress state on soil-water characteristics and slope stability, J. Geotech Geo-env. Eng, ASCE, 126(6) 1252–1264. Romero E.M. 1999. Characterization and thermo-hydromechanical behaviour of unsaturated Boom clay, PhD Thesis, UPC, Barcelona. Roscoe, K.H. and Burland, J.B. 1968. On the generalized stress-strain behaviour of wet clay, Eng. Plast., Heyman, J. Lechie, F.A.A. Cambridge Press, Cambridge, pp. 535–609. Tamagnini R. 2000. Unsaturated soil modeling and FE implementation, MSc Thesis, (in Italian), Rome. Tamagnini R. 2003. The influence of hydraulic hysteresis in unsaturated soils FE analyses, Int. Conf.: From Experiment Evid. Towards Num. Mod. of Unsat Soils, September 18th–19th, 2003, Weimar, Germany. Tamagnini R. 2004. An extended Cam-clay model for unsaturated soils with hydraulic hysteresis, Geotechnique 54(3), 223–228.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Parametric investigations on a three-invariant implicit integration algorithm for unsaturated soils L.R. Hoyos The University of Texas at Arlington, Arlington, Texas, USA
P. Arduino The University of Washington, Seattle, Washington, USA
ABSTRACT: This paper introduces an implicit integration algorithm that has been implemented to simulate stress-strain response of unsaturated soils under suction-controlled multiaxial stress paths that are not achievable in a conventional cylindrical apparatus. The algorithm supports numerical analyses in a deviatoric stress plane (π-plane) by using a mixed control constitutive driver, in conjunction with a Generalized Cam-Clay model, within a constant-suction scheme, also incorporating the influence of a third stress invariant or Lode-angle θ. The classic Willam-Warnke surface, along with the generalized Barcelona model, is used for simulation of soil behavior in three-invariant stress space p-q-θ (mean stress-deviator stress-Lode angle). A thorough parametric investigation of the numerical algorithm has been undertaken for suction states ranging from 50 to 200 kPa using constitutive model parameters that were previously devised experimentally for compacted silty sand. Numerical predictions are presented in terms of deviatoric stress versus principal strain response as well as strength envelopes in octahedral plane. The developed algorithm will prove to have a wide application potential in geotechnical boundaryvalue problems involving unsaturated soil deposits or geotechnical infrastructure made of compacted soil.
1
INTRODUCTION
Soils are often subject to three-dimensional stress gradients due to continuous changes in stress state variables (σij − ua δij ) and (ua − uw )δij , as shown schematically in Figure 1. Therefore, in geotechnical boundary-value problems involving unsaturated soil deposits, the accurate predictions of the stress-strain Traffic load
Foundation load
Pavement (
1
– u a)
(ua – uw)
(
1
– ua)
(ua – uw)
(ua – uw) ( 2 – ua) (
3
– ua) (ua – uw)
(ua – uw) ( 2 – ua) (
3
– ua) (ua – uw)
Figure 1. Unsaturated soil systems subject to multiaxial stress states.
behavior of the soil-structure system require that the soil constitutive relations be valid for all multiaxial stress paths likely to be experienced in the field. In the present work, an implicit integration algorithm, originally introduced by Macari et al. (2003), has been refined to predict unsaturated soil response along a wide range of constant-suction multiaxial stress paths that are not achievable in a conventional cylindrical cell. The work is intended to facilitate more elaborate numerical solutions in geotechnical boundary-value problems that involve soil deposits oscillating under various partially saturated states as climatic conditions vary throughout the year. The developed algorithm is based on a few modifications made to the constitutive framework originally postulated by Alonso et al. (1990), referred to as the Barcelona model in this work. The refined algorithm supports numerical analyses in the deviatoric plane (π-plane) using a mixed control constitutive driver, in conjunction with a Generalized Cam-Clay model, that also accounts for the influence of a third stress invariant, i.e. Lode-angle θ, within a constant-suction scheme. The well-known Willam-Warnke (1975) elliptical surface was then used for simulation of unsaturated soil response in three-invariant stress space
721
(p:q:θ). Numerical predictions are presented in terms of deviator stress versus principal strain responses for different net octahedral stress levels and suction states, as well as in the form of failure surfaces on the π-plane. 2
MODEL PARAMETERS
Alonso et al. (1990) postulated a critical state based framework (Barcelona model) involving four state variables: net mean stress, p = (1/3)(σ1 + 2σ3 ) − ua , deviator stress, q = (σ1 − σ3 ), suction, s = (ua − uw ), and specific volume, v = (1 + e). The model rigorously respects the well-established framework of the Modified Cam-Clay model, featuring elastic strains when the soil state lies inside a state boundary surface, and plastic strains when this surface is reached. Elasto-plastic behaviour occurs as the soil state traverses the (p:q:s) boundary surface shown in Figure 2, causing an expansion or contraction of such surface. A detailed description of the model yield loci, flow rules, hardening laws, and elasto-plastic strain definitions is given by Alonso et al. (1990) and Macari et al. (2003). The best-fit values of Barcelona model parameters used for numerical predictions presented in this work can be summarized as follows: λ(0) = 0.22, slope of normal compression line in (v:p) plane for saturated case; k = 0.011, elastic swell index corresponding to a change of p; ks = 0.0096, elastic swell index corresponding to a change of suction; β = 17.9 (MPa)−1 , q
parameter controlling the rate of increase of slope λ(s) with suction; r = 0.21, parameter defining maximum stiffness; pc = 0.036 MPa, reference stress for which the LC locus becomes a straight line; G = 8.8 MPa, shear modulus; M = 0.982, slope of critical state line; k = 1.324, parameter controlling increase in cohesion with suction; and, po (0) = 0.041 MPa, yield stress for the saturated case. Model parameters were obtained from a previously accomplished series of constantsuction isotropic and axisymmetric loading tests on silty sand (Hoyos and Macari 2001).
3
IMPLICIT INTEGRATION SCHEME
In this work, the computational implicit integration driver is developed as a Backward Euler return rule based scheme for integrating the constitutive relations postulated by the Barcelona model. The solution of the unsaturated problem can be devised as the projection (via Closest-Point-Projection-Method) of a trial stress state (σ , s) onto an updated yield surface n+1 F, as depicted schematically in Figure 3. In this figure, σ = net stress tensor, s = matric suction, po = yield stress, and so = maximum past suction. Validation of the algorithm for the θ = 0◦ case, that is, axisymmetric case, is presented by Macari et al. (2003). A mixed-control driver was implemented as a usermodel operator. The updated surface n+1 Fi is expressed in terms of three stress invariants, that is, p, q, and Lode-angle θ. With the help of the Lode-angle θ, yield functions
CSL (s ) ( n+1 e , n+1 se )
CSL (s = 0)
1
e
M
Δ , Δse
1 M
q 2 M 2 {p + ps}{p o (s) p}= 0
d
p q
( n+1 , n+1 s )
( n , ns )
d s=0
( n , ns )
p p
s p
p o (0)
ps
p o (s )
n
F ( , s , po , so ) = 0
o
s
Figure 3.
(LC) s = so
n+1
F ( , s , po , so ) = 0
Implicit CPPM-based integration scheme.
SI LC
s
c = 1.0
c = 0.7
c = 0.53
k
Elastic region
1
⎧ p o (s ) ⎫ ⎧ p o ( 0 ) ⎫ ⎨ c ⎬=⎨ c ⎬ ⎩ p ⎭ ⎩ p ⎭
s=0 ps
Figure 2.
pc
(0) k (s) k
p
p o (0 )
g( , c) =
p o (s )
Barcelona model framework in (p:q:s) space.
Figure 4.
722
2(1 c2 ) cos(
/ 3) (1 2c) 4(1 c2 ) cos2 ( 4(1 c2 ) cos2 ( / 3) + (1 2c)2
/ 3 ) + 5c 2 4c
Willam-Warnke surface in octahedral plane.
values s = 50, 100, and 200 kPa. Likewise, Figures 8 and 9 show predicted deviator stress versus principal strain response from TC tests for the same variables. In general, predictions capture the compressive (+) or 0.50
0.40 Deviator stress, q : MPa
defined in 2-D space can be expanded into 3-D space via a function g (θ, c) in which parameter ‘‘c’’ controls the shape of yield surface in (p:q:θ) space, representing the ratio of yield stresses in extension to those in compression, as shown in Figure 4. In this work, a function g (θ, c) originally proposed by Willam and Warnke (1975) for characterization of concrete behavior under general stress states was adopted. The function has been successfully used to capture constitutive response of soils (Manzari and Dafalias 1997) and is defined in Figure 4. With the developed algorithm, the influence of Lode-angle θ on unsaturated soil response in (p:q:θ) space is parametrically investigated using the Barcelona model parameters described in section 2 above for compacted silty sand.
s = 200 kPa 0.30
0.20
s = 100 kPa
0.10 s = 50 kPa
PREDICTIONS OF SOIL RESPONSE Volumetric strain : cm/cm
4
0.00 -0.10
4.1 General multiaxial stress response The parametric investigations of the developed algorithm are based on simulations of silty sand response along constant-suction, monotonic triaxial compression (TC), triaxial extension (TE), and simple shear (SS) stress paths imposed on cubical, normally consolidated soil specimens. Test schemes are depicted schematically on a deviatoric plane in Figure 5. In this work, the net octahedral stress σoct and deviator stress q are both defined in terms of total principal stresses σ1 , σ2 , and σ3 as follows: σ1 + σ 2 + σ 3 − ua 3
0.000
0.005
0.010
0.015 0.00
s = 100 kPa
s = 50 kPa 0.20
0.10
b=
Volumetric strain : cm/cm
TC (b = 0, θ = 0o)
σ2 – σ3 σ1 – σ3
θ σoct = 50, 100, or 200 kPa
(σ2 – ua)
Figure 5.
0.10
0.30
0.00 -0.10
A
0.05 Major principal strain : cm/cm
0.40
(1)
(σ1 – ua)
TE (b = 1, θ = 60o)
s = 50 kPa
s = 200 kPa
Figs. 6 and 7 show predicted deviator stress versus principal strain response of silty sand from TC tests at σoct = 50 and 200 kPa, respectively, for suction
SS (b = 0.5, θ = 30 )
s = 200 kPa s = 100 kPa
0.50
1 q = √ (σ1 − σ2 )2 + (σ2 − σ3 )2 + (σ1 − σ3 )2 (2) 2
o
0.10
Simulated response from TC test at σoct = 50 kPa.
Figure 6.
Deviator stress, q : MPa
σoct =
-0.05 0.00 0.05 Principal strain : cm/cm
s = 50, 100, or 200 kPa
-0.05 0.00 0.05 Principal strain : cm/cm
0.10
0.000 s = 200 kPa 0.005 s = 100 kPa 0.010
0.015 0.00
s = 50 kPa
0.05 Major principal strain : cm/cm
0.10
(σ3 – ua)
Simulated suction-controlled testing schemes.
Figure 7. 200 kPa.
723
Simulated response from TC test at σoct =
4.2 Strength loci in deviatoric plane
0.50
As previously mentioned, the Willam-Warnke elliptical surface defined in Figure 4, along with the generalized Barcelona framework, was used for simulation of unsaturated soil response in a three-invariant stress space. By using this approach, critical state lines
Deviator stress, q : MPa
0.40
0.30 s = 200 kPa 0.20 s = 100 kPa
0.50
0.10 0.40
s = 50 kPa 0.10
0.000
0.005
s = 200 kPa
Deviator stress, q : MPa
-0.05 0.00 0.05 Principal strain : cm/cm
s = 200 kPa
0.30 s = 100 kPa 0.20
s = 50 kPa
s = 100 kPa 0.010
0.015 0.00
Figure 8.
0.10
s = 50 kPa 0.00 -0.10
0.05 Major principal strain : cm/cm
-0.05 0.00 0.05 Principal strain : cm/cm
0.10 Volumetric strain : cm/cm
Volumetric strain : cm/cm
0.00 -0.10
Simulated response from TE test at σoct = 50 kPa.
expansive (−) nature of the principal strains depending on the nature of the simulated stress path. In all cases, matric suction is predicted to have a significant effect on soil’s shear strength, with a considerable increase in strength for s = 200 kPa. As it is expected, confinement, in the form of net octahedral stress σoct , also plays a significant role in soil’s multi-axial response, with a considerable increase in strength for σoct = 200 kPa. Matric suction is also predicted to have a paramount influence on soil’s volumetric response, with a considerable increase in volumetric stiffness for s = 200 kPa. Volumetric strain in Figures 6 through 9 is defined as: εv = ε1 + ε2 + ε3 . During TC testing, the major principal stress σ1 is increased while the minor principal stresses σ2 and σ3 are reduced of the same amount, hence the net octahedral stress σoct remains constant (Fig. 5). Hence, the corresponding minor and intermediate principal strains are predicted to be expansive (−) whereas the major principal strain will be compressive (+). During TE testing, the major and intermediate principal stresses σ1 and σ2 are equally increased while the minor principal stress σ3 is decreased (Fig. 5). Consequently, the major and intermediate principal strains are predicted to be compressive (+) while the minor principal strain will be expansive (−).
0.10
0.000 s = 200 kPa 0.005 s = 100 kPa s = 50 kPa
0.010
0.015 0.00
Figure 9. 200 kPa.
0.05 Major principal strain : cm/cm
0.10
Simulated response from TE test at σoct =
(
1
– ua)
o
=0
50.0
37.5 o
= 30
25.0
o
= 60
12.5 s = 200 kPa s = 100 kPa s = 50 kPa
00.0
(
Figure 10. 50 kPa.
724
2
– ua)
(
3
– ua)
Predicted strength loci in π-plane for σoct =
(
1
– ua)
o
=0
50.0
(a)
37.5 o
= 30
25.0 o
= 60
12.5
s = 200 kPa s = 100 kPa s = 50 kPa
00.0
(
2
– ua)
(
3
– ua) (b)
Predicted strength loci in π-plane for σoct =
Figure 11. 100 kPa.
( 1 – ua) o
=0
50.0
o
= 30
37.5 (c) o
= 60
25.0 s = 200 kPa s = 100 kPa s = 50 kPa
12.5
00.0
( 2 – ua)
Figure 12. 200 kPa.
( 3 – ua)
Predicted strength loci in π-plane for σoct =
(failure loci) predicted by Barcelona model for different matric suction states can be extended to a 3-D stress space with different strengths in compression and extension. It is assumed that the strength ratio ‘‘c’’ (Fig. 4) remains constant with suction s, and also that the soil behaves as an isotropic material.
(d)
Figure 13. (wetting).
725
Predicted failure by decreasing suction
Figures10–12 show the predicted strength loci of unsaturated silty sand in the π-plane along with predictions of the Willam-Warnke failure criteria for all TC, TE, and SS tests simulated at σoct = 50, 100, and 200 kPa for the various matric suctions, s = 50, 100, and 200 kPa. From these figures, it can be readily observed, in all cases, the significant influence that matric suction exerts on the size and position of the shear strength envelopes, with a considerable expansion of the envelopes for s = 200 kPa. 5
SIMULATING WETTING-DRIVEN FAILURE
Simulations presented in the previous section correspond to constant-suction stress-strain responses that can be experimentally validated via axis-translation technique. However, the implicit algorithm also supports analyses with varying matric suction. Figure 13(a) shows a simulated stress path illustrating the possibility of failure of a stressed unsaturated soil when suction is considerably reduced due to a wetting front. This type of failures is significant in partially saturated soil slopes subjected to wetting due to infiltration from rainfalls (Alonso et al. 1990). Suction was first increased (drying) to a value of 200 kPa at constant net mean stress of 150 kPa. The net mean stress was then increased at constant suction to a value of 250 kPa. A deviatoric stress was then applied at constant suction and constant net mean stress from 0 to 250 kPa, following a TC stress path. At this point, suction was finally steadily reduced until failure was achieved. The effect of final wetting stage on soil deformation is illustrated in Figures 13(b)–(d). Soil failure, so simulated, takes place at almost full saturation condition (s → 0). 6
CONCLUDING REMARKS
Numerical predictions with the refined implicit integration algorithm summarized in this work are able to capture the compressive (+) or expansive (−) nature of the principal strain response of silty sand, depending on the nature of the simulated stress path. Adoption of the Willam-Warnke function g (θ, c), with a constant strength ratio ‘‘c’’ in compression and
extension, can be considered reasonably appropriate in predicting unsaturated soil response in the threeinvariant stress space. The predicted response of unsaturated silty sand underscores the potential of the developed CPPMbased implicit algorithm for numerical analyses of geotechnical boundary-value problems involving unsaturated soil deposits that are subject to simultaneous, three-dimensional stress gradients defined by the net stress tensor (σij − ua δij ) and the matric suction tensor (ua − uw )δij . The implicit algorithm also supports analyses with varying matric suction states. Currently, a comprehensive series of multiaxial, suction-controlled tests on cubical specimens of silty sand are being conducted by the first author for further refinement and fine-tuning of the developed algorithm. To this end, a novel true triaxial (cubical) device has been implemented. ACKNOWLEDGEMENT The true triaxial device has been implemented under U.S. National Science Foundation Award # 0216545. This research support is gratefully acknowledged. REFERENCES Alonso, E.E., Gens, A. and Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique, 40(3), 405–430. Hoyos, L.R. and Macari, E.J. 2001. Development of a stress/suction-controlled true triaxial testing device for unsaturated soils. Geotechnical Testing Journal, ASTM, 24(1), pp. 5–13. Macari, E.J., Hoyos, L.R. and Arduino, P. 2003. Constitutive modeling of unsaturated soil behavior under axisymmetric stress states using a stress/suction-controlled cubical test cell. International Journal of Plasticity, 19(10), 1481–1515. Manzari, M.T. and Dafalias, Y.F. 1997. A critical state twosurface plasticity model for sands. Géotechnique, 47(2), 255–272. Willam, K.J. and Warnke, E.P. 1975. Constitutive model for the triaxial behavior of concrete. Proceedings of the International Association for Bridge and Structural Engineering (IABSE), Bergamo, Italy, May 1974, Paper III-1, 19, 1–30.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A multi-cell extension to the Barcelona Basic Model W.T. Solowski & R.S. Crouch Durham University, Durham, UK
D. Gallipoli University of Glasgow, Glasgow, UK
ABSTRACT: One of the sources of discrepancy between laboratory observations and the predicted behaviour of unsaturated soil (by many existing constitutive models) is the sharp transition between the elastic and elastoplastic regimes exhibited by the latter but not the former. Such a transition is present in, for example, the Barcelona Basic Model. This paper suggests that by using the water retention curve and a multi-cell approach it is possible to overcome this limitation. The proposed enhancement may be incorporated relatively easily into many existing elasto-plastic models for unsaturated soils without addition of any new constitutive variables. The introduction of the algorithm presented here can improve the predictions in pre-yield states. In this paper the multi-cell approach has been implemented into the Barcelona Basic Model (BBM). The algorithm is described in detail using an illustrative stress path that involves hydrostatic compression, drying and wetting. The paper closes with a comparison of the modified model with the original BBM.
1
2
INTRODUCTION
The Barcelona Basic Model (BBM) proposed by Alonso et al. (1990) is perhaps the most widely used nonlinear continuum constitutive model for unsaturated soils. Despite its attractiveness this model has several shortcomings. For example, the model predicts an abrupt transition from elastic to elasto-plastic behaviour in a similar fashion to the Modified Cam Clay (MCC) model. In the light of laboratory evidence, such a response simplifies the behaviour of unsaturated soil substantially. To rectify this issue, the commonly employed solution is to create a constitutive model within a multi- or bounding surface plasticity framework (e.g. Russell & Khalili, 2005). Unfortunately, such an approach leads to (i) an increase in number of constants required by the model and (ii) additional numerical complexity. Therefore multior bounding surface plasticity models require greater experience to calibrate when compared with conventional elasto-plastic models. The proposed modifications to the BBM allow for a smoother modelling of the transition between the elastic and elasto-plastic regimes. The modified model uses only the BBM constants with the additional information given by the water retention curve. Also, the numerical algorithms required remain mostly the same as for the original BBM. The calibration process of the modified model is, however, more involved, but this is not a serious limitation.
UNSATURATED SOIL MICROSTRUCTURE
The main idea of the proposed constitutive model stems from an examination of the microstructure and water retention in unsaturated soils. Most constitutive models (with the exception of models using a double structure framework, such as developed by Gens & Alonso, 1992) ignore important aspects of microscopic soil fabric and thus assume a homogeneous medium, simply extending the continuum constitutive frameworks developed for fully saturated soils. However, fine grained unsaturated soil can have a much more complex fabric at microscopic level than saturated soil. The clay platelets combine together creating larger clusters commonly referred to as aggregates (this fact has been pointed out already by Alonso et al., 1987). The pores between the aggregates (macropores) are larger than within the aggregates (micropores) which leads to a double porosity structure. Such a structure can be seen in environmental scanning electron microscopy (ESEM) images and is confirmed by mercury intrusion porosimetry (MIP) tests (see e.g. Monroy, 2005). The non-homogeneous microstructure of unsaturated soil is also indirectly confirmed by the water retention curve. This curve describes the relationship between the suction and the water content for a given soil. The amount of water retained under a given suction is related to pore size distribution of the soil according to the Young-Laplace equation. Therefore,
727
the water retention curve can be used to calculate the radius of the largest pores filled with water at a given suction. As the water content of soil is known, the volume of pores with a smaller radius than this can also be estimated. Such an estimation of pore sizes in unsaturated soil via the water retention curve is helpful but imperfect, as drying/wetting of the soil leads to changes in its structure. The soil structure (skeleton) may change irreversibly as the wet portion of soil is drawn together or undergoes swelling due to variation of suction. So, while the water retention curve can be used to estimate the pore size distribution, the outcome will not be entirely representative for the soil given the nonuniqueness of the relationship between suction and water content caused by both irreversible strains and hydraulic hysteresis. This dependence of water retention behaviour on the soil deformation history has indeed been observed during experiments and partially incorporated in recent models for water retention behaviour (Gallipoli et al., 2003). 3
USING WATER RETENTION CURVE TO ENHANCE THE CONSTITUTIVE MODEL
Despite the shortcomings mentioned above, the water retention curve carries useful information about the microstructural behaviour of unsaturated soil. It is thus appropriate to use this information in constitutive modelling. Here, to keep the modification as simple as possible, it is assumed that a unique water retention curve, independent from the deformation and wetting/drying history of soil, exists. Such a water retention curve can be expressed as a direct relationship between suction and degree of saturation. Given this relationship, it is straightforward to determine what percentage of soil has experienced a maximum given value of suction—it is the corresponding value of degree of saturation Sr read from the water retention curve. It follows that at a given value of suction, the average mean stress acting on the soil skeleton is equal to the sum of the external stress p and the current suction multiplied by the corresponding degree of saturation sSr . This follows from the stress definition given by Houlsby (1997). Such an average stress does not account, however, for the history of soil, i. e. it does not take into account that the parts of soil which are currently dry, previously experienced suction. An assumption has been made here that the dried part of soil behaves ‘as though’ the suction value that it has recently experienced is still acting. The soil then may be thought of as being composed of a large number of internal cells. In Sr percent of cells the suction is equal to the current suction s. It is assumed that in each of the remaining cells the amount
of suction acting is equal to the latest value of suction experienced in that cell. Then, for every cell a separate instance of the constitutive model is run. During the analysis each cell experiences the same mean stress, but has a separate hardening parameter value and suction. After the computations, the deformations are averaged. During implementation, the number of cells, n, must be chosen to arrive at a balance between computational efficiency and realism.
4
IMPLEMENTATION OF MULTI-CELL FRAMEWORK FOR BBM
The multi-cell concept based on the use of the water retention curve as described above has been implemented in the BBM. It is convenient to assume that in the initial state the material is saturated, so that the initial value of suction in all cells is set equal to zero. The other assumption made at the beginning of the simulation is that the hardening parameter p∗0 (BBM preconsolidation stress for saturated conditions) in all cells is identical. Once suction is applied, the values of current preconsolidation pressure p0 in each cell are dependent on the value of hardening parameter p∗0 and the most recently experienced suction s p0 = p0 ( p∗0 , s) = pc
p∗0 pc
λ(0)−κ λ(s)−κ (1)
where pc is the value of the reference stress and λ(s) is the slope of the virgin compression line at suction s. This slope is calculated as: ! λ(s) = λ(0) (1 − r)e−βs + r (2) where λ(0)is the slope of the virgin compression line for the fully saturated soil, r and β are BBM constants. In every cell a separate instance of the BBM is used and, subsequently, the values from all cells are averaged.
5
EXAMPLE
In this section an illustrative example is given. To keep the example as simple as possible it was decided to use 5 cells (n = 5). The water retention curve is given in Figure 2. Initially (Fig. 1, point A) the soil is fully saturated, with a mean net stress p of 10 kPa which is also the value used for the reference pressure pc in BBM. The soil is normally consolidated, so the hardening parameter p∗0 is equal to 10 kPa. The other BBM parameters used were: elastic stiffness parameter for changes in net mean stress κ = 0.02, elastic
728
stiffness parameter for changes in suction κs = 0.05, atmospherics pressure patm = 100 kPa, stiffness parameter for changes in net mean stress for virgin states of the soil (with suction s = 0) λ(0) = 0.2, parameter defining the maximum increase of soil stiffness with suction β = 0.01 1/kPa and parameter defining the maximum soil stiffness r = 0.75. The initial specific volume at the reference pressure pc is set to 2.6. The initial soil state is given in Table 1. The stress path and corresponding values of the specific volume of soil are summarised in Figure 1. First, the soil is isotropic loaded until p = 100 kPa (Fig. 1, path A-B). The state of soil after such loading is given in Table 2. At this stage (Fig. 1, point B) the values of specific volume for each cell ν1i in Table 2 are equal and calculated as
ν1i = N (0) − λ(0) ln
Table 1.
i = 1..5
ν 1 + ν12 + ν13 + ν14 + ν15 1" i = 2.139 ν1 = 1 5 n i=1 n
ν1 =
(4) where n is the number of cells used. The soil is then dried until suction reaches 200 kPa (Fig 1, B–C). The values of suction corresponding to Sr equal to 0.9, 0.7, 0.5 and 0.47 are 30 kPa, 100 kPa, 180 kPa and 200 kPa respectively (see Fig. 2). The cells are dried in a sequence, assuming that the cell is dry when it is less then half full. This fully arbitrary assumption leads to drying the cells once the degree of saturation reaches 0.9, 0.7, 0.5, 0.3 which correspond to 30 kPa, 100 kPa, 180 kPa and 460 kPa suction respectively (see Fig. 2). As at final suction 200 kPa the corresponding degree of saturation is 0.47 > 0.3, so the cells 4 & 5 remain wet. The evolution of cell suction is given by Table 3, where s(Sr ) denotes suction corresponding to the value of degree of saturation as given by the water retention curve (Figs 2 & 3). The soil state after drying is summarized in Table 4. The specific volume for each cell ν2i and preconsolidation pressure pi0 in Table 4 are calculated using: si + patm , patm
i = 1..5
Stress path, as calculated in the example. Initial condition of soil (Fig. 1, point A).
Cell (i)
1
2
3
4
5
Hard. par. p∗0 [kPa] Suction [kPa] Specific vol. N (0)*
10 0 2.6
10 0 2.6
10 0 2.6
10 0 2.6
10 0 2.6
*N (0) is the specific volume at the reference pressure pc . Table 2.
Soil state at p = 100 kPa (Fig. 1, point B).
Cell (i) p∗0 [kPa]
Hard. par. Suction [kPa] Specific volume ν1i
1
2
3
4
5
100 0 2.139
100 0 2.139
100 0 2.139
100 0 2.139
100 0 2.139
(3)
The average specific volume is
ν2i = ν1i − κs ln
Figure 1.
p∗,i 0 , pc
Figure 2.
729
Water retention curve.
(5)
Table 3.
1 " i ν21 + ν22 + ν23 + ν24 + ν25 = 2.097 (7) ν = n i=1 2 5 n
Evolution of suction during drying.
ν2 =
Suction Value [kPa] Cell (i)
1
2
3
4
5
Sr > 0.9 Sr = 0.9 0.9 > Sr > 0.7 Sr = 0.7 0.7 > Sr > 0.5 Sr = 0.5 0.5 > Sr > 0.3 Sr = 0.47
s(Sr ) 30 30 30 30 30 30 30
s(Sr ) 30 s(Sr ) 100 100 100 100 100
s(Sr ) 30 s(Sr ) 100 s(Sr ) 180 180 180
s(Sr ) 30 s(Sr ) 100 s(Sr ) 180 s(Sr ) 200
s(Sr ) 30 s(Sr ) 100 s(Sr ) 180 s(Sr ) 200
After drying, the soil is isotropically loaded to p = 500 kPa (Fig 1, C–D). This final value of mean net stress is higher than the value of the preconsolidation pressure p50 given in Table 4, so all the cells will be at stress states on the yield locus. The evolution of elastic and elasto-plastic loading is given in Table 5. The soil state after loading to 500 kPa is given in Table 6. Note that after loading the cell hardening parameters are different, ∗,3 ∗,4 ∗,5 ∗,2 p∗,1 0 > p0 > p0 > p0 = p0 ,
whereas the preconsolidation pressure p0 is the same for each cell. This is because the values of suction are different for cells 1, 2, 3 and 4. As the cells do not start yielding at the same mean net stress (compare Table 5) the transition between elastic and elasto-plastic regime appears smoother than in the original BBM. The greater the number of cells used in the model, the smoother the transition. The value of hardening parameters p∗,i 0 and specific volumesν3i in Table 6 are calculated using:
p∗,i 0
=p
Table 5. Figure 3. Illustration of suction distribution within cells after drying to s = 200 kPa (Fig. 1, point C). A cell is assumed to be dry when its Sr > 0.5.
c
pi0 pc
i )−κ λ(s λ(0)−κ
,
i = 1..5
(8)
Evolution of hardening during loading.
Loading Cell (i)
1
2
3
4
5
Table 4. Soil state after drying to s = 200 kPa (Fig. 1, point C).
p < p10
e
e
e
e
e
p10 < p < p20
ep
e
e
e
e
Cell (i)
1
2
3
4
5
p20 < p < p30
ep
ep
e
e
e
Hard. par. p∗0 [kPa] Suction [kPa] Specific volume ν2i Precons. pres. pi0 [kPa]
100 30 2.126 119.6
100 100 2.104 163.3
100 180 2.088 200.4
100 200 2.084 207.1
100 200 2.084 207.1
p30 < p < p40
ep
ep
ep
e
e
p > p40 = p50
ep
ep
ep
ep
ep
e–elastic; ep–elasto-plastic.
Table 6.
i c pi0 = p0 ( p∗,i 0 ,s ) = p
p∗,i 0 pc
λ(0)−κ i
λ(s )−κ
,
i = 1..5
(6)
where patm = 100 kPa is atmospheric pressure. The average specific volume is, similarly to equation (4), given by:
Soil state at p = 500 kPa (Fig. 1, point D).
Cell (i)
1
2
3
4
5
Hard. par. p∗,i 0 [kPa] Suction [kPa] Specific volume ν3i Precons. pres. p0 [kPa]
377.3 30 1.855 500
253.6 100 1.906 500
202.6 180 1.929 500
195.4 200 1.932 500
195.4 200 1.932 500
730
p0 si + patm − κs ln , c p patm
ν3i = N (0) − λ(si ) ln
i = 1..5
Table 9.
(9)
Loading Cell (i)
The average specific volume is:
p < p∗,1 0
n ν 1 + ν32 + ν33 + ν34 + ν35 1" i = 1.911 ν3 = 3 ν3 = n i=1 5
(10) In the next stage, the soil is unloaded until it reaches the mean stress of 100 kPa (Fig. 1, D-E). The specific volume for each cell is then: ν4i = ν3i − κ ln
p , p0
i = 1..5
(11)
The average specific volume is calculated similarly as before (see e.g. 4). At this stage the sample is wetted until fully saturated (Fig 1, E–F). The evolution of suction during wetting is given in Table 7 and the soil state after wetting is identified in Table 8. After saturation, the hardening parameters are unchanged and the value of preconsolidation pressure in each cell is equal to the value of hardening parameter in this cell. The specific volume in Table 8 is calculated as ν5i = ν4i + κs ln
Table 7.
p + patm , patm
Evolution of hardening during loading.
i = 1..5
p∗,1 0 p∗,2 0 p∗,3 0
p>
p∗,4 0
p∗,2 0 p∗,3 0 p∗,4 0 p∗,5 0
1
2
3
4
5
e
e
e
e
e
ep
e
e
e
e
ep
ep
e
e
e
ep
ep
ep
e
e
ep
ep
ep
ep
ep
e—elastic; ep—elasto-plastic. Table 10.
Soil state at p = 500 kPa (final, Fig. 1, point G).
Cell (i)
1
2
3
4
5
Hard. par. p∗0 [kPa] Suction [kPa] Specific volume ν6i Precons. pres. p0 [kPa]
500 0 1.818 500
500 0 1.818 500
500 0 1.818 500
500 0 1.818 500
500 0 1.818 500
(12)
Evolution of suction during wetting [kPa].
Loading Cell (i)
1
2
3
4
5
Sr = 0.47 Sr < 0.5 Sr = 0.5 0.5 < Sr < 0.7 Sr = 0.7 0.7 < Sr < 0.9 Sr = 0.9 Sr > 0.9
30 30 30 30 30 30 30 s(Sr )
100 100 100 100 100 s(Sr ) 30 s(Sr )
180 180 180 s(Sr ) 100 s(Sr ) 30 s(Sr )
200 s(Sr ) 180 s(Sr ) 100 s(Sr ) 30 s(Sr )
200 s(Sr ) 180 s(Sr ) 100 s(Sr ) 30 s(Sr )
e—elastic; ep—elasto-plastic. Table 8.
Soil state after wetting (s = 0 kPa) (Fig. 1, point F).
Cell (i)
1
2
3
4
5
Hard. par. p∗,i 0 [kPa] Suction [kPa] Specific volume ν5i Precons. pres. pi0 [kPa]
377.3 0 1.900 377.3
253.6 0 1.972 253.6
202.6 0 2.012 202.6
195.4 0 2.019 195.4
195.4 0 2.019 195.4
Figure 4. Influence of number of cells used in simulation—comparison between simulation with 2 and 100 cells.
The average specific volume is the mean of the specific volumes of calculated in each cell (see eq. 4). Finally, the soil is loaded until the mean net stress p reaches a value of 500 kPa (Fig. 1, F–G). The loading is initially elastic, but as the mean stress increases, so the cells yield. The evolution of hardening during this loading is given in Table 9, and the final soil state is given in Table 10.
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Figure 5. Influence of number of cells used in simulation—enlarged detail from Figure 4. Comparison between simulations using 2, 3, 5, 10 and 100 cells.
Figure 6. Comparison of the modified BBM with the original formulation.
The value of specific volume for each cell is then calculated as in (3) and the average specific volume as in (3). Note that the plastic behaviour will start gradually, with some yielding of the material before reaching the virgin compression line. This gradual transition will be better approximated when more cells are used. The influence of the number of cells used is illustrated in Figures 4 and 5.
shrinking and swelling behaviour are different, and the slope of the unsaturated compression line λ(s) is steeper in the case of the modified model, the amount of collapse predicted by the original model is larger. Finally, it is evident that the modified model predicts a smoother transition between the elastic and elasto-plastic regions. This smooth transition occurs also in the case of loading a fully saturated soil when it has previously been in an unsaturated state and was loaded beyond the yield point (of any of cells).
6
COMPARISON WITH THE ORIGINAL BBM
The comparison has been made using a problem given in section 5. All the parameters used for the BBM were the same as in the previous example. The test began with a mean net stress p = 10 kPa on a saturated virgin compressed soil and the water retention curve is as depicted in Figure 2. The comparison of the modified model prediction with the original BBM prediction (Fig. 6) reveals the differences. The slopes of the unsaturated compression lines are slightly different. This is to be expected, as the modified model effectively averages the specific volume and a range of suctions are operating within the material, whereas the original BBM uses only the current value of suction. The model can be calibrated, however, such that the fully yielded behaviour is similar. The other noticeable difference is the amount of elastic shrinking and swelling predicted by the models. This occurs because in the original formulation the shrinking depends on the final value of suction whereas in the modified form it is averaged over different changes in suction across the cells. As the
7
CONCLUSIONS
The proposed modifications to the BBM improve the capabilities of the model by offering more realistic material behaviour during yielding. The number of parameters in the model is unchanged as the water retention curve is also a pre-requisite for the BBM. On the other hand, the proposed solution may be just regarded as a convenient ‘fix’ to the model, as it does not work for the particular case of a saturated soil. The calibration of the model requires some care, as calculations of the slope of the unsaturated compression line slope λ(s) and amount of elastic shrinking/swelling is not so straightforward. The calibration process could employ an optimisation algorithm which would allow for automation of the process. Alternatively, the model parameters may be computed in a series of approximations. The latter approach would require an algorithm that would calculate deformations under given loading. It should be pointed out that the calibration of the model still does not require a greater
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number of tests than those required for the BBM. This is certainly an advantage over a model that would introduce a bounding surface plasticity framework into the BBM. The amount of computer resources required is higher than for the BBM. However, on current machines, it is entirely feasible to perform 2D Finite Element simulations with more than 105 elements using the enhanced model. Given that the speed (and memory) of computers continues to increase, it is very likely that in few years 3D analyses will be almost as quick as current 2D simulations. It is worth adding that the algorithm complexity of this enhanced model is not significantly increased compared with the original BBM, as much of the code used for each of the cells is the same. The proposed modified model is in the process of being validated against a wide range of experimental data. Only then can the improvements in prediction of unsaturated soil behaviour given by the modified model can be truly assessed. ACKNOWLEDGMENTS The authors gratefully acknowledge funding by the European Commission through the MUSE Research
Training Network, contract: MRTN-CT-2004-506861. The authors would like to also thank the reviewer for valuable comments and insights. REFERENCES Alonso, E.E., Gens, A., Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique 40(3): 405–430. Alonso, E.E., Gens, A., Josa, A., Hight, D.W. 1987. Special problems soils. General Reports. In proceedings of the 9th European Conference on Soil Mechanics and Foundation Engineering. Dublin. 3: 1087–1146. Gallipoli, D., Wheeler, S.J., Karstunen, M. 2003. Modelling the variation of degree of saturation in a deformable unsaturated soil. Géotechnique 53(1): 105–112. Gens, A., Alonso, E.E. 1992. A framework for the behaviour of unsaturated expansive clays. Can. Getech. J. 29: 1013–1032. Houlsby, G.T. 1997. The work input to an unsaturated granular material. Géotechnique 47(1): 193–196. Monroy, R. 2005. The influence of load and suction changes on the volumetric behaviour of compacted London Clay. PhD thesis. Imperial College, London. Russell, A.R., Khalili, N. 2005. A unified bounding surface plasticity model for unsaturated soils. Int. J. Numer. Anal. Meth. Geomech. 30: 181–212.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A numerical simulation of triaxial tests of unsaturated soil at constant water and air content by using an elasto-viscoplastic model F. Oka, H. Feng & S. Kimoto Department of Civil and Earth Resources Engineering, Kyoto University, Kyoto, Japan
T. Kodaka Department of Civil Engineering, Meijo University, Nagoya, Japan
H. Suzuki Osaka Gas, Osaka, Japan
ABSTRACT: It is known that air can be trapped in some parts of embankments during heavy rain or overflow. In this case, air pressure, as well as water pressure, may change under partially drained conditions. However, most laboratory test programs have been conducted under constant air pressure conditions. In this paper, a numerical model for unsaturated soils based on the mixture theory and an elasto-viscoplastic constitutive model is presented. The collapse behavior, due to a decrease in suction, is expressed by the shrinkage of the overconsolidation boundary surface, the static yield surface, and the viscoplastic potential surface. The theory used in the analysis is a generalization of Biot’s two-phase mixture theory for saturated soil. A soil-water-air coupled finite element method is developed in the present study using the governing equations for multiphase soil based on the nonlinear finite deformation theory. Three-dimensional numerical analyses at constant water and constant air content are conducted and the applicability of the proposed method is confirmed. The performance of the model is examined with reference to triaxial compression tests preformed on unsaturated soil at constant water and air content.
1
INTRODUCTION
Most laboratory test programs have been conducted on unsaturated soils under constant air pressure. However, drained conditions for water and air cannot always be attained in engineering problems. For example, the air pressure in river embankments increases during the seepage processes and air pressure may also vary during soil compaction. Yamamura (1971) indicated that air can be trapped in parts of embankments during heavy rain or overflow. In these cases, the air pressure changes under partially drained conditions. It means that constant water and constant air content tests are necessary to accurately verify numerical models of unsaturated soil for general boundary value problems. In this work, triaxial tests on silty clay at constant water and air content have been conducted where both the pore water and air pressures have been accurately measured. The stress variables of suction and excess of total stress over air pressure (or the excess of total stress over water pressure) have usually been employed to describe the mechanical behavior of unsaturated soils (Bishop 1960; Fredlund & Morgenstern 1977; Alonso
et al. 1990). Recently, the so called average skeleton stress has been used from the viewpoint of the mixture theory (Bolzon et al. 1996; Jommi 2000; Ehlers 2004), where an average pore pressure composed of pore water pressure and pore air pressure is adopted to determine the stress acting on the soil skeleton. Hereafter, the average skeleton stress is called skeleton stress to avoid confusion of the average skeleton stress with the mean skeleton stress. A number of constitutive models have been proposed for unsaturated soil (Alonso et al. 1990; Wheeler & Sivakumar 1995; Wheeler & Karube 1996; Cui & Dleage, 1996; Thomas & He 1998; Sheng et al. 2003; Kohgo et al. 1993) but most of them are formulated within a rate-independent framework such as elasto-plastic models. By adopting the skeleton stress from the viewpoint of mixture theory and by introducing the suction effect into an elasto-viscoplastic constitutive model for saturated soils with structural degradation (Kimoto & Oka 2005), an elasto-viscoplastic model for unsaturated soils has been recently developed (Kim et al. 2005). Although the collapse behavior, which is brought about by a decrease in suction, can be reproduced, such model is still based on two phases, which can
735
not reflect the evolution of pore water pressure and pore air pressure separately. For this reason, a van Genuchten type of equation is employed as the constitutive equation between degree of saturation and suction. Based on this, an air-water-soil three-phase coupled model has been proposed (Oka et al. 2006; Feng et al. 2006) and used for two-dimensional numerical simulations under plane strain conditions. In the present study, this research is extended by employing a three-dimensional multiphase finite element method incorporating an elasto-viscoplastic constitutive equation to simulate the triaxial behavior of unsaturated cylindrical specimens.
2
ELASTO-VISCOPLASTIC CONSTITUTIVE MODEL INCLUDING SUCTION EFFECT
The constitutive model for unsaturated soils used in this work is formulated in terms of the skeleton stress. The definitions of the skeleton stress and the average pore fluid pressure are given as follows: σij = σij − P F δij
(1)
P F = sP W + (1 − s)P G
(2)
where σij is the skeleton stress, P W and P G are the pore water pressure and the pore gas pressure respectively, s is the degree of saturation and P F is the average pore pressure. The adoption of the skeleton stress represents a natural extension of the mixture theory to unsaturated soil. Therefore, it is possible to formulate a model for unsaturated soil starting from a model for saturated soil by substituting the skeleton stress for the effective stress. In addition, it is necessary to incorporate the effect of suction into the constitutive model. This means that two independent stress variables are needed, i.e. the skeleton stress and the suction. The skeleton stress has been called average skeleton stress by Jommi (2000) but the term skeleton stress is preferred here to avoid confusion with the mean skeleton stress. In this study, the saturated elasto-viscoplastic model for overstress-type viscoplasticity with soil structure degradation proposed by Kimoto & Oka (2005) has been extended to unsaturated soils using the skeleton stress and including suction effects. The collapse behavior of unsaturated soils is macroscopic evidence of the structural instability of the soil skeleton and it is totally independent of the chosen stress variables (Oka 1988; Jommi 2000). In the present model, the collapse behavior is described by the shrinkage of the overconsolidated boundary surface, the static yield surface, and the viscoplastic surface due to the decrease in suction.
It is assumed that the strain rate tensor consists of the elastic stretching tensor Dije and the viscoplastic vp stretching tensor Dij as vp
Dij = Dije + Dij
(3)
The elastic stretching tensor is given by a generalized Hooke type law, namely, Dije =
1 ˙ κ σ˙ m δij Sij + 2G 3 (1 + e) σm
(4)
where Sij is the deviatoric stress tensor, σm is the mean skeleton stress, G is the elastic shear modulus, e is the initial void ratio, κ is the swelling index, and the superimposed dot denotes time differentiation. 2.1 Overconsolidation boundary surface The overconsolidated boundary surface separates the normally consolidated (NC) region, fb ≥ 0, from the overconsolidated region, fb < 0, as follows: ∗ fb = η¯ (0) + Mm∗ ln
σm =0 σmb
(5)
∗ ∗ ∗ η¯ (0) = {(ηij∗ − ηij(0) )(ηij∗ − ηij(0) )} 2 1
(6)
where ηij∗ is the stress ratio tensor (ηij∗ = Sij /σm ), and (0) denotes the state at the end of the consolidation, in other words, the initial state before the shear test. Mm∗ √ is the value of η∗ = ηij∗ ηij∗ when the volumetric strain increment changes from negative to positive dilatancy, which is equal to ratio Mf∗ at the critical state. σmb is the strain-hardening parameter, which control the size of the boundary surface. The suction effect is introduced into the value of σmb as
1 + e vp εkk λ−κ
c Pi − 1 × 1 + SI exp −Sd Pc
= σma exp σmb
vp
(7)
where εkk is the viscoplastic volumetric strain, P c is the present suction value, Pic is a reference suction, SI denotes the increase of yield stress when suction increases from zero to the reference value Pic . Sd controls the rate of increasing or decreasing of σmb with suction and σma is a strain-softening parameter used to describe degradation caused by structural changes, namely
736
σma = σmaf + (σmai − σmaf ) exp (−βz)
t z˙ dt
z=
# vp vp with z˙ = ε˙ ij ε˙ ij
(8)
2.3 Viscoplastic potential function The viscoplastic potential function is given by
(9) ∗ ˜ ∗ ln +M fp = η¯ (0)
0
σm =0 σmp
(14)
and σmaf are the initial and the final in which σmai values of σma while β controls the rate of degradavp tion with viscoplastic strain, and ε˙ ij is the viscoplastic strain rate.
denotes the mean skeleton stress at the interwhere σmp section of the viscoplastic potential function surface and the σm axis.
2.2 Static yield function
2.4 Viscoplastic flow rule
To describe the mechanical behavior of the soil at its static equilibrium state, a Cam-clay type static yield function is assumed:
Finally, the viscoplastic stretching tensor is based on Perzyna’s type of viscoplastic theory (Perzyna 1963) and is given as
˜ ∗ ln fy = η∗(0) + M
σm
(s) σmy
=0
(10)
˜ ∗ is assumed to be constant in the NC region where M and varies with the current stress in the OC region as ⎧ ∗ : NC region ⎪ ⎨ Mm # ˜∗= ηij∗ ηij∗ M ⎪ : OC region ⎩− ) ln(σm /σmc
σmc = σmb exp
Mm∗
(11)
(12)
∂fp ∂σij
(15)
where the symbol is defined as 1 (fy ) =
denotes the mean skeleton stress at the interwhere σmc section of the overconsolidated boundary surface and the σm axis as
# ∗ ∗ ηij(0) ηij(0)
vp
Dij = γ 1 (fy )
1 (fy ); fy > 0 0;
(16)
fy ≤ 0
in which 1 denotes a material function for rate sensitivity. Herein, the value of fy is assumed to be positive for any stress state in this model, in other words, the stress state always exists outside of the static yield function, so that viscoplastic deformation always occurs. Based on the experimental results of constant strain-rate triaxial tests, the material function 1 is defined by an exponential function (Kimoto & Oka 2005).
(s) controls The static strain hardening parameter σmy the size of the static yield surface. In the same way as the overconsolidation boundary surface, the parame(s) ter σmy varies with the changes in suction as well as with the changes in viscoplastic volumetric strain and structural degradation:
(s) = σmy
1 + e vp εkk σma exp λ−κ
c Pi × 1 + SI exp −Sd −1 Pc (s) σmyi
exp m
∗ ˜ ∗ M η¯ (0)
ln
σm
(s) σmy
(17)
where m is the viscoplastic parameter that controls rate sensitivity and the viscoplastic parameter Cijkl is a fourth rank isotropic tensor given by Cijkl = aδij δkl + b(δik δjl + δil δjk ),
σmai
(s) (s) where σmyi is initial value of σmy .
γ 1 (fy ) =
Cijkl σm
C2 = 3a + 2b
C1 = 2b, (18)
(13) where a and b are material parameters, which have a relation with the deviatoric component C1 and volumetric component C2 of the viscoplastic parameter.
737
The viscoplastic deviatoric and volumetric strain rates are obtained as follows: vp
e˙ ij
vp
ε˙ kk
η∗ − η∗ ij ij(0) ∗ ˜ ∗ ln σm = C1 σm exp m η¯ (0) +M σmb η¯ ∗ (19) ∗ ˜ ∗ ln σm +M = C2 σm exp m η¯ (0) σmb ∗ ∗ ∗ η (η − ηmn(0) ) ˜ ∗ − mn mn (20) × M η¯ ∗
In case of isotropic consolidation, the suction effect on the over consolidation boundary surface, fb static yield function, fy and viscoplastic potential function, fp are illustrated in the σm − Sij Sij space in Figure 1. For this overstress type viscoplastic model, the viscoplastic strain rate depends on the current stress state and the static hardening parameters given by Equation 13. The collapse behavior is due to the viscoplastic strains caused by shrinkage of the static yield surface due to a decrease of suction. 2.5
Soil-water characteristic curve
The soil-water characteristic curve (SWCC) is defined as the relationship between the degree of saturation and suction. The SWCC is a measure of the waterholding capacity of the soil when subjected to changes of suction. In this model, the van Genuchten (1980) type of equation is adopted as %−m $ s = (smax − smin ) (1 + (αP C )n + smin
3
NUMERICAL RESULTS AND DISCUSSION
Based on the Theory of Porous Media (TPM), an airwater-soil coupled finite element model has been used for a numerical investigation of the triaxial compression behavior of unsaturated silty clay under constant water and constant air conditions. Based on the finite deformation theory, a three-dimensional soil-waterair coupled finite element code has been developed (Kimoto et al. 2007). Figure 2(a) shows a twentynode isoparametric element with a reduced Gaussian (2 × 2 × 2) integration for the soil skeleton and an eight-node isoparametric element with a full (2×2×2) integration for pore water and pore air. Figure 2(b) shows the finite element mesh together with the boundary conditions. All boundaries are assumed to be impermeable and the horizontal deformation is constrained at both top and bottom boundaries. The main material parameters and the initial conditions used in the analysis are listed in Table 1. Soil parameters are obtained by triaxial compression tests (Suzuki 2006). The numerical examples presented in this paper exhibit typical behavior of unsaturated soil under undrained conditions for water and air, such as changes in volumetric strain, shear strength, and pore air pressure. Predictions of the variation in suction were compared against the experimental results. Figure 3 illustrates the stress paths of samples with different levels of initial suction. A good agreement can be observed. By introducing the suction effect into the model, the model can reflect the fact that strength of
(21)
10cm
where smin and smax are the minimum and the maximum degree of saturation, α and n are material parameters and m = 1 − 1/n.
Z Y X
× Gauss point Displacement Pore fluid pressure (a) Figure 1. surfaces.
Static yield and overconsolidation boundary
2.5cm Fixed Horizontally fixed (b)
Figure 2. (a) Isoparametric elements and (b) Finite element mesh and boundary conditions.
738
500
Initial suction (kPa)
0
30
Initial void ratio e0 Shear modulus G0 (GPa) (kPa) Yield stress σmbi Swelling index κ Compression index λ Parameter m Parameter C1 (1/s) Parameter C2 (1/s) Critical ratio Mm∗ (kPa) Parameter σmaf Structure parameter β Suction parameter SI Suction parameter Sd Reference suction PiC Parameter α (1/kPa) Parameter n Permeability of water at s = 1 k W (m/s) Permeability of gas at s = 0k G (m/s) Shape parameter a Shape parameter b Saturation (Max) smax Saturation (Min) smin
1.0 1.05 34.8 40.6 160 160 0.0086 0.0094 0.095 0.105 52 1.0 × 10−11 1.5 × 10−11 1.23 160 0.0 0.5 0.25 100 0.03 1.45
50
100
1.07 45.1 160 0.0102 0.114
1.05 46.8 160 0.0102 0.114
Deviator stress (kPa)
Material parameters and initial condition.
400 300 c
P =100kPa c P = 50kPa c P = 30kPa c P = 0kPa
200 100 0 0
100
200
300
400
500
Mean skeleton stress (kPa)
(a) 500
Deviator stress (kPa)
Table 1.
1.0 × 10−6 1.0 × 10−5 3.0 2.3 1.0 0
400 300 200 100 0 0
100
200
300
400
500
Mean skeleton stress (kPa)
(b) Figure 3. Stress paths with different levels of initial suction (a) simulated results; (b) experimental results. 400
Deviator stress (kPa)
unsaturated soil increases with the increase in the initial suction. The mean skeleton stress also increases with compression due to the presence of gas phase. Deviator stress-axial strain curves under different initial suctions are presented in Figure 4. It can be seen that the deviator stress is higher in the case of a higher initial suction. Predicted volumetric strain during triaxial compression with different levels of initial suction for silty clay is shown in Figure 5. In the model, the pore air is assumed to be compressible and the volumetric strain can be seen as the compression of air. For this reason, the volumetric strain is higher in the case of a higher level of suction due to a higher air content. Figure 6 illustrates the relationship between suction and axial strain for different levels of initial suction. It shows that suction (P G − P W ) decreases during compression, which is similar to the experimental results except at the very beginning where a sudden drop in suction is observed. This might be due to changes in the initial soil structure of the samples. In such multiphase coupled analysis, the displacement, the pore water pressure, and the pore air pressure are unknown values. The change of pore pressures with compression can be calculated under constant water content and constant aiir content conditions. Figure 7 gives the changes in pore water pressure P W and pore air pressure P G with compression (P c = 50 kPa).
300
200
c
P =50kPa c P =30kPa c P =50kPa(exp) c P =30kPa(exp)
100
0 0
5
10
15
Axial strain (%) Figure 4.
4
Deviator stress vs. axial strain.
CONCLUSIONS
An air-water-soil three-phase coupled finite element model incorporating an elasto-viscoplastic constitutive soil model has been proposed. This method adopts
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A van Genuchten type soil water characteristic curve is employed as the constitutive equation linking suction and degree of saturation. Three-dimensional numerical simulations of triaxial compression tests under constant water and air conditions have been conducted using the proposed model. Comparisons with experimental results show that the model makes it possible to reproduce the behavior of unsaturated soil during triaxial compression under undrained conditions for pore water and air, including changes in pore air pressure, pore water pressure, degree of saturation and volumetric strain.
Volumetric strain (%)
0
c
1
P =30kPa c P =50kPa
2
3
4 0
4
8
12
16
Axial strain (%) Figure 5.
REFERENCES
Volumetric strain vs. axial strain.
50
Suction (kPa)
40 30 20
c
P =30kPa c P =50kPa c P =30kPa(exp) c P =50kPa(exp)
10 0 0
4
8
12
16
Axial strain (%) Figure 6.
Changes in suction with axial strain. c
Deviator stress (kPa)
P =50kPa
360
G
P
320 w
P
280 240 200 0
5
10
15
20
25
Mean skeleton stress (kPa) Figure 7.
Pore pressure vs. axial strain.
the average skeleton stress from the viewpoint of the mixture theory, and the suction effect is introduced in the hardening and softening of the yield surface and the over-consolidation boundary surface.
Alonso, E.E., Gens, A. & Josas, A. 1990. A constitutive model for partially saturated soils. Geotechnique 40(3):405–430. Biot, M.A. 1941. Three-dimensional theory of consolidation. J. Appl. Physics 12:155–164. Bishop, A.W. 1960. The measurement of pore pressure in the triaxial test. Proc. Conf. Pore pressure and suction in soils: 38–46; Butterworths, London. Bolzon, G., Schrefler, B. & Zienkiewicz, O.C. 1996. Elastoplastic soil constitutive laws generalized to partially saturated states. Geotechnique 46(2):279–289. Cui, Y.J. & Delage, P. 1996. Yielding and plastic behaviour of an unsaturated compacted silt. Geotechnique 46(2):291–311. Ehlers, W., Graf, T. & Ammann, M. 2004. Deformation and localization analysis of partially saturated soil. Compt. Methods Appl. Mech. Engrg. 193:2885–2910. Feng, H., Kimoto, S., Oka, F., Kodaka, T. & Suzuki, H. 2006. Three-dimensional multiphase analysis of elastoviscoplastic unsaturated soil. Proc. 19th KKCNN Symp. on Civil Engg.:449–452. Fredlund, D.G. & Morgenstern, N.R. 1977. Stress state variables for unsaturated soils. J. Geotech. Engng Div. Am. Soc. Civ. Engr. 103, GT5:313–321. Gallipoli, D., Gens, A., Sharama, R. & Vaunat, J. 2003. An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour. Geotechnique 53(1):123–135. Jommi, C. 2000. Remarks on the constitutive modeling of unsaturated soils. In Tarantino, A. & Manvuso, C. (eds), Experimental Evidence and Theoretical Approaches in Unsaturated Soils: 139–153. Balkema. Kim, Y., Kimoto, S., Oka, F. & Kodaka, T. 2005. Numerical simulation of the triaxial compression behaviour of unsaturated silt using an elasto-viscoplastic model. Proc. 11th IACMAG 1:361–367. Torino, Italy, 19–24 June 2005. Kimoto, S. & Oka, F. 2005. An elasto-viscoplastic model for clay considering destructuralization and consolidation analysis of unstable behavior, Soils and Foundations 45(2):29–42. Kimoto, S., Oka, F. & Higo, Y. 2004. Strain localization analysis of elasto-viscoplastic soil considering structural degradation. Compt. Methods Appl. Mech. Engrg. 193:2845–2866.
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Kimoto, S., Oka, F., Fushita, T. & Fujiwaki, M. 2007. A chemo-thermo-mechanically coupled numerical simulation of the subsurface ground deformations due to methane hydrate dissociation, Computers and Geotechnics, Vol. 34, No. 4, pp. 216–228. Kogho, Y., Nakano, M. & Miyazaki, T. 1993a. Theoretical aspects of constitutive elastoplastic model for unsaturated soils. Soils and Foundations 33(4):49–63. Kogho, Y., Nakano, M. & Miyazaki, T. 1993b. Verification of the generalized elastoplastic model for unsaturated soils. Soils and Foundations 33(4):64–73. Loret, B. & Khalili, N. 2000. A three phase model for unsaturated soils. Int. J. Numer. Anal. Meth. Geomech. 24(11):893–927. Loret, B. & Khalili, N. 2002. An effective stress elasticplastic model for unsaturated porous media. Mechanics of materials 34: 97–116. Oka, F., Kodaka, T., Kimoto, S., Kim, Y. & Yamasaki, N. 2006. An elasto-viscoplastic model and multiphase coupled FE analysis for unsaturated soil. Unsaturated Soils 2006(2):2039–2050; Proc. 4th Int. Conf. Unsat. Soils, Carefree Arizona, 2–6 April 2006. ASCE. Oka, F. 1988. The validity of the effective stress concept in soil mechanics. In M. Satake & J.T. Jenkins (eds), Micromechanics of Granular Materials:207–214. Elsevier Science Publisher B.V.: Amsterdam. Oka, F. 1982. Elasto-viscoplastic constitutive equation for overconsolidated clay. In Zurich, Dungar, R., Pande, G.N. & Studer, J.A. (eds), Numerical Models in Geomechanics; Proc. 1st Int. Symp.:147–156, Balkema.
Perzyna, P. 1963. The constitutive equation for work hardening and rate sensitive plastic materials, Proc. of Vibrational Problems, Warsaw, 4(3):74–85. Sheng, D., Sloan, W., Gens, A. & Smith, D.W. 2003. Finite element formulation and algorithms for unsaturated soils Part I: Theory. Int. J. Numer. Anal. Meth. Geomech 27:745–765. Suzuki, H., Kodaka, H. & Oka, F. 2006. Mechanical Properties of Unsaturated Silt under Unexhausted and pore air pressure controlled condition. Proc. 41st Annual Meeting of JGS: 323–324, Kagoshima (in Japanese). Thomas, H.R. & He, Y. 1998. Modeling the behaviour of unsaturated soil using an elastoplastic constitutive model. Geotechnique 48(5):589–603. Van Genuchten, M.T. 1980. A Close-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Science Society of America Journal 44: 892–898. Wheeler, S.J. & Karube, D. 1996. State of the art reportconstitutive modeling. 1st Int. Conf. on Unsaturated soils, Paris 3: 1323–1356. Wheeler, S.J. & Sivakumar, V. 1995. An elasto-plastic critical state framework for unsaturated soil. Geotechnique 45(1):35–53. Yamamura, K. 1971. Soil engineering research of river embankment. Doctoral thesis, Kyoto University, Japan; (in Japanese).
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Stress condition of an unsaturated pendular state granular soil C. Medina & M. Zeghal Rensselaer Polytechnic Institute, Troy, New York, USA
ABSTRACT: A micro-mechanical analysis is used to investigate the impact of inter-particle water bridges on the stress condition of unsaturated pendular-state granular soils. The discrete element method was used to idealize the soil skeleton. Bridge suction forces were used to model the effects of pendular water bridges, which develop at interparticle contacts. Computational simulations were employed along with analytical derivations to propose an expression providing the suction and effective stresses within unsaturated pendular-state granular soils. Suction stress was found to be a direct function of porosity, water content, and water bridge coordination number and fabric tensor. The outcome of the conducted simulations provided a valuable insight into the stress condition of unsaturated pendular-state granular soils.
1
INTRODUCTION
The principle of effective stress is a fundamental concept in soil mechanics. However, its applicability to unsaturated soils has been a subject of debate for a long time and remains a highly active area of research. The mechanical behaviour of unsaturated granular soils depends not only on interparticle forces and contact conditions but also on the interaction with pore water. At low levels of moisture, pore liquid within an unsaturated granular soil exists in a pendular state (Newitt & Conway-Jones 1958) and consists only of isolated water bridges. These bridges generate suction forces that hold neighbouring soil particles together; increasing shear strength and stiffening soil response. In this study, the discrete element method (DEM) is used to idealize the particles of unsaturated soils and a suction force model is used to account for the effects of pendular water bridges. Numerical simulations were used along with analytical derivations to assess the suction and effective stresses within unsaturated pendular-state granular soils.
2
A MICRO-MECHANICAL MODEL FOR UNSATURATED SOILS
A DEM model (Cundall & Strack 1979) was used to idealize a deposit of unsaturated pendular-state granular soil as a collection of discrete spherical particles. For these soils, the particles are subjected to gravity forces, interparticle (repulsion) contact forces and suction (attraction) forces exerted by pendular water bridges. A complete description of the motion
of the soil is provided by solving the equations of linear and angular momentum for each particle (i.e. Newton’s second law). For a particle p these equations are given by: mp v˙ p = mp g + Ip ω˙ p =
"
" c
rc × fc
fc +
"
fb
(1)
b
(2)
c
where vp and ωp are translational and rotational velocity vectors of particle p (a superposed dot indicates a time derivative), mp and Ip are particle mass and moment of inertia, g is gravity vector, fc refers to the interparticle contact force at contact c(c = 1, 2, . . . ), rc is vector connecting the centre of particle p to the location of contact c, and fb is force exerted by the pendular water bridge b(b = 1, 2, . . . ). The bridge forces are assumed to be radial and do not generate a moment. When the particles are in contact, the contact force, fc , and the bridge force, fb , (due to the generation of a water bridge) are taken into account. Only the bridge force, fb , is considered when two particles, formerly in contact are moving away from each other until the critical rupture distance of the pendular water bridge is reached (Lian et al. 1993). A constitutive law provided the contact forces, fc , as a function of the relative movement of the particles. The normal interparticle contact forces were modeled using a nonlinear Hertz spring (Mindlin & Deresiewicz 1953) in parallel with a dashpot. The shear interparticle contact forces were idealized using a Kelvin model (elastic spring in parallel with a dashpot) in series with a frictional slider. The shear and
743
normal interparticle contact forces are related by a slip Coulomb relationship (Itasca 2003). Bridge forces develop when pendular water bridges form between particles. This force includes suction, fs , and viscous, fν , components. The viscous component arises when the involved two particles move with respect to each other leading to a water flow in the bridge. This component is only significant when the pore liquid viscosity is high or particles are approaching each other at high relative velocities (Adams & Perchard 1985). This study focused on static soil conditions and the viscous component of the bridge force was not considered. The suction component of the bridge force accounts for the reduced hydrostatic pressure, P, within the water bridge and the force caused by the water surface tension, Ts , at the water-air-particle interface. For a pendular state and small particles (diameters less than about 1 mm), the effects of gravity on water bridges are negligible. The bridge force is then given by (Hotta et al. 1974): ' & (3) fs = π R22 P + 2πTs R2 nˆ where nˆ is unit vector connecting the centers of the particles and P is the reduced hydrostatic pressure (or better known in soil mechanics as matric suction) given by the Laplace-Young equation (e.g., Lu & Likos 2004): P = Ts
1 1 − R1 R2
(4)
in which R1 and R2 are radii of the principal curvature of the pendular bridge. Assuming a toroidal approximation of the liquid bridge (Fisher 1926), R1 and R2 may be related geometrically to the volume of the bridge (Fig. 1). This procedure gives an implicit relationship between the suction force and the water bridge geometrical parameters. An alternative explicit relationship (similar to those published
Figure 2. Explicit (solid lines) and implicit (discrete points) functions of the variation of the normalized suction force component fs∗ between two particles as a function of the normalized interparticle separation distance δ (for equal size particle, ρ = Rp2 /Rp1 = 1, different size particle, ρ = Rp2 /Rp1 > 1, and the limiting case of a particle and a wall, ρ = Rp2 /Rp1 ∼∞).
by others, e.g., Weigert & Ripperger 1999) was developed by the authors using regression and optimization techniques. This explicit relationship is appropriate for discrete element implementations. Details of the computation of fs as a function of water content and particle separation distance are given by Medina (2007). Figure 2 shows the normalized suction force fs∗ = fs /(2πTs Rp1 ) as a function of normalized interparticle separation distance δ = d/Rp1 for monosize particles, different size particles and a particle and a wall. 3
EFFECTIVE STRESS TENSOR OF UNSATURATED PENDULAR-STATE GRANULAR SOILS
The principle of effective stress is a fundamental wellestablished concept in the mechanics of fully saturated soils. Numerous efforts have been made to extend this concept to unsaturated soil since the late 1950s. A well known expression for the effective stresses for an unsaturated soil is given by (Bishop, 1959): σ = (σ tot − ua δ) − χP δ
Figure 1. Geometry of a pendular water bridge between two particles of different size (Rp1 and Rp2 are the particle radii, R1 and R2 are radii of principal curvature of the pendular bridge, and d is the separation distance between the particles).
(5)
where σ is the effective stress tensor, σ tot is the total stress tensor, ua is atmospheric pressure, δ is the Kronecker delta, and χ is a scalar quantity called effective stress parameter. Researchers have debated over the last four decades the issue of whether there exists a state variable for unsaturated soils that plays a role equivalent to that of the effective stress in the mechanics of saturated soils. Applicability of the effective stress principle to unsaturated soils remains a highly
744
active area of research, and experimental investigations have been carried out by researchers to explore the validity as well as the limitations of this concept (e.g., Jennings & Burland 1962; Khalili et al. 2004). Strictly speaking, stress is a continuum characteristic which does not apply to an assemblage of discrete particles in a granular soil. Averaging procedures may be used to evaluate stress fields consistent with particle contact forces (Cundall & Strack, 1983). For unsaturated pendular-state granular soils, the water bridges exert attractive forces that push the particles against each other leading to an increase in interparticle contact forces. Averaging of these forces gives a tensile suction tensor such as: σ = σ net − s
(6)
where σ is effective stress tensor which reflects the interparticle contact forces, σ net = (σ tot − ua δ) is net stress tensor associated with all external and internal forces except suction forces, and s is suction tensor associated to bridge suction forces. This tensor is obtained by homogenization of the water bridge suction forces acting on the particles (Medina, 2007). The suction tensor is essentially diagonal in view of the fact that the suction forces are normal to interparticle contacts. The negative sign in Equation 6 is used to conform to the soil mechanics sign convention (i.e., compressive forces produce positive average stresses). Numerical simulations of regular periodic packing of spherical particles and analytical derivations were employed to derive an expression for the suction tensor as a direct function of soil properties (Medina, 2007): s = − (1 − n) bn f (, ρavg )PFb
Figure 3. Variation of f (, ρavg ) as a function of the normalized average bridge volume (Medina, 2007).
(7)
where n is soil porosity, bn is average number of bridges per particle or bridge coordination number, Fb is average fabric tensor of the water bridges, and f (, ρavg ) is a scalar soil characteristic function that depends on soil properties such as, grain size distribution, packing arrangement, and water content. Numerical simulations and analytical derivations were employed to obtain an expression linking the variations of this function f to the normalized average size ratio ρavg of particles linked by a water bridge and normalized average bridge volume (where normalization is obtained by dividing the volume bridge by the volume of the smaller of the two involved particles). This function was found to depend primarily on the normalized average bridge volume (i.e. on water content). The variation of ρavg has a minor impact that manifest mostly at very low levels of water content, as shown in Figure 3. Using Equations 6 and 7, the effective stress
Figure 4. Normalized suction stress as a function of water content: Effect of average particle size ratio ρavg on random packing of spherical particles.
tensor of an unsaturated pendular-state granular soil, may be expressed as: σ = σnet + χPFb
(8)
' & where χ = (1 − n) bn f , ρavg . Figure 4 exhibits the variation of the normalized suction stress components as a function of water content for three simulations of random packing of spherical particles with three different grain size distributions (Table 1). In order to ensure a concise comparison that includes all suction stress components, the component of the suction tensor were normalized by the matric suction, P and the corresponding fabric tensor component, i.e., [s]ij /(P[F]ij ). Good agreements were obtained between the stress ratios computed using Equation 7 and those provided by numerical simulations using the discrete element model for unsaturated pendular-state granular soil (Medina, 2007). Equation 8 shows that the stress state of an unsaturated soil in a pendular state is a direct function of the matric suction P, which in turn is a function
745
Table 1.
was found to depend on water bridge fabric tensor Fb , matric suction P and a newly defined pendular effective stress parameter χ. This parameter is a direct function of porosity, water content, and water bridge coordination number.
Numerical data for random packing of particles.
Particles Diameter (mm) ρavg Porosity, n (%) bn
0.55–0.85 1.00 43 4.55
0.085–0.85 1.16 42 4.78
0.85 2.09 41 4.90
Fluid Water content (%) F11 F22 F33
0.5–4 0.315 0.320 0.365
0.5–4 0.318 0.319 0.363
0.25–0.75 0.315 0.320 0.365
REFERENCES
Computation parameters Time step for DEM
1.0 × 10−7 s
Figure 5. Soil water characteristic curve (SWCC) for cubic and hexagonal periodic packing of spherical particles.
of moisture content. The relationship between matric suction and moisture content is generally expressed by the soil-water characteristic curve (SWCC). This curve was evaluated for numerical simulations of cubic and hexagonal periodic packing of spherical particles, as displayed in Figure 5. This figure also shows a good agreement between the results of conducted simulations in comparison and the SWCC theoretical curve proposed by Reinson et al. (2005).
4
CONCLUSIONS
A discrete element model and numerical simulations were used to investigate the impact of pendular water bridges on the stress condition of unsaturated soils. These simulations were employed along with analytical derivations to develop an expression providing the suction and effective stresses within unsaturated pendular-state granular soils. The suction stress
Adams, M.J. & Perchard, A. 1985. The cohesive forces between particles with interstitial liquid. In IChemE Symposium Series (91):147–160. Cundall, P.A. & Strack, O.D.L. 1979. A discrete numerical model for granular assemblies. Géotechnique 29(1):47–65. Cundall, P.A. & Strack, O.D.L. 1983. Modeling of microscopic mechanisms in granular material. In J.T. Jenkins & M. Satake (eds.), Mechanics of Granular Materials, New Models and Constitutive Relations; Proc. US-Japan seminar on new models and constitutive relations in the mechanics of granular materials, Ithaca, New York, 23–27 August, 1983: 137–149. Elsevier Science Publishers B.V., Amsterdam. Fisher, R.A. 1926. On the capillary forces in an ideal soil; corrections of formulae given by W.B. Haines. Journal of Agricultural Science 16:492–505. Itasca. 2003. Particle Flow Code, PFC3D, release 3.0. Itasca Consulting Group, Inc., Minneapolis, Minnesota. Jennings, J.E. & Burland, J.B. 1962. Limitations to the use of effective stresses in partly saturated soils. Géotechnique 12(2):125–144. Khalili, N., Geiser, F. & Blight, G.E. 2004. Effective stress in unsaturated soils: Review with new evidence. International Journal of Geomechanics 4(2):115–126. Li, X.S. 2003. Effective stress in unsaturated soil: a microstructural analysis. Géotechnique 53(2):273–277. Lian, G., Adams, M.J. & Thornton, C. 1998. Discrete particle simulation of agglomerate impact coalescence. Chemical Engineering Science 53:3381–3391. Lu, N. & Likos, W. 2004. Unsaturated soil mechanics. John Wiley and Sons, Inc. Medina, C. 2007. A micro-mechanical study of the response of unsaturated pendular state granular soils. Ph. D. Thesis, Rensselaer Polytechnic Institute, Troy, NY, USA. Mindlin, R. & Deresiewicz, H. 1953. Elastic spheres in contact under varying oblique forces. Journal of Applied Mechanics, ASME 20:327–344. Newitt, D.M. & Conway-Jones, J.M. 1958. A contribution to the theory and practice of granulation. Transactions of the Institution of Chemical Engineers 36:422–442. Reinson, J.R., Fredlund, D.G. & Wilson, G.W. 2005. Unsaturated flow in coarse porous media. Canadian Geotechnical Journal 42:252–262. Weigert, T. & Ripperger, S. 1999. Calculation of the liquid bridge volume and bulk saturation from the half-filling angle. Particle and Particle Systems Characterization 16:238–242.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A numerical investigation of steady-state unsaturated conductivity tests G. Steger & S. Semprich Graz University of Technology, Graz, Austria
M.P.H. Moncada, T.M.P. de Campos & E. Vargas Jr. Pontifícia Universidade Católica do Rio de Janeiro, Rio de Janeiro, Brazil
ABSTRACT: The determination of hydraulic conductivity of unsaturated soils in steady-state permeameters is experimentally challenging. Apart from the experimental difficulties there is, however, another important aspect which has not yet been investigated in detail: The non-uniform distribution of matric suction in the soil specimen. The results of unsaturated permeability tests are usually referred to the arithmetic average of matric suction. This implies a linear approximation to the strongly non-linear unsaturated hydraulic conductivity function of soils. It is the aim of this paper to investigate the correctness of this simple approach. Beyond, two simple methods to improve inaccurate hydraulic conductivity data are discussed.
1
qw
INTRODUCTION
water pump
The steady-state method for the determination of hydraulic conductivity of unsaturated soils is carried out at constant magnitudes of matric suction respectively water content. Common steady-state methods are the ‘‘constant-head’’ method and the ‘‘constantflow’’ method. Recently developed constant-head permeameters are Gan & Fredlund (2000) or Agus et al. (2003), and recently developed constant-flow permeameters are Lu et al. (2006) or Moncada (2008). Figure 1 shows the experimental system for a constant-flow permeameter, similar to Moncada (2008). A controlled water flow rate is applied at the top of the permeameter, while the water pressure at the base high air entry (HAE) disk is maintained constant. The induced pressure change behind the top HEA disk is measured. The described experimental system will be the basis for the subsequent numerical investigations. The results obtained, however, do not depend on a specific permeameter system, and are equally valid for the constant-head as well as the constant-flow method. Physically, all the different steady-state permeameter methods are the same. The unsaturated hydraulic conductivity is computed using Darcy’s law: ν=
q = −k(ψ) · (hw,b − hw,t )/l A
(1)
where ν = Darcy velocity; q = flow rate; A = cross section; k(ψ) = suction dependent unsaturated
pore water pressure measurement air pressure supply at constant pressure
soil specimen
confining wall filter paper HAE disk qw
reservoir at constant water pressure ua = u w
Figure 1. Experimental system of a constant-flow permeameter.
hydraulic conductivity; hw,b = water pressure head at base; hw,t = water pressure head at top; and l = height of soil sample. The steady state method is usually considered as the most accurate method for determining the unsaturated hydraulic conductivity (Benson & Gribb 1997). There are, however, various difficulties associated with this method. Experimental challenges include the long testing periods and the adherent problems of water losses and air diffusion, and measurement uncertainties. System head losses may also falsify the obtained conductivity values.
747
There is a further aspect which may contribute to misinterpretation of unsaturated hydraulic conductivity data, and which is usually not accounted for: The non-uniform distribution of matric suction in the soil specimens. 2
NON-UNIFORM DISTRIBUTION OF MATRIC SUCTION AND ASSOCIATED PROBLEMS
Different magnitudes of pore water pressures are applied behind the base and the top HEA disk of the permeameter. This results in a (necessary) matric suction gradient across the soil specimen. All the recent permeameter developments (see previous references) left the idea of measuring pore water pressures inside the sample. The distribution of matric suction in the soil specimen is therefore unknown. However, the derived hydraulic conductivity from a permeameter test has to be referred to a certain suction value. This ‘‘average’’ suction is usually computed as the arithmetic average of the suction at the base and the top of the soil sample. It has long been recognized that the obtained hydraulic conductivity from the permeameter does not necessarily correspond to the ‘‘average’’ matric suction (e.g. Benson & Gribb 1997). To reduce the problem of the non-uniform distribution of matric suction, Benson & Gribb (1997) suggest applying suction gradients as small as possible while maintaining measurable flow rates. Lu et al. (2006) state that the problem may be greatly reduced in future by reducing the magnitude of the imposed flow rates of constant-flow permeameters. Improvements of the experimental systems will certainly allow applying lower flow rates and measuring lower head differences and vice versa. But apart from a technical point of view further considerations have to be taken into account. Firstly, low flow rates respectively low suction gradients result in low flow velocities. Times to reach steady-state increase rapidly and for silty and clayey soils they are fast beyond practical limits. With adherent long testing times, the problems of water leakage and air diffusion turn more and more severe. Secondly, below a certain threshold gradient the water may show non-Newton properties. Small countercurrents along the pore walls may occur. This phenomenon may result in flow not obeying the Darcy law or no flow at all before the threshold gradient is exceeded. For clay soils the threshold gradient may even exceed 30 (Bear 1988). Due to the latter considerations we are convinced that the non-uniform distribution of matric suction will always affect steady-state unsaturated conductivity testing, even with improved experimental equipment. It is therefore important to investigate these effects in detail.
3
BASICS OF NUMERICAL INVESTIGATIONS
3.1
General concept
The purpose of the numerical investigations is to simulate a series of unsaturated steady state tests for two reference soils. For the reference soils, a set of parameters describing the matric suction function and hydraulic conductivity function is assumed. The pressure change due to the imposed flow rates obtained from the numerical simulation is used to compute the hydraulic conductivity with Darcy’s law given in (1). The derived conductivity is then referred to the arithmetic average matric suction. This procedure corresponds to the commonly adopted approach for the steady-state method. In a second step, the ‘‘true’’ unsaturated conductivity for the assigned ‘‘average’’ suction value is computed solely with a hydraulic conductivity function. Finally, the conductivities obtained from the numerical simulation (= permeameter approach) are compared with those computed directly with the hydraulic conductivity function (= true value). Thus, the data interpretation error caused by the arithmetic average suction-approach becomes obvious.
3.2
Software
For the numerical investigations the multi-phase fluid and heat flow simulator TOUGH2 (Transport of Unsaturated Groundwater and Heat; Pruess et al. 1999) is employed. The use of a multi-phase flow code allows taking explicitly into account the air flow to the simulated permeameter tests. Possible influences of the air phase to the test results are therefore incorporated. TOUGH2 sets up identical mass and energy balance equations for all phases (e.g. water or air). Depending on the thermodynamic state (pressure, temperature, saturation), the thermophysical parameters (relative permeability, capillary pressures) are then assigned to the mass balance equation for each flow phase. The mass balance equations set up by TOUGH2 have the following structure: ∂ ∂t
Vn
M κ dVn =
FK • ndn +
n
qκ dVn
(2)
Vn
where Vn = an arbitrary sub-domain, bounded by the closed surface n ; M = mass or energy per volume, κ = labeling the different mass components; F = mass or heat flux; q = sinks and sources; and n = normal vector on the surface element n . The introduction of the intrinsic permeability k allows a multiphase formulation of Darcy’s law for
748
Table 1.
Numerical modeling parameters.
0.7 cm
soil specimen
HAE disk
N-BC; q=0 Dirichlet-BC; pa = const.
3.0 cm
HAE disk
Dirichlet-BC; pw = const. r = 3.5 cm
Figure 2.
Numerical model of permeameter.
computation of the phase fluxes F β : Fβ = ρβ uβ = −k
' krβ ρβ & ∇Pβ − ρβ g μβ
ksat
θs
θr,w
α
n
Material
m/s
–
–
m−1
–
Esperance Sand Beit Netofa Cl. HEA disk 1 HEA disk 2
4.9 · 10−7
0.39 0.45 0.40 0.40
0.02 0.0 0.2 0.2
1.8 0.15 0.1 0.2
1.6 1.17 100 100
(3)
where uβ = Darcy velocity (volume flux), krβ = relative permeability; μβ = viscosity with respect to phase β and Pβ = fluid pressure in phase β (Pruess et al. 1999).
Two different soil types are chosen to carry out the numerical simulations. The first one, Esperance Sand, is poorly graded, medium-fine sand, characterized by Lu et al. (2006). For the second soil, Beit Netofa Clay, results were presented by van Genuchten (1980). For both soils the matric suction function and the hydraulic conductivity function are described by the van Genuchten model (1980) respectively the van Genuchten-Mualem model (1976, 1980). Table 1 contains the assigned parameters. Two different HEA disks are modelled, depending on whether a high or a low suction value is applied. An n-value of 100 and α-values of 0.1 respectively 0.2 ensure full water saturation in the disks, independent of the applied suction. 4
3.3
9.5 · 10−9 8.6 · 10−8 8.6 · 10−6
3.4 Reference soils and material parameters
N-BC; q=0
0.7 cm
Neumann-BC; qw = const.
Permeameter model
The experimental system is assumed as characterized in Figure 1, but with flow in horizontal direction. A diameter of 7 cm and a height of 3 cm for the soil specimen are chosen. The HAE-disks have a thickness of 7 mm. Flow is induced via application of a constant flow rate at the top of the model. Below the base HAE disk the water pressure is kept constant. Matric suction is applied by distributing an elevated air pressure via a filter paper around the perimeter of the soil column. The cross section of the numerical model and assigned boundary conditions are shown in Figure 2. A rather fine meshed axis-symmetric model, with 72 element rows in axial and 10 element rows in radial direction, is used. A Neumann-boundary condition with a constant flux according to the injected water volume is assigned at the top HAE disk. Neumann boundary conditions with zero flux are also assigned to the lower and upper lateral wall of the permeameter. The filter paper strip in between is simulated with a Dirichlet-boundary condition at constant air pressure. The water reservoir at constant pressure below the base HAE disk is also represented by a Dirichlet-boundary condition, but here a constant water pressure is assigned.
RESULTS OF NUMERICAL SIMULATIONS
In this section, the results of four simulation series are presented. Six different flow rates at different matric suction values were simulated for both Esperance Sand and Beit Netofa Clay. Very low flow rates in the order of 1 · 10−7 cm3 /s were also assigned to show convergence of the numerical model. The results are summarized in tables presented below. The key information, the error caused by referring the obtained unsaturated conductivity of the permeameter test to the linear average suction, is given in the last column of the tables. Additionally, figures indicate the simulated distributions of matric suction for hydraulic conductivities in the soil specimens. 4.1
Esperance sand
Table 2 contains the simulation results for an applied suction of 5 kPa at the base HAE disk. The maximum data interpretation error is 32.5% for the flow rate of 5 × 10−3 cm3 /s. The resulting gradients for the four lower flow rates are very low and not recommendable for practical applications. Figure 3 shows the distribution of matric suction in the soil sample for the first four flow rates. It can be seen that for the two highest applied flow rates the
749
Table 2.
Simulation results for 5 kPa matric suction applied at base-HAE-disk.
Flow rate cm3 /s
savg kPa
p kPa
grad –
kperm m/s
ktrue m/s
error %
5 · 10−3 2.5 · 10−3 1 · 10−3 5 · 10−4 1 · 10−4 1 · 10−5
2.900 3.454 4.087 4.451 4.867 4.986
4.200 1.907 1.804 1.086 0.264 0.028
14.0 10.2 6.04 3.62 0.88 0.09
9.3 · 10−8 6.4 · 10−8 4.3 · 10−8 3.6 · 10−8 2.9 · 10−8 2.8 · 10−8
7.0 · 10−8 5.4 · 10−8 4.0 · 10−8 3.4 · 10−8 2.8 · 10−8 2.7 · 10−8
32.5 20.1 7.6 4.9 3.2 2.6
savg = arithmetic average of matric suction; p = pressure difference due to induced flow; grad = gradient; kperm = conductivity computed due to p; and ktrue = ‘‘true’’ permeability for savg . Table 3.
Simulation results for 20 kPa matric suction applied at base-HAE-disk.
Flow rate cm3 /s
savg kPa
p kPa
grad –
kperm m/s
ktrue (savg ) m/s
error %
1 · 10−3 5 · 10−4 1 · 10−4 1 · 10−5 1 · 10−6 1 · 10−7
12.372 13.634 16.728 19.427 19,939 19.995
14.079 12.129 6.417 1.126 0.122 0.011
46.9 40.4 21.4 3.75 0.41 0.04
5.4 · 10−9 3.2 · 10−9 1.2 · 10−9 6.9 · 10−10 6.2 · 10−10 6.0 · 10−10
2.7 · 10−9 2.0 · 10−9 1.1 · 10−9 6.6 · 10−10 6.1 · 10−10 6.0 · 10−10
102 58.5 13.1 3.8 2.1 −0.3
30
30
q = 1*10-3 cm³/s
q = 5*10-3 cm³/s 25
25
q = 2.5*10-3 cm³/s
q = 5*10-4 cm³/s q = 1*10-4 cm³/s
q = 1*10-3 cm³/s
20
q = 5*10-4 cm³/s
height [mm]
height [mm]
20
15 10
5
q = 1*10-5 cm³/s
15
10
5
0
0 0,0
1,0
2,0 3,0 matric suction [kPa]
4,0
5,0
0.0
5.0
10.0 matric suction [kPa]
15.0
20.0
Figure 3. Distribution of matric suction for Esperance Sand for 5 kPa matric suction applied at base-HAE-disk.
Figure 4. Distribution of matric suction for Esperance Sand for 20 kPa matric suction applied at base-HAE-disk.
distribution is rather non-linear, thus explaining the high deviations between permeameter permeability kperm and true permability ktrue . Table 3 contains simulation results for a suction of 20 kPa applied at the base disk. The induced flow rates are even lower than before but conductivity computation errors are as high as 102%. The first flow rate, where the conductivity error with 3.8% is an acceptable range, is 1 × 10−5 cm3 /s. In contrast, the according gradient of 3.75 is already rather low. Figure 4 shows the strong non-linearity of matric suction distribution for the simulation series given in
table 3. Evidently, referring the obtained conductivity values to the arithmetic average suction is highly erroneous for the first three flow rates. Figure 5 additionally depicts the wide range of hydraulic conductivity across the soil specimen. 4.2 Beit netofa clay Table 4 shows the simulation results for an applied suction of 20 kPa at the base HAE disk. The maximum flow rate is 2 × 10−4 cm3 /s. Higher flow rates cause full water saturation of the top end of the specimen.
750
Table 4.
Simulation results for 20 kPa matric suction applied at base-HAE-disk.
Flow rate cm3 /s
savg kPa
p kPa
grad –
kperm m/s
ktrue (savg ) m/s
error %
2 · 10−4 1 · 10−4 5 · 10−5 1 · 10−5 1 · 10−6 1 · 10−7
10.878 13.741 16.215 19.018 19.901 19.991
17.913 12.352 7.487 1.949 0.198 0.019
59.7 41.2 25.0 6.50 0.66 0.06
8.6 · 10−10 6.3 · 10−10 5.2 · 10−10 4.3 · 10−10 4.1 · 10−10 4.0 · 10−10
7.0 · 10−10 5.8 · 10−10 4.9 · 10−10 4.2 · 10−10 4.0 · 10−10 4.0 · 10−10
22.7 8.7 4.7 2.8 2.1 −0.1
Table 5.
Simulation results for 70 kPa matric suction applied at base-HAE-disk.
Flow rate
savg
p
grad
kperm
ktrue (savg )
error
cm3 /s
kPa
kPa
–
m/s
m/s
%
2 · 10−4 1 · 10−4 5 · 10−5 1 · 10−5 1 · 10−6 1 · 10−7
38.252 46.421 53.770 65.323 69.480 69.948
60.039 46.422 32.090 9.275 1.033 0.105
200.1 154.7 107.0 30.9 3.44 0.35
2.6 · 10−10 1.7 · 10−10 1.2 · 10−10 8.4 · 10−11 7.5 · 10−11 7.3 · 10−11
1.8 · 10−10 1.4 · 10−10 1.1 · 10−10 8.1 · 10−11 7.3 · 10−11 7.2 · 10−11
46.0 20.3 9.3 3.2 2.7 1.6
30
30
q = 2*10-4 cm³/s q = 1*10-3 cm³/s 25
25
q = 5*10-5 cm³/s
q = 1*10-4 cm³/s
20
-5
q = 1*10 cm³/s
height [mm]
height [mm]
20
15
10
q = 1*10-5 cm³/s
15
10
5
5
0 0.0E+00
q = 1*10-4 cm³/s
q = 5*10-4 cm³/s
0 5.0E-09
1.0E-08
1.5E-08
2.0E-08
0.0
2.5E-08
hydraulic conductivity [m/s]
5.0
10.0 matric suction [kPa]
15.0
20.0
Distribution of hydraulic conductivity.
Figure 6. Distribution of matric suction for Beit Nefota Clay for 20 kPa matric suction applied at base-HAE-disk.
The maximum data interpretation error is 22.7%. Once again the flow rates with acceptable data interpretation errors produce rather low gradients, requiring equilibrium times of several days. Figure 6 depicts the distribution of matric suction for the flow rates from 2 × 10−4 cm3 /s to 1 × 10−5 cm3 /s. The distributions do not exhibit the extreme non-linearity as seen for Esperance Sand though the suction varies approximately in the same range. Table 5 contains the results for an applied suction of 70 kPa at the base disk. The error for the flow rate
of 2 × 10−4 cm3 /s is 46.0%. Only the permeameter test with the flow rate of 1 × 10−5 cm3 /s produces an acceptable deviation of 3.2% while maintaining a reasonable high gradient of 30.9. The equilibrium time for this gradient is, however, about one week. Figure 7 shows the suction distributions for the simulations presented in Table 5. The range of matric suction from 10 to 70 kPa is very wide and shows again strong non-linearity, but still not as strong as for Esperance Sand. Figure 8 displays the according distribution of hydraulic conductivity.
Figure 5.
751
30
8.0E-09 q = 2*10-4 cm³/s q = 1*10-4 cm³/s
25
q = 5*10-5 cm³/s
v*h [m²/s]
height [mm]
6.0E-09
q = 1*10-5 cm³/s
20
15
4.0E-09
k( l)
10
1 2.0E-09
5
0 0.0
15.0
30.0 45.0 matric suction [kPa]
60.0
30
Figure 9. ductivity. Table 6.
q = 2*10-4 cm³/s
Data interpretation errors for different approaches.
height [mm]
arithmetic suction
q = 1*10-5 cm³/s
15 10
5
2.0E-10
4.0E-10
6.0E-10
8.0E-10
hydraulic conductivity [m/s]
Figure 8. Distribution of hydraulic conductivities for Beit Netofa Clay for 70 kPa matric suction applied at base-HAE-disk.
IMPROVEMENT OF HYDRAULIC CONDUCTIVITY DATA
The results of the numerical simulations indicate that referring the derived permeameter conductivities to an arithmetic average suction is likely to be highly erroneous. This holds especially true for flow rates producing reasonably high gradients over low testing times. Smiles & Towner (1968) presented a simple but effective way to obtain the ‘‘correct’’ hydraulic conductivities. Integrating the Darcy-equation over the length of the soil sample, and subsequent differentiation leads to the following formulation (for details see Smiles & Towner 1968): l·
∂v = −k(φt ) ∂φt
(4)
where l = height of the soil sample; φt = suction head at the top of the soil column; and k(φb ) = hydraulic conductivity at a suction of φt .
1.75
l[m]
Determination of ‘‘correct’’ hydraulic con-
q = 5*10-5 cm³/s
5
1.25
q = 1*10-4 cm³/s
20
0 0.0E+00
0.75 suction head
Figure 7. Distribution of matric suction for Beit Nefota Clay for 70 kPa matric suction applied at base-HAE-disk.
25
l
0.0E+00 0.25
75.0
equation 5,6 S & T (1968)
Soil & Flow rate cm3 /s
savg,lin kPa
error %
savg(6) kPa
error %
error %
E. Sa. 1 · 10−3 E. Sa. 5 · 10−4 E. Sa. 2 · 10−4 BNC. 2 · 10−4 BNC. 1 · 10−4 BNC. 5 · 10−5
12.4 13.6 15.0 38.9 46.4 53.8
101.7 58.3 32.8 44.2 20.3 9.3
10.0 11.6 13.4 28.7 38.7 48.4
10.1 −1.6 2.2 −2.9 −6.3 −3.0
7.4 6.3 3.3 3.8 2.3 5.6
E.Sa. = Esperance Sand; BNC. = Beit Netofa Clay; savg,lin = arithmetic average suction; savg(5) = reference suction computed with (5) and (6); error = conductivity interpretation error.
Suppose that the suction head φb at the base of the soil column is maintained constant, the left side of equation (4) gives the hydraulic conductivity for different values of φt . This curve can be obtained by performing various experiments with different flow rates at the same applied matric suction at the base of the soil sample. The hydraulic conductivity for a certain φt -value is given by the slope of this curve, see Figure 9. The curve in the diagram corresponds to the numerical simulations with Esperance Sand at 20 kPa matric suction. Results of improved unsaturated permeability values obtained with the Smiles & Towner method (1968) are given in Table 6. Obviously, the more experiments that are carried out, the higher the accuracy of the obtained hydraulic conductivities. Therefore, the Smiles & Towner method is primary of interest for soils with relatively high unsaturated conductivity values. Considering the suction distributions in Figures 3 and 4 compared to Figures 6 and 7, it becomes clear
752
that the true average suction is always lower than the linear mean suction. This does not necessarily imply that the true average suction corresponds to the permeability obtained with the permeameter. However, a more appropriate average matric suction obviously has to be lower than the linear mean suction. In addition to the presented results, further simulations for soils with n-values up to 2.5 were conducted. These simulations proved that a slight correction of the arithmetic average suction leads to a significantly more appropriate reference suction sref : sref =
' 1 1& s b + st − sb − st 2 8
' sb & if sb − st ≤ 2 (5)
where sb = (higher) suction at the base HAE disk; and st = (lower) suction at the top HEA disk. For higher relative suction differences a stronger correction is required: sref =
' 1& ' & ' sb 1& sb + st − sb − st if sb − st > 2 6 2
(6)
It was found that for all conducted simulations, Equations (5) and (6) prove to be more accurate than the usual approach with the arithmetic average of suction. Notable improvements were obtained for the higher flow rates. Table 6 shows results for: 1) assigning a linear mean suction to the permeameter results; 2) assigning a reference suction employing equation (6); and 3) employing the Smiles & Towner method (1968). Results are given for the simulation series of Esperance Sand at 20 kPa and Ben Netofa Clay at 70 kPa for the three highest flow rates each. Table 6 shows that employing Equation (5) and (6) instead of computing an arithmetic average suction significantly reduces data interpretation errors. 6
SUMMARY AND CONCLUSIONS
Interpretation of the hydraulic conductivity of unsaturated soils in steady-state permeameters is troubled by the non-uniform distribution of matric suction. Several arguments speak in favor of applying higher flow rates, even though improved experimental equipment may be available. Firstly, testing times are much shorter. Secondly, short testing times decrease the likelihood of experimentally caused errors. Thirdly, low flow rates imply very low gradients and thus, flow may be non-Darcian nature. Numerical simulations were carried out for two reference soils. It showed that for flow rates with reasonable high gradients and therewith reasonable testing times, the non-uniform distribution of matric
suction causes high errors in the determination of unsaturated hydraulic conductivity. The method of Smiles & Towner (1968) was checked for its ability to correct unsaturated conductivity data from steadystate tests. Considerable increase of the accuracy of the data was gained. However, this method is experimentally tedious. Additionally, a new formula to compute an improved reference suction was presented. This simple formula shows a very good performance particularly for higher flow rates. It is therefore suggested to use expression (6) in future to assign appropriate matric suction values to hydraulic conductivity data obtained with the steady-state method. REFERENCES Agus S.S., Leong, E.C. & Rahardjo, H. 2003. A flexible wall permeameter for measurements of water and air coefficients of permeability of residual soils. Can. Geotechn. J. 40(3): 559–574. Bear, J. 1988. Dynamics of fluids in porous media. Mineola: Dover. Benson C.H. & Gribb M.M. 1997. Measuring hydraulic conductivity in the laboratory and in the field. Unsaturated soil engineering practice. ASCE Geotechnical Special Publication No. 68, 113–168. Gan, J.K.M. & Fredlund, D.G. 2000. A new laboratory method for the measurement of unsaturated coefficients of permeability of soils. In Rahardjo, H., Toll DG. & EC Leong (eds.), Unsaturated Soils for Asia, Singapore, 381–386. Rotterdam: Balkema. Lu, N., Wallace, A., Carrera, J. & Likos, W. 2006. Constant Flow Method for Concurrently Measuring SoilWater Characteristic Curve and Hydraulic Conductivity Function. Geotech. Testing. J. 29(3): 230–241. Pruess, K., Oldenburg, C. & Moridis, G. 1999. TOUGH2 User’s Guide. Version 2.0. Berkeley: Earth Sciences Division, Lawrence Berkeley National Laboratory. Moncada, M.P.H. 2008. Avaliação da curva de retenção e da função de permeabilidade em solos não saturados (in portugese). PhD-thesis. Rio de Janeiro: Pontifícia Universidade Católica do Rio de Janeiro (in prep.). Mualem, Y. 1976. A New Model for Predicting the Hydraulic Conductivity of Unsaturated Porous Media. Water Res. Res. 12(3): 513–522. Smiles, D.E. & Towner, G.D. 1968. The steady-state measurement of the relation between hydraulic conductivity and moisture content in soils. Water Resources Res. 4(5): 1029–1030. Van Genuchten, M. Th. 1980. A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Sci. Am. J. 44: 892–898.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Numerical modelling of hydraulic hysteresis in unsaturated soils A.A. Javadi Computational Geomechanics Group, School of Engineering, Computer Science and Mathematics, University of Exeter, Exeter, UK
A.S.I. Elkassas Ove Arup and Partners, Cardiff, Wales
ABSTRACT: This paper presents the implementation of a constitutive model for coupling of hydraulic hysteresis and mechanical behaviour of unsaturated soils in a fully coupled hydro-mechanical finite element model. The constitutive model considers the effects of plastic changes of degree of saturation on stress-strain behaviour and the influence of plastic volumetric strains on the water retention behaviour. The mathematical framework and the numerical implementation of the model are presented and discussed. The model is validated by application to standard experiments on unsaturated soils involving various combinations of loading-unloading and dryingwetting tests. The model can be used to study various aspects of the behaviour of unsaturated soils under drying and wetting as well as loading and unloading paths. The merits and limitations of the model are highlighted.
1
INTRODUCTION
Modelling the hydraulic hysteresis in unsaturated soils has become the subject of many research works in recent years. Hydraulic hysteresis is defined as the occurrence of irreversible changes in degree of saturation during wetting and drying of soils. When subjecting unsaturated soils to cycles of wetting and drying a large component of plastic volumetric strain may accumulate. Many of the existing elasto-plastic constitutive models for unsaturated soils are not able to simulate the influence of the change in the degree of saturation on the stress-strain behaviour of unsaturated soils. Alonso et al. (1995) carried out a series of suction controlled oedometer tests which showed that a large component of plastic compressive volumetric strain occurred on the first wetting path during stages of wetting and drying cycles. The amount of irreversible strain in the first drying path was greater than the amount in the second drying path, the third one, and so on. Although the Barcelona Basic Model is able to predict the swelling and collapse in the first wetting path it is unable to predict the irreversible strains due to cycles of wetting and drying in the subsequent stress paths. Sharma (1998) presented experimental results that showed the effect of changes in the degree of saturation on the mechanical response of unsaturated soils. He carried out several triaxial experiments, including drying and wetting tests, on samples of compacted kaolin. The results indicate that swelling occurred
during the wetting path associated with an increase in the degree of saturation, while a significant component of volumetric compressive strain appeared in the drying stage associated with a decrease in the value of the degree of saturation. In general, it has been considered insufficient to describe the behaviour of unsaturated soils based on suction and net mean stress only. Incorporating the effects of the degree of saturation on the stressstrain response of unsaturated soils has become one of the recent modifications to the classical constitutive models (Gallipoli, et al. 2003). Wheeler et al. (2003) proposed a theoretical elastoplastic framework to model the hysteresis in the water retention curve. In the work presented in this paper, the elasto-plastic model proposed by Wheeler et al. (2003) has been implemented in a fully coupled hydro-thermo mechanical finite element model for unsaturated soils. In what follows, the finite element model is presented briefly followed by the governing equations used in the numerical model. The validation of the model is then presented based on some experimental results from literature.
2
FINITE ELEMENT MODELLING OF UNSATURATED SOILS
The authors have developed a fully coupled transient hydro-thermo-mechanical finite element model to simulate the behaviour of unsaturated soils (Javadi
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and Elkassas, 2004; Elkassas, 2006). The model includes full coupling between hydraulic (air and water flow), thermal and mechanical (stress and strain) fields in unsaturated porous media. In the model, unsaturated soil is treated as a multiphase medium in which the voids in the deformable solid are filled partly with liquid water and partly with gas phase (ideal mixture of air and water vapour). The model consists of four main equations including two mass balance equations for the liquid and air phases, conservation of energy for temperature and a stress equilibrium equation for the solid skeleton. In the mass balance equation for the air phase, both diffusional and advectional transport mechanisms are considered. The balance equation for the water phase includes both liquid water and water vapour. In what follows, a brief description of the governing equations, the constitutive model for hydraulic hysteresis and its incorporation in the FE model are presented and discussed. 3
GOVERNING EQUATIONS
Ignoring the temperature terms (the thermal effects are outside the scope of this paper) the governing differential equations of the model, expressed in terms of three state variables, i.e., air pressure, ua , water pressure, uw and displacement vector of the solid matrix, u may be written as (Elkassas, 2006):
−
Moisture flow equation: Cll
∂u ∂ul ∂ua − + Cla + Clu = ∇ [Kll ∇ul ] ∂t ∂t ∂t + ∇ [Kla ∇ua ] + ρ∇ (Kl ∇z)
(1)
Air flow equation: ∂u ∂ul ∂ua − + Caa + Cau = ∇ [Kal ∇ul ] ∂t ∂t ∂t + ∇ [Kaa ∇ua ] + ρda Ha ∇ (Kl ∇z)
Cal
(2)
Deformation equation: [Cul dul ] + [Cua dua ] + [Cuu duu ] − HDdεpp − HDdεsp db = 0
(3)
In the above equations, the coefficients C and K are defined as: ∂Sl ∂h dψ − nSa ρ◦ Cll = −n (ρl − ρv ) ∂s ∂ψ ds Cla = n (ρl − ρv )
∂Sl ∂h dψ + nSa ρ◦ ∂s ∂ψ ds
Clu = (Sl ρl − Sa ρv ) m H T − −
ρSl + n(Sa + Ha Sl ) Cal = −nρda (Ha − 1) ds dh dψ Rv ρ◦ Rda dψ ds ∂Sl + n(Sa + Ha Sl ) Caa = nρda (Ha − 1) ds Rv dh dψ 1 − ρ◦ Rda T Rda dψ ds Cau = ρda (Sa + Ha Sl ) m H T − −
Cul = H D As − − −
Cua = −H D As − H m −
− −
Cuu = H D H
− −
T
− − −
ρl Kl ∂h ∂ψ + Datms vv n ρ◦ Kll = ∂ψ ds γl ∂h ∂ψ Kla = ρv Ka − Datms vv n ρ◦ ∂ψ ds Kal =
ρda Ha Kl γl
Kaa = ρda Ka −ks As = m − v (s + patms ) where n is porosity, ρl and γl are density and unit weight of liquid respectively, ρv is density of water vapour, Sl is degree of saturation of pore fluid, Sa is degree of saturation of pore air, s is suction, ρ◦ is density of saturated soil water vapour, h is relative humidity, ψ is capillary potential, m = {1, 1, 0}, −
∂/∂x 0 ∂/∂y , Datms is molecular difH= 0 ∂/∂y ∂/∂y − fusitivity of vapour through air, vv is mass flow factor for the vapour flow, Kl is unsaturated hydraulic conductivity to water, Ka is unsaturated conductivity to air, Rv is specific gas constant for water vapour, Rda is specific gas constant for dry air, Ha is Henry’s volp p umetric coefficient of solubility, dεp and dεs are the plastic volumetric strains due to changes in stress and suction respectively, b is the body force, D is elasticity −
matrix, z is the elevation, v is the specific volume and patms is the atmospheric pressure. The above equations define the complete formulation of the coupled transient hydro-mechanical behaviour of unsaturated soils. Simultaneous solution
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4.1 Stress and strain variables
of these equations, after consideration of appropriate constitutive relationships and boundary and initial conditions, provides the values of state variables at various points and times in the soil medium.
The first stress variable used in this framework is defined as: σij∗ = σij − [Sr uw + (1 − Sr )ua ] δij
4
CONSTITUTIVE RELATIONSHIPS
Modelling the hysteresis in the soil-water characteristic curve (SWCC) represents a major challenge in modelling the behaviour of unsaturated soils. The hysteresis in the relation between suction s = ua − uw and the degree of saturation Sr is an important factor in the mechanical response of unsaturated soils. It is generally accepted that suction plays an important role in understanding the mechanical behaviour of unsaturated soils and therefore, it has been used as a fundamental stress state variable in many constitutive models. Many of the existing constitutive models such as those proposed by Alonso et al. (1990), Wheeler and Sivakumar (1995), Cui and Delage (1996) and others, use suction together with net mean stresses (the difference between total mean stress and air pressure) to describe the stress state in an unsaturated soil. One of the major factors which is strongly related to suction is the degree of saturation. In general, it has been considered insufficient to describe the behaviour of unsaturated soils based on suction and net mean stress only. Incorporating the effects of the degree of saturation on the stress-strain response of unsaturated soils has become one of the major modifications to the classical constitutive models (Gallipoli, et al. 2003). In recent years, many researchers have proposed different sets of stress state variables incorporating the effect of the degree of saturation. For example Bolzon, et al. (1996), Lloret and Khallili (2000) and Karube and Kawai (2001) used a stress state variable as: σ = σt − δ (ua − χs)
(4)
where σ is the average effective stress, σt is the total stress, s is the matrix suction, δ is the Kronecker delta and χ is a soil parameter. Bolzon et al. (1996) assumed that χ can be considered as the degree of saturation Sr with a value ranging from 1.0 corresponding to saturated conditions to zero at dry conditions. Although these models have incorporated Sr in the stress state variable σ , they are not able to explain two observed behaviours of unsaturated soils including the large plastic volumetric strains that occur during wetting from a high value of suction, which cannot be recovered during subsequent drying and wetting of the soil, and the difference in behaviour during isotropic loading at constant suction between samples subjected to cycles of wetting and drying and other samples (Wheeler et al. 2003).
(5)
where σij is the total stress tensor and the stress tensor σij∗ is usually termed Bishop’s stress. It is similar to the Bishop’s effective stress (equation 4) where the weighting factor is replaced with Sr (Bolzon et al. 1996). In addition to σij∗ , the modified suction s∗ = ns (Houlsby, 1997) is used as the second stress variable to account for the effect of the meniscus water. In this way, the porosity nis incorporated with the stress state variables rather than with the strains. The model uses the following stress state variables: p∗ = p − Sr uw − (1 − Sr )ua ∗
s = ns q
(mean Bishop stress),
(modified suction) and
(deviator stress in the case of anisotropic loading).
The advantage of using these stress variables is that it gives more power of modelling the behaviour of soils as s∗ includes porosity n and p∗ includes the degree of saturation. Another advantage of using Bishop’s stress is that it retrieves to the saturated effective stress when the soil changes to saturated conditions even if the suction is not zero. For the complete theoretical formulation of the hysteresis constitutive model the reader is referred to Wheeler et al. (2003). 5
IMPLEMENTATION IN THE FE MODEL
The constitutive model described above has been implemented in a fully coupled hydro-mechanical finite element model, developed by the authors for simulating the behaviour of unsaturated soils. The constitutive model includes coupling of the effects of hydraulic hysteresis and mechanical behaviour of unsaturated soils. In the finite element model, the changes in suction can be applied either by changing the pore air pressure while keeping the pore water pressure constant, by changing the pore water pressure while keeping the pore air pressure constant or by changing both air and water pressures. The shape functions are assumed to be the same for the deformation analysis and the hydraulic analysis. The plastic strain is a non-linear function of the stress level, suction and hardening parameters, and thus can be evaluated only by an iterative procedure. The solution using a finite element method is based on spatial discretisation of the domain into small elements and temporal discretisation of the solution with a time-stepping procedure.
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6
DISCRETISATION IN TIME
The governing equations of the model, expressed in terms of the three state variables, may be written in a general compact form as (Elkassas, 2006): C(φ)φ + K(φ)φ + f (φ) = 0
(6)
where φ T = {u, ul , ua } is the vector of unknown state variables, K(φ) and C(φ) are assembled stiffness matrix and capacitance matrix respectively and f (φ) is the assembled load vector. The final forms of the governing equations can be written in a matrix form as: ⎛
⎞⎛ ⎞ ⎛ ⎞ − − − u Cuu Cul Cua ⎝ − Kll Kla ⎠ ⎝ ul ⎠ + ⎝ Clu Cll Cla ⎠ − Kal Kaa ua Cau Cal Caa ⎞ ⎛ ⎞ ⎛ fu ∂u/∂t × ⎝ ∂ul /∂t ⎠ = ⎝ fl ⎠ ∂ua /∂t fa
(7)
A time discretisation of equation (7) is applied by the application of a fully implicit mid-interval backward difference algorithm (Thomas and Rees 1990). The general form of a two level difference scheme is:
A φ −
(1 − θ ) φ
n
−
−
n+1
+θφ
n
+B φ −
−
n
−
n+1 n φ φ − /t + C φ n = 0 × −
−
−
(8)
−
⎛
⎛ ⎞ ⎞ − − − Cuu Cul Cua where A = ⎝ − Kll Kla ⎠, B = ⎝ Clu Cll Cla ⎠ , − − − Kal Kaa Cau Cal Caa ⎛ ⎞ ⎛ ⎞ fu u C = ⎝ fl ⎠ and φ = ⎝ ul ⎠ . − fa ua
between successive time steps and is considered to have been achieved when n+1 n φ φ (10) − − < Tolerance − A maximum number is set for iterations to achieve convergence. If the maximum number of iterations is reached before the solution is converged, the time step t is halved and the equations are solved with the new time step. If the convergence is quick, the time step is doubled to provide a quicker solution to the equations in the following steps.
7
In this example the behaviour of compacted kaolin is studied under isotropic loading and unloading followed by wetting and drying and then re-loading under constant suction. The experiment starts with an isotropic loading from A (see Fig. 1) at net mean stress of p − ua = 10 kPa to C at net mean stress p − ua = 50 kPa followed by unloading from C to D, back to net mean stress of p − ua = 10 kPa at a constant suction of s = 200 kPa. The loading continues with a wetting and drying cycle DEF, performed at D with suction decreasing to 120 kPa and then increasing back to 200 kPa followed by reloading (under the constant suction s = 200 kPa) to J at net mean stress = 1200 kPa. The soil parameters are summarised in Table 1. The developed finite element model has been used to simulate the behaviour of the soil under the above stress paths. Figure 1 shows the results of the FE analysis. As shown in the figure, during loading path AB, the Bishop stress p∗ increases as a result of increasing net mean stress which causes a reduction in the porosity and consequently causes a slight reduction in the modified suction s∗ = ns. During the loading path AB and due to the reduction in s∗ , the soil yields on the SD line causing a slight increase in the degree of saturation as shown in the Figure. At point B the LC line is reached and significant reduction in specific volume
(φ n ) is the level at which the matrices A, B and C are − −
−
−
to be evaluated, and it is given by the equation: (φ n ) = θ (φ n+1 ) + (1 − θ ) φ n −
−
−
NUMERICAL EXAMPLE
(9)
where θ defines the required time interval such that θ ∈ (0,1) and θ = 0, 0.5, 1 represent backward difference, central difference and forward difference schemes, respectively. The convergence is checked
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Table 1.
The parameters used in the example.
Parameter
Value
λ κ λs κs k1 k2 p∗◦ SD SI
0.15 0.02 0.12 0.02 0.7 0.8 140 109.1 1091.1
and plastic changes in the degree of saturation Sr . The soil reaches the saturated conditions at I and from I to J the soil is on the isotropic normal compression line. These results are in close agreement, both qualitatively and quantitatively, with the results of the constitutive model simulations presented by Wheeler et al. (2003). It is shown that the developed finite element model, incorporating this constitutive model, can be applied to boundary value problems involving stress paths with various combinations of cycles of loading, unloading, wetting and drying.
Modified suction s*(kpa)
120 A
110 F D
100
B C G H
90
(a)
80 I
J
70 60 0
200
400
600
800
1000
1200
Mean bishop stress p* (kpa)
2.3 A
Specific volume v
2.2
B
D, F
2.1 2
C
8
(b)
1.9 1.8 1.7 I
1.6
J
1.5 10
100
1000
10000
Mean net stress (p-ua)
Degree of saturation Sr
1 I
J
0.9 F
0.8
G H
0.7
D A
0.6
C
(c)
B
0.5 10
100
1000
10000
Mean net stress (p-ua)
Figure 1.
SUMMARY AND CONCLUSIONS
H
G
Results of the FE analysis.
starts to occur as plastic volumetric strains accumulate up to point C. The yielding on the LC line causes a subsequent upward movement of the SD and SI yield curves which leads to plastic changes in Sr from B to C (Fig. 1c). During the wetting and drying cycle DEF the stress path remains inside the LC line, and as a result, no collapse or yielding occurs on the LC line. On the wetting path DE, due to the yielding occurring on the SD line, only the plastic changes in the Sr start to accumulate with a coupled inward movement of the LC line. As a result, for the final isotropic loading from F to J the soil yields on point G at a p∗ value less than the maximum previous applied load experienced by the soil. From G to H yielding occurs only on the LC line which causes coupled upward movements of the SD lines; no plastic changes occur in Sr and only plastic volumetric changes are predicted due to yielding on LC. From H to I, yielding occurs on both LC and SD lines causing both plastic volumetric changes
This paper has presented the incorporation of an elasto-plastic constitutive model for coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils, into a fully coupled transient hydromechanical finite element model. The constitutive model considers the effects of plastic changes of degree of saturation on stress-strain behaviour and the influence of plastic volumetric strains on the water retention behaviour. The basic concepts and mathematical formulation of the constitutive model and its implementation in the finite element model were presented. The governing partial differential equations of unsaturated soils, including the mass balance equation for water, mass balance equation for air and the stress equilibrium equation for the solid skeleton, were solved simultaneously after incorporation of the constitutive relationships and appropriate boundary and initial conditions. The model was validated by application to an example from literature. The application of the model to study various aspects of the behaviour of unsaturated soils under cycles of loading-unloading and wetting-drying was presented and discussed. It appears that the constitutive model for hydraulic hysteresis provides a relatively simple and efficient way of coupling the hydraulic and mechanical behaviour of unsaturated soils. It was shown that the developed finite element model incorporating the above constitutive model is able to predict various aspects of behaviour of unsaturated soils subjected to different combinations of loading, unloading, wetting, drying paths. It should be noted that the constitutive model of Wheeler et al. (2003) in the current form, has been specifically developed for isotropic stress states and therefore, the developed finite element model is only applicable to isotropic loading conditions.
REFERENCES Alonso, E.E., Gens, A., Josa, A. 1990. A constitutive model for partly saturated soils. Geotechnique, 40(3): 405–430.
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Alonso, E.E., Lloret, A., Gens, A., Yang, D. Q. 1995. Experimental behaviour of highly expansive double-structure clay. Proc. 1st Int. Conf. Unsaturated Soils, Paris, 1: 11–16. Bolzon, G., Schrefler, B.A., Zienkiewicz, O.C. 1996. Elastoplastic soil constitutive laws generalised to partially saturated states. Geotechnique, 46(2): 279–289. Cui, J.J., Delage, P. 1996. Yielding and plastic behaviour of an unsaturated compacted silt. Geotechnique, 46(3): 405–430. Elkassas, A.S.I. 2006. Numerical modelling of unsaturated soil behaviour. PhD thesis, University of Exeter, UK. Estabragh, A.R. 1998. Yielding and critical state of unsaturated silty soils. PhD thesis, University of Bradford, UK. Gallipoli, D., Gens, A., Sharma, R.S., Vaunat, J. 2003. An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour. Geotechnique, 53(1): 123–135. Feng, M., Fredlund, D.G. 1999. Hysteretic influence associated with thermal conductivity sensor measurements. Proceedings From Theory to Practice of Unsaturated Soil Mechanics, In association with 52nd Can. Geotech. Conf., Regina, Saskatchewan, 651–657. Houlsby, G.T. 1997. The work input to an unsaturated granular material Geotechnique, 47(1): 193–196.
Javadi, A.A., Elkassas, A.S.I. 2004. Finite Element Modelling of the Behaviour of Unsaturated Soils. Proceedings of the 6th World Congress on Computational Mechanics (WCCM VI), Beijing, China, 5–10 Sept. 2004. Karube, D., Kawai, K. 2001. The role of pore water in the mechanical behaviour of unsaturated soils. Geotechnical and Geological Engineering, 19: 211–241. Li, X.S. 2005. Modelling of hysteresis response for arbitrary wetting/drying paths. Computers and Geotechnics, 32: 133–137. Lloret, B., Khalili, N. 2000. An effective stress elastoplastic model for unsaturated porous media. Mechanics of Materials, 34: 97–116. Sharma, R.S. 1998. Mechanical behaviour of unsaturated highly expansive clays. DPhil Thesis, Univ. of Oxford, UK. Thomas, H.R. and Rees, S.W. 1990. Modelling field infiltration into unsaturated clay. J. Geotechnical Engineering Division, ASCE, 116(10): 1483–1501. Wheeler, S.J., Sharma, R.S., Buisson, M.S.R. 2003. Coupling of hydraulic hysteresis and stress-strain behaviour in unsaturated soils, Geotechnique, 53(1): 41–54. Wheeler, S.J., Sivakumar, V. 1995. An elasto-plastic critical state framework for unsaturated soil. Geotechnique, 45(1): 35–53.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
The drift shadow phenomenon in an unsaturated fractured environment Claudia Cherubini Politecnico di Bari, Bari, Italy
T.A. Ghezzehei & G.W. Su Lawrence Berkeley National Laboratory, Berkeley, California
ABSTRACT: The presence of subterranean holes creates a capillary barrier in an unsaturated environment. This phenomenon has been referred to as ‘‘Drift Shadow’’ and indicates a region that is sheltered from the downward percolating water. If the lateral hydraulic conductivity is insufficient to divert the water, fully saturated conditions are reached locally, and seepage occurs as the capillary barrier fails. Natural heterogeneities in hydrological properties can reduce the probability of seepage only if the flux is largely diverted around the drift. Previous numerical studies have been performed investigating various aspects of capillary barrier performance in engineered or naturally layered systems. Many authors examined the impact of heterogeneity on the distribution and rate of water seepage across a capillary barrier and into a drift, but the seepage exclusion problem has not been formally analyzed for fractured formations, in which the physical processes governing seepage in porous media also represent key factors. This paper analyzes the effect that a fracture network can have on the drift shadow. In a fractured environment, the effectiveness of the capillary barrier is determined by the capability of individual fractures to hold water by capillary forces and by the permeability and connectivity of the fracture network, which allow water to be diverted around the drift. The orientation of any individual fracture in relation to the opening, the discreteness and the anisotropy of the fracture network are all geometric factors affecting seepage, because they have a relevant influence on the hydraulic properties in the immediate vicinity of the drift wall.
1
INTRODUCTION
The presence of a cavity in an unsaturated zone results in flow diversion around the cavity. In such environments, the zone immediately below the cavity is typically much drier than the surrounding rock, because the capillary forces that draw water back to the dry zone are often weaker than the gravitational forces. In the context of drifts mined in homogeneous medium, the shape of the dry zone is similar to that of a shadow cast by an object of similar geometry and is commonly referred to as ‘‘drift shadow’’ (Fig. 1). The presence of a drift shadow below a cavity can potentially minimize the escape of substances from the cavity by limiting the pathways available for water and dissolved species. This feature is one of many desirable characteristics of underground contaminant isolation schemes. Whether the drift shadow provides significant retardation of contaminant release from cavities depends on a number of factors including the size and shape of the cavity, the flux of water around the cavity, and the hydrologic properties of the surrounding medium. Most studies (Philip et al. 1989, Finsterle 2000a, Finsterle et al. 2003, Houseworth
et al. 2003) that deal with drift shadow assume an unfractured homogeneous media (Fig. 2) or a continuum representation of fractures. The role of discrete fractures around cavities on drift shadow is not well understood yet. In this study, we provide some insights on how discrete fractures could affect the drift shadow by using high-resolution simulations. The remainder of this paper is organized as follows: first we provide a brief overview of the theory behind drift shadow (Section 2) followed by description of the modeling study that was performed (Section 3). Subsequently, we present the main results and discussions of our studies to date (Section 4) and we conclude with a summary of the main results and future research directions (Section 5). 2
THEORY
Flow in unsaturated homogeneous media is commonly described using the Richards equation, ∂θ/∂t = ∇ · {K(∇h − 1)}
761
(1)
Table 1.
Sandstone properties.
Permeability Porosity Van Genuchten residual saturation M α
9.869 · 10−14 m2 0.35 0.23 4.5 12000 Pa
proportional to s = α ro /2. However, this simple approach does not apply to fractured media. Therefore, we use high-resolution numerical modeling to analyze the phenomenon of drift shadow in fractured rocks. Figure 1.
Conceptual model of drift shadow (Su et al. 2006).
Figure 2. Definition of terms for drift shadow analysis in homogeneous media (Kneafsey et al. 2005).
where θ and h are water content and matric suction head respectively, and K is the hydraulic conductivity and can be described using the Gardner (1953) relationship K(h) = KS exp(α [h − he ])
(2)
where he is air-entry pressure and α is the sorptive number. Under steady state conditions, Equation 1 can be solved analytically (Philip et al. 1989) subject to the conditions provided by Equation 2 and no seepage into the cavity. The solution can be modified to provide estimates of the length and width of the shadow zone as shown in Figure 2. For a cylindrical cavity of radius ro , the size of the shadow is
3
MODEL DESCRIPTION
On the basis of the examinations of many sites, a silica-sand mine located in California was chosen, whose location and configuration makes it an excellent site to analyze the drift shadow phenomenon. The mine is located in a porous sandstone unit of the Domengine formation, an approximately 230 m thick series of interbedded Eocene-age shales, coals, and massive–bedded sandstones (Su et al. 2006). Measured hydrologic properties of the proposed site were not available. Therefore, for modelling purposes, porosities and permeabilities of the matrix were approximated to be as that of the Hygiene Sandstone (van Genuchten 1980) and are given in Table 1. The modeling work used in this study was performed using the numerical simulator TOUGH2 (Finsterle 2000b). The domain size used is two dimensional, 8 m wide and 10 m long, and contains a circular drift of 1 m radius. The grid has a regular mesh of 2 cm × 2 cm, with no refinement. It has been chosen to consider the fractures as discrete elements having a constant aperture, and distributed over a homogeneous matrix. The fracture intersections were not given any special considerations. The different fracture characteristics are discussed in Section 4. The top boundary condition is set to a constant flow rate that represents the long term mean percolation flux. All of the side boundaries are set to no-flow condition. The bottom of the flow domain is set to free (gravitational) drainage.
4
RESULTS AND DISCUSSION
Initial simulations were run first with only one fracture, whose position was changed inside the model domain. We analyzed how the drift shadow varies with the position of the fracture at two infiltration rates of 10−4 and 10−5 m/s.
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Figure 5. Figure 3. Drift shadow with infiltration rate equal to 10−4 m/s (a) no fracture (b, c, d) with a single fracture in different positions.
Table 2.
Different configurations of drift shadow. Fractures properties.
b (mm)
φ = b/a
Ks = b3/12a
1/α = 2σ/b
0.01 0.1 0.5
0.00025 0.0025 0.0125
2.08333E-15 2.08333E-12 2.60417E-10
14400 1440 288
a = mesh size; σ = 0.072 N/m.
Figure 4. Drift shadow with infiltration rate equal to 10−5 m/s (a) no fracture (b, c, d) with a single fracture in different positions.
The corresponding distributions of water saturation are shown in Figures 3 and 4, respectively. The presence of only one fracture, even if intercepting the drift, does not influence significantly the phenomenon.
The number of fractures was afterwards increased and different scenerios were considered, varying fracture angles and positions (Fig. 5): for some configurations it is easy to detect how certain fractures inclinations make drift shadow discontinuous, and the discontinuity increases with the number of fractures. A setting of three fractures was finally chosen and nine scenerios were analyzed, by combining three different apertures (0.01 mm, 0.1 mm, 0.5 mm) and background degree of saturations (0.1, 0.5 and 0.9). The permeability and van Genuchten α parameter were calculated from fracture aperture using the cubic-law approximation (Witherspoon et al. 1980) and YoungLaplace equation, respectively, and are given in Table 2 (equations given in first row of Table 2). The behavior of the fractures with the lowest aperture (0.01 mm) is quite similar to that of the matrix as far as saturation levels and capillary pressures are concerned. The wider fracture aperture is, the more the fractures behave as capillary barriers. For each value of background saturation (0.1, 0.5 and 0.9) both the 0.5 mm and the 0.1 mm fractures are drier than the matrix (Fig. 6).
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presence of fractures characterized by significant apertures, fracture flow appears to be insignificant as compared to matrix flow in unsaturated conditions. On the contrary, when fractures are characterized by very small apertures, they behave like voids, that is to say they are always more conductive than the matrix. REFERENCES
Figure 6. Three fractures with different apertures (0.01 mm, 0.1 mm and 0.5 mm) and initial saturations (0.1, 0.5 and 0.9).
Moreover, if the three fractures are distributed in such a way that just one intercepts the drift shadow completely, then its interference does not visibly affect much the drift shadow.
5
CONCLUSIONS
The drift shadow phenomenon has seldom been studied for fractured formations, where the physical processes governing seepage in porous media also represent key factors. The effectiveness of the capillary barrier is determined by the capability of individual fractures to hold water by capillary forces and by the permeability and connectivity of the fracture network, which allow water to be diverted around the drift. However, the discreteness of the fractured system increases the importance of the geometric and hydraulic properties in the immediate vicinity of the drift wall (Finsterle 2000a). From the simulations carried out it is possible to infer that fracture orientations and position in relation to the drift are the factors affecting the shape of the dry zone; moreover it becomes more discontinuous if the number of fractures intercepting the drift increases. Finally, as far as unsaturated fracture flow is concerned, the simulation results proved to be coherent with what previous studies (Wang & Narasimhan 1993, Singhal & Gupta 1999) have stated: in the
Finsterle, S. 2000a. Using the continuum approach to model unsaturated flow in fractured rock, Water Resources Research, 36 (8): 2055–2066. Finsterle, S. 2000b. iTOUGH2 Users’ Guide, Lawrence Berkeley national Laboratory, Pub. No 40040, Berkeley, Cal. Finsterle, S., Ahlers, C.F., Trautz, R.C. and Cook, P.J. 2003 Inverse and predictive modeling of seepage into underground openings, Journal of Contaminant Hydrology, 62–63: 89–109. Houseworth, J.E., Finsterle, S. and Bovardsson G.S. 2003. Flow and transport in the drift shadow in a dualcontinuum model, Journal of Contaminant Hydrology 62–63: 133–156. Kneafsey, T.J., Su G., Ghezzehei, T., Onishi, T., Marshall, B.D., Stuckless, J., Petermann, Z. and Paces, J. 2005. Natural Analogue Studies of the drift shadow effectS&T Natural Barriers Thrust FY Second Quarter Progress report—LBL Internal Use only. Philip, J.R., Knight, J.H., and Waechter, R.T. 1989. Unsaturated seepage and subterranean holes: conspectus and exclusion problem for circular cylindrical cavities. Water Resour. Res., 25: 16–28. Singhal, B.B.S. and Gupta R.P. 1999. Applied hydrogeology of fractured rocks Kluwer Academic Publishers, Netherlands. Su, G. and Kneafsey, T.J., Ghezzehei, T., Cook, P.J. and Marshall, B.D. Field investigation of the drift shadow. 11th International High-Level Radioactive Waste Management Conference (IHLRWM), April 30–May 4, 2006, Las Vegas, Nevada, American Nuclear Society, 2006. Su, G. and Ghezzehei T. 2006. Preliminary modeling of the drift shadow at the Black Diamond mine LBL Internal report. Van Genuchten, M.T. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils, Soil Science Society of America Journal, 44 (5): 892–898. Wang, J.S.Y. and Narasimhan. 1993. Unsaturated flow in fractured porous media, in ‘‘flow and contaminant transport in fractured rock’’ (eds J. Bear, C.F. Tsang and G. De Marsily) Academic Press, San Diego: 325–95. Witherspoon, P.A., Wang, J.S.K., Iwai, K. and Gale, J.E. 1980. Validity of Cubic Law for fluid flow in a deformable rock fracture, Water Resources Res.: 1016–1024.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Identification of hydraulic parameters for unsaturated soils using particle swarm optimization Y. Zhang & C.E. Augarde Durham University, Durham, UK
D. Gallipoli University of Glasgow, Glasgow, UK
ABSTRACT: Determination of material parameters for unsaturated soils from laboratory or field tests can be difficult due to the large number of parameters required for many constitutive models. With increasing computing power readily available, parameter search using modern optimisation procedures is now feasible. In this study the identification of hydraulic parameters from the back analysis of a transient infiltration problem is illustrated. Particle Swarm Optimization (PSO) is utilized in the search for the optimal set of parameter values. Two approaches are described: one where a limited set of the parameters is sought and the second where the whole set is sought. For the latter it is shown that a multi-step range contracting method is appropriate and leads to a computationally economic solution.
1
INTRODUCTION
The movement of water in unsaturated soils is an important scientific problem in many areas, such as geotechnical, environmental and agricultural engineering. Water flow through an unsaturated soil can be predicted by using two coupled constitutive models: the soil-water retention curve, which links the water content to pore water pressure head, and the unsaturated water conductivity, which defines the rate of movement of water through unsaturated soil. The estimation of the parameters for these two models can be achieved through laboratory and field tests. Laboratory tests are usually carried out on soil samples taken from the field. However, due to in-situ soil heterogeneity and disturbance caused by sampling, the parameters from laboratory tests may not be the same as those from in-situ tests (Eching & Hopmans, 1993; Nutzmann et al. 1998). In-situ tests therefore often provide a more reliable and convenient way of estimating hydraulic parameters than laboratory tests (Tyner & Brown, 2004). This study attempts to identify the hydraulic parameters from one-dimensional transient infiltration tests. These tests can be performed in-situ as well as in the laboratory (on a representative soil column). The parameter values correspond to the solution of an optimization process enforcing agreement between a computational model (formulated in terms of the hydraulic parameters being sought) and experimental
results. Two types of optimization algorithms exist: gradient-based algorithms, such as Newton methods, and stochastic evolutionary algorithms, such as genetic algorithms. For gradient-based optimization algorithms, when the objective function has many local minima, it is usual for the solution to converge to a local (and incorrect) minimum unless the initial guess is very close to the global minimum. In addition, numerical errors can dominate gradient-based approaches and lead to many local minima (Mous, 1993). Evolutionary algorithms as population-based global optimization methods are more robust. A particular evolutionary algorithm is the particle swarm optimization (PSO), which is briefly outlined below. This algorithm was introduced relatively recently by Kennedy & Eberhart (1995) and is both simple and robust. In this research, PSO is used to determine the values of the whole set of parameters in the two constitutive models that govern water infiltration in unsaturated soils. This is a challenging problem and, to the authors’ knowledge, no similar studies have been reported. 2
PARTICLE SWARM OPTIMIZATION
The general optimization problem consists in finding the optimal solution vector X, which corresponds to the minimum value of a nonlinear objective function F(X), with X = [x1 , x2 , . . ., xr ]T where r is the
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dimension. The domain of the objective function is limited to the interval X ∈ [Xmin , Xmax ] where Xmin = [x1 min , . . ., xmin ]T and Xmax = [x1 max , . . ., xr max ]T are the lower and upper limits of the interval. PSO is a population-based bio-inspired optimization method making use of ‘‘swarm’’ intelligence. It is based on social-psychological principles and provides insights into social behaviour (Kennedy & Eberhart 1995). In a PSO system, particles ‘‘fly’’ in the r-dimensional search space. The value of the objective function corresponding to the current position of a given particle is used to define a measure of that particle’s ‘‘fitness’’. The goal for particles is to fly to the best position (i.e. the global minima). During the flight, each particle adjusts its position according to the memory of its own best position and the best position of neighbouring particles. In doing so, each particle goes trough an iterative process where the current position Xki is updated to the new position Xk+1 i based on the current ‘‘velocity’’ Vk+1 as: i
The maximum ‘‘velocity’’ Vmax is set relative to the upper and lower limit of the search interval: Vmax = s (Xmax − Xmin )
(4)
where the factor s is equal in this study to 0.3. The learning coefficients c1 and c2 are both set to 2 (this gives good results for most problems) and a swarm of 50 particles is used. 3
UNSATURATED TRANSIENT INFILTRATION
3.1 Mathematical description of infiltration process
(1)
The movement of water in unsaturated soils is governed by Richards’ equation. The ‘‘θ-based’’ onedimensional form of this equation is written as (Celia & Bouloutas, 1990):
∂θ ∂ ∂θ ∂K(θ) = D(θ) + (5) ∂t ∂z ∂z ∂z
where k, k + 1 are the iteration numbers and i is the particle number. The particle’s velocity is also updated in each iteration as: & ' & ' Vik+1 = wk Vik + c1 r1 Pi − Xik + c2 r2 Pg − Xik (2)
where K(θ) is the hydraulic conductivity (m/s), θ is the volumetric water content, D(θ) is the unsaturated diffusivity (m2 /s), t is time (s), z is the vertical coordinate (m) measured positive upwards. The initial and boundary conditions for the onedimensional infiltration problem are:
where Pi is the best position achieved so far by the particle, Pg is the best position achieved by neighbouring particles, r1 and r2 are two random factors in the [0,1] interval which generate diversity of the swarm, wk is the inertia weight and c1 and c2 are constants weighting the ‘‘cognitive’’ and a ‘‘social’’ component of the search method respectively.
h(z, 0) = h0
0
h(0, t) = ht
t>0
h(L, t) = hb
or
Xik+1 = Xik + Vik+1
2.1
Choice of algorithmic parameters in PSO
The selection of suitable parameters is crucial for the performance of the PSO algorithm. The most important parameter is the inertia weight wi , which was introduced by Shi & Eberhart (1998b) to control the particles momentum. A large inertia weight favours global search while a small one favours local search. A linear decrease of inertia weight during iteration was proposed by Shi & Eberhart (1998a) as:
(7) t>0
(8)
where h is the pressure head (m), hb and ht are the constant pressure head at the bottom and top of the soil column respectively, h0 is the hydraulic head at the initial time, q0 is the flux at the top and L is the height of the soil column. 3.2
Numerical simulation of infiltration test
To solve Richards’ equation numerically, the modified Picard scheme is adopted here (Celia et al. 1990). This is based on a Taylor expansion of the time derivative that maintains perfect mass conservation. The temporal discretisation uses the backward Euler approximation,
wk = (wmax − wmin ) (MaxIter − k)/MaxIter + wmax (3) where wk is the inertia weight for the current iteration, MaxIter is the maximum number of iterations set by the user and wmax and wmin are the maximum and minimum inertia weight (usually set as 0.9 and 0.4).
q(L, t) = q0
(6)
θ n+1,m+1 −θ n ∂K n+1,m ∂ ∂ = Dn+1,m θ n+1,m+1 + t ∂z ∂z ∂z (10) where t is the time increment, n is the time step number and m is the Picard iteration number.
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Equation 10 is rewritten in the following equivalent form:
. /" n " / m & ' & '!2 & ' & '!2 w1 F =0 + w2 Q∗ tj − Q tj h∗i tj − hj tj j=1
∂ θ n − θ n+1,m ∂ θ − Dn+1,m (θ ) = t ∂z ∂z t +
(14) ∗
∂ ∂K n+1,m ∂ Dn+1,m θ n+1,m + ∂z ∂z ∂z
(11)
where the incremental change in water content is θ = θ n+1,m+1 − θ n+1,m . Discretization in space by the finite difference method leads to:
n+1,m Dj+1 Dn+1,m 1 /2 + j−1/2 + t z 2 z 2
θj −
n+1,m Dj−1 /2 θ j−1 z 2
+
−
+
θjn t
+
n+1,m Kj+1 /2
n+1,m Dn+1,m Dj+1 1 /2 + j−1/2 + t z 2 z 2
− z
n+1,m Kj−1 /2
θjn+1,m
(12)
where z is the spatial distance between nodes and j is the node number. Incorporation of the boundary conditions yields a tri-diagonal system of equations: ⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣
bm 1 am 2 0 0 .. . 0 0 0
c1m bm 2 am 3 0 .. . 0 0 0
0 c1m bm 3 am 4 .. . 0 0 0
0 0 c1m bm 4 .. . 0 0 0
··· ··· ··· ···
0 0 0 0 .. .
··· · · · bm N −2 · · · am N −1 ··· 0
0 0 0 0 .. . cNm −2 bm N −1 am N
0 0 0 0 .. . 0 cNm −1 bm N
⎤⎡ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎦⎢ ⎣
Seamless integration of PSO and unsaturated flow simulator
In PSO, for each particle one unsaturated flow calculation using different parameters in each iteration is carried out. So some variables in the code are continuously changed by particles using different parameters. These variables should be maintained properly in order to obtain the correct results. Some of them should be reinitialized, and some should reset to 0, so as to provide the correct start values for the next computation. To achieve this, in this implementation the finite difference calculation is integrated directly with the PSO. For the former only the mesh, initial conditions and the boundary conditions remain the same for the θ1m+1 θ2m+1 θ3m+1 θ4m+1 .. . θNm+1 −2 θNm+1 −1 θNm+1
where ai , bi , ci and di are coefficients depending on the unsaturated diffusivity and conductivity. 3.3
where Q (tj ), Q(tj ) are the observed and computed cumulative water content change for the whole domain at time tj · h∗i (tj ) and hi (tj ) are the observed and computed pressure head at point i and time tj . n is the number of points where measurements of hydraulic head are taken andm is the number of times when measurements of water content change and hydraulic head are taken over a given period. w1 and w2 are weighting factors making the magnitude of the two parts of the same order. In this study, w1 and w2 are set to 1.0 and 10.0 respectively. 3.4
n+1,m n+1,m Dj+1 Dj+1 2 / /2 θ n+1,m θj+1 = − z 2 z 2 j+1 n+1,m Dj−1 /2 θ n+1,m z 2 j−1
i=1
Objective function
The success of the optimization procedure depends much on the objective function chosen. Ideally enough information should be included in the objective function to make the solution unique. Usually pressure head and cumulative flow are employed to define the objective function. Here the objective function is set similar to Simunek et al. (1998).
⎤
⎡
⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥=⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎦ ⎣
d1m+1 d2m+1 d3m+1 d4m+1 .. . dNm+1 −2 dNm+1 −1 dNm+1
⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦
(13)
problem with different constitutive parameters, while other variables in the code need to be reinitialized to 0. A maximum number of iteration and a minimum value of objective function are the termination criterions. Either of the two criterions meets, the calculation terminate. The integrated algorithm is as follows:
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Step 1: swarm initialization for i = 1 to number of particles randomize parameter vector Xi ∈ [Xmin , Xmax ] randomize velocity vector Vi ∈ [−Vmax , Vmax ] end
Step 2: evaluate particle fitness for i = 1 to number of particles set Xi as parameters in finite difference code re-initialize finite difference simulator perform finite difference simulation extract data and calculate objective function end Step 3: update positions and local and global best for i = 1 to number of particles update particle velocity using Equation 2 update particle position using Equation 1 update local best and global best end Step 4: check the termination conditions
4 4.1
Table 1. Typical Mualem-van Genuchten parameters (Schaap et al., 1998; Budiman, 2002).
CONSTITUTIVE MODELS
θr
θs
α
n
Ks
Texture
−
−
m−1
−
m/s
Clay C Loam Loam L Sand Sand S Clay S C Loam S Loam Silt Si Clay Si C Loam Si Loam
0.098 0.079 0.061 0.049 0.053 0.117 0.063 0.039 0.05 0.111 0.09 0.065
0.459 0.442 0.399 0.39 0.375 0.385 0.384 0.387 0.489 0.481 0.482 0.439
2.55 2.74 2.05 4.48 3.79 4.86 3.77 3.83 0.73 2.60 1.25 0.74
1.26 1.44 1.50 1.80 3.30 1.21 1.35 1.47 1.71 1.34 1.55 1.70
3.44e-7 5.78e-7 4.28e-7 2.81e-6 2.83e-6 5.03e-7 8.03e-7 1.79e-6 3.86e-7 3.67e-7 2.58e-7 2.03e-7
Mualem-van Genuchten model
In this study, the Mualem-van Genuchten model (Mualem, 1976; van Genuchten, 1980) is employed to describe the soil water retention relationship between effective degree of saturation and pressure head: Se = 1 + |αh|n
!−m
Table 2. Parameters’ ranges used in this study for the Mualen-van Genuchten model.
(15)
where α(m−1 ) is a parameter related to the air-entry pressure head, n is a parameter related to the pore-size distribution and m = 1 – 1/n. The effective degree of saturation Se is given by: Se = (θ − θr )/(θs − θr )
(16)
where θs is the saturated water content and θr is the residual water content. Similarly, the unsaturated hydraulic conductivity K is a function of the effective degree of saturation Se and saturated conductivity Ks :
1 2
K = Ks kr = Ks Se 1 − 1 − Se1/m
m 2 (17)
The unsaturated diffusivity D(θ) can be derived as, D=K
! dh Ks (1 − m) 1/2−1/m −1 = S A +A−2 dθ αm(θs − θr ) e (18) 1/m m
where A = (1 − Se 4.2
) .
Ranges of parameter values
As shown in Section 4.1, there are five parameters in the Mualem-van Genuchten model. Budiman (2002) sorted the results from Schaap et al. (1998) to provide
Parameter
Unit
Minimum
Maximum
n α θs θr Ks
− m−1 − − m/s
1.001 0.1 0.21 0.001 5.0e-8
3.5 9.6 0.7 0.20 5.0e-4
a guide on the parameter values to be used for different soils (see Table 1). The ranges of parameter values used in this study are listed in Table 2. These are slightly larger than the ranges in Table 1 to ensure a wider search.
5
NUMERICAL EXAMPLES
The coupled water retention and conductivity relations given in the previous section were used for the numerical simulations of one-dimensional water infiltration in unsaturated soil. These simulations were used within an optimization procedure to search for the values of the hydraulic parameters in Table 2. From initial calculations it was apparent that some parameters are more sensitive than others. In particular, it was found that n is the most sensitive parameter, i.e. n approaches the optimal value very quickly, with α being the second most sensitive parameter. This sensitivity allows a multi-step range control procedure, which progressively restricts the range of variation of the most sensitive parameters and therefore facilitates the search of the least sensitive parameters. The first search is performed for all parameters over a wide
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range of values whereas, for the second search, smaller ranges are set for n and α. The process goes on with progressively smaller ranges for n, α, θr , θs , and Ks . It is expected that, for each search, the final value of objective function shall be smaller than in the previous one. 5.1 Forward analysis of infiltration problem The above optimisation procedure is tested against a numerical simulation (named a ‘‘forward’’ analysis) of one-dimensional water infiltration in a 1 m high unsaturated soil column subjected to an uniform initial water pressure head of −10 m. The objective is to determine if and how quickly the optimization procedure returns the same parameter values used in the forward analysis. These values are α = 3.35 m−1 , n = 2, Ks = 9.22e-5 m/s, θs = 0.368 and θr = 0.102 and correspond to a site in New Mexico described in Celia et al. (1990). During infiltration the water pressure at the top of the column is set to −0.75 m while the bottom pressure is maintained at −10 m. The time increment is set to 36 s and 100 elements are used for the spatial discretization of the column. Transient profiles of water content and pressure are shown in Figures 1 and 2. 5.2
Back analysis and parameter identification
Two optimizations are carried out: one in which some selected parameters are initially known and one in which no parameter is known at the beginning of the search. All optimisations were carried out using a -11.0 1
-9.0
-7.0
-5.0
-3.0
-1.0
t = 1 hr t = 2 hr t = 3 hr t = 4 hr t = 5 hr t = 6 hr
depth(m)
0.8 0.6 0.4 0.2
personal computer with 3.20 GHz Xeon CPU, 3.00 GB RAM, and MS WindowsXP. Case 1: Ks and θ s are known In this case, it is assumed that the saturated water conductivity Ks and the saturated water content θs are known beforehand (and equal to the values given in section 5.1). This is realistic because both these parameters can be accurately measured by means of relatively simple tests on saturated samples. The goal is therefore to estimate the remaining three parameters α, n, and θr . It only takes 380 iterations to achieve the values of α = 3.35 m−1 , n = 2 and θr = 0. 101999 with a corresponding value of the objective function F = 6.660e-6. The details of this search are presented in Table 3 and Figures 3–6. Case 2: no parameters are known This case, where no one of the five hydraulic parameter values is initially known, proved to be very challenging. The reason for the difficulties could be due to the multi-modal properties of the objective function. The optimal parameter values were found by gradually contracting the search ranges as shown in the upper part of Table 4 where the ranges of parameter values used for subsequent searches are provided. The lower part of Table 4 shows the parameter values identified at iteration i during each search together with the corresponding value of the objective function. In the first run, parameter values were sought over relatively wide ranges and the optimal values for n and α were equal to 2.00 and 3.30 respectively. In the second run, the ranges of variation for these two parameters were contracted to [1.8, 2.1] and [2.0, 4.0] respectively and this helped to locate θr close to its optimal value. This process goes on until a satisfactory small value of the objective function is achieved. For each search, the calculation is terminated by users when the results are acceptable. In the last (fourth) run, n is set to 2.0 and all parameters become very close to the optimal values. Selected iterations for the fourth search are listed in Table 5 and the variation of objective function with iteration number is given in Figure 7.
0
Figure 1.
0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 1
depth (m)
0.8 0.6 0.4 0.2 0
Figure 2.
Table 3. Values α, n, θr and F at different iterations in case 1. (correct parameters are α = 3.35, n = 2, Ks = 9.22e-5, θs = 0.368, θr = 0.102).
Water pressure profile.
Water content profile.
t = 1 hr t = 2 hr t = 3 hr t = 4 hr t = 5 hr t = 6 hr
Iteration
F
α
n
θr
1 10 50 100 150 250 350 380
9.847 2.401e-1 2.883e-2 4.176e-3 3.162e-3 5.374e-4 3.108e-5 6.660e-6
3.671 3.335 3.345 3.348 3.349 3.35028 3.34999 3.350
1.111 1.985 1.994 2.001 2.001 2.000 2.000 2.000
0.04721 0.09286 0.09933 0.10179 0.10233 0.10202 0.101997 0.101999
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2.4
1.0
2.3
0.0
2.2 2.1
-2.0
2.0
n
log(F)
-1.0
1.9
-3.0
1.8
-4.0
1.7
-5.0
1.6
-6.0
1.5
0
Figure 3.
50
100
150 200 iteration
250
300
350
0
Objective function vs. iteration for case 1.
Figure 5.
8.0
50
100
150 200 iteration
250
300
350
Value of parameter n vs. iteration for case 1.
0.14 0.13
7.0 residual water content
6.0 5.0 4.0 3.0 2.0
0.12 0.11 0.10 0.09 0.08 0.07 0.06 0.05 0.04
1.0 0
Figure 4.
50
100
150
200 iteration
250
300
0
350
Value of parameter α vs. iteration for case 1.
Figure 6.
50
100
150 200 iteration
250
300
350
Value of parameter θ r vs. iteration for case 1.
Table 4. Estimated values at different iteration number. (correct parameters are α = 3.35, n = 2, Ks = 9.22e-5, θs = 0.368, θr = 0.102). 1st search
2nd search
3rd search
4th search
n α θr θs Ks
[1.001, 3.5] [0.1, 9.6] [0.001, 0.2] [0.21, 0.9] [5. e-8, 5. e-4 ]
[1.8, 2.1] [2.0, 4.0] [0.001, 0.2] [0.21, 0.9] [5. e-6, 5. e-4 ]
[1.8, 2.1] [3.2, 3.8] [0.08, 0.12] [0.2, 0.6] [5. e-6, 4. e-4 ]
2.0 [3.2, 3.7] [0.09, 0.12] [0.34, 0.39] [7. e-5, 2. e-4 ]
i F n α θr θs Ks
250 6.97e-2 2.00 3.30 0.073 0.668 1.59e-5
3000 1.25e-2 1.99 3.56 0.098 0.425 1.38e-4
850 5.42e-3 2.00 3.46 0.103 0.364 1.00e-4
3000 9.7e-5 2.00 3.35 1.0196 0.3684 9.24e-5
770
Table 5. Values α, n, θr and F at different iterations in case 2 (4th search, correct parameters are α = 3.35, n = 2, Ks = 9.22e-5, θs = 0.368, θr = 0.102). Iteration
F
α
θr
Ks
θs
1 100 500 1000 1500 2000 2500 3000
1.329 1.00e-2 7.00e-4 4.66e-4 2.36e-2 1.93e-4 1.21e-4 9.70e-5
3.31 3.33 3.35 3.35 3.35 3.35 3.35 3.35
0.110 0.102 0.102 0.102 0.102 0.102 0.102 0.102
8.32e-5 9.17e-5 9.26e-5 9.27e-5 9.26e-5 9.25e-5 9.24e-5 9.24e-5
0.374 0.372 0.369 0.369 0.369 0.369 0.369 0.368
0.5 0.0 -0.5
log(F)
-1.0 -1.5 -2.0 -2.5 -3.0 -3.5 -4.0 -4.5 0
Figure 7. search).
6
500
1000
1500 iteration
2000
2500
3000
Objective function vs. iteration for case 2 (fourth
CONCLUSIONS
Automated optimisation procedures appear to be useful in determining geotechnical properties from laboratory or field experiments. In this study, an example of parameteridentificationfortheMualem-vanGenuchten water retention and permeability model is presented using an optimisation procedure for a one-dimensional infiltration problem. It is shown that, if one seeks all parameters at once, the optimal parameter values may not be found easily. Alternatively, if certain parameters are excluded from the search (such as those which can be easily determined through alternative tests), then the search efficiency is much improved. In addition a multi-stageapproach, whererangesofparametervalues are adjusted and the optimisation procedure restarted, shows considerable promise. The procedures outlined in this paper are clearly applicable to a wide range of geotechnical problems and the authors are currently engaged in research on parameter identification from pressuremeter data.
REFERENCES Budiman, M. 2002. Efficient Methods for Predicting Soil Hydraulic Properties, Ph. D. Thesis, Department of Agricultural Chemistry and Soil Science, The University of Sydney: 19–20. Carsel, R.F. & Parrish, R.S. 1988. Developing joint probability distributions of soil water retention characteristics. Water Resour. Res. 24: 755–769. Eching, S.O. & Hopmans, J.W. 1993. Optimization of hydraulic functions from transient outflow and soil water pressure data. Soil Sci. Soc. Am. J., 57: 1167–1175. Freeze, R.A. & Cherry, J.A. 1979. Groundwater. Prentice Hall, New Jersey. Kennedy, J. & Eberhart, R. 1995. Particle swarm optimization, Proc. of the IEEE Int. Conf. on Neural Networks, Piscataway, NJ, pp. 1942–1948. Kool, J.B. 1985a Parker, J.C. & Van Genuchten M.T. Determining soil hydraulic properties from one-step outflow experiments by parameter estimation: I theory and numerical studies. Soil Sci. Soc. Am. J. 49: 1348–1354. Mous, S.L.J. 1993. Identification of the movement of water in unsaturated soils: the problem of identifiability of the model. Journal of Hydrology 143: 153–167. Mualem, Y. 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media, Water Resour. Res. 12: 513–522. Mualem, Y. 1976. A new model predicting the hydraulic conductivity of unsaturated porous media. Water Resour. Res. 12: 513–522. Nutzmann, G. Thiele, Maciejewski M.S. & Joswig, K. 1998. Inverse modeling techniques for determining hydraulics properties of coarse-textured porous media by transient outflow methods. Advances in Water Resources, 22(2): 273–284. Schaap, M.G., Leij, F.L. & van Genuchten, M.T. 1998. Neural network analysis for hierarchical prediction of soil hydraulic properties. Soil Science Society of America Journal 62: 847–855. Shi, Y. & Eberhart, R.C. 1998a. Parameter selection in particle swarm optimization. Proceedings of the 1998 Annual Conference on Evolutionary Computation. 591–600. Springer-Verlag, New York. Shi, Y. & Eberhart, R.C. 1998b A Modified Particle Swarm Optimizer, IEEE International Conference on Evolutionary Computation, Anchorage, Alaska, May 4–9. Simunek J. van Genuchten M.T. Gribb, M.M. & Hopmans, J.W. 1998. Parameter estimation of unsaturated soil hydraulic properties from transient flow processes. Soil & Tillage Research, 47(1): 27–36. Tyner, J.S. & Brown, G.O. 2004. Improvements to estimating unsaturated soil properties from horizontal infiltration. Soil Sci. Soc. Am. J., 68: Van Genuchten, M.T. 1980. A closed form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J. 44: 892–898.
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A precipitation boundary condition for finite element analysis P.G. Smith Geotechnical Consulting Group, London, UK
D.M. Potts Imperial College, London, UK
T.I. Addenbrooke Formerly Imperial College, London, UK
ABSTRACT: This paper describes a precipitation boundary condition for use in numerical analysis of unsaturated soils that enables the simulation of rainfall on a ground surface (i.e. precipitation). A novel application of the boundary condition to simulate the ground water recharge that occurs at the base of the computational domain when modelling a partially saturated slope is also described.
1
INTRODUCTION
When using numerical methods (e.g. finite element or finite difference techniques) to analyse boundary value problems involving partially saturated soils it is often necessary to account for both the mechanical and fluid flow components of soil behaviour. This leads to a coupled analysis in which both the equilibrium and fluid flow equations are solved simultaneously. Appropriate boundary conditions will be required and for the fluid flow component of behaviour this implies the specification of either prescribed pore water pressures (or head) or fluid flow values at boundary nodes. In this respect the simulation of infiltration resulting from a precipitation process can be problematic as the choice of boundary condition (i.e. prescribed pore pressure or fluid flow) will depend on the intensity and duration of the rainfall, the geometry of the soil surface and its porosity, and the initial conditions prior to the start of precipitation. Consequently the type of boundary condition (i.e. prescribed pore pressure or fluid flow) is likely to change throughout an analysis. This paper describes the implementation of such a boundary condition for use in unsaturated numerical analysis to simulate rainfall on a ground surface (i.e. precipitation). It acts either as an infiltration (specified flow) condition, or as a prescribed pressure (variable flow) condition. Its operation requires that an infiltration rate (i.e. the rainfall at the ground surface) be specified, along with a maximum threshold value of the pore water pressure at the surface boundary. As it is only possible to specify either a flow or pore pressure condition at a node or grid point
during any increment (stage) of a numerical analysis, an algorithm is described that decides which boundary condition (flow or pore pressure) to apply and how to automatically adjust the increment size when the boundary condition switches. This algorithm has been successfully implemented in the Imperial College Finite Element Program (Smith 2003) and its use to model rainfall infiltration into level ground and its novel application to simulate the ground water recharge that occurs at the base of the computational domain when modelling a partially saturated slope is described. 2
MODELLING PRECIPITATION
The potential for precipitation to either infiltrate into soil or pond/run off has long been recognized: Rubin and Steinhardt (1963) studied rain infiltrating into soil, and showed how either infiltration or ponding occurred, depending on the infiltration rate relative to the (fully saturated) permeability of the soil. This has been demonstrated in reality by the work of Ng et al. (2003), who describe a field experiment where a slope was subjected to artificial rain, with the slope run-off collected and measured. For the slope studied (which was composed of fissured clay) 100% of the precipitation became infiltration for the first day and a half, but this reduced to approximately 30% precipitation as infiltration, with the remaining 70% becoming run-off, thereafter. Numerous authors have made some attempt to model infiltration and run-off. Ng & Shi (1998)
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modelled an unsaturated soil slope, but modelled the rainfall as a specified infiltration rate on the boundary surface, and allowed compressive pore water pressures to develop (i.e. ponding). However, such results are clearly nonsensical where the soil surface is steeply sloping. Fredlund and Barbour (1992) presented an example analysis that followed a similar approach; the specified infiltration rate was equal to the average annual precipitation for the area of the slope being modelled, though on part of the slope, infiltration was reduced to 10% of this value, to reflect slope protection and steepness of the slope. Chapuis et al. (2001) recognized that simply specifying an infiltration rate could generate unrealistically high pore water pressures, and suggested adding a surface layer of (high permeability) gravel into the analysis model, to mimic more open surface material and to more readily allow lateral flow, to prevent this problem. Ng et al. (2001) state the difficulty in determining the actual infiltration pattern, and in their analysis, modelled the infiltration/run-off ratio by taking 60% of the actual rainfall as infiltration, this being the statistical value typical for Hong Kong, the location of the slope modelled. This ratio of 60% precipitation as infiltration, 40% as run off, for Hong Kong is repeated in Ng and Pang (2000). Tsaparas et al. (2002) adopted an approach whereby the surface pore water pressure at any particular boundary node was set to 0 kPa if, after any step of the analysis, the surface pore water pressure became compressive. This prevents unrealistically high pore pressures at the surface, so gives a more realistic boundary condition, but can still result in unrealistic pore water pressure distributions below the surface, depending on the size of the time step used in the analysis, as demonstrated below. To accurately model the infiltration process therefore requires some method by which the division of rainfall into infiltration and run-off is automatically and continuously calculated, and which can accurately determine the correct infiltration rate at all boundary surface nodes of the analysis. This has been done through the implementation of a precipitation boundary condition. The operation of the precipitation boundary condition is illustrated in Figure 1. The boundary condition requires that an infiltration rate (i.e. the rainfall intensity at the ground surface) be specified, along with some maximum threshold value (THV) of the pore water pressure at the surface boundary. If at the start of an increment (stage) of an analysis, the pore water pressure at the surface boundary is below (that is, is more tensile than) the THV, then an infiltration (specified flow) boundary, using the specified infiltration rate, is used.
Figure 1.
Precipitation boundary condition.
Alternatively if at the start of the increment the pore water pressure at the surface boundary equals or exceeds (that is, is more compressive than) the THV, then the boundary condition is set to be that of a prescribed pore water pressure with a value equal to the THV. This implies that throughout the increment the pore water pressure will be maintained at the THV and that this will be achieved by applying an inflow of water that is some proportion of the specified infiltration rate. Any ‘excess’ proportion of the specified infiltration is disregarded. If on subsequent increments of the analysis the specified infiltration rate is reduced after the boundary has been set to a constant pore pressure boundary, then it may switch back to being an infiltration boundary if the new maximum inflow rate is insufficient to maintain the THV pressure. In applying the precipitation condition, the specified infiltration rate is normally taken as the actual rainfall for the site under investigation. If allowance is required for canopy intercept, this must be done by inputting a reduced rainfall rate. However, no allowance needs to be made for run off: the boundary condition automatically determines the portion of the specified inflow that enters the mesh and treats the remainder as run-off, based on the THV chosen. The proportion of the infiltration that becomes run-off is not, however, explicitly modelled. Rather, it is simply discounted from the analysis, since this flow occurs outside of the analysis mesh.
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Typically for slope analysis, the THV would be set to 0 kPa. Thus the soil could develop an allcompressive (‘fully saturated’) pore water pressure profile, but a compressive pore water pressure greater than zero could not build up at the ground surface. Non-zero THVs may also be specified: Compressive pore water pressures greater than zero may be specified for the THV, to allow surface ponding to occur. The maximum depth of ponding that can be achieved will thus be determined by the value of the THV specified. Alternatively, a tensile THV may be specified, which prevents total loss of suction at the ground surface. As stated above, boundary pore water pressures are adjusted back to the THV if at the start of an increment the pressure exceeds the THV as a result of the previous increment’s infiltration. This could occur if during the previous increment infiltration conditions (i.e. prescribed nodal flows) had been active. Where inflows are relatively small and the increment time step is short, the amount by which the pore water pressures exceed the THV is likely to be small, thus the method of operation is reasonable. However, problems can be encountered if the infiltration rate is high (relative to the soils permeability) and/or the time step is large. In such cases very high compressive pore water pressures can be generated at the slope surface on the last increment in which the inflow boundary condition is active. This is illustrated in Figure 2. ‘Increment 0’ represents some pre-existing pore water pressure distribution at the beginning of an analysis. Precipitation is then applied from increment 1, and the precipitation inflow rate is high relative to the permeability of the soil, while the time step of the increment is relatively long. As the THV = 0 kPa at the beginning of increment 1 an inflow boundary condition (prescribed flow) is activated. The pore water pressure distribution at the end of increment 1 is as shown in Figure 2 and can be seen to give values in excess of the THV at the ground surface. At the beginning of increment 2 this overshot is detected and the boundary condition at the ground surface is switched to a prescribed pore pressure. While this has the effect of reducing the pore water pressure on the ground surface to equal the THV at the end of increment 2, the shallow sub-surface pore water pressure distribution is in error. The increment 2 pore water pressure distribution shown is obviously unrealistic given that the surface pore water pressure should not be able to exceed 0 kPa. Clearly it is desirable to modify the boundary condition to limit the amount by which the THV can be exceeded before the condition switches from inflow (prescribed nodal flow) to a constant prescribed pore water pressure. This can be achieved by subdividing any increment in which a serious overshoot occurs into a series of smaller sub-increments.
Figure 2. Precipitation boundary condition with large timestep and inflow rate.
Figure 3. The tolerance zone for the precipitation boundary condition.
Applying such a procedure requires the specification of a tolerance around the precipitation threshold value (THV) (for a THV of 0 kPa, the tolerance should be of the order of ±0.1 kPa), see Figure 3. Should the
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boundary pore water pressure remain more tensile then the THV and lie outside the tolerance, the boundary condition remains an infiltration condition for the next increment (sub increment). If the boundary pore water pressure becomes more compressive, such that it lies within the tolerance zone
Figure 4. Determination of sub-increment size during application of the precipitation boundary condition.
Figure 5.
surrounding the THV, then it can be accepted as being equal to the THV, and the boundary condition changed to a pore water pressure condition for the next increment (or sub increment), with the pressure being set exactly equal to the THV. However, if the calculated pore water pressure on the boundary at the end of an increment (sub increment) is more compressive than the THV and lies outside of the tolerance specified, then the increment is rejected. Instead, a smaller sub-increment size is automatically calculated, and the increment (sub increment) repeated to calculate the pore water pressure changes over the shorter period of time compatible with the new sub-increment size. The new sub-increment size is calculated as a proportion of the failed increment. This proportion can be determined by comparing the difference between the boundary pore water pressure at the start of the increment and the THV to the change of the pore water pressure at the boundary calculated over the failed sub-increment. From this and assuming a linear variation of pore water pressure over the failed increment, the new subincrement size is determined as a proportion of the old one, see Figure 4. Since non-linear behaviour is being modelled, this linear method rarely gives a sufficiently accurate result immediately. That is, at the end of the new sub-increment under or overshoot can occur. If undershoot is experienced (i.e. the boundary pore water pressure remains more tensile then the THV and lies outside the tolerance) then the subincrement can be accepted and the analysis moves on
Schematic operation of existing ICFEP AI procedure for precipitation.
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to the next sub-increment still with an inflow condition applied at the boundary. However if overshoot is experienced (i.e. the boundary pore water pressure is more compressive than the THV and lies outside of the tolerance) then the process is repeated and the subincrement size recalculated with the new data and the analysis for the sub-increment repeated. This process continues until the boundary pore water pressure is approximately equal to (within the specified tolerance) the THV at the end of a sub-increment. At this point the boundary condition is changed and what remains of the full increment is applied, with a pore water pressure boundary condition. This is often completed in a single sub-increment, but if the soil behaviour is highly nonlinear may be broken into several sub-increments. This procedure is illustrated schematically in Figure 5, where for simplicity, each sub-increment is shown as being half the size of the preceding one. 3
MODELLING RECHARGE
As noted above the precipitation boundary condition enables a flow rate to be specified to a boundary unless and until the pore water pressure on that boundary becomes more compressive and reaches a user-prescribed value. This capability can be used to model processes other than precipitation. One issue that needs to be addressed in slope stability problems is the presence of groundwater, and specifically, how to model the phreatic surface. While it may be appropriate to place an impermeable boundary along the base of a slope mesh in some situations, this is not generally the case. Additionally, the head and foot of an analysis mesh will rarely if ever be impermeable boundaries. It is therefore generally the case that some degree of flow needs to be permitted through these boundaries. While a fixed pore pressure boundary would enable flow through the boundaries to develop freely, such boundaries place artificial restraints on the pore water pressure response to other stimuli, such as precipitation. The alternative, of a specified flow boundary condition, leaves the pore water pressure free to vary, but can instead result in an unrealistic build up of pore water pressure, since accurately determining the flow rate is difficult, especially since it may well vary throughout the duration of the analysis. The precipitation boundary condition provides an alternative to these options, by providing a form of ‘recharge’ into the analysis when the boundary condition is specified along the base of the analysis mesh. The inflow rate, instead of being based on rainfall data, is set equal to the fully saturated permeability of the soil, specifically, the permeability of the soil underlying the mesh, and therefore outside the analysis. The THV may be set to give the maximum permissible
compressive pore water at the base of the mesh. This can be set to be consistent with the maximum height of the phreatic surface above the base (assuming a hydrostatic profile), during ‘normal’ conditions. The effect of this is illustrated in Figure 6. Hydraulic boundary conditions for the sides of the mesh may be set as specified flow or specified pore water pressure boundaries. However, since the aim is to allow the phreatic surface freedom to move, it is clearly preferable to set no-flow side boundaries, which will provide no restraint on the response of the phreatic surface, while also avoiding the imposition of potentially unrealistic inflows across these boundaries. During dry periods, the slope will tend to dry out as water drains down and out of it under gravity, but continuous recharge from the greater part of the soil mass that is not explicitly modelled will maintain a deep phreatic surface. Wetter periods will tend to raise the phreatic surface, as the precipitation rate begins to match the drainage, and may do so sufficiently to switch the base boundary conditions to a fixed pore water pressure condition. Under extreme rainfall, transient perched water tables or non-hydrostatic pore water pressure profiles are free to develop. Hence use of the precipitation boundary condition as a recharge condition on the base of the analysis mesh enables a variable pressure boundary condition to be maintained, which is relatively sensible and realistic, and does not restrict the pore water pressure response to precipitation events.
Figure 6. Precipitation boundary condition used to simulate recharge.
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4
CONCLUSIONS
A precipitation boundary condition for numerical analysis of either fully saturated or partially saturated soil has been presented and an outline of its implementation into a finite element program described. This involves the specification of both an infiltration rate and a maximum threshold value of pore water pressure (or head) for the same surface boundary. The decision process for deciding which of these two boundary conditions to impose in an increment (stage) of an analysis is discussed. This is likely to involve splitting of the increment of the analysis into a series of sub-increments. An algorithm to automatically select the size of these sub-increments is described. The novel application of the boundary condition to simulate the ground water recharge that occurs at the base of the computational domain when modelling a partially saturated slope is discussed. REFERENCES Chapui, R.P., Chenaf, D., Bussiere, B., Aubertin, M. and Crespo, R. 2001. A user’s approach to assess numerical codes for saturated & unsaturated seepage conditions. Canadian geotechnical journal, vol 38, pp 1113–1126. Fredlund, D.G. and Barbour, S.L. 1992. Integrated seepage modelling and slope stability analysis: A generalised
approach for saturated/unsaturated soils. Chapter 1 in Geomechanics and water engineering in environmental management, ed R.N. Chowdhury, Balkema. Ng, C.W.W. and Shi, Q. 1998. A numerical investigation of the stability of unsaturated soil slopes subject to transient seepage. Computers and Geotechnics, vol 22, No 1, pp 1–28. Ng, C.W.W. and Pang, Y.W. 2000. Influence of stress-state on soil—water characteristics and slope stability. Journal of Geotechnical and Geoenvironmental Engineering vol 126, No 2, Feb 2000 ASCE. Ng, C.W.W., Wang, B. and Tung, Y.K. 2001. Three dimensional numerical investigations of groundwater responses in an unsaturated slope subject to various rainfall patterns. Canadian Geotechnical Journal, vol 38, pp 1049–1062. Ng, C.W.W., Zhan, L.T., Bao, C.G., Fredlund, D.G. and Gong, B.W. 2003. Performance of an unsaturated expansive soil slope subjected to artificial rainfall infiltration. Geotechnique 53, No 2, pp 143–157. Rubin, J. and Steinhardt, R. 1963. Soil water relations during rain infiltration: 1 Theory. Soil Science Society of America Proceedings, vol 27, pp 246–251. Smith, P.G. 2003. Numerical analysis of infiltration into partially saturated soil slopes. PhD thesis, Imperial College of Science, Technology & Medicine, London. Tsaparas, I., Rahardjo, H, Toll, D.G. and Leong, E.C. 2002. Controlling parameters for rainfall—induced landslides. Computers and Geotechnics, vol 29, pp 1–27.
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On boundary condition in tunnels under partial saturation P. Gerard, R. Charlier & F. Collin University of Liège, Department ArGEnCO, Belgium
ABSTRACT: A new hydraulic boundary condition modelling the hydraulic transfers between porous medium and ambient atmosphere occurring during gallery excavations is described. It combines two modes of water exchanges in partial saturation: seepage and evaporation flows. Numerical simulations of a gallery excavation in dilatant geomaterial are carried out in isothermal conditions. The results show the influence of hydric boundary condition on the convergence of the gallery and the importance of the determination of vapour transfer coefficient between atmosphere and porous medium.
1
INTRODUCTION
Nowadays, the solution for the high level radioactivity waste lies in nuclear waste disposals in deep and low permeable geological layer. All the processes altering this natural barrier are thus crucial issues. An important topic concerns the development of a damaged zone (named EDZ) during the excavation of the galleries. The extent of the EDZ increases the permeability of the host formation and consequently the radionuclides migration as well. A correct numerical prediction of the coupled processes occurring during the excavation is therefore needed. For this purpose, the hydraulic boundary condition at the gallery wall has a deep influence on the response of the low-permeability dilatant geomaterial. Indeed the usual boundary condition (for the flow problem) during excavation is a progressive decrease of the pore pressure down to the atmospheric pressure at the end of the excavation. On one hand, such boundary condition can lead to unphysical pore pressure distribution. On the other hand, the relative humidity in the gallery is usually controlled through an ‘‘air conditioning system’’. This could be modelled by a decrease of the pore pressure down to the corresponding suction at the end of the excavation [Hoxha et al., 2004]. This boundary condition relies on the assumption of a quasi-instantaneous equilibrium between the gallery relative humidity and the wall pore pressure. This highlights the need of a more detailed expression of the water exchanges between air gallery and gallery wall. Two modes of exchange can occur: seepage flow and vapour flow. The seepage flows are liquid flows that tend to reduce the gallery wall pore pressure down to the atmospheric pressure. Vapour exchanges occur when the relative humidities of air gallery and rock mass are different. Several formulations of the vapour
flows can be found in the literature, which usually assume that the flow is proportional to the difference of relative humidity [Anagnostou, 1995], vapour pressure [Zhongxhuan et al., 2004], the vapour potential [Kowalski, 1997] or the volumetric vapour mass [Ben Nasrallah & Pere, 1998]. In this paper, the expression of the new flow boundary condition in isothermal conditions is first developed (Section 2). After, an example of the influence of the hydraulic boundary condition will be presented for the excavation and ventilation of a deep cylindrical cavity (Section 3), before the discussions and the conclusions. 2
WATER AND VAPOUR EXCHANGES AT THE GALLERY WALL
During the excavation processes, the pore pressure at the gallery wall is decreasing. After excavation, for long term predictions, we can consider that a thermodynamical equilibrium has to be reached between the air gallery and rock mass. The wall moisture has to be in equilibrium with the air humidity in the tunnel. Water and vapour exchanges take place at the boundary between gallery and rock mass. Water exchanges in liquid phase can occur according to the difference of water pore pressure between rock mass and gallery. In some coupled phenomena like dilatancy, numerical responses with classical boundary conditions of the flow problem provide totally unphysical results as an injection of a huge amount of water in the medium during excavation. An unilateral flow condition is thus imposed in order to avoid water inflow into the rock mass: water outflows can only be created if pore pressure in the formation
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is higher than the air pressure in the gallery. Seepage flow S can be expressed as follows:
f
S = β · (pw − patm )2 S=0
f
gal
f pw
gal pw
q=S +E
f
if pw ≥ pw and pw ≥ patm if
<
or
f pw
< patm
(1) f
gal
with pw and pw the water pressures respectively in the formation and in the gallery, patm the atmospheric pressure and β a seepage transfer coefficient. This transfer coefficient should be as high as possible (penalty condition) in order to respect the seepage condition. Vapour exchanges occur when a difference between relative humidities of air gallery and rock mass exists. Vapour inflows or outflows are physically possible. Several formulations of these fluxes can be found in the literature. Each of them is using a mass transfer coefficient which can be expressed as a function of the degree of saturation, the porosity or the air windspeed in the gallery [Dracos, 1980; Anagnostou, 1995; Zhongxhuan et al., 2004]. To obtain the evaporation flow, this mass transfer coefficient can be multiplied by the difference of relative humidity [Anagnostou, 1995], vapour pressure [Zhongxhuan et al., 2004] or vapour potential [Kowalski, 1997] between air gallery and the geological formation. As proposed by Ben Nasrallah & Pere [1998], we choose to express vapour exchanges as the difference of volumetric vapour mass between the tunnel atmosphere and rock mass: E = α · (ρνf − ρνgal ) f
(2)
gal
with ρν and ρν volumetric mass respectively in the formation and in the gallery and α a vapour transfer coefficient. The volumetric vapour mass is given by the following thermodynamic relationship: ρν = h · ρν,0
vapour exchange flux, which can occur near tunnel surface:
Because of permanent air ventilation of the galleries in the tunnel, we can consider that air relative humidity and volumetric mass in the tunnel are constant. Evaporation and seepage flows evolve thus according to the f value of water pressure pw at the gallery wall (Fig. 1). Initially, if: • rock mass humidity is higher than air gallery f gal humidity ( pw ≥ patm > pw ). Vapour exchanges take place from the geological formation to the gallery. Evaporation flow remains constant as long as rock mass is totally saturated f (pw > patm ). When soil surface water pressure is lower than atmospheric pressure, the geological formation is desaturated and vapour exchanges decrease until the equilibrium between porous medium and ambient atmosphere is obtained. Seepage flow exists only if pore pressure at the gallery wall is higher than gallery pore pressure. • rock mass humidity is lower than air gallery f f gal humidity ( pw < patm and pw < pw ). Evaporation flows take place from the tunnel atmosphere into the formation in order to re-saturate the rock mass. The saturation increases progressively to reach the gallery relative humidity level. On the other hand, no seepage flow occurs, because only gaseous exchanges exist. In order to solve numerically in finite element code the field equations using this new boundary condition, a linear auxiliary problem can be defined following the ideas of Borja & Alarcon [1995] and the field of unknowns is obtained through a Newton-Raphson scheme. The linear auxiliary problem is discretized
(3)
where h is the relative humidity and ρν,0 the saturated vapour volumetric mass. Relative humidity in porous medium is related to the suction by the Kelvin’s law and saturated vapour volumetric mass is obtained by ideal gas law. The saturated vapour pressure given by the experimental expression following [Collin, 2003]: pν,0 = a · exp(−b/T )
(4)
with a = 112659 MPa and b = 5192, 74 for temperatures included between 273 and 373◦ K. On the basis of previous relations, the total flow q between air gallery and the geological formation is simply expressed as the sum of the seepage flow and
(5)
Figure 1.
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Evaporation and seepage flows.
using the finite element methodology [Zienkiewicz & Taylor, 2000]. Large strain isoparametric coupled finite elements and a specific element for the boundary condition have been introduced in the finite element code Lagamine [Collin, 2003] for the modelling. 3
NUMERICAL MODELLING OF AN EXCAVATION
Within the framework of nuclear waste disposals in deep geological layer, a correct numerical prediction of the coupled processes occurring during disposal excavations is needed. With the aim of studying the influence of hydric boundary condition, the excavation of a cylindrical gallery located in a homogeneous low permeability formation is simulated. The geometry and the mechanical law used are those proposed in the GdR-Momas benchmark exercise [Chavant & Fernandez, 2005]. A cylindrical unsupported cavity of 3 m diameter is located in an homogeneous low permeability formation. The excavation process is modelled by decreasing the initial total stress and pore pressure towards atmospheric pressure. An initial isotropic stress state allows one dimensional axisymetrical modelling: σr = 7 MPa and pw = 5 MPa. Two steps are considered in the simulation: first the excavation process (duration T = 1.5 Ms, around 17 days) and a second phase during which the radial convergence of the cavity evolves due to the water diffusion process. The final modelling time is 300 Ms (about 9.5 years). At the external boundaries of our model, the initial conditions are assumed to be preserved in terms of total stress and pore pressure. This supposes that the external boundaries are far enough from the cavity. In the modelling, they are located at a radial distance seven times the cavity radius. This distance, maybe a little short to avoid boundary influence, is imposed by the geometry of the GdR-Momas benchmark. The conditions are isotherms (T = 293◦ K) and gas pressure is assumed constant (equal to the atmospheric pressure). 3.1 Mechanical constitutive law In order to reproduce the progressive decrease of the material strength, the elasto-plastic strain-softening model (with an associated Drucker-Prager yield criterion) proposed previously in the frame of GdR-Momas benchmark exercises [Chavant & Fernandez, 2005] is used. Due to the associated plastic law, the resulting behaviour of the material is highly dilatant, which increases the coupling effects between the mechanical and the flow problem. The following simulations have been performed with the parameters values defined in Table 1.
3.2 Hydraulic properties The mass flow mti is defined as follows: mti = −ρwt
t κkr,w
μ
∂pt + ρwt gi ∂xit
(6)
t where κ is the intrinsic permeability, kr,w is water relative permeability and μ is the fluid viscosity. The compressible fluid is assumed to respect the following relationship [Lewis & Schrefler, 2000]. This predicts an increase of fluid density as a function of the pore pressure, defining χw as the fluid bulk modulus:
ρ˙wt =
ρwt t p˙ χw
(7)
The following parameters have been used in the excavation gallery simulation (Table 2). The retention curve of the medium and the water relative permeability function are given by the following relationships, proposed previously in the frame of GdR-Momas benchmark exercises [Chavant & Fernandez, 2005]:
Sr,w
p 1 c 1−0.412 = 1+ 107
−0.412 and Sr,w = 1 if pc < 0
(8) kr,w = 1 + (Sr,w −2.429 − 1)1.176
!−1
(9)
with Sr,w the water relative saturation, kr,w the water relative permeability and pc the capillary pressure (pc = pg − pw ). Table 1.
Parameters of the mechanical model.
E0 υ0 C0 ϕ α p γR
Young modulus Poisson ratio Initial cohesion Friction angle Residual cohesion Dev. Strain threshold
Table 2.
Parameters of the flow model.
κ ρw,0 0 χw μ
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Intrinsic permeability Water density Initial porosity Bulk modulus Dynamic viscosity
5800 0.3 1 25 0.01 0.015
10−19 1000 0.15 2000 0.001
MPa – MPa Degree – –
m2 kg/m3 – MPa Pa.s
3.3
Reference case
In this axisymetrical modelling, a classical flow boundary condition is imposed: the pore pressures at the wall are decreased towards the atmospheric pressure during excavation and then remain constant (Fig. 2). Due to the hydro-mechanical coupling (dilatancy effect), a pore pressure decrease is observed in the damaged zone, which implies an unphysical ‘numerical’ injection of water into the formation. Figure 3 presents the stress path followed in the first finite element at the wall. The behaviour is first elastic before the stress path reaches the initial yield surface. Due to softening, the cohesion is decreasing, inducing dilatancy at the same time. At the end of the modelling, the stress state tends to zero as no more deviatoric stresses are allowed. The radial displacement is equal to 1.75 cm at the end of the excavation and reaches 21.2 cm after 300 Ms. The coupling effects between the water diffusion and the mechanical process are thus important. 3.4
Influence of hydraulic boundary condition
6
5
5
4
4
3
3
Pore pressure [MPa]
6
2 1 0 2
4
6
8
10
12
14
16
18
20
-1
t = 1.5 E6 s t = 5.0 E6 s t = 50 E6 s t = 300 E6 s
-2 -3
0 -1
2
4
6
1—Reference
Case—Pore
pressure
Figure 4.
Second deviatoric stress invariant [MPa]
12 Initial yield surface Final yield surface
10 8 6 4 2
End of excavation 0 -5
0
5 10 15 First stress invariant [MPa]
20
25
8
10
12
14
16
18
20
30
35
-3 Radial distance [m]
Radial distance [m]
Figure 2. Case distribution.
Figure 3.
1
-4
-4
-10
t = 1.5 E6 s t = 5.0 E6 s t = 50 E6 s t = 300 E6 s
2
-2
Second deviatoric stress invariant [MPa]
Pore pressure [MPa]
The reference case highlights the need of a more detailed expression of the water exchanges between air gallery and gallery wall. Furthermore, relative
humidity in the tunnel is usually controlled by an ‘‘air conditioning system’’ maintaining constant air relative humidity. After excavation, for long term predictions, a thermodynamical equilibrium might be reached between the air gallery and the geological formation. In these simulations (Case 2), a combined boundary condition with seepage and evaporation flows is thus used, as defined in Equation (4). A relative humidity of 0.96 (corresponding to a negative pore pressure of −5 MPa) is imposed for the gallery atmosphere, but pore pressures at the wall are not controlled. The seepage transfer coefficient β of Equation (1) is assumed equal to 10−7 s3 · kg−1 . The results depend on the vapour mass transfer coefficient α, defined in Equation (1). However, this coefficient is difficult to determine. With a small vapour transfer coefficient (Case 2-1 − α = 10−4 m/s), only seepage flows have influence on flow boundary behaviour. The pore pressure profiles (Fig. 4) tend towards atmospheric pressure on the wall and are thus similar to those from a simulation using only seepage boundary condition. Using 100 times larger mass transfer coefficient (Case 2-2 – α = 10−2 m/s), evaporation flow becomes preponderant on seepage flow. Pore pressure remains negative and close to the imposed pore pressure in
30
Case 1—Reference Case—Stress path curve.
12
Initial yield surface Final yield surface
10 8 End of excavation 6 4 2 0 -10
Figure 5.
782
Case 2-1—Pore pressure distribution.
-5
0
5 10 15 20 25 First stress invariant [MPa]
Case 2-1—Stress path curve.
1
-4 = 10 m/s
4 0.99
t = 1.5 E6 s t = 5.0 E6 s t = 50 E6 s t = 300 E6 s
2 0 2
4
6
8
10
12
14
16
18
Relative humidity (-)
Pore pressure [MPa]
6
20
-2
0.98 -3 = 10 m/s 0.97 -2 = 10 m/s
-4
Air gallery relative humidity
-6
Figure 6.
0.96 0.0E+00
Radial distance [m]
Case 2-2—Pore pressure distribution.
Figure 8.
5.0E+07
1.0E+08
1.5E+08 Time (s)
2.0E+08
2.5E+08
3.0E+08
Case 2—Relative humidity evolutions.
16 Initial yield surface Final yield surface
Second deviatoric stress invariant [MPa]
14
Table 3.
Cavity convergence for different cases.
12 10 End of excavation
8
1.5 Ms 3 Ms
6
Case 1
Case 2-1
Case 2-2
Case 2-3
1.75 cm 21.2 cm
1.50 cm 5.28 cm
1.41 cm 1.47 cm
1.48 cm 1.73 cm
4 2 0 -10
Figure 7.
0
10 20 First stress invariant [MPa]
30
40
Case 2-2—Stress path curve.
the gallery (Fig. 6). The pore pressure profiles in the formation are quite similar to those obtained when a relative humidity (corresponding to a negative pore pressure of −5 MPa) is imposed at the cavity wall as boundary condition. Due to these different pore pressure distributions relative humidity at the wall evolves according to the vapour transfer coefficient. Figure 8 presents the temporal evolution of relative humidity of geological formation at the wall in different cases. With small vapour transfer coefficient (Case 2-1 – α = 10−4 m/s), seepage flow is predominant and the equilibrium between the gallery atmosphere and the wall is not reached at the end of the simulation. In the other hand, with high vapour coefficient (Case 2-2 – α = 10−2 m/s), the equilibrium is quickly reached. In an intermediate situation (Case 2-3 – α = 10−3 m/s), seepage and evaporation flows are both influent. In a first time formation relative humidity increases, before decreasing to stabilize finally. These different pore pressure distributions have a direct influence on the convergence predicted. Table 3 presents the results for the different cases. At the end of the excavation, the convergences are more or less the same. But as far as the long-term response is concerned, the predicted displacements are rather different. Indeed in Case 2-2, due to the high vapour transfer coefficient used, the remaining suction near
the tunnel ensures an additional strength and limits the material deformations. The stress paths followed in the first finite element near the wall confirm these results. Indeed, Figure 7 presents more or less the same stress states at the end of the excavation and after 300 Ms. The geological formation recovers an elastic behaviour at the end of the simulation and the high final value of the deviatoric stress is an indicator of the low plastic deformations. The comparison with the stress path in Case 1 (Fig. 3) shows clearly the difference of final value of the deviatoric stress and allows explaining the obtained convergences. With small vapour transfer coefficient (Case 2-1), the stress path shows that the residual value of cohesion is reached and the behaviour is still plastic at the end of the simulation (Fig. 5). The final value of the deviatoric stress is a little higher than in Case 1, so that the convergence is less important. It is also interesting to note that the stress paths become purely deviatoric (constant mean stress) during excavation when atmosphere in the tunnel begins to be unsaturated, due to the expression of seepage flow (Eq. 1). In the reference case (Case 1), the EDZ extends on 2.1 times the internal radius. With the mixed flow condition (Case 2-1/3), the simulations predict a rather narrow EDZ in comparison with the Case 1. However, the EDZ in Cases 2-1, 2-2 and 2-3 are quite similar (between 1.71 and 1.74 times the internal radius), which means that the mass transfer coefficient has a small influence on the EDZ. The intensity of the corresponding plastic deformations is not the same, which involves the differences of convergence.
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4
and training Framework Programme (FP6) on nuclear energy (2002–2006).
DISCUSSIONS AND CONCLUSIONS
Within the framework of nuclear waste disposals in deep geological layer, a correct numerical prediction of the coupled processes occurring during theses excavations is needed. With the strain-softening constitutive model used, the coupling effects between water diffusion and the mechanical aspects are very important. A new boundary condition combining seepage and evaporation flows has been developed and the modelling has shown that the flow boundary condition at the cavity wall deeply influences the cavity convergence. In low permeability and highly dilatant medium, wall pressure decreased (Case 1) leads to unphysical phenomenon, as the model predicts a massive injection of water into the formation. Furthermore thermodynamical equilibrium has to be reached between air gallery and rock mass, due to ‘‘air conditioning system’’ in the tunnel. This highlights the need of this new boundary condition, combining two modes of exchange: seepage flow and vapour flow. Depending on the value of vapour transfer coefficient, this boundary condition predicts low convergence, as for suction imposed condition or higher radial displacement as with only seepage flow condition. But with such coefficients, the computations provide realistic responses, that means ‘physical’ water flow and equilibrium between gallery atmosphere and rock mass relative humidities reached at the end of the simulation. However, the value of the vapour exchange coefficient is difficult to determine. Experimental studies with clay sample will be realised to determine and analyze the influence of this coefficient. ACKNOWLEDGEMENTS The authors would like to thank the FRS-FNRS and the European project TIMODAZ for their financial support. TIMODAZ is co-funded by the European Commission (EC) as part of the sixth Euratom research
REFERENCES Anagnostou, G. 1995. Seepage flow around tunnels in swelling rock. Int. J. Numer. Anal. Meth. Geomech. 19:705–724. Ben Nasrallah, S. & Pere, P. 1998. Detailed study of a model of heat and mass transfer during convective drying of porous media. Int. J. Heat Mass Transfer 31-5:957–967. Borja, R. & Alarcon, E. 1995. A mathematical framework for finite strain elastoplastic consolidation part 1: balance law, variational formulation and linearization. Comput. Methods Appl. Mech. Engrg. 122:765–781. Chavant, C. & Fernandez, R. 2005. Evaluating the reliability of hydro-mechanical simulation: a benchmark of numerical techniques carried out by Research Group of MoMas. 2nd International Meeting Clays in Natural and Engineering Barriers for Radioactive Waste Confinement, Tours; 249–250. Collin, F. 2003. Couplages thermo-hydro-mécaniques dans les sols et les roches tendres partiellement saturés. Thèse de doctorat. Université de Liège. Dracos, Th. 1980. Hydrologie, Eine Einführung für Ingenieure. Springer-Verlag: Wien New York. Hoxha, D., Giraud, A., Blaisonneau, A., Homand, F. & Chavant C. 2004. Poroplastic modelling of the excavation and ventilation of a deep cavity. Int. J. Numer. Anal. Meth. Geomech. 28:339–364. Kowalski, S.J. 1997. Moisture transport, thermodynamics, and boundary conditions in porous materials in presence of mechanical stresses. Chemical Engineering Science 52–7:1141–1150. Lewis, R.W. & Schrefler, B.A. 2000. The Finite Element Method in the Static and Dynamic Deformation and Consolidation of Porous Media. Wiley: New York. Zhongxuan, L., Fengzhi, L., Yingxi, L. & Yi, L. 2004. Effect of the environmental atmosphere on heat, water and gas transfer within hygroscopic fabrics. Journal of Computational and Applied Mathematics 163:199–210. Zienkiewicz, O. & Taylor, R. 2000. The Finite Element Method (5th edn). Butterworth-Heinemann: Stonchem, MA.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Numerical modelling of tree root-water-uptake in a multiphase medium S. Hemmati Institut Navier, CERMES/ENPC, Université Paris-Est, France
B. Gatmiri Institut Navier, CERMES/ENPC, University of Tehran, Iran Université Paris-Est, France
ABSTRACT: Water uptake by tree roots can change the water content of a soil in a significant manner and cause ground settlement in unsaturated expansive soils. Ground settlement can damage light buildings supported by shallow foundations through cracking. A root-water-uptake model is implemented in a three phase fully coupled finite element program θ-stock (Gatmiri/CERMES). Various expressions of root water extraction term are studied. A two dimensional root water extraction term, i.e. sink term is considered. This model takes into account the root density distribution, potential transpiration and soil suction.
1
INTRODUCTION
Water uptake by tree roots can change the water content of a soil in a significant manner. Soil shrinkageswelling phenomena and ground settlement occur due to water content changes in unsaturated soils. Ground settlement can damage light buildings supported by shallow foundations through cracking. This phenomenon is more prevalent in long periods of drought with greater fluctuations in the soil water content. In this paper the development of a two-dimensional model for root-water-uptake integrated in the finite element program θ-stock (Gatmiri 1997) is presented. This code is a fully-coupled Thermo–Hydro– Mechanical program for multiphase porous media. Studies for water uptake by plant roots have been classified into three categories. The first category includes microscopic approachs which deal with radial flow of moisture to a single root. This method needs detailed information on the geometry of root system. In the second category which is a macroscopic approach, water extraction by plant root is treated as a sink term distributed in the root zone. The third category or hybrid approach is similar to the second one, but also takes into account the time dependent plant root and soil parameters such as root density distribution, root water potential and soil suction in the sink term. In this work the third category is used.
be characterized by a number of different parameters (Lynch 1995) including morphology, topology, distribution and architecture. In general, trees tend to have deeper root systems whilst shrubs tend to concentrate roots at superficial levels in the soil (Becker and Castillo 1990). The need for efficient resource exploitation determines not only the extent of root system but also the density of the root mass. Dupuy et al. (2005) note that most root systems can be classified according to four basic arrangements: heart, tap, herringbone and plate. A series of principles can guide the selection of root zone geometries. It is important to have some idea of the root mass structure. For example Table 1. Ratio of the influence distance D to the height H of a single tree (data collected by Fityus et al.). D/H
Species
Ref.
<0.5
Significant effect for a row of elm trees A range of tree species Highly affected zone for a single eucalypt Highly affected zone for a row of mature eucalypts Single eucalypt in relatively consistent deep clay Row of eucalypts in relatively consistent deep clay Single tree Row of trees
Bozozuk, 1962
Up to 1.5 <0.7 <1.5 0.5 to 1 0.8 to 1.1
2
ROOT ARCHITECTURE AND ROOT ZONE
The ‘‘root system’’ of a plant refers to the ‘‘entire below ground structure of a plant’’ (Berntson 1994). It may
1 1.5
785
Biddle, 1983 Cameron, 2001 Cameron, 2001 Jaska et al. 2002 Jaska et al. 2002 Blight, 2003 Blight, 2003
the ratio of the influence distance of some species to their heights is presented in Table 1. Some examples of depth of affected zone and the maximum active root length density can be found in Biddle (1983), Fatahi (2006), etc.
where α is a reduction function due to soil suction ψ that can be expressed as a function of soil suction or water content θ or pressure head h, β is root density distribution and TP is potential transpiration. The functions of Smax and α are described in following paragraphs.
3
3.1
ROOT-WATER-UPTAKE MODELS
The transpiration rate of trees is dependent of rootwater-uptake (Figure 1): T (t) = SdV (1) V (t)
where T is the transpiration rate and S is the rootwater-uptake. The root-water-uptake models found in literature are similar but they use different extraction functions or sink terms. These models are generally based on Richards’ equation including a sink term S which describes water uptake by plant roots. Based on macroscopic model of Feddes et al. (1978), S is expressed as: S = αSmax
(2)
Smax = g(β)f (TP )
(3)
Maximum root-water-uptake Smax
Smax is the maximum possible root water extraction rate, if there is no limiting with soil water content. Various equations proposed for Smax are presented in Table 2. Empirical and experimental coefficients in these equations should be calibrated considering soil and tree conditions such as soil texture, tree species and age, etc. In this work, the functions proposed by Indraratna et al. (2006) are used. These functions have been defined considering a non linear relationship between root length density and relative water up take after Landsberg (1999), and a linear potential transpiration distribution proposed by Nima and Hanks (1973). 3.2 Reduction function α Existing expressions of the reduction function α in the literature are mostly like the one presented in Figure 2, with different definitions. For example a function of suction (Feddes et al. 1978) or a function of pressure head (Prasad 1988). Different points of reduction function can be defined: Field capacity, maximum soil water deficit, permanent wilting point. Following definitions are taken from British Columbia, Water conservation factsheet. – Field capacity (FC) The water content of the soil where all free water has been drained form the soil through gravity. Sandy soils may drain within a few hours but fine textured soils such as clay may take a few days to drain. Proper irrigation brings soil moisture up to field capacity. – Maximum soil water deficit (MSWD) Only a portion of the available water is easily used by the crop. The maximum soil water deficit is the amount of water stored in the plant’s root zone that is readily available to the plant. – Permanent wilting point (PWP) The soil moisture content at which the plant will wilt and die. While there still may be water in the soil, the plant is not able to extract sufficient water from the soil to meet its needs.
Figure 1. function.
Relation of transpiration rate and extraction
– Plant available soil moisture (PAW) Available soil moisture is defined by the difference between the amount of water in the soil at field capacity and the amount at the permanent wilting point.
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Table 2.
Maximum root-water-uptake suggested by different authors.
Smax Smax =
Tp zr 2Tp zr
Smax (z) =
1−
z zr
f (z) = −β z ln β
1 zr
Ref.
1D model
Feddes 1978
1D linear model
Prasad 1988, Hayhoe and DeJong 1988
1D model considering water availability and root distribution in depth
Li et al. 2001
Axisymmetric model considering root distribution density in both horizontal and vertical directions, and potential transpiration distribution
Vrugt et al. 2001
Axisymmetric model considering root distribution density in both horizontal and vertical directions, and potential transpiration distribution
Indraratna et al. 2006
Tp α(h) f (z) Smax (h, z) = 1 zr 0 α(h) f (z)dz
β = 0.01
Model description
π R2 β(r, z)Tp 1 Zm 1 Rm 2π 0 0 rβ(r, z)dr dz z r β(r, z) = 1 − 1− e−A zr rr
Smax (r, z) =
A = ( pz /zr )| z ∗ − z | + ( pr /rr )| r ∗ − r | pz , pr : empirical parameters Smax (r, z, t) = G(β)F(Tp ) tan h(k3 β) tan h(k3 β)
G(β) = 1 with
1
V (t)
V (t)
G(β)dV = 1
β(r, z, t) = βmax (t)e−k1 | z−z F(Tp ) = 1
V (t)
∗ (t) |−k | r−r ∗ (t) | 2
TP (1 + k4 (zr − z)) G(β)(1 + k4 (zr − z))dV
k1 , k2 : empirical coefficients k3 , k4 : experimental coefficients
Typical values for different soil classes are presented in Table 3.
4 4.1
FINITE ELEMENT CODE AND GOVERNING EQUATIONS Presentation of θ-stock
Soil deformation due to water content changes is significant in expansive soils. The coupling effects among
deformation, moisture, and heat should be also regarded. The theory of Philip & de Vries (1957) is known as a basic framework and a comprehensive theory of moisture and heat movement in an incompressible porous medium. In this theory, moisture and heat transfer equations are formulated in terms of temperature (T) and volumetric water content (θ). In this theory, in the absence of water continuity all transfers are in vapor phase and with increasing moisture content, the liquid phase transfer becomes dominant. A suction-based mathematical model for thermo-hydro-mechanical
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4.2 Equations 4.2.1 Solid skeleton behavior – Equilibrium equation: (σij − δij pg ) j + pg, j + bi = 0
(4)
Incremental constitutive law under small deformation assumption: d(σij − δij pg ) = Ddε − Fd( pg − pw ) − CdT
(5)
– Thermal void ratio state surface: Figure 2. Reduction function α as a function of soil suction or water content or pressure head.
e= exp
σ − pg σ − pg pg − pw 1−m A= a +b 1− patm σc patm
Table 3. Average estimated plant available water for various soils (after Evans et al. 1996). Textural class (Soil Classification)
Plant available water inches of water per inch of soil (Volumetric water content)
Coarse sand and gravel Sand Loamy sand Sandy loam Loams Silt loam Silty clay loam Clay loam Sandy clay loam Silty clay Clay
0.02–0.05 0.05–0.11 0.09–015 0.11–0.15 0.11–0.17 0.11–0.18 0.11–0.15 0.09–0.16 0.09–0.15 0.10–0.16 0.10–0.16
1 + e0 −1 exp [ce (T − T0 )]
A Kb (1−m)
(6) – Thermal degree of saturation state surface: Sr = 1 − B exp (ds (T − T0 )) where B = [as + bs (σ − pg )][1 − exp(cs (pg − pw ))] (7) 4.2.2 Moisture phase movement equations – Total moisture transfer equation: qvap qliq q = + = V + U = (DTV + DTW ) ∇T ρw ρw ρw − (Dθv + Dθw ) ∇θ − Dw ∇Z
behavior of unsaturated media is presented by Gatmiri (1997) and Gatmiri et al. (1997a, b, 1999 and 2002). In this approach, heat and moisture transfer equations are given in an alternative form based on water and air pressures. Temperature-dependent state surface formulations are given for void ratio and degree of saturation variations within porous media. The coupling effects of temperature and moisture content on deformation of skeleton, and the inverse effects are included in this model via thermal state surface concept. The non-linear constitutive law for strain-stress relationship is considered. In this form of formulation, the soil nonhomogeneity and hysteretic effect can be included. The phase change between liquid and vapor phases is taken into account. As root-water-uptake can be considered as a hydraulic loading, only final principal equations of solid skeleton behavior and moisture transfer and conservation and energy equation, used in the computer code θ stock are presented in the following paragraphs.
(8)
– Moisture mass conservation equation: ∂Sr ∂T ∂pw + nSr βP + (ρw − ρv ) n ∂t ∂t ∂t ∂n ∂ρv + n (1 − Sr ) + (Sr ρw + ρv (1 − Sr )) ∂t ∂t = div (ρw Dw ∇z) + div (ρw DT ∇T )
nSr βT
+ div(ρw Dp ∇(pw − pg )) + Qm
(9)
4.2.3 Energy equations – Total heat flow (Philip & de Vries, 1957):
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Q = −λ∇T + [Cpw ρw U + Cpv ρw V + Cpg ρg Vg ] (T − T0 ) + ρw hfg V + ρv hfg Vg λ = (1 − n)λs + θλw + (n − θ) λv
(10)
– Energy conservation equation: ∂ (CT (T − T0 ) + (n − θ )ρv hfg ) ∂t − div(λ(θ )∇T ) + Cpw ρw div(U (T − T0 )) + Cpv ρw div(V (T − T0 ) + Cpg ρg div(Vg (T − T0 )) + ρw hfg div(V ) + hfg div(ρv Vg ) = 0
5
(11)
BOUNDARY CONDITIONS
In this work, boundary conditions of root zone elements are time dependent hydraulic boundary conditions. Flux boundary conditions are imposed. Calculated water uptake volume in corresponding time step will be applied as an outlet discharge of each root element: ρw (U ) n − (qw ) = 0 S (t) = −qw (t)
∀x ∈ QW
Figure 3.
Created mesh with tree root elements.
Figure 4.
Degree of saturation.
Figure 5.
Suction.
(12) (13)
where qw (t) is water discharge of an element at time t. A preliminary example of numerical modelling of root water uptake is performed in order to demonstrate the functionality of the implemented program. A row of trees is considered in this plane-strain example. A water flux boundary condition equal to rootwater-uptake is applied on the root elements. The created mesh with tree root elements is presented in Figure 3. The applied water flux boundary condition is variable in different time steps as a function of the results obtained in the previous time step. The contour graph of degree of saturation is presented in Figure 4. As can be seen the degree of saturation in the tree root zone is considerably decreased due to root water uptake. Consequently the suction is increased in the same zone (Figure 5). Figure 6 presents the vertical displacement. As can be seen, the vertical displacement near the tree centre is more important and reduced with the distance from the tree. This preliminary example shows that using this thermo hydro mechanical model we can model the effect of tree roots water uptake in the expansive soils. The variations of water content, suction and finally the vertical displacements can be predicted by the numerical model. It is clear that the model should be calibrated for the site specific soil characteristics, climatic data and the type of the tree.
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Figure 6.
6
Vertical displacements.
CONCLUSION AND PERSPECTIVE
In this study, a mathematical model is presented and implemented in the finite element program θ-stock (Gatmiri, Cermes 1997). Series of different root-water-uptakes models have been studied. A sophisticated model of root-water-uptake proposed by Indraratna et al (2006) is considered. This rootwater-uptake model is programmed and integrated in θ-stock. Hydraulic and heat boundary conditions are calculated and then applied on root zone elements. Validation of this model with the existing examples found in literature has been performed. REFERENCES Becker, P. & Castillo, A. 1990. Root architecture of shrubs and saplings in the understory of a tropical moist forest in lawland Panama, Biotropica, 22:242–249. Bernston, G. 1994. Modelling root architecture: are there tradeoffs between efficiency and potential of resource acquisition? New Phytologist, 127:483–493. Biddle, P.G. 2001. Patterns of drying and moisture deficit in the vicinity of trees in clay soils. Géotechnique, 33:107–126. Blight, G. 2005. Desiccation of a clay by grass, bushes and trees, Geotechnical and geological engineering, 23, 697–720. Bozozuk, M. 1962. Soil shrinkage damages shallow foundations at Ottawa, Canada, Div. of Building Research NRCC Canada, Research paper 63. British Columbia, Ministry of Agriculture. 2002. Water Conservation Factsheet, Order No. 619.000-1. Evans, R., Cassel, D.K. & Sneed, R.E. 1996. Soil, water, and crop characteristics important to irrigation scheduling.
North Carolina Cooperative Extension service, Publication Number: AG452-1. Fatahi, B. 2006. Pers. Comm. Uni. of Wollogong. School of civil, Mining and Enviro. Engg. Feddes, R.A., Kowalik, P.J. & Zarandy, H. 1978. Simulation of field water use and crop yield. Wageningen, The Netherlands. Fytius, S., Cameron, D. & Driscol, C. 2007. Observation of root architecture and their implications for modelling water movement in partially saturated soils, 3rd Asian Conf. on Unsat. Soils, pp. 207–212. Gatmiri, B. 1997. ‘‘Effect of nonlinearity in thermohydromechanical coupling’’, XIV International Conference on Soil Mechanics and Foundation Engineering, September 6–12, 1997 at Hamburg. Gatmiri, B., Delage, P. & Fry, J.J. 1997. ‘‘Numerical Aspects Of Thermoelastoplastic Behaviour Of Saturated Soil’’, NAFEMS World congress ‘97, Stuttgart, April 9–11. Gatmiri, B., Seyedi, M., Delage, P. & Fry, J.J. 1997. A new suction-based mathematical model for thermohygromechanical behaviour of unsaturated porous media’’, NUMOG VI. Gatmiri, B. 1997. Analysis of fully coupled behaviour of unsaturated porous media under stress, suction and temperature gradient, Final report of CERMES-EDF, France. Gatmiri, B., Jenab-Vossoughi, B. & Delage, P. 1999. Validation of θ-STOCK, a finite element software for the analysis of thermo-hydro-mechanical behaviour of engineered clay barriers. Proceedings of NAFEMS WORLD CONGRESS 99 on Effective Engineering Analysis, Vol. 1:645–656. Gatmiri, B. & Jenab-Vossoughi, B. 2002. Effects of heat convection and phase changes on heat and fluid transfer in unsaturated porous media, Third International Conference on Unsaturated Soils, UNSAT 2002, Recife, Brasilia, 10–13 March 2002, pp. 77–82. Hayhoe, H.N. & De Jong, R. 1988. Comparison of two soil water models for soybeans. Can. Agric. Eng. 30:5–11. Indraratna, B., Fatahi, B. & Khabbaz, H., 2006. Numerical analysis of matric suction effects of tree roots. Geotechnical Engineering, 159, Issue GE2, 77–90. Jaska, M., Kaggwa, W., Woodburn, J. & Sinclair, R. 2002. Influence of large gun trees on the soil suction profile in expansive soils, Australian Geomechanics, 36:23–33. Li, K.Y., Bisvert, B.J. & De Jong, R. 2001. An exponential root-water-uptake model with water stress compensation. J. Hydrol., 252:189–204. Lynch, J. 1995. Root architecture and plant productivity, Plant Physiology, 109:7–13. Nimah, M.N. & Hanks, R.J. 1973. Model for estimating soil water plant, and atmospheric interrelations. I. Description of sensivity. Soil Sci. Soc. Am. Proc., 37:522–527. Philip, J.R. & de Vries, D.A. 1957. Moisture movement in porous materials under temperature gradients. Trans. Am. Geophys. Un., 38:222–232. Prasad, R. 1988. A linear root-water-uptake model. J. Hydrol. 99:297–306.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Numerical modelling of the soil surface moisture changes due to soil-atmosphere interaction S. Hemmati Institut Navier, CERMES/ENPC, Université Paris-Est, France
B. Azari Civil Engineering Department, University of Tehran, Iran
B. Gatmiri Institut Navier, CERMES/ENPC, University of Tehran, Iran and Université Paris-Est, France
ABSTRACT: In this paper, a two-dimensional model for soil-atmosphere interaction developed by considering the mass and energy balance equations is presented. This model is integrated in θ-stock (Gatmiri, 1997a), a finite element program for modelling Thermo-Hydro-Mechanical (THM) behaviour of unsaturated soils. In this research, the exchange of moisture and heat between a multiphase soil and an atmosphere layer is simulated. Considering the latent and sensible heat transport equations and consequently the moisture exchange (evaporation and condensation), equations are developed by taking into account climatic measured factors such as wind, temperature, precipitation, humidity and radiation. These boundary conditions are coupled with a system of equations incorporating THM behaviour for multiphase medium integrated in θ-stock. The numerical results are then compared with the available experimental test results in order to validate the model.
1
INTRODUCTION
The computation of soil-atmosphere water fluxes (e.g. infiltration, evapotranspiration, runoff, precipitation, and interception) is required for the analysis of numerous problems in geotechnical engineering, geoenvironmental engineering and hydrology. Direct measurement of evapotranspiration is difficult or expensive at field scale; hence numerous equations exist to estimate it. Evapotranspiration includes evaporation of water from the soil or other surfaces and transpiration through plant stomata (Tahiri et al., 2006). Energy balance models provide a viable means of estimating evapotranspiration, but are subject to large sensitivity to input variables, especially air temperature, humidity and wind. Solar radiation plays an important role in estimating evapotranspiration. Incoming solar radiation is partially reflected, with the reminder absorbed by vegetation and wetland water. This net radiation is partially intercepted by the vegetative canopy, and drives transpiration in plants. The second portion of net radiation is absorbed by wetland water, and drives evaporation. Convection and diffusion carry water away from the surface, and transfer heat from air to the wetland (Kadlec 2005). In this
paper, a two-dimensional model for soil-atmosphere interaction, developed by considering the mass and energy balance equations, is presented. This model is integrated in θ-stock (Gatmiri, 1997a), a finite element program for modelling Thermo-Hydro-Mechanical (THM) behaviour of unsaturated soils. The exchange of moisture and heat between a multiphase soil and an atmosphere layer is simulated. 2
ENERGY BALANCE EQUATIONS
The main driving force for evapotranspiration (ET) is solar radiation. A good share of that radiation is converted to the latent heat of vaporization. Therefore, the energy balance is the proper framework to interpret and predict not only evaporative processes, but also wetland water temperature. A modification of the Penman (1948) approach is described here (Wright, 1982). It is to be noted that there are many other versions of the energy balance (Priestly & Taylor, 1972; Montieth, 1981; Shuttleworth & Wallace 1985; Walter et al., 2000). Several of these have been evaluated for green crops, because of the importance of irrigation requirement in arid regions (ASCE 1990).
791
The total energy balance equation can be expressed by: Rn + WE = G + H + Le
(1)
where Rn = net radiation in potential conditions; WE = wind energy; G = the convective transfer to ground; H = the convective transfer to air; and Le = latent heat flux for vaporization.
pressure gradient with height above ground level, Dv = diffusivity for vapour in air. The latent heat for vaporization of water is given by: hfg = 4.186(607 − 0.7T) where T = water temperature. 2.3
2.1 Net radiation in potential conditions
Wind energy
Wind energy is expressed in the form:
Extraterrestrial radiation is depleted by the clear atmosphere and by cloud cover. A fraction α, the wetland albedo, of this amount is reflected. The remainder reaches the soil-plants system. Plant transpiration partially intercepts it while another portion reaches the wetland. The part absorbed by the surface is called net radiation in potential condition. The net radiation in potential conditions can be obtained as: 4 Rn = (1 − α) Rg + εs εa σ Ta4 − σ Tsp
(6)
(2)
WE =
1 ρa ZU 3 200
(7)
where Z = thickness of air layer; and U = air velocity. The value of WE is approximately 2% of net radiation in potential conditions hence; it can be neglected. Then equation (1) reduces to: Rn = G + H + Le
(8)
where α = the surface albedo; Rg = the incoming solar radiation; εa = the air emissivity; σ = the Stefan-Boltzman constant; Ta = the air temperature at reference height; εs = the surface emissivity; and Tsp = the surface temperature in potential conditions. The albedo factor is: ⎧ 2 ⎨1 − 1 − v v ≤ vfc vfc (3) α= ⎩ 1 v > vfc
3
where v = the volumetric soil water content of the top soil layer; and vfc = the volumetric soil water content at field capacity.
where I = infiltration; P = precipitation; Roff = runoff ; E = surface evaporation; and Iinte = interception.
2.2
3.1 Surface evaporation
The convective heat transfer from the water to the air and latent heat flux for vaporization
The convective heat transfer from the water to the air can be expressed by: H = ρa Ca Dta T
(4)
where ρa = density of air; Ca = specific heat of air; and Dta = heat diffusivity in air. The latent heat flux for vaporization is: ρa Le = hfg εDv Pv Pa
(5)
where hfg = latent heat for vaporization of water; Pa = atmospheric pressure; and ε = ratio of molecular masses of water and dry air, Pv = vapour
MASS BALANCE EQUATIONS
The net soil-atmosphere moisture flux is a function of some of the key components of the hydrology cycle; namely, precipitation, actual evaporation, run off, and interception. The net soil-atmosphere flux may result in either infiltration (positive flux) or exfiltration (negative flux). The total mass balance equation can be expressed by: & ' I = P − Roff + E + Iinte (9)
Infiltration, I , corresponds to a natural boundary condition. The amount of precipitation, P, runoff, Roff , and interception, Iinte , are ‘‘known’’ inputs which can be obtained by direct measurement at field scale. Surface evaporation can be expressed by many equations. Here surface evaporation is obtained by the Penman (1948) equation:
E=
r (Rn −G) hfg
+ γ Ea
r + γ
(10)
where r = slope of the saturation vapour pressuretemperature curve; γ = psychrometric constant; and Ea = evaporation rate.
792
Saturated vapor pressure (kPa)
wind function obtained by Blight (1997) is used:
14
U2 f (u) = 0.165 0.8 + 100
12 10 8
where U2 = the wind speed at 2 m height. The wind speed at 2 m height can be obtained from the wind speed Uw at the generic height Zw by using the following equation:
6 4 2 0 0
10
20
30
40
50
U2 = Uw
Temperature (˚C)
Figure 1.
4.87 ln(67.8Zw − 5.42)
(15)
Saturation vapor pressure curve.
4 A graph of the saturation vapour pressure against temperature is shown in Figure 1. This is called the psychrometric chart. The gradient of the curve is denoted r and is a function of temperature, T , and saturation vapour pressure Pvs (Dodds et al. 2005). Allen et al. (1998) calculate r using: r =
(14)
4098Pvs (T + 237.3)2
(11)
where Pvs = the saturation vapour pressure; and T = temperature. The saturation vapour pressure is calculated using the equation: Pvs = 0.618 exp
17.27T T + 237.3
MODEL DESCRIPTION
The key variables that effect energy and mass balance have been briefly described in previous sections while, in this section, the numerical model is described. The model uses a subroutine which has been designed for taking into account soil-atmosphere interaction. The climatic data (e.g. temperature, the incoming solar radiation, precipitation, and runoff) is inserted in the subroutine. These data are separated into two parts: the first part is used for estimating temperature flux by considering the energy balance equation while another part is used for estimating water flux by considering the mass balance equation. Temperature and water flux (infiltration) are input data to the main program which estimates soil stresses, strains, suctions, etc. Thermal and hydraulic loading of each time step, are calculated based on the results of preceding time step. Soil
(12)
where T = temperature. Modern study of evaporation began with Dalton in the late eighteenth century. Dalton ‘‘theorised that evaporation from a surface, must be a consequence of the combined influence of the wind, atmospheric moisture content, and characteristic of the surface (Rosenberg et al., 1983). The Dalton aerodynamic equation for evaporation from a free water surface is: Ea = f (u)(Pvs − Pva )
(13)
where f (u) = wind function; Pvs = the vapour pressure at the evaporating surface; Pva = the vapour pressure of the atmosphere above (Penman 1948). There are many versions of wind function (Penman, 1984; Wilson 1990; Blight 1997). Here the
Figure 2.
793
Model description.
Thermal void ratio state surface:
surface temperature and vapour pressure, calculated in the preceding time step, together with the climatic data, that are independent of soil condition, are used to calculate the thermal and hydraulic loading for the current time step. A schematic view of this process is depicted in Figure 2.
5 5.1
exp
(18)
FINITE ELEMENT CODE AND GOVERNING EQUATIONS
Thermal degree of saturation state surface: Sr = 1 − B exp (ds (T − T0 ))
Presentation of θ -stock
where B = [as + bs (σ − pg )][1 − exp(cs (pg − pw ))]
qliq qvap q = + =V +U ρw ρw ρw = − (DTV + DTW ) ∇T − (Dθ v + Dθ w ) ∇θ − Dw ∇Z
(20) Moisture mass conservation equation: ∂Sr ∂T ∂pw + nSr βP + (ρw − ρv ) n ∂t ∂t ∂t ∂n ∂ρv + n (1 − Sr ) + (Sr ρw + ρv (1 − Sr )) ∂t ∂t = div (ρw Dw ∇z) + div (ρw DT ∇T ) & '' & + div ρw Dp ∇ pw − pg + Qm (21)
nSr βT
5.2.3 Energy equations Total heat flow (Philip & de Vries, 1957): Q = −λ∇T
Equations
! + Cpw ρw U + Cpv ρw V + Cpg ρg Vg (T − T0 )
+ ρw hfg V + ρv hfg Vg λ = (1 − n)λs + θλw + (n − θ) λv
(22)
Energy conservation equation:
(16)
Incremental constitutive law under small deformation assumption: d(σij − δij pg ) = Ddε − Fd(pg − pw ) − CdT
(19)
5.2.2 Moisture phase movement equations Total moisture transfer equation:
5.2.1 Solid skeleton behaviour Equilibrium equation: (σij − δij pg ),j + pg,j + bi = 0
1 + e0 −1 exp [ce (T − T0 )]
A Kb (1−m)
σ − pg σ − pg pg − pw 1−m A= a +b 1− patm σc patm
Soil deformation due to water content changes is significant in expansive soils. The coupling effects among deformation, moisture, and heat should be also regarded. The theory of Philip & de Vries (1957) is a basic framework for moisture and heat movement in an incompressible porous medium. In this theory, moisture and heat transfer equations are formulated in terms of temperature (T ) and volumetric water content (θ). In the absence of water continuity all transfers are in the form of vapour while, with increasing moisture content, the liquid phase transfer becomes dominant. A suction-based mathematical model for thermo-hydro-mechanical behaviour of unsaturated media is presented by Gatmiri (1997b), Gatmiri et al (1997) and Gatmiri and Jenab (2002). In this approach, heat and moisture transfer equations are written using water and air pressures. Temperature-dependent state surface formulations are given for void ratio and degree of saturation variations within porous media. The coupling effects of temperature and moisture content on deformation of skeleton, and the inverse effects are included in this model via the thermal state surface concept. A non-linear constitutive law for the strain-stress relationship is considered. In this type of formulation, soil heterogeneity, hysteretic effects and phase changes between liquid and vapour phases can all be taken into account. In the following part, only the main equations of solid skeleton behaviour, moisture transfer and energy conservation used in the computer code θ-stock are presented (a list of symbols is provided at the end of the paper). 5.2
e=
(17)
794
' ∂ & CT (T − T0 ) + (n − θ) ρv hfg ∂t − div (λ (θ) ∇T ) + Cpw ρw div (U (T − T0 )) + Cpv ρw div (V (T − T0 )) & ' + Cpg ρg div Vg (T − T0 ) ' & + ρw hfg div (V ) + hfg div ρv Vg = 0
(23)
6
BOUNDARY CONDITIONS
surface element: G (t) = qh (t)
In finite element simulations, surface elements are subjected to time dependent hydraulic and thermal boundary conditions. Flux boundary conditions impose in each time step calculated inflow or outflow infiltration rates to each surface element: I (t) = qw (t)
(25)
where qh (t) is a positive or negative heat flux on each surface element.
(24)
7
where qw (t) is water discharge of an element at time t. Heat flux boundary condition in the corresponding time step is applied as an energy flux on each
RESULTS AND CONCLUSIONS
A two-dimensional model for soil-atmosphere interaction conforms to the equations of THM formulation integrated in θ-stock (Gatmiri, 1997a) is developed. A preliminary example is presented. In this example an
800 -2
Energy flux (Wm )
700 600 500
Rn
400
Le
300 G
200 100
H
0 -100 0
5
10
15
20
25
30
Time (day)
Figure 3.
Evolutions of net radiation Rn, sensible heat H, soil heat G, and latent heat for evaporation Le.
Temperature (˚C)
30 25 d=0.0
20 15 d=0.1
d=0.68
10
d=1.16
d=0.2
d=2.12
5 0 0
5
10
15
20
25
30
Time (day)
Figure 4.
Evolution of temperature at different depths, d(m). 30000
Suction (Pa)
25000 d=0.1
20000
d=0.0
15000
d=0.2 d=0.68
10000
d=1.16
5000 0
d=2.12
-5000 0
5
10
15 Time (day)
Figure 5.
Evolutions of soil suction at different depth, d(m).
795
20
25
30
unsaturated soil with an initial degree of saturation equal to 0.9, and initial temperature equal to 7◦ C is analysed. Meteorological data used in this problem relates to the Rouen test embankment constructed at the LCPC experiment centre, France (Gao et al., 2006). Energy and mass flux is calculated from meteorological data and soil condition and is used as boundary condition on the surface elements. Calculated energy flux is presented in Figure 3. Temperature and suction evolution on the soil surface and at different depths are presented in Figure 4 and Figure 5 respectively.
8
LIST OF PARAMETERS OF θ -STOCK
σij : total stress tensor, D: strain tensor, e: void ratio n: porosity δij : Kronecker symbol, pw : water pressure pg : air pressure pv : vapour pressure patm : atmosphere pressure pg − pw : suction ρw , ρv , ρg : density of water, vapour and air θw , θv , θg : volumetric content of water, vapour and air U , V , Vg : flux of water, vapour and air hfg : latent heat of water λs , λv , λw : thermal conductivity of solid, vapour and water λ: Fourier homogenized diffusivity DTV , DTW : thermal diffusivity of vapour and water Dθ V , Dθ W : isothermal diffusivity of vapour and water DW : gravitational diffusivity Cpv , Cpg , Cpw : specific heat at constant pressure vapour, air and water Q: heat flux
ACKNOWLEDGEMENT The authors gratefully acknowledge BRGM for financial supporting of this research.
REFERENCES ASCE 1990. Evapotranspiration and Irrigation Water Requirements, ASCE Manuals and Reports on Engineering Practice No.70, American Society of Civil Engineering. New York. Allen, R.G., Pereira, L.S., Raes, D. & Smith, M. 1998. Crop evapotranspiration-guidlines for computing crop water requirements. FAO Irrigation and Drainage Paper, No.56, FAO, Rome.
Blight, G.E. 1997. Interactions between the atmosphere and the Earth. (37th Rankine Lecture). Geotechnique. London, United Kingdom. 47(4) 715–767. Dodds, P.E., Meyer, W.S. & Barton, A. 2005. A review of methods to estimate irrigated reference crop evapotranspiration across Australia. CRC for Irrigation Futures Technical Report No. 04/05. Gao, Y.B., Cui, Y.J. & Audiguier, M. 2006. From meteorological data to the prediction of embankment stability, Final report. ENPC/CERMES. Gatmiri, B. & Jenab, B. 2002. Effects of heat convection and phase changes on heat and fluid transfer in unsaturated porous media. Third International Conference on Unsaturated Soils, UNSAT 2002, Brasilia, 77–82. Gatmiri, B., Seyedi, M., Delage, P. & Fry, J.J. 1997. A new suction-based mathematical model for thermohygromechanical behaviour of unsaturated porous media, NUMOG VI: 291–296. Gatmiri, B. 1997a. Analysis of fully coupled behaviour of unsaturated porous media under stress, suction and temperature gradient. Final report of CERMES-EDF, France. Gatmiri, B. 1997b. Effect of nonlinearity in thermohydromechanical coupling. XIV International Conference on Soil Mechanics and Foundation Engineering, Hamburg: 1815–1818. Kadlec, R.H. 2005. Water temperature and evaporation in surface flow wetlands in hot arid climate. Ecological Engineering: 1–13. Montieth, J.L. 1981. Evaporation and surface temperature. Quart. J. Roy. Meteor. Soc. 107(451): 1–27. Penman, H.L. 1948. Natural evapotranspiration from openwater, bare soil and grass. Proc. Roy. Soc. Acad. 193: 120–145. Philip, J.R. & de Vries, D.A. 1957. Moisture movement in porous materials under temperature gradients, Trans. Am. Geophys. Un. 38: 222–232. Priestley, C.H.B. & Taylor, R.J. 1972. On assessment of surface heat flux and evaporation using large scale parameters. Mon. Weath. Rev. 100: 81–92. Rosenberg, N.J., Blad, B.L. & Verma, S.B. 1983. Microclimate: The biological environment, 2nd edition. New York: John Wiley & Sons. Shuttleworth, W.J. & Wallace, J.S. 1985. Evaporation from Sparse Crops-an energy combination theory. Quart. J. Roy. Meteorol. Soc. 111: 839–855. Tahiri, Z.A., Anyoji, H. & Yasuda, H. 2006. Fixed and variable light extinction coefficients for estimating plant transpiration and soil evaporation under irrigated maize. Agricultural Water Management 84: 186–192. Walter, I.A., Allen, R.G., Elliott, R., Jensen, M.E., Itenfisu, D., Mecham, B., Howell, T.A., Snyder, R., Brown, P., Eching, S., Spofford, T., Hattendorf, M., Cuenca, R.H., Wright, J.L. & Martin, D. 2000. The ASCE Standardized Reference Evapotranspiration Equation. ASCE, New York. Wilson, G.W. 1990. Soil evaporative fluxes for geotechnical engineering problems, PhD thesis, University of Saskatchewan. Wright, J.L. 1982. New evapotranspiration crop coefficients. J. Irrig. Drain. Div. ASCE 108 (IR2): 57–74.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Identification of coupled hydro-mechanical parameters with application to engineered barrier systems T. Schanz Laboratory of Soil Mechanics, Bauhaus-Universitat Weimar, Germany
M. Datcheva Institute of Mechanics, Bulgarian Academy of Sciences, Sofia, Bulgaria
M. Zimmerer VAROCON, Weimar, Germany
ABSTRACT: Bentonite based buffer materials are well recognized as an important component in engineered barrier systems. Due to the bentonite component their main mechanical characteristic is the ability of swelling while encountering water. Because of the complex and coupled behaviour mathematical modelling is a difficult task and results in sophisticated constitutive models with a large number of associated parameters. These call for advanced, unique, time to develop methodology for model identification based on less experiments combined with numerical simulation and consequently back calculation of the model parameters. The aim of the presented study is to investigate the ability of a direct iterative model calibration to serve as a tool for complex coupled hydro-mechanical (HM) model parameters identification. As a result a critical discussion is presented regarding the importance of boundary and initial conditions applicable to the experimental installation in calibration of the constitutive functions. Application examples are given based on laboratory experiments on highly compacted bentonite-sand mixtures.
1
INTRODUCTION
In practice, it may not be always possible directly to measure or provide sufficient and reliable laboratory tests data for determining the material model parameters and to fit the constitutive functions. This is specially applicable to models coupling different physical processes and particulary for boundary value problems involving mechanical and hydraulic forces. That is why often in numerical simulations the constitutive functions and the involved parameters are subjected to assumptions and simplifications. In the literature devoted to parameters calibration in unsaturated soil mechanics the common approach is to perform and use data from two types of experiments, namely constant suction and constant net stress tests. It is a rare practice to verify the procedure used in best fit analysis and to validate the model calibration. This deficiency reflects to the quality of the numerical simulations and respectively reduces the trust in the numerical predictions. The analysis presented here concerns the identification of coupled HM
model parameters that are difficult to be determined directly and reliably from laboratory or field measurements. 2
CONCEPTUAL MODEL
An important point in completing successfully the model identification procedure is to choose the solution strategy that is the most proper regarding the model features, the available observation data and suitable concerning the requested applications. The solution strategy consists of: a) selection of the back analysis approach; b) sensitivity analysis; c) selection of the subset of parameters to be subject of an optimization; d) assessing the parameters constraints or trusted zone and initial values, if requested; e) selection of the most suitable optimization problem algorithm. It is of paramount importance to build the model and the identification procedure in the way they provide efficient, robust and resource provident analysis.
797
2.1
Back analysis approach
Back analysis problems may be solved in two different ways, defined as inverse and direct approaches, see (Cividini et al. 1981). The inverse back analysis consists in inverting the model equation with respect to the parameters that are unknown and subject to identification. The direct approach is based on an iterative procedure correcting the trial values of the unknown parameters by minimizing error functions. This way the model response data are provided by trial forward solutions of the problem used for model parameters identification. For the analysis presented here the iterative direct approach has been chosen. The decision is based on the fact that such approach gives the opportunity to be coupled with standard and well approved finite elements/differences programs and does not require access to the source code. Additionally for complex and nonlinear problems direct approach is not only more robust but may be the only possible solution. 2.2
Sensitivity analysis
The aim of sensitivity analysis is to estimate the rate of changes in the output of a given model with respect to changes in the model input. Such knowledge is important for evaluating the applicability of the model and for understanding the behaviour of the system being modelled. Sensitivity analysis provides information for model parameters whose values determination requires specific measurements, precision and amount of data. In spite of its restrictions we have chosen to perform local sensitivity analysis for accessing our model response. In this analysis the focus is on estimating model sensitivity to parameter variation in the vicinity of a sample point. This sensitivity is often characterized by gradients or partial derivatives at the chosen sample point. In this study the sensitivity has been assessed using a scaled sensitivity (SS) analysis. Let note the vector of model parameters with x and the model output vector with y . The latter is called in this section ‘‘observation’’. The SS analysis indicates the amount of information provided by the i-th observation for the estimation of j-th parameter, (Zhang et al. 2003). The scaled sensitivity SSi, j of the yi observation to the model parameter xj is defined by: SSi, j =
∂yi ∂xj
√ xj wi
(1)
Weighting factor wi is related to the i-th observation and is evaluated based on some statistics, i.e. variance, standard deviation or coefficient of variation of the error of the observations (Hill 1998). The overall model sensitivity to a given model parameter xj
is assessed by a composite scaled sensitivity, CSSj (Anderman et al. 1996; Hill 1998): . / N / 1 " 0 2 SS CSSj = N i=1 i, j
(2)
Low values of CSSj indicate large uncertainty in the parameter estimate. For comparing CSS values the following measure is used: γj =
CSSj max(CSS)
(3)
Comparatively small value of γj is a warning for possible evolving of poor confidence to the identified xj if using the observations involved in computing the CSS. As it has been stated in (Zhang et al. 2003), the dimensionless sensitivity measures are required to compare the relevance of different types of observations or the overall appropriateness of the observations for the estimation of a given model parameter.
2.3 Optimization procedure The optimization problem in its general formulation reads: minimize f (xx ) subject to constraints
cj ≤ xj ≤ Cj , ∀j
where f (xx ) is a proper measure of the disagreement between model prediction and experimental observations, called hereafter objective function. The proper choice of the parameter estimation technique and the method for solution of the objective function minimization problem are of a paramount importance for the efficiency and robustness of the back analysis results. Over the past decade a number of optimization algorithms have been used extensively in optimization tasks, from gradient-based algorithms using continuous and in most cases convex design spaces, to non-gradient probabilistic- based search algorithms widely applied for global and nonconvex design exploration. Representative for the former are local search Newton—Raphson method (e.g. Levenberg & Marquart algorithm) and gradient based derivative free method, (Davidon and Nazareth 1977). Non gradient methods are derivative free solution strategies such as downhill simplex method (Nelder and Mead 1965) and global search evolutionary algorithms, one of whose representatives is Particle Swarm Optimization (PSO) technique, (Eberhardt and Kennedy 1995).
798
3
as candidates for optimization, namely: αi , κs0 , αsp , pref and αss .
CONSTITUTIVE MODEL
The identification strategy has been built up taking into account the specific features of both the constitutive model and the finite elements (FE) code this model has been implemented. The material model considered here is the thermoelastoplasic (TEP) model for soils which is a part of the material models library of the FE code Code_Bright, (Code_Bright 2002). The acceptance of two stress state variables concept is basic for the TEP model. The two stress state variables are the net stress, computed as the excess of the total stresses σ total − pg I ) and the over the gas pressure pg : σ = (σ matric suction s = pg − pl , where I is the unit tensor, pl is the pore liquid pressure. Here only the elastic part of the TEP model is presented. For the full model description one has to refer to (Code_Bright 2002) and for further details to (Alonso et al. 1999). 3.1
Mechanical phenomena
The increment of the strain state variable is decomposed to elastic (e) and plastic (p) parts: dεε = dεε e + dεε p . Following the two stress state concept, the elastic part of the strain increment is taken to be a sum of suction induced and net stress induced strain increments: dεε e = dεε σ −e + dεε s−e . The constitutive equations for net stress and suction induced elastic strains read: dε σv −e =
κi (s) dp ; 1+e p
= dε s−e v
κs (p, s) ds (4) 1 + e s + 0.1
The mean stress p is positive for compression and e is the void ratio. The two constitutive functions associated with Equation 4 are defined as: κi0 (1 + αi s) if s ≤ −0.999αi κi (s) = (5) 0.001 κi0 if s > −0.999αi κs (p, s) = κs0 κsp exp(αss s)
(6)
−20 ⎧ 10 ⎪ ⎪ 1 + α ln if p ≤ 10−20 ⎪ sp ⎪ ⎪ pref ⎪ ⎨ −1 κsp = 0 if p ≥ pref exp ⎪ αsp ⎪ ⎪ ⎪ p ⎪ ⎪ ⎩1 + αsp ln elsewhere pref The coefficient κi0 gives the slope of the rebound part of the void ratio versus effective pressure compression-rebound test graph at saturated condition. This parameter is supposed to be easy and confidently determined directly from the experimental data. Hence 5 parameters are chosen to be investigated
3.2 Hydraulic phenomena The liquid flow follows the generalized Darcy’s law and therefore we have two constitutive functions to be determined and calibrated. These functions are retention curve and relative permeability. The former is taken to obey the following analytical form: ⎡ Se =
Sl − Srl ⎢ = ⎣1 + Sls − Srl
p g − pl P0
1 ⎤−λ 1−λ⎥ ⎦
(7)
where Sl is the degree of saturation; Srl and Sls are model parameters related to the residual and maximum saturation. The relative permeability is supposed to be directly related to the retention curve equation and is given by: krl =
'λ 2 & Se 1 − 1 − Se1/λ
(8)
Intrinsic permeability is supposed to be isotropic, that is k11 = k22 = k33 The parameters k11 , λ, P0 , Srl are considered as prospective for optimization. The total number of the coupled HM model parameters is 23 with 8 for the elastic law, 10 for the plastic law and 5 for the constitutive functions characterizing soil-water interaction.
4
NUMERICAL IMPLEMENTATION
The material used for this example of model parameters identification is a mixture of calcium—type bentonite Calcigel and quartz sand. The material is heavily compacted based on dry mass 50% Calcigel and 50% sand mixture, (Agus ans Schanz 2005). Extensive experimental data for this material is reported in (Agus 2005). The liquid used in experiments and simulations presented in this section is distilled water. The gas pressure is taken equal to zero because the only gas considered here is air and it is freely drained from the sample. Results from swelling pressure tests were used for calibration of TEP model parameters. The swelling pressure test offers valuable information related to the behaviour of expansive soils. What makes this test exceptional is that both stress state variables, namely the net mean stress and the suction, are not constant during the test. The reason we chose elastic constitutive functions to be back analysed is that the swelling pressure target for optimization is less than the preconsolidation
799
pressure calibrated in (Agus 2005). Therefore we expect less influence of plastic law parameters. 4.1
Table 1.
Formulation of the forward problem
In this section simulations of the tests carried out by (Agus 2005) and (Arifin and Schanz 2007) on samples of Calcigel—sand mixture are presented. The swelling pressure cell used for obtaining the data and an exemplary FE model are given in Figure 1. The model predicted variables that serve as model ‘‘estimation’’ for the optimization procedure are obtained solving two types of problems, namely simulating multistep (MSP) and one-step swelling pressure (1SP) tests. The data from SP-HC-50B-4 test (axis translation test ATT) and SP-HC-50B-3 test (vapor equilibrium technique VET), (Agus 2005) are used as ‘‘observation’’ data for the MSP optimization. The ‘‘observation’’ data for the 1SP test is taken from (Arifin and Schanz 2007). Boundary conditions for displacements are imposed in the way to satisfy the constant volume condition. Boundary conditions for pore water pressure pl are: impervious top and lateral sides of the sample and at the bottom side imposed constant for 1SP and stepwise variable for MSP. The height of the sample is 0.02 m and the radius is 0.025 m. Initial suction of 22 MPa is imposed at each point of the domain. Initial porosity is taken according as reported in the corresponding experimental data. The problem is solved as axisymmetric even some problems with this type of FE has been observed during the simulations. The axial stress (σyy ) at a chosen point in the vicinity of the midpoint of the sample top side has been extracted from the solution and used to build the objective function for the consecutive optimization. It has to be mentioned that Code_Bright provides the output of the solution including stress values in prescribed domain points and not in the integration points. 4.2 Parameter constraints The two constitutive functions from the mechanical model that have to be fit in conformity with experimental data are given with Equations 5 and 6. Based on the observation that both κi and κs decrease
Figure 1.
Swelling pressure cell (UPC) and the FE model.
Constraints—retention curve, permeability.
Parameter
Unit
Min
Max
P0 λ k11 (log scale)
MPa
0.01 0.01 −21
10 0.8 −15
Table 2.
log m2
Constraints—TEP elasticity.
Parameter
Unit
Min
Max
αi κs0 αss αsp pref
MPa−1
−0.0066 0.0057 −0.4506 −0.9410 0.657
−0.0054 0.0171 −0.15019 −0.3137 0.803
MPa−1 MPa
with increasing their arguments an implicit constraint is that parameters αi , αsp and αss are not positive. Constraints intervals used in the optimization procedure are listed in Table 1 and Table 2. 4.3 Parameter sensitivity analysis For the sensitivity analysis, each of the parameters xj was varied over the constraint interval (Table 1 and Table 2) keeping at the same time all other parameters fixed allowing this way to evaluate γj from Equation 3. The vector y used to calculate CSS is obtained from the solutions of the 1SP and MSP problems. This procedure has been performed for 100 sets of parameters that are randomly chosen and belong to the entire admissible domain. The mean of the calculated γj , that is 2 i γ¯j = (1/100) 100 i=1 γj is used to compare the sensitivity of the model response to the corresponding parameter xj . Figure 2 shows the results for sensitivity analysis including both hydraulic and mechanical model parameters. The ‘‘observation’’ variables vector is the time evolution of the swelling pressure (σyy ) at a given point from the solution of the MSP problem. The analysis of the results in Figure 2 suggests special attention to intrinsic permeability and the parameters involved in the constitutive function κsp . Figure 3 depicts the results for the case where the solution of the 1SP problem has been used for collecting ‘‘observations’’. The pronounced significance of the retention curve parameters λ and P0 and the intrinsic permeability may be due to the poor ability of the model to simulate the first step of suction loading from the experiment. Still the importance of αsp is manifested and this is one of the parameters that are difficult to be assessed directly from experimental data.
800
1
pref alphasp alphai alphass kappas k11 lambda P0
Figure 2.
Sensitivity analysis—MSP numerical simulation.
pref alphasp alphai alphass kappas k11 lambda P0
Figure 3.
4.4
0.2
0.4 0.6 mean gamma
0.8
1
pref
alphasp
4 Loading Steps - PSO
Results of different optimization procedures.
Results—retention curve, permeability.
Parameter
Unit
Unitial
Final
P0 λ k11
MPa
1.2 0.386 6e-19
7.6 0.2685 2e-19
m2
Sensitivity analysis—1SP numerical simulation.
Table 4.
Results of the parameter optimization
Different optimization algorithms, part of VARO PT (VAROCON, Weimar) optimization program, have been used and we found the downhill simplex method (SNM) to provide fast, robust and reliable solution. The chart in Figure 4 compares the solutions obtained by two different optimization methods, namely SNM and PSO for MSP back analysis. It presents also the difference in optimization solution depending on whether we take 3 or 4 loading steps. The objective function reads: N "
3 Loading Steps - SNM
3 Loading Steps - PSO
Table 3.
2
F=
Initial
Figure 4.
0
1SP
alphai
1
alphass
0.8
kappas0
0.4 0.6 mean gamma
k11
0.2
P0
0
lambda
MSP
0
fn wn
(9)
n=1
2m i i where fn = i=1 ymeas − ycalc ri , wn and ri are weight factors, n = 1, . . . , N is the counter of loading steps used in optimization process. Therefore not only different optimization procedures give different results, but also different data sampling. The initial values for the parameter vector have been taken from (Agus 2005) where model calibration has been done by best fit to constant suction and constant net stress type of experimental data without doing back analysis. The solution obtained after SNM optimization procedure is given in Tables 3 and 4. The observed discrepancy between conventionally derived model parameters and the optimized after 1SP and MSP tests
Results—TEP elasticity.
Parameter
Unit
Initial
Final
αi κs0 αss αsp pref
MPa−1
−0.006 0.0047 −0.1128 −0.3 0.73
−0.0062 0.0123 −0.334 −0.6454 0.71
MPa−1 MPa
back analysis may be due to the much smaller number of data points specially for calibration of κs . It has to be pointed out that for the nonlinear function κs (p, s) even the variables are separated, it is difficult to prove the goodness of fit done as section fit with respect to each of the function variables (conventional model calibration practice). The reason is that constant suction type of tests can not be used for calibration of κs (p, s) because in this type of tests dε s−e = 0 and κs v plays no role. Uniqueness of the optimization problem solution has been verified by cross section graphs of the objective function along each of the back analysed parameters xj . An example of such matrix graph is given in Figure 5 and it shows well represented minima except for the intrinsic permeability . Figure 6 shows the results of MSP (ATT) simulations. These results are discussed here because of the discrepancy between calculated and measured
801
4.5
αi
κs0
αss
5
k11
Swelling Pressure
Cross sections of the objective function along xj .
Calculated
Figure 5.
To verify the parameters obtained after back analysis of the MSP and 1SP tests we performed a simulation of a compression-rebound test. The test procedure and the results of CR-3 test are reported in (Agus 2005). Results are given in Figure 7.
αsp
λ
MSP Measured
0
Figure 6.
.55 0
Time [h]
1500
Calculated vs measured swelling pressure.
axial displ. [mm]
0
0.5
experiment TEP model
1
1.5 10
axial stress [kPa]
Verification
CONCLUSIONS
The paper presents a procedure for identification of TEP model parameters based on swelling pressure tests data. The procedure consists in sensitivity analysis based on numerical simulations of swelling pressure tests, choice of optimization algorithm, solution of the optimization problem and verification of the calibrated model using compression—rebound tests data. The quality of the forward calculation is of significant importance and it has to be monitored during the run of the back analysis. The influence of the finite elements discretization and the loading path has to be taken into account when accepting the goodness of the fit. Large increments of suction in ATT tests lead to a solution with not constant porosity along the sample height. It is an object of future research to analyse this observation. The next outcome of the performed analysis is that within the experimental error the solution of the optimization procedure is not unique. The uniqueness of the solution particularly, is strongly dependent on the quality of the numerical model and on the error involved at different stages of the test. Different optimization procedures may also give different solutions. That is why the verification of the back analysis is important and integral part of the identification procedure. Finally one can state, that using swelling pressure test data and the proposed identification procedure a successful back analysis of the unknown TEP model parameters can be done.
100000
ACKNOWLEDGMENT Figure 7.
Compression—rebound test (verification).
swelling pressure at the first stage of the suction loading. Possible reason is the problem with the ceramic disk and the influence to the experimental data of its hydraulic conductivity of 1.12e-10 m/s. Another observation is the influence of the loading program to the porosity distribution at final equilibrium. The application of suction in ATT test is with large initial increment which leads to non constant porosity along the sample height at maximum swelling pressure. For this reason at this stage of our research we did not include the measured water intake in the definition of the objective function.
The financial assistance of German Federal Ministry of Education and Research (grant 02C0881) is gratefully acknowledged. Authors wish to express their gratitude to Mr Yulian Arifin for the valuable help with the experimental data. REFERENCES Agus, S. (2005). An experimental study on hydro— mechanical characteristics of compacted bentonite–sand mixtures. Ph.D. thesis, Bauhaus—Universitat Weimar. Agus, S.S. and T. Schanz (2005). Swelling pressure and total suction of compacted bentonite—sand mixtures. In Proc Int Conf on Problematic Soils, Cyprus, pp. 61–70.
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Alonso, E.E., J. Vaunat, and A. Gens (1999). Modelling the mechanical behaviour of expansive clays. Engng Geol 54(12), 173–183. Anderman, E., M. Hill, and E. Poeter (1996). Twodimensional advective transport in ground-water flow parameter estimation. Ground Water 34(6), 1001–1009. Arifin, Y. and T. Schanz (2007). Modified isochoric cell for temperature controlled swelling pressure test. In T. Schanz (Ed.), Proc 2nd Int Conf Mech Unsat Soils, Weimar, Germany, pp. 229–242. Springer. Cividini, A., L. Jurina, and G. Gioda (1981). Some aspects of characterization problems in geomechanics. Int J Rock Mech Min Sci and Geomech Abstr 18(6), 487–503. Code_Bright (2002). USER’S GUIDE: A 3-D program for Thermo–Hydro–Mechanical analysis in geological media. UPC, Barcelona.
Davidon, W.C. and L. Nazareth (1977). OCOPTR—A Derivative Free FORTRAN Implementation of Davidon’s Optimally Conditioned Method. Argonne Nat Lab—Appl Math Div, Tech Memorandum No 303. Eberhardt, R. and J. Kennedy (1995). A new optimizer using particle swarm theory. In Proc 6th Int Symp on Micro Machine and Human Science, Nagoya, Japan, pp. 39–43. IEEE Service Center. Hill, M.C. (1998). Methods and Guidelines for Effective Model Calibration. Denver, Colorado: U.S. Geological Survey Water–Resources Investigation Report 98–4005. Nelder, J.A. and R. Mead (1965). A simplex method for function minimization. Computer Journal 7, 308–313. Zhang, Z.F., A.L. Ward, and G.W. Gee (2003). Estimating Soil Hydraulic Parameters of a Field Drainage Experiment Using Inverse Techniques. Vadose Zone Journal 2, 201–211.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Surface flux boundary simplifications for flow through clay under landscaped conditions H.B. Dye, S.L. Houston & W.N. Houston Arizona State University, Tempe, AZ, USA
ABSTRACT: The quality of the solution of moisture flow through expansive soils for the purpose of depth of moisture influence determination for residential foundation design depends on properly described flux boundary conditions including appropriate environmental factors and inclusion of the microclimate created by human activity. In this study, both climatic and human imposed conditions typical to Phoenix, Arizona, were considered in 1-D unsaturated flow modeling. Many years of recorded precipitation data were obtained, and common irrigation practice from surveys of municipalities, together with evapotranspiration data from the regions, were used to determine the surface flux conditions for modeling. Rigorously described surface flux boundary conditions were used in the analyses, and simplifications to these conditions were systematically made to determine the impact of simplified boundary conditions on the final solution. It was found that major simplifications, through averaging of flux conditions and increased time-steps for application, result in only negligible difference in computed matric suction compared to more detailed simulations of flux when the capacity of the soil to absorb applied surface water is not exceeded, such as for the desert landscape conditions of this study. Otherwise, as observed for the turf irrigation case of this study, averaging surface flux can result in significant over-estimate of the extent and degree of wetting in the profile.
1
INTRODUCTION
It is well established that damage to structures built on expansive soils is mainly caused by changes in soil suction (Chen 1988, Fredlund 1993). The suction change is generally attributed to environmental conditions, change in depth of water table, water uptake by vegetation, removal of vegetation or landscape irrigation. Foundations on expansive soils must resist short-term cyclic swell/shrinkage due to seasonal moisture variation and long-term swell/shrinkage. It was established by Fredlund (1993) that the prediction of expansive soil movement requires implementation of unsaturated soil mechanics where the moisture flow and deformation are analyzed in a coupled or uncoupled manner. There is a large body of literature on the measurement and prediction of swell/shrinkage of soils and analysis of actual soil behavior in the field. Some of these studies have resulted in numerical analyses for evaluation of unsaturated flow and heave in the soil profiles (e.g. Fredlund et al. 1984, 1993, and 2004). The implementation of these numerical methods involves a detailed description of the flux boundary condition that reflects the actual wetting and drying at the surface of the soil profile. The process of mathematically describing the surface flux condition
is tedious, and complex input generally requires long finite element code run-time. This paper focuses on the moisture flow portion of the problem, where the impact of input flux simplification on the solution is analyzed. Two different conditions were considered: desert landscape and turf landscape in an arid region. The analysis was performed for one Phoenix area expansive soil using SVFlux 5.80, a finite element computer program for unsaturated flow (Fredlund 2004). 2
PROBLEM SET-UP
The 1-D flow analyses were carried out on a 10-m deep profile using a finite element program, SVFlux 5.80. SVFlux utilizes adaptive unstructured mesh generation and adaptive time stepping using implicit 2nd order Backwards Difference (Gear’s method) to solve Richard’s equation adapted for both infiltration and evapotranspiration (SVS 2005a). The study was carried out to obtain soil response due to typical input flux discretized first on an hourly basis, and then monthly for both desert and turf landscapes. The profiles were assumed to be well-sloped at the surface so that run-off would occur. For all runs, mesh refinements and time-step refinements
805
Boundary and initial conditions
The profile has two boundary conditions (BCs). Total head of−153 m was applied to the bottom boundary. This value is based on laboratory testing of field samples, illustrating a 1000 to 2000 kPa matric suction range at depths of approximately 2 to 3 meters for undeveloped regions in the Phoenix area. A Neumann BC was applied at the soil surface. It consists of precipitation, typically applied irrigation, potential evaporation, relative humidity and temperature parameters representative of Arizona climatic conditions (see section 2.3 for details). The initial total head profile of was assumed to be constant with depth and equal to −153 m. 2.2
Soil properties
The expansive soil properties used in this study are given in Table 1 and Figure 1. The following required parameters were determined experimentally: specific gravity, saturated hydraulic conductivity, ksat , Soil Water Characteristic Curve (SWCC), and saturated volumetric water content. The SWCC experimental data were fitted using the Fredlund and Xing (1994) equation to yield the SWCC curve fitting parameters. The unsaturated hydraulic conductivity curve was estimated using the Leong and Rahardjo equation, where the slope of the curve was assumed to be similar to other clayey soils published in literature and available though SoilVision (Leong & Rahardjo 1997, SVS 2005b). Table 1.
Soil properties.
Parameter name LL PI γd Gs P-200 % clay θsat SWCC parameters (Fredlund and Xing, 1994) af bf cf hr kunsat parameters (Leong and Rahardjo, 1997) ksat p
Parameter value 85 53 13.4 kPa 2.80 86 33 51.2 140 0.6 0.9 2000 8.7e-6 m/h 12
1.0
1E-04
0.9
1E-05
0.8
1E-06
0.7
1E-07
0.6
1E-08
0.5
1E-09
0.4
1E-10
0.3
SWCC Lab Data
1E-11
0.2
SWCC, Fredlund Fit
1E-12
0.1
Kunsat, Leong Fit
1E-13
Hydraulic Conductivity [m/h]
2.1
Saturation [decimal]
were performed to assure convergence and stability of the matric suction response.
1E-14 0.0 1.E-02 1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 1.E+04 1.E+05 1.E+06
Suction [kPa]
Figure 1.
Unsaturated soil property functions.
2.3 Input flux Expansive soils in the Phoenix metropolitan area can experience a wide range of flux conditions that include precipitation, evaporation and irrigation. Two extreme flux conditions typical for the Phoenix region were identified. They are turf landscape, where the lawn is irrigated every day, and desert or ‘‘xeriscape’’, where a negligible amount of water is introduced to the soil surface. These two fluxes were used in the one-year long analysis requiring four flux components to be described, flux onto the soil such as irrigation or precipitation, potential evaporation, relative humidity and temperature. 2.3.1 Desert landscape The potential evaporation data for the Phoenix region were obtained from three internet sources 1) US Weather Service, Arizona Department of Water Resources, 2) NOAA, Western Regional Climate Center, and 3) Arizona Meteorological Network (Internet source a, b & c 2006). Measured data for one year were available from source 1 and 2, while source 3 provided 6 years of estimated PE based on measured relative humidity, RH, and temperature data, T . The average from all three sources was used to develop PE flux used in the analysis, and is presented in Table 2. The SVFlux code utilizes the formulation developed by Wilson et al. (1994) for computation of actual evaporation, AE. The general relationship between AE and PE in terms of soil surface total suction is illustrated in Figure 2, where AE is equal to PE for soil suction smaller then 3000 kPa (Wilson et al. 1995). As the soil surface suction increases the AE decreases to a value of 0, corresponding to suction value at applied RH. The 6-year averages of RH and T from source 3 were further used to develop RH and T program input, Table 2. The amount of water typically applied to desert landscape or ‘‘xeriscape’’ is negligible. Therefore, the amount of water applied to the soil surface is assumed
806
Table 2.
Desert flux input.
0.0020
#Rainy #Rainy PE hours days [m/h]
RH T Ave. Prec. [%] [C] [m/h]
1 2 3 4 5 6 7 8 9 10 11 12
7 8 8 5 1 1 5 2 3 4 6 6
53 49 45 34 26 25 32 42 39 50 50 52
7.1E-04 6.2E-04 7.2E-04 7.1E-04 1.7E-03 8.0E-04 1.1E-03 1.5E-03 1.5E-03 1.2E-03 8.8E-04 7.6E-04
6 6 7 4 3 2 8 9 5 4 4 5
1.2E-04 1.5E-04 2.3E-04 3.1E-04 4.0E-04 4.2E-04 4.3E-04 3.6E-04 3.1E-04 2.3E-04 1.5E-04 9.8E-05
12 13 17 21 27 31 34 32 30 22 15 10
3.3E-05 3.4E-05 3.8E-05 1.1E-05 5.1E-06 1.1E-06 3.5E-05 2.8E-05 2.5E-05 2.0E-05 2.4E-05 2.7E-05
Precipitation Evaporation Average Flux
0.0015 Flux [m/h]
Prec. Mo. [m/h]
0.0010 0.0005 0.0000
-0.0005 0
Figure 3.
Figure 2. Relationship between AE/PE to total suction for sand, silt and clay (after Wilson et al. 1995).
to be from precipitation only. For the purpose of developing a reasonable input flux, 24-year daily precipitation and 9-year hourly precipitation data obtained from National Climatic Data Center website was studied for the Phoenix area. The data revealed that the average rainfall in Phoenix is 20 cm/year with a standard deviation of 7.6 cm/year. Furthermore, the rainy days within a given month occurred close together and rainy hours within a day, for the most part, occurred one after another. The input used in this analysis consisted of a stepped function flux where a net precipitation of 20 cm is applied per year. The precipitation was applied on an hourly basis where the rainy days as well as the rainy hours within a day were grouped together because this grouping was consistent with typicallyobserved rain patterns. During each rainy day the precipitation was applied for the determined number of hours and then the rain was followed by a period of evaporation. Other than the rainy days, the flux BC consisted of evaporation only for the remaining portion of the month. Table 2 gives the applied desert landscape input data, which are plotted in Figure 3. The simplified average flux scheme consists of the same PE, RH and T input data and averaged precipitation over the period of each month. The last column of Table 2 gives the monthly averaged precipitation.
2000
4000 Time [h]
6000
8000
Desert landscape input.
2.3.2 Turf landscape The potential evapotranspiration data, ET0 , for tall, well watered, cool season grass were obtained from University of Arizona for a golf course in Cave Creek, Arizona (UA 2000). The evapotranspiration rates were modified by a 0.6 landscape coefficient to simulate the evapotraspirationexperiencedbywarmseasonBermuda grass, a plant commonly used in Phoenix landscapes. The plant evapotranspiration rate is, in part, a function of leaf length, since ET 0 was determined for long leaf vegetation, the correction was necessary to adequately describe the typical site conditions (UA 2000). Proper irrigation of turf landscape consists of a yearly flux equal to the yearly evapotranspiration rate. Therefore, the warm season Bermuda grass requires 117 cm/year (0.6 ∗ 196 cm/year) of water. The grass is semi-dormant in the wintertime (November through February) when a reduced watering regimen is required when compared to the summer months. The local recommendation on irrigation is to apply 1.9 cm of water during every irrigation event. In general, the warm season grass should be provided with about 2.5 cm of water once a month between November through February and 5 to 7.6 cm of water a week from May through September when the plants are irrigated once every few days. This kind of infrequent watering pattern encourages the plants to develop a deep root system and produces hardy plants (McCaleb 2005 and City of Mesa 2005). Based on information obtained from the landscape professionals and Phoenix area government agencies, it is estimated that the turf landscapes are often overwatered by 2 to 5 times the above recommended amount. The mismanagement of water use is mainly attributed to homeowners’ lack of knowledge about grass needs. Landscapes are typically irrigated every day where the water is applied once or twice a day. The common once a day option consists of 15–20 minute watering period equivalent to application of 0.1 to 1.6 cm of water per irrigation event. The twice a day watering pattern typically last 5 to 10 minutes and corresponds to 0.04 to 0.8 cm of water per application.
807
Table 3.
3
3.1 Desert or low water use landscape The desert or low water use landscape consisted of 2.3-m of PE and 0.2-m of rainfall annually. The analysis with hourly discretized flux, HF, produced large matric suction variations at the soil surface ranging from 190 000 kPa at the end of dry period in Jun to 0 kPa after a precipitation event. These suction swings are not present in the average flux, AF, analysis as expected. The soil surface suctions approach the values calculated with HF analysis except for very shallow depth. Just below the surface, the soil response in terms of suction is similar for both types of analysis as illustrated in Figure 5. Figure 6 (suction variation with depth at the end of year) further shows that the discrepancy between these two approaches exists only in the initial 0.2-m of the profile. At larger depths the solutions are identical. 0
Turf flux input.
Mo.
Prec. m/h
PE m/h
Ave. Prec. m/h
1 2 3 4 5 6 7 8 9 10 11 12
4.61E-3 4.62E-3 4.64E-3 4.68E-3 1.06E-2 1.06E-2 1.06E-2 1.06E-2 1.06E-2 1.05E-2 4.65E-3 4.62E-3
4.45E-5 6.35E-5 9.59E-5 1.39E-4 1.81E-4 2.11E-4 2.16E-4 1.97E-4 1.72E-4 1.38E-4 9.75E-5 5.75E-5
1.32E-4 1.35E-4 1.42E-4 1.13E-4 4.41E-4 4.37E-4 4.82E-4 4.68E-4 4.63E-4 4.57E-4 1.25E-4 1.25E-4
MODELING RESULTS
Pore Water Pressure [kPa]
The typical flux input scheme for the numerical models of this study for turf landscape consists of one hour of irrigation every day followed by 23 hours of evapotranspiration. There are two magnitudes of applied irrigation. The first flux has magnitude of 0.19 cm/hour and is applied between November through April; it is referred to as the Winter irrigation. The second flux, also called the Summer irrigation is applied during the remaining portion of the year and has magnitude of 1.16 cm/hour. The evapotranspiration rate increases from winter months to the mid-summer and then it decreases towards December. The actual evapotranspiration rate varies parabolicly with time, but for the purpose of modeling, the rate was simplified to vary on a monthly basis. The applied flux consists of precipitation and irrigation where the precipitation data are given in Table 2, while the irrigation and PE data are provided in Table 3. The turf surface flux boundary condition is plotted in Figure 4. The simplified average flux scheme consists of the same PE, RH and T input data and averaged both precipitation and irrigation over the period of each month, as given in Table 3.
-50000
-100000 0m - HF 0m - AF 0.1m-HF 0.1m-AF 0.2m-HF 0.2m-AF
-150000
-200000
0
50
100
150
200
250
300
350
Time [d]
Figure 5. Desert landscape. Pore water pressure variation with time at selected depths for hourly flux (HF) and average flux (AF).
Distance from Surface [m]
-0.2 0.012 0.010
Flux [m/h]
0.008 0.006 0.004 0.002 0.000 -0.002 0
2000
Irrigation and Precipitation
Figure 4.
4000 Time [h]
6000
Evaporation
Turf landscape surface flux input.
8000 Average Flux
0 0.2 0.4 0.6 0.8
HF AF
1 -100000 -80000
-60000
-40000 -20000
0
Pore Water Pressure [kPa] Figure 6. Desert landscape. Pore water pressure variation with depth at the end of year for hourly flux (HF) and average flux (AF).
808
The net flux, as calculated by the computer program for 1 m2 surface area, is presented in Figure 7 for both HF and AF analyses. The cumulative flux is similar for HF and AF runs, and approaches −0.058 m3 at the end of one year. This helps explain why the results obtained with both approaches produce similar results. Although runoff of water that does not infiltrate is an option utilized for the desert landscape condition (i.e. well-graded/sloped soil surface), the surface flux conditions are such that essentially no runoff occurred for either hourly or monthly averaged flux steps.
3.2
Turf landscape
The turf landscape consists of 1.16-m of PE, 0.2-m of precipitation and 2.37-m of irrigation per year. The hourly discretized flux was applied daily per half an
0.01
HF
AF
0
Distance from Surface [m]
Cumulative Flux [m3]
0.02
hour during the winter regimen and per one hour during the summer irrigation schedule. The analysis with hourly discretized flux, HF, produced large matric suction variations at the soil surface ranging from 50 000 kPa at the end of April to about 0 kPa after precipitation or irrigation event as illustrated in Figure 8. The suction fluctuations due to individual irrigation or precipitation events were observed to a depth of 0.05-m from the surface. Figure 9 shows that although the suction variation at the soil surface might be quite large, the immediate influence of the wetting event does not exceed 0.05-m. Fluctuations due to monthly averaged input occur to a depth of about 0.5-m. The results obtained with monthly average flux are very different from the results obtained with hourly discretized conditions (Fig. 8). For the averaged monthly flux, the surface matric suction decreases from the initial condition to near 0 kPa, increases to about 200 kPa in April and goes back to 0 kPa after April, where it remains essentially constant. In contrast, the
-0.01 -0.02 -0.03 -0.04 -0.05 -0.06
0
50
100 150 200 250 300 350
Time [d] Figure 7. Desert landscape. Cumulative flux (for a 1 m2 surface area) for hourly flux (HF) and average flux (AF) analyses.
0.00 0.02 0.04 0.06 0.08
before rainfall after rainfall
0.10 -10000 -8000
-6000
-4000 -2000
0
Pore Water Pressure [kPa] Figure 9. Turf landscape. Pore water pressure variation with depth before and after a rainfall event (HF).
Distance from Surface [m]
Pore Water Pressure [kPa]
0 -10000 -20000 -30000 -40000
0m - HF 0m - AF
-50000 0
50
100 150
200
250
300
0 2 4 6
10 -2000
350
HF AF
8
-1500
-1000 -500
0
Pore Water Pressure [kPa]
Time [d]
Figure 8. Turf landscape. Pore water pressure variation with time at the soil surface for hourly flux (HF) and average flux (AF) analyses.
Figure 10. Turf landscape. Pore water pressure variation with depth at the end of year for hourly flux (HF) and average flux (AF).
809
deformations. Further studies evaluating the effect of shrinkage soil cracking on moisture flow, coupled and decoupled flow and soil deformation will be useful in refining recommendations of surface flux simplifications for modeling suction change-induced foundation movements for expansive soil profiles.
Cumulative Flux [m3]
0.35 HF
0.3
AF
0.25 0.2 0.15 0.1
ACKNOWLEDGMENTS
0.05 0
0
50
This work was supported by the Homebuilders Association of Central Arizona (HBACA) and Construction Inspection and Testing Co. (CIT). This support is gratefully acknowledged. The views presented are those of the authors, and not necessarily those of the supporting organizations.
100 150 200 250 300 350
Time [d] Figure 11. Turf landscape. Cumulative flux for hourly flux (HF) and average flux (AF) analyses.
surface suction varies widely for the HF input. The depth of influence obtained with AF is 2.5-m, compared to 1.9-m with HF, Figure 10, and the AF results in higher degree of saturation. The increased depth of wetting is associated with larger amount of water absorbed in the AF scheme, Figure 11. After one year, the cumulative flux, as calculated by the computer program, is 0.33-m3 for AF and 0.11-m3 for HF. The difference is attributed to runoff and reduced time for infiltration in the HF analyses. 4
CONCLUSIONS
The analysis of desert landscape revealed that simplification of precipitation data by averaging produces adequate approximation of soil behavior. This finding is applicable to flux conditions dominated by evaporation. However, the flux simplification scheme, wherein averaging of flux over each month is employed, is not appropriate for irrigation or precipitation dominated scenarios such as the turf landscape example of this study. The averaging overestimates both the degree of saturation and the depth of wetting for cases where there is surface run-off resulting from exceeding of the soil surface capacity to absorb water. It is recommended that the effect of simplification of surface flux conditions be carefully considered on a case-by-cases basis. While there is a high price to pay with regard to run-times for detailed modeling of actual surface flux conditions, it is clear that there are many important problems for which highly detailed flux input is required to achieve reasonable simulation of field conditions. Finally, the most important soil response with which to judge appropriate surface flux simplifications for the case of foundations on expansive soils is the surface
REFERENCES Chen, F.H. 1988. Foundations on Expansive Soils, Development in Geotechnical Engineering, 54, New York, Elsevier Science Publishers. Fredlund, D.G. and Rahardjo, H. 1993. Soil Mechanics for Unsaturated Soils, Wiley, New York. Fredlund, D.G., Vu, H., Fredlund, M.D. and Thode, R. 2004. Modeling soil-structure interaction of slabs on expansive soils. Soil Vision Systems Ltd. Saskatchewan, Canada. Fredlund, D.G. and Xing, A. 1994. Equations for the soil water characteristic curve. Canadian Geotechnical journal, 31(3): 521–532. Internet Source. 2006. http://ag.arizona.edu/azmet/15.htm Internet Source. 2006. http://www.peoriaaz.com/Utilities/ oldfiles/xeriscapef.htm Internet Source. 2006. http://www.wrcc.dri.edu/htmlfiles/ westevap.final.html#ARIZONA Leong, E.C. and Rahardjo, H. 1997. Permeability Functions for Unsaturated Soils. Journal of Geotechnical and Geoenvironmental Engineering, Dec., 1118–1126. Personal Communication. 2005. City of Mesa, Department of Water Use. Discussion about landscape schemes, irrigation systems and common issues. Personal Communication. 2005. McCaleb, Kevin, Orovalley owner, Discussion about landscape schemes, irrigation systems and common issues. Soil Vision Systems Ltd. 2005. SoilVision User’s and Theory Guide, Version 4. Saskatchewan, SK, Canada. Soil Vision Systems Ltd. 2005b. SVFlux User’s and Theory Guide, Version 5. Saskatchewan, SK, Canada. University of Arizona Cooperative Extension. 2000. Basics of Evaporation and Evapotranspiration. Turf Irrigation Management Series: I, paper #1194. Wilson, G.W., Fredlund, D.G. and Barbour, S.L. 1994. Coupled soil-atmosphere modeling for soil evaporation. Can. Geotech. J., 31: 151–161. Wilson, G.W., Barbour, S.L. and Fredlund, D.L. 1995. The prediction of Evaporative Fluxes from Unsaturated Soil Surfaces. Unsaturated Soils, Alonso, E.E, Delage, P. (eds.): 423–429.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Preliminary analysis of tree-induced suctions on slope stability N. Ali & S.W. Rees Cardiff School of Engineering, Cardiff, Wales
ABSTRACT: This paper explores the development and application of a numerical model of water uptake in the vicinity of established trees. A preliminary assessment of the significance of water content (and therefore suction) changes on the stability of soil slopes is provided. This is a problem that is exacerbated by climate change and increasingly intense rainfall events. Design, repair, maintenance and operation of railway and road earthworks are particular areas where this issue is important. For a typical slope geometry the research indicates that tree-induced suction variations can cause the factor of safety against failure to vary by between 5% and 7%. This result is independent of other associated contributions that may arise from root reinforcement, windthrow, weight of vegetation etc. Therefore, further work is needed to consider the overall effect of vegetation and to reduce parametric uncertainty.
1
INTRODUCTION
It is now recognized that variations in soil suction that may occur in the presence of vegetation, and indeed those that can occur on removal of vegetation, have an important role to play in the performance of engineered and natural soil slopes. This is a problem that is exacerbated by climate change and increasingly intense rainfall events. Repair, maintenance and operation of railway and road embankments are particular areas where this issue is important. Previous experience in Malaysia indicates that removal of vegetation can be the main cause for the failure of a slope (Technical Committee of Investigation 1994). In this tragedy, investigation of the substructure and the surroundings revealed that clearing of trees on the adjacent slope led to the water level in soil to rise, thus causing the instability of slope. Some researchers (Thorne, 1990, Simon et al. 2000, MacNeil 2001) claim that vegetation is widely believed to increase the stability of slope. Simon and Collison (2001) suggested that the impact of vegetation on slope or bank stability can be divided into mechanical and hydrologic effects. Mechanical effects are associated with the root tensile strength and hydrologic effects include increased slope stability by extraction of soil moisture for transpiration. In their work, it was found that hydrologic effects can be as important as mechanical effects and in certain cases. Ridley et al. (2004) discussed the relationship between climate, in the form of soil moisture deficit, the presence of trees and pore water pressures
in embankments. The study showed that most embankment failures in London were due to an increase in soil moisture content. Recently Greenwood (2006) considered the potential engineering influences of vegetation and how it can be characterized on site within a geotechnical framework for slope stability assessments. Greenwood’s software (SLIP4EX—based on equilibrium of forces) may be used for estimating the factor of safety (FOS) against slope failure and can be readily adapted to include vegetation effects. The program uses the method described by Greenwood et al. (2004) to include the influence of vegetation mass, effects on the groundwater regime, enhanced cohesion due to fine roots, wind forces and the anchoring effects of the larger roots. Changes in ground water table due to vegetation were included however the effect of negative water pressure was excluded from the equation. For the situations where the ground water table is deep and where tree root activity is involved, treeinduced suctions may be significant. In these cases, it may be appropriate to perform slope stability analyses which include the shear strength contribution from the negative pore pressure. A modified form of the MohrCoulomb equation can be used to link shear strength to soil suction. Therefore, this paper explores the application of the water uptake model described previously (Rees and Ali 2006) to provide a preliminary assessment of the significance of water content (and therefore suction) changes on the stability of unsaturated soil slopes. This research only considers hydrological effects (i.e. water uptake) at this stage.
811
Where (ua − uw ) is the matric suction and φ b is an angle indicating the rate of increase in shear strength relative to matric suction. (σn − ua ) is the net normal stress, c is the effective cohesion and φ is angle of friction. Combining equations (1) and (2), gives,
THEORETICAL AND NUMERICAL BACKGROUND
2.1
Limiting equilibrium forces for unsaturated slope stability
This study uses the theory of limit equilibrium of forces and moments to compute the FOS against failure. The limit equilibrium method of slices is widely used for its simplicity particularly when compared to the finite element method (Fredlund and Rahardjo 1993, Renaud et al. 2003). The FOS is defined as that factor by which the shear strength of the soil must be reduced in order to bring the mass of soil into a state of limiting equilibrium along a selected slip surface. Calculations for the stability of a slope are performed by dividing the soil mass above the circular slip surface into vertical slices. The limit equilibrium formulation assumes that the factor of safety is equal for all soils involved and for all slices. The current work aims to explore the importance of suction changes on shear strength. Therefore, in the example considered, the water table is assumed to be below the zone of interest. Tension cracks are, therefore, excluded from the current work. It is also assumed that there are no interslice shear forces involved in the equation for both horizontal and vertical forces. This assumption has been made for the following reasons; i. Vertical interslice forces can be assumed equal and opposite (Bishop, 1955). ii. The resultant of the interslice forces acting on a slice can be assumed to act parallel to the base of the slice. By resolving forces normal to the base of the slice, the interslice forces are eliminated. 2.2
FOS for an unsaturated slope
To calculate the FOS of an unsaturated soil slope and link this with the effect of tree-root-water uptake, a force equation which includes matric suction must be established first. The analysis is an extension of conventional limit equilibrium analysis where an equation is formed using the basic principle of static equilibrium of forces and moments. The mobilized shear force at the base of a slice can be written as (Lambe and Whitman, 1969) τl F
Sm =
l c + (σn − ua ) tan φ + (ua − uw ) tan φ b Sm = F
(3)
From Figure 1, (taking point O as centre of the moments) the summation of moments in the slope, yields: "
Wx −
"
Sm R = 0
(4)
Substituting equation (3) into (4) and substituting (ua − uw ) = S (matric suction) and assuming air pore pressure is atmospheric, ua = 0, equation (4) becomes 2 F=
c lR + NR tan φ + SRl tan φ b 2 Wx
(5)
Equation (5) has been used throughout this research for calculating the FOSs. Note that if the matric suction is zero (i.e. the soil is saturated) Equation (5) becomes the standard Fellenius’s method (Fellenius, 1936). 2.3 The water-uptake model The two-dimensional water-uptake model provided by Rees and Ali (2006) is used here. In Cartesian form, the sink term can be written as: 4T z x S(ψ, x, z) = α(ψ) 1 − 1− (6) zr xr zr xr Where S (ψ, x, z) is the sink term (cm3 /cm3 /s), T is the potential transpiration rate (cm/s), xr is the maximum rooting horizontal distance (cm), zr is the maximum rooting depth (cm), α(ψ) is a dimensionless water stress function (see Feddes et al. 1976), o
7
(1)
8 350cm
6 5
27˚cm
4
750cm
τ = c + (σn − ua ) tan φ + (ua − uw ) tan φ
b
(2)
2 2
Origin
Figure 1.
812
1
3
8 7
1
250cm
Where τ is shear strength of unsaturated soil. Fredlund et al. (1978) provided the following expression for shear strength:
!
3
1600cm
Test slope geometry.
4
5
6
500cm
2
z is the vertical coordinate (cm) and x is the horizontal coordinate (cm). Combining the Richards equation (Richards 1931) and the sink term in Equation (6), provides the following moisture transfer equation:
∂ψ ∂ ∂ψ = K(ψ) ∂t ∂x ∂x
∂ψ ∂K (ψ) ∂ K(ψ) + − S(ψ, x, z) + ∂z ∂z ∂z
The time dependent nature of Equation (9) is dealt with via a mid-interval backward difference technique, yielding: K n+1/2 ψ n+1 + C n+1/2
(7)
A solution of Equation (7) is obtained via a finite element spatial discretisation procedure and a finite difference time-stepping scheme. In particular, adopting a Galerkin weighted residual approach yields: − e
− e
∂Nr ∂Ns ψs ∂e − K ∂z ∂z
+
Nr λ∂ −
−
Nr Ns C e
e
∂K ∂e Nr ∂z
Nr S(x, z)∂e
∂ψs ∂e = 0 ∂t
(8)
For the purposes of this paper, a typical 1 in 2 slope has been considered. In this study, location of the critical slip surface has been determined using SLOPEW—employing 147 trial surfaces. For stability analysis, the slope has been divided into eight slices, numbered from 1 at the toe, to 8 at the crest of the slope. Figure 1 shows the geometry of the slope, the position of each slice and the location of the critical slip surface. 3.2 Soil properties
Using, Green’s formula and introducing boundary terms leads to the final discretised form: Kψs + C
∂ψs +J +S =0 ∂t
(9)
where
m " ∂Ns ∂Nr ∂Ns ∂Nr K= · +K · ∂e K ∂x ∂x ∂z ∂z e=1 e
(10) C=
CASE STUDY
3.1 Slope geometry and slip surface
e
(14)
This finite element spatial discretisation procedure and a finite difference time-stepping scheme has been coded in FORTRAN and used throughout the simulation in this study. Further detail of the water-uptake model can be found in Rees and Ali (2006). 3
∂Ns ∂Nr ψs ∂e K ∂x ∂x
+ J n+1/2 + S n+1/2 = 0
C(ψ)
ψ n+1 − ψ n t
m "
[Nr Ns C]∂e
The soil chosen for consideration here follows from the work of Rees and Ali (2006). In particular, the behaviour of Boulder clay is considered. The relevant shear strength properties of Boulder clay are given in Table 1. The water retention curve and the hydraulic conductivity relationship for this material are shown in Figures 2 and 3 respectively. The figures also show measured data for three other soils as references: typical sand, Kimmeridge clay and typical Loam (Rees 1990). A comparison of results would appear to suggest that the assumed relationship for Boulder clay is within the range of previously published data for this soil type.
(11)
e=1 e
J =
m "
Nx
e=1 e
S=
m " e=1 e
m " ∂K [Nx λ]∂ e ∂e − ∂x e=1
Table 1.
(12)
e
[Nx S (x, z)]∂e
(13)
Material properties (Bishop et al. 1960).
Soil type
γ (kN/m3 )
c (kPa)
φ (degrees)
φb (degrees)
Boulder clay
22
9.6
27.3
21.7
813
(Biddle, 1998). The mesh consists of seven hundred, eight-noded isoparametric elements with 2231 nodes in total. The mesh was configured to offer some refinement within the root zone area since this is the region where the most significant moisture content variations were expected to occur. The simulated period covered a spring/summer soildrying phase of 9 months (270 days). The simulation employed a time-step size of 21600 seconds, which was held constant for the entire period considered. A transpiration rate of 5 mm/day is used for this tree (Biddle, 1998). In this case, water extraction is assumed to take place at its potential rate. Throughout the simulation, capillary potential was dry from −20 cm to −130 cm. Therefore α(ψ) in Equation (6) has been taken as unity as this range of capillary potential is within the range of optimal water extraction (Feddes et al. 1976). A uniform initial value of capillary potential of −20 cm is assumed to apply throughout the domain. This indicates that this soil is close to field capacity (Biddle 1998). The drying phase was represented via the application of the above transpiration rate within the root-water uptake model. The surface boundary, the lower boundary and the far-field vertical boundary were unconstrained (natural) throughout the simulation. The results of the drying phase water-uptake simulation were first determined via the solution of Equation (7). The suction values this obtained were then fed into a slope stability analysis based on Equation (5).
Boulder Clay
1.0E+05 Capillary Potential (negative value,cm)
Sand Kimmeridge Clay 1.0E+04
Loam
1.0E+03
1.0E+02
1.0E+01
1.0E+00 0.05
Figure 2.
0.20
0.50
0.65
Water retention curve for Boulder clay.
0.05 1.0E-05
0.15
1.0E-06 Hydraulic Conductivity (cm/s)
0.35 Volumetric Water Content (%)
Volumetric Water Content (%) 0.25 0.35 0.45
0.55
0.65
Boulder Clay Kimmeridge Clay
1.0E-07
Silt
1.0E-08 1.0E-09 1.0E-10 1.0E-11
Figure 3.
Hydraulic conductivity for Boulder clay.
700 elements
Mature Tree
4
2231 nodes
2m
5m
5m
16m
Figure 4.
Finite element mesh.
The water-uptake problem considered here represents drying of the soil from a near-saturated initial state. Hysteresis is not considered.
RESULTS
Figure 5 summarizes the results of the water-uptake simulation. The figure shows simulated contours in terms of capillary potential after a 270 day drying period. The numerical solution yields raw output in terms of capillary potential. These values have been converted to matric suction for each node at the centre of the base of each slice. The resulting suctions have then been employed in Equation (5) to calculate the FOS of the slope.
7
8
6
Numerical representation
4 1
2
12.311.1 9.9
3 5m
In the first instance the case study presented here considers the effect of a mature lime tree located near the toe of the embankment. Figure 4 shows a diagrammatic representation of the tree, the extent of the root zone and the finite element mesh. The root zone is assumed to extend a depth of 2 m and a radial distance of 5 m both left and right direction
Origin line
3.3
5
8.8 6.5 4.2 2.0
6m 7.5 m 10 m 16 m
Figure 5.
814
Matric suction (kPa) contours at 270 days.
12.0
Slice 1 Slice 2
10.0
Matric Suction (kPa)
Slice 4 8.0
Slice 8
6.0
2.96 2.94
FOS
2.92 FOS
Although the active root zone of the tree lies below the start of the slope, Figure 5 reveals that suctions have been generated within on the lower section of the slope itself. The water-uptake model, only applies the sink (extraction) within the pre-defined geometry of the root zone. However, moisture is free to migrate towards this zone from the surrounding soil. Hence, a ‘drawdown’ of moisture from the slope can be expected. Figure 6 shows the changes of matric suction at nodes located at the centre of the base of some selected slices (see Figure 3). The most significant changes in matric suction occur near the centre of tree (i.e. slice no 1). This effect diminishes as the distance from the centre of tree increases (slice no 2 > slice no 4 > slice no 8). For ease of interpretation, Figure 7 also shows the results in terms of volumetric moisture content at these slices. Figure 8 shows the corresponding changes in the FOS computed at various times during the drying period. This figure shows that FOS varies with time and increases with matric suction.
2.90 2.88 2.86 2.84 0
50
Figure 8. Table 2.
100
150 Days
200
250
300
Variation of FOS with time. Comparison of FOS at various conditions.
Conditions Fully saturated Tree near toe
Description
Trial slope with no tree water up-take Position of tree; x = 6 m, y = 2.5 m Tree at Position of tree; mid-slope x = 10 m, Coordinate y = 4 m Tree near Position of tree; crest x = 12.5 m, y = 5.0 m
FOS
Percentage difference (%)
2.74
0
2.95
7.7
2.89
5.47
2.88
5.11
4.0
2.0
0.0 0
50
100
150
200
250
300
Days
Figure 6. Matric suction (kPa) at the base of selected slices (Refer to Figure 3).
Volumetric Moisture Content (%)
4.0E-01 3.8E-01 3.6E-01 3.4E-01 3.2E-01
Slice 1 Slice 2 Slice 4 Slice 8
3.0E-01 2.8E-01 2.6E-01 0
50
100
150
200
250
300
Days
Figure 7. Volumetric moisture content (%) at the base of selected slices (Refer to Figure 3).
Further work has also been undertaken to examine the effect of changing the position of the tree in relation to the slope. Presentation of the detailed results is not possible in this paper due to space limitations. However, a brief summary of the overall result is presented for two cases; 1) tree located at mid-slope, and 2) tree located at crest of slope. Based on these variations, two new water-uptake simulations have been performed. All other characteristics of these simulations remain as described above. Table 2 shows a comparison of the resulting FOS calculated at the end of each simulation. The table also indicates the percentage difference in the FOS as compared to the saturated base-line. The coordinates are based on the origin at lower left corner of the model (see Figure 1). This comparison indicates that changes in matric suction considered here can result in a variation in the FOS against slope failure of between 5 % and 7 %. This result is indicative of one particular possible benefit of root water uptake. It should be noted, however, that this variation in FOS arises as a result of only one specific aspect of the problem, i.e. suction induced variation in shear strength.
815
5
CONCLUSIONS
The application of a numerical model for the simulation of moisture migration patterns due to tree water uptake in relation to a soil slope has been presented. An approach has been illustrated that enables the resulting prediction of soil suction variations to be related to a subsequent calculation of slope stability. Stability calculations have been performed by application of the standard theory of limit equilibrium of forces and moments. The model proposed then extends the standard framework to include a shear strength equation that is suction dependent. Suction variations generated in relation to a mature lime tree located on (or near) a typical soil slope have been presented. A range of tree locations have been considered. The problem chosen for consideration covered a full spring/summer drying period. The results of this study indicate that matric suction generation caused by the presence of a mature tree can readily increase the factor of safety against slope failure by more than 5%. These results are independent of related vegetation effects e.g. weight of vegetation, windthrow, root strength etc. and must therefore be treated only as a one component of the overall problem. In addition, it is evident that vegetation may induce much higher suctions than those considered here. Further work is therefore needed to validate the approach presented and to set it in a more general context. REFERENCES Biddle, P.G. 1998. Tree Root Damage to Buildings. Willowmead Publishing Ltd, Wantage. Bishop, A.W. 1955. The use of the slip circle in the stability analysis of earth slopes. Géotechnique, 5(1): 7–17. Bishop, A.W., Alphan I., Blight, G.E. & Donald, I.B. 1960. Factors Controlling the Shear Strength of Partly Saturated Cohesive Soils. Proc. ASCE conf. cohesive soils, Colorado, 503–532. Fellenius, W. 1936. Calculation of the Stability of Earth Dams. Trans. 2nd Int. Cong. Large Dams, Washington, 445–459. Fredlund, D.G., Morgenstern, N.R. & Widger, R.A. 1978. The shear strength of unsaturated soils. Canadian Geotechnical Journal, 15: 313–321. Fredlund, D.G. & Rahardjo, H. 1993. Soil Mechanics of Unsaturated Soils. John Wiley & Sons: New York.
GEO—SLOPE ver 6.17 Software, GEO-SLOPE/W International Ltd, Calgary Alberta, Canada, 2004. Greenwood, J.R. 2006. SLIP4EX—A program for routine slope stability analysis to include the effects of vegetation, reinforcement and hydrological changes. Geotechnical and Geological Engineering, 24: 449–465. Greenwood, J.R., Norris, J.E. & Wint, J. 2004. Assessing the contribution of vegetation to slope stability. ICE Proc. Geotechnical Engineering, 157: 199–207. Janbu, N., Bjerrum, L. & Kjaernsli, B. 1956. Soil mechanics applied to some engineering problems. Norwegian Geotechnical Institute Publication, 16. Lambe, T.W. & Whitman, R.V. 1969. Soil Mechanics. Wiley, New York, 363–365. Morgenstern, N.R. & Price, V.E. 1965. The analysis of the Stability of General Slip Surfaces. Géotechnique, 15: 79–93. Rees, S.W. 1990. Seasonal Ground Movement Effects on Buried Services, PhD thesis, University of Wales, Cardiff. Rees, S.W. & Ali, N. 2006. Seasonal water uptake near trees: A numerical and experimental study. Geomechanics and Geoengineering, 1(2): 129–138. Renaud, J.P., Anderson, M.G., Wilkinson, P.L., Lloyd, D.M. & Wood, D.M. 2003. The importance of visualisation of results from slope stability. ICE Proc. Geotechnical Engineering, 156(1): 27–33. Richards, L.A. 1931. Capillary conduction of liquids in porous media. Physics, 1: 318–333. Ridley, A., Ginnity, M. & Vaughan, P. 2004. Role of pore water pressures in embankment stability. ICE Proc. Geotechnical Engineering, 157: 193–198. Simon, A. & Collison, A.J. 2002. Quantifying the mechanical and hydrologic effects of Riparian vegetation on streambank stability. Earth Surface Processes and Landforms, 27: 527–546. Simon, A., Curini, A., Darby, S.E. & Langendoen, E.J. 2000. Bank and near-bank processes in an incised channel. Geomorphology, 35: 193–217. Spencer, E. 1967. A Method of Analysis of the Stability of Embankments Assuming Parallel Interslice Forces. Géotechnique, 17: 11–26. Technical Committee of Investigation 1994. The Collapse of Block 1 and the Stability of Blocks 2 and 3 Highland Towers Condominium. Report of the Technical Committee, Hulu Klang, Malaysia. Terzaghi, K. 1936. The Shear Resistance of Saturated Soils. Proc. Conf. Soil Mech. Found. Eng., Cambridge, 54–56. Thorne, C.R. 1990. Effects of vegetation on riverbank erosion and stability. In Vegetation and Erosion: Processes and Environments, John Wiley and Sons, 125–144.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Numerical predictions of seasonal pore water pressure fluctuations using FLAC tp flow O.C. Davies, M. Rouainia & S. Glendinning School of Civil Engineering and Geosciences, University of Newcastle upon Tyne, UK
ABSTRACT: This paper details the development of a transfer method of the hydraulic boundary conditions from a hydrological finite difference code, SHETRAN, into a geotechnical finite difference code, FLAC two phase (tp) flow. This transfer allows the daily predicted surface pore water pressures from SHETRAN to be applied to the surface boundary of the FLAC tp flow model. Once the surface pore water pressures have been applied then any of the constitutive soil models within FLAC tp flow can be used to model the mechanical response. This process offers the advantage that actual or predicted climate data can be used together with soils and vegetation data to model the seasonal responses of an embankment. Ultimately this model will be used with predicted future climate data to predict the response of infrastructure embankments to climate change.
1
BACKGROUND
Observations have shown that embankments shrink and swell due to the cyclic changes in pore water pressures. These movements can lead to the progressive failure of an embankment. The rate of progressive failure depends upon the severity of the shrink/swell cycle together with the number of cycles (Kovacevic et al. 2001). SHETRAN is hydrological modelling software capable of modelling the complex surface boundary conditions of a catchment area together with saturated and partially saturated subsurface flow. It is for this reason that this model has been chosen to predict the pore water pressure changes within an embankment. FLAC tp flow is geotechnical modelling software capable of modelling saturated and partially saturated subsurface flow and coupling this with a mechanical simulation. However FLAC tp flow is not capable of modelling the surface boundary condition to the same accuracy as SHETRAN. It is for this reason that a method has been developed to allow the transfer of daily surface pore water pressures from SHETRAN to the FLAC tp flow boundary thus allowing a fully coupled simulation to be carried out. 1.1
face pore pressures to the FLAC tp flow model. The third test imitates the second but for an embankment model with bare slopes. The fourth test is as the third but with grass covered slopes. 1.2
SHETRAN
SHETRAN is a 3D coupled surface/subsurface physically based spatially distributed finite difference model for coupled water flow together with sediment and solute transport modelling capabilities (Ewen et al. 2000). For the purpose of this modelling only the water flow component is considered. The SHETRAN flow model for an embankment (Figure 1) can be thought to consist of 3 components: 1. Interception and evapotranspiration 2. Overland flow 3. Subsurface flow
Examples
For the purpose of this paper four tests have been conducted. The first test consists of a simple caisson where the SHETRAN—FLAC models have been run separately in order to validate the newer FLAC tp flow model against the more established SHETRAN model. The second test involves first running the SHETRAN model with actual climate data and transferring the sur-
Figure 1.
817
SHETRAN surface model.
Data requirements for the model are meteorological data, soils data, vegetation properties and overland flow data together with boundary and initial condition settings. SHETRAN will then automatically output pore pressures for each cell within the grid. At the surface boundary, interception of precipitation is modeled by a modified Rutter model (Rutter et al. 1971) allowing the calculation of net rainfall reaching the ground together with the amount of stored water on the vegetation canopy and evaporation from the canopy. Evapotranspiration, the movement of water from the soil and within plants, is modelled within SHETRAN using the Penman-Montieth equation for actual evapotranspiration (Monteith 1965). This is calculated as a loss term to describe the uptake of water through plant roots. Overland flow is also calculated within the program. The depth of runoff water is determined from the available water from the interception evapotranspiration component and the rate of infiltration into the subsurface. Flow resistance parameters are then used to model the overland flow using approximations of the St. Venant equations of continuity and momentum. The subsurface is assumed to consist of a porous medium with saturation a function of moisture content. Flow through the medium is calculated by solving the non-linear partial differential Richards equation. 1.3
FLAC tp flow
The FLAC finite difference code allows the numerical modelling of structures built of soil and rock. The twophase flow option within the FLAC program considers two immiscible fluids within a porous medium. This allows the modelling of an unsaturated soil assuming the fluids present within the soil are water and gas. FLAC tp flow is capable of solving a fluid only calculation and a fully coupled fluid mechanical calculation. For the purpose of this paper, only the fluid flow calculation is considered. FLAC tp flow requires soil properties, water properties and boundary and initial conditions to be specified. Water is able to enter the grid by specifying either a discharge or a pore water pressure at the boundary. The two phase calculation approximates the Richards equation if it is assumed that air within a partially saturated medium is at atmospheric pressure and has a density of zero, and that the porous medium has a constant volume and cannot deform. These assumptions are specified in the following examples in order to validate FLAC tp flow against the more established SHETRAN model. 2
with the more established SHETRAN model. This validation exercise involved the modelling of a partially saturated caisson. The caisson was 6 m deep and the pore pressure was hydrostatic with an initial head of −6 m at the surface and 0 m head at the base. Infiltration of the caisson took place at a rate of 0.2 m/day until full saturation was reached. The caisson was then permitted to drain. Each software model requires different input parameters for the soil. The soil parameters were set for the FLAC tp flow calculation and the SHETRAN parameters derived from these, as shown in Tables 1 and 2. Table 1.
FLAC tp flow soil properties.
Saturated mobility coefficient Porosity Residual saturation P0 a b c
2.92 × 10−10 m2 /(Pa-s) 0.33 0 0.699 × 104 Pa 0.336 0.5 0.5
where P0 , a, b and c are Van Genuchten parameters used in the FLAC tp flow program. Saturated hydraulic conductivity in SHETRAN is equal to the Saturated mobility coefficient in FLAC multiplied by ρω g. The parameters α and n used in SHETRAN are defined as follows: α=
ρω g P0
(1)
where ρω is the density of water = 103 Pa/m3 and g is the force due to gravity = 10 ms−2 . The Van Genuchten parameter n used in SHETRAN is defined as n=
1 1−a
Table 2.
(2)
SHETRAN soil properties.
Saturated hydraulic conductivity θs θr A N
2.92 × 10−6 m/s 0.33 0 1.43 (1/m) 1.506
CAISSON COMPARISON
Before a transfer of pore water pressures was attempted a simple validation exercise was conducted in order to compare the relatively new FLAC tp flow model
where θs is the saturated volumetric moisture content (porosity) and θr is the residual volumetric water content.
818
2.1
Saturation
2.2 Drainage
Figure 2 shows the variation of moisture content for both models during the saturation phase of the modelling. It can be seen that both models have identical initial conditions. Through the first 2.5 days the SHETRAN caisson was marginally more saturated than the FLAC tp flow caisson. This divergence of the models continued over time as can be seen from the plots at 4.25 days. Figure 3 shows the variation of head with depth for both SHETRAN and FLAC tp flow models for the caisson. Again both models have almost identical initial conditions. At 2.5 days negative pore pressures within both models were almost identical, however the FLAC tp flow model showed a slight positive pore pressure within the saturated zone. At 4.25 days the positive pore pressure continued within the saturated zone stabilising at just above 0.5 m within the top third of the caisson. Within the area of negative pore pressures both models again gave similar results.
Figure 4 displays the variation in pore pressure with depth under drainage from the base of the caisson (base boundary condition, head = 0 metres). The SHETRAN and FLAC codes correlate well with only some divergence at the base of the model. At this point over time the SHETRAN model loses some moisture content and is not fully saturated as within the FLAC model. Figure 5 displays variation of head over depth within the two modelled caissons. Due to the FLAC model having a much higher initial pore pressure throughout the grid the two models differ at day one but by no more than 0.2 m. The later measurements of head after day 4 correlate very well. These results provide confidence in the capabilities of the FLAC tp flow program to calculate the flow of water through a porous partially saturated medium. The next example attempts the transfer of the SHETRAN surface pore pressures to the surface of the FLAC tp flow grid.
Variation of moisture content with depth
Moisture content during drainage
6
6
5
2
4
elevation
elevation
3
initial SHETRAN day 1 SHETRAN day 4 SHETRAN day 20 SHETRAN day 100 FLAC day1 FLAC day 4 FLAC day 20 FLAC day 100
5
SHETRAN initial SHETRAN 2.5 days SHETRAN 4.25 days FLAC initial FLAC 2.5 days FLAC 4.25 days
4
3 2
1 1
0 0.1
0.2
0 0.15
0.3
moisture content
0.2
0.25
0.3
0.35
moisture content
Figure 2. Comparison of variation of moisture content within the caisson for SHETRAN and FLAC tp flow.
Figure 4. drainage.
Moisture content profiles of caisson during
Variation in pore pressure with depth Variation head with depth under drainage 6
6 5
SHETRAN initial 5
FLAC initial
3
4
SHETRAN initial SHETRAN 2.5 days SHETRAN 4.25 days
2
SHETRAN day 1 SHETRAN day 4
FLAC 2.5 days FLAC 4.25 days elevation
elevation
4
SHETRAN day 20 SHETRAN day 100
3
FLAC initial FLAC day 1
2
FLAC day 4
1
FLAC day 20
1
FLAC day 100
0 -6
-4
-2
0
0 -3
pore pressure (m)
-2
-1
0
1
head (m)
Figure 3. Comparison of variation of pore pressure within the caisson for SHETRAN and FLAC tp flow.
Figure 5.
819
Pore pressure profiles of caisson during drainage.
CAISSON WITH PORE PRESSURE TRANSFER
Saturation profile at 100 days
For this test the caisson model was run within the SHETRAN program but this time with climate data obtained for north Yorkshire, UK in 1994. A pore pressure boundary input file was then created from the SHETRAN results file. This file contained the daily pore pressures for the uppermost cell within the SHETRAN grid. Pore pressures within SHETRAN were calculated for the centre of each cell. These daily pore pressures were then transferred to the top of the FLAC tp flow grid at grid points. A pore pressure reading was transferred for day 1 and the FLAC tp flow model allowed to run for 1 day. The next day’s pore pressure was then applied and the model run again, and so on until the end of the simulation. Within the FLAC tp code, if a pore pressure is applied at the boundary then water is effectively exchanged with the outside world to maintain that pore pressure, i.e. for a negative pore pressure water is extracted from the grid and for a positive pore pressure water is pumped into the grid. This will effectively simulate the infiltration of water at positive pressures and the extraction of water due to evapotranspiration at negative pore pressures. The test was run for a period of 100 days. Figure 6 shows the variation in pore pressure within the caisson at depths of 0.9 m and 1.8 m below the surface of the caisson for both the SHETRAN simulation and the FLAC tp flow simulation. The figure again shows a slight delay within the FLAC tp flow calculation compared with the SHETRAN calculation. The differences are, however, negligible and the same steady states are achieved with reasonable correlation. Figure 7 shows the correlation between the models. At the surface there is an exact match due to the pore pressure calculated from SHETRAN being applied to the FLAC tp flow surface. Lower down in the grid FLAC tp flow shows marginally less saturation than
Variation of head over 100 days -1.00 -1.50 FLAC 0.9 m depth
-2.00
head (m)
-2.50 -3.00
SHETRAN 0.9 m depth
-3.50
FLAC 1.8 m depth
-4.00 SHETRAN 1.8 m depth
-4.50 -5.00
elevation (m)
3
6 5 4
FLAC saturation profile 100 days
3 2 1 0
SHETRAN saturation profile 100 days 0.4
0.6
0.8
1
saturation
Figure 7.
Saturation profiles after 100 days.
SHETRAN. Again it is apparent that the SHETRAN grid ‘wets up’ slightly faster than the FLAC tp flow grid. Below the 2 m mark both models show there has been no infiltration of water and initial conditions persist. The combined caisson modelling show that the FLAC tp flow model is capable of modelling the flow of water through the unsaturated zone and that the method of transfer of pore water pressure from the SHETRAN surface cells to the FLAC surface is effective. These tests were carried out under a onedimensional condition only, for the next test the same process was attempted for a two-dimensional problem.
4
EMBANKMENT TEST WITH BARE SLOPES
For this exercise an embankment was modelled in SHETRAN with initial very dry conditions and with the same climate data as used for the caisson with pore pressure transfer example (see above). The pore pressures within the centre of the top cell from the SHETRAN grid were then imported daily to the boundary grid points of the FLAC tp flow grid. Figure 8 shows how the FLAC tp flow grid and the SHETRAN grid overlap each other. The grey cells represent the cells for which daily pore pressures have been transferred. Several files were created from the SHETRAN simulations, one for each of the surfaces cells. Each file again contained the daily calculated pore pressures from the SHETRAN calculation. For day 1 the pore pressures were applied and the model run for a day, then day 2 pore pressures applied and so on as within the caisson examples. The soil properties for this simulation are given in Table 3.
-5.50 0
20
40
60
80
100
days
4.1 Comparison of results Figure 6. Pore pressure time series for SHETRAN and FLAC tp flow after transfer of surface pore pressures.
Figures 9, 10 and 11 show the variation in head over the SHETRAN grid and the FLAC tp flow grid for a
820
Head Variation 4yrs 0 -0.5 -1 -1.5 Head m
period of 4 years for 3 points within the grids (indicated by the dots on the grid on ech figure). It can be seen that the transfer method was efficient in applying the SHETRAN boundary condition to the FLAC boundary condition. Just below the embankment surface (Figures 9 and 10) the FLAC tp flow calculation shows an initial lag behind the SHETRAN simulation, this is due to the two phase model assumptions not exactly approximating to the Richards equation, but after a period of 100 days both models correlate well. Deeper within the embankment (Figure 11) the lag is more pronounced; good correlation is not achieved until 300 days. This initial lag deep within the embankment is caused by the excessively dry initial conditions. As it can be seen for the remaining 3 years the models correlate well. Such excessively dry initial conditions
-2 -2.5 -3
Flac tp flow 7.5m from cent 2m elevation
-3.5
Shetran 7.5m from cent 2m elevation
-4 0
200
400
600
800
1000
1200
1400
Days
Figure 10. Pore pressure variation for 4 years for embankment with bare lopes at height 2 m above foundation.
head variation 4yrs 0 -0.5 -1
head m
-1.5 -2 -2.5 -3
Flac tp flow 1.5m from cent 2m elevation -3.5
Shetran 1.5m from centre 2m elevation -4 0
200
400
600
800
1000
1200
1400
days
Figure 8. Table 3.
Overlap of SHETRAN and FLAC tp flow grids. Figure 11. Pore pressure variation for 4 years for embankment with bare slopes at height 2 m above foundation.
Embankment test FLAC tp flow soil properties. 2.04 × 10−10 m2 /(Pa-s) 0.5 0.15 9.810 × 104 Pa 0.16667 0.5 0.5
Saturated mobility coefficient Porosity Residual saturation P0 A B C
are unlikely to be encountered for a real embankment problem and were only used to create a robust test for the comparison.
5
EMBANKMENT TEST WITH GRASS COVERED SLOPES
Head over 4yrs 0.00 -1.00 -2.00
head (m)
-3.00 -4.00 -5.00
shetran 0.5m cent 5.5m elevation -6.00
Flac tp flow 0.5m cent 5.5m elevation
-7.00 -8.00 0
200
400
600
800
1000
1200
1400
days
Figure 9. Pore pressure variation for 4 years for embankment with bare slopes at height 5.5 m above foundation.
Figures 12, 13 and 14 show the variation of pore pressure over a period of 4 years for the embankment with a grass canopy. All other variables remained the same as for the previous simulation. It can be seen from these Figures when compared to Figures 9, 10 and 11, which represent the simulation for bare ground, there is a much greater range between the summer and winter pore pressures. This greater range is much more pronounced at the surface (Figures 8, 9, 11 and 12). The SHETRAN program results and the FLAC tp program results still compare well for the three areas investigated despite the greater variance in pore pressures.
821
6
Head variation over 4 years 1.00
From these simple tests it has been established that FLAC tp flow is capable of modelling unsaturated flow through a porous medium with a high degree of accuracy. It has also been shown that the method of transferring surface pore pressures from the SHETRAN grid to the surface grid points of the FLAC tp flow grid is an efficient way to apply the more complex surface condition model of SHETRAN to the FLAC tp flow calculation. It will now be possible to run a simulation within SHETRAN for a fully vegetated embankment with actual measured or predicted climatic data and transfer the pore pressures over to FLAC tp flow to run a fully coupled analysis and establish the mechanical response of the embankment.
-1.00
head (m)
-3.00 -5.00 -7.00 -9.00
Flac tp flow 0.5m from cent 5.5m elevation SHETRAN 0.5m from cent. 5.5m elevation
-11.00 -13.00 -15.00 0
200
400
600
800
1000
1200
CONCLUSIONS
1400
days
Figure 12. Pore pressure variation over 4 years for embankment with grass covered slopes at height 5.5 m above foundation.
Head variation over 4 years
REFERENCES
0.00 -1.00
head (m)
-2.00 -3.00 -4.00 -5.00
Flac tp flow 7.5m from cent 2m elevation
-6.00
SHETRAN 7.5m from cent. 2m elevation
-7.00 0
200
400
600
800
1000
1200
1400
days
Figure 13. Pore pressure variation over 4 years for embankment with grass covered slopes at height 2 m above foundation.
Head variation over 4 years
Ewen, J., Parkin, G. & O’Connell, P.E. 2000. SHETRAN: Distributed River Basin Flow and Transport Modelling System, Journal of Hydrologic Engineering, 5, (3), pp. 250–258. Kovacevic, K., Potts, D.M. & Vaughan, P.R. 2001. Progressive failure in clay embankments due to seasonal climate changes, 5th Int. Conf. Soil Mech. Geotech. Engng. Istanbul, 2127–2130. Monteith, J.L. 1965. Evaporation and environment. Proc. 18th Symposium Society for Experimental Biology. Swansea: Cambridge University Press, London, 205–234. Rutter, A.J., Kershaw, K.A., Robins, P.C. & Morton, A.J. 1971. A predictive model of rainfall interception in forests, 1. Derivation of the model from observations in a plantation of Corsican pine. Agricultural Meteorology, 9, pp. 367–384.
-1.00 -1.50
head (m)
-2.00 -2.50 -3.00 -3.50
Flac tp flow 1.5m from cent. 2m elevation
-4.00
SHETRAN 1.5m from cent. 2m elevation
-4.50 0
200
400
600
800
1000
1200
1400
days
Figure 14. Pore pressure variation over 4 years for embankment with grass covered slopes at height 2 m above foundation.
822
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Infiltration analysis in unsaturated soil slopes J.F. Xue & K. Gavin University College Dublin, Dublin, Ireland
ABSTRACT: This paper describes a simple model which can be used to estimate the time needed for a wetting front to develop in an unsaturated soil slope. The model is an extended form of the traditional Green-Ampt method. The first extension recognises that ponding of water cannot occur on a soil slope. It further allows the user to indirectly account for antecedent rainfall conditions by separating slopes into two categories depending on their initial suction profiles. In the first category, where the initial suctions are large, the rate of the development of the wetting front depth is controlled by the rainfall intensity. In the second, where the initial suction is low, the time taken for a wetting front to develop to a given depth depends on the infiltration capacity of the soil. In the final section of the paper results from the new model are compared to numerical predictions of wetting front depth in a fine sand slope.
1
INTRODUCTION
To analyse landslides triggered by rainfall, it is important to understand the infiltration process. In most current methods, such as the Green-Ampt model, the infiltration analyses are based on theories derived for saturated soils. However, the mechanisms controlling infiltration into unsaturated soil are different to the saturated condition. Key differences include the fact that the permeability of unsaturated soil changes continuously throughout infiltration, and that a major driving force for water flow in saturated soils is the head of water. In unsaturated soil flow problems such as slope failures, where there is no surface ponding, the main driving force is not gravity, but differential suction. In this paper a model which was developed to analyse the rainfall infiltration into unsaturated soils is presented and applied to a published case history of a numerical analysis of infiltration into a fine sand slope.
2
BACKGROUND
The stability of many man-made and natural slopes is enhanced by near surface negative pore water pressure (suctions). An understanding of how rainfall infiltrates into these slopes and reduces suction is critical to a full understanding of slope stability problems. Predicting the rate of infiltration of water into unsaturated soils is a complex process. This is due in part to the variable rainfall and irrigation patterns that occur, and the highly non-linear permeability of unsaturated soil. In addition the geometry, vegetation and the roughness of the ground surface will influence the infiltration
process (See Fredlund et al. 1994, Ng and Shi 1998, Zhan and Ng 2004, and others). Field measurements of the variation of suction in an instrumented slope by Rajhardjo et al. (2005) reveal some of the complexities involved in attempting to predict the infiltration response of soil slopes. The authors show that during the early stages of a low intensity rainfall event, when the infiltration capacity of the slope is highest, all of the rainfall infiltrates into the slope. As the rainfall continues, the in-situ suction and therefore the infiltration capacity of the slope reduce and run-off begins. The time at which run-off begins depends on the initial suction in the slope and the rainfall intensity, with the time to run-off, increasing when the initial suctions are highest and the rainfall intensity is low. By placing suction probes at various depths in the slope, and along the slope face, the effect of subslope drainage was observed, with the water content at a given depth in the slope being highest near the toe of the slope and lowest near the crest. There are several methods commonly used to analyze the infiltration process, ranging from simple methods such as the Green-Ampt model, to the more complex finite element method (FEM). Some of the simple methods are briefly reviewed as the new method is essentially an extended form of an existing model. 2.1
Green-Ampt model
The Green-Ampt (1911) model was first developed to analyze the infiltration process under ponded conditions (i.e. assuming standing water on a horizontal ground surface). The basic assumption underpinning the model is that infiltration causes the development
823
2.2 Horton equation H Infiltrating water Saturated soil
Wetting front; matric suction pulls water into dry soil
Figure 1. model.
Run-off from a slope will occur only when the rainfall intensity exceeds the infiltration capacity of the soil. Considering Equation 2 we see that the infiltration capacity of the slope reaches a limiting minimum value, equal to the saturated permeability of the soil (Ks ) when the near surface soils become saturated. Field measurements contradict this assumption. Rahardjo et al. (2005) revealed that run-off occurred on slopes when the rainfall intensity was lower than Ks . The Horton equation (Jury & Horton 2004) is used to describe the infiltration capacity of soil with time (t).
Zf
Wetting front moves down into dry soil
Two-layered soil profile defined in Green-Ampt
of well-defined wetting front (See Figure 1). The soil above the wetting front is fully saturated, whilst below the wetting front it remains at the initial (preinfiltration) water content. Gravity and matric suction effects control the movement of water in the saturated zone, and the hydraulic gradient (hi ) at the wetting front is: hi =
H + Zf + S Zf
(1)
where H is the depth of ponded water, Zf is the wetting front depth and S is the suction at the wetting front. Since the soil above the wetting front is assumed to be fully saturated, using the permeability coefficient of the saturated soil Ks , and applying Darcy’s Law, the infiltration rate of the soil can be calculated: H + Zf + S i = Ks Zf
(2)
The model was originally developed to analyse the infiltration of ponded water into homogenous soils. Variations of the Green-Ampt model to account for steady (Mein & Larson 1973) and unsteady (Chu 1978) rainfall events have been developed. However, the basic assumption of the two-layer model (with the wetting front forming a boundary between the saturated and unsaturated zones) remains. Research on infiltration in the field by Mishra et al. (2003) found the Green-Ampt model to be conservative, with the time predicted for a wetting front to develop being much lower the in-situ measurements reveal. This is at least partly due the use of the saturated soil permeability in Equation 2 (Bouwer 1966), and the assumption that the near surface soils are fully saturated. Field measurements show that near surface soils rarely become fully saturated Williams et al. (1998). Therefore the applicability of the Green-Ampt model for unsaturated soil infiltration analysis is questionable.
i = if + (i0 − if ) exp(−βt)
(3)
where: i0 is the initial infiltration capacity at t = 0; if is the steady state final infiltration capacity; β is a constant which describes the rate of decrease of the infiltration capacity; and t is time. From Equation 3, we see that the final infiltration capacity is not constrained to the limiting value Ks , rather a limiting value if , which is typically lower than Ks , can be used. Considering Equation 3, run-off will occur at any time when the rainfall intensity exceeds the infiltration capacity of the soil. Although Horton’s equation provides a simple mathematical description of the reduction of the infiltration capacity of a soil during rainfall, in practice it is difficult to implement because of difficulties associated with the choice a unique β value for a given slope, see Mishra et al. (2003) and Xue & Gavin (2007). 3
PROPOSED METHOD
Considering some of the drawbacks outlined above a modified model based on the Green-Ampt model, Darcy’s Law and the Law of mass conservation is developed in this section to analyse one-dimensional vertical infiltration into unsaturated soil slopes. 3.1 Infiltration capacity of unsaturated soil slopes Making the assumption that: 1. During rainfall on a slope where ponding cannot occur, the soil is continuously supplied with water, but not fully saturated within the wetted zone. 2. After rainfall the final suction profile in the wetted zone is linearly distributed within the wetting front (See Figure 2), where St and Sb are the initial suctions at the top and base of the wetting front, and Su is the limiting final suction. 3. The permeability of the soil above the wetting front is uniform with depth and time. In the class of simple infiltration models considered, the soil permeability is often assigned a constant value
824
and the hydraulic head in this zone is controlled exclusively by matric suction. Since the water supply at the ground surface is continuous during rainfall, suction values at the ground surface are zero. Setting the ground surface as the reference elevation and considering vertical flow only, the hydraulic gradient at depth y should be:
e
fac
p
slo
fall
ain er r
aft
r e su
tion
suc
fall
St Su
re efo
b
rain
ng
tti we
nt
fro
Hf Sb
hi =
Sy y
(4)
suction profile
where Sy is the suction value at depth y. The infiltration capacity of the soil at depth y is:
y Figure 2.
Suction profile assumed in the new model.
i=K
(5)
in which K is the permeability of the soil at the depth y. In Equation 4, the infiltration capacity is controlled by the permeability of the soil and the hydraulic gradient due to matric suction. The infiltration capacity will be greater than the permeability of the soil when Sy /y > 1. This situation occurs in dry soils with high initial matric suction. If during a rainfall event, the rainfall intensity (Ri ) is less than the infiltration capacity i, all the precipitation will infiltrate into the soil. In contrast if the rainfall intensity is larger than infiltration capacity, runoff will occur. As soils within the wetting front become more saturated and the matric suction at the wetting front reaches a limiting value, the infiltration capacity in Equation 5 converges to a constant value. This agrees with the trend of infiltration capacity decay described with the Horton equation. We therefore consider the infiltration process in two stages:
Figure 3. Hydraulic head due to water pressure from higher up the slope.
(usually the saturated permeability because of the assumption that the soil becomes fully saturated during infiltration). If the soil is partially saturated the permeability depends on the negative porewater pressure (or the degree of saturation), Ng & Shi (1998). Whilst it is strongly recommended that the permeability of the soil over the appropriate range of suction values is measured using the Soil Water Characteristic Curve (SWCC), in the absence of specific information the recommendation by Bouwer (1966) that K = 0.5 Ks can be adopted. 4. The model assumes one-dimensional vertical infiltration only. The water table is well below the ground surface and the slope is gentle. The head difference due to the sloping water table (See Figure 3) is small in comparison to matric suction effects. 5. Because of the assumption of 1-D flow, only flow perpendicular to the slope surface is considered; flow parallel to the ground surface is ignored. Since ponding cannot occur on a slope, the hydraulic gradient originating from the ponded water (H) in Equation 1 is neglected. As the water phase in the wetting front is not continuous, the water in this zone cannot impart a hydraulic gradient to the water beneath. Thus, the static hydraulic head (Zf ) in Equation 1 does not exist
Sy y
Stage 1: When the rainfall intensity is smaller than the infiltration capacity: Ri ≤ i. From Equation 5 we have: in stage 1, Sy ≥ (Ri /K)y. Stage 2: When Ri exceeds the infiltration capacity: Ri > i. In this stage we have: Sy < (Ri /K)y. Given the initial and final suction profile in the soil, the wetting front can be divided into two zones with the line Sy = (Ri /K) y as shown in Figure 4. The ratio Ri /K, which can be defined as the relative rainfall intensity (Rri ), describes the ratio between the actual rainfall intensity and the permeability of the soil. If the initial suction values in the soil are such that part of the profile falls into zone 1, the soil will initially have an infiltration capacity higher than the rainfall intensity. If the suction values in the soil fall into zone 2, and the rainfall intensity exceeds the infiltration capacity of the soil, run-off will occur (at the rate Ri − i).
825
4
zone 1
H2
H1 zone 2 Sy=(Ri/K)*y
H
Sb y Figure 4.
Suction profile divided into two zones.
According to the Law of mass conservation, in zone 1, we have: Ri dt = θ1 dy
(6)
Rewriting the equation and integrating with depth (y), we have the time required to form the wetting front to depth H1 in zone 1 (Figure 4): T1 =
θ1 H1 Ri
(7)
Tami et al. (2004) performed numerical simulations using SEEP/W (Geoslope Int.) to investigate the effect of the duration of a rainfall event on the infiltration response of a slope which was subjected to a fixed rainfall intensity of 86.4 mm/hr. Two rainfall durations were considered, 15 and 42 minutes. This rainfall intensity was chosen to correspond to a rate of 10% of the saturated permeability of the sand. The 30◦ slope considered was made up of a 400 mm deep fine sand layer overlying a 200 mm thick gravely sand. The fine sand had a saturated permeability (Ks ) of 2.4×10−4 m/s, and the variation of suction with water content is shown in Table 1. The initial and final suction profiles for the 15 minute infiltration event is shown in Figure 5. It is apparent that after 15 minutes rainfall there was a significant reduction in suction at the slope surface, a small reduction at a depth of 200 mm and no change at Table 1.
K
Sb y
Water content of the fine sand at different suctions.
Suction (kPa)
5.4
4
3.5
2.5
1
1.5
Water content
7%
8%
8.5%
10%
22%
15%
As infiltration continues, suction values in the soil decrease and eventually fall into zone 2. In this zone, the infiltration capacity is lower than the rainfall intensity. So in this zone we have:
APPLICATION OF THE MODEL
1.5 kPa
5.4 kPa Zone 1
Final
Initial
3.5 kPa
dt = θ2 dy
400 mm
St
200 mm
Su
(8) 2.5 kPa
T2 =
θ2 (H 2 − H22 ) 2KSb
Figure 5. Initial and final suction profile in the slope with the 15 min precipitation of 86.4 mm/h.
(9)
1.0 kPa Zone 1
So the total time is: T = T1 + T2
5.4 kPa
Final Initial
(10)
It should be noted that in stage 2 as the soil becomes nears full saturation, it may behave as a saturated soil. In such cases Equation 10 may be overestimate the actual time required for a wetting front to form in latter parts of stage 2.
400 mm
in which Sb is the suction value at wetting front and θ2 is the change of volumetric content in zone 2. So the time for zone 2 to develop can be calculated with:
Sy=0.2y
2.5 kPa Sy=0.2y Figure 6. Initial and final suction profile in the slope with the 42 min precipitation of 86.4 mm/h.
826
Table 2. Comparison of result from FEM and proposed method in this paper. Time (min) This paper Case
FEM
Green-Ampt
T1
T2
Total
1 2
15 42
2.2 10.2
10.4 37.5
0 0
10.4 37.5
controlled by the infiltration capacity of the wetted soil. When compared to the results from FEM analyses and the Green-Ampt model, the new model provided estimates that were compatible with FEM results and a significant improvement on the Green-Ampt model, especially during the early stage of infiltration. This method has an obvious advantage in performing preliminary design prior to the decision to carry out a full FEM analysis. ACKNOWLEDGEMENT
400 mm, suggesting that the wetting front depth just exceeded 200 mm. When the duration was increased to 42 minutes the wetting front depth evidently penetrated through the entire 400 mm depth of fine sand (See Figure 6). Calculation of the time needed to form these wetting front depths was carried out using the Green-Ampt method and the new model and the results are shown in Table 2. Consideration of Figures 5 and 6 show that in both cases, because the rainfall intensity is low in comparison to the infiltration capacity, the soil falls completely in zone 1, and therefore only T1 needs to be calculated. Whilst the predictions made using the new model are compatible with the FEM analyses, the Green-Ampt model severely under-predicted the infiltration time. This is presumably due to the combined effect of the use of Ks and the role of the static water head (imparted by the wetting front) increasing the hydraulic gradient.
5
CONCLUSION
To determine the stability of unsaturated soil slopes, it is important to determine the depth of the wetting front. The Green-Ampt model and FEM analyses are widely used to predict the formation of the wetting front. Whilst FEM analyses can provide rigorous results, the input data required for the models is not readily available for all soils. Whist the Green-Ampt model is widely used and relative easy to apply, some of the fundamental assumptions used in its derivation are shown to be questionable when the soil surface is not subject to ponding. A simple extension of the Green-Ampt model is proposed in this paper. In the model the soil above the wetting front is assumed to remain unsaturated throughout infiltration. The time for a wetting front to develop is considered in a two-stage process. In the first stage infiltration is controlled by the rainfall intensity and in the second part infiltration is
This project is funded by Iarnród Éireann. The authors would like to thanks Mr. Brian Garvey, former Chief Civil Engineer with Iarnród Éireann for financial assistance received. The first author was the recipient of a Geotechnical Trust Fund award from the Geotechnical Society of Ireland. REFERENCES Bouwer, H. (1966). Rapid field measurement of air entry value and hydraulic conductivity of soil as significant parameters in flow system analysis. Water Resources Research 2(4): 729–738. Chu, S.T. (1978). Infiltration during an unsteady rain. Water Resources Research 14(3): 461–466. Green, W.H. & C.A. Ampt (1911). Studies on soil physics: Flow of air and water through soils. Journal of Agricultural Science 4: 1–24. Jury, W.A. & R. Horton (2004). Soil Physics. New Jersey, John Wiley & Sons, Inc. Mein, R.G. & C.L. Larson (1973). Modeling infiltration during a steady rain. Water Resources Research 9(2): 384–394. Mishra, S.K., J.V. Tyagi & V.P. Singh (2003). Comparison of infiltration models. Hydrological processes 7: 2629–2652. Ng, C.W.W. & Q. Shi (1998). A numerical investigation of the stability of unsaturated soil slopes subjected to transient seepage. Computer and Geotechnics 22(1): 1–28. Rahardjo, H., T.T. Lee, E.C. Leong & R.B. Rezaur (2005). Response of a residual soil slope to rainfall. Canadian Geotechnical Journal 42: 340–351. Tami, D., H. Rahardjo, E.C. Leong & D.G. Fredlund (2004). Design and laboratory verification of physical model of sloping capillary barrier. Canada Geotechnical Journal 41(9): 814–830. Williams, J.R., Y. Ouyang, J.S. Chen & V. Ravi (1998). Estimation of infiltration rate in the vadose zone: Compilation of simple mathematical models (2), United States Environmental Protection Agency. Xue, J. & K. Gavin (2007). Effect of rainfall intensity on infiltration into partly saturated slopes. Journal of Geotechnical and Geological Engineering. Published online October 2007, DOI 10.1007/s10706-007-9157-0.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Prediction of changes in pore-water pressure response due to rainfall events M. Karthikeyan, D.G. Toll & K.K. Phoon Department of Civil Engineering, National University of Singapore, Singapore
ABSTRACT: Global climate change is expected to result in worldwide increases in temperature and alteration of rainfall patterns. Such changes have the potential to activate rainfall triggered landslides and a study is underway in Singapore to investigate these possible effects. The main objective of this work is to calibrate a numerical model for future prediction by making use of cases where in-situ measurements of pore-water pressures/suctions have been made in Singapore. The results presented in this study show that the prediction of changes in the pore-water pressure profile is highly sensitive to the soil-hydraulic properties used in the analysis. It was found that a SEEP/W flow model is able to capture the general trend of field behaviour of the changes in the pore-water pressure profile response due to rainfall events. However, the results from the numerical models indicate that further research is warranted to improve the accuracy of the numerical analysis by better definition of critical input parameters.
1
INTRODUCTION
Rain-induced slope failures are a common geotechnical problem in tropical areas like Singapore (Pitts 1984, Chatterjea 1989, Toll et al. 1999). The tropical climate of Singapore causes slopes to remain unsaturated during long hot and dry periods. However, there are numerous cases of slope failures in Singapore during severe rainfall events. Recent predictions of climate change as a consequence of increased greenhouse-gas production suggest that the evapotranspiration—precipitation balance is likely to change. This will affect the hydrological environments governing slope instability through, for example, changes in antecedent pore-water pressures and alteration of triggering event magnitudes. This could increase the frequency of occurrence of high positive pore pressures, and thus the activity of rainfall-triggered landslides (Buma 2000, Dehan et al. 2000, Dixon and Brook 2007). Transient pore-water pressure in response to short intense rainfall plays an important role in shallow landslide occurrence. Highly negative pore-water pressures may exist in the slope because of moisture loss either through evaporation or evapo-transpiration. These negative pore-water pressures may be lost with the occurrence of rainfall. Landslides are generally caused by a gain in pore-water pressure (or loss of suction) as a result of rainfall infiltration from the slope surface. Field observations show that significant suctions (in excess of 80 kPa) can develop near the surface of a slope during dry periods in Singapore (Gasmo et al. 1999, Tsaparas et al. 2003). However, after
even relatively small amounts of rainfall the suctions can be lost, and small positive pore-water pressures (up to about 5 kPa) can develop to depths of 1–2 m (Tsaparas et al. 2003). The data show that, for a scenario where the water table is at significant depth, most pore-water pressure changes take place near the surface (<2m) (Tsaparas et al. 2003). This is consistent with the observation that many minor landslides in Singapore are quite shallow in nature. Failures tend to occur within the near-surface zone where pore-water pressures increase close to hydrostatic levels. The infiltration and internal flow processes within slopes need to be modelled using numerical models calibrated against measurements of pore-water pressures. An understanding of the hydrological behavior of residual soil slopes under different climatic conditions is needed to develop an appropriate strategy to limit or prevent rainfall-induced slope failures in the future. In this paper, a comparison is made between prediction of pore-water pressure response due to rainfall events from the numerical model and field data from an instrumented slope in Singapore. The effects of water retention curve and permeability functions on the changes in the predicted distribution of pore water pressure are also discussed. 2
DESCRIPTION OF INSTRUMENTED SLOPE
The case study under investigation was reported by Tsaparas et al. (2003). They present data from an instrumented slope located on the campus of Nanyang
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Technological University (NTU), Singapore, where the Jurong sedimentary rock formation is the predominant geological formation. The residual soils derived from the Jurong formation are usually clayey materials with sand or silt (Pitts 1984). Due to the warm and humid climate of Singapore, the residual soils have an unsaturated zone, which extends to large depths, above the usually deep groundwater table. Failures of residual soil slopes in the Jurong formation during severe rainfall are usually shallow and associated with the development of a perched water table near the ground surface and the build-up of high positive pore-water pressures. The detailed description of this instrumented slope can be found in Tsaparas et al. (2003). The NTU-ANX slope has an inclination of 29◦ , height of 21 m, and length of 43 m. The instrumented area of the site is relatively small (6 m in length) in comparison with the size of the slope. The ground surface of the NTU-ANX slope is covered with Buffalo Grass. The simplified soil profile consists of two soil layers. Layer 1 is the surface soil layer that extends to a depth of 10 m. Layer 1 is a hard silty to sandy clay that has an orange color, moderate plasticity, and 58% fines. Layer 2 is clayey silt with siltstone and sandstone fragments and a fines content of 32%. The ground table lies at depths between 15 m and 17 m from the ground surface and is not greatly affected by rainfall events. Hence, in this numerical analysis, the hydrological properties of soil layer 2 were less important. The main instrumentation of the NTU-ANX slope consisted of three rows of tensiometers, a rain gauge, and a piezometer. Three rows (A, B & C) of jet-fill tensiometers were spaced 3 m apart. Each row consisted of five tensiometers (spaced 0.5 m apart) for measuring the pore-water pressures at depths of 0.5, 1.1, 1.7, 2.3 and 2.9 m. These measuring depths were chosen to study the variation of the pore pressure increase with depth during a rainfall event. A rain gauge was also installed next to the study area.
information pertaining to the hydraulic properties such as water retention capacity and permeability functions of the soil is important. Agus et al. (2001) reported a large number of water retention curves for Singapore residual soil samples, at various depths. Soils near the ground surface are expected to undergo more severe weathering compared to the underlying soils. These soils have less water retention capacity as they are commonly looser with some micro structure, such as cracks and fissures. Figure 1 shows the wetting water retention curve of a soil sample obtained from the NTU-ANX slope at a depth of 0.4 m (denoted as Tsarapas 2002). The saturated volumetric water content was 0.53 and when an applied negative pore-water of 200 kPa was established in the sample, then the volumetric water content reduced to 0.38. Agus et al. (2001) reported an envelope for water retention curves established for Jurong Sedimentary formation residual soils and these are included in the Figure 1 for comparison. The upper, average and lower water retention curves shown in Figure 1 were established using saturated volumetric water content of 0.53 and the curve fitting parameters reported in Agus et al. (2001). Other water retention curves from the NTU campus reported by Agus et al. (2003) are also shown in Figure 1. These are for different depths (5.60 m and 4.0 m). The figure shows that there is similar trend in the shape of the water retention curve for Jurong Sedimentary Formation residual soils even though there is difference in the saturated volumetric water content. Agus et al. (2001) also examined the effect of weathering on the shape of the water retention curves and reported that there are no significant difference between the shape of these curves and the depth of weathering for Jurong sedimentary formation residual soils. Measurement of permeability functions for unsaturated soils is tedious, time consuming and labor intensive process and there are often limited data. However, 0.60 Tsaparas(2002)
REVIEW ON WATER RETENTION CURVES AND PERMEABILITY FUNCTIONS
UP-1 (Agus et al. 2003) 0.50
Fundamental to a transient seepage analysis is an understanding of the relationship between matric suction (in terms of pore water pressure) and volumetric water content. As water flows through soil, a certain amount of water is stored or retained within the soil structure. The amount of water stored or retained is a function of pore water pressure and this is described by the water retention curve. Since the water content is a function of pore water pressure this means that the hydraulic conductivity is also a function of pore water pressure. For unsaturated geotechnical analysis,
Volumetric water content
3
UP-3 (Agus et al. 2003)
Upper Bound
0.40
0.30
0.20
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Note: Upper and lower water retention curves obtained from Agus et al. (2001) using saturated volumetric water content of 0.53.
Average
Lower Bound
0.00 0.1
1
10
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1000
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Matric Suction (kPa)
Figure 1. Water retention curves envelopes for Jurong formation residual soils.
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Unsaturated coefficient of Permeability (m/s)
Agus et al. (2003, 2005) presented unsaturated permeability functions measured in the laboratory for Singapore residual soils. Figure 2 shows the unsaturated permeability functions measured for Jurong sedimentary formation residual soil samples. From Figure 2, it can be seen that there is close agreement between these two soil samples for suctions above 20 kPa. Even though the saturated permeability values are different (due to differences in saturated volumetric water content as can be seen in Figure 1) the unsaturated permeability functions are almost identical in the higher suction range. The commonly used integration functions for predicting the unsaturated permeability function from water retention data (Green and Corey 1971, Van Genuchten 1980, Fredlund et al. 1994) were investigated for the Jurong residual soil. The predicted curves showed significant differences between the experimental data reported by Agus et al. (2003) and the predictions. The Green and Corey (1971) method gave a curve closest to the experimental results but was still very different. This indicates the danger in using such expressions without an experimental confirmation of their validity. 1.0E-06 1.0E-07 1.0E-08 1.0E-09 1.0E-10
4
UP-1 (Agus et al. 2003) UP-3 (Agus et al. 2003) Fitted Permeability function Green and Corey (1971)
1.0E-11 1.0E-12 1.0E-13 0.1
1
10 Matric Suction (kPa)
100
1000
Figure 2. Measured unsaturated permeability function for Jurong Sedimentary Formation. 1.0E-10 Saturated coefficient of permeability (m/s)
In situ permeability measurements at the study area showed that the saturated coefficient of permeability with respect to water, ks , for the surface soil is 6 × 10−7 m/s, measured at approximately 0.4 m deep using a Guelph Permeameter (Tsaparas et al. 2003). Other measurements for ks of Jurong soil are shown in Figure 3. It can be seen that ks can vary between 10−10 m/s and 10−6 m/s. The saturated volumetric water content for these soils varies between 0.25 and 0.60. No clear trend is seen in the saturated coefficient of permeability and saturated volumetric water content, which highlights the difficulty of generalizing the properties of residual soils. However, the field measurement by Tsaparas (2002) falls within the range of values, and is in agreement with data by Agus et al. 2003. It can be seen from Figure 2 that there is lack of information on experimental data near the air entry of value of the soil (below a matric suction of 20 kPa). Therefore, the Green and Corey (1971) equation was used to estimate the unsaturated coefficient permeability values near the air entry of value up to the matric suction of 20 kPa using the water retention curve shown in Figure 1 (identified as Tsaparas, 2002) with saturated coefficient of permeability of 6 × 10−7 m/s. The fitted permeability function shown in Figure 2 is based on the Green and Corey equation to 20 kPa suction and on experimental observations for higher suctions. This curve has been used in the analyses that follow.
Rahardjo et al (2005) Agus et al (2003)
1.0E-09
Gasmo et al (2000) Rezaur et el (2003)
1.0E-08
Rahardjo et al (2001) Tsaparas (2002)
1.0E-07
DESCRIPTION OF NUMERICAL MODEL
The commercial finite element code, SEEP/W (GeoSlope International, 2004) was used for the numerical modelling of the field measurements, adopting a twodimensional and transient seepage model in an infinite slope. The geometry of the slope used in the numerical analysis is shown in Figure 4. The boundaries of the finite element mesh are at great distance from the study area (rows A to C), to avoid any influence of the boundary conditions on the computed pore-water pressure changes. The finite element mesh used in this analysis is very fine with dimensions 0.25×0.25 m and consists of 8 node iso-parametric elements, in order to avoid any possible numerical instability that may occur in the solution (Karthikeyan et al. 2001).
1.0E-06
1.0E-05
5
MODELLING OF FIELD RESPONSE
1.0E-04 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Saturated volumteric water content
Figure 3. Variations of Saturated coefficient of permeability and volumetric water content.
In this study, a comparison is made between the predictions of the numerical model and the field observation of changes in the pore-water pressure for the period from 23 March 2000 to 24 March 2000
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to −2 kPa for all depths. The file generated by steady state analysis was used as the initial condition file for transient seepage analysis. During the transient analysis, the rainfall event shown in Figure 5 was applied as a flux boundary condition along the slope surface to predict the changes in the pore-water pressure profiles. 6
Geometry of the slope used in the numerical
2.5E-05 23-24 March 2000
Rainfall (m/s)
2.0E-05 1.5E-05 1.0E-05 5.0E-06 0.0E+00 0
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Figure 5.
Recorded rainfall events from 23–24 March 2000.
(Tsaparas et al. 2003). During this time period two natural rainfall events were recorded on this slope. Figure 5 shows the recorded rainfall events from 23 to 24 March 2000. The pore-water pressures near the ground surface (at a depth of 0.5 m) were affected by these rainfall events but there was no significant change in the porewater pressure profiles for deeper depths (at depths 1.1 m, 1.7 m, 2.3 m and 2.9 m). Hence, in this study, the pore water pressure variation in Row A obtained at a depth of 0.5 m below ground surface is compared with the numerical solution. From the field measurement on 23 March 2000, the pore-water pressure profiles for all depths were close to −2 kPa. The piezometeric measurements showed that the groundwater table stands between 15 m and 17 m below the ground surface. In order to simulate the initial condition for transient analyses, a steady state analysis was performed by specifying an initial pressure head equal to 0.2 m at all nodes in the mesh. This gave a matric suction of up
A comparison between the field observation and numerical simulation of the variation of pore-water pressure was carried out using the rainfall data from the field measurement on 23–24 March 2000. The water retention curve of a soil sample obtained from the NTU-ANX slope, denoted as Tsarapas (2002) in Figure 1 and the fitted unsaturated permeability function shown in Figure 2 were used in this numerical analysis. Figure 6 shows the comparison of measured porewater pressure in the field with numerically predicted values at a depth of 0.5 m below the ground surface. The comparison of the results shows the numerical model under-predicts the change in the pore water pressure profile. This is due to relatively low saturated coefficient of permeability of 6 × 10−7 m/s used in this analysis. Infiltration of water into such low permeability soils is normally very slow and frequently accompanied with surface runoff (Novak et al. 2000, Tsaparas & Toll 2003). In reality, the ground surface of the slope is covered by grass and may have dessication cracks. Due to root pathways and surface cracks the coefficient of permeability can be significantly higher at the ground surface than at greater depths (Anderson et al. 1996). Chappell and Lancaster (2007) reported that the wet-period determined saturated coefficient of permeability (ks ) values were typically lower than the values determined in the dry-period by up to a factor of two orders of magnitude. The lower wet period values are most likely due to closure of desiccation cracks with prolonged exposure to moisture. 4 Pore-water pressure (kPa)
Figure 4. analysis.
RESULTS AND DISCUSSION
3 2 1 Field (Depth 0.5m)
0
Numerical model
-1 -2 -3 -4 0
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Time (sec)
Figure 6.
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Pore water pressure variations at 0.5 m depth.
4 Pore-water pressure (kPa)
One of the major issue facing researchers dealing with the unsaturated zone is the overwhelming heterogeneity of the subsurface soils due to fractures, fissures, cracks and inter-aggregation pores (Novak et al. 2000). Ignoring the infiltration through these features usually leads to severely underestimated infiltration rates and hence an unrealistic description of the soil water regime (Van Genuchten et al. 1999). Flow in structured porous media is frequently described using dual permeability models (Fig. 7) in which soil consists of two regions, one associated with macro pores (the crack network) and the other with the less permeable matrix region (Van Genuchten et al. 1999). Tsaparas & Toll (2002) recognized the effect of the higher permeability surficial layer and tried to take account of it by including a more permeable surface layer of 0.25 m (the depth affected by rooting). In this analysis, studies were also conducted by introducing a 0.25 m thick higher permeabity layer. However, unlike the analysis of Tsaparas and Toll, this layer was modelled with highly anisotropic permeability, using a high permeability perpendicular to the surface (taking account of cracking and root passages in this direction), but maintaining the same value of permeability as the matrix soil for flow parallel to the ground surface. The ratio of hydraulic conductivities (kx /ky ) was set to 1 × 10−3 m3 /s, with the saturated value of kx set to 6 × 10−7 m/s (and hence ky = 6 × 10−4 m/s). Figure 8 shows the comparison of the measured pore-water pressure in the field with the numerically
2 1 0 -1 -2
Field (Depth 0.5m)
-3
0.25m thick permeable layer
-4 0
10000
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30000
40000
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Figure 8. Comparison of pore water pressure variations for 0.25 m thick permeable layer.
predicted values when including the 0.25 m thick more permeable layers. The trend in the results is the same as that shown by the field measured values. However, the numerical predication still underestimates the magnitude of the pore water pressure change when compared with field measurement. Nevertheless they show significantly improved predictions compared to Figure 6. Further attempts have been made to introduce dual porosity and permeability models in the analysis. However, the numerical results show the inability of SEEP/W to handle the steep changes in material properties required; the solution tends to diverge instead of converge and oscillate between two extreme solutions represented by the extremities of the hydraulic conductivity function. This is a short coming that needs to be addressed by developing solvers that can ensure convergence under highly non-linear conditions (Fredlund 2007). The results from the numerical models indicate that further research is warranted to improve the accuracy of the numerical analysis. The critical input parameters required for models needs to be refined based on the measurements made in the field and laboratory to a far greater extent than is commonly undertaken. To improve the accuracy of the numerical model representations, better definition of the soil hydraulic properties is required. This is the case even for the Jurong residual soil where significant efforts have been made to carry out research on its properties. 7
Figure 7. Schematic of increasingly of complex models that may be used to simulate preferential flow (Van Genuchten et al. 1999).
3
CONCLUSIONS
This paper describes a comparison of changes in the observed pore-water pressure profile with predictions from a numerical model. This is to allow the model to be calibrated against observed events, so that it can be used to predict the effects of future expected climate change. The results presented in this study shows that the prediction of changes in the pore-water pressure
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profile with field observation is highly sensitive to the soil hydraulic properties used in the analysis. It was found that the SEEP/W flow model was able to capture the general trend of field behaviour of the changes in the pore-water pressure profile due to rainfall events. This could only be achieved by taking account of a more permeable surficial layer to allow for the presence of root passages and desiccation cracking. The results from the numerical models indicate that further research is warranted to improve the predictive ability of the numerical analysis by better definition of critical input parameters. REFERENCES Agus, S.S., Leong, E.C. and Rahardjo, H. (2003). A flexible wall permeameter for measurements of water and air coefficients of permeability of residual soils, Canadian Geotechnical Journal, Vol. 40, pp. 559–574. Agus, S.S., Leong, E.C. and Rahardjo, H. (2005). Estimating permeability functions of Singapore residual soils, Engineering Geology, Vol. 78, pp. 119–133. Agus, S.S., Leong, E.C. and Rahardjo, H. (2001). Soilwater characteristic curves of Singapore Residual soils. Geotechnical and Geological Engineering, Vol. 19, pp. 285–309. Anderson, M.G., Collison, A.J.C., Hartshorne, J., Lloyd, D.M. and Park A. (1996). Developments in Slope Hydrology-Stability Modeling for Tropical Slopes, Advances in Hillslope Processes, Vol. 2, pp. 799–821. Buma, J. (2000). Finding the most suitable slope stability model for the assessment of the impact of climate change on a landslide in SE France, earth Surface Processes Landforms. Vol. 25, pp. 565–583. Chappell, N.A, and Lancaster, J.W. (2007). Comparison of methodological uncertainties within permeability measurements. Hydrological Processes, Vol. 21, pp. 2504–2514. Chatterjea, K. (1989). Observations on the fluvial and slope processes in Singapore and their impact on the urban environment. PhD thesis, National University of Singapore, Singapore. Dehan, M., Burger, G., Buma, J. and Gasparetto, P. (2000). Impact of climate change on slope stability using expanded downscaling. Engineering Geology, Vol. 55, pp. 193–204. Dixon, N. and Brook, E. (2007). Impact of predicted climate change on landslide reactivation: case study of Mam Tor, UK. Landslides, Vol. 4, pp.137–147. Fredlund, D.G. (2007). Engineering Design protocols for unsaturated soils. Proceedings of the 3rd Asian Conference on Unsaturated Soils, eds. Yin, Z., Yuan, Z and Chiu, A.C.F. Science Press, Beijing, China, pp. 27–45. Fredlund, D.G., Xing, A. and Huang, S. (1994). Predicting the permeability functions for unsaturated soils using the soil-water characteristics curve, Canadian Geotechnical Journal, Vol. 31, pp. 533–546.
Gasmo, J.M., Hritzuk, K.J., Rahardjo, H. and Leong, E.C. (1999). Instrumentation of an unsaturated residual soil slope. Geotechnical Testing Journal, ASTM, 22(2), pp. 128–137. Geo-Studio (2004). User’s manual for SEEP/W, Geo-Slope International Ltd., Canada. Green, R.E. and Corey, J.C. (1971). Calculation of hydraulic conductivity: A further evaluation of some predictive methods, Soil Sci. Soc. Am. Proc. Vol. 35, pp. 3–8. Karthikeyan, M., Tan, T.S. and Phoon, K.K. (2001). Numerical oscillation in seepage analysis of unsaturated soils. Canadian Geotechnical Journal, Vol. 38, pp. 631–651. Novak, V., Simunek, J. and Genuchten, M. Th. (2000). Infiltration of water into soil with cracks. Journal of irrigation and Drainage Engineering, Vol. 126, No. 1, pp. 41–47. Pitts, J. (1984). A Review of Geology and Engineering Geology in Singapore, Quarterly Journal of Engineering Geology, Vol. 17, pp. 93–101. Rahardjo, H., Lee, T.T., Leong, E.C. and Rezaur, R.B. (2005). Response of a residual soil slope to rainfall. Canadian Geotechnical Journal, Vol. 42, pp. 340–351. Rahardjo, H., Li, X.W., Toll, D.G. and Leong, E.C. (2001). The Effect of Antecedent Rainfall on Slope Stability, Geotechnical and Geological Engineering, Vol. 19, No. 3/4, pp. 369–397. Rezaur, R.B., Rahardjo, H., Leong, E.C. and Lee, T.T. (2003). Hydrologic behavior of residual soil slopes. Journal of hydrologic Engineering, ASCE, Vol. 8, No. 3, pp. 133–144. Toll, D.G. (2001). Rainfall induced Landslides in Singapore, Proc. Institution of Civil Engineers: Geotechnical Engineering, Vol. 149, 4, pp. 211–216. Toll, D.G., Rahardjo, H. and Leong, E.C. (1999). Landslides in Singapore, Proc. 2nd International Conference on Landslides, Slope Stability and the Safety of InfraStructures, 27–28 July 1999, Singapore. Tsaparas, I. (2002). Field measurements and numerical modeling of infiltration and matric suctions within slopes, PhD Thesis, School of Engineering, University of Durham, United Kingdom. 314p. Tsaparas, I. and Toll, D.G. (2003). Factors affecting infiltration into an unsaturated soil slope. Proceedings of the 2nd Asian Conference on Unsaturated Soils (UNST-ASIA 2003), Osaka, Japan, pp. 463–468. Tsaparas, I., Rahardjo, H., Toll, D.G. and Leong, E.C. (2003). Infiltration characteristics of two instrumented soil slopes. Canadian Geotechnical Journal, Vol. 40, pp. 1012–1032. Van Genuchten, M.T. (1980). A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, Vol. 44, pp. 892–898. Van Genuchten, M.Th., Schaap, M.G., Mohanty, B.P. Simunek, J. and Leij, F.J. (1999). Modeling flow and transport processes at the local scale, in Modeling of transport process in soils at various scales, J. Feyen and K. Wiyo (eds.), Wageningen, The Netherlands, pp. 23–45.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Modelling unsaturated soil slopes subjected to wetting and drying cycles Y.D. Zhou, C.Y. Cheuk, L.G. Tham & E.C.Y. To Department of Civil Engineering, The University of Hong Kong, Hong Kong
ABSTRACT: Water infiltration changes the pore pressure distribution in unsaturated slopes leading to slope movement, and therefore has been one of the most common triggering mechanisms for landslides in tropical areas. Field monitoring data suggest that seasonal wetting and drying cycles cause gradual and progressive downward slope deformation, despite the fact that limited upward movement also occurs in dry seasons. This paper presents a numerical study aimed at examining the deformation and stress path characteristics in an unsaturated slope subjected to wetting and drying cycles. The results demonstrate that progressive deformation is caused by plastic deformation when the stress path of a soil element intercepts the failure criterion during wetting. The amount of plastic strain varies with locations, and depends on the initial stress state of the soil element as well as the amount of pore pressure change. The global behaviour of the slope is largely affected by stress re-distribution.
1
INTRODUCTION
Rainfall infiltration has been the major cause of many slope failures and landslides in many countries and regions where rainfalls of high intensity are frequent. Hong Kong is particularly susceptible to landslide risk due to its steep natural topography and prolonged periods of high intensity rainfall. In addition, many old fill slopes were formed in the early 1970’s by end-tipping on top of the natural ground with hardly any compacting effort. Rain-induced failures of loose fill slopes pose significant geotechnical threats and have caused severe damages and losses during the past decades (Lumb, 1975; Brand, 1984; Wong et al., 1998). The 1976 Sau Mau Ping landslide in Hong Kong (Hong Kong Government, 1977) that killed 18 people is a typical failure of loose fill slope. Relevant issues concerning rainfall-induced slope failures, such as the physical process of rainfall infiltration into unsaturated soil slopes (Li et al., 2005; Olivares & Damiano, 2007; Zhan et al., 2007), the influence of infiltrated water on soil suction and shear strength (Collins & Znidarcic, 2004; Farooq et al., 2004; Melinda et al., 2004; Zhang et al., 2004), and the relationship between periods of rainfall and appearance of sliding failures (Lumb, 1962; Ho & Fredlund, 1982; Brand, 1985; Fredlund & Barbour, 1992) have been investigated by many researchers using experimental or numerical approaches. Slope behaviour under cyclic changes of pore water pressure due to wetting and drying has not received as much attention. Field monitoring data collected from some local slopes which comprise residual soils suggest that,
during seasonal wetting and drying cycles, progressive downward slope displacements were mobilised, but the field records also reveal that limited upward movement occurred in some parts of the slopes during dry seasons. Nevertheless, the rebound could only partially recover the downward deformation triggered during the wetting process, leading to significant permanent deformation and possibly final collapse of the slope (Endicott, 2007). Very similar observations were also made in a field test conducted on a purpose-built loose fill slope (Li, 2003). A numerical study was carried out to examine the deformation pattern and the stress paths involved in the wetting and drying process. The numerical model considers an initial unsaturated slope formed by loose completely decomposed granite (CDG) which is commonly found in Hong Kong. This paper presents the representative results of the analyses and the implication of the bounce-back behaviour of slope movement is also discussed.
2 2.1
MODEL FOR UNSATURATED SOILS Basic assumptions
It has been identified that, for most decomposed soil slopes, the upper 3–4 metres of material remains unsaturated in its natural state due to the low groundwater table. This zone is therefore subjected to changing pore pressure distribution during seasonal rainfall. Hence, the role of matric suction has to be taken into account, which has been found to be absolutely crucial to the
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stability of unsaturated slopes (Fredlund & Rahardjo, 1993). Redistribution of moisture content may influence the slope deformation and stress distribution, as well as the global stability. In this study, the decomposed soil is treated as a porous medium and modelled by the conventional approach that considers soil as a multi-phase material and adopts the effective stress principle to describe coupled flow and deformation behaviour. The finite element packages ABAQUS were used as a platform for the analysis (ABAQUS 2006). The elementary volume of the soil material, dV , is made up of a volume of solid grains, dVg , and a volume of voids, dVv , i.e., dV = dVg + dVv . A volume of pore water, dVw ≤ dVv , is free to flow through the soil. It is assumed that the decomposed soil is permeable enough for the air phase to be exposed to the atmosphere, and a simplified effective stress principle originally proposed by Bishop (1955) can be formulated as follows: σ¯ = σ − χ (Sw ) uw I
(1)
where σ¯ and σ are the effective and total stresses respectively; uw denotes the pore water pressure; χ is a factor that depends on water saturation degree Sw , and is assumed to be equal to the saturation degree of soils; I is a second-order unit tensor.
The fundamental equations describing the stress equilibrium for the solid phase and flow continuity for pore water flow inside the soil are as follows: σ : δεdV = t · δvdS + f · δvdV s
V
Sw nρw g · δvdV
+
(2)
V
⎛
d⎝ dt
V
Sw nvw = −k ·
⎞ ρw ⎠ = − ρw Sw nn · vw dS S ndV w ρw0 ρw0
(3)
∂h ∂x
2.3
Solution algorithm
As the deformation behaviour of unsaturated soils is strongly coupled with pore fluid flow, the above stress equilibrium and flow continuity equations are solved simultaneously. The stress equilibrium equation is discretised using a Lagrangian formulation for the solid phase of the soil, with displacements taken as nodal variables, whilst the continuity equation is integrated in time using the backward Euler approximation method discretised with finite elements using pore pressure as a basic variable. It would be in general a nonlinear case when the seepage and deformation behaviour are coupled in the established system equations, and the Newton-Raphson method is applied during the incremental numerical solutions.
3.1
SLOPE MODEL Slope geometry and finite element discretisation
A simple 2-D slope model is established, as shown in Figure 1. The geometry of the slope is the same as the central section of a real slope on which field tests were conducted (Li, 2003). The exemplary slope has an inclination angle of 33◦ to the horizontal, which is equivalent to an average slope angle of 1 on 1.5, similar to many existing loose fill slopes in Hong Kong (Sun, 1999). The slope is 4.75 m high with a flat crest of 4 m. The slope is discretised using a finite element mesh which is made up of 1142 plane strain 4-node bilinear
s
where δε = sym (∂δv/∂x) denotes the virtual rate of deformation; δvis a virtual velocity field; t are surface tractions per unit area; f are body forces (excluding pore water weight) per unit volume; n is the porosity of soils; ρw is the water density, and g is the gravitational acceleration; vw is the seepage velocity; n is the outward normal to S; ρw0 is the reference density of pore water for normalization of the flow continuity equation. Darcy’s Law (Equation 4) is adopted to simulate the pore water flow in the soil, which has been shown to
(4)
where k denotes the soil permeability and h is the piezometer head, defined as h = z +uw /ρw g, in which z is the elevation above a reference datum and g is the gravitational acceleration.
3
2.2 Governing equations
V
be valid for unsaturated soils as well as saturated soils (Fredlund & Rahardjo, 1993).
Figure 1.
836
Finite element model of a loose fill slope.
elements. To allow coupling between pore fluid and mechanical calculations, finite elements with multiple degrees of freedom including pore pressure and displacements are adopted. Material model and parameters
The model slope is formed entirely by CDG, a common soil type in Hong Kong. For simplicity, the CDG is modelled by an elasto-plastic model with a MohrCoulomb (M-C) failure criterion and non-associated flow. As assumed in most critical state models, nonlinearity is incorporated into the elastic part of the stress-strain relationship, and the bulk modulus K is assumed to be a function of the effective mean stress p according to K=
ν ∂p = p ∂εve κ
(5)
where εve denotes the elastic volumetric strain, ν is the specific volume, and κ is the slope of an unloadingreloading line in the ν −ln p space. The Poisson’s ratio μ is assumed to be constant, and the shear modulus G can be written as G=
3(1–2μ) K 2(1 + μ)
(6)
τ = c + (σ − χ · uw ) tan φ
Properties
Summary of material parameters. Loose fill
γd = 1.41 Mg/m3 , e0 = 0.86, w0 = 14.9%, μ = 0.05 Elastic Function (Equations 5 and 6) κ = 8.4 × 10−3 Shear strength c = 2 kPa, φ = 30◦ , ψ = 5◦ Hydraulic Function (Figures 2 and 3)
Basic
To incorporate the contribution of matric suction to shear strength, Fredlund et al. (1978) proposed a modified M-C failure criterion based on unsaturated soil mechanics, in which two friction angles, φ and φ b are used to quantify the increased shear strength associated with the net normal stress and the matric suction respectively. For residual soils in Hong Kong, the value of φ b was found to be equal to or less than φ (Gan & Fredlund, 1996), and an equality of these two angles is assumed in this paper such that the original M-C failure criterion follows:
Table 1.
Note: w, γd , e are moisture content, dry density, void ratio respectively, and the subscript ‘‘0’’ denotes the initial value.
7 Permeability coefficient (10–5m/s)
3.2
A smooth flow potential function proposed by Menétrey and Willam (1995) is adopted in the numerical model, which has a hyperbolic shape in the meridional stress plane and a piecewise elliptic shape in the deviatoric stress plane. It should be noted that plastic flow in the deviatoric and meridional planes is in general non-associated. Table 1 summarises the model parameters adopted in the analyses which are derived from relevant experimental results (Li, 2003). A perfect plastic hardening law is assumed in the calculations. To control possible dilation caused by the flow potential, the angle of dilation (ψ) is chosen as a small value (ψ = 5◦ ). Hydraulic properties of the CDG, including the permeability coefficient as a function of saturation degree (Sw ) and the adopted soil water characteristics curve (SWCC), are shown in Figures 2 and 3 respectively. No hysteresis is considered in this study, since field measured results suggested that the SWCC during wetting and drying are very similar (Li, 2003). Nonetheless, the possible influence due to hysteresis should be explored as a further study.
(7)
where τ is shear strength on the failure plane; c is the intercept of the ‘‘extended’’ M-C failure envelope on the shear stress axis where the net normal stress and the matric suction at failure are zero; σ is the total normal stress on the failure plane; uw is the pore water pressure on the failure plane and φ is the angle of internal friction. When uw is negative, its magnitude is equivalent to matric suction (ua − uw ) since pore air pressure, ua , is assumed to be zero. It should be noted that the assumption of φ = φ b may not be valid, particularly at low degrees of saturation. As a preliminary study, this assumption has been adopted.
6 5 4 3 2 1 0 30
40
50 60 70 Degree of saturation (%)
80
Figure 2. Permeability coefficient vs. degree of saturation for the loose fill.
837
Volumetric moisture content (%)
50 45 40 35 30 25 20 15 10 5
defined on the right vertical edge of the model to simulate free water flow out of the slope when the soil at this location is fully saturated, whilst other boundaries are assumed to be impervious. 4 4.1 0
Figure 3.
5
10
15 20 Suction (kPa)
25
30
Water retention curve for the loose fill.
10 AB C D Flux (Litre/minute)
8 6 4 2 E 0
0
Figure 4.
3.3
1
2
3
4 Day
5
6
7
Time history of wetting flux.
Loading and boundary conditions
The initial values of the void ratio and saturation degree of the soil are taken as 0.86 and 0.454 respectively. These values are chosen based on the initial conditions measured in a field test (Li, 2003). The initial distributions of internal stresses and pore water (including suction) pressures within the slope under the gravity loads are obtained by a long-term redistribution through attaining equilibrium conditions in the numerical model, before applying the flux (loading) conditions. The prescribed wetting and drying process is shown in Figure 4. Two cycles of a half day rainfall with a total boundary flux of 8 litres per minute (equivalent to 63 mm/hour) separated by half day of drying are applied in the upper region of the slope (Figure 1). The calculations continue for five and a half days to achieve equilibrium pore pressure distribution. The displacement boundary conditions of the numerical model are taken as vertical rollers on the left and right vertical boundaries, with full fixity along the base. Moreover, free drainage boundary condition is
RESULTS AND DISCUSSIONS Displacements
Figure 5 plots the variation of horizontal displacement at some typical points within the slope during the wetting and drying process. Three nodes, located on the slope crest (Node 703), at the middle of the slope surface (Node 475) and near the slope toe (Node 1559) are chosen. Their locations are shown in Figure 1. Corresponding soil elements containing these nodes are also marked in Figure 1 and their centroid points are denoted as ‘‘CPx’’, in which x represents the element number. It can be observed that at all the three locations, the horizontal displacements generally increase during the wetting periods. The horizontal displacements, which are mainly pointing downwards, are caused by water infiltration which reduces the suction, and hence shear strength of the material. It is, however, interesting to see that only the soil at the mid-height of the slope (Node 475) exhibits reserved uphill movement during the half-day pause between the first and the second rainfall events. The deformation occurred at the slope crest and slope toe remains permanent. This is mainly caused by pore pressure redistribution occurred during the first drying period. On the other hand, a consistent reversed trend is observed under the effect of longterm drying process. Despite the consistent general displacement trends, there are some differences between the deformation patterns at different locations. For Node 703 at the slope crest, small negative horizontal and upward displacement is initially mobilised during the first two
Figure 5. Variation of horizontal displacement at typical points during the wetting and drying process.
838
hours of wetting and then the direction of the deformation changes to downward. Similar deformation pattern can be observed at this location during the second wetting period. This observation can be explained by the elastic swelling behaviour exhibited by the soil on the upper surface of the slope crest when the effective mean stress of the soil is reduced during water infiltration. For the Nodes 475 and 1559 located on the inclined surface, the rate and magnitude of the downward movement at the slope toe (1559) are much smaller than those at the middle of the slope (475), which can be attributed to the fact that Node 1559 is outside the wetting area. Moreover, it can be seen that only small horizontal bounce-back is observed for the soil at Node 1559 during the first drying period, whilst the soil at Node 475 displays prominent reversed movement. The calculated results also suggest that larger horizontal displacements are triggered in the soils beneath the central part of the inclined slope surface, up to a depth of ∼2 m. The numerical results suggest that the soils at typical positions would not rebound back to the initial locations corresponding to the start of first wetting process, even after a sufficiently long drying process. The permanent and progressive downward movements are consistent with field observations. 4.2 Stress path characteristics It is expected that, for a soil element subjected to an increase in pore pressure due to water infiltration, the effective mean stress, denoted as p , would decrease. The deviatoric stress, denoted as q, would also change due to stress redistribution. Figure 6 presents the stress path of some typical elements in the q − p plane during the wetting and drying cycles. These points are located at the upper region (CP573), middle region (CP425) and lower region (CP1306) of the slope as shown in Figure 1. Different stages during the wetting and drying cycles are marked, which can be referred to Figure 4. The M-C shear failure surfaces are shown for reference. It should be noted that the slope and the location of the M-C failure criterion are not unique when the three dimensional surface is plotted in the q − p plane due to the change in the intermediate principal stress. Therefore, both the upper and lower bounds of the failure surface, which represent the highest and lowest projections of the yield function on the q − p plane respectively, are presented for indication of possible yielding in shear. In general, significant changes in the stress state caused by the wetting and drying effect can be observed for all the three chosen locations. For elements CP425 and CP573, which are directly affected by the surface infiltration, a reduction in both q and p is induced during the wetting periods, i.e., from A to B, and from C to D, whilst a reversed pattern is observed
Figure 6.
Stress path in the q − p plane at typical points.
during the drying periods, i.e., from B to C, and from D to E. However, the trend of the response at CP1306 is opposite, showing an increasing trend during the wetting stages and a reduction during the drying stages. The opposite observation can be attributed to the fact that CP1306 is positioned near the slope toe where the mobilised shear stress is increased when the shear
839
strength at the upper portion of the slope is reduced due to wetting. It is also found that the stress states at most of the material points would not return back to the initial state corresponding to the start point of first wetting process, which can be mainly attributed to the effect of redistribution of internal stress and pore water pressure by the wetting and drying cycles. Particularly for the soil at CP573, significant plastic deformation is mobilised during the two wetting stages, and additional plastic strain is also induced during the long drying process due to the redistribution of pore water within the loose fill, as presented in Figure 6(b) the stress path approaches the upper failure bound during the later period. 5
CONCLUSIONS
To investigate the deformation behaviour of unsaturated slopes during the wetting and drying cycles, a preliminary numerical study has been carried out on a typical loose fill slope subjected to periodical wetting and drying. Some representative results of horizontal displacement and stress path at typical points are presented. It is found that the simple numerical model is capable of predicting the bounce-back behaviour which is consistently observed from field monitoring records collected from some local slopes. Nevertheless, gradual permanent deformation is also predicted during each wetting process. The mobilisation of plastic deformation is accompanied by stress redistribution. The results indicate that the global behaviour of the unsaturated slope is largely influenced by stress redistribution during and after rainfall infiltration. More detailed analyses are underway aiming to identify if this behaviour would reach a steady state after a large number of wetting and drying cycles, and also the sensitivity of the major governing parameters including the soil properties and the rainfall pattern. REFERENCES ABAQUS Inc. 2006. Analysis user’s manual, Version 6.6. Bishop, A.W. 1955. The principle of effective stress. Lecture delivered in Oslo, Norway, in 1955; published in Teknisk Ukeblad, 106 (39): 859–863, 1959. Brand, E.W. 1984. Relationship between Rainfall and Landslides in Hong Kong, Proceedings of 4th International Symposium on Landslides, Toronto, 1: 377–384. Brand, E.W. 1985. Landslides in Hong Kong. VIII Southeast Asian Geoth. Conference Kuala Lumpur: 1–15. Collins, B.D. & Znidarcic, D. 2004. Stability analyses of rainfall induced landslides. Journal of Geotechnical and Geoenvironmental Engineering, 130 (4): 362–372. Endicott, L.J. 2007. Private communication. Farooq, K., Orense, R. & Towhata, I. 2004. Response of unsaturated sandy soils under constant shear stress drained condition, Soils and Foundations, 44 (2): 1–13.
Fredlund, D.G. & Barbour, S.L. 1992. In R.N. Chowdhury (ed.), Integrated seepage modelling and slope stability analysis: A generalized approach for saturated /unsaturated soils. Balkema: 3–35. Fredlund, D.G., Morgenstern, N.R. & Widger, R.A. 1978. Shear Strength of unsaturated soils. Canadian Geotechnical Journal, 15 (3): 313–321. Fredlund, D.G. & Rahardjo, H. 1993. Soil mechanics for unsaturated soils, Wiley: New York. Gan, J.K.M. & Fredlund, D.G. 1996. Direct shear and triaxial testings of a Hong Kong soil under saturated and unsaturated conditions. Geotechnical Engineering Office, Hong Kong Government. Ho, D.Y. & Fredlund, D.G. 1982. Increase in strength due to suction for two Hong Kong soils. ASCE Conference on Engineering and Construction in Tropical and Residual Soils. Honolulu: 263–295. Hong Kong Government. 1977. Report on the Slope Failure at Sau Mau Ping, August 1976, Hong Kong Government Printer. Li, A.G., Yue, Z.Q., Tham, L.G., Lee, C.F. & Law, K.T. 2005. Field-monitored variations of soil moisture and matric suction in a saprolite slope, Canadian Geotechnical Journal, 42 (1): 13–26. Li, J. 2003. Field study of a soil nailed loose fill slope. PhD. Thesis, The University of Hong Kong, Hong Kong. Lumb, P. 1962. Effects of rain storms on slope stability. Symposium on Hong Kong Soils: 73–87 Lumb, P. 1975. Slope Failures in Hong Kong, Q.J. Engng. Geol, 8: 31–65. Melinda, F., Rahardjo, H., Han, K.K. & Leong, E.C. 2004. Shear strength of compacted soil under infiltration condition, Journal of Geotechnical and Geoenvironmental Engineering, 130 (8): 807–817. Menétrey, P. & Willam, K.J. 1995. Triaxial failure criterion for concrete and its generalization. ACI Structural Journal, 92 (3): 311–318. Montgomery Watson Hong Kong Limited (MWH). 2000. Re-assessment of stability conditions and proposal of remedial works for feature No. 8SW-C/CR175. Report to Water Supplies Department, Hong Kong SAR Government. MWH Limited, Hong Kong. Olivares, L. & Damiano, E. 2007. Postfailure mechanics of landslides: Laboratory investigation of flowslides in pyroclastic soils, Journal of Geotechnical and Geoenvironmental Engineering, 133 (1): 51–62. Sun, H.W. 1999. Review of fill slope failures in Hong Kong. GEO Report No. 96, Geotechnical Engineering Office, Hong Kong. Wong, H.N., Ho, K.K.S., Pun, W.K. & Pang, P.L.R. 1998. Observations from Some Landslide Studies in Hong Kong, Slope Engineering in Hong Kong, Balkema: Rotterdam: 277–286. Zhan, T.L.T., Ng, C.W.W. & Fredlund, D.G., 2007. Field study of rainfall infiltration into a grassed unsaturated expansive soil slope, Canadian Geotechnical Journal, 44 (4): 392–408. Zhang, L.L., Fredlund, D.G., Zhang, L.M. & Tang, W.H. 2004. Numerical study of soil conditions under which matric suction can be maintained. Canadian Geotechnical Journal, 41 (4): 569–582.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Numerical analysis of piezocone penetrometer testing in partially saturated marine sediments A. Haghighi, B. Gatmiri & V. De Gennaro Ecole des Ponts (Université Paris-Est, Navier Institute – CERMES), Paris, France
N. Sultan IFREMER, Brest, France
ABSTRACT: During exploration and exploitation in deep offshore areas (beyond 1000 metres depth) oil companies have recently been faced with geotechnical problems related to the presence of shallow gas in marine sediments leading to eruptions during drilling, difficulties in conductor installation and anomalous high pore pressures measurements during piezocone penetrometer testing (PCPT). Gassy soils can result from various factors, including hydrates dissociation. They represent a critical issue for the oil and gas industry, at least for two reasons: (i) the detection of gas is still not reliable, and (ii) the effect on the mechanical properties of the soil is still rather unclear. In this paper a preliminary numerical analysis of an ideal piezocone penetration in gassy sediment is presented. This study will serve as a basis in view of a possible interpretation of available in situ measurement of cone penetration resistance in gas-bearing sediments.
1 1.1
INTRODUCTION Procedure of gas production in soil
Gas-bearing soils, which are called ‘‘gassy soils’’, are the subject of renewed research interest. Gases that can be found in marine sediments are: carbon dioxide, hydrogen sulphide, ethane and methane, but methane is the only gas that can be found in large quantities. Methane is produced from a biogenic or an abiogenic process. The former is related to bacterial activity that could develop at depth below the seabed, and time has a significant effect in this process (Mitchell & Santamarina, 2005). The latter could be the result of thermal degradation of organic matter in deep sediments. The gases produced by these two procedures may migrate toward the surface and become trapped as shallow gas accumulation. Although the organic origin of methane is the most commonly accepted source, hydrothermal or volcanic emanations may also result in shallow gas accumulations (Floodgate & Judds, 1992; Grozic & Kvalstad, 2001). These two sources are considered to be the most plausible for natural shallow gas accumulations on continental shelves, and destabilization of methane gas hydrates is a further potential source of shallow gases. The most interesting subject in this area in the last two decades is mainly related to the engineering properties of deep offshore gassy sediments (i.e. their compressibility and strength) closely related
to the increasing activity of the oil production industry and offshore installations safety (Wheeler, 1988a, b). Free gas phases can be encountered not only in deep offshore gassy sediments (typically from 300 m to 1500 m water depth) but also at shallower depths in cold areas (e.g. Arctic). The presence of undissolved gases in pore water has an important impact also in other fields of geomechanics. Decrease of shear strength and increase of the sediment compressibility could be the result of the presence of voids in the soil, and could also alter the response to cyclic loading (e.g. tidal waves) affecting the mechanical stability of the sediments. Therefore, understanding of the mechanical behaviour of gassy sediments should be placed in the broad context of environmental risks and geohazards. An important environmental risk is gas release in marine sediment which could cause the destabilization of submarine slopes (Sultan et al., 2004). These slopes (even at angles of a few degrees) are often close to their stability limit. It is therefore important that the geotechnical identification of marine sediments using the piezocone penetrometer test (PCPT) is better understood particularly the influence of gases on the response of the piezocone in terms of pore water pressure and tip resistance measurements. This understanding will then be useful to propose a method for the interpretation of piezocone tests in gassy soils and help develop, if needed, improved probes for this type of soil. In this
841
work the effect of the penetration of a piezocone in a partially saturated medium is studied. The piezocone penetration is simulated using the finite-element code θ-STOCK (Gatmiri, 1997; Gatmiri & Delage, 1997; Jenab, 2000) and the similarity between this process and a cavity expansion problem in partially saturated (gassy) sediment is to be noted. Special attention is paid to the development of elasto-plastic formulations capable of reproducing the characteristic features of the mechanical behaviour of unsaturated soils. A fully coupled thermo-hydro-mechanical approach able to take into account the effect of partial saturation will be used, considering gas-liquid suction as an additional state variable. Emphasis is given to the effect of partial saturation on the evolution of the pore water pressure in the vicinity of the probe shaft.
2
FIELD EQUATIONS AND FEM FORMULATION
Unsaturated soil mechanics is a relatively new area of research in geotechnical engineering and possibly the area where the most significant advances have been made during recent years. There is now a general consensus on the choice of adequate and independent state variables able to present most of the significant effects involved in the coupled process of a deformable unsaturated porous medium with three phases (skeleton, water and air). The two independent tensorial variables: net stress σ − ua and suction ua − uw , (where σ is the total stress, and ua and uw the air and water pressures, respectively) have been adopted. Based on this choice, the basic assumptions for the description of the thermo-hydro-mechanical behaviour of an unsaturated porous medium are presented. The finite element code θ -STOCK is used here to integrate the resulting field equations and to simulate the penetration of a piezocone probe in a partially saturated sediment. 2.1
Mechanical equations
The total deformation of the porous medium can be evaluated by using the equilibrium equation of the skeleton with a constitutive law. In this paper isotropic nonlinear elastic behaviour has been considered. The equilibrium equation and the stress-suction-strain relation which considers the effect of suction on strain can be written as follows: (σij − δij ua ),j +ua,j + bi = 0 dεij =
−1 Cijkl d(σkl
− δkl ua ) +
Fij−1 d(δij (ua
modulus matrix. The nonlinear elasticity matrix Cijkl is a function of the independent variables σ − ua and ua − uw . 2.2 Hydraulic equations Mass conservation equation of water and air can be written as follows: ∂ (ρw nSr ) + div(ρw vw ) = 0 ∂t ∂ [ρa n(1 − Sr + HSr )] + div[ρa (va + Hvw )] = 0 ∂t
where σij is the stress tensor, εij is the strain tensor, Cijkl the elasticity matrix, and Fij the suction
(4)
where n is porosity, Sr is degree of saturation, H is the Henry’s constant, ρa and ρw are the air and water densities. Water and air flow are assumed to be governed by Darcy’s law: uw vw = −K w .grad +Z (5) γw ua va = −K a .grad +Z (6) γa Water and air permeabilities (Kw , Ka ) are tonsorial values and depend on the suction (Gatmiri et al., 1998). Figure 1 presents an example of variation of gas relative permeability as a function of e and Sr . The total moisture movement in unsaturated soil due to temperature gradient and its resulting moisture content gradient is equal to the sum of the flows which take place in both phases, vapor and liquid. Thus: q = −DT ∇T − Dθ ∇θ − Dw ∇Z ρw
(7)
where DT is thermal moisture diffusivity and its equal to DTV + DTW , and Dθ is thermal moisture diffusivity and it is equal to DθV + DθW . Combining, therefore, equations (3) and (7) yields the general differential equation in an alternative form: ∂Sr ∂ρw ∂T ∂ρw ∂P nSr + nSr + (ρw − ρv )n ∂T ∂t ∂P ∂t ∂t ∂n ∂ρv + n(1 − Sr ) ∂t ∂t = ρw div(Dw ∇z) + div(ρw DT ∇T )
+ (Sr ρw + ρv (1 − Sr ))
(1) − uw )) (2)
(3)
(8)
+ div(ρw Dθ ∇θ) + Qm 2.3 State surface During the last three decades, various constitutive laws have been proposed, such as the incremental
842
3
Figure 1.
Cavity expansion has been the subject of extended studies in soil mechanics, mostly related to the behaviour of saturated soils (e.g. Carter et al., 1979; Collins & Yu 1996). When dealing with unsaturated soils few contributions are available and, with few exceptions (e.g. Schnaid et al. 2005), contributions are essentially theoretical (e.g. Russell & Khalili 2002). One of the issues associated with the use of CPT or pressuremeters for the mechanical characterization of unsaturated soils is the evolution of suction during probing (Gallipoli, 2005). This is an open question which deserves further analysis, both theoretically and experimentally, for a correct interpretation of these tests. In what follows a preliminary numerical analysis, based on the state surface approach proposed in θ-STOCK code, is presented and results are briefly discussed.
Gas relative permeability (Gatmiri 1997).
elastic formulation suggested by Coleman (1962) and Fredlund (1979), and the state surface concept developed in order to describe the volumetric behaviour of soil under the coupled effects of net stress and suction changes. Alonso et al. (1988) have adapted two independent expressions for state surface of void ratio and degree of saturation. These two state surfaces are the following: Sr = 1 − [as + ds (σ − ua )]th[bs (ua − uw )]
(9)
e = de + ae log(σ − ua ) + be log(ua − uw ) + ce log(σ − ua ) log(ua − uw )
(10)
The formulations of the state surfaces proposed by Gatmiri and Delage (1995) considered in the code of θ-STOCK are as follows: Sr = 1 − [as + ds (σ − ua )][1 − exp(cs (ua − uw ))] (11)
e=
⎡
1+e0
(σ −ua ) (σ − ua ) + b 1− ⎢ a P σe ⎢ atm exp ⎢ ⎣ Kb (1 − m)
(ua − uw ) Patm
CAVITY EXPANSION MODELLING IN UNSATURATED SOIL
1−m ⎤−1 ⎥ ⎥ ⎥ ⎦
(12)
3.1
Mechanical properties of the sediment
The sediments used for the mechanical characterization were retrieved at 1500 m depth in Gulf of Guinea, in an area rich of methane hydrates. Development of petroleum activity in this area may cause a change in the thermodynamic conditions of stability of gas hydrates (in terms of pressure, temperature, salinity) and the dissociation of gas hydrates may result in the generation of gas in the sediment around. Four oedometric tests were carried out on the samples at different depths (3, 5, 8 and 10 m below the seabed). These oedometric tests allowed the identification of the coefficients of compressibility Cc and swelling Cs of the sediment and its consolidation state. The sediment at the shallower depth, from 0 to 7 m, is slightly overconsolidated (OCR between 1.8 and 2); in the deeper layer beyond 7 m, the OCR ranges between 0.68 and 0.8. Granulometric tests carried out along the core sample showed a very fine homogeneous sediment with a majority of argillaceous and silt fractions. Measurements of the coefficients of permeability were carried out during the oedometric tests. The variation of the coefficients of permeability according to the void ratio presents the same tendency on the whole of the sample (Fig. 2). The permeability varies between 1.5 × 10−8 and 5 × 10−9 m/s for a void ratio between 2 and 3.8. Measurements of undrained cohesion by means of vane tests were carried out on core sample N2-KSF43 to obtain information on the consolidation state of the sediment. Indeed, through knowledge of the relationship between undrained cohesion Su and the effective stress σv we can approximately define the consolidation state of the sediment (Skempton & Bishop, 1950). The result can be clearly seen in Figure 3. A ratio Su /σv close to one is
843
Figure 3. Consolidation state of the sediment: (a) undrained cohesion vs. depth and (b) Vp measurements (Vernant et al., 2004).
10 cm
Axis of cavity
0.1 R0
R0
100 cm
Figure 4. Axisymmetric model for the spherical cavity expansion. Figure 2. a) Oedometric curve b) Variation of the permeability as a function of void ratio (Vernant et al., 2004).
typical of normally consolidated clays. Values of Su /σv exceeding unity identify an overconsolidated state. When Su /σv is lower than one a state of underconsolidation is suspected, with pore-water pressures that exceed the hydrostatic pressure (Hutchinson, 1970). Thus, a state of under-consolidation of the sediment is possible below a depth of 5 m (Fig. 3a). Measurement of velocity of the P-waves was carried out using an ‘‘IFREMER-celerimeter’’. A sharp reduction of approximately 10 m/s in Vp (compression wave velocity) below a depth of 5 m is clearly identified. The results of Figure 3 confirm the state of underconsolidation of the sediment below a depth of 5 m (Vernant et al., 2004). 3.2
Modelling and results
The numerical analysis focussed on a soil layer 100 centimetres in radius and 10 cm in depth (Fig. 4) simulated using an axisymmetric model. The speed of
penetration of the piezocone is 2 cm/sec, the depth of the piezocone is 10 cm and the diameter is 3.56 cm. There are several methods described in the literature to analyse and interpret the piezocone penetration problem: Bearing capacity methods (BCM), Cavity expansion methods (CEM), Strain path methods (SPM), and finite element methods (FEM) are examples. In this paper, the finite element simulation of the piezocone penetration is assumed to be completed in two stages by the use of the cavity expansion theory. In the first stage, the piezocone is radially expanded from an initial small radius (0.1 R0 ) to the piezocone radius, R0 (piezocone volume expansion). The use of an initial small radius in the cavity expansion is necessary in numerical analysis to avoid infinite strain (Abu-Farsakh et al., 2003). In the second stage, the continuous penetration of the piezocone penetrometer is simulated by imposing incremental vertical displacements of the nodes representing the piezocone boundary. The rate of volume expansion in the first stage was set up such that the time required for expansion is equal to the time needed to penetrate the piezocone to that depth at the rate of 2 cm/s. This stage
844
1.0
8
Sig-Pa=25 Kpa Sig-Pa=50 Kpa Sig-Pa=100 Kpa Sig-Pa=150 Kpa Sig-Pa=200 Kpa Sig-Pa=250 Kpa Sig-Pa=300 Kpa Sig-Pa=350 Kpa Sig-Pa=400 Kpa
7 0.9
Degree of saturation
Sig X (MPa)
6 5 4 3 Stage 1, s=15 (Kpa), D=5 (m)
2
0.8
0.7
0.6
Stage 1, s=5 (Kpa), D=5 (m)
1
Stage 2, s=15 (Kpa), D=5 (m) 0.5
0 1
10
100
1000
10000
0
100000 1000000 10000000
50000
100000
150000
200000
Capillary pressure (Pa)
Time (S)
Figure 7. Trace of surfaces of the degree of saturation for the various values of net stress.
Figure 5. Variation of horizontal stress close to the surface cavity as a function of time.
40
1
Stage 1, s=5 (Kpa), D=5 (m) 30
Stage 2, s=15 (Kpa), D=5 (m)
0.9 Succion (Kpa)
degree of saturation
Stage 1, s=15 (Kpa), D=5 (m)
35
0.95
0.85 0.8
25 20 15
0.75 Stage 1, s=15 (Kpa), D=5 (m)
0.7
Stage 1, s=5 (Kpa), D=5 (m)
0.65
Stage 2, s=15 (Kpa), D=5 (m)
10 5 0
0.6 1
10
100
1000
10000
1
100000 1000000 10000000
10
100
1000
10000
100000
1000000
10000000
Time (S)
Time (S)
Figure 6. Variation of degree of saturation close to the cavity surface as a function of time.
provides the initial conditions for the second stage. The second stage simulates the continuous penetration of the piezocone by applying incremental vertical displacements at the nodes representing the piezocone boundary. The finite element mesh and boundary conditions used in this study are presented in Figure 4. An axisymmetric finite element mesh of eightnoded quadrilateral elements with four Gaussian integration points per element was used in this simulation. The proposed numerical model is used to study the effects of the vertical and lateral stresses caused by cone penetration on the variation of suction, degree of saturation and stresses in the soil elements around the piezocone. For the current analysis the effect of temperature is not considered. In this modelling four different depths have been simulated and for each depth, two different suctions are considered. The numerical results of both stages at 5 m depth are presented in Figures 5–8 considering two values of suction: 5 kPa and 15 kPa. These low values of suction correspond to the situation in which the sediments
Figure 8. Variation of suction close to cavity surface as a function of time.
is almost water saturated but still gas-water menisci are present. The evolution of horizontal stresses is presented in Figure 5. It is noticeable that after stabilization, the value of the stress only depends on the depth and is not changed by suction, however for the points near the cavity surface the horizontal stress decreases with the increase in the initial suction value. The variations of degree of saturation during expansion are presented in Figure 6. It is clear that increasing the amount of suction causes a decrease in the degree of saturation. It should be noted that the degree of saturation changes very little with the depth. The relationship between suction and degree of saturation plays an essential role in determination of mechanical and hydraulic behaviour of unsaturated soils. Several mathematical equations have been proposed for determination of soil water retention curves by several researchers (e.g. Lloret and Alonso, 1985; Fredlund and Xjng, 1994). The water retention curve used in this research, is given by equation (11). Parameters as , bs and ds were adjusted to best fit the soil water retention curve of the marine sediment found in the
845
laboratory. The values of these parameters used in this research are 0.75, 0.1 × 10−4 and 0.11 × 10−4 respectively. The water retention curves in terms of degree of saturation are illustrated in Figure 7, for the various values of mean net stress. The variations of suction close to the cavity surface during expansion are presented in Figure 8. It can be seen that during the horizontal loading, suction in the first centimetres of the model, during 5 seconds of loading, increases and then decreases. These evolutions are not influenced by the depth, but do depend on initial suction. 4
CONCLUSION
An axisymmetric modelling of the piezocone penetration in partially saturated marine sediment is simulated using the finite element code θ -STOCK, developed at CERMES by Gatmiri (1997), and the concept of the cavity expansion theory is extended to accommodate the framework of unsaturated soil behaviour. The variables considered were net stress and suction. The adopted thermo-hydro-mechanical approach allows the analysis of the effect of suction on the deformation of the skeleton and the permeability of water and air, as well as the influence of the stress state on the evolution of the degree of saturation and the pore water pressure. For the given initial condition (almost saturated sediment) it was found that suction decreases during cavity expansion and that the limit value of horizontal stress is not dependent on suction but only on initial stress state (i.e. depth). However, for points near the surface cavity, horizontal stress decreases with an increase in initial suction value. Further work is planned to validate the theoretical approach and to correlate numerical analyses with available in situ measurements. REFERENCES Carter, J.P., Randolph, M.F. & Wroth, C.P. 1979. Stress and pore pressure changes in clay during and after the expansion of a cylindrical cavity, International Journal for Numerical and Analytical Methods in Geomechanics 3: 305–322. Collins, I.F. & Yu, H.S. 1996. Undrained cavity expansion in critical states soils. International Journal for Numerical and Analytical Methods in Geomechanics 20: 489–516. Coleman, J.D. 1962. Stress strain relations for partly saturated soil. Géotechnique 12 (4): 348–350.
Floodgate, G.D. & Judds, A.G. 1992. The origin of shallow gas. Continental shelf Research 12 (10): 1145–1156. Fredlund, D.G. & Xjng, A. 1994. Equations for the soilwater characteristic curve. Canadian Geotechnical Journal 31: 521–532. Fredlund, D.G. 1979. Appropriate concepts and technology for unsaturated soils. Can. Geotech. J. 16: 121–139. Gallipoli, D. 2005. Unsaturated constitutive surfaces from pressuremeter tests—Discussion. Journal of Geotechnical and Geoenvironmental Engineering, 130 (2): 1181–1183. Gatmiri, B. 1997. Analysis of fully Coupled Behaviour of Unsaturated Porous Media under Stress, Suction and Temperature Gradient. Final report of CERMES-EDF, ENPC. Gatmiri, B. & Delage, P. 1997. A formulation of fully coupled thermal-hydraulic-mechanical behaviour of saturated porous media—numerical approach. Int. J. Numer. Anal. Meth. Geomech 21 (3): 199–225. Gatmiri, B. & Delage, P. & Cerrolaza, M. 1998. UDAM: A powerful finite element software for the analysis of unsaturated porous media. International journal of advances in engineering software 29 (1): 29–43. Grozic, J.L.H. & Kvalstad, T.J. 2001. Effect of gas on deepwater marine sediments. Conference on Marine Geotechnical Engineering 1: 329–344. Hutchinson, J.N. 1970. A coastal mudflow on the London clay cliffs at Beltinge, North Kent. Géotechnique, 20 (4): 412–438. Jenab, B. 2000. Etude numérique de la modélisation thermoélasto-plastique des sols non saturés. Thèse ENPC, CERMES. Lloret, A. & Alonso, E.E. 1985. State surface for partially saturated soil, In proceedings international conference soil mechanics and foundation engineering, San Francisco 1: 557–562. Mitchell, J.K. & Santamarina, J.C. 2005. Biological considerations in geotechnical engineering. J. Geotech. Geoenviron. Eng. 131 (10). Russell A.R. & Khalili, N. 2002. Cavity expansion in unsaturated soils. Proc. Unsaturated soils conference, Recife (Brasil) Jucà, de Campos & Marinho (eds): 233–238. Schnaid, F., Kratz de Oliveira, L.A. & Gehling, W.Y.Y. 2005. Unsaturated constitutive surfaces from pressuremeter tests. Journal of Geotechnical and Geoenvironmental Engineering, 130 (2): 174–185. Skempton, A.W. & Bishop, A.W. 1950. The measurements of the shera strength of soils. Géotechnique, 2 (2): 90–116. Sultan, N., Cochonat, P., Foucher, J.P. & Mierent, J. 2004. Effect of gas hydrates melting on seafloor slope instability. Marine Geology 213: 379–401. Vernant, A.M., Sultan, N. & Colliat, J.L. 2004. Etude des propriétés acoustiques d’un sédiment marin en présence de gaz. Journées AUM/AFM, France. Wheeler, S. 1988. A conceptual model for soils containing large gas bubbles. Géotechnique 38 (3): 399–397. Wheeler, S. 1988. The undrained shear strength of soils containing large gas bubbles. Géotechnique 38 (3): 399–413.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Experimental and numerical studies of the hydromechanical behaviour of a natural unsaturated swelling soil H. Nowamooz, M. Mrad, A. Abdallah & F. Masrouri Laboratoire Environnement Géomécanique & Ouvrages, École Nationale Supérieure de Géologie, Institut National Polytechnique de Lorraine, France
ABSTRACT: This paper presents an experimental study of a natural swelling soil using oedometer tests by imposing the suction variations with the osmotic technique. Three successive swelling-shrinkage cycles were applied in a suction range comprised between 0 and 2 MPa under three different values of constant vertical net stress (20, 40 and 60 kPa). The test samples showed cumulative swelling strains during the cycles. The volumetric strains also reached an equilibrium stage which indicates an elastic behaviour of the samples at the end of the suction cycles. Based on these results, the parameters of the elastoplastic model for swelling unsaturated soils BExM (Barcelona Expansive Model) are derived. This model implemented in the finiteelement code (Code_Bright) is then applied to the practical problem of a shallow foundation based on the natural swelling soil. This application studies the effects of hydraulic changes due to the variations of climatic conditions (rainfall and drought) on settlements of this shallow foundation. The obtained results show the capacity of the model to solve complex hydromechanical coupled problems.
1
INTRODUCTION
Shrinkage-swelling of clayey soils causes many disorders in structures built on their surface (shallow foundations, retaining structures, landfill liner systems, earth dam cores . . .) and also buried structures (tunnels, drains, deep foundations . . .). These clayey materials are likely to be subjected to complex suction/stress paths involving significant variations of their hydromechanical properties. In this context, it is important to be able to study the hydromechanical behaviour of these materials, in order to better control their use. The expansive soils contain generally smectite clayey particles which join the other soil components to form aggregates. Two structural levels were observed by Pusch (1982): the microstructure which corresponds to the aggregates, and the macrostructure which corresponds to the arrangement of the aggregates. Experimental cyclic wetting and drying results reported by Dif and Bluemel (1991), Al-Homoud et al. (1995) and Alonso et al. (2005) show evidence of a shrinkage accumulation that increases under high vertical stresses. This behaviour was explained in terms of a continuous rearrangement of soil particles, leading to a less active microstructure. On the other hand, Chu and Mou (1973) and Pousada (1984) observed an opposite effect, in which the amount of swelling increased with the number of cycles. Day (1994) and
Basma et al. (1996) reported cumulative shrinkage or expansive strains, depending on the suction reached during the drying paths. These tests show that the equilibrium elastic state can be reached at the end of several cycles. The swelling behaviour of unsaturated expansive clays has often been described through relatively simple and empirical laws which relate the material response to suction changes and applied stresses. There are few formulations that integrate the main aspects of their coupled hydro-mechanical behaviour in a unified framework. In that sense, the model proposed by Gens & Alonso (1992) and Alonso et al. (1999) (BExM: Barcelona Expansive Model) can be mentioned as a reference framework to analyse the behaviour of unsaturated expansive materials which takes into account the accumulation of strains during the wetting and drying cycles.
2
EXPERIMENTAL PROGRAM
2.1 Studied material The experimental site is in the region of MignalouxBeauvoir, in proximity of Le Deffend, about 4 km south-east of Poitiers. An in-situ coring was performed to the depth of 7 metres for the geological and geotechnical investigations within the framework of ANR
847
Table 1. Properties of the clayey soil in the experimental site of Le Deffend. Suction (MPa)
Liquid limit (%) Plasticity index (%) Specific gravity, Gs Passing sieve 80 μm (%) Clay content (<2 μm)
10
85.6 31.9 2.60 99% 72%
1
N
H
I
J
A
B
C D
M P Test D1 Test D2 Test D3
0.1
0.01
L 10
E
K
F G 100
1000
10000
Vertical net stress (kPa)
Table 2. Description of the followed stress paths for the natural soil of Le Deffend. Test
Followed stress path
D1 D2 D3
A-B-E1 -H1 -E2 -H2 -E3 -H3 -E4 -H4 -E5 -K-L A-C-F1 -I1 -F2 -I2 -F3 -I3 -F4 -I4 -C’-P-A’ A-D-G1 -J1 -G2 -J2 -G3 -J3 -G4 -J4 -M-N
ARGIC project (Vincent et al., 2006). The studied clayey layer is located between 6.10 m and 6.80 m of depth. The dry density of the clayey soil varies between 1.05 and 1.25 Mg/m3 and its water content is between 41 and 50 %. The total suction measured by the filter paper technique (ASTM, 1995a) varies between 200 and 700 kPa. The geotechnical characteristics of the clayey material are presented in Table 2. The measurement of the swelling potential and the swelling pressure was carried out on the soil from 6.25 m depth by using the free swelling method (ASTM 1995b). The sample presents an initial dry density of 1.20 Mg/m3 and an initial water content of 41%. The swelling potential and the swelling pressure are 7% and 225 kPa respectively. 2.2
Osmotic technique
The principle of this method is to put in contact the soil sample and a solution of macromolecules with the semi-permeable membrane between them (Zur, 1966). This membrane prevents the solution of macromolecules to move towards the sample but it allows water exchange. Water movements, and thus suction variations, are controlled by the osmosis phenomenon. The higher the concentration of the solution, the higher the imposed suction. The relation proposed by Cui (1993): s = 11 c2
(1)
where c is the concentration and s is the imposed suction, was characterized and justified by the data by various authors (Williams & Shaykewich, 1969; Delage et al., 1998; Cuisinier & Masrouri, 2005). The molecular weight of PEG (polyethylene glycol)
Figure 1. Description of (σv -s) plan for the natural soil of Le Deffend.
chosen for these tests is 6 000 Da (1 Dalton, Da = 1.6605 10−24 g) which makes it possible to impose a maximum suction of 8.5 MPa. The study of the hydromechanical behaviour of the natural mixture used in this paper was performed in the osmotic oedometer proposed by Kassif & Ben Shalom (1971) and modified by Delage et al. (1992). 2.3 Followed stress path The oedometric tests (D1, D2 and D3) were carried out on the soil located between 6.25 and 6.35 m of depth. The initial state of the samples is represented by point A on Figure 1 for the three tests. This point corresponds approximately to an initial dry density of 1.22 Mg/m3 and an initial water content of 43%. The initial height of the samples is 11.6 mm and their diameter is 70 mm. The initial suction of the soil is 0.5 MPa. The initial vertical pressure applied is about 10 kPa. Three different loads were applied to the three samples: 20 kPa (Point B) for the D1 test, 40 kPa (point C) for the D2 test and 60 kPa (point D) for the D3 test. Then, three successive cycles of wetting and drying were applied between 0 and 2 MPa. The followed stress paths of three tests (D1, D2 and D3) are shown in Figure 1 and in Table 2. At the end of the successive cycles, a loading/unloading cycle was applied at three constant suctions. These applied suctions are 0 MPa for the test D1, 0.5 MPa for the test D2 and 2 MPa for the test D3.
3
EXPERIMENTAL RESULTS
The volumetric strains of the three samples are presented in Figures 2a to 2c where the swelling strains are considered positive. The samples present a swelling accumulation at the end of the successive cycles and the volumetric strains converge towards an equilibrium stage. A completely reversible behaviour is reached for the D3 test, whereas one or two additional cycles could
848
1.5
0.10 D1 ( σv=20 kPa)
E 0.08 E45 E3 0.06 E2
H4 H3 H2
0.04 E1 0.02 0.00 0.02 0.01
H1
A
S = 0 MPa S = 0.5 MPa S = 2 MPa
1.4 Void ratio (–)
Volumetric strain (–)
(a)
E
1.3
C'
1.2 1.1
J4 L, N, A'
1 P
0.9
B
KM
0.8 10
0.1
1
100
1000
10000
Vertical net stress (kPa)
10
Suction (MPa)
(b)
0.10
Volumetric strain (–)
Compression curves at different suctions.
Table 3. suctions.
Mechanical parameters at different applied
D2 ( σv =40 kPa)
0.08 F4 0.06 F3 F2 0.04 F1
C' I4 I3 I2
0.02 A C
0.00 0.02 0.01
Figure 3.
0.1
I1
1
10
Test
Suction (MPa)
P0 (kPa)
λ(s)
κ
D1 D2 D3
0 0.5 2
500 550 700
0.19 0.17 0.16
0.04 0.04 0.04
Suction (MPa)
Volumetric strain (–)
(c)
0.10 D3 ( σv =60 kPa)
0.08
Free swelling tests let us find out the mechanical soil parameters at the saturated state without the influence of suction cycles. Accordingly, we can state that for this material, the wetting and drying cycles introduce a swelling accumulation and therefore decrease the preconsolidation stress from 600 to 500 kPa. These suction cycles do not influence the λ and κ values.
0.06 G4 0.04 G3 G2 0.02 G1 A D
0.00 0.02 0.01
J2 J3 J4 J1
0.1
1
10
Suction (MPa)
Figure 2. Volumetric strains in cyclic controlled-suction paths under the vertical stresses a) 20 kPa, b) 40 kPa and c) 60 kPa for the natural soil of Le Deffand.
have been necessary for the tests D1 and D2 in order to reach completely this elastic state. Three loading/unloading cycles at three different suctions (0, 0.5 and 2 MPa) were carried out after having reached the equilibrium state at the end of the successive suction cycles (Figure 3). The compression curves made it possible to estimate the final mechanical behaviour of soil, i.e. the virgin compression index λ(s), the preconsolidation mean net stress p0 (s) and the elastic compression index κ at the corresponding imposed suction (Table 5). A suction increase tends to rigidify the soil, which results in an increase in the preconsolidation stress. The virgin compression index λ(s) decreases monotonously when suction is increased and the elastic compression index κ is constant with suction. The majority of the results available in the literature agree with these results.
4
NUMERICAL MODELLING
In this section, we study the influence of the hydraulic change due to the variation of the climatic conditions (evaporation and precipitation) on displacements of a shallow concrete foundation based at 60 cm depth in the natural soil of Le Deffend. 4.1 Soil and foundation Characteristics The shallow foundation is located on a homogeneous layer of clayey soil of Le Deffend (Figure 4). The behavior of this soil is supposed to be elastoplastic and represented by the BExM model (Alonso et al., 1999). The parameters of this model were obtained based on the test results. Table 4 summarizes the values of these parameters. The saturated hydraulic conductivity ks of this soil is about 8 × 10−12 m/s. The soil water retention curve parameters (van Genuchten, 1980) were determined by fitting the experimental data. Table 5 summarizes the values of these parameters.
849
0.6 m
2m
ux= 0
H=6m
Zero flux
100 kPa
Clayey Soil of Le Deffend
ux= 0 ux = 0 et uy = 0 Zero flux L=7m
Figure 4.
Clayey soil parameters.
Parameter
Value
Saturated hydraulic conductivity ks Parameters of the soil water retention curve (van Genuchten, 1980) Sr − Sr(res) Se = = [1 + (αS)n ]−m Sr(sat) − Sr(res) α n m = 1–1/n Sr(res) Sr(sat)
8 × 10−12 m/s
0.2 m
0.6 m Concrete foundation
Zero flux
Table 5.
0.15 m
Zero flux
Geometry and boundary conditions of the model.
Table 4. Parameters of the BExM model for the clayey soil of Le Deffend.
0.00886 MPa−1 3.582 0.721 0.1 1
Parameters of the hydraulic conductivity curve (Mualem, 1976; van Genuchten, 1980) m 2 1 √ k = ks Se 1 − 1 − Sem m Sr(res) Sr(sat)
0.721 0.1 1
Parameters of the macrostructure κ λ(0) r β κs pc
0.04 0.19 0.7 0.6 MPa−1 0.01 200 kPa
p∗0 s0 sh k M
Table 6. Parameters characterizing the foundation concrete (Burlion et al., 2005).
600 kPa 1 MPa 0 MPa 0.09 0.57
Material Behaviour
Parameters of the microstructure κm
0.025
em
Specific gravity γs Saturated hydraulic conductivity ks Parameters of the soil water retention curve (van Genuchten, 1980) Sr − Sr(res) Se = = [1 + (αS)n ]−m Sr(sat) − Sr(res) α n m = 1–1/n Sr(res) Sr(sat)
0.74
Interaction functions fI 1 = 0.519 fI 2 = −0.460 kI = 10 xI = 0.15
fD1 = −1.161 fD2 = 1.183 kD = 10 xD = 0.15
The concrete foundation is assumed to exhibit linear elastic behaviour. Its mechanical and hydraulic properties used in the calculations are presented in Table 6 (Burlion et al., 2005).
4.2
Modelling
A strip foundation subjected to a vertical stress of 300 kPa is modelled in a 2D plane-strain finite-element analysis (Figure 4). The influence of the building protection was taken into account. The soil and the concrete were discretized by 4 noded-quadrilateral
Concrete Elastic linear E = 27000 MPa ν = 0.2 2.65 10−12 m/s
0.0235 MPa−1 2.105 0.525 0 1
Parameters of the hydraulic conductivity curve (Mualem, 1976; van Genuchten, 1980) m 2 1 √ k = ks Se 1 − 1 − Sem m Sr(res) Sr(sat)
0.17 0 1
finite elements. The mesh was made up of 1344 elements and 1419 nodes. Before any loading, an initial stress state corresponding to the soil weight was defined. Initially, the soil of Le Deffend was almost saturated with initial suction of 0.5 MPa.
850
Table 7.
Phase Description 0 I II
Vertical displacements
Description of calculation phases. Duration (month)
Boundary conditions applied on the surface
Initial state and Instantaneous __ mechanical loading Evaporation 6 Suction = 100 MPa Rainfall 2 Suction = 0 MPa
The vertical displacements predicted by the model at different points under the base of the foundation are shown in Figure 6. The mechanical loading produces a maximum displacement of 5,8 mm under the foundation (points B, C, D). During the evaporation phase, the soil settles down gradually with time at different points: 4 mm at point A, 5 mm at the point B, 6.34 mm in the center of the foundation (point C), 7.71 mm at the point D and 12 mm at the point E. For the points A
The boundary conditions of the model are as follows (Figure 4):
0.65 m A: x = –1m
C B: x = – 0.3 m x = 0 D: x = 0.3 m
– vertical and horizontal displacements are fixed at 6 m depth and horizontal displacements are fixed on the model side borders; – a zero water mass-flow is imposed on the lower soil base and on the model side borders – because of the building protection, a zero water mass-flow is imposed on the top left borders of the model (under the building); – the nodes at the base of the foundation are loaded up to a uniform vertical stress of 100 kPa, and a null flow for water is imposed on the surface of the foundation. For these calculations two consecutive phases were considered (Table 7). In each phase, a boundary condition simulating a rainfall or a drought period was imposed on the soil surface. 4.3
E: x = 1 m
4 3.5
Suction (MPa)
3 A B C D E
2.5 2 1.5 1 0.5 drying
wetting
0 0
30
60
90
120
150
180
210
240
Time (day)
Figure 5. Suction variations versus time for the different points of the studied swelling soil.
Simulations results
Suctions 0.65 m A: x = –1m
E: x = 1 m
C B: x = – 0.3 m x = 0 D: x = 0.3 m 0 –2 Vertical displacement (mm)
The evolution of suction versus elapsed time for different points of the soil located under the base of the foundation is presented in Figure 5. The values of suction increase gradually with time during the drying phase (phase I) and decrease quickly during the wetting phase (phase II). For the points situated under the building and at the base of the foundation (points A, B, C, D), the suction increase during the drying phase is less than the other points (Point E) located at the same level but outside the foundation, because the building and its foundation prevent the flow entrance. For the points C, D and E, during the wetting phase (Phase II) the suction initially increases before it starts to decrease. This period of suction increase is even more significant for the point E. This is due to the fact that it takes a certain time for the water to pass through the surface. For the points A and B the suction decrease starts immediately once the null suction is applied on the surface because the soil under the building remains almost saturated even after 8 months of drying.
–4 –6
A B C D E
–8 –10 –12 –14 drying
–16 0
30
60
90
wetting 120
150
180
210
240
Time (day)
Figure 6. Vertical displacement versus time for the different points of the studied swelling soil located under the foundation.
851
numerical model is able to predict qualitatively soil displacements during the different hydraulic changes. The mechanical loading produces a maximum displacement in the center of the foundation. The soil (initially saturated) settles down during the 6 months drying, with a maximum compression on the righthand of the foundation. The wetting period causes a rotation of the rigid foundation and consequently a compression of the soil located under the building. At this stage, it would be interesting to have the in-situ measurements of the volumetric deformations during the wetting and drying cycles in order to validate the obtained numerical results for the natural swelling soil.
Figure 7. Schematic rotation of the rigid foundation at the end of the wetting phase.
and B, during the drying phase the soil initially experienced expansion because of the great amount of soil settlement on the right-hand side of the foundation. The rainfall phase produces soil heaving for the points to the right from the foundation center (0.53 mm at the point D and 1.16 mm at the point E) and a settlement on the left of the center of the foundation (4.22 mm at point A, 4 mm at the point B and 1.64 mm as in point C) due to the rotation of the foundation (Figure 7). It can also be observed that a small immediate wetting in a lower suction range produces a significant settlement for points A and B (Figures 5 and 6).
5
CONCLUSION
This paper has presented an experimental study of a natural swelling soil using oedometer tests by imposing suction variations with the osmotic technique. Three successive swelling and shrinking cycles were applied in a suction range between 0 and 2 MPa under different values of constant vertical net stress (20, 40 and 60 kPa). The test samples showed cumulative swelling strains during the cycles. The volumetric strains also reached an equilibrium stage which indicates an elastic behaviour of the samples at the end of the suction cycles. Within the framework of BExM model, the hydromechanical behaviour of a shallow foundation resting on a swelling-shrinking soil is presented. The scope of this study was to analyze the effects of a drying path (drought) and a wetting path (rainfall) on soil settlement under a shallow foundation built on a natural clayey soil. The results showed that the
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Delage, P., Howat, M.D. & Cui, Y.J. 1998. The relationship between suction and the swelling properties in a heavily compacted swelling clay. Engineering Geology, 50: 31–48. Gens, A. & Alonso, E.E. 1992. A framework for the behaviour of unsaturated expansive clays. Revue Canadienne de Géotechnique, 29: 1013–1032. Kassif, G. & Ben Shalom, A. 1971. Experimental relationship between swell pressure and suction. Géotechnique, 21: 245–255. Mualem, Y. 1976. A new model for predicting the hydraulic conductivity of unsaturated porous media. Water Resources Research, 12: 513–522. Pousada, E. 1984. Deformabilidad de arcillas expansivas bajo succión controlada. Doctoral Thesis, Universidad Politécnica de Madrid, Spain. Push, R. 1982. Mineral-water interactions and their influence on the physical behaviour of highly compacted Na-bentonite. Revue Canadienne de Géotechnique, 19:381–387.
Romero, E., Lloret, A. & Gens, A. 1999. Water permeability, water retention and microstructure of unsaturated Boom clay. Engineering Geology, 54: 117–127. van Genuchten, M.TH. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society American Journal; 44: 892–898. Vincent, M., Bouchut, J., Fleureau, J.M., Masrouri, F., Oppenheim, E., Heck, J.V., Ruaux, N. Le Roy, S., Dubus, I. & Surdyk, N., 2006. Étude des mécanismes de déclenchement du phénomène de retrait-gonflement des sols argileux et de ses interactions avec le bâti. Rapport final du projet RGC& U, BRGM/RP-54862-FR, Octobre, 2006. Williams, J. & Shaykewich, C.F. 1969. An evaluation of polyethyleneglycol (PEG) 6000 and PEG 20 000 in the osmotic control of soil water matric potential. Canadian Journal of Soil Science, 49: 397–401.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Numerical modelling of shallow foundations on swelling clay soil using the swelling equilibrium limit G.A. Siemens GeoEngineering Centre at Queen’s-RMC, Royal Military College of Canada, Kingston, Canada
J.A. Blatz Department of Civil Engineering, University of Manitoba, Winnipeg, Canada
ABSTRACT: Damage caused to shallow foundations constructed on swelling clay soil is extensive and is usually observed as deformations and cracks in the superstructure as well as basement walls and floor. Generally this is due to swelling soil responding to changes in the surrounding moisture content regime as a result of removal of vegetation including trees and grasses as well as covering the ground with a basement. Both lead to increases in water content in a soil with swell potential. Siemens and Blatz (2008) reported on a new Swell Equilibrium Limit (SEL) for swelling soil. This limit forms an upper bound for volume expansion and stress increase in specific volume-mean stress (V-p) space. The final location along the SEL depends on the initial conditions and boundary conditions encountered during wetting. Boundary conditions can range from constant stress to constant volume with deformation boundary conditions between the two extremes. In this paper, the SEL is formulated in a numerical modelling program to model construction and long-term behaviour of shallow foundations constructed on swelling clay soils. The attempt is intended to be a simplified modelling approach to capture complex swelling mechanisms by applying an elastic solution to model volume changes due to both total stress and suction. Triaxial and oedometer results are used to calibrate and validate the numerical model as well as illustrate the approach. Using the validated model, deformations and swelling induced stresses around a shallow foundation and basement constructed in swelling clay soil are modelled. Two different scenarios are modelled including removal of vegetation followed by basement construction, and influence of drainage around a building. Model results are interpreted and mitigation measures proposed to attenuate deformations and swelling induced stresses.
1
INTRODUCTION
Swelling soils are found in many locations around the world. They are often used in geoenvironmental applications for protection of the environment from contaminants. Swelling soils are also responsible for extensive damage to structures founded in them. In particular, light-framed structures such as residential buildings are susceptible to ground movements as shown in Figure 1. This is due to the relatively light loads provided by the buildings combined with changes in suction in the near-surface environment. Figure 1 illustrates potential problems that can occur to foundations on swelling soil. Significant heave is observed under the house due to wetting that will occur since the ground is now covered by the basement. Previously a vegetative cover contributed to increased suction due to evapotranspiration. On the right side, shrinkage occurs in response to the suction induced by the
Figure 1. Damage to houses caused by ground movements of swelling soils (Domaschuk, 1986).
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tree roots. As the tree grows taller and its root system expands, this effect increases. The result is differential displacements in the foundation that cause damage to the adjacent structure. Unsuspecting home owners can unknowingly increase the effect of swelling soil by changing vegetation as well local drainage around their homes. Incurred costs to fix damages after they have occurred are quite significant in relation to the value of standard homes. Therefore, homeowners have the choice to live with the damage, periodically perform surficial repairs, or go through with costly and intrusive remediation measures. A change in foundation type, such as piles, can be required and other more drastic measures are also attempted. This paper investigates the effect of swelling on a residential foundation through numerical modelling of the Swell Equilibrium Limit (SEL, Siemens 2006, Siemens and Blatz 2008). The SEL was discovered through laboratory testing of a highly swelling soil that investigated the influence of hydraulic and mechanical boundary conditions on the behaviour of swelling soil during infiltration. This model is intended to be a simplified approach for researchers and practitioners to predict displacements and swelling induced stresses in swelling soil. In this paper, results from the laboratory testing are used to calibrate and validate the SEL in a finite element modelling program. The limit is then formulated for Lake Agassiz Clay using oedometer results and two different scenarios for a shallow foundation including basement construction and the influence of ponding around a building are modelled. Numerical modelling shows that, despite the significant assumptions and simplified approach of the formulation, the SEL can be used to predict plausible displacements and swelling induced stresses around shallow foundations and basement walls. 2
speaking, examples of constant volume boundary conditions are rare since soil requires some finite displacement in order to mobilize strength however these conditions are approached in examples such as a reinforced retaining wall or adjacent to a rigid wall. 2.1
Swell Equilibrium Limit (SEL) development
Laboratory evidence for the SEL is displayed in Figure 2, which plots specific volume versus mean stress (V-p) from laboratory tests on a highly swelling material known as Bentonite Sand Buffer (BSB, details of the laboratory testing can be found in Siemens and Blatz 2008 and Siemens 2006). Boundary conditions ranging from constant mean stress (CMS) to constant volume (CV) as well as constant stiffness (CS25 and CS75), which is a spring-type boundary condition that includes both increasing volume and stress were imposed on the soil during wetting. Each specimen was prepared in the same manner and brought to the same stress state prior to wetting and, therefore, the influence of boundary conditions can be viewed directly. The CMS specimen experiences the greatest expansion while the CV specimen experiences the highest swelling induced stresses, which are required to maintain initial volume. The constant stiffness specimens also swell up to the limit. The line on the figure is the SEL which was determined by fitting a line to the final stress, water content and volume states that occurred during the physical tests. Siemens and Blatz (2008) showed the SEL agreed with 1-D ‘‘swell pressure’’ measurements that were converted to equilibrium mean stresses using an assumption of elasticity. All specimens approached the SEL during wetting and the point at which they meet the limit is determined by their initial stress and volume conditions as well as the boundary conditions
SWELL EQUILIBRIUM LIMIT
The SEL is an upper bound on expansion and swelling induced stresses that can occur during infiltration or wetting (increasing water content). As a swelling soil increases in water content, water is taken up by the clay particles and they expand at the molecular level. Large-scale behaviour of the soil depends on the boundary conditions imposed. Boundary conditions range from constant stress to constant volume with an infinite number of possibilities between that include both expansion and stress increase. Regardless of the applied boundary condition, the same mechanism of water uptake by the clay particles occurs at the pore scale. The SEL gives evidence for this unifying concept for swelling soil. Displacements, stresses, and water content are predicted by the SEL. In the field, constant stress boundary conditions are found beneath shallow foundations. Strictly
Figure 2. Laboratory evidence for the Swell Equilibrium Limit (SEL) plotted in total specific volume versus mean stress (V-p) space (after Siemens and Blatz 2008).
856
imposed during wetting. The SEL is the upper bound on expansion and swelling induced stresses observed in the tests shown (250 kPa pre-wetting mean stress) as well as in tests with pre-wetting mean stress up to 1500 kPa. In general, as pre-wetting mean stress increases, potential expansion as well as swelling induced stresses decreases. This is because of the greater confining stresses prior to contact with water.
3
NUMERICAL FORMULATION
The finite element programs SIGMA/W and SEEP/W (GeoStudio 2007) were used to formulate the Swell Equilibrium Limit (SEL). SIGMA/W was used to determine stresses and deformations while pore pressure modelling was performed using SEEP/W. 3.1
Laboratory test calibration and validation
The first step was to calibrate and validate the SEL from the laboratory samples. An axi-symmetric finite element model was used to model the 50 mm diameter by 100 mm tall specimens. Original development of the SEL relied on elasticity and a linear elastic constitutive model was selected for the swelling soil. Laboratory results from the tests with pre-wetting mean stresses of 250 kPa, 1000 kPa, and 1500 kPa tests were used to calibrate the SEL and then the model was validated using the 500 kPa results. Modelling was completed in a three-step process that included isotropic compression, wetting under constant mean stress boundary conditions and finally recompression to pre-swelling volume. Schematics of the experimental and modelling stress-volume paths are shown in Figure 3. Isotropic compression and free swell wetting paths are modelled directly. Isotropic compression models consist of modelling increasing mean stress and corresponding decrease in suction. Wetting under a CMS boundary modelled the pore pressure change from the measured pre-wetting suction to the final pore pressure applied during the experiments. This assumes air pressure is constant and the resulting deformations are only due to changes in the pore water pressure. Modelling CV infiltration involved a final step following free swell. The additional step was recompression of the specimen to initial volume. In the physical testing, CV conditions were automatically controlled as water ingress occurred. The selected analysis type did not allow this to be modelled directly so this recompression step was required. The intent of the model is to represent CMS and CV infiltration stress-volume paths using an elastic constitutive model. In each case this final state is achieved using an elastic model to represent the experimental results.
Figure 3. Schematics of laboratory and model stressvolume paths in specific volume-mean stress (V-p) and suction-mean stress spaces.
3.1.1 Isotropic compression Isotropic compression modelling consisted of increasing confining stress incrementally. Elasticity parameters were taken from Chandler (2000) (E = 30,000 kPa, ν = 0.18). In parallel to the stressdeformation modelling, steady-state groundwater models were performed to represent suction measurements at the beginning and end of isotropic compression at each level. Numerical results compared very well with the laboratory measurements however since the purpose of this paper is to display the SEL the isotropic results will not be included here. 3.1.2 Constant mean stress wetting Modelling wetting at constant mean stress represented the CMS laboratory tests. As mentioned earlier, as pre-wetting isotropic stress level is increased, reduced expansion during wetting was observed. In the numerical model, this was represented by varying Young’s Modulus with pre-wetting mean stress while holding Poisson’s ratio constant. Throughout each individual model, Young’s Modulus was held constant. The interpreted Young’s Modulus versus pre-wetting mean
857
stress relationship is shown in Figure 4. In the experimental results, reduced expansion was observed when pre-wetting mean stress was increased even though the change in suction was relatively similar. Reduced expansion corresponds with increasing stiffness as shown in Figure 4. In SIGMA/W, the ‘‘Volume Change’’ Analysis Type requires an initial stress condition as well as initial and final pore pressures to calculate volume changes. Total stresses are not permitted to change during the analysis. The stress-volume paths are shown schematically in Figure 3. Initial pore pressures were known from suction measurements in the laboratory tests. The final pore pressure was taken as the water pressure applied during wetting (200 kPa), which assumed the specimen reached equilibrium throughout. In this analysis type, displacements due to positive pore pressure changes are calculated using Young’s Modulus (E). Displacements due to changes in negative pore pressure are calculated using the suction modulus, H, which is set by the program as H = E/(1 − 2υ). Therefore, change in volume due to changes in pore water pressure (both positive and negative) was determined from elastic constitutive models. For calibration, Young’s Modulus (and therefore the calculated suction modulus) was modified until volume changes observed during CMS wetting were modelled. Since total stresses were held constant, deformations modelled were entirely due to pore water pressure changes. As shown in Figure 4, the free swell modulus increases with increasing mean stress as anticipated. Physically this represents a stiffer material that experiences less expansion as pre-wetting mean stress increases. A second order polynomial was fit to the 250 kPa, 1000 kPa, and 1500 kPa tests and the resulting equation was used to calculate the elastic modulus for the 500 kPa test. Again, good agreement was found between the model and physical results.
Figure 4. Variation of constant mean stress and recompression moduli versus pre-wetting mean stress.
3.1.3 Recompression The third step of modelling was recompression to pre-swelling volume to model the swelling induced stresses as illustrated in Figure 3. The constant mean stress model results were used as initial conditions in the models and displacement boundary conditions were imposed to the periphery of the cylindrical specimens to bring them back to their pre-wetting volume. As shown in Figure 3, pore pressures were held constant in this step. In the physical tests, swellinginduced stress changes were less than the changes in suction observed during wetting. This is represented in the numerical model as a lower ‘‘recompression modulus’’ relative to the ‘‘free swell modulus’’ as observed in Figure 4. In the CV wetting experiments, volume was held constant. Therefore the recompression modulus was varied to calibrate against swelling-induced stresses measured in the physical tests. Once again, the 250 kPa, 1000 kPa, and 1500 kPa tests were used to calibrate the recompression modulus function, which was validated with the 500 kPa test. Similar to the free swell modulus, the recompression modulus increases with increasing mean stress. This is representative of a stiffer material. Interestingly, although the recompression modulus is less than the free swell modulus, at lower stresses, they appear to converge (Figure 4). As mentioned above the swelling induced stresses observed during CV wetting were significantly less than the pore pressure change. From the free swell and recompression modulus relationships, this behaviour is confirmed with the free swell moduli being consistently 5–7x greater than the recompression moduli.
3.2 Lake Agassiz Clay calibration Following calibration and validation of the SEL using the laboratory tests, the model was also calibrated for Lake Agassiz Clay. The resulting parameters could then be used directly in basement models. First the SEL was calculated for Lake Agassiz Clay by determining the EMDD from its montmorillonite content of 30% (Dixon et al. 2002) as well as elasticity parameters given in Graham and Houlsby (1983). Infiltration tests such as those used to develop the SEL have not been performed on Lake Agassiz Clay specimens so the model was calibrated using a free swell oedometer test that allowed vertical swell under a nominal load followed by compression to original volume. Similar to above, models were completed in a three-step process of insitu stresses, free swell and recompression. The results agreed with earlier observations that the free swell modulus is relatively greater than the recompression modulus although they are almost equal (Efreeswell = 1.8 MPa, Erecompression = 1.2 MPa) for Lake Agassiz Clay at low initial stresses.
858
4
BASEMENT MODEL
20
Following calibration of the SEL for Lake Agassiz Clay, the impact of changing pore pressure regimes due to construction of a residential basement was considered to predict displacements as well as swelling induced stresses. Parameters used in the basement model were taken from the previous calibration exercise.
Local Elevation (m)
4.1
Insitu
An insitu model was completed to calculate the existing stresses prior to construction and following excavation of the basement. Half the basement was modelled in two-dimensional space with the depth of 2 m and total width of 10 m. To ensure validity of the mechanical parameters, similar suction levels were used as a boundary condition at the surface (150 kPa suction) and the groundwater table was maintained at 5 m depth. The initial pore pressure conditions are shown in Figure 5.
Surface ponding 0
15 0 sec
10 40
5 80 0 0
5
10
15
20
Distance (m)
Figure 6. Pore pressure distribution for ponding underneath foundation. 40
Basement construction
The first scenario investigated is basement construction. During construction, a vapour barrier is placed below the floor to prevent moisture from entering the house. As a result, water vapour can be trapped below the floor and could result in development of ponding, especially if the drainage plumbing becomes clogged. Ponding was modelled using SEEP/W as a zero pore pressure boundary at the base of the excavation while the surface boundary condition was maintained at 150 kPa suction. The resulting pore pressure distribution is shown in Figure 6 and the induced displacements below the foundation are shown in 20
150 kPa suction at surface
Local Elevation (m)
-120 -80 -40 0 sec
0
5 80 120 0
5
10
15
Distance (m)
Figure 5.
20 40.7 mm differential displacement 10
0
-10 0
1
2
3
4
5
Distance (m)
Figure 7. Vertical displacements as a result of ponding at foundation base.
4.3 Drainage modelling
40
0
30
Figure 7. Ponding results in rising of the groundwater table at the base of the foundation. The vertical displacements as a result of increase in pore pressure are 34.6 mm at the centre of the house with some compression observed at the edge. The resulting differential displacements of over 40 mm over a length of just 5 m would be extremely damaging to the above structure.
15
10
Vertical displacement (mm)
4.2
Initial pore pressure distribution.
20
The second scenario considers the effect of poor drainage adjacent to a house. Following construction, homeowners can inadvertently affect their foundation performance through changing vegetation as well as having the ground slope towards the house. To investigate the swelling induced stresses along side a house foundation caused by poor drainage or a loss of vegetation, ponding at the surface was modelled. This would also be representative of a long-term rain event
859
that raises the water table to the surface. Similar to the calibration and validation modelling procedures, first a free swell model was performed and then horizontal displacement boundary conditions were imposed along the side of the basement wall to maintain preswell conditions. The result was swelling induced stresses that a rigid wall foundation would experience. The free swell model results including a deformation mesh (1x magnification) are shown in Figure 8 and the resulting stresses are plotted in Figure 9. Horizontal displacements as high as 0.24 m are shown in Figure 8 and the resulting swelling induced stresses range from 60–110 kPa which is greater that the theoretical passive earth pressures (c = 5 kPa, φ = 15◦ ). In the longterm, these high horizontal pressures could result in damaging deformations to the house foundation. 20
Local Elevation (m)
15
.24 .18 -0
-0
12
-0.
-0.06
CONCLUSIONS
Environmental factors play an important role in performance of a foundation on swelling soil. In this paper, the Swell Equilibrium Limit (SEL) was formulated for Bentonite Sand Buffer and Lake Agassiz Clay in a finite element modelling program. The calibration and validation procedure showed the SEL was giving results as anticipated with increasing stiffness with increasing mean stress and also represented the physical tests. The SEL was then used to model a house foundation under two scenarios including construction and surface ponding. The model predicted differential deformations and swelling induced stresses that represent plausible field conditions. This model shows the destructive deformations and stresses that can result from environmental loadings and (relatively) low changes in suction. More extreme changes in suction would increase the effects. To prevent potential problems effort is required prior to construction. Ideally, surface vegetation would be removed and the surface covered with a vapour barrier so the foundation soil could come into equilibrium with the new hydraulic boundary conditions prior to construction.
10
REFERENCES
0 5
0 0
5
10
15
20
Distance (m)
Figure 8. Horizontal deformations induced from surface ponding and a deformation mesh (1x magnification).
15
Local elevation (m)
5
14
Horizontal total stress
13 0
20
40
60
80
100
120
Stress (kPa)
Dixon, D.A., Chandler, N.A. and Baumgartner, P. 2002. The influence of groundwater salinity and influences on the performance of potential backfill materials. In Proceedings of the 6th International Workshop on Design and Construction of Final Repositories, Backfilling in Radioactive Waste Disposal, Brussels, March 2002. ONDRAF/NIRAS. Transactions, Session IV, paper 9. Chandler, N.A. 2000. Water inflow calculations for the isothermal buffer-rock-concrete plug interaction test. Ontario Power Generation Report Number: 06819-REP01200-10046-R0, 40 pp. Domaschuk, L. 1986. Is your house suffering? Cantext Publications, 18 pp. Geo-slope international Ltd. 2007. Stress Deformation Modeling with SIGMA/W 2007, An Engineering Methodology, 2nd Edition, 317 pp. Graham, J. and Houlsby, G.T. 1983. Anisotropic elasticity of a natural clay. Geotechnique, 33(2): 165–180. Siemens, G.A. and Blatz, J.A. 2008. Examination of boundary condition influence on hydraulic-mechanical behaviour of an unsaturated swelling soil. Submitted to Canadian Geotechnical Journal. In review. Siemens, G.A. 2006. The influence of boundary conditions on the hydraulic-mechanical behaviour of an unsaturated swelling soil. Ph.D. Thesis, Department of Civil Engineering, University of Manitoba, Winnipeg, MB. Available for download at http://www. collectionscanada. ca/obj/s4/f2/dsk3/MWU/TC-MWU-262.pdf
Figure 9. Horizontal swelling induced stress distribution and theoretical passive earth pressures plotted for comparison.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Meshfree modelling of two-dimensional contaminant transport through unsaturated porous media R. Praveen Kumar, G.R. Dodagoudar & B.N. Rao Department of Civil Engineering, Indian Institute of Technology, Chennai, India
ABSTRACT: This paper presents a new numerical tool to model two-dimensional contaminant transport through unsaturated porous media using a meshfree method, called the Element Free Galerkin Method (EFGM). In the EFGM, an approximate solution is constructed entirely in terms of a set of nodes and no characterization of the interrelationship of the nodes is needed. The advection-dispersion equation with sorption is considered to illustrate the applicability of the EFGM. The Galerkin weak form of the governing equation is formulated using 2D meshfree shape functions constructed using moving least square approximants, which are constructed by using a weight function, a linear basis function and a set of non-constant coefficients. MATLAB code is developed to obtain the numerical solution. Two numerical examples are presented and the results are compared with those obtained from the finite element method.
1
INTRODUCTION
Interest in the unsaturated zone, which plays an inextricable role in many aspects of hydrology, has dramatically increased in recent years because of growing concern that the quality of the subsurface environment is being adversely affected by the disposal of a wide variety of domestic and industrial wastes on the surface. Though significant progress has been made in modelling contaminant transport through unsaturated porous media, it is still a formidable task as the volumetric water content, the coefficient of hydrodynamic dispersion, and the discharge velocity vary both in space and time. In recent years a group of new numerical methods called Meshfree methods have been developed; whose main aim is to eliminate the structure of the mesh and construct the approximate solutions for the discrete equation entirely in terms of a set of nodes. Numerical models based on the meshfree methods are not being extensively used for modelling the transport processes in unsaturated porous media. Hence, there is a need to understand the potential of meshfree methods properly and to formulate a numerical model to represent the migration of contaminants through unsaturated porous media. The objective of this paper is to propose a methodology for modelling the two-dimensional advection—dispersion—sorption—decay processes through unsaturated porous media using the Element Free Galerkin Method (EFGM). Student’s t distribution weight function proposed by Rao & Rahman
(2000) is used in the meshfree analysis. The Lagrange multiplier method is used to enforce the essential boundary conditions. A MATLAB program has been developed to implement the procedure of the EFGM for modelling the contaminant migration. The results of the EFGM are compared with standard finite element results.
2
ELEMENT FREE GALERKIN METHOD
The EFGM is a meshfree method because only a set of nodes and a description of the model’s boundary are required to generate the discrete equations. The EFGM employs moving least-square (MLS) approximants as formulated by Lancaster & Salkauskas (1981) to approximate the function C(x) with C h (x) in which the C(x) is the contaminant concentration at x, where x is a position coordinate. More details of the EFGM can be found elsewhere (e.g. Dolbow & Belytschko, 1998). According to the moving least squares (MLS) proposed by Lancaster and Salkauskas (1981), the approximation, C h (x) of C(x) is: C(x) ∼ = C h (x) =
n "
I (x)CI = ΦC
(1)
I =1
where n is numbers nodes in the domain. MLS shape function: Φ = {1 , 2 , 3 , . . . , n } (2)
861
The Student’s t distribution weight function is written in terms of normalized radius r as ⎧ ⎫ (1 + β) (1 + β) − 2 2 − 2 2 ⎪ ⎪ − (1 + β 2 ) ⎨ (1 + β r ) ⎬ r ≤ 1 (1 + β) − 2 2 1 − (1 + β ) w(r) = ⎪ ⎪ ⎩ ⎭ 0 r > 1 (3)
discharge (Darcy) velocity, C0 and g are the concentration of contaminant at the source and the concentration gradient at the exit boundary respectively, ns is a unit normal to the domain and, S and E are the portions of the boundary where the source concentration and concentration gradient are prescribed. The hydrodynamic properties of the soil are described by the functions of van Genuchten model (1980):
where β is the parameter controlling the shape of the weight function and x = [x, y] ;
r=
x − xI dmax zI
(4)
in which xI is the sampling point, dmax is the scaling factor and zI is the distance to the nearest node in the neighbourhood. As the shape functions of the EFGM do not satisfy the Kronecker delta criterion, the Lagrange multiplier technique (e.g. Dolbow & Belytschko, 1998) is used to enforce the essential (Dirichlet) boundary conditions. 3
S=
(5)
ρd Kd θ
(7a) if h ≥ 0
1
!2
for χ>1
(7b)
and
(7c)
where θr and θs are the residual and saturated volumetric water contents of the soil respectively, S is the degree of saturation of the soil, K and KS are the hydraulic conductivities of the soil at pressure head h, and at saturation respectively and, α and χ are the empirical constants determining the shape of the function. The weak form of Equation (5) with boundary conditions is expressed as
The initial and boundary conditions are: C (x, y, 0) = Ci ∀ (x, y) ∈
if h ≤ 0
!1 − 1/χ
where = 1 − 1/χ
∂ ∂C ∂C ∂ ∂ θ DL + θ DT (RθC) = ∂t ∂x ∂x ∂y ∂y
R=1+
1 + (α |h|)χ
−α (θs − θr ) 1/ ∂θ = S (1 − S 1/ ) ∂x 1−
A two-dimensional form of the governing equation for contaminant migration through unsaturated porous media is expressed as:
∂ (uC) − ηθC ∂x
⎪ ⎩
1
K = Ks (S)0.5 1 − (1 − S (χ/χ−1) )(1−(1/χ))
DISCRETISATION OF GOVERNING EQUATIONS
−
⎧ ⎪ ⎨
δC T (6a)
C (x, y, 0) = C0 on s (Dirichlet boundary conditions) (6b) ∇ (C) · nS = g on E (Neumann boundary conditions) (6c) where (x, y) are the spatial coordinates, θ is the volumetric water content of the soil, ρd is the bulk density of the soil, η is the decay constant, Kd is the distribution coefficient, C is the concentration of contaminant, Ci is the initial concentration of contaminant, DL and DT are the longitudinal and transverse dispersion coefficients respectively, R is the retardation factor, u is the
862
∂C ∂ θDL d ∂x ∂x
+
δC T
L δC
+ 0
−
∂C ∂ θDT d ∂x ∂x
T
∂θ ∂x
∂C DL dx − ∂x
∂ δC T (RθC)d − ∂t
−
δC T 0
∂ (uC)dx ∂x
δC T ηθC d
δλT(C − C0 )d −
S
L
λT δC d = 0 S
(8)
where λ is a Lagrangian multiplier for enforcing the essential boundary conditions and is expressed by: λ(x) = NK (κ)λI ,
x ∈ s
δλ(x) = NK (κ)δλI ,
(9a)
x ∈ s
(9b)
where NK (κ) is a Lagrange interpolant and κ is the arc length along the boundary; the repeated indices designate summations. By using the divergence theorem, Equation (8) is written as: δC T θ DL E
∂C ns ds + ∂x
δC T θ DT E
∂C ns ds ∂y
The δC and δλ are arbitrary values and by using Equations (1) and (2) in the discretisation of Equation (11), the following relationship is obtained [Equation (12)]: ! ! K (1) {C} + K (2) {C},t + [G] {λ} = {Q} ! (12) G T {C} = {q} where ⎡
I ,x J ,y
(1)
K IJ
L T ∂C ∂C ∂C T ∂θ θ DL d − δC DL dx − δ ∂x ∂x ∂x ∂x
0
δ
−
T
∂C ∂x
∂C θDT d − ∂y
δC ηθCd −
−
T
0
S
K (2) IJ =
(10)
0
λ δCd =
+
δC T uC,x dx
S
δC T Rθ C,t d T
δC θ DT gy d
δλ (C − C0 ) d = 0
(13b)
I NK d
(13c)
I Dgd
(13d)
NK C0 d
(13e)
∗
(15a)
K (1) = εt[K (1) ]
(11b)
in which ε is the constant varying between 0 and 1, C n and C n−1 are the nodal concentrations at start and end of the time increment and, Qn and Qn−1 are the nodal mass fluxes at start and end of the time increment.
S
d
(11a)
E T
I J
+ εt{Q}n + (1 − ε)t{Q}n−1
+
θR
Rn = ([K (2) ] − (1 − ε)t[K (1) ]){C}n−1
E T
T
where
δC θ DL gx d
T
I J
where I (x) is the MLS shape function. Using the Crank-Nicholson method for time approximation, Equation (12) can be written as ∗ Cn Rn K (1) + K (2) G (14) = T q 0 G λ
0
δC T ηθC d +
+
⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ d ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦
s
⎤
qK =
L δC T θ,x DL C,x dx +
E
+
I ,x J ,y
QI =
δC,yT θ DT C,y d
L
s
0 DT
G IK =
Equation (10) can be split into two parts: δC,xT θ DL C,x d +
S
DL 0
(13a)
λT δCd = 0
θ
⎢ ⎢ ⎢ ⎢ T
T
⎢ I I ,x I I ⎢ u η + ⎢ + J ,x J J ⎢ J = ⎢ ⎢ T
⎢ ⎢ I I ,x ⎢ + ⎢ J J ,x ⎢ ⎢ ⎣ −α (θs − θr ) 1/ D S (1 − S 1/ ) 1−
∂ (uC) dx ∂x
∂ δC (Rθ C) d ∂t
δλT (C − C0 )d −
−
δC T
T
L
T
863
(15b)
4
NUMERICAL EXAMPLES: RESULTS
The analysis procedure of the EFGM is impleneted through MATLAB for modelling contaminant transport through unsaturated homogenous porous media. Two numerical examples are given to illustrate the Table 1.
Data used for advection dominant transport.
Parameter
Value
Length of reach (cm) Width of reach (cm) Initial condition for flow (cm) Boundary condition for flow at upper surface (cm) Boundary condition for flow at bottom surface (cm) Saturated volumetric water content Residual volumetric water content Saturated hydraulic conductivity of soil (cm/hr) α (cm−1 ) χ Longitudinal dispersivity (cm) Transverse dispersivity (cm) Total duration of simulation (hours) Initial concentration (μg/cm3 ) Concentration at source boundary (μg/cm3 )
40 1.0 −40 0.0 −40 0.368 0.102 0.332 0.033 2.0 0.005 0.005 24 0.0 1.0
Figure 1.
Sketch of the problem domain—example 1.
methodology and they are: (1) Advection dominant transport and (2) Advection-dispersion-sorptiondecay. The source of the contaminant is assumed to be continuous. In the analysis, a central finite difference scheme (ε = 0.5) is used for time integration. In the EFGM, a linear basis function is used for constructing the shape functions. As the shape functions are linear, it is required to take the shape parameter β = 2 in the weight function. Based on the parametric study, it has been found that dmax = 2.5 for the present analysis and the same value is used in the EFGM. 4.1
Example 1: advection dominant transport
This example presents the case of contaminant transport for which advection is highly dominant [Peclet
Figure 2.
864
Finite element mesh—example 1.
as shown in Figure 2. The centerline concentration profiles obtained from both the FEM and EFGM are shown in Figure 3. It is seen from the figure that the results obtained from the present EFGM model for advection dominated problem are stable. Thus, it ensures that the model is free from numerical oscillations and insensitive to Peclet constraints.
FEM (VS2DTI) EFGM
1.2
Normalised Concentration
1.0 0.8 0.6 0.4
4.2 Example 2: advection-dispersionsorption-decay
0.2 0.0 0
5
10 15 20 25 30 Longitudinal Distance (cm)
35
40
Figure 3. Normalised concentration profiles along the centreline of the domain—example 1.
Table 2. Parameters considered dispersion-sorption-decay.
in
the
advection-
Parameter
Value
Length of reach (m) Width of reach (m) Initial condition for flow (cm) Boundary condition for flow at upper surface (cm) Boundary condition for flow at bottom surface (cm) Saturated volumetric water content Residual volumetric water content Saturated hydraulic conductivity of soil (m/day) α(m−1 ) χ Decay constant (day−1 ) Density of the soil (kg/m3 ) Distribution coefficient (m3 /kg) Longitudinal dispersivity (m) Transverse dispersivity (m) Concentration at source boundary (0 ≤ width ≤ 50 m)(μg/cm3 )
200 100 −200 0
The parameters used for this example are given in Table 2. The problem domain is shown in Figure 4. The EFGM model has been divided into 41× 12 uniformly spaced nodes and the problem domain is divided into 440 cells. Nodes of the background mesh are chosen such that they coincide with the meshfree nodes. In this case, the simulation has been carried out for 365 days with a time step of 14.6 days. A finite element package, HYDRUS–2D (Šimunek et al., 2006), has been used for solving this problem and the results are compared with that of the EFGM results. In the finite element analysis, the domain is discritised into 3-noded 560 triangular elements
−200 0.3 0.0 0.3 0.05 2.0 0.01 1500 0.0004 1.0 0.5 1.0
number (Pe ) = 50]. The parameters used in the analysis are presented in Table 1 and the problem domain is shown in Figure 1. The EFGM model has been divided into 161 × 5 uniformly spaced nodes and the problem domain is divided into 640 cells. Nodes of the background mesh are chosen such that they coincide with the meshfree nodes. The simulation has been carried out for 24 hours with a time step (t) of 2 hours. A finite element package, VS2DTI (Paul et al., 2000), has also been used for solving this example problem and the results are compared with that of the EFGM. In the finite element analysis, the domain is discritised into 161 × 5 nodes with 640 elements
Figure 4.
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Sketch of the problem domain—example 2.
the problem of two-dimensional contaminant transport through the unsaturated porous media. 5
CONCLUSIONS
The details of the Element free Galerkin method and its numerical implementation for modelling the two-dimensional contaminant transport through the unsaturated porous media are presented. In the EFGM, a structured mesh is not required and only a scattered set of nodal points is needed in the domain of interest. Shape functions based on 2D local support domains are constructed using the moving least square approximants. The implementation of the EFGM is very simple and straightforward, irrespective of the dimension of the problem and shape of the domain. Numerical results obtained from the EFGM are compared with finite element results. It is seen that the EFGM generates excellent results in comparison with the FEM thereby ensuring the correct formulation of the EFGM. Further work is currently underway using the EFGM for three-dimensional contaminant transport modelling through the saturated and unsaturated porous media. REFERENCES Figure 5.
Finite element mesh—example 2.
0.6 x = 20 m
Normalised Concentration
0.5
FEM (HYDRUS - 2D) EFGM
0.4 0.3
x = 40 m
0.2 0.1
x = 80 m
0.0 0
73
146 219 Time (days)
292
365
Figure 6. Comparison of break through curves at x = 20, 40 and 80 m.
Dolbow, J. & Belytschko, T. 1998. An introduction to programming the meshless element-free Galerkin method. Archives in Computational Methods in Engineering 5: 207–241. Lancaster, P. & Salkauskas, K. 1981. Surfaces generated by moving least-squares methods. Mathematics of Computation 37: 141–158. Paul, A.H., William, W. & Healy, R.W. 2000. VS2DI—a graphical software package for simulating fluid flow and solute or energy transport in variably saturated porous media. Water Resource Investigations Report 9, USGS, Denver, USA. Rao, B.N. & Rahman, S. 2000. An efficient meshless method for fracture analysis of cracks. Computational Mechanics 26: 398–408. Šimunek, J., van Genuchten, M. Th. & Sejna, M. 2006. The HYDRUS software package for simulating the two—and three-dimensional movement of water, heat, and multiple solutes in variably-saturated media. Technical Manual, Version 1.0, PC Progress, Prague, Czech Republic. van Genuchten, M. Th. 1980. A closed—formed equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal 44: 892–898.
with 315 nodes as shown in Figure 5. A comparison between the break through curves obtained from the present model and the FEM for three cross-sections along the longitudinal direction is shown in Figure 6. From the figure it is noted that the results obtained from the EFGM and FEM are agreeing well, thus ensuring the correct formulation of the EFGM for
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Numerical modeling of hydraulic behavior of bioreactor landfills M.V. Khire & M. Mukherjee Michigan State University, East Lansing, USA
ABSTRACT: A lab-scale physical model of a landfill consisting of a permeable blanket was developed. Waste was simulated by coarse sand. The permeable blanket and the sandy soil below the blanket were instrumented with sensors consisting of pressure transducers and Time Domain Reflectometry (TDR)—based water content sensors connected to a datalogger, to monitor the migration of injected liquid in the blanket and in the sand. Liquid injection in the blanket was carried out at a fixed rate using a magnetic drive pump. This manuscript presents the numerical modeling of the pressure heads and water contents measured in the physical model using the finite element model HYDRUS-2D. The numerical model was able to simulate the pressure heads and water contents relatively accurately when a steady state was reached. However, the model was not able to capture the pressure heads and water contents before the steady state was reached.
1
INTRODUCTION
Bioreactor landfills are designed and operated to accelerate the decomposition of organic constituents of municipal solid waste (MSW) by re-circulating leachate (or injecting other liquids) as a means to enhance moisture levels within the landfill and creating an environment conducive to rapid degradation of waste. Leachate recirculation or liquid injection can be performed using multiple techniques, both surface and subsurface. Subsurface application techniques are: (1) vertical wells; (2) horizontal trenches; and (3) permeable blankets. Haydar and Khire (2005), Haydar and Khire (2007) and Khire and Mukherjee (2007) have presented design guidelines for horizontal trenches, permeable blankets and vertical wells, respectively, through numerical studies using finiteelement numerical model HYDRUS-2D. However, it has not been possible to verify the modeling results because controlled field testing is almost impossible to verify such numerical models commonly used for modeling liquid flow in landfills. Hence, there is a need to verify the numerical models that are commonly used to design subsurface injection systems. A relatively large laboratory scale physical model of landfill was developed to conduct controlled lab tests to simulate hydraulics of liquid injection consisting of a permeable blanket. The lab model has sensors embedded in the sand simulating waste underlying the blanket to understand the hydraulics of liquid flow due to subsurface injection. While the ultimate objective of the research project is to estimate the real-time hydraulic conductivity of the underlying waste using
the pressure and flow data from the sensors embedded in the blanket, the landfill model developed for this purpose can be used for validation of numerical studies related to subsurface injection. The objective of the study presented here is to numerically simulate the pressure heads measured in the permeable blanket and the water contents of the underlying soil. This paper presents the design of the landfill model, data collected from the model, and numerical modeling results obtained from the finite-element model HYDRUS-2D. 2 2.1
MATERIALS AND METHODS Physical model
Figure 1 presents a schematic of the landfill model fabricated to simulate a horizontal permeable blanket. The dimensions of the landfill model are presented in Figure 1. All acrylic panels of the model were screwed together with rubber seals in-between the panels to provide a watertight box to contain the soils subjected to injection of water. A silicone sealant was applied at the seams to prevent potential leakage. A separate acrylic panel was used to make the bottom of the leachate collection system (LCS) raised to a slope of 3%. 2.1.1 Sensing system The sensing system used in the landfill model consisted of these sensors: (1) pressure transducers with built-in thermistors; (2) time domain reflectometry (TDR) water content sensors; and (3) flow sensors. All sensors were connected to a datalogger through
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and the volumetric water content measured by the TDR water content sensors was observed. The flow sensor is capable of measuring relatively low flow rates ranging from 8 to 165 cm3 /s. The flow sensor incorporates a pelton-type turbine wheel to measure the flow rate of water. Electrical pulses are generated as the turbine wheel rotates in response to the rate of flow. The sensor provides analog DC voltage output proportional to the flow rate. During calibration, a linear relationship was observed between the flow rates recorded by the flow sensor and the flow calculated from the levels measured by the pressure transducer. The accuracy of the flow sensor was within ±0.5%. Figure 1.
Schematic of fabricated lab-scale landfill model.
multiplexers to continuously monitor and log the data at frequencies ranging from 5 s to 30 min. The length and diameter of pressure transducer are 8.5 cm and 1.2 cm, respectively. The sensitivity of the pressure transducers is ±1% and have a measurement range of 0 to 92 cm of water head. Because the sensors are vented, barometric pressure is not recorded by the diaphragm. A thermistor is embedded within the pressure transducer to record temperature. The signal drift in the sensor performance resulted in pressure readings with errors ranging from 0.3 to 0.6 cm during the 6 month testing period. In recognition of the concern for zero drift and offsets, the accuracy of all sensors was checked from time to time by ponding water and checking the measured static heads during the course of the experiments. The pressure transducers were calibrated by adding de-ionized (DI) water at depths ranging from 15 to 35 cm in a container. A linear relationship between the depth of water and recorded pressure head readings was observed. The accuracy of the pressure transducer was within ±0.5 cm. The mini-TDR water content sensors selected for this study consisted of three pronged 0.15 cm diameter stainless steel rods mounted into an encapsulated plastic head. The probe rod length is 6 cm and spacing between the probe rods is 0.6 cm. The TDR sensors are connected to the datalogger via an electro-magnetic pulse generator and multiplexer. The TDR water content sensors were calibrated by inserting vertically in a container filled with dry sand and then water was gradually added in known steps until the sand became saturated. Topp’s (Topp et al. 1980) empirically derived calibration equation is used to convert the dielectric constant values obtained from the water content sensors to actual volumetric water content. A linear relationship between the volumetric water content calculated from known addition of water
2.1.2 Materials Accurate hydraulic characterization of the system is required in order to verify numerical models. Because MSW is highly heterogeneous and anisotropic (Haydar and Khire 2004) and measurement of representative hydraulic properties (both saturated and unsaturated) of waste is challenging, actual or surrogate waste was not used. In order to allow relatively precise hydraulic characterization, relatively homogeneous and isotropic standard sand (Ottawa sand) was used to simulate waste. The selection of Ottawa sand to simulate waste was based on preliminary numerical modeling which indicated that the chosen hydraulic property of the sand would generate pressure heads which would be within the dimensions of the model and the pressure heads would be large enough for measurement using the sensors for various magnitudes of rates of liquid injection. Besides, the saturated hydraulic conductivity (Ks ) of Ottawa sand is consistent with the typical values of hydraulic conductivities of MSW published by Fungaroli and Steiner (1979), Korfiatis et al. (1984) and Chen and Chynoweth (1995). Peagravel was chosen as LCS drainage material because it results in lower liquid heads in LCS (Khire et al. 2006). The saturated hydraulic conductivities (K) of the Ottawa sand and pea gravel were measured in the laboratory using a rigid wall permeameter (ASTM D 2434-68) using a constant head setup. The saturated hydraulic conductivities of the soils presented in Table 1 are average values obtained from triplicate tests. The soil water retention characteristics were measured under static equilibrium by hanging column method (ASTM D 6836). The experiments for determining the sorption curves for the soils were repeated twice. The soil water characteristic curves are described in terms of the van Genuchten (1980) fitting equation. Table 1 shows the hydraulic characteristics of the soils used in the landfill model and the fitting parameters.
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Table 1.
Properties of soils used in the landfill model. Saturated and unsaturated hydraulic properties with VG fitted parameters
Soil type
Simulated landfill unit
Ks (cm/s)
θs
θr
α (1/cm)
n
Ottawa sand Pea gravel
MSW Blanket and LCS
0.07 2
0.4 0.43
0.03 0.01
0.09 0.45
4.5 3
Notes: θs = saturated volumetric water content [-]; θr = residual volumetric water content [-]; and α [1/L] and n are van Genuchten’s fitting parameters (van Genuchten 1980).
Unsaturated hydraulic conductivity was also measured using an instantaneous profile method on an instrumented sand sample which was 30 cm high and had 20 cm diameter.
2.1.3 Fabrication of landfill model Figure 1 presents the schematic of the physical model. A 4-cm thick LCS drainage layer made up of washed pea gravel was constructed at the bottom of the plexiglass model. Two 1.5-cm diameter perforated pipes discharging freely into the atmosphere were placed in the LCS pea gravel layer. The perforated seepage pipes for LCS had at least 10 times higher flow capacity than the flows injected in the model to maintain the pressure head in the LCS within its thickness of 4 cm. About 38-cm thick dry Ottawa sand having dry density equal to 1.6 g/cm3 and porosity equal to 0.42 was placed below the permeable blanket. In the sand layer, two pressure transducers were embedded in vertically upright position at 10-cm intervals (not shown in Figure 1). A TDR water content sensor was placed immediately next to the sensing tip of the pressure sensors. The permeable blanket for the recirculation system was made up of the same pea gravel used in LCS. The blanket was about 50 cm long and 30 cm wide. The thickness of the blanket was 2.0 cm. The pressure sensors were vertically placed in the sand below the blanket such that the tips of the sensors were in the blanket. TDR sensors were placed horizontally in the blanket. In total six pressure transducers and a TDR water content sensor were embedded in the blanket. A 40-cm long perforated PVC pipe of 1 cm diameter was placed at the center of the blanket in the direction parallel to the width of the blanket where water was injected under pressure. One end of the injection pipe inside the blanket was capped and the other end was connected to a pressure transducer and a flow sensor to measure the injection pressure and flow rate, respectively. The flow sensor was connected to magnetic drive pump to pump water from a storage tank into the blanket. The magnetic drive pump was operated with a variable DC power supply to obtain variable injection flow rates. This
pump was chosen because of its ability to deliver a pulseless flow. A pressure transducer was also placed in the storage tank to monitor the change in head of water in the tank to monitor when and if a steady-state is reached. A closed loop recirculation system was implemented. The injected water after flowing through the soil and discharging freely in the atmosphere from the seepage pipes was collected in the storage tank. It was injected back into the blanket as shown in Figure 1. 2.2
Numerical model
HYDRUS-2D is a numerical computer model that simulates water, heat, and solute migration in unsaturated, partially saturated, or fully saturated porous media (Simunek et al. 1999). The program numerically solves the Richards’ Equation for saturatedunsaturated water flow and uses van-Genuchten function for soil-water characteristic curves and van-Genuchten-Mualem model for predicting the unsaturated hydraulic conductivity function. This model has been used for saturated/unsaturated liquid and solute transport through porous media in several studies (Haydar and Khire (2007); Khire and Mukherjee (2007); Haydar and Khire (2005); Khire and Haydar (2004); Scanlon et al. 2002; Henry et al. 2002; Pang et al. 2000; Rassam et al. 2002). 2.2.1 Boundary conditions and mass balance Because the boundary conditions are the driving force, specifying conditions on the boundaries is a key component of numerical analysis. Figure 2 shows the finite-element mesh generated in HYDRUS-2D and the boundary conditions applied to the model. All external boundaries were simulated as zero-flux boundaries. The evaporation from the model was negligible compared to the amount water that was injected in the model. The perforated injection pipe was simulated as a constant flux boundary because water was injected at a constant rate to simulate steady state continuous injection. Leachate collection pipes embedded in the LCS were simulated as seepage face boundaries. At seepage face boundaries, the model simulates flow only when the pore water pressure becomes zero.
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Mesh discretization and boundary conditions.
The minimum size of the finite-elements used for discretization of the problem domain, the time step, and the error tolerances for pressure head and water content were selected such that cumulative water balance error did not exceed 0.1%. We used an error tolerance of 0.1% for the volumetric water content and 0.1 cm for the matric suction. A minimum time step of 10−10 h and a maximum time step of 0.1 h was input to the model.
3
RESULTS
3.1 Pressure heads in blanket In the landfill model, de-ionized water was injected in the blanket at a constant rate of approximately 120 cm3 /s. The hydraulic conductivity of the permeable blanket being two orders of magnitude greater than the underlying sand, the water traveled through the blanket before infiltrating into the underlying sand. As the injected water traveled through the blanket,
6
Continuous injection, Q = 120 cm 3/s
6
5
h m and :hS
5
4
2.5 cm from injection pipe (IP) HYDRUS-2D
4
3 2 1
3 7.5 cm from IP
1
HYDRUS-2D
0 -1 Injection started -2 -40 0
2
HYDRUS-2D 12.5 cm from IP
40
80
0 -1
120
-2 160
Hydrus-2D simulated heads in blanket, hS (cm)
2.2.2 Initial conditions and other input The initial conditions input to the numerical model were consistent with those measured in the physical model before the injection was begun. The initial condition was entered in the form of volumetric water contents, measured by the water content sensors. The saturated and unsaturated properties tabulated in Table 1 were input as material properties for all landfill components. The total injected flow rate per cm length of the injection pipe within the blanket was input as the constant flux boundary for the injection pipe. The locations of sensors were input as observation nodes in order to obtain simulated pressure heads and water contents (Figure 2).
Experimental pressure heads in blanket, hm (cm)
Figure 2.
the hydraulic pressure heads (henceforth referred to as pressure heads) in the blanket increased. All pressure transducers in the blanket indicated an increase in the pressure head in response to the liquid injection event. The pressure heads in the blanket increased rapidly at the beginning of the infiltration event and approached a steady-state value within about 60 hours. The increase in the pressure head was earliest and greatest for the sensors located closest to the injection pipe. Responses of the pressure sensors embedded in the blanket are presented in Figure 3 as scatter points. The initial pressure heads developed in the blanket are a function of hydraulic conductivity as well as the initial degree of saturation of underlying sand. Hence, at the beginning of the injection event, the pressure heads were higher because the unsaturated hydraulic conductivity of sand was low because the sand was unsaturated. When the liquid injection started, the average degree of saturation of the sand below the blanket was about 70%. As the degree of saturation of the sand increased due to continuous injection of water, the pressure heads in the blanket decreased because of increase in the hydraulic conductivity of the underlying sand. In about 60 hours after the injection began, the pressure heads reached a steady-state value. A steady-state was assumed to have reached when the injected flow in the blanket equated the outflow from the LCS and the pressure heads in the blanket did not show substantial upward or downward trend for several hours after the flows became equal. Some pressure sensors had shown increase in pressure heads initially. As the degree of saturation of the underlying sand increased and hydraulic conductivity of the sand increased, the readings of those sensors dropped to zero as shown in Figure 3. Simulated pressure heads are also presented in Figure 3. The pressure heads in the blanket simulated by HYDRUS-2D were relatively close to the
Time elapsed (hours)
Figure 3. Comparison of experimental and numerically simulated pressure heads in the blanket.
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measured pressure heads at steady-state. As observed in the physical model, the simulated pressure heads decreased as the distance from the injection pipe increased. However, the numerical model was unable to simulate the initial high pressure heads in the blanket. The simulated pressure heads reached steady-state immediately. It took many hours (>60 hrs) for the heads to reach steady state in the physical model. 3.2
Degree of saturation
4
The water content sensors in the blanket showed increase in water content. The water content sensors embedded in the sand registered increase after the sensors in the blanket did. Thus, the injected water filled the blanket before substantial quantity of water started infiltrating into the underlying sand. The water content sensors were able to detect the gradual progressive changes in the degree of saturation of the underlying sand. The time when the pressure heads reached steady state as shown in Figure 3 synchronized with the water contents in the sand reaching saturation. However, HYDRUS-2D was not able to simulate the gradual increase in the water contents. The modeling results indicated that the increase in water content of the underlying sand was immediate as compared to the measured water contents which increased gradually and sequentially from top down. 3.3
phase flow of water, under the assumption that the air phase is always at a constant atmospheric pressure and is able to escape freely and does not impact the infiltration of water into soil. Hence, the model may not have calculated the initial increase in the water pressure heads measured in the blanket. The pressure heads in the blanket observed in the physical model subsided as the trapped air gradually escaped the sand. CONCLUSIONS
Pressure heads in a lab-scale blanket due to liquid injection were measured using an automated sensing system consisting of pressure sensors. The degree of saturation of the sand simulating waste below the blanket was measured using water content sensors and known porosity of the sand. HYDRUS-2D was used to numerically simulate the flow processes observed in the landfill model. The measured and simulated pressure heads matched at steady state. However, the numerical model was not able to simulate the measured initial high pressure heads and the gradual increase in average degree of saturation of the sand. Experiments and numerical simulations aimed to prove the hypotheses to explain the discrepancy are planned and other experiments using surrogate waste to explore hydraulic parameters associated with liquid injection systems are planned to be carried out in the near future.
Simulated versus observed results
The simulated and observed pressure heads in the blanket and water contents in the sand due to injection at steady state are relatively close. The initial high heads and the gradual increase in water content were not captured by HYDRUS-2D. A possible reason is hypothesized which might have contributed to why simulated results did not replicate the observed results before the steady state was reached. Air entrapment and compression of air that is below the vertically downward moving infiltrating front would result in an air pressure in the soil pores that is greater than atmospheric pressure. The air could not easily leave the system due the boundaries of the model and due to partially saturated pores aided in restricting the air escape under the sudden gush of vertically downward moving water front. The flow equations describing the flow of water in unsaturated soil are usually written with the implicit assumption that the air phase is continuous, is in equilibrium with the atmosphere pressure, and can move freely between the atmosphere and the unfilled pores of the soil. It is also assumed that the density and viscosity of air is negligible in comparison to water. Hence, most of these numerical models like HYDRUS-2D are designed to model only the single
ACKNOWLEDGEMENT Financial support for this project has been provided by the National Science Foundation (Grant No. CMS0510091) and Environmental Research and Education Foundation (EREF). We also express sincere appreciation to Jason Ritter of Campbell Scientific for his help related to datalogger programming and James Brenton for his help with the fabrication of the landfill model. The findings and opinions presented in this manuscript are those of the authors. REFERENCES Chen, T. and Chynoweth, D.P. 1995. Hydraulic conductivity of compacted municipal solid waste. Bioresour. Technol., 51(2–3), 205–212. Fungaroli, A. and Steiner, R. 1979. Investigation of sanitary landfill behavior. Vol. 1, Final Report, U.S. EPA 600/279-053a. Haydar, M.M. and Khire, M.V. 2004. Numerical evaluation of heterogeneity and anisotropy of waste properties on leachate recirculation in bioreactor landfills. The Journal of Solid Waste Management & Technology, Vol. 30(4): 233–243.
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Haydar, M. and Khire, M. 2005. Leachate Recirculation using Horizontal Trenches in Bioreactor Landfills. Journal of Geotechnical and Geoenvironmental Engineering, Vol. 131(7): 837–847. Haydar, M. and Khire, M. 2007. Leachate Recirculation using Permeable Blankets in Engineered Landfills. Journal of Geotechnical & Geoenvironmental Engineering, Vol. 133(4): 360–371. Henry, E.J., Smith, J.E. and Warrick, A.W. 2002. Twodimensional modeling of flow and transport in the vadose zone with surfactant-induced flow. Water Resources Research, Vol. 38(11): 331–3316. Khire, M.V. and Haydar, M.M. 2003. Numerical Evaluation of Granular Blankets for Leachate Recirculation in MSW Landfills. Proceedings of the Ninth Sardinia Solid Waste Conference, Cagliary, Italy, Oct. Khire, M., Haydar, M. and Mukherjee, M. 2006. Liquid head on landfill liners due to leachate recirculation. Proceedings of Geocongress 2006, Feb26–Mar1, Atlanta, GA. Khire, M. and Mukherjee, M. 2007. Leachate Injection Using Vertical Wells in Bioreactor Landfills. Waste Management, Vol. 27(9): 1233–1247. Korfiatis, G., Demetracopoulos, A., Bourodimos, E. and Nawy, E. 1984. Moisture transport in a Solid Waste Column. Journal of Environmental Engineering, Vol. 110(4): 789–796.
Pang, L., Close, M. Watt, J. and Vincent, K. 2000. Simulation of picloram, atrazine, and simazine leaching through two New Zealand soils and into groundwater using HYDRUS2D. Journal of Contaminant Hydrol., Vol. 44(1): 19–46. Rassam, D., and Cook, F. 2002. Numerical simulations of water flow and solute transport applied to acid sulfate soils. J. Irrig. Drain. Eng., Vol. 128(2): 107–115. Scanlon, B., Christman, M. Reedy, R. Porro, I. Simunek, J. and Flerchinger, G. 2002. Intercode comparisons for simulating water balance of surficial sediments in semiarid regions. Water Resources Research, Vol. 38(12): 5901–5915. Simunek, J., Sejna, M. and Van Genuchten, M. Th. 1999. HYDRUS 2D, Simulating water flow, heat, and solute transport in two-dimensional variably saturated media, Version 2.0, US Salinity Laboratory, ARS/USDA, Riverside, California and International Ground Water Modeling Center, IGWMC- TPS 53, Colorado School of Mines, Golden, Colorado. Topp, G.C., Davis, J.L. and Chinnick, J.H. 1980. Electromagnetic Determination of Soil Water Content: Measurements in Co-axial Transmission Lines. Water Resources Research, Vol. 16(3): 574–582. van Genuchten, M. Th. 1980. A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils. Soil Science Society of America Journal, Vol. 44: 892–898.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Finite element modelling of contaminant transport in unsaturated soil A.A. Javadi Computational Geomechanics Group, School of Engineering, Computer Science and Mathematics, University of Exeter, Exeter, UK
M.M. Al-Najjar Department of Engineering, Higher College of Technology, Al-Khuwair, Muscat, Oman
ABSTRACT: The movement of contaminants through soils to the groundwater is a major cause of degradation of water resources. In many cases, serious human and stock health implications are associated with this form of pollution. This work presents the development and validation of a numerical model for simulation of contaminant transport through unsaturated soils. The governing differential equations include two mass balance equations for the water and air phases and another balance equation for contaminant transport in the two phases. The governing equations are solved using a finite element method in the space domain and an implicit finite difference scheme in the time domain. The mathematical framework and the numerical implementation of the model are presented. The model has been validated and applied to a case study. A sensitivity analysis is performed to illustrate the influence of several coefficients on contaminant transport. The merits and limitations of the model are highlighted.
1
2
INTRODUCTION
In recent years, interest in understanding the mechanisms and prediction of contaminant transport through soils has dramatically increased because of growing evidence and public concern that the quality of the subsurface environment is being adversely affected by industrial, municipal and agricultural waste. In assessing the environmental impacts of waste discharges, engineers seek to predicate the impact of emission on contaminant concentration in nearby air and water (Nazaroff and Alvarez-Cohen, 2001). The high costs, large time scales and lack of control over the boundary conditions have prevented the development of field scale experiments (Hellawell and Sawidou, 1994). In this paper, the main governing phenomena of the miscible contaminant transport including advection, mechanical dispersion, molecular diffusion and adsorption are considered. The contaminant transport equation together with the balance equations for flow of water and air are solved numerically using the finite element method, subject to prescribed initial and boundary conditions. The model is used to analyse the transport of a petroleum-based contaminant in a site in the south west of the UK. The results of the model prediction are compared with those measured on the site. It is shown that the developed model is capable of predicting the variations of the contaminant concentration with time and space with a very high accuracy.
GOVERNING EQUATIONS
There is a broad range of issues that are of interest in relation to transport of contaminant in soils. The problem becomes more complex when the soil is unsaturated. Unsaturated soil is a multiphase system, because at least two fluid phases are present: water and air. The governing equations that describe fluid flow and contaminant transport in the unsaturated zone will be presented in this section. 2.1
Modelling of water and air flow
The governing differential equation for water flow is based on the conservation of mass of the groundwater, leading to (Javadi, et al. 2006): cww
∂uw ∂ua + cwa = ∇[Kww ∇uw ] ∂t ∂t + ∇[Kwa ∇ua ] + Jw
(1)
where cww = cfw + cvw ; cvw = nSa Kfw ;
cwa = cfa + cva ; cva = nSa Kfa ;
cfw = −n(ρw − ρv )
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∂Sw ; ∂s
cfa = n(ρw − ρv )
∂Sw ; ∂s
Kww =
ρw Kw + Kvw ρw ; γw
∂h ∂ψ ∇ua ; Kfa = ρ0 ∂ψ ∂s Kvw = −
Kwa = ρv Ka + ρw Kva ; Kfw
Datms Vv n Kfw ; ρw
2.2 Modelling of contaminant transport In porous media, contaminant transport occurs by various processes including advection, diffusion and mechanical dispersion. The mass balance equation of contaminant transport can be written as:
∂h ∂ψ ∇uw ; = −ρ0 ∂ψ ∂s
Kva = −
Datms Vv n Kfa ; ρw
∂(Rθw cw ) + ∇(vw cw ) − ∇(θw Dw ∇cw ) + λw θw cw = F w ∂t
Jw = ρw ∇(Kw ∇z)
(3)
in which n is the porosity of the soil, Kw is the conductivity of water, Ka is the conductivity of air, Sw is the degree of saturation of water, Sa is the degree of saturation of air, ρw is the density of water, ρv is the density of water vapour, ρ0 is the density of saturated soil vapour, s is the soil suction, Vv is the mass flow factor, uw is the pore-water pressure, ua is the pore-air pressure, Datms is the molecular diffusivity of vapour through air, γw is the unit weight of water, ψ is the capillary potential, h is the relative humidity and ∇z is the unit normal oriented downwards in the direction of the force of gravity. The governing differential equation for air flow is based on the conservation of mass of the ground air, leading to (Javadi, et al. 2006):
where the four terms on the left hand side of the equation represent the variations of contaminant concentration with time, effect of advection, effect of dispersion and diffusion and effect of chemical reactions respectively and F w represents the source/sink term for water. In this equation θw is the volumetric water content, vw groundwater velocity, Dw the coefficients of dispersivity tensor, λw is the reaction rate for water, cw is the contaminant concentration, R = [1 + θs ρs Kd /θw ] is the retardation coefficient, ρs is the density of the solid phase, Kd is the distribution coefficient and θs is the volumetric content of the solid phase (McElwee, 1982).
3 ∂uw ∂ua caw + caa = ∇ [Kaw ∇uw ] ∂t ∂t + ∇(Kaa ∇ua ) + Ja
(2)
where caw = caw1 + caw2 ;
caa = caa1 + caa2 ;
∂Sw ; ∂s ∂Sw ; = nρda (Ha − 1) ∂s
caw1 = −nρda (Ha − 1) caa1
caw2 = n(Sa + Ha Sw )cdaw ; caa2 = n(Sa + Ha Sw )cdaa ; cdaw = − Kaw =
Rv Kfw ; Rda
Ha ρda Kw ; γw
cdaa =
Rv 1 − Kfa ; Rda T Rda
Kaa = Ka ∇uw ;
NUMERICAL SOLUTION
The nonlinear governing differential equations of fluid flow and contaminant transport were solved using a finite element method in the space domain and a finite difference scheme in the time domain. The governing equations describing transport of contaminants in unsaturated soil include two sets of equations. The first set describes the flow of water and air and the second set describes the transport of a miscible contaminant through the water and air phases. In this work, it is assumed that the flow processes do not depend on the transport processes while the transport processes are dependent on the flow fields as they rely on the way in which each fluid phase transports the contaminant. This allows the flow equations to be solved independently of the transport equations. It would therefore be logical to breakdown the solution procedure into two stages: in the first stage the flow equations for water and air are solved simultaneously and then in the second stage, the calculated values of pore water and pore air pressures (from the first stage) are used to solve the transport equation and to calculate the values of contaminant concentration in the domain.
Ja = Ha ρda ∇(Kw ∇z) 3.1 in which Ha is the Henry’s volumetric coefficient of solubility, ρda is the density of dry air, Rda is the specific gas constant for dry air and Rv is the specific gas constant for water vapour.
Numerical solution of governing differential equations for water and air flow
The governing differential equations for water flow and air flow (equations 1 and 2) as defined above, have two variables uw and ua . These variables are primary
874
unknowns and can be approximated using the shape function approach as:
fw =
n "
! ∇N T (Kw ρw ∇z) de
e=1
e
uw = uˆ w =
n "
Ns uws
−
(4)
n "
Ns uas
(5)
1
where, Ns is the shape function, uws and uas are the nodal pore-water and pore-air pressures respectively, and n represents the number of nodes in each element. Replacing the primary unknowns with shape function approximations, equations (1) and (2) can be written as: ∇[Kww ∇ uˆ w ] + ∇[Kwa ∇ uˆ a ] + Jw − Cww
(6)
Caw
Caw =
n "
! N T Caw N de ;
Caa =
n "
! N T Caa N de ;
e=1
e
(7) Kaw =
n "
! ∇N T (Kaw ∇N ) de ;
e=1
e
Kaa =
n "
! ∇N T (Kaa ∇N ) de ;
e=1
e
fa =
n "
! ∇N T (Kw ρda Ha ∇z) de
e=1
e
(8)
−
n "
% $ N T ρ vˆ fn + vˆ an .d e
e=1 e n "
! N T Cww N de ;
e=1
e
n "
! N T Cwa N de ;
e=1
e
Kww =
n "
! ∇N T (Kww N ) de ;
In the above equations vˆ fn is the approximated velocity of free dry air and vˆ an is the approximated velocity of dissolved dry air. Spatially discretised equations for coupled flow of water and air, given by the above equations, can be combined in a matrix form as:
Kww Kwa uws Cwa u˙ ws C f + ww − w =0 Kaw Kaa uas Caw Caa u˙ as fa
e=1
(10)
e
Kwa =
(9)
e=1
where,
Cwa =
∂uws ∂uas + Caa + Kaw uws + Kaa uas = fa ∂t ∂t
e
where, Rw and Ra are the residual errors introduced by the approximation functions. A finite element scheme is applied to the spatial terms, employing the weighted residual approach, to minimise the residual error represented by equations (6) and (7) and integrating the equations over the spatial domain (e ). Spatial discretisation of the governing differential equation for water flow can be written as: ∂uws ∂uas + Cwa + Kww uws + Kwa uwa = fw Cww ∂t ∂t
in which vˆ wn is the approximated water velocity normal to the boundary surface, vˆ vd is the approximated diffusive vapour velocity normal to the boundary surface, vˆ va is the approximated pressure vapour velocity normal to the boundary surface and e is the element boundary surface. Similarly, the spatial discretisation of governing differential equation for air flow leads to:
where,
∂ uˆ w ∂t
∂ uˆ a = Rw − Cwa ∂t ' & ∂ uˆ w ∇ Kaw ∇ uˆ w + ∇(Kaa ∇ uˆ a ) + Ja − Caw ∂t ∂ uˆ a = Ra − Caa ∂t
Cww =
Nr {ρw vˆ wn + ρw vˆ vd + ρw vˆ va }d e
e=1 e
1
ua = uˆ a =
n "
n " e=1
e
! ∇N T (Kwa N ) de ;
where u˙ ws =
875
∂uws ∂uas and u˙ as = . ∂t ∂t
A time discretisation of equation (10) is achieved here by application of a fully implicit mid interval backward difference algorithm. Applying a finite difference scheme (Stasa, 1985) to equation (10) will result in: φ
n+1/2 n+1
A
+B
n+1/2
φ n+1 − φ n t
+C
n+1/2
where
1
H=
=0
C Kww Kwa ; B = ww Caw Kaw Kaa
u f C = W ; φ = ws fa uas
Cwa ; Caa
and n, n+1 stand for time levels (tn and tn+1 = tn +t). Equation (11) can be further simplified to give:
3.2
Numerical solution of contaminant transport governing equation
In the absence of the source and sink terms, equation (3) will reduce to: ∂(θ c) + ∇(vc) − ∇(D∇c) + λc = 0 ∂t
(13)
The primary unknown can be approximated using the shape function approach as: θ c = θˆ cˆ =
n "
Ns θ c s
(14)
vcBij + DcEij + λcAij ;
a
n "
Applying a finite difference scheme (Stasa, 1985) to equation (16) will result in: M
−1 n+1/2 n φ Bn+1/2 B φ n+1 = An+1/2 + − C n+1/2 t t (12)
b
∂c ∂c b ∂c ∂c +λ N 2 vc − D ; ∂x ∂y a ∂x ∂y 1 ∂N ∂N Aij = NNdxdy; Bij = N N dxdy; ∂x ∂y ∂N ∂N ∂N ∂N Eij = dxdy ∂x ∂y ∂x ∂y
F=
where
a
n " 1
(11)
A=
n " θc Aij ; t b
M=
! (θ c)n+1 − (θ c)n + H (1 − γ )cn + γ cn+1 + F n+1 = 0 t (17)
where, t is the time step. The value of γ is usually taken as 0, 0.5 and 1.0 for the forward, central and backward difference schemes respectively. The backward difference scheme (γ = 1) has been used in the model as it is unconditionally stable for all values of t . The solution of equations (11) and (17) using the two-stage procedure described above, will give the distribution of the contaminant concentrations at various points within the soil and at different times, taking into account the interaction between the flow of air and water and various mechanisms of contaminant transport. 4
NUMERICAL RESULTS
1
c = cˆ =
n "
4.1 Case study Ns cs
(15)
1
where cs is the nodal contaminant concentration and n is the number of nodes per element. In the present work, eight-node quadratic element has been used (n = 8). Replacing the primary unknowns with shape function approximation in equation (13) and employing the Galerkin weighted residual approach to minimise the residual error represented by this approximation; the discretised global finite element equation for single component of contaminant takes the form: M
dc + Hc + F = 0 dt
(16)
The developed finite element model has been validated against a wide range of test cases from the literature. In this paper, the application of the model to a case study is presented which involves analysis of transport of a petroleum-based contaminant at a site in south west of England, in order to study the potential for contamination from previous commercial use as a fuel filling station and vehicle repair workshop. 4.1.1 Site description The local geology comprises Yeovil Sand beds to 60 m depth, with Jurassic limestone immediately to the north. The surface geology of the site includes shallow, fine alluvial deposits containing organic matter, and
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4.1.3 Sampling Eight boreholes for monitoring groundwater have been used for the survey as shown in Fig. 1. These were all sampled at 0.3 m below groundwater surface to provide a comprehensive sample containing possible dispersed and dissolved fuel compounds. Such contaminates can be expected to show greatest mobility and hence potential for migration off-site.
Figure 1.
Plan of the site.
layers of coarse grained material, probably weathered limestone with limestone fragments. The site is underlain by a major aquifer and is on the boundary of a fluvial floodplain, having an annual flooding risk of 1%. The garage is adjacent to the junction of two minor roads. It is surrounded by domestic dwellings, with a watercourse approximately 10 m to the north and 2 m below forecourt level, draining to the east. The plot is approximately 20 m by 20 m and consists of a building formerly used as a shop and office, together with two attached workshops with concrete floors, used for repairs and storage (Fig. 1). Adjacent to the current office entrance is a store containing two paraffin or light oil tanks, each of 1300 litres capacity. The forecourt is concrete surfaced above the fuel tanks, with a tarmac and gravel access road to the rear. The fuel filling area is directly adjacent to the public pavement and consists of four diesel pumps. Five manhole covers are nearby, two of which provide access to fuel storage tanks, with two adjacent surface drains. 4.1.2 Site observation Numerous inspection covers are present on the site, providing access to fuel tank fillers, pipe manifolds, water supply pipes and two surface drains, with two further drains on the site periphery. Tests carried out by a consulting engineering company, showed that one drain adjacent to the fuel pumps discharges directly into a receptor, which means that any spillages from pump operation has a direct pathway to local surface water. Water present beneath some inspection covers has shown considerable contamination by heavy oils.
4.1.4 Water Four monitoring boreholes had previously been installed to three meters depth, adjacent to the storage tanks and pump areas. For the tier in investigation, four additional boreholes were installed by the consultant in charge of the investigation as close as possible to the site boundaries. The installation points were selected to surround the site as far as practicable, with emphasis on the north and west boundaries, as observations suggest that groundwater is likely to flow in this direction. The new boreholes, B5 –B8 , were of a similar design to the original, slotted from 1 m below ground level, and were installed to a depth of five metres. Groundwater in the boreholes was allowed to equilibrate and was sampled four days after installation. Water samples were taken at 0.3 metres below groundwater surface to exclude floating product, which may be constrained on the site, and to detect dispersed and dissolved fuel components which are more vulnerable to migration with groundwater. The receptor was also sampled upstream and downstream of the site, adjacent to the site boundaries. 4.1.5 Soil During installation of the boreholes, soil samples were taken, where possible, at a depth just below first water strike Fig. 6. A survey was initiated in January 2003 in order to assess the extent of contamination throughout the site and to assess general groundwater movement. This survey found hydrocarbon contamination at all sample points within the site and around the periphery as shown in Table 1. A section of the site, 40 m wide and 10 m deep (Fig. 2) was analysed using the developed finite element model. The section was divided into 400 Table 1. 2003).
Analysis of contaminants in groundwater (Jan
Sample ID
Total Petroleum Hydrocarbons (TPH) Mg/l
B2 B5 B6 B7
115034 22000 20100 2462
877
Figure 2.
contaminant concentration (mg/l)
140000
A conceptual model of the site.
120000
Dm = 10
100000
Dm = 10
80000
6
Dm = 10
8
Dm = 10
7
5
60000 40000 20000 0 0
140000
Source
10
15
20
25
30
35
40
distance from concentration source (m)
FEM-Model - Feb 2003 FEM-Model - Mar 2003
Figure 4. Distributions of contaminant concentration in Feb. 2003 for different values of diffusion coefficient.
FEM-Model - Jun 2003 FEM-Model - Sep 2004
100000
5
Measured data - Jan 2003
Measured data - Sep 2004
80000
140000
B6
60000
contaminant concentration (mg/1)
contaminant concentration (mg/l)
120000
B2
40000
20000
0 0510152025303540
distance from concentration source (m)
Figure 3. Comparison between measured data and finite element model predictions.
k w = 10 7
120000
100000
kw = 10 6
kw = 10 5
80000
kw = 10 4
60000
40000
20000
0 0
(40 by 10) eight-node quadratic rectangular elements. The boundary conditions included hydrostatic water pressure distributions on the left and right boundaries and fixed (zero) fluxes on the bottom boundary. The air pressure was fixed at all nodes (saturated region). The transport of the contaminant by advection, diffusion and dispersion mechanisms was considered. In the model the water velocity vw was estimated (by taking the hydraulic gradient as the gradient of the groundwater surface) from the levels of water observed in boreholes B2 and B5 . Fig. 3 shows the distributions of contaminant concentration between January 2003 and September 2004. It can be seen that the contaminant concentration decreased gradually over this period of time from an initial distribution of amplitude (c = 115034 mg/l) centred at (x = 17.5 m). The figure also compares the results of the model prediction with the measured values of contaminant concentration recorded in September 2004. It is shown that the results of the developed model are in good agreement with field measurements, both in terms of magnitude and trend of variations. After 16 months, the concentration of contaminant in the soil reduced by 99.3% and the slight difference between the measured and predicted concentrations could be attributed to the errors in determination of coefficients
5
10
15
20
25
30
35
40
ditance from concentration source (m)
Figure 5. Distributions of contaminant concentration in Feb. 2003 for different values of effective permeability.
of diffusivity and permeability as well as the simplifications adopted in numerical modelling. Considering the fact that a two dimensional model was used to simulate a complex problem; such small differences in predictions are inevitable, expected and acceptable for practical applications. 4.1.6 Sensitivity analysis Sensitivity is a measure of the effect of change in one parameter on another parameter. The sensitivity of a model dependent variable to a model input parameter is the partial derivative of the dependent variable with respect to that parameter (McElwee, 1987). The values of diffusivity Dm and permeability kw coefficients used in the above case study were determined in the site investigation. A sensitivity analysis is performed to examine the sensitivity of the model to variations of these two major parameters. Figs. 4 and 5 show the effect of variations in the coefficients of diffusion Dm and effective permeability kw on concentration distribution. It can be seen that these parameters
878
play a significant role in transport of the contaminant and changes in concentrations with time. In both cases, the contaminant concentration decreases considerably with increasing the value of the coefficients of diffusion Dm and effective permeability kw . 5
presented model in simulating the transport of contaminants in soils in a real case study. The sensitivity analysis illustrated the influence of a number of coefficients on contaminant transport. The results show that the developed numerical model is capable of predicting, with a good accuracy, the effects of various mechanisms of contaminant transport through soils.
CONCLUSIONS
This paper presented a numerical model for predicting contaminant transport through unsaturated soils. The model is capable of simulating several phenomena governing miscible contaminant transport in the soils including advection, dispersion and diffusion, adsorption and chemical reactions. A transient finite element model was developed to solve the governing equation of contaminant transport together with the equations for air and water flow. After validation, the numerical model was applied to a case study involving transport of a petroleum-based contaminant at a site in south west of England. The model was used to study the distribution of the contaminant with time and to evaluate the potential and degree of contamination of the site from previous commercial use as a fuel filling station and vehicle repair workshop. The numerical results illustrated the performance of the
REFERENCES Hellawell E.E. & Sawidou, C. 1994. A study of contaminant transport involving density driven flow and hydrodynamic clean up. Proc. Centrifuge Conference. University of Cambridge, UK. Javadi, A.A., AL-Najjar, M.M. & Elkassas, A.S.I. 2006. Numerical modelling of contaminant transport in unsaturated soil. Proc. 5th International Congress on Environmental Geotechnics. Cardiff University, UK: 1177–1184. McElwee, C.D. 1987. Sensitivity analysis of ground water models. Advanced in Transport Phenomena in Porous Media. NATO Advanced Study Institute Series. 751–817. Nazaroff, W.W. & Alvarez-Cohen L. 2001. Environmental Engineering Science. John Wiley & Sons Inc. USA. Stasa, F.L. 1985. Applied Finite Element Analysis for Engineers. Holt, Rinehart and Winstone, Inc., Orlando, USA.
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Case studies
Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Gulfs between theory and practice in unsaturated soil mechanics G.E. Blight University of the Witwatersrand, Johannesburg, South Africa
ABSTRACT: It has often been observed that the adoption of new theories or practical innovations in engineering practice is an exceedingly slow process. The time lapse between publication of a new idea and its adoption as a commonly used article or procedure may be as long as 25 to 30 years. The paper suggests that one of the main reasons for this tardy progress is that new theories and other innovations are published prematurely, or in incomplete form. The potential client or user of an innovation is not given the complete story from theory to practical application, to verification and validation by field testing. Thus a hiatus or gulf develops and persists between potential advances of practice and the actual progress of their implementation. The paper presents two examples of cases where it has been possible to go through this complete process and produce an essentially complete concept, immediately available for wider use, and resulting in rapid progress.
1
INTRODUCTION
The motivation for this paper arose from listening to three invited lectures delivered at a recent international conference on unsaturated soils. The first lecture (Nelson et al., 2007) detailed the development of semi-empirical methods for estimating the heave of expansive clay profiles in Colorado and uplift forces in foundation piers constructed to resist heave. The second lecture (Alonso and Pineda, 2007) dealt (amongst other topics) with field measurements of the swelling generated within soft rocks by the crystallization of soluble salts in the pore water. The third lecture (Fredlund, 2007) set out protocols for the application of unsaturated soil mechanics theory to practical problems. Similar methods to those set out in the Nelson lecture have been developed in several parts of the world. Being semi-empirical, each requires field testing to establish its validity, and is not transferable to other geological and climatic regions without re-evaluation for the new conditions. This was not brought out in the lecture, nor was satisfactory evidence of the proposal’s validity in Colorado presented. The Alonso lecture described the problem and discussed its causes, but made no suggestions as to how to avoid or overcome it, except to resist the swelling forces (in the case discussed) by providing a massively reinforced concrete lining to a tunnel passing through the potentially swelling rock. The Fredlund lecture dealt almost entirely with the prediction of the SWCC from a choice of one of 14 equations and gave the impression that once the SWCC had been determined, all other required soil properties could be satisfactorily predicted there from.
Thus in each case, the listener was left wondering how to proceed, what solutions were possible, and in the case of the suggested procedures, how applicable, realistic, transferable and valid they were. In each lecture a hiatus or gulf was left between theory and implementation. Unless such gulfs can be bridged, the prudent practising geotechnical engineer will continue to use his present tried and trusted methods and progress in the application of advances in the theory of unsaturated soils to practice will continue to be slow. In an effort to show that gulfs like these can be bridged, this paper will briefly recall two case histories in which successful solutions were found, demonstrated to be valid and applied to practical problems caused by the effects of unsaturation. In the first (Blight, 1984), the problem was caused by a water table depressed by evapotranspiration from a eucalyptus plantation. In the second (Blight, 1976), the cause of the problem was the upward. migration and subsequent crystallization of salts in solution in the pore water of crushed stone road bases. In an era when basic soil phenomena and test techniques are re-discovered at ten-yearly intervals, e. g. the recent re-discovery of the principle of the pressure plate (Buckingham, 1907, Sawangsuriya, et al., 2007), it is probably not untimely for these two cases to be recalled. 2
UPLIFT FORCES MEASURED IN PILES IN EXPANSIVE CLAY
The site of the 3600 MW coal-fired power station at Lethabo is underlain by soils residual from horizontally bedded siltstone. The site is also crossed by a
883
Figure 1.
Depression of water table by evapotranspiration from eucalyptus plantation.
meandering palaeochannel of the nearby Vaal river, the palaeochannel being filled with river alluvium consisting of desiccated, fissured and shattered claysands. The residual siltstone occurs as a fissured and shattered clayey silt. Prior to construction, the site was partly covered by a plantation of closely spaced mature eucalyptus trees, 20 m in height, the remainder being farmland on which maize was grown as a summer crop. During the site investigation it was established that the water table under the cropped areas was 2 to 3 m below surface. However, under the trees, the water table had been depressed to depths of 18 to 22 m below surface, as shown diagrammatically in Figure 1. Once the trees had been cleared, it was obvious that the water table would eventually recover. The desiccated state of the soils as well as the high measured swell indices would result in severe swelling of the soil as the water table rose. The potential extent of the water table recovery was unknown, but because there is usually a lot of spillage and accidental leakage of water on the site of an operating water-cooled thermal power station, it was reasonable to assume that the final rest level of the water table would match the 2 m below surface observed in the cropped land (it eventually rose to 4 m below surface). On this basis the amount of surface heave was calculated to vary from 85 mm on the eastern boundary of the power station to 120 mm on the western boundary. It was therefore decided to found all structures, and especially the level-sensitive turbo-alternator and boiler foundations on deep piles designed to resist uplift. The shear strength of the soil was measured by means of drained triaxial tests on undisturbed specimens measuring 76 mm dia. by 150 mm long,
Figure 2. Summary of strengths measured in small-scale saturated drained triaxial tests and pulling tests on 1 m dia by 2 m long plugs.
after saturating and consolidating the soil to the estimated final effective overburden stress. Because of the fissured nature of the soil and the known scale effect between small and large specimens, it was later decided also to carry out a series of plug-pulling tests on concrete plugs approaching the size of the piles that would be used. The plugs were 2 m in length and were cast at the bottom of 1.050 m dia. augered holes, drilled to various depths. A drain tube was provided to release suction from the base of each plug, and the plugs were cast on waxed cardboard void formers to prevent adhesion of the base to the soil. Two plugs,
884
forces each amounted to 1500 kN. Thus the test measurements were valid and design and installation of the piles proceeded, based on the test results. The completed power station has now operated for over 20 years with no problems arising from the pile foundations. Level measurements have confirmed the
Figure 3. Development of tension in test pile 2 with time and comparison of measured and predicted depth-tension relationships.
one in alluvium and one in siltstone were tested with the soil at in situ water content. For the remainder the soil was soaked for 3 to 4 weeks by flooding the hole to a depth of 0.5 m above the plug and also filling the drain tube with water. Figure 2 summarises the results of the laboratory and plug-pulling tests. On the basis of the plug tests, a group of seven 1.050 m dia. by 33 m deep instrumented piles was installed with a centre-to-centre spacing of 2.625 m. Three of the piles were instrumented to measure pile tension and were arranged to give the equivalent of a corner, a side and an interior pile of a pile group. The soil surrounding the pile group was flooded via a grid of sand-filled water injection holes, and the development of the pile tensions was observed by means of the built-in instruments. Figure 3 shows the development of tension in one of the test piles with time and compares the measurements with the design tension based on the plug-pulling tests. Figure 4 provides a check on the overall validity of the test results. It represents the differentiation with depth of the pile tensions to give the distribution of shear stresses developed down the depth of each of the pile shafts. For vertical force equilibrium of the pile, the area of the shear stress diagram above the depth at which the shear stress line crosses zero must equal that of the shear stress diagram below, i.e., the measured uplift and anchorage forces must be equal. For piles 1 and 2 (the corner and side piles), the areas of the uplift and anchorage force diagrams were each 2000 kN, while for pile 3 (the interior pile) the uplift and anchorage
Figure 4. Shear stresses developed down length of pile and comparison with measured shear strength-depth relationship.
Figure 5. Profiles of soluble salt content beneath (a) a damaged asphalt surfacing and (b) an undamaged surfacing.
885
Figure 6. (a) White salt stains on a road surface after a light rain shower (b) Salt blisters on the surface of the road shown in (a).
886
have allowed pore water to evaporate through it. The migration of salt shown in Figure 5b must have taken place before the surfacing was applied. Thus an effective preventive measure would be to use thicker surfacings, designed to be impervious. c. As a third possible prophylactic measure, the solubility of the salts can be substantially reduced by treating the aggregate with a high calcium slaked lime. This converts the more soluble sodium, magnesium and iron sulphates to calcium sulphate which has a much lower solubility of only 0.02 g/litre, and reduces the mobility of the salts.
predicted heave movements of the soil surface surrounding the power station. The foundations for the next power station to be built on similar soils, that at Majuba, were designed following a similar procedure. Thus the process was complete, leaving no gulf between theory and application.
3
DAMAGE TO PAVEMENT SURFACINGS CAUSED BY UPWARD MIGRATION OF SOLUBLE SALTS
Problems with soluble salts in road-making materials have been reported from Australia, India, South Africa and the United States (e.g. Netterberg, 1970). In coastal areas, salts commonly consist of sodium and magnesium chlorides derived from seawater. Inland, sulphates of sodium, magnesium, iron and calcium are common, and derive from oxidation by natural weathering processes of metallic sulphides. Mine waste rock, ash, clinker, slag, and other rocklike industrial wastes frequently contain soluble salts. If waste containing salts is used to construct road or pavement layers, and especially in arid to semi-arid climates, evaporation will cause the salts to migrate to the surface in solution and may cause physical damage to road or pavement surfacings when they crystallize out at or just below the surface. Figure 5 shows profiles of soluble salt content (a) for a damaged asphalt surfacing and (b) for an undamaged surfacing. Typically, the first sign of damage to a road surface is the appearance of white streaks and patches on the surface after a light rain shower, as shown in Figure 6a. The damage may progress to the formation of saltfilled blisters in the surfacing, as shown (at the same site) in Figure 6b. Depending on the size and intensity of the blistering (individual blisters may be as large as 150 mm in dia. and 50 mm high), traffic may break up the blistered surface and cause pot-holes to form. Figure 5 gives two clues as to how to overcome the problem of salt blistering: a. For new construction, material containing more than a defined maximum of soluble salts should not be used. b. It will be noted from Figure 5a that the damaged surfacing is only about 10 mm thick, whereas (Figure 5b) the undamaged one is 40 mm thick. Moreover, the salt content of the damaged surfacing is higher than that of the material below it, showing that salt has concentrated within the pores of the asphalt. This indicates that the surfacing is relatively permeable and has allowed salt-laden pore water to move upwards and evaporate at the surface, depositing the salt. In contrast, the salt content of the undamaged surfacing is negligible, showing that it is sufficiently impervious, not to
Further investigation in several localities showed that salt blistering did not occur, provided that the overall salt content of the road aggregate was less than 0.2% by dry mass. Also, if the ratio of the asphalt permeability in mm/s to the surfacing thickness in mm was les than 30 × 10−6 /s, no salt blistering was observed. Of a), b) and c) above, a) is the most useful for new construction. Sources of crushed rock, or other granular material are now routinely tested for soluble salt content. If the salt content exceeds 0.2% by dry mass, it is rejected for use as road or surfacing aggregate, or it may be treated with lime. For the repair of salt-damaged surfacings, an overlay of impervious asphalt is used in a thickness to give a maximum ratio of permeability to thickness of 30 × 10−6 /s. The results of the completed investigation could be applied immediately, no hiatus existed between theory and application, and progress was made immediately.
4
CONCLUSION
If they are to contribute to progress in the applied practice of the geotechnics of unsaturated soils, potential advances, such as new theories or techniques must be demonstrated to be valuable and viable by field application and testing, followed by a report or publication that details the complete progression from theory, to testing, to design, to practical application and evaluation. Publication of parts of the progression have a value as milestones toward progress, but will only result in progress once all of the steps have been completed and a comprehensive report has been made available.
REFERENCES Alonso, E.E. and Pineda, J.A. 2007. Degradation of argillaceous rocks: a challenge for unsaturated geomechanics. 3rd Asian Conference on Unsaturated Soils, 3–26, Nanjing, China: Science Press. (ISBN 7-03018739- 0/TU.535).
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Blight, G.E. 1976. Migration of subgrade salts damages thin pavements. Transportation Engineering Journal, ASCE, Vol. 102, No. TE4, 779–791. Blight, G.E. 1984. Uplift forces measured in piles in expansive clay. 5th International Conference on Expansive Soils 363–367, Adelaide, Australia. Buckingham, E. 1907. Studies of the movement of soil moisture. U.S. Department of Agriculture, Bureau of Soils, Bull 10. Fredlund, D.G. 2007. Engineering design protocols for unsaturated soils. 3rd Asian Conference on Unsaturated Soils, 27–46, Nanjing, China: Science Press. (ISBN 7-03-018739-0/TU.535).
Nelson, J.D., Chao, K.-C. and Overton, D.D. 2007. Design of pier foundations on expansive soils. 3rd Asian Conference on Unsaturated Soils, 97–108, Nanjing, China: Science Press (ISBN 7-03-018739-0/TU.535). Netterberg, F. 1970. Occurrence and testing for deleterious salts in road construction materials with particular reference to calcretes. Symposium on Soils and Earth Structures in Arid Climates, 87–92, Adelaide, Australia. Sawangsuriya, A., Edil, T.B., Benson, C.H. and Wang, X. 2007. A simple setup for inducing matrix suction. 3rd Asian Conference on Unsaturated Soils, 499–504, Nanjing, China: Science Press (ISBN 7-03-018739-0/ TU.535).
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The repeatability of soil water balances at the same site from year to year G.E. Blight University of the Witwatersrand, Johannesburg, South Africa
ABSTRACT: The soil water balance has been shown to be a characteristic that is essential to establish for an unsaturated soil site, if the subsequent engineering behaviour of the site is to be fully understood. Establishing a soil water balance requires at least a year of observations and measurements. Even then there may be some doubt if the water balance measurements are repeatable, let alone representative for future years. If it can be shown that water balance measurements are repeatable and reliable, the effects of variation in annual rainfall can be estimated with fair confidence, and the long term soil behaviour predicted more reliably. It so happened that the annual rainfall for the site described in this paper was near-identical in the 2004/2005 and 2005/2006 wet seasons, both in total quantity and distribution with time. This has allowed a comparison to be made, showing that water balance measurements for the two similar years were also similar. Unfortunately, variability of soil water distribution and uncertainty in its measurement does not permit a more definite statement. However, the similarity is close enough to strengthen the case for a water balance to be defined whenever an important unsaturated soil site is to be characterized.
1 1.1
1.2 The experimental site
INTRODUCTORY INFORMATION The soil water balance
To understand the interaction between local climate and the soil water system, it is necessary to evaluate the annual soil water balance, which can be written symbolically as:
R−
RO + S −
E=
RE + losses (1)
In which the summation is carried out over at least a full year and where R = rainfall, RO = runoff and therefore (R −RO) = infiltration at the soil surface, S = water stored in the soil, E = evapotranspiration at the soil surface and RE = recharge to water table. ‘‘Losses’’ represent inaccuracies in the measurements or lack of definition of boundary conditions in the water balance or soil system. For a complete evaluation of equation (1) data must be available for each of the terms in the equation. In the present case, measurements are available for all of the terms on the left hand side of the equation for the two years being considered, although those for E are a composite of values measured over a period of several years, and not specifically for the years under consideration.
The site under study is at Clarens, situated in the Free State Province of South Africa at latitude 28◦ 31 South and longitude 28◦ 26 East, at an elevation of 2000 m above sea level. Clarens is in the foothills of the Maluti mountain range and is ringed by mudstone and sandstone cliffs of the Clarens formation, which in turn are capped by strata of basaltic Stormberg lavas. The test site is situated on a gently sloping plain of colluvium consisting of clayey silt deriving from the decomposition of the sandstones, mudstones and lavas. The soil is moderately expansive/shrinkable and contains closely spaced slickensides and extensive microfissuring between slickensides. The sand, silt and clay contents vary as follows: Sand 20 to 25% Silt 47 to 53% Clay 22 to 33% The soil profile varies in depth from 0.5 to 2 m and is almost unchanged from surface down to the underlying sandstone. The water table lies within the sandstone at 5 to 7 m below surface. At the part of the site which was investigated, the soil depth is a uniform
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0.5 m and the profile changes abruptly from soil to weathered sandstone. The climate at the site is continental with warm moist summers (daily temperatures between +10 and +25◦ C) and cool dry winters (−10 to +15◦ C). 1.3 The experimental objectives Although, with the aid of equation (1) and a set of appropriate measurements for a year, the water balance for a site can be defined, the equation can seldom be closed perfectly because of the unknown losses and difficulties in accurately defining the recharge term RE and the evapotranspiration E (e.g., Smethurst et al., 2006). As the main input to the equation is rainfall, and this can vary widely from year to year and has an effect on evapotranspiration, it is seldom possible to compare the water balance for one year with that of another having identical rainfall. Thus it is seldom possible to confirm the accuracy of the process of defining a water balance, by direct comparison of years with the same rainfall. It was noticed that the total rainfall for the periods from 01 November 2004 to 31 October 2005, and 01 November 2005 to 31 October 2006 were very similar, thus providing a rare opportunity for comparing
the water balances for two different years. The paper will describe the comparison and show that although the water balances are similar, measurements are not sufficiently accurate to say they are identical. It is believed that the main differences arise from difficulties in accurately measuring in situ water content in the highly fissured soil at Clarens. 2
THE RAINFALL AND EVAPOTRANSPIRATION RECORDS
Figure 1 shows the cumulative rainfall for the two periods 01 November 2004 to 31 October 2005 (878 mm) and 01 November 2005 to 31 October 2006 (855 mm, 97% of the previous year). Because antecedent rainfall will have some effect on the following year, an overlap from 01 May to 31 October is shown in both cases. Also, the cumulative rainfall for the antecedent year, 01 November 2003 to 31 October 2004 was 658 mm. That is, the two year period of study was preceded by a drier year in which the rainfall was 76% of that in the two subsequent years, for which year 1 was slightly wetter than year 2. In both cases, the line representing E is a composite line, established by energy balance measurements (e.g. Blight, 2006) over a period of several years.
Figure 1. Comparison of cumulative rainfall recorded at Clarens for the 2004/2005 and 2005/2006 wet seasons (The evapotranspiration (E) line has been built up from observations made over several years; it does not relate specifically to 2004, 2005 or 2006).
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The line applies specifically to a grass-covered surface, unaffected by the presence of trees or shrubs. In each case, the point at which the R line crosses the E line represents the time at which the rainfall starts to exceed the evapotranspiration and the soil water goes from deficit to surplus. Note that in the two May to October periods studied, this occurred in late December. 2.1
Analyses of rainfall records
Figure 1 gives a visual impression of the similarity of the cumulative rainfall records for the two periods under consideration, and this is supported by the analyses that follow. Figure 2a shows analyses of the annual rainfall by 24 hour events and Figure 2b by quantity of rainfall in each 24 hour event. The analysis by 24 hour events shows that the rainfall event distribution was very similar for the two years, with small rainfall events (<20 mm) being slightly less frequent in 2004/2005 than in 2005/2006 and bigger events (>20 mm) slightly more frequent. The analysis by quantity is a combination of the records for the two one-year periods and shows that 74% of the annual rainfall quantity fell almost evenly distributed in 24 hour events of between 5 and 40 mm
Figure 2. Analyses of 2004/2005 and 2005/2006 rainfall distributions by (a) % of 24-hour events and (b) % of total annual rainfall.
with only 15% of annual rain falling in 24 hour events of more than 40 mm. 2.2 Runoff at this site The rainfall analysis by 24 hour event has an important bearing on the runoff term RO in equation (1). In a set of artificial rainfall and runoff measurements, made on a 10 m2 runoff plot, 80 mm of artificial rainfall was applied by a sprinkler in 7 hours (i.e., according to Figure 2a, the equivalent of a rare and intense 24 hour event). The cumulative runoff was only 0.7 mm, or 0.9% of rainfall, with 99% infiltrating, 4% re-evaporating, 68% adding to storage and 27% exiting the base of the soil profile as recharge. At this site, the soil is clayey, but it is also intensely fissured, and the fissuring controls the rate of infiltration. Thus, runoff will be negligible for all likely rainfall intensities, and all rainfall can be assumed to infiltrate. Thus equation (1) can be simplified to
3
R+S−
E=
RE + losses
(1a)
A COMPARISON OF WATER CONTENT PROFILES FOR THE TWO YEARS
Figure 3 compares two water content profiles at right angles to a line of Populus nigra trees, measured by means of a ‘‘Diviner’’ instrument in late September 2005 and 2006. (These are referred to as ‘‘tree profiles’’ in Figure 1. The ‘‘bush profiles’’ also referred to in Figure 1 have not been shown for lack of space.) In Figure 3, the numbers represent the measured percentage of gravimetric water content, with the decimal point marking the location of the measurement. The Diviner instrument, which senses the in situ water content of the soil by measuring its electrical capacitance, had been carefully calibrated for the Clarens soil against gravimetric water contents measured on hand-augered soil samples during 2005/2006 (Blight, 2007). Figure 4 shows the calibration line for Diviner readings versus gravimetric measurements on auger samples taken on the same grid as the Diviner measurements. Figure 4 also shows the calibration line in the laboratory using a compacted uniform fine sand. In the end, 70 pairs of measurements were made to establish the calibration between the Diviner reading and the in situ soil gravimetric water content. The calibration for in situ water content is not only very different to that for the uniform soil, but also has considerable scatter probably because of the discontinuous fissured nature of the soil. Even though the correlation coefficient for the calibration data was 0.93, measurements by the Diviner were uncertain. For example, a measurement for which the correlation
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Figure 3. Comparison of water content contours adjacent to a line of Populus nigra trees measured in September 2005 and 2006.
Figure 4.
Laboratory and field calibrations of the Diviner.
line indicated a gravimetric water content of 30% was actually 30% ± 7%. This uncertainty must be borne in mind when considering the water content contours in Figure 3. It is tempting to blame the uncertainty entirely on short-comings of the Diviner instrument which is obviously badly affected by fissuring of the soil, but actual variability in the distribution of soil water in the highly fissured soil, which may also be more heterogeneous than it appears to be, may also be an important source of the variability. The biggest discrepancy between the 2005 and 2006 contours occurs at depths of 400 to 500 mm (Figure 3). In this region, the largest discrepancy is 39.6 − 24.3 = 15.6% which is slightly larger than the total calibration uncertainty of 14%. Apart from this, the contours bear a visual resemblance to each other. In particular, the water content depression caused by the trees is clearly evident, and was similar in both years.
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Figure 5. Comparison of water stored in soil profile adjacent (a) to a line of trees and (b) to a line of bushes, measured in September 2005 and July 2006.
Figure 5a shows the water stored in the soil (S), corresponding to the water contents shown in Figure 3, and Figure 5b for the line of bushes mentioned earlier. For the trees, the 2005 storage quantities everywhere exceed those for 2006, but the 2005 rainfall was slightly higher than in 2006. The two profiles are much closer in the drier region adjacent to the trees. For the bushes, the stored water profiles are very much closer, and almost coincide at distances of more than 5 m from the bushes. It is, however, necessary to consider that because of the uncertainty of the water content measurements, the profiles for the bushes may actually be further apart than they appear to be, and the water profiles for the trees, closer.
4
CONCLUSIONS
A water content measurement appears to be one of the simplest and most fundamental that can be made in soil mechanics. However, Figure 4 shows that it is far from simple to make consistent and variation-free measurements of in situ water content, particularly in fissured soils. If an indirect method of water content measurement is used, the method will be difficult to calibrate in the field and the uncertainty in the calibration may arise both from instrumental and soil characteristics. If allowance is made for these difficulties, it is probably fair to say that in years that have rainfall with similar distributions in quantity, time and intensity,
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soil water distributions by water content and storage will be similar. Hence the water balances for these years will be similar, and hence suitable to use for predicting soil water conditions in other years. REFERENCES
Blight, G.E. 2007. Experience with calibrating an instrument for ascertaining the in situ water content of soil by measuring the soil electrical capacitance. In: UnSat-Asia 2007, Proceedings, 3rd Asian Conference on Unsaturated Soils, 451–456, Nanjing, China, Science Press. Smethurst, J.A., Clarke, D. & Powrie, W. 2006. Seasonal changes in pore water pressure in a grass-covered cut slope in London clay. Geotechnique, 56(8), 523–537.
Blight, G.E. 2006. Measuring evaporation from grassed surfaces and trees by energy balance. In G.A. Miller, C.E. Zapata, S.L. Houston & D.G. Fredlund (eds), Unsaturated Soils 2006, Geotechnical Special Publication No. 147:1:293–303, Reston, VA, U.S.A., American Society of Civil Engineers.
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Near-surface movement of water in unsaturated soil during evapotranspiration G.E. Blight University of the Witwatersrand, Johannesburg, South Africa
ABSTRACT: Although the overall thermodynamics of the process of evapotranspiration is reasonably well understood, the way in which water moves up to a soil surface prior to being evapotranspired does not seem to have been studied in detail. After examining the variation of evaporation potential throughout the day, by means of measurements of solar surface energy, the paper examines diurnal and nocturnal near-surface moisture movement. This is followed by a longer-term study of the depletion of near-surface soil water by evapotranspiration, and its replenishment by upward water flow from deeper soil layers.
1
INTRODUCTION
A series of experiments designed to give information on the mechanisms by which water migrates to the surface of a soil and is lost to the atmosphere by evapotranspiration is described. The experimental area is covered by a thick growth of a creeping grass, growing in a colluvial silty sand for which the particle size analysis is shown in Figure 1. The daily quantity of evapotranspiration can be measured quite simply by measuring the components of the surface energy balance equation (e.g. Calder 1990, Schmugge & Andre 1991): LE = Rn + W − (G + H + P)
The measurements were made on the experimental site at the autumnal equinox. LE in kJ/m2 can be used to calculate the quantity of daily evapotranspiration by dividing the daily total LE by the latent heat of vaporization λ in kJ/kg, i.e. evapotranspiration = LE/λ in kg/m2 /day, the equivalent of mm of water/day. For water, λ varies almost linearly with temperature (e.g. Calder, 1990) from 2 477 kJ/kg at 10◦ C to 2 417 kJ/kg at 35◦ C, i.e. by 2.4 kJ/kg per ◦ C. In an unsaturated soil, evaporation
(1)
where LE is the latent heat consumed in evapotranspiration, Rn is the net incoming solar energy, W is the wind energy, G is the energy expended on heating the near-surface soil (the soil heat), H is the energy consumed in heating the near-surface air (the sensible heat), and P is the energy used in plant photo-synthesis (usually less than 2% of Rn and therefore negligible). In maritime climates W and H are linked because the wind can move large volumes of warm or cold air in from the sea or out from the land. However, in continental climates, where these experiments were per formed, both W and H are negligible (Blight 2002) and equation (1) becomes LE = Rn − G
(1a)
Figure 2 shows measurements of the variation of Rn , the net solar power in W/m2 , Rn the integration with time of Rn in kJ/m2 and (Rn − G), also in kJ/m2 .
Figure 1.
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Particle size analysis for soil from test area.
Figure 2. Measurements of net solar power Rn (W/m2 ) and cumulative net solar energy Rn (kJ/m2 ) received by grassed surface at experimental area. The inset shows near-surface soil temperature profiles at sunrise (06.00), noon and sunset (18.00).
could occur throughout the depth of heating of the soil (see Figure 2). Hence it is probably fair to use a value for λ that corresponds to the mean temperature in the depth of heated soil. Although an estimation of the daily quantum of evapotranspiration can be made, the way in which the water moves up to the surface and escapes as vapour is obscure. It is known that evapotranspiration can draw water to the surface from depths of more than 10 m (e.g. Blight, 2006), thus the reservoir of water available for transpiration may be large. It will be seen from Figure 2 that the solar power input is negligible between sunset and sunrise, so that the major impetus for upward water flow to the soil surface prevails only during the daylight hours. One can envisage this as happening in two stages: 1.1 During daylight hours, water will be evapotranspired from the soil surface, inducing increased soil water suction in the near-surface layers. The suction gradient will induce an upward wave of water flow in the soil. 1.2 In general, upward flow of the available nearsurface water will not, by nightfall, have equilibrated with the solar-induced increase in suction.
During the night, upward flow will continue, but evapotranspiration from the surface will not occur as available latent heat of evaporation will be negligible. In addition, because of cooling of the soil surface during the night (see the temperature profiles in Figure 2) there will be a slight upward flow induced by the temperature gradient. The water content of near-surface soil will decrease during the day, but the suction and temperature equilibration processes will cause a slight increase of water content during the night.
2
MEASUREMENTS OF NEAR-SURFACE SOIL WATER CONTENT
To check the correctness of the above concept, two soil cores, each 100 mm diameter by 100 mm length were cut from the test area about 1 m apart. They were extracted by driving in a 1 mm wall thickness corecutter, carefully undercutting and loosening the core cutter (plus grass-covered soil core) using a trowel with a face curved to 100 mm diameter, and then extracting the core cutter with its contained soil. Both cores
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Figure 3. Results of water content sampling in ‘‘undisturbed’’ cores of soil.
(in their core cutters) were returned to their holes. Core 1 was sampled at 18h00 (sunset) by removing it from its hole, carefully extruding it upwards from its core-cutter and then drilling sample holes in its sides, by hand, on a vertical line, at depths of 15, 45 and 75 mm below the soil surface, using a 12.5 mm diameter spade drill bit. The core was then pushed back into the core-cutter and returned to its hole. The process was repeated at 06h00 (sunrise) and 18h00 the next day and 06h00 on the third day, each time sampling on a line at 90◦ in plan to the previous sample line. Sampling of core 2 was started at 18h00 on day 3 with sampling being completed at 06h00 on day 5. The results of the water content sampling operation are shown in Figure 3. For core 1, the nocturnal increases in water content, followed by the diurnal decrease are clearly shown. By the end of day 3, core 2 had dried out considerably, and the nocturnal increases are not very clear. Measurements at 75 mm depth were abandoned on day 4 because the lower part of the core was crumbling. Nevertheless, the experiment showed that the two-stage process, described above, does indeed occur.
3
LONGER TERM MEASUREMENTS USING GYPSUM BLOCK AND GLASS FIBRE WATER CONTENT SENSORS
The longer-term measurements were intended to study near-surface changes in water content over periods of two or more weeks, and hence destructive sampling could not be used. The measurements were made by
means of gypsum block (Soil moisture) and glass fibre mat (ELE) sensors. (See Figure 5) The sensors were installed as follows. An undisturbed core of soil was extracted as described above. The core, in the corecutter, was placed in a sealed plastic bag in the shade while the sensors were installed in the sides of the corehole. The gypsum blocks were installed (one each) at depths of 15, 45 and 75 mm below the surface (at 120◦ in plan) by hand-drilling a hole horizontally into the soil using a spade bit slightly smaller in diameter than the sensor. The three sensors were then pushed into their holes in the side of the core hole and the electrical leads taken up the side of the hole. The core was then carefully extruded from the core-cutter and returned to its hole. The glass fibre mats were installed in a similar way, except that slots to fit the flat sensors were gouged out using a knife blade. The two instrumented holes were left for two months to equilibrate and for the grass to re-grow, before starting the measurements. In the meantime, a third 100 mm × 100 mm core with grass growing on its surface and with a gypsum block and a glass fibre mat mounted in it on opposite sides at a depth of 50 mm, was introduced into a Perspex cylinder of 100 mm diameter and height, with a closed base, in order to calibrate the sensor readings against the overall water content of the core. (See Figure 6). The calibration core was kept under cover and allowed to dry out very slowly from the surface by allowing four hours of drying (06h00 to 10h00), followed by 20 hours with the top surface sealed to allow moisture equilibration, before reading the sensors. The sensors installed in the experimental plot were measured over a period of 15 days in June (the winter solstice) and 7 days in September (the spring equinox). Space limitations allow only one set of detailed results to be included in this paper, and those for June have been chosen. Surface energy measurements (similar to those in Figure 2) gave an estimate of the daily loss by evapotranspiration at this time of year of 0.9 mm/day (0.9 kg water/m2 /day). The measurements were made at 06h00 each day, when the sensors were most likely to be at equilibrium, and the results are shown in Figure 4. The graphs show a slowing decline of water content that is similar at depths of 15, 45 and 75 mm. For both sets of sensors, the overall water content loss was about 15% at all depths which is equivalent to 0.5 mm of water per day. Surface energy measurements had indicated a daily total loss of 0.9 mm/day and hence the daily upflow from the soil below 75 mm depth was about 0.4 mm/day. It will be seen that the water contents in Figure 3 are much lower than those shown in Figure 4. This apparent discrepancy is because measurements in Figure 4 are based on the dry mass of an undisturbed soil core, riddled with grass roots and having a dry density of only 650 kg/m3 , whereas the measurements in
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Figure 4.
Decline of water content of near-surface soil as a result of evapotranspiration.
Figure 3 are based on samples of soil solids with about twice the dry density of the core. To confirm that the overall evapotranspiration was partly drawn from soil below the depths of the sensors, the soil in the vicinity of the two sets of sensors was sampled for water content both before and after the
tests in September. The results of this sampling are shown in Figure 7. For the observations in September, surface energy measurements indicated a daily total water loss of 1.9 mm/day. The sensor measurements indicated a water loss from the top 75 mm of soil of 0.6 mm/day, and hence an upflow from deeper soil of
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Figure 5.
Gypsum block on the left and glass fibre sensor on the right (scale is centimetres).
Figure 6. Set-up for calibration of the sensor readings against the water content of the soil core.
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Figure 7.
Water content profiles before and after observations in September.
1.3 mm/day. The water content sampling confirmed that an average of 0.6 mm of water per day was lost from the surface down to 75 mm, and also showed that an additional 0.5 mm/day was lost from 75 to 200 mm, a total loss of 1.1 mm/day. This left 0.8 mm/day to be drawn to the surface from below a depth of 200 mm. (Measurements could not be extended below 200 mm because of a dense gravel layer that occurs below this depth.)
75 mm, and possibly to greater depths than this. The measurements in Figure 4, when compared with surface energy measurements, show that water lost from the surface is partly replaced by upflow from deeper soil layers. d. The changes in the water content profile, observed during the September tests, and shown in Figure 7, confirm that water lost from the soil by evapotranspiration is drawn partly from soil at shallow depths and partly from deeper layers.
4
Thus the results of the experiments confirm the principles of the process of water loss from soil by evapotranspiration, as described in sections 1.1 and 1.2, as well as providing details of the process.
CONCLUSIONS
The measurements following:
described
here
show
the
a. Because evapotranspiration from a soil surface is driven by the availability of latent heat of evaporation, as shown in Figure 2, almost all loss of water from the soil surface must take place during daylight hours. b. Evapotranspiration from the surface depletes water in the near-surface and deeper soil. The depletion near the surface is partly offset by upward flow from deeper soil during the hours of darkness, as shown by Figure 3. c. Over periods of several days, if there is no replenishment of water by rain or irrigation at the surface, the water content of the near-surface soil continually declines. Figure 4 shows that the decline occurs more or less uniformly down to a depth of at least
REFERENCES Blight, G.E. 2002. Measuring evaporation from soil surfaces for environmental and geotechnical purposes. Water S.A. 28(4), 381–394. Blight, G.E. 2006. The infiltrate-stabilize-evapotranspire or ISE landfill cover. In G.A. Miller, C.E. Zapata, S.L. Houston & D.G. Fredlund (eds), Unsaturated Soils 2006, Geotechnical Special Publication No. 147: 1: 753–764, American Society of Civil Engineers. Calder, I.R. 1990. Evaporation in the Uplands, Chichester, U.K.: Wiley. Schmugge, T.J. and Andre, J.-C. 1991. (Eds). Land Surface Evaporation. Measurement and Parameterization, New York, U.S.A.: Springer.
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Studies of rainfall-induced landslides in Thailand and Singapore A. Jotisankasa & B. Kulsawan Department of Civil Engineering, Kasetsart University, Bangkok, Thailand
D.G. Toll School of Engineering, Durham University, Durham, UK Department of Civil Engineering, National University of Singapore
H. Rahardjo Department of Civil and Environmental Engineering, Nanyang Technological University, Singapore
ABSTRACT: The paper reports on field, laboratory and computational studies of the mechanisms of rainfall-induced landslides carried out in Thailand and Singapore. Shallow landslides due to rainfall are common in both countries, as well as other parts of South East Asia. In both countries, field studies have been performed to monitor the changes in pore-water pressure resulting from rainfall infiltration. In Thailand, suctions have been measured using a new miniature tensiometer developed by Kasetsart University. In Singapore, commercially available ‘‘jet-fill’’ tensiometers were used. The observations include suction changes due to natural rainfall events and also using rainfall simulators to impose precipitation with controlled intensity and duration. The field data suggest the formation of a near-saturated zone along the slope surface (where most of the pore-water pressure changes take place) explains why many failures are shallow in nature (1–2 m deep). Experience in Thailand and Singapore shows many similarities between the mechanisms of failure and the paper highlights this common experience.
1
INTRODUCTION
Landslides are often triggered by rainfall, particularly in tropical climatic regions such as South East Asia where rain storms can be very intense. Major landslides occur all too often, but minor landslides occur even more frequently (Figure 1). Although minor landslides may not lead to loss of human life, they still have economic and social impact. This paper draws parallels between research on rainfall-induced landslides in Singapore and Thailand. Field, laboratory and computational studies of the mechanisms of rainfall-induced landslides have been carried out in both countries. The common experiences between the two countries can contribute to a wider understanding of the landslide problem in South East Asia. 2
LANDSLIDE STUDIES IN THAILAND
Rainfall-induced landslides have occurred frequently in many hill slope areas of Thailand during the wet seasons of the past several years. These slides were
of several failure modes, such as shallow movement, deep-seated slide, and rock fall. The most destructive mode of landslide in Thailand is generally the shallow mass movement of the soil with depths of about 0.5–3 m. As shown in Figure 1b, where torrential rain brought about numerous shallow soil slides in the North of Thailand, which were mixed with flash floods, and transformed into rapid debris flows with considerably destructive force. As pointed out by a number of pioneer researchers (e.g. Crozier & Eyles, 1980, Lumb, 1975), landslide occurrence can be correlated with rainfall pattern. Rainfall patterns when major landslides occurred in Thailand are plotted in Figure 2. Landslide events in the figure involved 30–160 shallow slides with depths of 0.5–3 m. These rain patterns provide a useful tool for roughly indicating when major landslides are likely to occur. Of course, rainfall is not sufficient in itself to explain slope failures (evapo-transpiration and runoff are also important components) but nevertheless rainfall provides an easily measured indicator. In Thailand early warnings will be issued to communities near hill slopes when the daily rainfall or accumulated rainfall over a couple of days exceeds
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Figure 1. Rainfall-induced landslides in a) NTU campus, Singapore (1995) and b) Uttaradit, Northern Thailand (2007). 500
400 1999 at CD (40slides)
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Figure 2. Rainfall events leading to major landslide events in Thailand.
100, 200, and 300 mm for areas with medium, high, and very high risk of landslide, respectively. Nevertheless, the criterion of rain patterns used for issuing warnings is largely empirical and would be subjected to a number of factors such as soil type, vegetation covers, slope gradient as well as geological structures. Soil slopes in Thailand are normally unsaturated during the dry season and the groundwater is normally at depth of more than 10 m most of the year.
When the soil is unsaturated, suction or negative porewater pressure provides additional strength to the soil, hence stabilizing the slope. This additional strength disappears during an intense rainstorm when the soil becomes saturated and pore-water pressure becomes zero. The pore-water pressure can also become more positive due to seepage forces or perturbation of the soil slope, and the shear strength can be reduced even further as effective stress decreases. The increases in excess pore-water pressure and its threshold effect in destabilizing the slope in tropical areas can be explained by the reduction of permeability with depth (Vaughan, 1985) or by changes in permeability with suction or degree of saturation (Tsaparas and Toll, 2002). In order to understand the infiltration process and consequently the relations between rainfall, soil moisture, and landslide occurrence, field infiltration tests were carried out on 6 research slopes located in the areas where landslides had occurred (Figure 3). Infiltration characteristics of four research slopes (OMK, UD, TK, CB, and PP) were studied using artificial rainfall for a period of about 2 days, while the slope TD was monitored under natural climatic condition for longer period. Only site CB is presented here. The CB test area was a square plot of about 5 × 5 m2 , sloped at about 18◦ and instrumented with tensiometers, runoff collector and rain gauge. The tensiometers used were developed by Kasetsart University (KU), using a commercially available MEMs pressure sensor, and are described in Jotisankasa et al. (2007). The tensiometers were installed at depths of 0.04, 0.15, 0.30, and 0.50 m. The depth to hard weathered granitic bedrock varied between 0.50 to 1.00 m within the test plot. The probable failure plane was considered to take place within these depths. The materials found at the test area are mainly low plasticity clayey sand, silty sand, and well-graded gravel at greater depth. They have liquid limit of 40–60%, plasticity index of 10–25%, and typically contain 20–40% of silt and clay sized particles. The saturated permeability varies between 10−5 m/s and 10−6 m/s. The rainfall intensity and runoff collected during rainfall simulation are shown in Figure 4. The variations of suction profile with time are also shown in Figures 5 and 6. The rainfall simulation was carried out in stages over a period of about 45 hours. The first stage (Hours 0–16) involved installation of tensiometers and other instruments, as well as equilibration of reading. Initial suctions were only around 1–4 kPa, indicating relatively moist profiles before the test. During Hours 16–22, there was some slight rain falling naturally, which was followed by rapid reduction of suction at a depth of 0.04 m at Hour 22 (Figure 5). The first simulation of rainfall with an intensity of 174 mm/day (7.25 mm/hour) then started from Hour 22, until Hour 26 when suction became zero to a depth of 0.5 m.
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Figure 3.
Figure 6. Variation of pore-water pressure during rainfall simulation (stage 2).
Locations of research slopes in Thailand.
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Figure 5. Variation of pore-water pressure during rainfall simulation (stage 1).
The total rainfall during Hours 22–26 was about 29 mm. It can be seen that the suction at 0.5 m remained unchanged until the wetting front reached the depth of 0.5 m around Hours 24–25. The decreases in suctions at depths 0–0.5 m resulted from infiltration alone and not from the ground water table rising.
After the first artificial rainfall, the tensiometers were left in the ground overnight during Hours 26–41. The suctions at Hour 41 reached values of around 1–3 kPa due to evaporation and redistribution of soil moisture during Hours 26–41 (Figure 6). The second stage of artificial rain was then imposed on the slope at the intensity of 283 mm/day (11.8 mm/hour) for a period of about 3 hours. The soil depth of 0.5 m became nearly saturated when the 2nd simulation continued for about 0.8 hour, equivalent to rainfall of 9.4 mm. The difference between the total amount of rainfall required to saturate the soil thickness during 1st and 2nd simulation (29 mm and 9.4 mm, respectively) is caused by the difference in initial soil suction, as well as the soil wetness. The soil-water retention curves of the undisturbed soil samples from the research slope were also determined using the Kasetsart University (KU) tensiometer. Undisturbed samples with diameter of about 60 mm were collected from an open test pit using miniature soil core at depths of 0.10, 0.50 and 1.0 m. The suction of a soil sample as collected from the ground was 4.5 kPa. The samples were gradually wetted and dried and their suctions during each stage were monitored incrementally. Figure 7 shows the retention curve of sample from 0.1 m. The hysteresis of the curve is evident during first wetting and first drying. The difference in the soil moisture-suction relationship would also be an explanation for the aforementioned difference in saturating rainfall for the 1st and 2nd simulations. In other words, the amount of water required to reduce the suction from say 1 kPa to 0.1 kPa would be much less if the sample was on the ‘‘first wetting’’ path than if it was on the ‘‘first drying’’ path. These data thus show that during rainfall the porewater pressure increase would be most significant near the slope surface, while the ground water table level is
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45 First wetting initial state
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Figure 7. Soil-water retention curve of undisturbed sample from 0.10 m depth.
expected to be affected at a later stage. The hysteresis of the soil water retention curve and wetting-drying history of the slope also play an important role in determining the amount of rainfall required to saturate the soil slope.
3
LANDSLIDE STUDIES IN SINGAPORE
Minor, shallow landslides have occurred frequently on the island of Singapore, particularly as urban development has greatly increased since the 1970s (Tan et al. 1987). However, very few major landslides have occurred; where slides have occurred, the volumes of material involved have generally not been large, and serious damage has been uncommon (Brand, 1984; Toll et al. 1999). Tropical residual soils cover almost two-thirds of Singapore Island. They are derived mainly from the weathering of the sedimentary Jurong and granitic Bukit Timah formations. The residual soils are typically medium plasticity clayey silt, sandy clay and clayey to silty sand materials (Poh et al. 1985; Chang, 1988). They commonly contain 50–60% of silt and clay sized particles with typical values of liquid limit being 40–60% and plasticity index of 15–25%. The saturated permeability can vary between 10−10 m/s and 10−6 m/s (Agus et al. 2003). It is clear that rainfall has been the dominant triggering event for landslides in Singapore (Ramaswamy & Aziz, 1980; Toll, 2001). Studies of minor landslides on the Nanyang Technological University (NTU) and National University of Singapore (NUS) campuses show spates of landslides occurring after unusually wet periods. It may not be a single rainfall event that causes a landslide (Rahardjo et al. 2001). In low permeability clayey soils (as is typical of the residual soils of Singapore) the pore-water pressures may build up over a number of days (due to a series of rain storms) eventually culminating in
the final triggering rainfall event that precipitates a failure. Figure 8 shows rainfall data for a large number of landslides in Singapore (Toll, 2001). It shows the rainfall on the day of the landslide (triggering rainfall) plotted against the rainfall in the five day period preceding it (antecedent rainfall). Some minor landslides have occurred after heavy 1-day rainfalls with little antecedent rainfall. In February 1984, the daily rainfall inducing failures was almost 100 mm, whereas those in March 1984 were higher. However, it can also be seen that other minor slides take place with low 1-day rainfall but where the 5-day antecedent rainfall is significant. For instance, there is the case of 28 Dec 1984 where a slide occurred with only 18 mm of daily rainfall, but after a 5-day antecedent rainfall of 85 mm. This suggests that the conditions for failure are dictated by total rainfall, since either daily or antecedent rainfall can induce failures. The diagonal line drawn in Figure 8, representing a total rainfall of 100 mm in a six day period, appears to define the minimum rainfall conditions that have led to minor failures. Although these empirical observations on rainfall patterns can be useful in identifying the minimum conditions that are likely to precipitate a landslide, they do not explain why the landslides occur. To properly understand such failures we need to apply an understanding of unsaturated soil behaviour. In many tropical regions, water tables exist at significant depth (>10 m). This means that pore-water pressures can be negative (suctions). Therefore, it is important to understand the role of suction in supporting the slope (increasing the strength of the soil) and how infiltration of rainwater causes changes in the pore-water pressures (or suctions). Four research sites in Singapore were instrumented as part of a major study of rainfall-induced landslides in Singapore (Rahardjo et al. 2000). Rainfall gauges were installed on each slope to provide specific rainfall data. Negative pore-water pressures were measured using jet-fill tensiometers. These were installed at depths of 0.5, 1.1, 1.4, 2.3 and 3.2 m on the NTUCSE site (the only site that will be discussed here). At this site, piezometer data indicated that the groundwater table was 10 m below the ground surface (Rahardjo et al, 2000). The pore-water pressures within the NTU-CSE slope were monitored from August 1999 until August 2000 (Tsaparas et al. 2003). Figure 9 shows the porewater pressures at the various measuring depths for a row of tensiometers installed near the mid-point of the slope (6 m down-slope from the crest). The daily rainfall is also shown as a bar graph in Figure 9. It can be seen from Figure 9 that the pore-water pressures within the NTU-CSE slope were, for a large part of the monitoring period, only slightly negative and at
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Figure 8. Rainfall events leading to landslides in Singapore.
Figure 9. Pore-water pressure and rainfall measurements for an instrumented slope in Singapore.
3.2 m depth were generally positive. However, there were six periods during the year when pore-water pressures reduced significantly following a drier period. During March 2000, pore-water pressures dropped to as low as −70 kPa near the surface (0.5 m depth). However, piezometer data shows that there was little change in ground water table level. Therefore, these suction changes are the result of infiltration and evapotranspiration occurring at the surface, rather than being due to changes in water table. Figure 10 shows pore-water pressure profiles within the slope, during and after two rainfall events in
December 1999 and March 2000 that are described in detail by Toll et al. (2001). These dates represent a ‘wet period’ (with high initial pore-water pressures) and a ‘dry period’ (with low initial pore-water pressures). The rainfall event in December 1999 was very large (86 mm) whereas that in March 2000 was small (1 mm). However, it can be seen from Figure 10 that the small rainfall in March during the dry period produces a significant change in the pore-water pressure near the surface. After a period of equalisation (24 hours after the rain) the pore-water pressure near the surface has dropped
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shallow in nature (Toll et al. 1999). Failures tend to occur within the near-surface zone where pore-water pressures increase close to hydrostatic levels. Deepseated failures are also limited by increased cohesion with depth as is common in such weathered profiles.
4
It is clear that rainfall has been the dominant triggering event for landslides in Thailand and Singapore. Studies show spates of landslides occurring after unusually wet periods. Observations of past landslides in Singapore suggest that a total rainfall of 100 mm within a six day period is sufficient for minor landslides to take place in Singapore. In Thailand, a total rainfall of 150–400 mm would tend to trigger major landslides. Measurements of pore-water pressures in slopes in Singapore and Thailand show that rainfall infiltration produces changes in pore-water pressure near to the surface. However, at greater depths (around 3 m) the pore-water pressures do not change significantly. This is because water tends to flow down the slope within the zone of higher saturation with higher permeability that develops near the surface. As a result, failures tend to occur within the near surface zone and are not usually deep-seated.
Figure 10. Pore-water pressure profiles within the instrumented slope.
back and pore-water pressures at 1–1.5 m deep have increased. This is due to the infiltrated water draining down from the surface to lower depths. However, it can be seen that at 2.5–3 m depth there has been no significant change in pore-water pressure. In contrast, the very large rain storm in December 1999 produced only a small change in pore-water pressure near the surface, but the pore-water pressure did approach a hydrostatic condition (defined by a porewater pressure of zero at the ground surface). Again, after the storm, pore-water pressures dropped back near the surface and increased slightly at depth. In both cases, the field measurements suggest that pore-water pressures do approach the hydrostatic condition near the surface due to infiltration. However at 2.5–3 m depth there is little change in pore-water pressure. The pore-water pressures remain significantly below the hydrostatic line, even at the wettest time of the year. Therefore, assuming that pore-water pressures were hydrostatic throughout the slope (as would often be assumed in a saturated soil analysis) would be over-conservative. A major factor in controlling the response is the change in water permeability that occurs in an unsaturated soil as a result of changes in degree of saturation (Tsaparas and Toll, 2002). The change in permeability can be 4–5 orders of magnitude. When water infiltrates at the surface, a near-surface zone with a high degree of saturation is produced. This produces a zone of much higher permeability. Further down (2–3 m below the ground surface) the unsaturated permeability remains low, so water is not encouraged to flow to greater depths, even though the hydraulic gradient will be greater in that direction; instead flow tends to take place down the slope within the near-saturated surface zone. These data shows that, for a scenario where the water table is at significant depth (>10 m), most pore-water pressure changes take place near the surface (<2 m). This is consistent with the observation that many minor landslides in Singapore are quite
CONCLUSIONS
ACKNOWLEDGEMENTS The authors gratefully acknowledges the Thai-UK CRN research grant by Commissions of Higher Education, Thailand, for financial assistance for visiting academic trips to UK and Singapore in 2007.
REFERENCES Agus, S.S., Leong, E.C and Rahardjo, H. (2003). A flexible wall permeameter for measurements of water and air coefficients of permeability of residual soils, Canadian Geotechnical Journal, Vol. 40, pp. 559–574. Brand, E.W. (1984). Landslides in Southeast Asia: A Stateof-the-art Report, Proc. 4th International Symposium on Landslides, Toronto, Vol. 1, pp. 17–59. Chang, M.F. (1988) In-Situ Testing of Residual Soil in Singapore, Proc. 2nd Int. Conf. on Geomechanics in Tropical Soils, Singapore, Rotterdam: Balkema, Vol. 1, pp. 97–108. Crozier, M.J. and Eyles, R.J. 1980. Assessing the probability of rapid mass movement. Proc. 3rd Aus. NZ Conf. Geomech., Wellington. 2: 2.47–2.51. Jotisankasa, A., Porlila, W., Soralump, S. and Mairiang, W. (2007). Development of a low cost miniature tensiometer and its applications. Proc. 3rd Asian Conference on Unsaturated Soils (Unsat-Asia 2007), Nanjing, China, pp. 475–480.
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Lumb, P. 1975. Slope failures in Hong Kong. Quarterly Journal of Engineering Geology. 8: 31–65. Poh, K.B., Chuah, H.L. and Tan, S.B. (1985). Residual Granite Soils of Singapore, Proc. 8th Southeast Asian Geotechnical Conf., Kuala Lumpur, Vol. 1, pp. 3:1–3:9. Rahardjo, H., Leong, E.C., Deutcher, M.S., Gasmo, J.M. and Tang, S.K. (2000). Rainfall-induced Slope Failures, Geotechnical Engineering Monograph No. 3, NTU-PWD Geotechnical Research Centre, Singapore. Rahardjo, H., Li, X.W., Toll, D.G. and Leong, E.C. (2001). The Effect of Antecedent Rainfall on Slope Stability, Geotechnical and Geological Engineering, Vol. 19, No. 3–4, pp. 371–399. Ramaswamy, S.D. and Aziz, M.A. (1980). Rain Induced Landslides of Singapore, Proc. International Symposium on Landslides, New Delhi, Vol. 1, pp. 403–306. Tan, S.B., Tan, S.L., Lim, T.L. and Yang, K.S. (1987). Landslides Problems and their Control in Singapore, Proc. 9th Southeast Asian Geotechnical Conference, Bangkok, pp. 1:25–1:36. Toll, D.G. (2001). Rainfall-induced Landslides in Singapore, Proc. Institution of Civil Engineers: Geotechnical Engineering, Vol. 149, No. 4, pp. 211–216.
Toll, D.G., Rahardjo, H. and Leong, E.C. (1999). Landslides in Singapore, Proc. 2nd International Conference on Landslides, Slope Stability and the Safety of InfraStructures, Singapore, pp. 269–276. Toll, D.G., Tsaparas, I. and Rahardjo, H. (2001). The Influence of Rainfall Sequences on Negative Pore-water Pressures within Slopes, Proc. 15th International Conference on Soil Mechanics and Geotechnical Engineering, Istanbul, Rotterdam: Balkema, Vol. 2, pp. 1269–1272. Tsaparas, I., Rahardjo, H., Toll, D. and Leong, E.C. (2003). Infiltration Characteristics of Two Instrumented Residual Soil Slopes, Canadian Geotechnical Journal, Vol. 40, No. 5, pp. 1012–1032. Tsaparas, I. and Toll, D.G. (2002). Numerical Analysis of Infiltration into Unsaturated Residual Soil Slopes, in Proc. 3rd International Conference on Unsaturated Soils, Recife, Brazil, Lisse: Swets & Zeitlinger, Vol. 2, pp. 755–762. Vaughan, P.R. (1985). Pore pressures due to infiltration into partly saturated slopes. Proc. 1st International Conference on Geomechanics in Tropical Lateritic and Saprolitic soils. Brazil, Vol. 2, pp. 61–71.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Field investigation on triggering mechanisms of fast landslides in unsaturated pyroclastic soils A. Evangelista, M.V. Nicotera, R. Papa & G. Urciuoli Dipartimento di Ingegneria Geotecnica, Università Federico II, Napoli, Italy
ABSTRACT: This paper reports the main results of in situ experiment for an ongoing experimental research project on mudflows in pyroclastic soils described in a companion paper presented at this conference. We present the geological and stratigraphic aspects of the test site selected to monitor climatic conditions (affecting infiltration), matric suction and water content in the subsoil. The planned in situ instrumentation consists of tensiometers, TDR probes and wire vibrating piezometers. At the present time only tensiometers have been partly set up. The monitoring data collected span about two years of observations and allow clear identification of seasonal variation in matric suction.
1
INTRODUCTION
Based on geological and geomorphological considerations, a test site was selected to collect experimental data from laboratory tests on undisturbed samples and to monitor climatic conditions (affecting infiltration), matric suction and water content in the subsoil. Monitoring results and experimental data concerning the hydraulic behaviour of the main soil layers identified at the test site are presented in the paper, whilst some of the experimental results regarding the mechanical behaviour of the investigated soils are presented in some detail in a companion paper (Papa et al. 2008). 2
DESCRIPTION OF THE TEST SITE
The test site is situated on the west side of a limestone relief called Monte Faggeto about 40 km northwest of the volcano Somma-Vesuvius. Five recent flowslides and a number of ancient accumulation zones were recognized, demonstrating the area’s high landslide susceptibility. The limestone massif has a pyroclastic unsaturated soil cover several metres thick constituted by the products of a series of eruptions of SommaVesuvius. The whole investigated area has the same exposure towards the eruption vent and is aligned along the principal axis of dispersion of some of the main plinian eruptions of Vesuvius (Di Crescenzo et al. 2007). These geological features are quite similar to those of other sites in Campania in which some huge mudflows have occurred in the recent past (e.g. Pizzo D’Alvano, Monti di Avella and Monte Partenio). Furthermore, the vegetation at the site
consisting of chestnut woods and shrubland is representative of the mountainous area of the Campania region. From a morphological point of view the test site is quite regular. The slope has an average slope angle of 25◦ –30◦ but this angle is locally higher, reaching 35◦ –40◦ . In situ experimentation focused on an area of about 14,500 m2 where the chestnut trees were previously coppiced. The geological features of this area were investigated by means of 5 boreholes (maximum depth 6.00 m) and 15 deep exploration trenches (maximum depth 6.00 m). This investigation yielded a high resolution model of the subsurface. The positions of boreholes and trenches and the traces of the inferred geological sections are presented in Figure 1. Section C-C is presented in Figure 2. Using the data collected it was possible to evaluate the total thickness of the soil cover quite accurately. In spite of the regularity of the slope morphology the buried surface of the limestone has quite an uneven pattern. In particular, a hidden depression deeper than 10 m was identified in the bedrock. The stratigraphic succession can be described as a series of soil layers essentially parallel to the ground surface. Starting from the ground surface the sequence consists of: topsoil (humified ashes including roots and organic matter); a weathered and humified ashy soil; three pumices layers of various colours and grain size from the Avellino eruption (3.7 ky b.p.); a palaeosoil consisting of weathered volcanic ashes; a layer of yellowish pyroclastic sand resting on some pumiceous strata from the Ottaviano eruption (8.0 ky b.p.); a palaeosoil consisting of weathered volcanic ashes; a volcanic sand from the Agnano eruption
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(10.5 ky b.p.); two strata of highly weathered finegrained brownish ashy soils. However, starting from the above sequence a simplified profile was derived (Figure 3), based on the experimental investigation of the geotechnical properties of the pyroclastic cover (Papa et al. 2008). By contrast, the continuity of the strata and their thickness were carefully considered in order to investigate the interaction of the pyroclastic cover with both the atmosphere and the limestone bedrock. As regards soil layer continuity, it is worth noting that accurate inspection of morphological and stratigraphical data showed that while the layers from the Ottaviano eruption are found throughout the investigated area those from the Avellino eruption and the underlying palaeosoil are absent in areas with slope angles higher than 35◦ . These observations suggest that in those areas with a slope angle exceeding 35◦ these
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5: pumiceous deposits of Ottaviano eruption 8.0 ky b.p. (2.80 ÷3.50 m) 6: palaeosoil (weathered volcanic ashes) (3.50÷4.40 m) 7: volcanic sand (4.40 ÷4.90 m) 8: highly weathered fine-grained ashy soil (4.90 ÷5.50 m)
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Figure 3. Instrumentation design of the test site: vertical distribution of sensors.
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layers were scoured as a consequence of some kind of instability phenomenon. Hence it is argued that slides may well have occurred along surfaces affecting the palaeosoil interbedded between eruptive products from Avellino and Ottaviano. We should also point out that the collected data left some doubts about the continuity of the two layers of highly weathered fine-grained brownish ashy soils at the bottom of the pyroclastic cover; hence some new boreholes were programmed to investigate this stratigraphic feature. 3
INSTRUMENTATION DESIGN
The field instrumentation was designed to measure matric suction and water content in the pyroclastic cover and the climatic conditions as well. An area of about 230 m2 was chosen on the slope in question. In this area 26 instrumented vertical sections were realised. These vertical sections were distributed at the vertex of a fairly regular rectangular grid formed by 14 square meshes 4 m × 4 m (see Figure 1). Four tensiometers and three TDR probes were arranged along the vertical section inside the shallower soil layers (see Figure 3). Installation in the deeper soil layers of two more tensiometers and two more TDR probes was planned (see Figure 3) along the vertical sections situated at the two ends of the instrumented area (points SS in Figure 1). Furthermore, in each of these sections a piezometer at the bottom of the pyroclastic cover was set up to measure any positive pore water pressure at the limestone upper surface (Figure 3). Finally, a weather station was installed to monitor the climate conditions affecting the pore water pressure field in the soil cover (i.e. rainfall, solar net radiation, soil temperature, air temperature, air pressure, air humidity, wind speed, etc.). Standard vacuum tensiometers were employed. In particular, the shallower instruments consisted of a transparent nylon water-filled tube with a high air entry value porous ceramic tip and a silicon plug at the top end. The measurements by means of these instruments had to be carried out manually with an electronic tensimeter equipped with a steel needle. The deeper tensiometers were the jet-fill type equipped with differential vacuum gauges. Previous experience in measuring matric suction in similar unsaturated pyroclastic deposits (Evangelista et al. 2003) showed that in such conditions vacuum tensiometers require weekly maintenance (i.e. diffused air removal by means of water flushing). Furthermore, in situ and lab equalisation tests (Nicotera & Tarantino 2004) demonstrated that vacuum tensiometers installed in pyroclastic soils have an equalization time varying from several hours for suction values smaller than 50 kPa up to some days for suction values of about 60–80 kPa. These
considerations suggested that manual readings be preferred to automatic data collection in the present study. The occurrence in the pyroclastic cover of two thick layers of coarse-grained soils (layers 3 and 5) significantly conditioned the instrumentation design. Both tensiometers and TDR probes were ineffective for measuring matric suction and water content inside these pumiceous strata. Furthermore, the hydraulic properties (water retention curve and permeability function) of these coarse grained soils differ immensely from those of the other soil layers. Hence the sensor probes were arranged in order to investigate the pore water pressure field: in the top part of the soil profile (layers 1 & 2), the intermediate part (layer 4) and the bottom part (layers 6, 7 and 8). At the time this paper was prepared the instrumentation was still being installed and only the shallower tensiometers (in layers 1 & 2 and layer 4) had been set up and had been working for about one year. Hence below only these preliminary results of monitoring are presented. 4
HYDRAULIC PROPERTIES OF INVESTIGATED SOILS
The results of hydraulic tests performed on undisturbed samples recovered at the site are briefly presented below. Soil physical and mechanical properties are reported in a companion paper (Papa et al. 2008). Constant head tests were used to determine saturated permeability while forced evaporation tests and drying tests in a pressure plate apparatus allowed both water retention curves and permeability functions to be determined. The test procedures adopted were quite innovative and are extensively described by Papa (2007). The water retention curves and the permeability functions of the studied soils are reported in Figure 4. All these curves were determined along a drying process starting from totally saturated conditions. As regards water retention properties, all the investigated soils behave like coarse-grained materials; they have an air entry value in the range from 6–8 kPa to 12 kPa. Starting from saturated conditions, they become almost dry when the applied matric suction reaches about 100 kPa. However, some differences can be recognised between the shallower and intermediate layers (1 & 2 and 4) and the deeper ones (6 and 8). Careful comparison of the water retention curves in Figure 5 reveals that layers 6 and 8 have a substantially higher air entry value than the shallower strata. Furthermore, saturated water permeability (the experimental determinations are conventionally reported in Figure 4 as isolated points corresponding to a suction value of 0.1 kPa) clearly decreases with soil layer depth. In particular, the
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0.8 0.7
hydraulic conductivity function (m/s)
soil 1 soil 2
0.6
2: mean drying curve
0.5 0.4 0.3 2: mean wetting curve
0.2 0.1
1E-06
2: mean function (drying)
1E-07
1E-08
2: mean function (wetting)
1E-09
1E-10
0 0.1
1
10 100 matric suction (kPa)
0.1
1000
1
10
100
1000
matric suction (kPa)
0.8
1E-05
0.7
hydraulic conductivity function (m/s)
soil 4 mean drying curve
0.6 0.5 0.4 0.3 mean wetting curve
0.2 0.1 0
1E-06 mean function (drying)
1E-07
1E-08 mean function (wetting)
1E-09
1E-10 0.1
1
10 100 matric suction (kPa)
1000
0.1
1
10
100
1000
matric suction (kPa)
0.8
1E-05
0.7
hydraulic conductivity function (m/s)
soil 6 soil 8
0.6 0.5 0.4 0.3 0.2 0.1 0
1E-06
1E-07
1E-08
1E-09
1E-10 0.1
1
10
100
1000
0.1
1
10
100
1000
Figure 4. Water retention curves and permeability functions; permeability of saturated soils is indicated by mean points on the hydraulic conductivity axis.
hydraulic conductivity of layer 8 is significantly lower than that of all other soils along the whole investigated suction range. 5
MONITORING RESULTS
Monitoring began in the autumn of 2005. Prior to completion of tensiometer installation a portable
quick-draw tensiometer was initially used weekly to measure matric suction up to 0.60 m depth inside the instrumented area. These measurements proceeded until summer 2006. In mid-autumn 2006, tensiometers in layers 1 & 2 and in layer 4 were installed and monitoring continued by means of these instruments. In Figure 5 some of the monitoring results are summarised. Figures 5a & b report daily rainfall registered by two neighbouring rain-gauge stations
912
daily rainfall (mm)
2006
2005
2007 Avella's rain gauge
Monteforte's rain gauge
a)
b)
c)
Total volume of tensiometers refilling (%)
d)
depth (m)
TL1 TL2 TL3 TL4 QD1 QD2
matric suction (kPa)
120 100 80 60 40 20 0 120 100 80 60 40 20 0 100 75 50 25 0 80
60
40
0.20÷0.25 0.40÷0.45 1.30÷2.20 1.35÷2.30 0.30 0.60
20
0
autumn
10/10/2005
winter
07/02/2006
spring
07/06/2006
summer
autumn
05/10/2006
winter
02/02/2007
spring
02/06/2007
summer
autumn
30/09/2007
Figure 5. Main monitoring results: a) Avella rain gauge readings; b) Monteforte rain gauge readings; c) total volume of tensiometer refilling; d) mean matric suction.
(Avella 198 m a.s.l. and Monteforte 502 m a.s.l.). Figure 5d represents matric suction measurements: as regards preliminary monitoring carried out using the portable tensiometer, the data collected are reported as mean measurements taken at two different depths (0.3 m and 0.6 m). Analogously, the mean measurements obtained with the tensiometers are presented as mean measurements carried out at similar depths. Finally, in Figure 5c the total water volume used for refilling the shallower tensiometers (TL1 and TL2) is reported as a percent of the total inner volume of the tensiometers. The data collected during preliminary monitoring with the portable tensiometer are in good accordance with subsequent measurements. Data reported in Figure 5d clearly show the seasonal trend in the measurements at different depths even if the monitoring periods did not continuously cover a complete seasonal cycle. Matric suction appears almost constant in winter while increasing in spring and summer; maximum suction values are measured by shallower tensiometers (TL1 and TL2) in summer; finally, matric suction progressively decreases as the wet season begins. During the dry season, matric suction values in the shallower part of the soil cover are significantly higher than those in the intermediate part. However, summer matric suction values in the shallower soil layers reach and sometimes exceed the upper limit
of the tensiometer operation range (about 70 kPa) as testified by the abrupt increase in the refilling volume reported in Figure 5c. On the other hand, only meticulous inspection of measurements reveals that in winter matric suction is much lower in shallower strata than in deeper ones, testifying to rain water infiltration into the soil. Interestingly, there are differences between measurements in the shallower part of the soil cover (TL1 and TL2) and those in the intermediate strata (TL3 and TL4). Tensiometers TL1 and TL2 seem to respond to singular rainfall events but the corresponding suction variations are relatively small compared to the seasonal trend. Conversely, tensiometers TL3 and TL4 follow a trend unaffected by individual rainfall events. Furthermore, it must be observed that the seasonal cycle in the intermediate part of the cover is quite delayed. The total fluxes of water filtrating vertically into the upper and the intermediate part of the soil cover were estimated on the basis of both monitoring and lab data (hydraulic conductivity). Concurrent readings of the tensiometers installed along the same vertical section were used to estimate the hydraulic gradients in each vertex of the instrumented grid at two different depths (i.e. between tensiometers TL1 and TL2 and between tensiometers TL3 and TL4). The mean permeability functions experimentally determined in the laboratory were used to estimate the value of the
913
30
2006
2007
a) TL1 - TL2: permeability along main drying curve TL3 - TL4 TL1 - TL2: permeability along wetting curve TL3 - TL4
water flux (mm/day)
25 20 15 10 5 0
cumulative water flux (mm)
1500
b)
1200 Monteforte's rain gauge
900 Avella's rain gauge
600 300 0
autumn N
winter D
J
spring F
M
A
M
summer J
J
A
autumn S
O
N
Figure 6. Water fluxes estimated on the basis of in situ suction measurements and lab determination of hydraulic permeability along the main drying and the wetting curves: a) fluxes; b) total fluxes and cumulative rainfall.
hydraulic conductivity corresponding to each of the aforementioned gradients. Finally, the fluxes calculated by applying Darcy’s law were integrated over the whole instrumented area. The results of this analysis are reviewed in Figure 6. In Figure 6a the mean calculated fluxes (positive when directed downward) are represented while in Figure 6b the cumulative fluxes are plotted against cumulative rainfall registered at the two rain-gauge stations. The fluxes calculated testify to a fairly continuous infiltration process occurring in both the upper and intermediate part of the soil cover during autumn, winter and early spring. By contrast, evaporation (negative flux) took place during late spring and summer. However, the data lack continuity in this period and hence outward fluxes are poorly estimated. The trends of the cumulative fluxes into the two investigated strata are in good mutual agreement and are comparable with the general trends in cumulative rainfall. Nevertheless, it is worth noting that the cumulative fluxes estimated with the described procedure are higher than the cumulative rainfall measured at both rain-gauge stations. It must be pointed out that the adopted relationships between
matric suction and hydraulic conductivity were determined by forced evaporation tests along the main drying curves of each soil. On the other hand, extension of the hysteresis domain in the matric suction versus water content relationship was evaluated by comparing the water retention curve of Figure 4 with a number of direct measurements of matric suction within undisturbed samples. The main wetting curve was considered as the bottom envelope of the above measurements. The matric suction versus hydraulic conductivity relation along the main wetting curve was estimated by assuming the relation between volumetric water content and hydraulic conductivity as unique. Hence water fluxes in the field were revised to allow for hydraulic conductivities along the wetting curve (see Figure 6). This second estimation seems to be more reasonable than the first; cumulative fluxes are indeed lower than the cumulative rainfall. These results show the need to allow for hydraulic hysteresis in analysing the interaction phenomena between the atmosphere and the pyroclastic cover. Obviously these considerations are significant for the shallower and intermediate parts of the soil cover while hysteresis could be unimportant for filtration in the deeper
914
soil layers. These points will be thoroughly examined in future research. 6
CONCLUDING REMARKS
The monitoring results clearly show the seasonal variation in matric suction at the test site. The soil cover can be subdivided into three portions characterised by different seasonal cycles of pore water pressure: matric suction in the top part of the cover seems to be affected by singular rainfall events but the corresponding suction variations are relatively small if compared to the seasonal trend; conversely, the suction in the intermediate part of the cover follows a trend unaffected by individual rainfall events; finally, pore water pressure in the bottom part of the cover has not yet been investigated. However, there are several arguments suggesting that suction variations in the intermediate part of the cover should be more effective at triggering landslide mechanisms (Papa et al. 2008).
Monteforte Irpino (AV). In C. Nunziata (ed.) Piattaforme Evolute di Telecomunicazioni e di Information Technology per l’Offerta di Servizi al settore Ambiente Petit-Osa: 263–272. Rome: Aracne. Evangelista, A., Nicotera, M.V. & Scotto di Santolo, A. 2003. Experimental and Theoretical validation of matric suction measurements in pyroclastic soils. Proc. of Int. Conf. on Fast Slope Movements prediction and prevention for risk mitigation, Naples, Italy, 173–177. Bologna: Pàtron Editore. Nicotera, M.V. & Tarantino, A. 2004. Laboratory measurement of matric suction in pyroclastic soil using vacuum and high-suction tensiometers. Proc. of Int. Conf.: From Experimental Evidences Towards Numerical modelling of Unsaturated Soils, Weimar, Germany, 193–208, Berlin: Springer. Papa, R., Evangelista, A., Nicotera, M.V. & Urciuoli, G. 2008. Mechanical properties of unsaturated pyroclastic soils affected by fast landslide phenomena. E-UNSAT 2008. Papa, R. 2007. Indagine sperimentale di una copertura piroclastica di un versante della Campania. PhD thesis, Università di Napoli Federico II.
REFERENCES Di Crescenzo, G., Rotella, M. & Santo, A. 2007. Il contributo della geologia per lo studio dei meccanismi di innesco di colate rapide di fango al campo sperimentale di
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Mechanical properties of unsaturated pyroclastic soils affected by fast landslide phenomena R. Papa, A. Evangelista, M.V. Nicotera & G. Urciuoli Dipartimento di Ingegneria Geotecnica, Università Federico II, Napoli, Italy
ABSTRACT: The paper describes some results of an ongoing experimental research project on mudflows in pyroclastic soils in the southern Italian region of Campania. Based on geological and geomorphological considerations a test site was selected in order to collect experimental data from laboratory tests on undisturbed samples, as well as monitor climatic conditions (affecting infiltration), matric suction and water content in the subsoil. Eight different soil layers were identified at the test site. The results of suction-controlled triaxial and direct shear tests on undisturbed unsaturated specimens from one of the soil layers are presented and tentatively interpreted. It emerges that matric suction is not suitable, as an independent stress variable, to describe the shear strength of this unsaturated pyroclastic soil. By contrast, a satisfactory interpretation is achieved by taking into account both matric suction and saturation degree, representing the data in terms of Bishop stress.
1
INTRODUCTION
In the last ten years a series of catastrophic mudflows, involving pyroclastic unsaturated soils, has caused severe damage and a number of fatalities in the region of Campania (Italy). Both geological and geotechnical scientific communities have made considerable research efforts to clarify triggering mechanisms and kinematic aspects of such phenomena (e.g. Bilotta et al. 2005; Calcaterra et al. 2003), but a substantial lack of experimental data regarding the mechanical behaviour of soils and field conditions still persists. Mudflows affect the pyroclastic cover resting on the limestone massif in the region. Rainwater infiltration is the likely mechanism that leads or predisposes to slope failures by reducing matric suction in unsaturated soils, thereby reducing the shear strength. Moreover, there are other hypotheses on triggering mechanisms for cases in which the subsoil water regime can play a major role due to local stratigraphic and hydro-geologic conditions (local factors). Although local factors could be responsible for landslides, it is the general condition of potential instability, produced by rain infiltration from ground surface, which predisposes the subsoil to failure. This paper will describe the results of an ongoing experimental research project on mudflows in pyroclastic soils in Campania, involving a wide-ranging group of researchers, with abilities in various topics (geology, geomorphology, soil mechanics, hydraulics, agronomy).
Based on geological and geomorphological considerations, a test site was selected to collect experimental data from laboratory tests on undisturbed samples, monitoring climatic conditions (affecting infiltration), matric suction and water content in the subsoil. The laboratory results are presented in the paper, whilst the morphological and geological features of the test site are described in some detail in a companion paper (Evangelista et al. 2008). 2
MATERIALS AND METHODS
At the test site the stratigraphic succession can be described as a series of soil layers essentially parallel to the ground surface. Starting from the ground surface the sequence consists of: 1) topsoil; 2) weathered and humified ashy soil; 3) pumices from the Avellino eruption (3.7 ky b. p.); 4) palaeosoil consisting of weathered volcanic ashes; 5) pumices from the Ottaviano eruption (8.0 ky b. p.); 6) palaeosoil consisting of weathered volcanic ashes; 7) volcanic sand; 8) highly weathered fine-grained ashy soil. Accurate inspection of morphological and stratigraphical data showed that layers 4 and 3 are absent in the area characterised by a slope angle higher than 35◦ (Di Crescenzo et al. 2007). Importantly, layer 3 is an air-fall pyroclastic deposit produced by Somma-Vesuvius plinian activity; the whole investigated area has the same exposure towards the eruption vent. Moreover, layer 3 consists of coarse-grained material sandy gravel with a critical friction angle significantly higher than 35◦ .
917
100 90 80 70 60 50 40 30 20 10 0 0.001
Figure 1. Irpino.
sand
gravel
100
100 90 80 70 60 50 40 30 20 10 0 0.001
100
100 90 80 70 60 50 40 30 20 10 0 0.001
2 (N=9) 1 (N=12)
a) 0.01 0.1 1 10 Particle diameter: mm silt
sand
6
gravel
8
c) 0.01
0.1
1
silt
10
sand
Percent finer
silt
gravel
4 (N=12)
b) 0.01 0.1 1 10 Particle diameter: mm silt
Percent finer
100 90 80 70 60 50 40 30 20 10 0 0.001
sand
100
gravel
5
3
7 d) 0.01
0.1
1
10
100
Grain size distributions of soils constituting the cover on the limestone substratum, in the trial field at Monteforte
These observations suggest that in those areas with a slope angle higher than 35◦ , layer 3 was whipped out as a consequence of some kind of instability phenomenon. Hence it has been argued that layer 4, due to both its position in the stratigraphic sequence and its mechanical properties, played a significant role in such instability. Therefore, even if the main goal of the experimental program was the mechanical and hydraulic characterisation of all the pyroclastic soils covering the limestone massif, the investigation primarily focused on soil 4. In all, 158 undisturbed samples were recovered at the site by means of a thin wall sampler either in drill holes or in deep trenches. However, recovery of undisturbed samples from coarse-grained soil was excluded a priori. Hence the mechanical behaviour of strata 3 and 5 was not investigated and will be disregarded below. Grain-size distributions of the eight layers are reported in Figure 1. The grain-size envelopes of investigated soils exhibit limited scatter, demonstrating the uniformity of the deposits. Shallower layers (1 & 2) have quite similar grain-size distribution: the two envelopes are partially superimposed (light grey area in Figure 1a) even if layer 1 is rather finer (dark
grey area in Figure 1a). Soil 4 (Fig. 1b) is well-graded, ranging from sand to silt with a small clay fraction. Layers 6 and 8 (Fig. 1c) are significantly finer than the others. Soils 3, 5 and 7 (Fig. 1d) should be described as quite uniform coarse-grained materials: soil 7 is a medium silty sand, soil 5 is a coarse sand and soil 3 is a gravel. Mean values of the main soil physical properties are reported in Table 1. All soils are extremely porous. This feature is evident in Figure 2 where the probability density functions of the porosity n as estimated on the basis of laboratory data are reported: the porosity of layers 1, 2 and 4 present bell-shaped distributions with a clearly defined mode; slight left stretching of the bell left tail is likely due to sampling disturbance. By contrast, density functions of deeper layers (not represented in the figure) are less clear, probably owing to both spatial variability and sampling disturbance. All layers are partially saturated but deeper layers have higher values of the saturation degree (see Table 1). However, the saturation condition varies on a seasonal basis. Mechanical and hydraulic behaviours of the pyroclastic material were investigated in both unsaturated and saturated conditions. As regards hydraulic
918
Table 1.
Mean soil physical properties.
200 7 fcv' = 40.3
Soil
Gs
γd (kN/m3 )
γ (kN/m3 )
n
2 fcv' = 36.2
Sr 150
1 2 4 6 7 8
2.65 2.66 2.57 2.57 2.47 2.49
8.06 7.77 7.11 7.13 7.71 10.64
11.91 12.49 12.11 12.51 11.93 15.49
0.69 0.70 0.71 0.72 0.69 0.58
0.57 0.69 0.71 0.77 0.64 0.87
1 M = 1.50; f’ = 36.9˚ N. 11
100
2 M = 1.47; f’ = 36.2˚ N. 9 4 M = 1.50; f’ = 36.9˚ N. 12
50
6 M = 1.62; f’ = 39.8˚ N. 4 7 M = 1.65; f’ = 40.3˚ N. 7
(n)
8 M = 1.51; f’ = 37.0˚ N. 5
25
25
2
0
4
1
15
Figure 3. samples.
15
100
150
200
Results of triaxial compression tests on saturated
10 1 & 2: 0.713 4: 0.723
10 5
0.65
0.70
5
3.1 Triaxial tests on saturated specimens 0.75
0.80
0
Figure 2. Probability density function of the porosity of investigated superficial soils.
properties, constant head tests were used to determine saturated permeability while forced evaporation tests and drying tests in a pressure plate apparatus allowed both water retention curves and permeability functions to be determined. Hydraulic test results are presented in a companion paper (Evangelista et al. 2008) while experimental techniques are extensively described by Papa (2007). Conversely, some of the results regarding the mechanical behaviour of the investigated soils are presented below.
3
50
20
20
0 0.60
0
EXPERIMENTAL RESULTS
In all, 48 stress-path controlled triaxial compression tests were performed on undisturbed specimens previously saturated in the triaxial cell. These tests were carried out on all the studied soils. By contrast, 9 suction-controlled tests on naturally unsaturated undisturbed specimens were executed only on soil 4. By means of triaxial tests, shear strength of soil 4 at high and intermediate stress levels was obtained. Moreover, 12 conventional and 19 suctioncontrolled direct shear tests were employed to investigate the shear strength of the same soil at very low stress.
Triaxial tests on saturated specimens consisted of the following phases: saturation under minimal effective confining stress (≈2 kPa) by means of backpressurising and upward flushing with de-aired water; isotropic compression; shearing. The shearing phases were performed either in drained or undrained conditions at constant mean stress ( p or p equal to 30, 50 and 70 kPa) or at constant confining stress (σr ) or σr equal to 30, 50 and 70 kPa). Stress levels were selected to be analogous to in situ stress states. However, it was not possible to carry out tests at stress levels as low as those acting in the shallower layers. The isotropic compressions were completed at a loading rate of 5 kPa/hour. The shearing phases were performed in strain-controlled conditions at a strain rate of 0.1 % hour. Soils 1, 2 and 4 showed a highly contractive and ductile behaviour in all the tests. By contrast, soil 6 behaved as brittle and rather dilative in tests executed under a mean effective stress equal to 30 kPa and as ductile and contractive in tests performed at higher stress levels. Finally, soils 7 and 8 behaved brittly in the entire stress range. Some of the experimental results are summarised in Figure 3: for each test deviatoric stress q = (σa − σr ) at ‘‘near’’ critical state is reported as a function of mean effective stress p [= 1/3(σ1 + 2σ3 ) − uw ]. Experimental points lay in quite a narrow area bounded by the critical strength envelopes of soil 2 and 7; it is worth noting that the estimated critical friction angles range from 36.2◦ to 40.3◦ . Although from the mechanical lab tests soil 2 appears to be the weakest of the stratigraphic series,
919
morphological evidence indicates that soil 4 is the most prone to landslides. This can be justified by the presence of roots inside soil 2, which reinforce it. 3.2
Suction-controlled triaxial tests
Triaxial tests on natural unsaturated specimens of soil 4 were carried out by means of a stress-path and suction-controlled triaxial apparatus (Aversa & Nicotera 2002). Each test consisted of the following phases: measurement of the initial suction by means of the axis translation technique; equalisation to an assigned suction value; isotropic compression at constant suction; shearing at constant suction (6 kPa, 12 kPa and 20 kPa) and constant mean net stress (30 kPa, 50 kPa and 70 kPa). Suction measurements lasted about 48 hours while equalisation phases took from 48 to 96 h. The isotropic compressions were completed at a loading rate of 5 kPa/hour. The shearing phases were performed in strain-controlled conditions at a strain rate of 0.1%/hour. As regards water retention properties, soil 4 actually behaves like coarse-grained material; it has an air entry value of about 6–8 kPa and starting from saturated conditions becomes almost dry when the applied matric suction reaches about 100 kPa. Suction values for the triaxial tests were selected in order to study the mechanical behaviour during the transition between fully saturated and partially saturated conditions. The results of the suction-controlled triaxial tests are reported in Figure 4 in terms of deviatoric stress q and volumetric strain εv as functions of shear strain εs [= 2/3 · (εa − εr )]. In Figure 4 the stress strain curve corresponding to the same mean net stress pnet [= 1/3(σ1 + 2σ3 ) − ua ] but to different values of the matric suction s(= ua − uw ) can be compared between them as well to three triaxial tests on a saturated specimen carried out at equivalent values of effective mean stress p . The maximum deviatoric stress reached in each constant suction test is much higher than that recorded in the corresponding test on the saturated specimen. However, the trend of the dependence of maximum deviatoric stress on the value of matric suction is not clearly recognizable: for the constant mean net stress of 30 kPa, there is an increase in the maximum deviatoric stress with the increase in applied suction. With an increase in constant mean net stress, this trend fails to become evident. It appears that matric suction is not suitable, as an independent stress variable, to describe the shear strength of a partially saturated soil. The comparison between the volumetric strain recorded in suction-controlled triaxial tests and triaxial tests on saturated specimens is reported in Figure 4b. It is evident that the unsaturated specimens behave as more contractive than the saturated one at a similar
stress state. Nevertheless, it must be observed (Fig. 4b) that at the end of the tests corresponding to a shear strain value of about 15% the volumetric strain of the unsaturated specimens was still rising while that of the saturated specimens was almost ‘‘stationary’’. Hence the deviatoric stress recorded at the end of the suctioncontrolled test may well be slightly smaller than the corresponding critical one. In Figure 5a the final value of the deviatoric stress recorded in each test is reported as a function of mean net stress and compared to the critical state line inferred for the saturated material. The experimental points corresponding to suction-controlled triaxial tests lie well above the saturated critical state line, indicating the matric suction effect on critical shear strength. Nevertheless, the shear strength increment cannot be justified by a linear dependence on matric suction as proposed by a number of authors (e.g. Fredlund & Morgenstern 1977). On the contrary, a better interpretation can be achieved by representing the data in terms of mean Bishop stress ( p ): p =
1 · (σ1 + 2 · σ3 ) + Sr · s 3
(1)
as originally proposed by Jennings (1960) and subsequently adopted by others (Jommi 2000; Gallipoli et al. 2003). This representation is proposed in Figure 5b: the experimental data seem to be arranged along a single envelope; moreover, this envelope is well described by the same line adopted for representing the critical state of the saturated soil. This result confirms that the stress state acting in unsaturated soils can be accurately represented only if the adopted stress variables take into account both matric suction and degree of saturation (e.g. Nuth & Laloui 2007). However, selection of the best variables is still a matter for debate (e.g. Nuth & Laloui 2007) and even in the present case some attempts to improve the data interpretation by means of different stress variables have been made (Papa 2007). Furthermore, the coincidence in the p , q plane of the critical state line for the unsaturated soil with the critical state line for the saturated soil indicates that the so-called ‘‘bonding effect’’ due to water menisci (Gallipoli et al. 2003) has a negligible effect on critical shear strength. Similar considerations have already been proposed by some authors though for quite different soils and stress levels (Tarantino & Tombolato 2005, Tarantino 2007). Indeed, careful inspection of Figure 5b reveals that a number of experimental points lie just below the critical state line, according to the observation that in unsaturated soil triaxial tests, critical state has not been attained at the ultimate strain. Therefore more accurate estimates of the slope of the critical state line in the p , q plane were performed by extrapolating the experimental data using a well-defined
920
05101520
150
0
p-ua = 70 kPa p' = 70 kPa
volumetric strain, e v:%
p-ua = 30 kPa
100 p-ua = 50 kPa p' = 50 kPa p-ua = 30 kPa
50
p' = 30 kPa
6 12 20 Sr = 1
suction : kPa
a)
p' = 30 kPa p' = 50 kPa p' = 70 kPa
1 2 3
5 6
0
p-ua = 50 kPa p-ua = 70 kPa
4
p-ua = 70 kPa
6 suction : kPa 12 20 Sr = 1
p-ua = 50 kPa p-ua = 50 kPa
p-ua = 70 kPa
b)
7 0
5
10
15
20
Figure 4. Mechanical behaviour of soil 4 in unsaturated triaxial compression tests: a) deviator versus shear strain, b) volumetric strain versus shear strain. 250
250
200
f cv' = 36.9
deviatoric stress, q: kPa
deviatoric stress, q: kPa
200
saturated CSL
150
100 suction: kPa 6
50
f cv' = 36.9 saturated CSL
150
100 suction: kPa 6
50
12
12
20
a)
20
b)
0
0
0
50
100
150
0
50
100
150
Figure 5. Critical shear strength of soil 4 from suction-controlled triaxial tests: a) net stress interpretation; b) Bishop’s stress interpretation.
stress-dilatancy relationship (Papa 2007). However, discussion of these points would go beyond the scope of the present paper.
3.3
Suction-controlled direct shear tests
In all, 19 direct shear tests on unsaturated undisturbed specimens were performed by means of a suction controlled direct shear apparatus (Evangelista et al. 2004). These tests were carried out at very low values of normal net stress ranging from 3 kPa to 250 kPa. The experimental program was conceived to assess the linearity of the shear strength envelope. However, some more tests at higher value of net normal stress were performed to depict the shape of the envelope in a
wider stress range. Each test consisted of the following phases: measurement of the initial suction by means of the axis translation technique; equalisation to an assigned suction value; vertical compression at constant suction; shearing at constant suction (6 kPa, 12 kPa and 20 kPa) and constant normal net stress (3–12–24–36–75–150 and 250 kPa). Suction measurements lasted about 24 hours while equalisation phases took from 48 to 72 h. The vertical compressions were completed at a loading rate of 5 kPa/hour. The shearing phases were performed in displacementcontrolled conditions at a rate of 0.1 mm/hour. The shearing rate was selected by scaling down the optimal displacement rate determined for saturated tests on the basis of a trial and error procedure (Papa 2007).
921
250
250 saturated CSL f cv' = 36.9
150
100 suction: kPa 0:6 6 12 20
50
a)
saturated CSL
200 shear stress, t : kPa
shear stress, t : kPa
200
f cv' = 36.9
150
100 suction: kPa 0:6 6 12 20
50 b)
0
0 0
50
100
150
200
250
300
0
50
100
150
200
250
300
Figure 6. Shear strength of soil 4 from suction-controlled direct shear tests: a) net stress interpretation; b) Bishop’s stress interpretation.
Data representations similar to those proposed in Figure 5a, b for triaxial shear strength data are reported in Figure 6a, b for data from suction controlled direct shear tests. Figure 6a shows that shear strength of unsaturated specimens in direct suction-controlled tests is significantly higher than the critical ones estimated on the basis of the triaxial saturated envelope. The same data drawn in terms of normal Bishop’s stress σ = σnet + Sr · s) seem to agree quite well with the same envelope. However, in this case some of the experimental data are just above the triaxial critical envelope. This result could be ascribed to the following factors: the effect of the deformation path (almost 2D in the direct shear apparatus); the higher strain levels reached in the direct shear tests (the shear strength was recorded at about 10 mm); the actual saturation degree inside the shear band being higher than the mean value employed to determine σnet (by contrast, no strain localisation was observed in triaxial tests).
4
CONCLUDING REMARKS
By performing triaxial tests on the undisturbed specimens recovered in the soil layers identified at the Monteforte Irpino test site the saturated shear strength of the pyroclastic cover resting on the limestone bedrock was defined with good accuracy. Although, from the mechanical lab tests, soil 2 appeared the weakest in the stratigraphic series, morphological evidence indicated that soil 4 was the most prone to landslides. Soil 4 lies in between two pumiceous layers and is extremely porous. This soil behaved in a highly ductile and contractive fashion in both saturated and suction-controlled triaxial tests. Matric suction effects
on critical shear strength of soil 4 could not be interpreted by a simple model such as the classical one proposed by Fredlund & Morgenstern (1977). The trend of the dependence of maximum deviatoric stress on the value of matric suction was not clearly recognizable. Hence it was concluded that matric suction was not suitable, as an independent stress variable, to describe the shear strength of this unsaturated pyroclastic soil. However, a satisfactory interpretation was achieved by taking account of both matric suction and saturation degree, representing the data in terms of Bishop’s stress. Furthermore the results from suctioncontrolled direct shear tests performed in a lower stress range confirmed these observations.
REFERENCES Aversa, S. & Nicotera, M.V. 2002. A triaxial and oedometer apparatus for testing unsaturated soils. Geotechnical Testing Journal, GTJODJ, 25(1): 3–15. Bilotta, E., Cascini, L., Foresta V. & Sorbino G. 2005. Geotechnical characterisation of pyroclastic soils involved in huge flowslides. Geotechnical and geological engineering, 23: 365–402. Calcaterra, D., de Riso, R., Evangelista, A., Nicotera, M.V., Santo, A. & Scotto di Santolo, A. 2003. Slope instabilities in the pyroclastic deposits of the Phlegraean district and the carbonate Apennine (Campania, Italy). In L. Picarelli (ed.) Occurrence and Mechanisms of Flows in Natural Slopes and Earthfills, Proc. of Intern. Workshop, Sorrento, 14–16 May 2003: 61–76. Bologna: Pàtron. Di Crescenzo, G., Rotella, M. & Santo. A, 2007. Il contributo della geologia per lo studio dei meccanismi di innesco di colate rapide di fango al campo sperimentale di Monteforte Irpino (AV). In C. Nunziata (ed.) Piattaforme
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Evolute di Telecomunicazioni e di Information Technology per l’Offerta di Servizi al settore Ambiente Petit-Osa: 263–272. Rome: Aracne. Evangelista, A., Nicotera, M.V. & Aversa, S. 2004. Un’apparecchiatura di taglio a suzione controllata per lo studio delle condizioni di innesco dei fenomeni franosi nelle coltri piroclastiche. Proceedings of the XXII Convegno Nazionale di Geotecnica, Palermo: 81–88. Patron, Bologna. Evangelista, A., Nicotera, M.V., Papa, R. & Urciuoli G. 2008. Field investigation on triggering mechanisms of fast landslides in unsaturated pyroclastic soils. E-UNSAT 2008. Fredlund, D.G. & Morgenstern, N.R. 1977. Stress state variables for unsaturated soils. Journal of the Geotechnical Engineering Division (ASCE), 103 (GT5): 447–466. Gallipoli, D., Gens, A., Sharma, R. & Vaunat, J. 2003. An elasto-plastic model for unsaturated soil incorporating the effects of suction and degree of saturation on mechanical behaviour. Geotechnique 53(1): 123–136.
Jommi, C. 2000. Remarks on the constitutive modelling of unsaturated soils. In A. Tarantino & C. Mancuso (eds.) Experimental evidence and theoretical approaches in unsaturated soils: 139–153. Rotterdam: Balkema. Jennings, L.E. 1960. A revised effective stress law for use in the prediction of the behaviour of unsaturated soils. Pore Pressure and Suction in Soils. London: Butterworths. Nutn, M. & Laloui, L. 2007. Effective stress concept in unsaturated soils: Clarification and validation of a unified framework. Intern. Journal for Numerical and Analytical Methods in Geomechanics. Pub. online in Wiley InterScience. Papa, R. 2007. Indagine sperimentale di una copertura piroclastica di un versante della Campania. PhD thesis, Università di Napoli Federico II. Tarantino, A. & Tombolato, S. 2005. Coupling of hydraulic and mechanical behaviour in unsaturated compacted clay. Geotechnique 55(4): 307–317. Tarantino, A. 2007. A possible critical state framework for unsaturated compacted soils. Geotechnique 57(4): 385–389.
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Stability of a tailings dam considering the hydro-mechanical behaviour of tailings and climate factors M.T. Zandarín & L. Oldecop Instituto de Investigaciones Antisísmicas ‘‘Ing. Aldo Bruschi’’, Facultad de Ingeniería, Universidad Nacional de San Juan, San Juan, Argentina
R.R. Pacheco Departamento de Química. Facultad de Ciencias. Universitat de Girona. Campus Montilvi, Girona, Spain
ABSTRACT: Tailings storage facilities are complex geotechnical structures. The present paper focuses on the study of a case-history, a tailing dam from the nickel industry from Cuba, with the objective of gaining knowledge about the geotechnical behaviour of such structures. The dam was modelled by means of a coupled hydro-mechanical finite element formulation. Due to the low permeability of tailings, the phreatic levels in the deposit remain high during and after its construction. Steady-state flow regime would be reached only after several decades after closure. Moreover, capillary rise causes the degree of saturation to stay high in the whole storage. Under the action of rain storms, phreatic levels rise quickly due to the presence of capillary water. At the end of the storm, phreatic levels fall slowly because of the low hydraulic conductivity. The results of the analysis show that the stability of the dam strongly depends on its hydraulic operation.
1
INTRODUCTION
Tailings storage facilities are complex geotechnical structures. They are commonly built by the discharge of slurry within an impoundment. Tailings are finegrained non-plastic materials. Their permeability is low and unsaturated phenomena play a significant role in their behaviour. A number of factors may influence the stability of tailings dams, such as the pluvial regime, evaporation, capillary rise, construction rate, drainage, consolidation and rain storms. The present paper focuses on the study of a case-history, with the aim of identifying which of those factors are relevant for the structural safety of tailings dams. The tailings dam studied is one of the facilities at Pedro Sotto Alba nickel mine, located in the province of Moa, in the southeast of Cuba. The impoundment is located on a low lying flood plain in the south bank of Moa River (Figure 1a). It is founded on alluvial sediments of quaternary age, underlain by stiff clays and cretaceous ultramafic serpentine (Figure 1b). (Chalkley et al. 2002; Greenaway et al. 2002). The climate at the site is tropical. Temperatures vary between 23◦ C and 27◦ C and the annual average rainfall is 2830 mm. The rainfall intensity can reach between 2 and 3 mm per minute, for rainfall events with 5 to 20 minutes duration, having a period of recurrence of
100 years (Moya, 1998). Two extraordinary rainstorms occurred in 1996 and 1998 (Chalkley et al. 2002). The first lasted 48 h with a total rain volume of 722 mm and a maximum intensity of 190 mm in 90 minutes. The second lasted 12 h with a 690 mm total precipitation. The annual average evaporation is 2296 mm. Figure 2 shows the monthly average rainfall and evaporation at the site. The operation of the facility began in 1970. Tailings were discharged in slurry form behind a laterite embankment built in stages, applying the upstream construction method. The mean rise rate of the impoundment was about a half metre per year until 1987. The facility had a system of decant pipelines to allow the drainage of the excess water accumulated in the decant pond. The section 1-1 shown in Figure 1b experienced a number of episodes of slope instability. Such episodes involved the release of important amounts of tailings covering the flood plain of the Moa River and Los Lirios Creek. Tailing relicts can be found even in the opposite bank (north) of Moa River, indicating that at some time the slurry flow was large enough to cross the main channel of the river. During the 1990 s a number of works were undertaken in order to rehabilitate the facility (Chalkley et al. 2002, Greenaway et al. 2002). In the present work, section 1-1 was modelled with the objective of gaining knowledge about the influence
925
stress and suction (Olivella et al. 1994). For the present analysis, only coupled flow and deformation problems were considered.
a)
1
Ri ve r
Original Embankment
1
oa M
Slurry Pipeines
3
Drainage Pipelines
Supernatant Pond Slurry Discharge Point
Scale
Los Lirios Creek
0 200 400m
ELEVATION (m)
b) Original Embankment
20 10 0 -10 -20 -30
Moa River
LEGEND:
Scale
Tailings Embankment Fill-Compacted Laterite Alluvial Sand and Silt
50meters
0
Organic Clay and Silt Marine Clay and Silt Highly Weathered Serpentine
400 350 300 250 200 150 100 50 0
Rainfall
December
October
November
September
July
Months
August
June
May
Marz
April
February
Evaporation
January
Average Rainfall and Evaporation [mm]
Figure 1. (a) Tailings dam planimetry. (b) Cross section 1-1 through the tailings facility (after Chalkley et al. 2002).
Figure 2. Average rainfall and evaporation registered at Moa site. (Rodriguez, 2002).
of the hydro-mechanical properties of tailings, the climate conditions and the operation procedures, in the stability of the dam. Sensitivity of the results to the different factors considered was studied.
2
FINITE ELEMENT CODE
The hydro-mechanical behaviour of the tailings dam was studied with the finite element code CODE BRIGHT, developed at the Department of Geotechnical Engineering of the Technical University of Catalunya, Spain. The code solves simultaneously, the balance equations for heat transfer, water flow, air flow and the mechanical equilibrium equations. It is formulated in terms of two independent stress variables: net
MODELLED SECTION
The complete construction history of the tailings deposit was simulated, including the influence of rainfall and evaporation. The discretized section geometry is shown in Figure 3. The section has a total length of 550 m, ranging from the north-eastern side of the impoundment up to the supernatant pond (centre of the tailing beach). The clay bed beneath the alluvial sand layer was assumed to be a lower impermeable boundary of the problem. Three different materials were considered: alluvial soil (sand and silt), embankment (compacted laterite) and tailings. The section modelled has a total height of 12.5 m on the embankment side, and 10 m adjacent to the decant pond. The embankment is 8 m high, with a slope of 1H:1V and the alluvial layer is 4.5 m thick. The tailings beach slopes down 0.5% in the upstream direction. The phreatic level downstream the embankment is determined by the water level in Moa River. The impoundment construction was simulated in 5 layers (Figure 3). Each layer was built in 1000 days, approaching the mean rising rate of the dam (Rodriguez, 2002). The layers were subdivided into 10 zones in order to take into account the variation of material properties within the dam. Due to hydraulic particle sorting during the flow of slurries along the tailing beach, grain size reduces with increasing distance from the slurry discharge point (Blight, 1994). During each stage of dam filling the presence of the supernatant water pond was assumed over the 9, 10 and 11th zones. 4
CONSTITUTIVE MODELS
The viscoplastic formulation of the Barcelona Basic Model (BBM) (Alonso et al. 1990) was adopted to describe the mechanical behaviour of tailings, embankment and foundation materials. Mechanical model parameters for tailings were determined on the basis of oedometer, triaxial and brazilian tensile tests performed by Rodriguez (2002). The mechanical parameters for the embankment material were assumed to be identical to tailings parameters, because of the same geological origin of both. However, a slight preconsolidation stress (0.1 MPa) was assigned to the embankment material, since a moderate compaction was applied during construction lifts. The parameters for the foundation soils were estimated on the basis of the soil classification (SM) and index properties measured by Greenaway et al. (2002).
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Supernatant pond 10 9 10 11 5 0 550 500 450 Figure 3. Table 1.
Tailings 6
7
8 400
350
5
300
250
200
2
3
4 150
100
1
Embankment
Foundation 50 0m
Tailings dam geometry for model calculation (vertical scale magnified by a factor of 2). Mechanical parameters.
Definition of parameter Elastic behaviour Elastic modulus Poisson’s ratio Plastic behaviour Virgin compressibility for saturated conditions Parameter that establishes the minimum value of the compressibility coefficient for high values of suction Parameter that controls the rate of increase in stiffness with suction Reference stress Slope of critical state strength line Parameter that controls the increase in cohesion with suction Parameter that defines the nonassociativeness of plastic potential Initial state for tailing dam model Initial yield mean net stress Initial porosity
Symbol
Units
Tailings
Embankment
Foundation
E n
MPa –
50 0.35
50 0.35
50 0.35
(l(0) − k)
–
0.084
0.084
0.077
r
–
0.2
0.2
0.2
b
MPa−1
2
2
2
pc M ks
MPa – –
0.0033 1.44 0.246
0.0033 1.44 0.246
0.0033 1.33 0
a
–
0.3
0.3
0.3
p∗o Fo
MPa –
0.003 0.66
0.1 0.6
0.03 0.4
Mechanical parameters for each material are shown in Table 1. Darcy’s law is used to describe the water flow behaviour. Saturated water conductivity decreases from the dam to the centre of the impoundment, due to the decrease in grain size. Permeability of samples taken in the outer zone of the deposit (zone 2) was measured by Rodriguez (2002). Tests have also shown that tailings permeability is significantly influenced by desiccation cracking (Rodriguez, 2006). A value of Kx = Ky = 1×10−6 m/s was used. The hydraulic conductivities for the rest of tailings zones were estimated by means of scaling, on the basis of the Hazen formula, decreasing proportionally to the square of D10 . Variation of permeability with changes in the material porosity during the consolidation process is described by means of the Kozeny model. Relative permeability (unsaturated) was described by means of the Van Genuchten model (Olivella, 1994). The horizontal hydraulic conductivity of the alluvial soil was estimated as Kx = 2 × 10−6 m/s on the basis of pumping test data (Rodriguez, 2002). A ratio of 10 was adopted between horizontal and vertical permeability for taking into account the effect of anisotropy.
Horizontal permeability of the embankment material was taken as identical to the outer tailings zone and vertical permeability was assumed to be 1/5 due to anisotropy (Ky = 2 × 10−7 m/s). Retention curves were fitted with the Van Genutchen model. The retention curve of a sample from the outer zone of the deposit was obtained by Rodriguez (2002), under different void ratios (e = 1.5, 1.75 and 2). According to the experimental data, the value of parameter l of the Van Genutchen equation, was taken constant (= 0.38). On the other hand, the air entry value, P0 , is assumed to vary exponentially with the change in porosity (Olivella, 1994). A value of P0 = 0.079 MPa was computed from the experimental data for the outer tailings zone, at a reference porosity of 0.66. For the rest of tailings zones, P0 was scaled, increasing inversely proportionally to D10 . 5
HYDRAULIC BOUNDARY CONDITIONS
Rainfall and evaporation influence the water content of the tailings deposit through its whole life. Their
927
0 2
Porosity at 26m Porosity at 120m Porosity at 420m
4 Depth [m]
long-term effect was included in the model by means of mean rates of infiltration and evaporation. Run-off water has no effect on the deposit water balance since the excess water accumulated in the supernatant pond is eliminated through decant piping. The run-off/infiltration ratio was estimated for the monthly rainfall record shown in Figure 2, by means of the SCS hydrological model (SCS, 1957). Parameter CN (Curve number) in SCS model was estimated as 91, on the basis of the material permeability and the bare condition of the deposit surface. Drying of soils due to evaporation generally occurs in three stages (Gowing et al., 2006): 1) the evaporation front coinciding with soil surface, hence the evaporation rate is controlled by the available energy (coming from sun radiation and wind) for latent vapour heat consumption; 2) evaporation rate is controlled by the rate of capillary rise of water from the phreatic level to the evaporation front; 3) evaporation rate is controlled by molecular diffusion of vapour from the evaporation front to soil surface. Considering the climate factors at the site and the tailings hydraulic properties, it was numerically checked for the case study that, even in the harshest evaporative condition, drying would always occur in the first stage. Hence, the mean evaporation rate can be estimated from pan measurements shown in Figure 2. A pan coefficient Kpan = 0.8 was selected (Smajstrla et al., 2000), on the basis of the mean RH (85%) and the average wind speed (2 m/s). The annual balance between infiltration-evaporation yields a positive value of 91 mm/year (net infiltration). This boundary condition was permanently applied to the model during the whole analysis time.
6 8
At the end of construction At 50 years after impoundment construction
10 12 0,59
0,63
0,61
0,65
porosity
0,67
Figure 4. Variation of porosity with impoundment depth at three vertical sections located at 26 m, 120 m and 420 m from the edge of the dam. S = 0.85 S = 0.90 S = 0.95 S = 1.0
Figure 5. period.
Degree of saturation at the end of construction
a) At end of impoundment construction.
b) 50 years after end of impoundment construction.
Figure 6. (a) Phreatic level after impoundment construction (6000 days) (b) Phreatic level after 50 years from impoundment construction.
6
BASE CASE
Sixteen years of continuous filling of the impoundment were simulated with the model. The effect of consolidation of tailings under the self-weight loads and the hydraulic boundary conditions imposed is shown in Figure 4. Porosity variation with depth is plotted at three vertical sections located at 26 m, 120 m and 420 m from the edge of the deposit (dam). A 50 year period after the end of construction was also analyzed, keeping active all boundary conditions except the tailings discharge. It may be observed that porosity decreases with depth, faster in the perimeter of the deposit than in the centre zone. This is due to the favourable drainage conditions in the vicinity of the dam, larger permeability and lower phreatic levels leading to higher effective stresses. The degree of saturation of tailings at the end of construction is high in the whole deposit, is shown in
Figure 5. Most of the tailings volume remains saturated, while in the dam crest Sr reaches a minimum value of 85%. This is due to the presence of capillary water above the phreatic level and the continuous addition of water with the slurry discharge. Figure 6 displays the position of phreatic surfaces at the end of construction and after 50 years. The later analysis shows that the steady-state flow regime is reached 20 years after end of construction.
7
EFFECT OF RAINSTORMS
An extreme rainfall event recorded at the site, as described by Greenaway et al. (2002), was applied to the model at the end of construction period. The storm comprised 722 mm rainfall in 48 hours, with a peak of
928
a) At the end of construction.
(a) 100
b) Atthe end of rain storm (48h.)
Rainfall [mm]
80
60
c) 11 days after end of rain storm.
40
20
Figure 8. case).
0
Variation of the position of phreatic surface (wet
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 Time [hours]
b) At10 h after storm initiation.
c)At the end of storm (48h)
d) 10 days after theend of the storm.
Figure 7. a. Rainfall storm. 7 b, c and d. Model results: variation of the position of phreatic surface.
140 mm in 90 minutes (Figure 7a). Figure 7b shows the model results at different times after storm initiation. The phreatic surface rises fast during rainfall, the highest position being reached at the end of the storm. On the contrary, phreatic drawdown is a slow process. Ten days after rainfall ends, the phreatic level is still in a higher position than the initial situation at the beginning of the storm (Figure 7c). Moreover, phreatic water intersects the slope face of the dam 2 m above the base. If the same amount of rainfall is applied over a longer time span (4 days), the rise of the phreatic surface is somewhat more pronounced. This due to lower runoff/infiltration ratios associated with lower rainfall rates. In this case, the highest position of the phreatic surface at the dam slope face is 2.4 m above its base and it is reached 4 days after the end of the storm.
The results of the sensitivity analysis show a strong influence of the assumed long-term infiltration/evaporation boundary condition, on the behaviour of the deposit under the action of the rain storm. Figure 8 depicts the rise of the phreatic surface for the wet case under the action of the storm of Figure 7. a. Phreatic water approaches the outer face of the deposit much faster than in the base case. Eleven days after the end of the storm, the phreatic surface reaches its maximum elevation intersecting the dam slope at 3.5 m above the base. This is a consequence of the presence of a larger volume of capillary water in the unsaturated zone, above the phreatic surface, reducing the available water storing capacity of tailings.
9
STABILITY ANALYSIS
Stability analysis of the deposit was performed by means of the limit equilibrium method. The analysis domain covered the zone of variation of the phreatic level. A summary of the strength parameters of the materials involved are presented in Table 2. Apparent cohesion due to matric suction was taken into account in the computed parameters. Stability analyses were carried out for the base and wet cases. The critical sliding surfaces obtained are shown in Figure 9 and 10 respectively. The values of computed safety factors are summarized in Table 3. In the base case, the storm causes a considerable decrease Table 2.
Mohr-Coulomb parameters.
Material
8
SENSITIVITY TO INFILTRATION – EVAPORATION BOUNDARY CONDITIONS
Additional cases were run to study the influence of the infiltration-evaporation boundary condition on the impoundment surface. In the ‘‘wet case’’ infiltration/evaporation model parameters were set to CN = 90 and Kpan = 0.75, resulting in a 367 mm/year net infiltration.
Saturated tailings Unsaturated tailings (above phreatic level) Saturated compacted laterite Unsaturated compacted laterite Foundation soil
C (KPa)
F
28.59∗
35.6◦∗ 35.6◦∗
11.00 45.40
∗ Obtained from triaxial tests (Rodriguez, ∗∗ Estimated from index properties.
929
2002).
31◦ 31◦ 33◦∗∗
of the safety factor in relation to the pre-storm values, although sliding is not triggered. The minimum safety factor is reached at the end of the storm. In the wet case, the deposit becomes unstable by the end of the storm. Moreover, it remains unstable 11 days after the storm. The amount of material released a)
FS=2.54 phreatic level
b) phreatic level
FS=1.13
c) phreatic level
FS=1.30
Figure 9. Sliding surfaces for base case, a. At the end of construction, b. At the end of storm c. 4 days after storm end. a) phreatic level
FS=1.55
b) phreatic level
FS=0.88 FS=1.04
c) phreatic level
FS=0.97 FS=1.02
Figure 10. Sliding surfaces for Wet Case a. At the end of construction, b. At the end of storm c. 11 days after storm ends. Table 3.
Factors of safety.
Situation
Base case (FS)
Wet case (FS)
At the end of construction At the end of rainfall After 4/11 days rainfall end
2.54 1.13 1.30
1.55 0.88 0.97
could be larger than the suggested by Figure 10 if static liquefaction of tailings is triggered as a consequence of sliding. 10
CONCLUSIONS
The numerical model developed is able to consider the influence of the variability of hydraulic properties of tailings, the presence of the supernatant pond, consolidation of tailings under self-weight loads, continuous addition of water with the tailings discharge rain and evaporation. The low hydraulic conductivities of tailings cause the phreatic levels to remain high during the impoundment construction and a long time after. Hence a large area of the impoundment remains saturated during the whole life of the facility. The steady-state flow regime is reached approximately 20 years after the end of construction. Therefore, it seems that the steady-state flow regime is not a suitable hypothesis for the design of these type of structures, as previously noted by Alonso and Gens (2006). At the end of the construction process of the impoundment, 94% of the stored tailings are beneath the phreatic surface, whereas the rest have degrees of saturation varying from 86% to 100%. High degrees of saturation are a consequence of capillary rise and the continuous addition of water with the slurry discharge and rainfall. As a consequence of the large volume of water stored in the tailings pores, the phreatic surface rises very fast during rainstorms. On the other hand, drawdown of the phreatic surface at the end of the storm occurs in a slow manner (several days). Due to this feature, closely repeated rainfall events could have seriously adverse effects on the dam stability. Higher phreatic levels are obtained for moderate rainfall intensities with larger duration due to higher infiltration/runoff ratios. The highest position of the phreatic surface occurs between the end of the storm and few days after (up to 11 days). Then, the critical condition for the impoundment stability is attained. The long-term infiltration-evaporation boundary conditions, imposed by climate factors, strongly affects the hydraulic response of the deposit to extraordinary rainfall events. Moreover, the final results of stability analysis are also strongly dependent on this analysis feature. Hence, accurate calibration of the infiltration-evaporation condition to reproduce real conditions becomes critical in the analysis procedure, if meaningful results are expected. Finally, the results of this work confirm that the stability of tailings dams strongly depends on their hydraulic operation. They also suggest that routine
930
measurement of capillary water (not detected by common piezometric monitoring) could be relevant for the assessment of the impoundment stability conditions and its overall safety. REFERENCES Alonso, E.E., Gens A. & y Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique 40, No. 3, 405–430. Alonso, E. & Gens, A., 2006. Aznalcóllar dam failure. Part 2: Stability conditions and failure mechanism. Géotechnique 56, No. 3, 185–201. Blight, G.E., 1994. The master profile for hydraulic fill tailing beaches . Proc. Instn. Civ. Engng., 107, 27–40. Chalkley, M., Kerr, T., Parfitt, M. & Greenaway, G., 2002. Rehabilitation of the acid leach tailings facility at Moa Nickel in Cuba. CDA 2002 Annual Conference, Victoria, BC, Canada. Fourie, A.B., Blight, G.E. & Papageorgiou, G., 2001. Static liquefaction as a possible explanation for the Merriespruit tailings dam failure. Can. Geotech. J, 38, 707–719. Gowing, J.W., Konukcu, F. & Rose, D.A.2006, Evaporative flux from a shallow watertable: The influence of a vapour—liquid phase transition. Journal of Hydrology 321 77–89.
Greenaway, G.R., Parfitt, M.R. & Kerr, T.F., 2002. Seismic stability assessment of the Moa nickel tailings facility. Canadian Dam Association 2002 Annual, Conference, Victoria, British Columbia, Canada. Olivella, S. 1994. Code_Bright User’s Guide. Departamento de Ingeniería del Terreno. Universitat Politécnica de Catalunya. Rodriguez, R. 2002. Estudio experimental de flujo y transporte de cromo, níquel y manganeso en residuos de la zona minera de Moa (Cuba): influencia del comportamiento hidromecánico. Tesis Doctoral, Universitat Politécnica de Catalunya, Barcelona. Rodriguez, R. 2006. Hydrogeotechnical characterization of a metallurgicalwaste. Canadian Geotechnical Journal 43, 1042–1060. SCS 1957. Hydrology National Engineering Handbook. USDA Soil Conservation Service. Smajstrla A.G., Zazueta F.S., Clark G.A. & Pitts D.J. 2000. Irrigation Scheduling with Evaporation Pans. Bulletin 254 Department of Agricultural and Biological Engineering, Florida Cooperative Extension Service, Institute of Food and Agricultural Sciences, University of Florida. Staple, W.J. 1974. Modified Penman Equation to Provide the Upper Boundary Condition in Computing Evaporation from Soil. Science Society of America Proceedings. Vol. 38, No. 5, pp. 837–839.
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A simplified model for the evaluation of the degree of saturation in slope stability analysis of shallow soils L. Montrasio & R. Valentino University of Parma, Italy
ABSTRACT: It is well known that the degree of saturation of a soil is time-varying in consequence of atmospheric conditions. Experimental data of matric suction at a site in Pilastro, Parma, Emilia Romagna Region, Northern Italy, have been used to compare against a simplified model, which is able to directly correlate the degree of saturation of a clayey-silt soil with rainfall events. The paper deals with the in-situ measurements of matric suction, the procedure to obtain the degree of saturation on the basis of assumed soil-water retention curves and comparison against the simplified model. This model, in turn, has been introduced in a simplified physically based stability method, recently set up by the authors to describe the most important factors influencing the rainfall-triggered mechanism of shallow landslides.
1
INTRODUCTION
It is known that rainfall-triggered shallow landslides are becoming an ever frequent problem all over the world. Many researchers have recently developed different approaches to describe the main features of the trigger mechanism of such phenomena, in order to evaluate the probability of their occurrence, both at local and regional scale (Cascini et al. 2005). A simplified physically based stability method has been set up by the authors (Montrasio 2000, Montrasio et al. 2002, Montrasio & Valentino 2003, 2007), in order to directly evaluate the safety factor of a slope on the basis of rainfall amount. This method considers that the soil of the shallow layers on steep hills or mountains, firstly unsaturated, becomes saturated in consequence of a certain amount of rainfall, which is strictly related to the initial soil water content. The time-varying safety factor of a slope is defined on the basis of the limit equilibrium method applied to an infinite slope, which takes into account the mechanical and hydraulic characteristics of the soil, the geometrical configuration of the slope and rainfall events. Experimental evidence shows that the stability equilibrium is guaranteed by the apparent cohesion, coming from the partial saturation of the matrix. So the method states that the shear strength of the unsaturated soil layer depends both on the effective cohesion and on the apparent cohesion, which represents the effect of partial saturation and can be expressed as a function of the degree of saturation (Sr ), which, as independent variable, unlike suction, assumes values
belonging to a restricted range. To make the method more efficient, it is useful to correlate directly the degree of saturation of the soil with rainfall amounts. In this paper a simplified model of such correlation is shown and compared with another method for Sr prediction, which in turn is based on experimental soil suction measurements. The goal of the study is the validation of the conceptual modeling of field process by comparing simulated field site conditions with a long-term time-series of field measurements in the unsaturated zone. 2
EXPERIMENTAL DATA
Experimental values of soil suction for a specified site and for a certain period are the basis for obtaining corresponding values of the soil degree of saturation. The first step has been the acquisition, from the scientific literature, of experimental soil suction data coming from field measurements. Although the aim of a previous work was to analyze data belonging to different latitudes of the Italian territory (Quintavalla 2006), in the present work only data regarding the site of Pilastro (Parma) in the Emilia Romagna Region (Northern Italy) will be shown. Moreover, to find a certain correlation between the time-varying degree of saturation and rainfall intensities, for certain soil characteristics, it was also necessary to acquire data regarding time-varying rainfalls, belonging to the same site and for a long period. This condition was easily obtainable for the ‘‘Pilastro’’ field site, which is a 6500 m2 level ground area,
933
200
Rainfall
0
22/11/06
40
0
30/05/06
6 05/12/05
80
12/06/05
120
12
18/12/04
18
25/06/04
160
Rainfall [mm]
Temp.
24
01/01/04
Temp. [˚C]
30
Figure 1. Temperature and rainfall depth for the ‘‘Pilastro’’ site during the monitoring period.
Suction [kPa]
100 80 60
0.3 m
40
0.6 m 0.9 m
20 0
100 80
22/11/06
01/01/04
0
30/05/06
1.8 m 05/12/05
1.5 m
20 12/06/05
1.2 m
40
18/12/04
60
25/06/04
Suction [kPa]
located on the side of the Po plain, near the hilly margin, close to the top of the alluvial fan of the Parma stream, at about 166 meters above sea level, where the water table typically ranges from 10 m to 30 m below the ground level. From a pedological point of view, the soil at the field site could be considered as an ‘‘Udic Haplusteps loamy skeletal, mesic’’ (Mantovi et al. 2005); from a geotechnical point of view it is classified as a clayey-silt. The shallow soil, which contains altered gravels near the surface, is not calcareous, while the substratum, which is more calcareous, presents a gravelly-sandy texture, with non altered cobbles, starting from 1.20 m below the ground level. From field measurements of the infiltration rate, the soil permeability was found to be very high. At a depth of 10 meters from the ground level, the presence of a thick clay layer that obstructed the vertical water flow was found. It could be supposed that the ground water, for the most part of the year, gathers and flows on the clay layer, so determining the presence of a relatively shallow water table (Mantovi et al. 2005). Field measurements of matric suction and rainfalls refer to a 3-year period under standard local agronomic practices: tomatoes, maize (corn), rye-grass. All the soil suction measurements had been acquired by common ‘‘Skye’’ automatic electronic tensiometers. For the aims of the work, particularly significant are data belonging to soil depth ranging from 0 m to 1.80 m, where the soil water content mainly depends on rainfall and air temperature. Tensiometers were installed at different depths from the ground level: 0.3 m, 0.6 m, 0.9 m, 1.2 m, 1.5 m, 1.8 m. Moreover, a well and a piezometer allowed the measurement of the position of the ground water level (Mantovi el al. 2005). It must be remembered that a common tensiometer allows measurements of matric suction limited in the field of gravity water and capillary water, to typically less than 80 kPa. The tensiometers were left in situ and connected to a datalogger for continuous recording of soil moisture measurements. Each tensiometer was fitted with a low pressure transducer, stabilised for temperature and linearity. The output was ratiometric for excitation voltage, and calibrated at 5 volts. The transducer behaved like a ‘‘bridge’’ type sensor and was suitable for connection to a logger with differential voltage inputs (Mantovi et al. 2006). Figure 1 shows the trend of both temperature and rainfall versus time for the monitoring period: temperatures ranged between a maximum of 37.5◦ C and a minimum of −10.5◦ C. Average atmospheric measured temperature was 13.4◦ C and cumulated total rainfalls, in nearly three years, were 2859.6 mm. Figure 2 shows soil suction measurements versus time, related to different depths from the ground level, and can be related to Figure 1 thanks to the coincidence
Figure 2. Field measurements of soil suction at different depths from the ground level for the ‘‘Pilastro’’ site, during the monitoring period (CRPA—Reggio Emilia).
of the abscissa (time). It can be seen that in shallow soil layers, the range of the matric suction was nearly always between 0 kPa and 15 kPa, except some short periods during the summer, between May and September, when the soil seemed to get dry in consequence of both high temperature and drought. On the contrary, in soil layers at a depth higher than 1.5 m, matric suction kept constantly near to 20 kPa even during summer. It is worth noting that suction measurements acquired by common tensiometers can be considered reliable for the aim of this work, even if the composition of the soil, that contains not a negligible percentage of cobbles, and the structure of the instrument, that utilizes a porous cup, leave some
934
doubts about the real hydraulic continuous connection between soil matrix and pressure sensor. For the same reason, it could be supposed that during summer soil matric suction was also higher than 90 kPa, which was the maximum value measurable by the tensiometers in use.
3
FROM MATRIC SUCTION TO THE DEGREE OF SATURATION
Most rainfall-induced shallow landslides occur on slightly steeper slopes and involve unsaturated soil. To model the trigger mechanism of these phenomena in a simplified manner, it was considered that the soil shear strength depends on the apparent cohesion, which represents the effect of partial saturation and can be expressed as a function of the degree of saturation (Sr ). In particular, when net normal stresses are kept constant, that is the condition of a shallow soil layer, a soil suction variation provokes changes in soil water content. The link between water content and suction is expressed by the soil moisture retention curve. It is known that the amount of retained water for a relatively low value of suction firstly depends on the capillary effect and on the distribution of pore dimensions: it is then deeply influenced by soil structure. On the other hand, the higher the value of soil suction the more water retention depends on adsorption and is influenced by soil texture and by grain specific surface more than by soil structure. Soil moisture retention curve is also influenced by the presence of air bubbles and changes in soil structure that are determined both by rapid moistening or prolonged saturation processes. It is known, moreover, that each soil retention curve, which is specific for each kind of soil, presents an hysteretic behaviour. Although many theoretical treatments allow hysteresis modeling (Parlange 1976, Mualem 1984), their relatively high complexity, the difficulty in determining some necessary experimental parameters, associated with the specific aim of the present work, that is the evaluation of the safety factor of slopes in a wide area (Montrasio 2000) led us consider, for simplification, as biunique the link between suction and water content. For the same reason, soil structure and fabric were assumed constant in time and the degree of saturation was assumed as a variable representing the water content, by using a common model to describe the soil retention curve. An analytical model, among those that in the course of time showed a strong applicability in different conditions, is expressed by the Van Genuchten equation, that is: ES =
1 [1 + (α · s)n ]m
(1)
where ES is the effective saturation, s is the suction, α, n and m are empirical coefficients that determine the shape and the slope of the curve. ES, in turn, is defined as the following: ES =
θ − θr θs − θr
(2)
where θ is the volumetric water content, θr is the residual water content, which represents the adsorbed water, while θs is the saturation water content, which represents the maximum volumetric water content and is usually 5–10% smaller than porosity, because of the presence of trapped or dissolved pore air (Ungaro et al. 2005). For these reasons θr and θs are usually considered as empirical constants in the definition of the soil retention curve (Van Genuchten and Nielsen 1985). Then from (1) and (2) the volumetric water content could be expressed as −m θ = θr + (θs − θr ) 1 + (α · s)n
(3)
Once the value of θ is determined, by using Equation (3) as a function of the suction (s), Sr can be evaluated by using the following equation: Sr =
θ θr + (θr − θs ) [1 + (α · s)n ]m = θs θs
(4)
In the present work, since the experimental data have been acquired by previous works (Mantovi et al. 2006, Merafina 2003), parameters for the Van Genuchten curve have been obtained by using Vereecken pedofunctions (Vereecken et al. 1989), as these are considered by Merafina (2003) the most suitable to represent the water retention behaviour of soils that are present in the Emilia Romagna Region. As input values, these pedofunctions need the apparent volume mass (AVM) and the percentage of organic carbon (Org. C), sand and clay. For the field site of Pilastro, the data have been obtained by laboratory experimental analyses on soil samples taken at different depths from the ground level (Merafina 2003) and are shown in Table 1.
Table 1.
Composition of the soil of Pilastro site.
Depth [m]
Sand [%]
Clay [%]
Org. C [%]
AVM
0–0.25 0.25–0.40 0.40–0.65 0.65–1.05 1.05–1.25
18 15 30 35 59
30 34 31 29 23
1.51 1.04 0.58 0.46 0.46
1.5 1.5 1.5 1.5 1.5
935
22/11/06
30/05/06
Sr
Sr
Sr calculated from rainfall 0.6 0.4 0.2 0.0 22/11/06
Rainfall
30/05/06
22/11/06
30/05/06
05/12/05
12/06/05
18/12/04
0
25/06/04
40
90 60 30 0
d = 1.2m 1.2 1.0 0.8
05/12/05
80
Sr calculated from suction
180 150 120
12/06/05
120
1.2 1.0 0.8 0.6 0.4 0.2 0.0
01/01/04
Sr
Sr
Suction 0.3 m
01/01/04
Suction [kPa]
160
0.6 0.4 0.2 0.0
Figure 6. Sr vs. time at 0.9 m below the ground level.
Rainfall [mm]
It is worth noting that these parameters strongly depend on soil composition.
05/12/05
m=1
12/06/05
2)
18/12/04
∧
25/06/04
n = e(−0.053−0.009·Sand−0.013·Clay+0.00015·Sand
Sr calculated from rainfall
Rainfall
18/12/04
α = e(−2.486+0.025·Sand−0.351·Org.C−2.617·AVM−0.023·Clay)
90 60 30 0
d = 0.9m 1.2 1.0 0.8
Sr calculated from suction
25/06/04
ϑr = 0.015 + 0.005 · Clay + 0.014 · Org.C ϑs = 0.81 − 0.283 · AVM + 0.001 · Clay
180 150 120
01/01/04
Rainfall [mm]
Vereecken pedofunctions used are given in the following:
Figure 7. Sr vs. time at 1.2 m below the ground level.
Sr
22/11/06
05/12/05
Sr calculated from rainfall 0.6 0.4 0.2 0.0 12/06/05
18/12/04
Rainfall
25/06/04
90 60 30 0
d = 1.5m 1.2 1.0 0.8
Sr calculated from suction
30/05/06
180 150 120
01/01/04
0.6 0.4 0.2 0.0
Sr
1.2 1.0 0.8
22/11/06
05/12/05
12/06/05
Rainfall [mm]
d = 0.3m
Sr calculated from rainfall
18/12/04
Rainfall
25/06/04
90 60 30 0
Sr calculated from suction
30/05/06
180 150 120
01/01/04
Rainfall [mm]
Figure 3. Experimental soil suction and relative calculated Sr vs. time for the Pilastro site at a depth of 0.3 m below the ground level.
Figure 8. Sr vs. time at 1.5 m below the ground level. Sr vs. time at 0.3 m below the ground level.
Figure 5.
22/11/06
05/12/05
18/12/04
12/06/05
Sr
S r calculated from rainfall 0.6
Rainfall
25/06/04
90 60 30 0
d = 0.6m 1.2 1.0 0.8
Sr calculated from suction
30/05/06
180 150 120
01/01/04
Rainfall [mm]
Figure 4.
0.4 0.2 0.0
Sr vs. time at 0.6 m below the ground level.
On the basis of the soil suction data, the trend of the degree of saturation has been obtained for each depth of the site-sample. In Figure 3 only the trend at a depth of 0.3 m is shown. It could be pointed out that the degree of saturation assumes a typical seasonal trend, becoming nearly fixed around the value 0.8 during summer and the value 0.98 during winter, as regards the most shallow soil layer. The calculated degree of saturation for different depths reported in Figures 4–9 reveal how Sr could be considered substantially constant in time for soil layers that are positioned more than 1.5 m below ground level.
936
Figure 9.
4
Sr
Table 2.
22/11/06
30/05/06
05/12/05
12/06/05
18/12/04
Sr calculated from rainfall d = 1.8m 1.2 1.0 0.8 Sr calculated from suction 0.6 Rainfall 0.4 0.2 0.0 25/06/04
90 60 30 0
01/01/04
Rainfall [mm]
180 150 120
Values of parameters assumed for the model.
Depth (d) [m]
S0
z
β∗
n
0.3 0.6 0.9 1.2 1.5 1.8
0.970 0.970 0.950 0.947 0.947 0.920
0.9940 0.9975 0.9983 0.9988 0.9990 0.9992
0.3 0.3 0.3 0.3 0.3 0.3
0.6 0.6 0.6 0.6 0.6 0.6
Sr vs. time at 1.8 m below the ground level.
the thickness of the potentially instable shallow soil layer, V can be replaced by H and Equation (8) can be written as:
A CORRELATION BETWEEN RAINFALL AND THE DEGREE OF SATURATION
We must remember that it is rather interesting to correlate directly the degree of saturation of a kind of soil with rainfall events, in order to assess the safety factor of a slope that could be subjected to rainfall-induced shallow landslides. That’s why a simplified model has been set up. It is well known that the unit weight of a representative element volume (REV) of soil in normal conditions can be expressed through Equation (5): Ws + Ww = γd + γw nS0 (5) V where Ws is the solid weight, Ww is the water weight, V is the total volume, γd is the dry soil unit weight, γw is the water unit weight, n is the porosity and S0 is the initial degree of saturation. Our interest is to evaluate the unit weight of the same REV after a rainfall event, that can be described in terms of rainfall depth (h). Obviously the total rainfall amount does not completely infiltrate the soil: only a portion of the rainfall, which is expressed by a reduction coefficient (β ∗ ), works in raising the degree of saturation of the soil. After a rainfall event, the new unit weight (γ ∗ ) of the soil can be then expressed by Equation (6): γ =
Ws + Ww + β ∗ hγw (6) V Moreover, disregarding volume deformations and changes of the soil porosity, γ ∗ can also be expressed through Equation (7): γ∗ =
γ ∗ = γd + γw nSr
(7)
where Sr is the new degree of saturation of the soil. By using Equations (5), (6) and (7) Sr can be expressed as: γ ∗ − γd 1 β∗h γw = S0 nγw + (8) Sr = nγw nγw V By considering a REV having a unit horizontal section area and a height H , which is also comparable with
Sr = S0 +
β∗h nH
(9)
If Sr is calculated by considering a time interval equal to one day, h is the daily cumulated rainfall depth and S0 is the degree of saturation of the soil on the day before. It must be considered that during a day the degree of saturation of the soil undergoes some changes, determined by weather conditions, and generally, in absence of rainfalls, slowly it tends to reduce. This aspect can be expressed through a reduction coefficient (z < 1), which is very close to one and allows to take into account the percentage of water that evaporates, undergoing a daily drying process. Equation (9) then becomes: Sr = S0 z +
β∗h nH
(10)
Equation (10) for Sr allows then a rapid and simple evaluation of the degree of saturation as a function of the rainfall depth (h), and results particularly capable of being implemented in the simplified method for the assessment of the safety factor of slopes subjected to shallow landslides. The model has been applied to the Pilastro field site, in order to compare the results with those obtained through the method explained in Section 3. Table 2 summarizes the values of parameters assumed for the model applied to the Pilastro site. Parameters z and β ∗ , in particular, have been determined through a procedure of adjustment so as to get to the best fitting between the values of Sr calculated from suction by using Equation (4) and those calculated from rainfall by using Equation (10). Figures 4–9 show the trend of the values of Sr , calculated through the two methods at different depths (d) from the ground level. It is worth noting that notwithstanding a fair number of assumptions are involved
937
4 3 Fs
APPLICATION OF THE MODEL TO A CASE HISTORY
0.05
CONCLUDING REMARKS
The paper deals with in-situ measurements of matric suction in the field site of Pilastro (Parma, Italy) over a long period and the procedure to estimate the degree of saturation of the soil on the basis of an analytical
27/12/05
28/10/05
29/08/05
30/06/05
01/05/05
0
02/03/05
1
Recently, a simplified physically based stability model has been set up by Montrasio & Valentino (2003, 2007) to describe the most important factors influencing the rainfall-triggered mechanism of shallow landslides. The method has been drawn up as a means of simplified analysis: it considers an infinite slope, made by a thin soil layer, whose permeability is greater than that of the bedrock. The phenomenon is triggered following the loss of shear strength: the soil, firstly unsaturated, becomes saturated in consequence of a certain amount of rainfall, which is strictly related to the initial water content of the soil. The safety factor, calculated on the basis of the limit equilibrium method, deeply depends on slope geometry (slope angle, thickness of the layer), soil properties (specific gravity, porosity, degree of saturation), shear strength parameters (effective cohesion, friction angle), drainage capability of the soil and rainfall depth. In particular, the shear strength is evaluated through an equation similar to Peterson’s relationship (1988), reported by Fredlund et al. (1996) (Montrasio & Valentino 2007). The method has been applied to the case history of ‘‘Ca’Bernini’’ (Neviano, Parma), a site that was a few kilometers far from the Pilastro field site and that had been subjected to a shallow rainfall triggered landslide on the 5th of October 2005. On the basis of geotechnical and rainfall data at that site, the method allows the trend of the safety factor versus time to be obtained, highlighting the instability condition (FS = 1) in correspondence to the time of the real event. In this case, cumulated daily rainfall depth, related to a period of 12 months in the neighbourhood of the real event date, has been assumed as input data. Moreover, as regards the evaluation of Sr , the following parameters have been assumed for Equation (10): β ∗ = 0.3, n = 0.4, H = 1.8 m, z = 0.999. Figure 10 shows that the model catches well the safety factor dropping to one in correspondence of the rainy event occurred on the 5th of October 2005.
6
0.10
2
01/01/05
5
0.15 Daily rainfall [m]
in the evaluation of Sr in both methods, the agreement between the two predictions appears not bad on the whole.
0.00
Figure 10. Trend of the safety factor versus time for the ‘‘Ca’ Bernini’’ site in the neighbourhood of the 5th of October 2005.
soil-water retention curve. The values of Sr calculated from field soil suction measurements have been compared with those calculated by using a simplified model, which is able to directly correlate Sr with rainfall events. The model, in turn, has been introduced in a simplified physically based stability method, recently set up by the authors, and has been applied to a case history, in order to catch, with a satisfactory result, the trigger instant of a rainfall-induced shallow landslide. ACKNOWLEDGEMENTS Experimental data of soil suction were provided by C.R.P.A. S.p.A. (Centro Ricerche Produzioni Animali—Reggio Emilia) and the authors would like to express their gratitude to Dr Paolo Mantovi and to Dr Letizia Fumagalli for their cooperation. REFERENCES Cascini, L., Cuomo, S., Sorbino, G. 2005. Flow-like mass movements in pyroclastic soils: remarks on the modeling of triggering mechanism, Italian Geotech. J. 4: 11–31. Fredlund, D.G., Anqing Xing, Fredlund, M.D., Barbour, S.L. 1996. The relationship of the unsaturated soil shear strength to the soil-water characteristic curve, Can. Geotech. J. 33 (3): 440–448. Mantovi, P., Ligabue, M., Dall’Olio, N. 2005. Rilascio di nitrati da un suolo vulnerabile, Estimo e Territorio 9: 56–64. Mantovi, P., Fumagalli, L., Beretta, G.P., Guermandi, M. 2006. Nitrate leaching through the unsaturated zone following pig slurry applications, Journal of Hydrology 316: 195–212. Merafina, P. 2003. Monitoraggio della dinamica dei nitrati nel mezzo insaturo in un’area vulnerabile della Provincia di Parma e applicazione del modello di simulazione CropSyst, Degree Thesis, Faculty of Science, University of Parma.
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Montrasio, L. 2000. Stability analysis of soil slip, Proc. Int. Conf. Risk 2000. Southampton: Wit Press. Montrasio, L., Re, F., Valentino, R. 2002. An approach to measure soil slip risk, Proc. 3rd Int. Conf. On Comp. Simulation in Risk Analysis and Hazard Mitigation. Southampton: Wit Press. Montrasio, L., Valentino, R. 2003. Experimental analysis on factors triggering soil slip. In Luciano Picarelli (ed.), Fast slope movements prediction and prevention for risk mitigation; Proc. Int. Conf., Napoli, 11–13 May 2003. Bologna: Patron Ed. Montrasio, L., Valentino, R. 2007. Experimental analysis and modelling of shallow landslides. Landslides 4 (3): 291–296. Springer-Verlag. Mualem, Y. 1984. Prediction of the soil boundary wetting curve. Soil Science 137: 379–389. Parlange, J.Y. 1976. Capillary hysteresis and the relationship between drying and wetting curves. Water Resour. Res. 12: 224–228.
Quintavalla, C. 2006. Valutazione del grado di saturazione in terreni superficiali per l’analisi di stabilità di pendii in terra, Degree Thesis in Engineering, University of Parma. Ungaro, F., Calzolari, C., Busoni, E. 2005. Development of pedotransfer functions using a group method of data handling for the soil of the Pianura Padano-Veneta region of North Italy: water retention properties. Geoderma 124: 293–317. Van Genuchten, M.T., Nielsen, D.R. 1985. On describing and predicting the hydraulic properties of unsaturated soils. Ann. geophysicae 3 (5): 615–627. Paris: Gauthier-Villars. Vereecken, H., Maes, J., Feyen, J., Darius, P. 1989. Estimating the soil moisture retention characteristic from texture, bulk density and carbon content. Soil Science 148 (6): 389–403.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Predicting the variation of stability with time for a slope in Switzerland A. Thielen & S.M. Springman Institute for Geotechnical Engineering, ETH Zurich, Swiss Federal Institute of Technology, Switzerland
ABSTRACT: The variation of stability with time due to suction changes was calculated for an instrumented slope in Switzerland using the software Slope/W. The motivation for this study was a heavy rainfall event in the area of this slope, which caused a great number of slope failures. The aim was to find the periods of lowest slope stability, which represent the most unfavourable initial condition for a subsequent rainfall event. The pore water pressure distributions used for the stability analysis came from precedent hydraulic calculations using the software Vadose/W. Field and laboratory experiments provided the data for the configuration, the calibration and the validation of the model. It is well known that the saturation of the soil has a significant influence on slope stability and that periods of high saturation are most unfavourable in terms of risk of failure, and this was quantified herein.
1
INTRODUCTION
During recent years, the topic of natural hazards gained more and more national and global significance. Extreme meteorological events are attributed to climatic change, and are accompanied by instabilities, whereby the most endangered slopes are those that are too steep for the existing soil conditions and are stabilized temporarily by suctions. A series of 42 landslides occurred, for example, in May 2002 in North Switzerland near the river Rhine after an extreme event, in which 100 mm rain fell in 40 minutes (Fischer et al. 2003). Figure 1 shows one of the failures that endangered the stability of a house.
2
The results of the field and the laboratory experiments have been introduced into a numerical analysis of the water balance and the stability of the slope using the software products Vadose/W and Slope/W from Geoslope International Ltd. Vadose/W is a Finite Element Software for the calculation of water-, vapourand heat flow in saturated and unsaturated soil zones. The effects of rainfall infiltration, runoff, evapotranspiration, frost and snow melt can be taken into account and also the effect of vegetation is considered. As a result, the time dependent pore water pressure
INVESTIGATION METHODS
A field experiment lasting two years was performed on a test slope in the vicinity of the above mentioned failures. After a detailed site investigation (Thielen et al. 2005, Friedel et al. 2005), the grass covered field (Fig. 2) was equipped with a large number of measuring devices for the meteorological survey and the observation of the volumetric water contents, suctions and soil temperatures at different depths up to 150 cm. A detailed description of the experimental design and a selection of results can be found in Thielen & Springman (2005 & 2006). Undisturbed and disturbed soil samples taken from the field have been analysed in the laboratory in order to determine the water retention curve, the saturated and unsaturated permeability and the saturated and unsaturated shear resistance.
Figure 1. Slope failure after an extreme rainfall event in North Switzerland in May 2002.
941
0.50 0.40
organic top layer clayey sand
20
z [m]
θ [-]
silty sand
0.30 0.20
10
silty sand
0.10
clayey sand
0
0.00
sandstone -10
0
10 x [m]
20
0.1
30
1
10
100
1000
suction [kPa]
Figure 2. Geometry, layering and spatial discretisation of the two-dimensional slope model.
Figure 3.
Water retention curves of the different soil types.
3.3 Material parameters distribution in the slope can be determined. With Slope/W the factor of safety against failure can be calculated using the limit equilibrium method. Pore water pressure distributions from Vadose/W calculations can be introduced into this analysis and the influence of suction on the shear strength formulation is taken into account.
3 3.1
MODEL DESCRIPTION
3.3.1 Water retention curve The water retention curve for the clayey and the silty soil was determined in the laboratory on undisturbed soil samples. The results have been modelled using the following equation by van Genuchten (1980):
Geometry and layering
Figure 2 shows the geometry and the soil layering that has been assumed based on the site investigation for the two-dimensional model of a vertical cut through the middle of the slope. The grass covered site is characterised by an average slope angle of 27◦ in the lower part and 17◦ in the upper part. An organic top layer of 30 cm thickness covers a layer of clayey sand that is up to 1.5 m thick. The underlying silty sand layer covering the sandstone basement is about 20 cm thick in the lower part of the field and becomes significantly thicker in the upper part, where it is also separated from the sandstone by a thin layer of clayey sand. 3.2
Material parameters have to be defined for the different soil regions. These include the water retention curve, suction dependent permeability, thermal conductivity, specific heat capacity, soil unit weight and shear resistance.
Discretisation
Spatial and temporal discretisation of the model have been chosen with respect to calculation accuracy and calculation time. A structured Finite Element mesh of 934 nodes and 869 quadrangular elements was constructed for the spatial discretisation (Fig. 2). The elements of the sandstone basement are ‘‘zero elements’’ which means that they are not taken into account for the calculations. Concerning the temporal discretisation, time steps of 24 hours have been chosen.
(θs − θr ) n m ψ 1+ a
θ = θr +
(1)
θis the volumetric water content, θs is the volumetric water content under saturated conditions and θr at the residual state. ψ is the suction in kPa and a, m and n are fitting parameters. The water retention curves for the silty and the clayey sand are plotted in Figure 3 and the chosen fitting parameters can be taken from Table 1. 3.3.2 Permeability Also the determination of the suction dependent permeability is based on laboratory investigations on undisturbed soil samples. The results have been modelled using the following equation by van Genuchten (1980): k(ψ) = ks
942
2 1 − aψ (n−1) 1 + (aψ n )−m m n 2 ((1 + aψ) )
(2)
Table 1.
3.3.4 Soil unit weight The soil unit weight is varying dependent on the volumetric water content of the soil. Table 1 shows the maximum and minimum values for each soil layer.
Material parameters.
Parameter
Organic soil
Clayey sand
Silty sand
Permeability and WRC a [−] m [−] n [−] ks [cm/s] θs [−]
8.37 0.18 1.22 7.5 ∗ 10−7 0.45
8.37 0.18 1.22 7.5 ∗ 10−7 0.45
5.60 0.29 1.40 3 ∗ 10−4 0.42
Thermal conductivity kt [kJ/(day m ◦ C) ]
35
155
155
Specific heat capacity cs [kJ/(kg ◦ C) ]
1.67
0.71
0.71
Soil unit weight γmax [kN/m3 ] γmin [kN/m3 ]
16.07 18.07
17.29 18.78
15.78 18.30
Shear parameters ϕ [◦ ] c [kPa] ϕb [◦ ]
31 15 28
31 0 28
37.5 0 28
3.3.5 Shear resistance Shear resistance for saturated and unsaturated soil conditions is calculated using the following equation from Fredlund et al. (1978): τ = c + (σ − ua ) tan φ + (ua − uw ) tan φ b
with τ as the shear resistance of the soil, c as the effective cohesion, (σ − ua ) as the effective normal stress, φ as the angle of internal friction, (ua − uw ) as matric suction and φ b as an additional friction angle depending on soil suction. The parameters c , φ and φ b of Equation 3 have been determined in the laboratory with the help of suction dependent direct shear tests and can also be taken from Table 1. 3.3.6 Summary of material parameters The above mentioned material parameters for the different soil types are summarised in Table 1.
1.E-03
3.4 Influence of vegetation
1.E-04
The influence of vegetation shows up in two ways. On the one hand it augments the evapo-transpiration rate compared to a bare soil surface. On the other hand, it influences the shear resistance of the organic top layer in form of a cohesion due to root reinforcement. This cohesion has been assessed to be represented by 15 kPa for grass (see Table 1). This empirical value has been proposed by Cazzuffi & Crippa (2005).
1.E-05 k(s) [cm/s]
(3)
1.E-06 1.E-07 1000
1.E-08 1.E-09
clayey sand
1.E-10
silty sand
1.E-11 1
Figure 4.
4
10 100 suction [kPa]
HYDRAULIC MODELLING
4.1 Initial conditions
Permeability curves of the different soil types.
k is the permeability, ks is the permeability under saturated conditions and ψ is the suction in kPa. a, m and n are the same fitting parameters as for the water retention curve. The permeability curves for the silty and the clayey sand are plotted in Figure 4.
3.3.3 Thermal conductivity and specific heat capacity Values for thermal conductivity and specific heat capacity have been estimated based on values from the literature and can be taken from Table 1.
For the calculations with Vadose/W, thermal and hydraulic initial conditions had to be defined. 1st January of 2005 has been chosen as the starting point for the calculations. Based on the soil temperature measurements from the field, an initial temperature distribution has been defined, which is plotted in Figure 5. Concerning the initial pore water pressure distribution, an overall suction of 4 kPa was applied, based on suction measurements at this date which varied around this value at all depths up to 150 cm. 4.2 Boundary conditions Boundary conditions had to be defined on the soil surface, at the interface between the silty/clayey sand
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25
soil temperature [˚C]
40 4˚ C 8˚ C 12˚ C6˚ C 1
z [m]
15
5
150 cm (c) 150 cm (m) 90 cm (c) 90 cm (m) 45 cm (c) 45 cm (m)
35 30 25 20 15 10 5 0
x [m]
15
25
Initial temperature distribution on 1st January
101
151 201 251 day of the year 2005
301
351
Figure 6. Comparison of the calculated (c) and measured (m) soil temperature at different depths for the year 2005.
layer and the sandstone basement (‘‘zero elements’’) and at the right and the left boundary of the model. Climate boundary conditions on the soil surface, in the form of daily data from field measurements, have been applied, including maximum and minimum air temperature, maximum and minimum value of air humidity, mean values of wind speed and net radiation and rainfall amount. It should be mentioned here that data for net radiation was estimated for most of the time steps because of a lack of field data. The soil-bedrock interface is considered as an impermeable hydraulic boundary condition. At the right and the left boundary of the model, the water is free to flow in and out. A heat flux has been applied between soil layers and bedrock to represent the thermal boundary conditions. 4.3
51
35
PWP [kPa]
5
0 -20 -40 -60 -80 -100 -120
PWP [kPa]
Figure 5. 2005.
1 -5
0 -20 -40 -60 -80 -100
PWP [kPa]
-5 -15
0 -20 -40 -60 -80 -100
15 cm (c) 15 cm (m)
95 cm (c) 90 (m)
122 cm (c) 120 (m) 1
51
101
151
201
251
301
351
day of the year 2005
Figure 7. Comparison of the calculated (c) and measured (m) soil suction at different depths for the year 2005.
Calibration of the model
The calibration of the hydraulic model has been performed in comparison with the field data of the year 2005. Permeability of the different soil types and net radiation assumptions have been the key factors varied in order to represent the measured data with the model. Net radiation is influencing the evapo-transpiration rate associated with the development of soil temperature. The development of soil suctions is, on the one hand, influenced by the evapo-transpiration rate, but also by the permeability of the soil. Consequently, the calibration procedure was chosen as follows: first of all, assumed net radiation values have been adapted until the model was able to represent the measured soil temperature development in a correct manner. Figure 6 shows the calculated soil temperatures in three different depths in the middle of the field over the year 2005, in comparison to the measured values. The remaining difference between measured and calculated data can be explained by the applied values of air temperature. In the field, temperature measurements have been carried out in the blazing sun so that the values are overestimated in summer, resulting in overestimated soil temperatures.
When this first calibration step was finished, permeabilities of the different soil types have been adapted until the model was also capable of representing the measured suction development over the year 2005 for different depths. Figure 7 shows the calculated values at three different depths over the year 2005, in comparison with the measured values. It can be seen that the model is able to represent the field data effectively. The short time variation of suction in the shallow soil layers are well defined and also the seasonal variation in greater depths correspond to the field data. To attain this degree of agreement, the permeability of the clayey soil had to be significantly augmented (500 times). This was expected, because soil samples on which permeability determination in the laboratory are performed are in general too small to take into account the effect of preferential flow. Studies of other authors confirm these observations (e.g. Gasmo et al., 2000, Rahardjo et al., 2000, Kawamoto et al., 2004). After Kawamoto et al. (2004), it is realistic that the permeability in the field is up to
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PWP [kPa]
0 -20 -40 -60 -80 -100
PWP [kPa]
0 -20 -40 -60 -80 -100
4 factor of safety
PWP [kPa]
0 -20 -40 -60 -80 -100 -120
15 cm (c) 15 cm (m)
3 2 1 0 1
95 cm (c) 90 cm (m)
51
101
151 201 251 day of the year 2005
301
351
Figure 9. Development of the factor of safety for the year 2005. 122 cm (c) 120 cm (m) 1
51
101
151
201
251
301
351
day of the year 2006
Figure 8. Comparison of the calculated (c) and measured (m) soil pore water pressure (PWP) at different depths for the year 2006.
1000 times higher than the permeability determined in the laboratory.
4.4
Figure 10. Slip circle corresponding to the smallest factor of safety during the year 2005.
Validation of the model
The validation of the hydraulic model has been performed in comparison to the field data of the year 2006 and the results confirm the good quality of the chosen model (Fig. 8).
5
STABILITY ANALYSIS
For every first day of the month for the year 2005, the calculated pore water pressures have been introduced into a stability analysis with Slope/W and the most probable slip circles with the corresponding factors of safety have been determined. Figure 8 shows the development of the factor of safety for the year 2005. Figure 9 shows the slip circle corresponding to the smallest factor of safety calculated for the 1st February 2005. It can be seen in Figure 8 that the stability of the slope was guaranteed all over the year 2005. If the seasonal development of the factor of safety (Fig. 9) is compared to the seasonal development of suctions (Fig. 6), the correlation shows up very clearly. The stability is highest when also suctions are highest. It could also be observed that the highest factors of safety correspond to the smallest slip circles with the highest ratio of depth over length (see Figure 10 in comparison to Figure 11).
Figure 11. Slip circle corresponding to the highest factor of safety during the year 2005.
6
CONCLUSIONS
This study has made a contribution to extending the understanding about the behaviour of unsaturated soils in slopes. The computer aided modelling of water balance and stability based on results from field and laboratory experiments can be judged as an appropriate engineering method in a correct manner, because it was possible to represent the slope behaviour, and
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especially the suction development, due to climate influences. The saturation of the soil and the corresponding suctions showed a significant influence on the stability of the test slope and, as a consequence, also on the stability of other slopes with similar soil structure. Even though the observed slope was stable all over the calculated period, the stability analyses have shown that in times of high saturation, the factor of safety becomes significantly smaller. Smallest factors of safety show up between January and June, which is interesting since the heavy rainfall event, which caused many failures in the vicinity of the test slope occurred in May. Many natural slopes have a greater inclination than this slope and, during their hydrological history, they were perhaps never fully saturated. Because of the climate change and the accumulation of extreme rainfall events, it is possible that these slopes may reach their critical saturation degree and will fail.
REFERENCES Cazzuffi, D. & Crippa, E. (2005). Shear strength behaviour of cohesive soils reinforced with vegetation. Proceedings of the 16th International Conference on Soil Mechanics and Geotechnical Engineering, Osaka, Japan. Millpress, Rotterdam. pp. 2493–2498. Fischer, C., López, J. & Springman, S.M. 2003. Remediation of an eroded steep slope in weathered sandstone after a major rainstorm. Proceedings of the International Conference on Landslides, Hong Kong, 8–10. Dec. 2003: 878–883.
Fredlund, D.G., Morgenstern, N.R. & Widger, R.A. 1978. The shear strength of unsaturated soils. Canadian Geotechnical Journal, 15(3): 313–321. Friedel, S., Thielen, A. & Springman, S.M. 2006. Investigation of a slope endangered by rainfall-induced landslides using 3D resistivity tomography and geotechnical testing. Journal of Applied Geophysics, 60(2): 100–114. Gasmo, J.M., Rahardjo, H. & Leong, E.C. 2000. Infiltration effects on stability of a residual soil slope. Computers and Geotechnics, 26: 145–165. Kawamoto, K., Kawamura, T., Kobayashi, K. & Oda, M. 2004. Soil Water Dynamics in a Forested Soil at a Landslide Site under Natural Precipitation. Report. Faculty of Engineering, Saitama University. Rahardjo, H., Leong, E.C., Deutscher, M.S., Gasmo, J.M. & Tang, S.K. 2000. Rainfall-induced slope failures. NTU-PWD Geotechnical Research Centre of Nanyang Technological University, Singapore. Thielen, A., Friedel, S., Plötze, M. & Springman, S.M. 2005. Combined approach for site investigation in terms of the analysis of rainfall induced landslides. Proceedings of the 16th International Conference on Soil Mechanics and Geotechnical Engineering, Osaka, Japan. Thielen, A. & Springman, S.M. 2005. First results of a monitoring experiment for the analysis of rainfall induced landslides. Proceedings of the International Symposium on Advanced Experimental Unsaturated Soil Mechanics— EXPERUS 2005, Trento, Italy. Thielen, A. & Springman, S.M. 2006. Monitoring field experiment in an unsaturated sandy soil slope in Switzerland. Proceedings of the The Fourth International Conference on Unsaturated Soils—UNSAT06, Phoenix, Arizona. van Genuchten, M.T. 1980. A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci. Soc. Am. J., 44: 892–898.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
In situ field experiment to apply variable high water levels to a river levee P.A. Mayor & S.M. Springman ETH Zurich, Institute for Geotechnical Engineering, Zurich, Switzerland
P. Teysseire Teysseire & Candolfi Ltd, Visp, Switzerland
ABSTRACT: A section of flood protection levee along the river Rhone in the canton of Valais has been identified as the site for a field experiment to investigate response due to extensive and repeated river floods. This section has been isolated and within a sheet pile box and a range of instruments have been installed for measuring degree of saturation and suction. The river side will be flooded in order to represent expected critical floods and thereafter cyclic water loading will occur in spring 2007. It is planned that breaching will also occur. This paper will report first results from this in situ experiment.
1
INTRODUCTION
Management of flooding risks in the upper Rhone valley between Lake Geneva and Brig has developed over the past two centuries. The first general and systematic correction project was initiated after the Rhone valley had suffered from severe floods in 1860. The first Rhone correction has been achieved between 1863 and 1893. This defined the path of the river, restraining it from meandering across the valley and freeing up land for subsequent agricultural use. The river was constrained between two parallel levees combined with inclined spurs every 30 m. The function of the spurs was to guide the river into the centre of the riverbed to assure a sufficient water speed to transport the sediments brought by the numerous feeder torrents. In spite of these measures, the level of the river bed rose gradually so that it became necessary to protect the neighbouring land by raising the height of the protection levees to reduce the likelihood of flooding. The second correction of the Rhone River took place between 1930 and 1960 (Service fédéral des routes et des digues, 1964). Recent floods, particularly the event in October 2000 (Federal Office for Water and Geology, 2002), in which thousands of hectares were flooded, causing damage of about 479 million Swiss Francs for the Valais only, concentrated the authorities on the essential nature of the third Rhone correction. The general objectives and the guiding principles of the project were approved and the ‘‘projet Rhône’’ started officially in November 2002. In principle, the work to
be carried out will focus upon strengthening old and weakened levees and broadening the riverbed where necessary and possible. First priority measures have been already planned and partially executed. An analysis of the levees from Visp to Martigny in 1999 had revealed that, for a length of 118.8 km about 59 km of the levee were in extreme danger, about 24 km in medium danger and 23 km in low danger. 12.8 km were not protected by a levee. These cannot be improved to acceptable risk levels immediately and the critical meteorologicalhydrological conditions expected over the next century have become more challenging (high river levels, closer frequency of extreme storms, warmer
Figure 1.
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Geographical location of the test cell.
summers that may dry out the levees (Schär et al. 2004). Furthermore, the construction period will be 30 years, so the stability must be investigated in more detail to aid optimal decision making on the sequence of remediation. The cost is estimated at 1 billion Swiss Francs, paid mainly by the Federal Government through the Office for Environmental Protection (BAFU), with additional financial support from the cantons of Valais and Vaud. The Institute for Geotechnical Engineering at ETH (IGT) was involved following the 2nd Rhone correction as advisory geotechnical experts to the cantonal authorities. A system of classification of the levees has been developed using history files, results of field tests like SPT, CPT and logs of boreholes (Teysseire et al. 1999). Most of the levees are built of sand and silt and these two materials control the behaviour of the levees. A classification system was developed by dividing the levees into 5 different risk scenarios. The studies came to the conclusion that the most dangerous scenario was that of hydraulic fracture mechanism caused by piping from an aquifer beneath a shallow fine grained layer below the levee. This rough but robust classification system allowed a first estimation of the amount of levees needing remediation works and has proved very useful for the first phase of the project. In a second step, the degree of risk of particular existing levees had to be evaluated more precisely. Critical levee cross sections in various locations along the Rhone were instrumented and data obtained during past extreme events contributed towards the preparation of the documents for the 3rd Rhone Correction. Three levee cross sections have been instrumented in the neighbourhood of Visp in 1999. They provided an insight into the response of the levee and the underlying soil layers to high river levels. The instrumentation was concentrated in the saturated zone of the levee and the underlying layers. They consisted mainly of piezometers to measure the water pressure at different depths and the river level. No measurements were made in the unsaturated zone of the levee. In order to improve the understanding of the behavior of the levee under the influence of river level variation and changing weather conditions, a test on an existing levee was planned with the following goals: • improved understanding of levee response under consideration of saturated and unsaturated state of the embankment and underlying soil layers, • impact of river level variations and weather conditions, • scrutiny of the response of the nominally unsaturated zones in the levee due to repeated cycles of saturation and desaturation, • investigation of extreme scenarios such as long lasting high water levels, both with and without significant (sometimes artificial) rainfall,
Figure 2. ground.
Geological section of the levee and the under-
• examination of the effect of the initial state of the levee (c.f. saturation degree) immediately prior to an extreme event. This test is expected to enhance the basic understanding of the response to environmental perturbations, to aid evaluation of the state of existing levees and for the design and construction of the newly planned ones. 2
GEOMETRY OF LEVEE & GROUND MODEL
The levee at the test site is 3.3 m high and has two different zones. The lower part (about 1.5 m) slopes at an average of 22◦ whereas the upper 1.8 m is steeper, at about 40◦ . Three boreholes were drilled, two through the existing levee on either side of the crown to a maximum depth of 15.5 m and one beyond the cell into the lower Rhone gravel and sand, down to a depth of 13.0 m. Undisturbed samples were taken. Figure 2 shows the results of the field investigations. The upper part of the levee is divided into two layers. The first 90 cm consists of fine silty gravel with some stones, the remaining 90 cm being formed by a silty sand with gravel and organic components. Stones were encountered in both boreholes at the border between the upper and the lower part of the levee. The lower part itself consists mainly of uniform sand (SP), with some rounded boulders. The levee is built on a layer of upper fluvial deposits, whose classification ranges between GP and SP. A layer of upper Rhone gravel follows under the first layer. A thin layer of organic material was encountered in the first two boreholes, on top of the lower fluvial deposit layer, which is classified as SW-SM. The lower Rhone gravel and sand lies below, whose classification varies from GW to SP. 3
INSTRUMENTED TEST CELL
An area of 35 m by 12.5 m, more or less centrally located across a section of levee near to a former test
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Figure 3. Air view of the (shortened) test cell (Photography: P. Mayor).
cross section, was isolated from water flows above ground level by piling around it to a depth of about 5 m from the river bed to create a test cell. Larssen 25 pile sections of 11 m length were used. While this would not prevent flow out of or into the base strata from river levels higher or lower than in the test cell, the instrumentation provided was planned to enable back analysis of this state (Figure 3). Along the walls, the cell was made as waterproof as necessary by means of Compactonit pellets and fitted with a pump and a control system to be able to provide a specially defined temporal series of water heights on the river side of the levee. While the existing measurement sections only concentrated on the saturated zone, the test cell was planned in order to investigate the behaviour of the levee in unsaturated as well as in saturated states. Therefore, in addition to measuring the pore water pressure, the water content in the soil as well as the suction has to be determined. Three different types of sensor were installed close to each other at four different spots. The volumetric water content is being measured by means of time domain reflectometers (TDR) and EnviroSmart gauges (ESM), the suction being measured by means of tensiometers (TSM). The four zones are shown in Figure 3. In three supplementary locations, TDRs and tensiometers were installed pair wise at the same depth (with lengths of 90 and 150 cm). A combination of some of these instruments has already been tested successfully in different research projects at IGT (Teysseire et al. 2000, Thielen & Springman 2006). Four EnviroSmart tubes, containing 6 water content gauges each, were installed on both sides of the levee (Figure 4). The EnviroSmart soil water content profile probes are mounted in a PVC access-tube with
Figure 4.
Overview of the instrumentation.
a diameter of 56.5 mm and driven into the soil. The access tube prevents the direct contact of the probes with the soil and the bottom stopper and the top cap prevents moisture and dirt from entering the tube. The access tube is equipped with a cutting ring and driven into the soil with a hammer during installation, while the soil entering the tube is removed with an auger. This method prevents the formation of cavities along the tube and causes minimum disturbance to the surrounding soil. The location of the gauges in the PVC tube can be adapted to suit the subsoil encountered. The minimal distance between two gauges is 20 cm, otherwise the repartition of the gauges in the tube can be fixed without any other restrictions. The sensor measuring principle is based on high frequency capacitance. The sensor output is a dimensionless frequency, which is converted via a normalization equation and then a calibration equation into volumetric soil water content (Sentek 2001). Water content measurements using the default calibration considered in this paper range from 0 to 70%. The sphere of influence of the sensor is situated to 99% within a 10 cm radius from the outside of the access tube. A laboratory characterization of this sensor has been published recently (Schwank et al. 2006). The tensiometers are equipped with electronic pressure transducers connected to the data logger. The instrumentation was completed by piezometers (vented vibrating wire and pressure transducer types) located in and outside the test cell at different depths. A meteorological station measuring air temperature, air humidity and air pressure, precipitation, wind
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force and direction and radiation has been installed on the valley side of the cell. Data are collected, usually every 10 min, and stored by means of a data logger. Measurements can then be downloaded as necessary to the office by phone.
4
PRELIMINARY TEST RESULTS
The variation of the water level during the first phase of the field tests is given in Figure 5 together with the response of the 2nd EnviroSmart tube, TDR 4 and Tensiometer 2 located on the river side of the levee. The depths of the sensors shown are given in Table 1. All sensors are located not far from the surface in vertical or in horizontal directions. This explains the
quick response of all the sensors including the TDR and tensiometer. After lowering the water level, the sensors near the surface registered a rapid decrease in water content. Deeper seated sensors reacted more slowly and the water content was still higher at the end than at the beginning of the test. The TDR measurements on the river side are shown in Figure 6. TDR 1 situated at a depth of 0.9 m reacts very quickly to changes in water level and shows the drying out of the levee after lowering the water level in the cell. The three other TDRs are located at a depth of 1.5 m and show less pronounced reactions, whereas TDR 4, which is the nearest to the centre of the levee, exhibits the slowest reaction and the highest water content at the end of the test. TDR 3 located closest to the slope shows a peak due to a rain event (16 mm in 3 hrs) after 68 days. There was no visible sensor response to the rising water level on the ‘air’ side of the levee. The 4 deeper seated EnviroSmart gauges and the TDR also showed no reaction during the entire test duration of about 80 days. The increase in water content measured from the 2 EnviroSmart gauges near the surface was caused by a rain storm (64 mm in 23 hours), as shown in Figure 7. The assessment of the slope stability of the levees is crucial for the whole project. The suction history of the soil must be taken into account for a reliable prediction of the safety factor. This has been confirmed in the field tests carried out in the forefield of the Gruben glacier by IGT, concerning instabilities on moraine slopes induced by loss of suction (Springman et al. 2003). The instrumentation enables the evolution of the suction and the volumetric water content to be monitored during the infiltration, due to high water level or/and rainfall and to drying processes. Combining the measurements of gauges located at the same depth and at the same distance from the river, the volumetric water content can be plotted as a function of the suction, thus obtaining a field water
Figure 5. Water level variation and response of EnviroSmart 2, TDR 4 and Tensiometer 2 on the river side of the levee. Table 1.
Sensors depth below ground (river side).
Sensor
ESM 2.1
ESM 2.2
ESM 2.3
ESM 2.4
Depth Sensor Depth
0.3 m ESM 2.5 1.2 m
0.5 m ESM 2.6 1.5 m
0.7 m TSM 2 1.5 m
0.9 m TDR 4 1.5 m Figure 6.
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Results of the TDR measurements (river side).
Figure 9. Volumetric water content vs. suction (river side) from TDR measurements. Table 2. Air entry values (AEV) based on tensiometer and EnviroSmart measurements. Tensiometer EnviroSmart
TSM 1 ESM 1.6
TSM 2 ESM 2.6
TSM 3 ESM 2.3
Depth [cm] AEV [kPa]
150 17.0
150 20.7
90 14.8
Table 3. Air entry values (AEV) based on tensiometer and TDR measurements.
Figure 7. Water level, rain and response of EnviroSmart 3, TDR 5 and Tensiometer 5 on the air side of the levee.
Figure 8. Volumetric water content vs. suction (river side) from EnviroSmart measurements.
retention curve. Figure 8 shows the curve resulting from the EnviroSmart and tensiometer measurements, whereas Figure 9 uses the results from the TDR measurements. The curves reflect the successive wetting and drying phases applied during the test. Analyzing the different curves, it can be seen that the EnviroSmart gauges show a change in the volumetric water content well before the suction changes (Figure 8). On the contrary, values of the volumetric water content measured by
Tensiometer TDR
TSM 1 TDR 3
TSM 2 TDR 4
TSM 3 TDR 1
TSM 4 TDR 6
Depth [cm] AEV [kPa]
150 18.6
150 22.6
90 14.1
150 11.8
TDR change well after the change in suction (Figure 9). In spite of this difference in reaction time, both measurements methods (EnviroSmart and TDR) give very similar results. Good agreement can be seen by comparing the air entry value measured by the two methods at different depths and locations (Tables 2 and 3). Differences in air entry value for the same depth can be explained by the variations in density due to the lack of systematic compaction during construction. The geometry of the levee and especially, the horizontal distance to the slope surface also plays an important role. The lower values (TSM 3/ESM 2.3, TSM 3/TDR 1, TSM 4/ TDR 6) were measured at points nearest to the river.
5
FUTURE TEST PLANS
After the end of the first series of water level changes, the test cell has been reduced in size to avoid the risk of flooding due to the constriction of the river
951
bed by the cell. Currently, the levee is being subjected to the normal environmental and climatic cycles and the response of the sensors to rainfall is being recorded. The levee has been gradually drying out, but still presents locally higher water contents than at the beginning of the first test. A second test with a high water level of sufficient duration will be performed in order to see when the water will reach the air side of the levee. In parallel, the levee material will be characterised in laboratory tests. As climate is very dry on site, the levee will be wetted by means of artificial rain in order to study the influence of a long lasting rainfall, followed by a high water level. The possibility of carrying out an overflow (breaching) test of the levee is also being considered. 6
CONCLUSIONS
A test cell encapsulating a portion of an existing levee on the River Rhone has been built. After a site investigation to confirm substrata, instrumentation was installed to measure water content, pore water pressures and suction under the influence of the variable water levels. The sensors installed on the river side of the levee reacted rapidly to the change of water level. Due to the very dry state of the levee at the beginning of the test, the percolating water did not reach the sensors located on the air side of the levee, in spite of a test duration lasting about 75 days. The sensors in place have already delivered very valuable data during the first test. More data will be available for the air side too following the planned tests, which will be a great help in understanding the behaviour of the levee subject to water level variations and changing atmospheric conditions. ACKNOWLEDGEMENTS The authors extend grateful thanks to the Department for Construction, Environment and Traffic of the Canton Valais for their technical and financial support
for this project, and in particular Alexandre Vogel. Hermann Rovina logged the borehole data from the site investigation. We are also very appreciative of the support from the IGT laboratories and workshop, in particular Ernst Bleiker, who was responsible for the data acquisition, and Rouven Mühletaler and Marco Sperl, who both contributed to the field work. REFERENCES Bundesamt für Wasser und Geologie (Federal Office for Water and Geology). 2002. Hochwasser 2000. Ereignisanalyse/Fallbeispiele. Bericht des BWG, Serie Wasser Nr. 2, Bern 2002. Schär, C., Vidale, P.L., Lüthi, D., Frei, C., Häberli, C., Liniger, M.A. & Appenzeller, C. 2004. The role of increasing temperature variability in European summer heatwaves. Nature 427: 332–336. Schwank, M., Green, T.R., Mätzler C, Benedikter, H. & Flühler, H. 2006. Laboratory characterization of a commercial capacitance sensor for estimating permittivity and inferring soil water content. Vadose Zone Jnl. 5: 1048–1064. Sentek 2001. Calibration of Sentek Pty. Ltd. Soil moisture Sensors. Sentek, Stepney, SA, Australia. Service fédéral des routes et des digues, 1964. La correction du Rhône en amont du lac Léman, Office fédéral des imprimés et du matériel, Bern. Springman, S.M., Jommi, C. & Teysseire, P. 2003. Instabilities on moraine slopes induced by loss of suction: a case history. Géotechnique 53(1): 3–10. Teysseire, P., Décorvet, R., Burchard, U., Zuber, F. & Clavien, F. 1999. 3rd Rhone correction, General project. Basic principles. Geotechnics, Department for Construction, Environment and Traffic, Canton Valais (in German), unpublished. Teysseire, Ph., Cortona L. & Springman S.M. 2000. Water retention in a steep moraine slope during period of heavy rain. In H. Rahardjo, D. Toll & C. Leong (eds), Proceedings of Unsaturated Soils for Asia: 831–836. Thielen, A. & Springman, S.M. 2006. Monitoring field experiment in an unsaturated sandy soil slope in Switzerland, The Fourth International Conference on Unsaturated Soils—UNSAT06, Phoenix, Arizona, USA.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
A new treatment for preventing landslides in expansive soil slopes H.P. Yang, Y.X. He & J.L. Zheng Changsha University of Science & Technology, China
ABSTRACT: Occurrence of landslides of cut slopes is an unavoidable and serious engineering problems during civil engineering construction in expansive soil areas, and for a long time there was no safe, economic and environmental protection treatment measure for the problem. As part of an expansive soils research project, properties of expansive soils, geological characteristics and features of expansive soil slope failures have been studied and analyzed. As a result a new treatment technique by reinforcing slopes with geogrid has been implemented for trial cut slopes in expansive soils in Ningming Guangxi. The effects of the new treatment technique shows that landslide problems, which once disturbed the construction of the Nan-You expressway, has been solved successfully. Properties of Ningming expansive soils, characteristics of slope failure and the new method of treatment are introduced and evaluated in the paper.
1
INTRODUCTION
2
The treatment for landslides in cut slopes in expansive soil is a worldwide problem. For the unique natural climatic and geological condition in the autonomous region of Guangxi Zhuangzu, China, expansive soil engineering problems are especially evident. In the 1990s, when the Nan-Kun Railway was built, expansive soil in the Baise district caused great trouble during the construction. As a result, the State Ministry of Railway has concentrated on a series of treatment measures mainly involving rigid inclusions. However, all attempts ended in failure. The Nanning to Youyi Guan Expressway (NYGE) was built in early 2003 traversed the edge of Ningming basin where expansive soil occurred over a 14 km length. After a rainy season, the excavated slopes in this section slid by different amounts. Some slopes were still unstable even after their grade (V:H) had been flattened to 1:3, which brought great difficulties for the construction. Hence, the expansive soils research group of ChangSha University of Science & Technology carried out many in-site geologic investigations for 23 slides and systematically analyzed the causes of damage. Based on a series of tests and referring to the successful experiences of treating expansive soils in engineering projects at home and abroad, the research group firstly put forward the new flexible treatment technique, and put it into practice, which successfully solved the technical difficulties in expansive soil subgrade construction of NYGE, and provided good engineering, economic and environmental benefits.
2.1
CHARACTERISTICS OF NINGMING EXPANSIVE SOIL Soil property and engineering geological characteristic
Ningming expansive soil is a weathered alluvialcolluvial expansive clay whose parent rock is early Tertiary Nadu lacustrine clay rock. The geological section of the excavated roadcut is divided into three layers: the surface layer is brownish red, high plasticity soil with yellow frecklings (thickness ranging from 0.5 m to 1.5 m); the middle part is tan or gray-white, moderate-high swelling, highly weathered soils with flecks (thickness ranging from 2 m to 6 m); the bottom part is charcoal grey or taupe, slightly weathered clay shale with moderate swelling properties (its thickness is rather large). Typical geological profiles exposed during the excavation of a slope clearly show welldeveloped structural joints and weathered fissures. The fissures are mainly vertical, horizontal and slanted and layers are apparent. Fissure extending through a slope’s layers were consistent with interlayers between soil and rock. From the tests of two layers of expansive soils (rocks) (Table 1), it can be seen that the expansive soils are mainly illite/montmorillonite (I/S) mixedlayer mineral, and has the typical properties of normal expansive soils, viz. large content of fine grained material, high water content, large PI (plastic index) and normal free swelling ratio. Furthermore, another obvious property of Ningming expansive soil is the anisotropy of swelling and shrinkage, and the direction of displacement is mainly horizontal.
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Table 1.
Type Hoar soil Deep grey soil
Soil property test results of Ningming expansive soil. Effective content Organic of montmatter morillo% nite %
Fines content Specific (<0.074 area mm) m2 g−1 %
Clay content (<0.002 mm) %
Free swelling ratio %
Unit weight kNm−3
Water content %
Satu- Plastic ration limit % %
19.2
24∼27
85∼9 2
31.5
1.38
20.10
70
264
94.9
50.18
57.5
21.5
25.0
57.3
31.0
2.78
16.52
60
226
93.7
25.9
42.0
As the natural water content of Ningming expansive soil is 24%∼27% and the saturation is 85%∼92%, Ningming expansive soil should be treated as an unsaturated soil.
2.2
Mixedlayer ratio %
Damage traits and reasons for cut slope failures
To understand the character of damage of roadcut slopes and to find an effective treatment measure, 23 sliding slopes of the 31 roadcut slopes along the Nanyou Expressway were investigated and analyzed in March 2004. Landslides involving Ningming expansive soils typically exhibited several characteristics: a. Landslides mainly involved shallow layers. 69% of small damage happen in gray-white expansive soil, and 78% happened on the interface between soil and rock, and in the strongly weathered shale. b. Landslides followed the direction of the underlying strata. Most (88%) of medium size landslides failed on the bedding. c. The obliquities of most sliding surfaces were gentle. The direction of rock layers in the sliding slopes was 138◦ ∼158◦ , the inclination of sliding faces was only 2◦ ∼5◦ , and their slope ratio (V:H) was 1:2.5∼1:3. d. Landslides occurred seasonally, generally late in the rainy season or following heavy rain. e. Most sliding surface were Z shaped rather than circular because of the bedding of soil and rock and because of fissures and cracks, joints in the rock, and the soft interlayer between soil and rock. The loss of soil strength is the main reason for landsliding in the cut slopes, and this is controlled by soil structure and water content. During excavation, topsoil within the slope swells as result of unloading and groundwater infiltration, and the change of climate, geological environment, engineering activities and fast moving water and change the stress in slopes all result in slopes losing their stability. However the
failures on the Nanyou Expressway possess special features and there are several reasons: a. Geological structure: almost all large-scale or shallow landslides occurred on the highway’s west side because the slopes on the west side were excavated along the bedding. b. Soil fabric: the fissures developed extensively due to the over-consolidation of the expansive soil and free faces formed easily following excavation due to stress release. c. Climate condition: Ningming Basin is located in the district of subtropical warm-humid climate zone, where there is the action of rainstorms, runoff and rainwater infiltration. d. Construction techniques: supporting measures were not adopted in time after excavation. e. Vehicle loading: during construction, the tops of cut slopes were used as a temporary construction road. Repeated vehicle loading accelerated sliding of the slopes.
3
THE PROPOSED FLEXIBLE TREATMENT TECHNOLOGY AND DESIGN SCHEMES
3.1 Proposed flexible treatment technology Although many engineering practices exist for treating cut slopes, they can be grouped into two basic types: methods providing rigid support and methods providing flexible support. Methods with rigid support are used most frequently to stabilize slopes. These typically use retaining walls or other masonry structures in conjunction with other measures necessary to reinforce an excavated slope. Such methods are effective when masonry structure’s weight achieves equilibrium with an excavated slope’s released stress. Supported in this way, a slope’s soil is not permitted to deform. However, expansive soil is bound to shrink and swell. If the expansive soil swells and caused significant deformation that cannot be released, the resulting pressure may
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destroy a retaining wall or some other structure proving rigid support. In the districts of expansive soil, the rigid support body is often moved and shows bulging, elucidating such a point. Flexible support uses reinforcement by geofabric. Its character is that it cannot only support soil pressure, but also allow certain distortion of soil and absorbs swelling forces in slopes caused by stress release and the change of water content resulting from over-consolidation. Liao (1984) indicates that if linear swelling content of expansive soil is allowed to reach 3%, its swelling pressure is lower by 25% than that when there is no swelling. Therefore, flexible support is suitable for cut slopes in expansive soil as it allows some movement. The concept of flexible support is put forward based on the understanding of ‘three characters’ (overconsolidation, cracking, shrinkage-swelling properties) of expansive soil and the the character of shallow damage. If geofabric is spread and anchored in layers, the compacted expansive soil fill forms a flexible reinforcing body of sufficient thickness to support the slopes’ top, a drainage system is installed in the subbase and at the back of reinforced structure, the approach can be designed to account for following factors: a. Friction and interlock between geogrid and fill material, along with the layered geogrid’s connection to outer covering, can provide shear strength sufficient to enable the reinforced structure as a whole to resist landslides. b. The flexible reinforced structure permits a slope to deform adequately to release the stress and pressure caused by swelling. c. The flexible reinforced structure has a slope of 1:1.5. Being more then 3.5 m thick and more than two-third the height of the cut slope, the structure can cover the main surface of a freshly cut slope and provide sufficient weight to resist soil pressure. d. Reinforcing soil with enough thickness (larger than the thickness of effective active layer) can obstruct or prevent the influence of weathering action in expansive soil and the development of crannies and landslides of shallow layers.
Referring to related experience and for prelimary calculations, a geogrid should be selected with design tensile strength of 35 kN/m (which is the result of geogrid pullout tests) as reinforcing material, and a layer of geogrid should be placed per two layers of filling soil (the effective length of reinforcing geogrid is 3.5 m according to the depth of weathering. The geogrid should be fixing to the fill using a U-shape nail every 1.2 m, and a counter-wrapping underlayer geogrid is required to connect with superstratum geogrid with linking rods, which makes the reinforcing body an integral part of the slope. The bottom 1∼3 layers of the reinforcing body should be filled with crushed stone, whose strength and drainage requirement are satisfactory; the upper 4 layers should be filled with excavated expansive soil. A drainage layer of 50 cm crushed stone should be designed between the reinforcing body and the excavated slope’s surface, to remove any fissure water in slopes. At the bottom of the reinforcing body, two longitudinal underdrains should be set to reduce groundwater level in the road bed and at the back of slope for drainage. The top and surface of slopes should be covered with 30 cm of top soil and planting should be done to prevent erosion by rain.
4
There are no special technical requirements and normal construction equipment can be used. Basic processes are: 1) excavate slopes to form working plane according to the design; 2) place the crushed stone layer at the bottom of slope, from base to top (thickness of 50 cm) in front of the excavated slope plane, and then place geogrid on which soil is filled and compacted; 3) the geogrid should be counter-wrapped and connected with the upper geogrid by linking rods to form the slope plane. Behind the reinforced body, a drainage layer of crushed stone should be available to drain fissure water.
5 According to the damage character of Ninming expansive soil cut slopes, the design scheme is put forward (Fig. 1). The explanation is following. The width of reinforcing body should be larger than 3.5 m to satisfy the requirement of mechanical construction, prevent the influence of atmosphere on the soil, and exert the effect of wrapping and support. A slope grade of 1:1.5 is adopted in reinforcing slopes for reducing soil pressure and ensuring stability of the reinforced soil body and the counter pressure effect on the soil.
CONSTRUCTION FOR FLEXIBLE SUPPORT
THE EVALUATION OF TREATMENT
Four experimental slopes researched by the project team were finished in Nov. 2004. As the technique proved successful in treated slopes in expansive soil, owners have since required construction units to adopt the flexible treatment technique to deal with landslides problems. Therefore, up to September this year, there were fourteen expansive soil cut slopes on the Nanyou expressway (with slope heights of 8–24 m) where such a technique was adopted, involving a total length of 4.8 km.
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.5
1:1
back fill with planting soil
note: 1 unit: m; 2 the design fits to the slope with height of over 12m
5
:1.
mortar top 1
intercepting fabric pavement 0.7m
back fill with crushed stone soil
Figure 1.
Slopes treated with flexible retaining wall.
Table 2. Displacement with time in observation point on right slopes in K136 + 380. Displacement in observation spots/mm Date
1
2
3
4
5
6
2005-2-20 2005-3-17 2005-4-11 2005-5-9 2005-7-23 2005-9-22 2005-10-25
0 5 1 −1 −4 −6 −9
0 2 −2 1 −6 −13 −16
0 5 −3 5 5 5 −1
0 2 −4 −3 −11 −13 −19
0 2 −4 −2 −8 −11 −16
0 0 −1 −1 −3 −6 −7
Figure 2.
The treated slopes have been through the proof of two dry and rainy seasons, including several big typhoons and rainstorms. The flexible treatment slopes have all worked well, and the plants on the slopes have grown well. At the bottom of the reinforced body, underdrains are working well, there is groundwater flowing, and the effect of drainage is good as in the rainy season underdrains can drain quickly, which decreases the static water pressure in fissures effectively. Fast drainage reduces swelling pressure as the groundwater is rapidly removed from the slopes. For the verification of treatment effects, the project team set a series of fixed level monitoring points to monitor displacement (Figure 2). Monitoring results are shown in Table 2 and Figure 3. However, the monitoring points have since been destroyed by men and vegetation has flourished on the slopes, the monitoring cannot go on. From the monitoring results, after a rainy season, the displacement of cut slopes was found to be small
Observation point on right slope at K136 + 380.
Figure 3. Displacement with time for the observation point on the right slope at K136 + 380.
(<20 mm). From photos in September this year, the treatment effects can be seen clearly (Figures 4–6). In all cases, flexible support has provided an effective treatment measure for expansive soil slopes. Compared with other treating techniques for cut slopes, the advantages of flexible supporting technique are fast and convenient construction and have
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Figure 4.
Comparison of untreated and treated cut slope from K138 + 420 to K138 + 820.
Figure 5.
Comparison of untreated and treated cut slope from K136 + 040 to K136 + 450.
Figure 6.
Comparison of untreated and treated cut slope from K133 + 804 to K134 + 100.
brought evident economic effects. For example, in Nanyou expressway, a section of expansive soil slope, whose length is 300 m and height is 10 m, adopted the scheme of flexible reinforced body (height is 7 m). For this scheme, 20 days would be needed to complete the work, and the required expense would not be larger than 600,000 yuan (Chinese RMB). According to past experience, the expense of adopting a scheme of gravity retaining wall with slope protection by masonry would be at least 1,200,000–1,500,000 yuan (Chinese RMB). For slopes with prestressed anchor reinforcement, the expense would be at least 1,800,000 yuan. Therefore, to treat the same slope, the expense of flexible support is half of an equivalent gravity
retaining wall scheme and one third of a prestressed anchor scheme. Moreover, the latter two methods would take at least a month to complete, and slopes treated with the latter two methods cannot be assured to be stable. 6
CONCLUSIONS
Geogrid flexible support is a comprehensive treatment technique for cut slopes in expansive soil which has been shown to be a credible solution, economical, provides environment protection and is simple and conventional in construction. However, using expansive
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soil directly as fill of reinforced structure has its distinct character. The successful application of such a technique, treating Ningming expansive soil cut slopes’ landslides in Nanyou expressway, has conferred significant economic and environmental benefits. However, it remains to be seen whether this novel technique will have worldwide validity in stabilizing cut slopes in areas of expansive soil. REFERENCES Feng Yu-yong, zhang Yong-shuang, Qu Yong-xin. 2001. The Mechanism Research of Expansive Soil Embankments’ Diseases in Nankun Railway in Baise Basin. Geotechnical Engineering Journal, 23(4):463–467.
Li Shenglin. 1992. The Engineering Geological Research of Expansive Soil in China. Nanking: Jiangsu Science & Technology Press. Yang Heping, Zhen Peng. 2005. Geological Investigation and Consideration of Expansive Soil Cut Slopes’ landslides in Nanyou Expressway. The Journal of Changsha Science & Technology University, 1(4):14–19. Yang Heping Qu Yongxin, Zheng Jianlong. 2005. New Advances in the Research of Ningming Expansive Soil. Geotechnical Engineering Journal, 27(9):981–987. Yang Heping, Zheng Jianlong, Wu Xuhao, Lian Xiangdong. 2005. The Engineering Treating Technique of Expansive Soil Embankments in Nanning∼Youyiguan Expressway in Guangxi Province. The Annual Academy Proceedings of China Road Association. Liao Shiwen. 1984. Expansive Soil and Railway Engineering. Beijing: China Railway Press.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Flow processes in the unsaturated Chalk of the Hallue Basin (France) N. Amraoui, H. Machard de Gramont, C. Robelin, A. Wuilleumier, M.L. Noyer & M.J. Feret BRGM Water Division, Orléans, France
ABSTRACT: During the spring of 2001, large floods occurred in the northern part of France (Somme catchment). The duration of this flood was particularly long (more than 3 months) and it resulted in very significant damages. Due to the dual porosity of the Chalk, the possibility is explored that a hydraulic continuity occurs between the unsaturated and saturated zones of the basin under abundant rainfall conditions, leading to a fast rise of the groundwater level. Until now, the role played by the unsaturated Chalk in the groundwater flooding events has not been clearly established and remains poorly understood. In 2005, an experimental site was designed and equipped in the Somme catchment in order to study the flow process in the unsaturated Chalk. The equipment includes 10 ‘‘shallow’’ tensiometers and 12 ‘‘jacking tensiometers’’ (borehole tensiometers) installed for the monitoring of the suction on a whole profile of the unsaturated Chalk; and an Envirosmart probe equipped with 16 sensors for the monitoring of the water content at various depths. The water table level and the rainfall were also monitored at the site. The analysis of the first data collected during one full year since December 2005 shows a very regular evolution of the pressure in the unsaturated Chalk with the same trend at different monitored depths, the negative pressures range from −800 to −70 cm of water. However, this suction variation does not lead to a significant variation of the water content (around 2%); in fact the water content is close to saturation in the whole unsaturated profile. The suction profiles show a slight and regular increase and decrease of suction during 2006; this means that under normal or rather dry climatic condition like in 2006, the water and pressure transfers are mainly controlled by the Chalk matrix. This was corroborated by a slow piezometric variation in 2006.
1
INTRODUCTION
During the spring of 2001 large floods occurred in the Somme basin (northern part of France) and in the southern part of UK. In both cases these flood events occurred in valleys developed on the Chalk outcrops and were characterized by their long duration (several weeks or months). The Somme basin shows certain similarities with other basins of Northern Europe (Crampon et al. 1993, Price 1993). The Chalk in this basin is a fractured rock with a fine grained porous matrix, where the matrix provide most of the porosity and storage capacity and the fractures greatly enhance the permeability (Roux 1965, Crampon et al. 1993, Price 1993). In the Somme basin, the high contribution of Chalk groundwater to the Somme river discharge during 2001 flood events has been highlighted by hydrological and hydrogeological data analysis (Mardhel et al. 2001) and confirmed by chemical and isotopic study of the groundwater and Somme river water (Négrel & Petelet-Giraud 2005). The modelling studies achieved on the Somme Basin hydrodynamic behaviour (Amraoui et al. 2002, 2003; Pinault et al. 2005) and different observations lead to the conclusion
that, in 2001, several previous wet years, a strong increase of the groundwater storage and, possibly the saturation of the unsaturated zone of the Chalk would be at the origin of the flood. In fact, due to complexity of this Chalk medium (dual porosity and dual permeability system), a hydraulic continuity between the unsaturated and saturated zones of the basin might have occurred under abundant rainfall condition leading to a fast rise of the groundwater level. Until now, the role played by the unsaturated Chalk in the groundwater flooding events has not been clearly established and remains poorly understood. Chalk has been described as a dual porosity and permeability system where water flow can occur both in the Chalk matrix and through the fractures between the Chalk blocks (Price et al. 2000). Since 1980, various experimental studies and modelling works have been carried out on the English Chalk (Wellings 1984, Price 1993, Price et al. 2000, Haria et al. 2003, Mathias et al. 2005, Ireson et al. 2006) and on the Belgium Chalk (Brouyère et al. 2004) to study the physical processes controlling the water and solute movement through the unsaturated zone. Very important progress has been achieved and various flow schemes have been proposed to explain the flow and solute transport in
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the unsaturated Chalk; but because of the complex nature of the conditions which govern the flow mechanisms within the unsaturated zone of Chalk, these mechanisms remain not fully understood yet. In the framework of the French-English INTERREG III A FLOOD1 Project (Noyer et al. 2006), an experimental site has been installed in the Hallue catchment and equipped for the monitoring of the saturated and unsaturated zones of the Chalk. One of the objectives of this monitoring is to study the flow processes in the unsaturated zone of the Chalk under normal and extreme climatic conditions like those of 2001. This paper represents a contribution to the understanding of the flow mechanisms in the unsaturated zone of Chalk in the Hallue catchment. The first results of the continuous water pressure monitoring between December 2005 and July 2006 are analysed and the dominant flow processes which occurred during winter and spring 2006 are discussed.
2 2.1
MATERIALS AND METHODS Experimental site
The experimental site is located at Warloy Baillon in the Hallue basin (Somme, Northern France) at 21 km north east of Amiens city (Fig. 1). In the Hallue basin, the aquifer is represented by the Upper Turonian and the Senonian permeable Chalks which are covered in the plateau zones by a few metres of quaternary silts and by actual alluvium in the valley bottoms (Crampon et al. 1993). The thickness of the unsaturated Chalk may reach 30 m to 50 m on the plateau. The Hallue River drains the Chalk aquifer in low water and high water conditions. A lithological description of three cored boreholes drilled within the site and geophysical logs
Experimental site in Hallue catchments
Somme basin Figure 1.
Location of experimental site in the Somme basin.
investigation enables a qualitative description of the stratification in the saturated and unsaturated Chalk profile. The top 0.7 m of the profile is a brown soil with scattered Chalk gravels and pebbles. The soil overlays a weathered Chalk horizon which extends down to 6.9 m below ground level. The weathering is more developed in the upper part of the weathered Chalk horizon. From 6.9 m down to 33.8 m below ground level (bgl) the fractured white Chalk is present. It was observed that the fracture density decreases with depth. The groundwater level is located at 28 m bgl. The underlying Greyish Chalk horizon extending down to 43.5 m bgl is harder than the white Chalk and the fractures in this Chalk horizon are less frequent.
2.2 Site equipment and in situ tests The installed equipment aims at a better understanding of the flow processes which occur in the unsaturated zone under various recharge conditions (dry, normal and extreme). The experimental site has been instrumented for the monitoring of the saturated and unsaturated zones of the Chalk and the recharge parameters (Machard de Gramont 2007). The water content and the matric potential in the soil and in the unsaturated zone of the Chalk are measured in situ using various instruments. The matric potential is measured from surface down to the water table by using two types of tensiometers: ‘‘Shallow’’ tensiometers developed by the German UMS company and jacking tensiometers developed by the UK Centre for Ecology and Hydrology (CEH). Ten UMS tensiometers (T8) with external refilling were used for the water pressure monitoring in the first eight meters of the unsaturated zone of Chalk. These tensiometers are also equipped with a temperature sensor for soil water temperature monitoring. They were installed in ten small boreholes at the following depths: 0.2 m; 0.5 m; 1 m; 1.5 m; 2 m; 3 m; 4 m; 5 m; 6.5 m and 8 m below ground level (bgl). The deeper unsaturated zone of the Chalk has been equipped with twelve ‘‘Jacking’’ tensiometers installed in a borehole (diameter 250 mm). The matric potential in Chalk was measured between 10 m and 26.5 m bgl at the following depths (10 m; 12 m; 14 m; 16 m; 18 m; 19.5 m; 21 m; 22.5 m; 23.5 m; 24.5 m; 25.5 m; 26.5 m); the average water table is observed at 28 m bgl. The water content monitoring was performed using Sentek’s EnviroSMART probe (from UMS Company) equipped with 16 sensors with flexible depth placement; this probe was installed in a borehole of 56.7 mm diameter. The sensors are located in the soil and Chalk along the first eight meters bgl and enable the water content monitoring at the following depths: 0.2 m;
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Table 1.
Dry density (g/cm3 )
Chalk matrix permeability (m/s)
Porosity (%)
10.3 to 10.6 21.4 to 21.6
1.62 1.58
1.6 × 10−8 1.2 × 10−8
40.3 41.6
Dry density (g/cm3)
Volumetric water content (%) 20 25 30 35 40 45
1.2
0
0
5
5
10
10
15
15
20
20
25
25
30
1.4
1.6
1.8
30 Febrary 2005
November 2005
Figure 2. Water content and dry density evolution in Chalk profile measured in the laboratory.
3 2.3
Results of triaxial permeability tests.
Sample depth (m)
Depth m
0.3 m; 0.4 m; 0.5 m; 0.7 m; 1 m; 1.2 m; 1.5 m; 1.7 m; 2 m; 2.5 m; 3 m; 4 m, 5 m; 6.5 m and 8 m. The EnviroSMART probe is based on the electrical capacitance method to measure the water content; this probe was calibrated at the laboratory on the Chalk and the soil in order to convert the mV output signal to volumetric water content. In addition, two theta probes (type ML2X from Delta T Devices) were installed in the soil and in the weathered Chalk respectively at 0.5 and 1.2 metre bgl in order to provide a control for the EnviroSMART measurements. For the saturated zone of the Chalk, the groundwater level was monitored in 2 boreholes P1 and P2. The rainfall, the relative humidity and the air temperature were also monitored. These equipments are connected to 2 data loggers and all the data have been continuously logged at an hourly time step since December 2005. The site instrumentation has been achieved with the assistance of the CEH and UMS—Sols Mesures and ANTEA Companies. Permeability tests in a borehole were performed to evaluate the vertical distribution of the in situ saturated hydraulic conductivity of the Chalk, eleven permeability tests have been operated at various depths from 8 m to 43 m bgl. Each permeability test consists in several steps of water injection at increasing and decreasing pressure. During each step, the pressure injection and the flux were continuously measured.
RESULTS AND DISCUSSION
Laboratory tests
Complementary laboratory tests were performed on Chalk core samples to determine the physical and hydraulic properties of weathered and fractured Chalk. The measured parameters are the water content, the dry density, the total porosity and the saturated hydraulic conductivity of matrix Chalk. More than 100 samples from the 2 borehole cores drilled in February and November 2005 were used to measure the dry density and water content profiles in the unsaturated zone of the Chalk from soil surface down to the water table. Two permeability tests using triaxial cell were achieved on Chalk core samples for measurement of the saturated hydraulic conductivity of Chalk matrix. The permeability measurement was performed in steady state conditions under constant head on Chalk sample confined in isotopic triaxial conditions. The hydrostatic pressure applied to the Chalk samples was equal to the in situ constraint (applied effective stress depends on the depth to which the chalk sample was taken; see Table 1). Before the test, a phase of saturation and consolidation with Skempton ‘B’ coefficient measurement was done to ensure the complete saturation of the Chalk sample.
3.1 Chalk characterisation The natural water content versus depth and the dry density profiles measured in the laboratory on core samples drilled in February and in November 2005 are reported in Figure 2. The water content values show a small variation with depth and confirm that the whole unsaturated zone of Chalk is close to saturation (saturated water content varies from 44.5% in shallow weathered chalk to 38% in deep compacted chalk). In addition, no significant variation in the water content profiles was observed between February and November 2005. The dry density increases with depth and varies between 1.45 g/cm3 in the weathered Chalk and 1.66 g/cm3 in deeper Chalk. The Chalk porosity decreases with depth; the values are around 44.5% in the weathered Chalk and vary from 38% to 42 % in the fractured Chalk. Table 1 summarises the results of triaxial permability tests performed on Chalk sample cored at 10 m and 21 m bgl. The saturated permeability of the Chalk matrix varies from 1.2 × 10−8 m/s to 1.6 × 10−8 m/s. The in situ hydraulic conductivity tests results show that the saturated hydraulic conductivity decreases
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Effective rainfall (mm/d)
with depth; in the white fractured Chalk the permeability varies between 1.2 × 10−4 m/s and 1 × 10−5 m/s; on the other hand in Grayish Chalk horizon the permeability decreases and varies from 2 × 10−6 m/s to 8 × 10−6 m/s. Compared to the in situ permeability of fractured Chalk the Chalk matrix permeability is 2 to 4 orders of magnitude lower.
40 30 20 10 0 -10
0 -10
Flow processes in the unsaturated chalk in the hallue catchment
-30 -40 -50 -60 -70 -80 -90 -100
0.2 m bgl
0.5 m bgl
0 -10 -20
Matric potential (kPa)
Chalk has been described as a dual porosity and permeability system where water flow can occur both in the Chalk matrix and through the fractures between the Chalk blocks. In situ water fluxes in the unsaturated Chalk could be quantified from the matric potential and water content evolutions in the unsaturated zone by using the zero flux plane method. The ratio between these fluxes and the saturated hydraulic conductivity of the Chalk matrix (Ks) allows inferring the flow mechanisms. In fact, when the fluxes are less than Ks, it can be expected that the flux would be transmitted through the matrix. Conversely, when the fluxes are greater than Ks, the excess of fluxes would have to be transmitted by flow fracture. As the fluxes could not be measured directly, Welling and Bell (1980) suggested the use of matric potential thresholds (associated with the fracture aperture) below which the fractures would be unable to hold water. Welling (1984) proposes, for the UK upper Chalk, a threshold of −5 kPa above which the fracture would hold and hence conduct water. At the Hallue basin, the flow processes which occurred in the unsaturated Chalk under normal climatic condition have been analysed by considering both the matric potential evolution in Chalk (negative water pressure in the unsaturated Chalk) and the water table response obtained at the experimental site during the winter and the spring of 2006. The water content evolution in the unsaturated Chalk measured during this period shows little variation (less than 3%) except in the soil and the first 2 metres at the top of the weathered Chalk. Comparable results have been reported by Ireson et al. (2006) in West Ilslay, UK where below 1 m bgl the variation of the water content in Chalk remains small with magnitude less than 4%. Price (1993) reported that, within the weathered Chalk and Chalk formation, changes in water content tend to be much smaller and that the Chalk matrix remains fully saturated due to capillary forces and the magnitude of changes could speculatively be associated with fracture porosity. Significant matric potential variations have been recorded in the soil and the unsaturated Chalk except close to the water table. Figure 3 shows the matric potential evolution in soil, weathered Chalk and
Matric potential (kPa)
-20
-30 -40 -50 -60 -70 -80 -90 -100
1.5 m bgl 5 m bgl
3 m bgl 12 m bgl
4 m bgl
10 0 -10
Matric potential (kPa)
3.2
-20 -30 -40 -50 -60 -70 -80 -90 -100
14 m bgl 24.5 m bgl
19.5 m bgl 26.5 m
22.5 m bgl
Figure 3. The matric potential evolution in shallow and deep unsaturated Chalk.
fractured Chalk recorded at various depths from surface down to groundwater level. In this figure we reported also the effective rainfall, i.e. rainfall minus Potential Evapotranspiration (PET).
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0
-1 0
-2 0
-3 0
-4 0
-5 0
-6 0
-7 0
Matric potential (kPa)
0
Depth bgl (m)
5 10 15 20 25 30 22 Dec 2005
22 Jan 2006
22 Feb 2006
07 March 2006
22 March 2006
0
-1 0
-2 0
-3 0
-4 0
-5 0
-6 0
-7 0
-8 0
Matric potential (kPa)
0 5
Depth bgl (m)
In the soil layer (tensiometers at 0.2 m and 0.5 m bgl), matric potential evolution is well correlated with the effective rainfall. Matric potential increases for positive effective rainfall (rainfall greater than PET) and decrease for negative effective rainfall. Increase and decrease of matric potential involve an increase and decrease in soil water content. In the unsaturated Chalk, all the tensiometers provide a similar response of the matric potential evolution due to the Chalk profile homogeneity. The response to rainfall events is observed at first in the shallow tensiometers and after in deeper tensiometers with progressive increase and decrease in the matric potential. The magnitude of this response is attenuated with depth and no evident correlation could be done with individual rainfall events. In general, the negative water pressure increases from the surface down to the groundwater level. The matric potential evolution shows various cycles of increasing and decreasing matric potential, these cycles correspond to water storage and water release in the unsaturated Chalk. Three mean refill episodes were observed in the shallow zone of the unsaturated Chalk down to 12 m bgl. The significant recharge episode occurred between February and April 2006. In the deeper unsaturated zone, the matric potential evolution shows the same general trend with less variation in amplitude. The negative water pressure is higher over the monitored period because the water table is close and the Chalk is almost saturated. In mid April 2006, the water table reaches the tensiometer located at 26.5 m bgl and the measured water pressure becomes positive. This positive pressure corresponds to the height of the water above the sensor. Figure 4 presents the matric potential evolution versus depth reported at different dates from December 2005 to March 2006 and from March to July 2006. These profiles show a regular increase in the matric potential between December and March which corresponds to progressive increase of the Chalk saturation. This wetting process, induced by a positive effective rainfall observed since December 2005, had occurred at all unsaturated chalk depths and was accompanied by water table rising. In fact, the water table starts rising during the third week of January. Water table depth measured in P1 borehole located at experimental site is reported in Figure 5. This wetting process was followed by progressive drainage of the unsaturated chalk represented by the regular decrease of the matric pressure observed between the end of March and July 2006 (Fig. 4). During this drainage period, the water table rising continued and the maximum level was reached in the first week of July. From this date the water table recession began. Except at the top of the Chalk profile and close to the water table, the matric potential measured from December to the end of February and after April 2006,
10 15 20 25 30
Groundwater level rises 31 March 2006
22 April 2006
22 May 2006
22 Jun 2005
Figure 4. Matric potential profiles measured at various dates from December 2005 to June 2006.
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08 /08 /06
19 /06 /06
30 /04 /06
11 /03 /06
20 /01 /06
01 /12 /05 24 25
4
CONCLUSIONS
26 27 28 29
-5
14/04/06
11/04/06
17/04/06 0 5 10
-10 15 -15 -20
20
Depth bgl (m)
Matric potential (kPa)
0
08/04/06
05/04/06
02/04/06
30/03/06
27/03/06
24/03/06
21/03/06
18/03/06
Water table evolution in P1 borehole.
12/03/06
Figure 5.
15/03/06
Water table depth bgl (m)
Close to the water table, Chalk is quasi saturated and the matric potential was close to zero. Fracture flow would be the main flow process in Chalk horizon near the water table.
25
Maximum value of matric potential Depth and Date corresponding to this maximum matric potential
Figure 6. Maximum matric potential measured in the unsaturated chalk and date at which this value was reached for different depths.
A significant set of measurement devices has been installed in an experimental site located in the Hallue basin (France) for monitoring the saturated and unsaturated zones of the Chalk from soil surface down to the water table. The objective is to study the flow processes in the unsaturated zone of the Chalk under normal and extreme climatic conditions. Analysis of both water pressure evolution in the unsaturated zone of the Chalk and water table response recorded between December 2005 and July 2006 suggest that under normal precipitation conditions the water transfer is mainly controlled by the Chalk matrix. However, other flow processes (by fracture) could take place if the pressures and saturation conditions are propitious. In addition, it seems that fracture flow represents the dominant flow process in the Chalk horizons near water table. Under extreme climatic conditions, like those of 2001, very small suction could occur, involving a fracture flow in the whole unsaturated zone and hence fast rise in the water table level. The monitoring of the saturated and unsaturated Chalk parameters is continuing and additional data have been collected in 2007.
ACKNOWLEDGEMENTS was always lower than −10 kPa. This means that for this period, water flow occurred mainly through matrix chalk if we consider the matric potential threshold value of −5 kPa, defined by Welling (1984) for the upper Chalk, above which fracture flow would be generated. The maximum matric potential values (Peak) have been measured in the unsaturated Chalk between March and April 2006. In Figure 6 are reported the matric potential peak measured at different depths and the date at which this maximum was reached. The analysis of this maximum matric potential data shows that at some depths (1.5 m, 2 m, 4 m, 10 m and 12 m bgl), values above −5 kPa have been reached showing that local fracture flow would have occurred. Elsewhere, at the depths of 5 m; 6.5 m; 8 m; 14 m and 19.5 m bgl, maximum matric potential values was always lower than −5 kPa indicating that in these unsaturated Chalk horizons, water transfer by chalk matrix has been the principal flow process.
The results were obtained in the framework of the INTERREG III A FLOOD1 project (www.flood1.info) in partnership with the British Geological Survey and the University of Brighton, the BRGM financial partners being the EU through ERDF funds, the MEDAD (Ministère de l’Ecologie et du Développement et de l’aménagement Durable) through the DIREN Picardie, and two local end-users: the Conseil Régional de Picardie and the Conseil Général de la Somme.
REFERENCES Amraoui, N., Golaz, C., Mardhel, V., Petit, V., Pinault, J.L., Pointet, T. 2002. Simulation par modèle des hautes eaux de la Somme. BRGM/RP-51827-FR report. Amraoui, N., Golaz, C., Mardhel, V., Pinault, J.L. 2003. Evaluation du risque d’inondation dans le bassin de la Somme: apport de l’approche globale et de l’approche distribuée, in SIRNAT Colloque—Thème risques naturels et modélisation, Orléans—France.
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Brouyère, S., Dassargues, A. Hallet, V. 2004. Migration of contaminants through the unsaturated zone overlying the Hesbaye Chalky aquifer in Belgium: a field investigation. Journal of Contaminant Hydrology 72: 135–164. Crampon, N.J., Roux, C., Bracq, P. 1993. Hydrogéologie de la craie en France. Hydrogéologie 2: 81–123. Haria, A.H., Hodnett, M.G, Johnson, A.C., 2003. Mechanism of groundwater recharge and pesticide penetration to a Chalk aquifer in southern England. Journal of Hydrology 275: 122–137. Ireson, A.M., Wheater, H.S, Butler, A.P., Mathias, S.A., Finch, J., Cooper, J.D. 2006. Hydrological processes in the Chalk unsaturated zone—Insights from an intensive fields monitoring programme. Journal of Hydrology 330: 29–43. Machard de Gramont, H. 2007. Projet INTERREG III A FLOOD1. Rôle des eaux souterraines dans le déclanchement des crues: choix du site expérimental et campagne de forages. BRGM/RP-55377-FR report. Mardhel, V., Négrel, Ph., Pointet, T. 2001. Première analyse des composantes des écoulements souterrains du bassin versant de la Somme en période des Crues. BRGM/RP51030-FR. Mathias, S.A, Butler, A.P., McIntyre, N., Wheater, H.S., 2005. The significance of flow in the matrix of the Chalk unsaturated zone. Journal of Hydrology 310: 62–77.
Négrel, Ph., Petelet-Giraud, E. 2005. Strontium isotopes as tracers of groundwater-induced floods: the Somme case study (France). Journal of Hydrology 305: 99–119. Noyer, M.L., Amraoui, N., Chretien, P. 2006. FLOOD1: role of groundwater in flooding events, in Catchment Scale Hydrogeology—The Geological Society— London—24/01/2006. Pinault, J.L., Amraoui, N., Golaz, C. 2005. Groundwaterinduced flooding in macropore-dominated hydrological system in the context of climate changes. Water Resources Research; 41 (5). Price, M. 1993. Groundwater movement in the Chalk aquifer in England. Hydrogéologie 2: 147–150. Price, M., Low R.G., McCann, C. 2000. Mechanisms of water storage and flow in the unsaturated zone of the Chalk aquifer. Journal of Hydrology 233: 54–71. Roux, J.C. 1965. Hydrogéologie du bassin de la Somme, Bull. BRGM, (1er série) 3: 1–44. Wellings, S.R., Bell, J.P., 1980. Movement of water and nitrate in the unsaturated zone Upper Chalk near Winchester, Hants. England. Journal of hydrology 48: 119–136. Wellings, S.R., 1984. Recharge of the upper Chalk aquifer at a site in Hamshire England, 1. Water balance and unsaturated flow. Journal of Hydrology 69: 259–273.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Loading-collapse tests for investigating compressibility and potential collapsibility of embankment coarse well graded material C. Hoffmann & A. Tarantino Dipartimento di Ingegneria Meccanica e Strutturale, Università degli Studi di Trento, Italy
ABSTRACT: The paper presents an experimental programme aimed at investigating compression and volume collapse behaviour of the coarse-grained material forming the Adige river embankment. Tests involved one-dimensional compression at constant water content and wetting at constant vertical stress. Results were interpreted within the framework of the BBM model. This model with parameters calibrated from compression paths could successfully predict the wetting-induced volume collapse. The calibrated model was then used to infer the potential collapsibility of the emplaced material. It is shown that the embankment is likely to not experience volume collapse upon wetting.
INTRODUCTION
The paper presents one-dimensional loading-collapse tests from a major experimental testing programme aimed at characterizing the hydro-mechanical behaviour of the Adige River embankment. This testing programme is part of a joint project carried out by the Autonomous Province of Bolzano (Italy) and the University of Trento to investigate the stability of the embankments forming the Adige River flood defence system. The project includes subsurface exploration, laboratory and field testing, and monitoring of water content, water pressure, vertical deformation at three sections of the embankment. In this paper, the attention is focused on a series of loading-wetting tests performed to study the wetting-induced volume collapsibility of the emplaced embankment material. The testing equipment including the modifications to allow suction measurements using high-capacity Trento Tensiometers is described. The experimental results are presented and interpreted within the constitutive framework of the Barcelona Basic Model (BBM) proposed by Alonso et al. (1990). The calibrated model is finally used to investigate the potential collapsibility of the emplaced material.
2
taken at 6 locations on the river left-hand side between the distances of 116.5 km and 118.2 km from source are also shown in the figure. It can be observed that the GSDs define a relatively narrow band indicating that the embankment has a high degree of homogeneity. The GSD of the material used in laboratory testing is also shown in Figure 1 (thick curve). This GSD has maximum grain size of 25 mm and can be considered to be representative of the embankment material. Atterberg limits were performed on the fraction passing the #40 sieve (425 μm) and showed that the material has low plasticity (wP = 16.1%; wL = 18.7%). Determination of the specific gravity Gs was carried out according to ASTM D854 considering fractions smaller than 75 μm, 400 μm and 1.18 mm respectively. An average value Gs = 2.81 was obtained.
Clay
Sand
Silt
100
Gravel
Cobbles and boulders
Other sections from 116.5 km to 118.2 km Instrumented section at 119.3 km Laboratory testing 80
Fraction finer (%)
1
60
40
EMBANKMENT MATERIAL 20
The grain size distributions (GSD) of 7 samples taken at one of the sections investigated in this programme (located on the river right-hand side at the distance of 119.3 km from source) are shown in Figure 1. The embankment material can be classified as well graded gravel sand. For comparison, the GSDs of 11 samples
0 0.0001
0.001
0.01
0.1
1
10
100
1000
Grain size (mm)
Figure 1. GSD of the embankment material. The GSD represented by the thick curve was used in laboratory testing.
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The dry density of the emplaced material was estimated to vary between ρd = 2.0 − 2.15 Mg/m3 based on crosshole tests and dynamic penetration tests. 3
TESTING EQUIPMENT AND EXPERIMENTAL PROCEDURE
Tests were performed on specimens prepared using the same GSD as in the field. To accommodate the large grain size (d < 25 mm), a Rowe-type large oedometer equipped with a pneumatic loading system was used to perform tests on specimens having 230 mm in diameter and maximum height of 120 mm. To measure the vertical displacement, a 50 mm circular plate was put in direct contact with the top surface of the specimen and connected to a ram passing through the rolling membrane. A vertical displacement transducer was therefore installed at the top of the ram (Figure 2a). Some modifications were introduced to the testing equipment. A membrane centrally incorporating a metal plate was designed to allow suction measurement of samples after compaction. The metal plate is provided with two holes to allow the installation of Trento high-capacity tensiometers (Tarantino & Mongiovì 2002) on the specimen top surface (Figure 2c). The membrane made it possible to seal the specimen and avoid water evaporation during suction measurement. To inundate the sample and reduce suction to zero in the collapse tests, the oedometer was connected to a water reservoir and water was allowed to infiltrate into the sample from the base of the oedometer cell. Water mass entering the sample was measured by weighing the water reservoir using an electronic balance. Testing configuration used in this step is shown in Figure 3. Two types of tests were performed on the embankment material. The first series of tests were aimed at investigating the compaction behaviour and
Figure 2. Views of the testing equipment. a) Loadingwetting configuration, b) specimen after removal from the cell and c) suction measurement configuration.
water retention behaviour of the embankment material. These tests involved constant water content loading to 75, 150, 300, or 600 kPa vertical stress and unloading to zero vertical stress. After compaction, the pneumatic loading system was removed and the cap equipped with the two tensiometers was installed for suction measurement. These tests were aimed at investigating the compaction behaviour of the soil in terms of dry density and compaction water content at different levels of compaction energy (vertical stress). In addition, the water retention behaviour of the compacted soil over a range of dry densities and water contents could be explored. This first series of compaction tests were performed by placing a stiff metal plate over the membrane to ensure a uniform vertical displacement and therefore an accurate control of the degree of saturation. The second series of tests was aimed at investigating the compression and collapse behaviour of the embankment material. The stress path followed in this second series of tests is shown Figure 4. Specimens were first compacted at constant water content by loading to 650 kPa vertical stress (0-1), unloading to 10 kPa vertical stress (1-2) and reloading to 150 kPa (2-3). Specimens were therefore inundated at the constant vertical stress of 150 kPa to reduce
Vertical Displacements Air pressure
LVDT
Water reservoir
Water valve Electronic balance
Figure 3. path.
Testing configuration during loading wetting
Figure 4.
General stress path followed in the collapse tests.
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4
EXPERIMENTAL RESULTS
The results from the compaction tests are presented in Figure 5. In the figure, results from dynamic compaction tests on samples having reduced grain size distribution (d < 10 mm) are also reported. It can be observed that compaction energy associated with static compaction up to 600 kPa vertical stress is slightly lower than 30% of standard Proctor energy. The range of dry densities in the field (ρd = 2.00 − 2.15 Mg/m3 ) based on field testing is also drawn in Figure 5 together with the presumed range of compaction water contents (w = 0 − 0.06). The upper limit of the water content used to emplace the material was assumed to be w = 0.06 because the material is very difficult to remould at greater water contents. The mean suction measured by the two tensiometers on specimens after compaction is shown in Figure 6. It can be observed that suction is essentially controlled by compaction water content and is practically independent of dry density. It was inferred that water is retained by the finer fraction of the material in this water content range and, hence, the water retention curve is not affected by the overall dry density.
Scattering of suction measurement is likely due to the small size of the tensiometer high-air-entry porous ceramic compared with the size of the soil specimen pores. According to the data shown in Figure 6, we tentatively assumed that suction remained constant during the compaction process and that suction could be directly related to water content according to the linear regression in the plane w- ln(s) shown in Figure 7. Loading, unloading and reloading compression paths (0-1-2-3) from the second series of tests are shown in Figure 8. It can be observed that the relationship between the vertical net stress σ and the void ratio e along the path 0-1 becomes linear at high stresses in a semi-log scale suggesting that the soil is moving along a virgin compression line. Small deformations recorded during the unloading path suggest an almost rigid response of the material in the ‘elastic’ range. Results from the second stage of the test (3-4-5-6) are shown in Figure 9. For the sake of clarity, only the tests that exhibited collapse upon wetting at constant vertical stress are presented. It can be observed that collapse brought the specimens on to the same saturated virgin compression line and that the amount of collapse was greater for the specimen having lower initial water content (i.e. higher initial suction). Wetting at constant vertical net stress for the sample having
1000
Suction, s (kPa)
suction to zero (3-4). The vertical stress applied during wetting was defined based on the stress level existing in the field due to the embankment overburden pressure. After saturation, specimens were loaded to 650 kPa vertical stress (4-5) and unloaded to 10 kPa vertical stress (5-6) to investigate the saturated compressibility of the material.
2.4
w=3.4% w=3.9% w=5.1% w=5.7%
100
10
Static compaction (d<25mm) Dynamic compaction (d<10mm) 2.3
r oc to
50
S a
.9
2
2.1
2.2
kP
Figure 6. samples.
.7
1000
r =0
a
kP
Suction measured on statically compacted
0
S
kP kP a a
30
r =0
15
0
2
.8
S
0
oc to
60
Pr 30
%
2.1
1.9
.0
r =0
r
2.2
1.8
r =1
%
10
S
Pr
Pr
75
.6
Suction, s (kPa)
=0 Sr
Dry density, ρd: Mg/m3
1
tor
oc
0%
1.9
.5
=0 Sr
0.08
.4
=0 Sr
0.06
0.3
0.04
S r=
0.02
0.2
S r=
1.8
100
10
0.1 1
Water content, w
0.03
Figure 5. Compaction results obtained using different sample compaction procedures and different scaled grain-size distributions.
0.035
0.04
0.045
0.05
0.055
Water content, w
Figure 7.
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Suction versus compaction water content.
0.06
0.8
2 w = 2.1% w = 3.3% w = 6.2% w = 8.7%
1.8
0.6
N(s)
Void ratio, e
0.7
1.9
0.5
1.7 1.6
At saturation after collapse
1.5
0.4
1.4
0.3
0.1
0.2 10 100 Net vertical stress, σ (kpa)
0.08
1000 λ(s)
1
Figure 8. One-dimensional compression tests at constant water content (loading, unloading and reloading to σv = 150 kPa). Dashed lines represent virgin compression lines.
At saturation after collapse 0.04
0.02
0.8
0.01
w = 2.1% w = 3.3%
0.1
1
10
100
1000
10000
Matric suction, s (kPa)
0.7
Figure 10. Slope λ and intercept N (at reference pressure σ = 1 kPa) as a function of suction of one-dimensional normal compression lines.
0.6 Void ratio,e
0.06
0.5 0.4 0.3
Wetting
0.2 1
10
100
1000
Net vertical stress, σ (kPa)
Figure 9. Loading-wetting paths of samples exhibiting collapse upon wetting at constant net vertical stress.
water content of 6.2% and 8.7% did produce neither collapse nor elastic swelling (tests not shown in Figure 9). The results shown in Figure 8 can be used to derive the coefficient of virgin compression corresponding to different water content and, hence, to different suction levels according to Figure 7. As shown in Figure 10, the slope of the virgin compression line λ first increases then decreases with decreasing suction. The value of the virgin compressibility λ recorded at suction s = 0.15 kPa corresponding to the water content w = 8.7% favourably agrees with the saturated virgin compressibility recorded after collapse (see Figure 9). The non-monotonic variation of λ with suction is likely to be due to the effect of void ratio on compressibility. In contrast to clayey materials, well-graded coarse materials are expected to become stiffer as porosity decreases. The non-monotonic
variation of λ observed in Figure 10 then results from two competing effects, void ratio and suction. At lower water content (w = 2.2%) it is the high suction that generate low compressibility whereas at higher water content (w = 8.7%) it is the low void ratio that makes the material stiffer. The suction variation of the intercept N of the virgin compression line (taken at the reference pressure σ = 1 kPa) follows a similar pattern as shown in Figure 10. Also in this case, the value of the intercept N recorded at suction s = 0.15 kPa corresponding to the water content w = 8.7% favourably agrees with the saturated intercept recorded after collapse.
5
MODELLING EXPERIMENTAL RESULTS
Results obtained from the collapse tests can be interpreted to define the collapsibility of the embankment. To this end, experimental data shown in Figure 8 and Figure 9 were modelled according to the isotropic part of the Barcelona Basic Model (BBM) (Alonso et al., 1990) by replacing the mean net stress with the vertical net stress σ . In the BBM model, volume changes induced by loading and wetting are described using principles of hardening plasticity and considering two independent stresses, the net stress σ , and the suction s. The model was slightly modified to account for the specific mechanical features of the coarse-grained materials investigated in this programme.
970
Elastic changes in specific volume are given by the following non-linear incremental law: dve = −k
dσ ds − ks σ (s + σat )
(1)
where σ it is the net vertical stress, s is the suction, k is the elastic stiffness parameter for changes in net stress, ks is the elastic stiffness parameter for changes in suction, and σat is the atmospheric pressure. According to the experimental data, we assumed ks = 0 and derived k = 0.0032 from the unloading-reloading compression lines shown in Figure 8. Irrecoverable volumetric deformations induced by loading-wetting paths are controlled by a single Loading-Collapse (LC) yield surface. The LC yield was derived according to Wheeler & Sivakumar (1995), i.e. without assuming that there exists a reference net stress at which the LC curve becomes a straight line in the plane σ -s. The LC curve was then written as follows: ∗ σ λ(0) − k N (s) − N (0) σ0 (s) = σ c ln 0c + λ(s) − k σ λ(s) − k (2)
The parameter σ0f∗ equals the vertical net stress at which the specimen is wetted (σ0f∗ = 150 kPa). Using Equations (1), (2), and (3), the paths in Figure 8 and Figure 9 could be simulated and the amount of plastic volume change occurring during wetting-induced collapse at constant net stress could be estimated using Eq. (4). As an example, the stress path simulated for the test carried out at the water content w = 2.1% is shown in Figure 11. The agreement is satisfactory except for the initial part of the compression path. This is because we disregarded the overconsolidation due to the initial suction of the specimen. The suction increase yield locus (SI) causes an initial rightward movement of the LC curve which has not been accounted for. Table 1. Saturated pre-consolidation stress associated with the initial compaction (path 0-1). w σ0i∗ (kPa)
2.1% 10.3
3.2% 21
6.2% 140
8.7% 650
0.7 w = 2.1% Simulation 0.6
dv p = − [λ(s) − k]
dσ0∗ σ0∗
(3)
Void ratio,e
where σ0 (s) is the yield stress at the suction s, σ0∗ is the parameter defining the size of the LC yield locus (corresponding to the preconsolidation stress for saturated conditions), λ(s) is the slope of the virgin compression line at a suction s and N (s) is the intercept of the virgin compression line at a suction s taken at the reference pressure σ c = 1 kPa. The functions N (s) and λ(s) were obtained by fitting data in Figure 10. The hardening law for the LC curve was written as follows:
0.2 1
σ0i∗
100
1000
Figure 11. Simulation of stress path for the test carried out at w = 2.1%. 0.1
(4)
where σ0i∗ and σ0f∗ are the parameters controlling the size of the LC yield locus before and after collapse. The parameter σ0i∗ can be derived by considering the expansion of the LC curve produced by the initial compression at constant water content (path 0-1 in Figure 4). The values of σ0i∗ for the four tests are given in Table 1.
10
Net vertical stress, σ (kpa)
Void ratio change, e
dv = − [λ(0) − k] ln
Wetting 0.4
0.3
where dvp is the plastic change in specific volume. The change in specific volume occurring during wettinginduced collapse at constant net stress σ is therefore given by: σ0f∗
0.5
Experimental Simulation
0.08 0.06 0.04 0.02 0 0.02
0.04
0.06
0.08
0.1
Compaction water content, w
Figure 12. Simulation of void ratio change upon collapse and comparison with the experimental data.
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Overall, it can be seen that the prediction of the amount of collapse is satisfactory. The same accuracy could be obtained for the three other tests as shown in Figure 12. It is worth noticing the collapse was predicted only based on the compression paths shown in Figure 8. In other words, the basic assumption behind the BBM model, that yielding associated with compression at constant suction also controls yielding occurring upon wetting at constant stress, fairly holds for this coarse-grained material. This result is noteworthy as the BBM was essentially formulated for fine-grained materials. 6
The calibrated BBM model was used to assess the potential collapsibility of the in-situ material. The relationship between compaction vertical net stress and soil dry density at two different compaction water contents is shown in Figure 13. These curves were obtained from the virgin compression curves derived in Figure 8. For the range of estimated in-situ dry densities (ρd = 2.00−2.15 Mg/m3 ), it is possible to infer a range of compaction vertical stresses and, hence, a range of LC curves generated by the compaction process. The LC curves generated by compaction at the water contents of 3.3% and 6.2% are shown in Figure 14. The LC locus moves leftward as the compaction water content increases and the compactioninduced dry density decreases. Since the compaction water content of 6.2% may approximately be assumed to be the maximum compaction water content of the emplaced material, the LC curve at the farthest left represents the ‘lowest’ LC that might have been generated by field compaction. If this curve is compared with the actual in-situ vertical stress in the embankment, it may 2.3
w=
Dry density, ρd (Mg/m3)
w = 6.2% w = 3.3%
Suction, s (kPa)
40
30 d
= 2.00 Mg/m3
20 In-situ stress state 10 d
0 0
500
1000 Net vertical stress,
1500
= 2.15 Mg/m3 2000
2500
(kpa)
Figure 14. LC curves generated by compaction at water contents of 3.3% and 6.2% compared with the in-situ stress state.
COLLAPSABILITY OF IN-SITU EMBANKMENT MATERIAL
2.2
50
6.2% w=
3.3%
be concluded that no volume collapse of the embankment would occur upon wetting associated with the advancing of the wetting front from the river side.
7
CONCLUSIONS
The paper has presented an experimental programme aimed at investigating compression and collapse behaviour of the coarse-grained material from a river embankment. It has been shown that the BBM model using parameters calibrated from compression paths could successfully predict the wetting-induced volume collapse. The calibrated model was then used to infer the potential collapsibility of the emplaced material. It has been concluded that the emplaced material is likely to not experience collapse upon wetting.
ACKNOWLEDGEMENTS The authors wish to acknowledge the support of the European Commission via the ‘‘Marie Curie’’ Research Training Network contract number MRTN-CT-2004-506861. They also wish to thank Mr Gianluca Benini who carried out part of the experimental tests.
2.1
REFERENCES 2
1.9
1.8 0
200
400
600
800
1000
Net vertical stress, σ (kPa)
Figure 13. Relationship between compaction vertical stress and dry densities at two different compaction water contents.
Alonso, E.E., Gens, A. & Josa, A. 1990. A constitutive model for partially saturated soils. Géotechnique, 40: 405–430. Tarantino, A. & Mongiovì, L. 2002. Design and construction of a tensiometer for direct measurement of matric suction. In Proceedings 3rd International Conference on Unsaturated Soils (eds J.F.T. Jucá, T.M.P. de Campos & F.A.M. Marinho), Recife, 1, pp. 319–324. Wheeler, S.J. & Sivakumar, V. 1995. An elasto-plastic critical state framework for unsaturated soil. Géotechnique, 45 (1): 35–53.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
An example of the impact of loess soils on foundations and earthworks in Kazakhstan S. Walthall & W.P. Duffy Bechtel Ltd, London, UK
ABSTRACT: This paper describes the practical aspects of investigation, design and construction of a large new petrochemical plant on unsaturated fine grained loess soils in Kazakhstan. For engineers used to working with British (BS) and North American Standards (ASTM) the contractual requirements to satisfy both local and international codes can be a challenge. In Kazakhstan the local codes and standards (derived from SNiPs and GOST) have a prescriptive ‘cook book’ approach to the design and construction of foundations and earthworks on loess soils. Such soils are classified into groups of swelling or collapsing soils, based on laboratory index testing; and foundations are designed based on these classifications. A complete review of the soils, including ground investigation by the local design institute, together with Electric Cone Penetration Testing and laboratory testing of samples in the UK determined in fact that the index tests related to the state of the loess soil in the field rather than a fundamental property. This determination meant that one design approach could be taken to the whole site; in particular the specification for earth works required the material to be compacted wet of optimum in the field to ensure the correct density and eliminate long term swelling or collapse of the soil. This particular project reflected the importance of understanding and working within local codes and standards as well as investigating the fundamental properties of the materials.
1
INTRODUCTION
This paper describes the practical aspects of the investigation, design and construction of foundations for a large petrochemical plant and associated infrastructure in the steppe lands of Northwest Kazakhstan on unsaturated fine grained loess soils. Design was required to comply with local building codes. The project design implementation was a cooperation between a local design institute and western project managers and therefore required a pragmatic understanding of the techniques and codes of practice of both parties. A special feature frequently encountered for loess soils is large pore volumes (which may be up to a few centimetres in diameter), mainly in the vertical direction. This often results in low unit weight. Without change in water content the structure is stable. However, when the water content of a loess soil with low dry density is increased, the soi1 structure can collapse resulting in large volume changes. Very large settlements can take place if water becomes available in collapsible loess. In the Former Soviet Union (FSU) the national standards (known as GOST) and codes of practice (known as SNiP), describe the methodologies and procedures
for the investigation, classification and design requirements for unsaturated fine grained soils. In particular the codes divide the soils discretely into either swelling soils or collapsible soils depending on the results of laboratory testing. However, a detailed investigation of the soils across the site using both local and British Standard (BS) together with ASTM tests showed that in fact there were no fundamental differences in traditional classification of the soil in terms of Atterberg Limits or gradation and that the key property of the soil, for design of foundations, was the stress history and present location on the P/e curve. This permitted a procedure to be developed for a single design philosophy for the foundations across the whole of the site. 2
GROUND INVESTIGATION
The ground investigation was carried out in two phases. 2.1
Local investigation
The first phase of investigation involved a detailed investigation in accordance with local standards and
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codes (GOST and SNiP) to satisfy local building code requirements. Local field investigations were implemented by drilling and sampling using large diameter hollow stem auger with a window sampler from which undisturbed samples were cut (Fig. 1). These were wrapped and waxed in the field before being sent to the laboratory for testing. These samples, known locally as ‘monoliths’, were undertaken in accordance with the local GOST standards, and by local code are required to have a full suite of laboratory tests include grading, classification, shear box and compression tests. The usual procedure for evaluating the collapsibility of loess soil is to run paired oedometer tests. One test is carried out on the material at natural moisture content and the other in fully saturated conditions. The results of these tests determine whether the soil is described as a swelling soil or as a collapsing soil. They are also used to determine the soil modulus, E, from which the predicted settlement of ground, due to self-weight swelling or consolidation when saturated, was calculated. Local practice in Kazakhstan is to classify soils, subject to a collapse potential, in accordance with SNiP 2.02.01-87 (Foundation Beds) as Class 1, soils where the self weight settlement is less than 50 mm and Class 2, where the settlement is predicted to be more than 50 mm. The design codes give rules for the design of foundations in these materials.
Figure 1.
Sampling techniques, showing window sampler.
2.2 Further investigation in accordance with British Standards A second phase of investigation, undertaking electric cone penetration tests (CPT) in the field and shipping undisturbed samples to UK labs for testing to BS 1377 and ASTM, was carried out in order to complete the design of the foundations. This was deemed necessary for the following reasons: – to gain an understanding of how local testing standards compared with BS5930 and ASTM practices. – to develop a ground model and design parameters using familiar testing procedures. – to allow a comparison between testing regimes and to provide confidence that relationships, conventionally used in BS and ASTM practice for foundation design and field control, were still applicable. Soil laboratory classification testing in the FSU was carried out in accordance with GOST 5180-84, Soils Laboratory methods for determination of physical characteristics. Equipment and procedures are different from those used in BS or ASTM testing (Fig. 2). For example whilst the plastic limit test was similar the liquid limit was measured by a fall cone method with very different dimensions to the one used in the BS1377 test. However, the local testing laboratories had carried out correlations with the Casagrande cup method. A comparison of the results of soil index tests between the local results and the BS tests (Fig. 3a) showed good agreement within the expected accuracy of the testing. The soil is therefore classified as a clay of low to intermediate plasticity. Gradation was uniform and typically within the envelope shown in Figure 3b. In the local laboratory,
Figure 2. Laboratory testing equipment including compaction, classification and dispersion tests.
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a) 80
Moisture Content %
Upper plasticity range Intermediate High Very high Extremely high
Low
5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 A 0%
0.00 2 .00
ir V
70
Dry Density (Mg/m3)
s
Liquid limit %
s
10
1 .60
void
20
1 .70
Void
Plasticity index %
1 .80
Air 30%
30
Plasticity testing Gost Results BS 1377 results
Air 20 %
40
s oid
50
s Void Air 10%
1 .90
60
1 .50
0 0
10
20
30
40
50
60
70
80
1 .40
90 100 110 120
b) 100
1 .30
90
1 .20
Proctor Compaction curves Natural Insitu density
Percentage Passing
80
Figure 4.
70
Compaction test results and insitu densities.
60 50
1
40 30 Soaked Sample
20
0.9 Soils swells on wetting
10
CLAY
Particle Sizein mm SILT
SAND
GRAVEL
0.8
COB- BOULBLES DERS
Figure 3. (a) Plasticity chart showing GOST and BS test results, (b) PSD chart showing uniform grading.
0.7
Voids ratioe
Swelling Zone
0
Natural moisture content Collapse Zone Soil collapses on wetting
0.6
the strength parameters were determined by the use of a direct loading shear box and this produced values of cohesion and angle of friction which are used directly in the local design equations to compute the allowable bearing capacity. Whilst these can be compared with values obtained from BS triaxial testing, they are not interchangeable in formulae. It is of interest to note that although bearing capacity formulae, used in the SNiP, are of a similar nature to those commonly used in the UK the parameters used are very different. Compaction testing was carried out locally according to GOST 22733, Laboratory method for determination of maximum density. This used a 2.5 kg hammer and was comparable to standard Proctor Test although the layer thickness and number of blows were different. Proctor testing yielded consistent results with well defined optimum moisture content. Figure 4 shows the tests results compared with the low insitu densities of the potentially collapsible material which had in excess of 20% air voids. The oedometer tests carried out locally (GOST 23161-78) were replicated using the BS1377 test in the UK. In addition ‘‘double oedometer’’ ASTM D5333,
Consolidation Pressure kN/m2
0.5 0.01
Figure 5.
0.1
1
10
100
1000
Consolidation testing.
Collapse Potential of Soils tests were carried. One subsample was tested at natural moisture content and a second sub-sample tested in the fully saturated condition. Swell was measured in a number of ways; free swell was considered the most appropriate with a nominal load in the oedometer. A typical set of curves are shown in Figure 5 where it can be seen that the differentiation into swelling soils and collapsible soils is a function of the stress history of the soil and not a fundamental property of the soil. This difference in interpretation is important when deciding how to prepare the site and design the foundations. Soil suction was not measured in either set of tests since at the time of testing this possibility was not available in the local testing laboratory.
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this site was about 6 m below ground level adjacent to stream courses and at least 25 m below ground level elsewhere. Construction activities can destroy this very delicate environment. Rainfall is captured on roofs and paved areas during the summer and discharged directly into the ground. Roads, construction areas, and compounds are covered with impermeable layers, ditches and pipelines are excavated, all of which change the ground water regime. The effect of covering the ground with an impermeable layer, thereby preventing evaporation and increasing the soil moisture, can be easily overlooked. Any change in the soil moisture content has the potential to cause swelling or collapse.
100.0
Gravel
Sand
Cone Resistance (MPa)
Sandy CLAY CLAY 10.0
1.0
Dry Site Saturated Site 0.1 0.0
Figure 6. soils.
2.0
4.0 Friction Ratio%
6.0
8.0
10.0
4
CPT Interpretation test showing effect of dry
The CPT testing revealed an important consideration when interpretation charts for determining soil properties were used. When plotted on a typical soil classification chart for interpretation of cone tests, it was found that the unsaturated soils plotted outside conventional boundaries for silty soils, with higher friction ratios than may be considered ‘‘normal’’ (Fig. 6). This was compared with tests in the same materials but from a saturated part of the site where the water table was within 3 m of the surface and the results plotted in the expected area on the chart.
3
DEMONSTRATION OF SOIL BEHAVIOUR
Explaining the behavior of these soils to other engineers and project managers who had no or limited experience of these soils required some ingenuity as the dense hard soil, in both its natural state and when compacted dry of optimum, looked to be an excellent material on which to build. However by taking a sample of this material, placing it in a clear beaker (Fig. 7) and adding water demonstrated the problem in a spectacular manner as the soil fizzes and collapsed rapidly to a heap of wet silt (Fig. 8). Whilst most silt soils
SWELLING AND COLLAPSE PROPERTIES
In order to develop the foundation design it was necessary to understand not only the test results but also the mechanisms at work and how the soils behave. Soils in the steppe lands, despite significant precipitation, remain dry. This is due to the fact that during the winter the surface freezes, preventing any ingress of moisture and the snow melt occurs before the surface thaws. None of the snow melt is therefore available to infiltrate the ground, other than in water courses. In the summer the ground reaches temperatures in excess of 50 degrees and any precipitation will immediately evaporate. It is therefore only at very limited times in autumn and spring when there is any possibility of infiltration. Cultivation in the steppes relies on catching the winter snow melt in farm dams constructed across streams and then using this water during the summer for irrigation. In addition wells are sunk adjacent to rivers and streams to extract ground water which in the case of
Figure 7.
Initial sample on immersion in water.
Figure 8.
Sample after 45 seconds of immersion.
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demonstrate collapse in water, the reaction with loess soils is dramatic. This demonstration was sufficient to convince most field engineers that these were special materials.
Bearing capacity kN/m2
5
7000
DESIGN OF FOUNDATIONS
The test results showed that the collapsible soils at this site were considered to be Type 1 according to SNiP 2.02.01_87 Foundation Beds. The SNiP gave the following alternative remedial measures to alleviate the problems associated with this type of soil: – Eliminate the subsiding properties of the soil – Deep foundations/piles that extend below the problem soil – A set of measures which partially eliminate the settling properties using waterproofing and structural measures. It was proposed that option 1 should be adopted for this site to provide a uniform platform for construction of a wide range of light to medium loaded structures that are normally associated with petrochemical plant. The preferred solution was to excavate the soil to the depth influenced by the shallow foundations and to recompact at appropriate moisture content to achieve a higher density which eliminated the settling properties. This solution was determined through a consideration of cost, availability of plant and equipment and local capabilities. The soils were to be compacted to a minimum density of 17 kN/m3 and at moisture contents between
9.0
Length of footing m
8.0 7.0 6.0 5.0 4.0 3.0 2.0 1.0 1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
9.0
10.0
Width of footing m
Figure 9.
Design chart showing allowable settlements.
5000 4000 3000 2000 1000 0 0
20 10 40 30 Angle of Internal friction (phi)
50
Figure 10. Comparison of bearing capacity factors for a 2 m wide footing showing effect of angle of friction.
0 and 2% wet of optimum. Compaction dry of optimum was not recommended in these soils. Raft, strip and pad foundations were then designed on these recompacted soils. By calculation bearing capacity of these soils was very high. Safe allowable bearing pressures were determined by settlement criteria. Design charts for different size footings were prepared, an example is given in Figure 9. The design charts satisfy both local and conventional BS/ASTM design. A comparison of computed bearing capacity using Terzaghi, Brinch Hansen and SNiP is shown in Figure 10. Large diameter bored piles were used for very heavily loaded foundations.
6 10.0
Brinch Hansen SNiP Terzaghi
6000
CONSTRUCTION
Compaction of the soils was the first requirement. This involved the excavation and recompaction of two metres of soil from underneath the foundations, soil below the water table was not affected. An increase in density to this depth was deemed adequate to prevent collapse of surface soils. The consequent increase the soil modulus also produced positive effects on settlement performance for large surface foundations, such as tank foundations. There is a tendency in the field to compact these soils dry with very little water as they compact to a very hard material. This is easily achieved with a sheepsfoot roller. However when wetted the compacted material absorbs water rapidly and turns to a ‘‘soup’’. The correct alternative is to compact the materials wet of optimum, thereby producing an apparently softer but stable material which is not affected by change in moisture content. Excavation for footings revealed the re-compacted material to be stable, uniform and ideal foundation stratum.
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7
REFERENCES
CONCLUDING REMARKS
The project was an interesting exercise in bring together different philosophies and methodologies for dealing with potential problematical fine grained loess soils. The following were among the lessons learned: – When dealing with specialist soil types an understanding of local practices is essential. – A comparison of test results obtained using local techniques with those obtained using familiar practice is essential to provide confidence in local methods and to identify anomalies. – It is necessary to understand all aspects of the soil behaviour before determining a solution. – It is necessary to use correct parameters in empirical equations, do not mix and match from one system to another. – Simple solutions, easily understood, easily amended and verified are the best. – Local available construction techniques are a driver in the determination of any foundation solution. – Change happens on large projects, the solution should accommodate change.
BS 1377 1990. Methods of test for Soils for Civil Engineering purposes British Standards Institution, London BS 5930 1999. Code of Practice for Site Investigations British Standards Institution, London GOST 22733-77 Soils. Laboratory method for determination of maximum density. USSR State Committee for Construction Matters GOST 23161-78 Soils. Laboratory method for determination of subsiding characteristics. USSR State Committee for Construction Matters SNiP 2.02.01-87. Foundation Beds, USSR State Committee for Construction Matters SNiP 3.02.01-87. Earth Structures, Foundation Beds and Foundations. USSR State Committee for Construction Matters ASTM D5333-03. Collapse Potential of Soils, American Society For Testing And Materials GOST 5180-84. USSR State Committee for Construction Matters
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Negative skin friction for cast-in-place piles in thick collapsible loess Z.H. Chen Logistic Engineering University of PLA, Chongqing, China
X.F. Huang Logistic Engineering University of PLA, Chongqing, China Lanzhou Science & Technology University, Lanzhou, China
B. Qin, X.W. Fang & J.F. Guo Logistic Engineering University of PLA, Chongqing, China
ABSTRACT: Large-scale field tests were performed on cast-in-place piles installed in self-weight collapsible loess with a thickness of over 35 m. The pile diameter was 0.8 m and the pile length was 40 m. The piles were constructed in a water immersion pit of 30 m diameter. Two types of piles were tested; a frictional end bearing pile and a suspension pile. Two kinds of measuring methods were adopted; a steel bar stress gauge and a slippage measurement micro-gauge. The results indicate that when the suspension pile is much shorter than the thickness of the collapsible loess layer, the measured negative frictional resistance values are small. However, the results obtained for the frictional end bearing pile penetrating through the whole collapsible loess layer are more appropriate for the real situation. The real measured negative resistance is far higher than the negative resistance values suggested by the loess codes. The values of negative frictional resistance have no apparent corresponding relationship with the form or magnitude of loess collapse at the site. Analysis of the test data from in-situ pile tests from several large-scale engineering projects shows that the neutral point positions exceed the reference ranges provided by the technical specifications. As a result, this research project can provide an important reference for the design of future similar piles and modification of the loess codes.
1
INTRODUCTION
The pile stressing mechanism and negative skin friction in collapsible loess are important problems of pile design in collapsible regions (Qian et al. 1985, Liu 1997, Liu 1990, Wang & Ming 2001). For this reason, many scholars have devoted great efforts to this (Wang & Ming 2001, Liu et al. 2002, Li 1994, Liu 1999). The research methods they have adopted are mainly in-situ immersion tests in such a way that the pile bearing force and negative frictional resistance can be directly obtained, with comparatively high accuracy and reliability. However, the method has high costs and involves a great deal of time, so there is little test data or information. The data listed in Table 1 are the basic data obtained from in-situ immersion tests of cast-in-place piles conducted within China since the 1980s. In the national key engineering construction project of pumping water from the Yellow River to help the poverty-stricken people in Ningxia, most engineering works such as pumping stations and aqueducts
are located in self-weight collapsible loess regions where the thickness of the loess layer can be over 60 m (and the thickness of self-weight collapsible loess layer of 20–35 m. Since in the past we never met with a loess site with self-weight collapsibility having such a large thickness, we lack knowledge of the pile force transmission mechanism, the magnitude of negative frictional resistance and the positions of neutral points. We also lack experience in the corresponding pile design; the bearing forces suggested by different designers are far from each other, to the extent that it is difficult to reach a common understanding. For this reason, the headquarters of the construction project of pumping water from the Yellow River have organized meetings with design institutes, scientific research institutes and their counterparts to discuss and study the problems. They finally decided to carry out testing work on the piles in the natural and immersed states at the work-site of No.11 pumping station. The testing work-site is located in Guyuan county of Ningxia, where the thickness of loess layer is over
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Table 1.
Test data of cast-in-place pile in loess.
Test location Lanzhou Donggang Lanzhou Hekou Puchen Power Plant Baoji 2nd Power Plant Ningxia Yanghuang
Table 2.
Thickness of self-weight Collapse low collapse loess limit depth Collapse Time m m grade
40
0.8
10
40
15
Self-wt Grade III Diameter 12 Self-wt Grade III Diameter 15
45
1.0
15
55
35
Non-self-wt Diameter 40
40
1.0
40
6.3
1993 18.2
20
95
0.8
22.85
8.5
2001 35
35
Self-wt 50 × 30 Self-wt Grade IV Diameter 30
68
0.8
40
1987 12
12
1988 15 1991
0
48.5
Design parameter and measurement for testing piles in Ningxia.
Pile number
Pile length m
Pile diameter m
Concrete strength
ZH4
40
0.8
C30
ZH5
20
0.8
C30
Setting feature and testing items Frictional end bearing pile, test the inner force in pile body, positive and negative frictional resistance in the case of immersion and saturated states Suspended pile, test the negative resistance
60 m and the thickness of the self-weight collapsible loess layer is about 35 m. Two groups of pile types were set up for the testing work. Two kinds of measurement methods were adopted. The diameter of the immersion pit was 30 m, with total water consumption of 31275 m3 . Immersion observation lasted for 56 days. After stopping the water, the observation continued for 12 more days. The range of surface settlement of the land outside of the pit was 30–35 m, being close to the thickness of the self-weight collapsible loess at the work-site. Accordingly, this research has accumulated valuable data and experience for pile designs in large thicknesses of self-weight collapsible loess. This paper introduces the related research achievements.
2
Immersion pit Immerse Pile Maximum Test pit dimension time diameter pile length collapse m d m m cm
GENERAL CONDITIONS IN TEST
2.1 Testing pile layout and instruments buried Piles constructed for this test all used dry operations with holes dug by man power and filled with concrete to form the piles. Based on the test requirements, two testing piles were arranged, numbered ZH4 and ZH5. There were 4 anchor piles using piles with expanded bases; the expanded base diameter was 1.6 m; and the height of the expanded section was 1.7 m. The 2 anchor piles used in ZH4 were 30 m long and the
2 anchor piles used in ZH5 were 40 m long. The sizes of each testing pile and the main measurement items are listed in Table 2. Testing pile ZH4 was a frictional end bearing pile, which was used to study the pile body axial force, side resistance and the negative and positive frictional resistance. A steel bar stress gauge was set up on the pile body with the spacing between the testing or measuring points being 1.5 m. Meanwhile, a slippage micrometer was set up with the spacing between testing points being 1.0 m to carry out parallel tests. The set-up of steel bar stress gauge and slippage micrometer is shown in Figure 1. ZH5 is called a ‘‘suspended pile’’ as the pile length was less than the thickness of the self-weight collapsible loess, being used to test or measure the average negative frictional resistance after immersion. It should be pointed out that the setup method for ZH5 was different from the usual method. The usual approach is to place the pile end of the testing pile on the non-collapsible loess layer (Qian et al. 1985); the pile body cannot settle in the course of immersion. However, the length of ZH5 was 20 m; the pile top was fixed; and the pile body was suspended under its self-weight. The pile body could not settle in the course of immersion, but the pile length was shortened by over 10 m in such a way that the cost can be saved. The disadvantage was the difficulty in obtaining the neutral point.
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Table 3.
Immersion settlement of observation and measurement point in different depths.
Depth mark point no. Buried depth/m Immersion settlement/cm
A1 2.5 48.5
A2 5 31.9
A3 10 17.1
The testing pit diameter was 30 m and pit depth was 0.5–1.2 m. In order to ensure the pile side negative frictional resistance was brought fully into play after the testing pit was immersed, a small pit with the diameter of 5 m and the depth of 1.5 m was arranged in the middle of the testing pit in which testing pile ZH4 was laid out. In order to measure the collapsible deformation of the inside and outside ground surface of the pit and the stratification in the soil after immersion, 19 points were set up for observing and measuring the ground surface settlement within the testing pit; 6 mechanical points were set up for observing and measuring the stratified settlement in the soil, and 28 points for observing and measuring the ground surface settlement were established outside of the pit. The settlement observation and measuring points were set up on testing piles ZH4, ZH5 and the 2 anchor piles of ZH5. The points for observing and measuring mechanical stratified settlement and the results of immersion deformation are shown in Table 3.
2.2
3.1
A5 25 3.0
A6 35 1.3
Figure 1. Arrangement of steel bar meter and slippage micrometer.
Methods for testing inner force of pile body
In this test, two kinds of methods were used to measure force within the pile body. The testing pile should be viewed as the elastic body. A steel bar gauge and slippage micrometer were used to test and measure the vertical strain in the steel bar and the pile body strain so as to further deduce the pile body axial force and pile side frictional resistance. The buried type of steel bar stress meter was installed on cross sections at different locations of the base pile main steel bars in symmetry (Fig. 1). The slippage micrometer was made in Sweden.
3
A4 15 8.0
PILE BODY AXIAL FORCE TRANSMISSION FEATURES AND NEGATIVE FRICTIONAL RESISTANCE VARIATIONS DURING THE IMMERSION AND UNDER SATURATED STATE
Figure 2.
Q-s curve in immersion process of pile ZH4.
the design loading of 1600 kN, the amount of settlement was 1.0 mm. During immersion when the loading was maintained at the design load of 1600 kN, the amount of collapse settlement was 17.0 mm. Under the saturated state when the maximum loading reached 5200 kN, the final amount of settlement was over 66 mm. When the loading reached 4000 kN the total amount of settlement was 31 mm. Based on analysis of Figure 2, the starting point of an obvious steep decline corresponds with a load of 4000 kN.
3.2 Evolution features of pile body axial force transmission and negative frictional resistance during immersion
Single pile limited bearing force during the immersion and under saturated state
Measured axial load–settlement [Q-s] curves of the testing pile ZH4 are shown in Figure 2. Under the natural state, when the pile top loading increased to
In the natural state, the top vertical loading on testing pile ZH4 increased to 1600 kN. During immersion and when saturated (for 62 days), the constant loading (1600 kN) was maintained. Accordingly, the curves of the distributions of measured axial force and frictional resistance are shown in Figures 3–4. With an
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Figure 3.
of immersion to occur and progress from the upper to the lower. This process also involves the positive frictional resistance diminishing and disappearing. Under the action of negative frictional resistance, the axial force of each cross section has undergone sharp increases and slow growth, and then tends to an almost constant value. 3. After the immersion is stopped, the consolidation deformation of the soil around the piles occurs so that the pile side frictional resistance grows rapidly; and the neutral point moves downwards rapidly. After immersion has stopped for 12d, the negative frictional maximum value is 33.1 kPa; and the corresponding neutral point located in the 10 m depth is located at 19 m depth. (Fig. 4) 4. When loading is continued in the saturated state, the negative frictional resistance gradually diminishes and disappears with an increase in loading, whose neutral point gradually moves upwards (Fig. 5).
Axial force of testing pile ZH4.
3.3
Figure 4. Frictional resistance of testing pile ZH4 in immersion and saturated state.
increase in the immersion time, collapsible deformation occurs in the soil surrounding the pile so that the positive frictional resistance in the upper part soil body decreases, tending to convert into negative frictional resistance gradually. However, the positive frictional resistance in the lower part of the soil body gradually increases. When the immersion is in the 15th day, the pile side produces negative frictional resistance, thereby forming the downward pulling loading. The evolution of negative frictional resistance is featured by the following: 1. With an increase in the immersion time, the negative frictional resistance increases sharply first and grows slowly, and then tends to become a certain constant value; the neutral point gradually moves downward with an increase in the negative resistance (Fig. 4). When the immersion is for 56d, the maximum value of the negative frictional resistance is 14.8 kPa; and the neutral point is located at the depth of 17 m. 2. The development of negative frictional resistance along the pile body requires prolonged continuation
Pile top loading ratio shared by pile side frictional resistance and end resistance
When testing the ZH4 pile in the saturated state, the contributions from frictional resistance, end resistance and pile top loading are shown in Figure 6. When the pile top loading is 1500 kN, the pile side frictional resistance bears all the loading, and the pile end is basically not subject to any force. When the pile loading exceeds 1500 kN, the pile end begins to be subject to force. When the pile top loading is 4000 kN (limited loading) or so, the frictional resistance and end resistance are brought into full play so that the distribution ratio between the frictional resistance and end resistance is 3:1. When the pile loading increases to 5400 kN, the pile top displacement increases sharply
Figure 5. Frictional resistance of testing pile ZH4 under loading in a saturated state.
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pile top loading was increased to 4000 kN, obvious inflection points appear; when loading continues to increase, the steep decline occurs so that the pile top settlement increases sharply to cause shear damages between the pile and pile side earth, while the pile body concrete elastic compression deformation curves appear to be in linear state, and no damage happened to the pile body concrete. Figure 6. Frictional resistance, end resistance against pile top loading for the testing pile ZH4.
Figure 7. Pile top settlement, pile body elastic deformation against loading for the testing pile ZH4.
in such a way that shear failure occurs between the pile and pile side soil. In this way, the pile side resistance decreases; and the pile end becomes subject to force increases. It is just at this time that the distribution ratio distribution between frictional resistance and end frictional resistance is close to 2:1. Accordingly, for the saturated state, frictional resistance apparently decreases; and the pile end becomes subject to relative force increases. 3.4
Relations among pile top settlement, pile body elastic compression deformation and loading
Curves of relations between pile top settlement, pile body elastic compression deformation and loading are shown in Figure 7. In the natural state, when the pile top loading increases to 1600 kN, the amount of pile top settlement is basically in agreement with total deformation of the pile body concrete elastic compression. It is at this time that the pile top steady pressure (loading 1600 kN) is held during immersion while waiting until the self-weight collapsible deformation of the soil body remained steady. The pile top additional deformation produced by the action of the negative frictional resistance was 17 mm, while the pile body elastic compression deformation was 4 mm so that the two curves begin to separate. When the soil body reached a completely saturated state, and the
3.5
Determination of neutral point position
When pile length passes below the lower limiting depth of self-weight collapsibility, and the pile end reaches a hard layer, the pile soil relative displacement at a certain depth will be as zero, that is, there is neither positive frictional resistance nor negative frictional resistance. As a result, this point is called the neutral point. The pile body axial force on the neutral point cross section is the maximum. (Fig. 3) Generally speaking, during immersion, the downward displacement of the soil layer is larger than the downward displacement of the pile. The neutral point moves downwards as soil displaces downwards. When the settlement of soil layer around the pile tends to be stable, the neutral point is also stabilized at a certain depth (Ln). After this test was immersed for 65 days, the stability depth (Ln) of neutral point was 19 m (Figs. 3–4). The lower limiting depth (Lo) of collapsible loess layer in this case was 35 m. The ratio between the neutral point depth and the lower limiting depth of collapsible loess layer is 0.54.
4 4.1
RESULTS OF NEGATIVE FRICTIONAL RESISTANCE AND THEIR ANALYSIS Testing results of suspended pile ZH5
The suspension method is the earliest method used to measure the negative frictional resistance. This method can only be used to measure the average negative frictional resistance of the pile side and not to measure the negative frictional resistance distributed along the pile body, the immersion time relation and the neutral point positions, etc. The method uses two supporting piles to support a steel beam. The testing piles are suspended from the steel beam (the supporting pile and steel beam do not deform) with a dynamometer installed. The varying curves of negative frictional resistance of the pile side unit area are shown in Figure 8 (notes: solid line is the immersion time; the dotted line indicates the time of water stoppage). During the immersion, with the development of the self-weight collapse in the loess around the pile, the pile side negative frictional resistance can become from nothing to a small value and from a small value to larger values. When the immersion lasted for
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56d, the data obtained from the dynamometer indicate that total amount of pile side negative frictional resistance was 300 kN, from which it is calculated that the average value of negative frictional resistance on the pile side unit area was 5 kPa. After the end of immersion, the drainage consolidation variation occurred in the pile side soil because of water dispersion. As a result, the pile side negative frictional resistance grew rapidly and reached a maximum value 1110 kN in the 7th day after the water stoppage, from which it can be calculated that the average value of negative frictional resistance on the pile side unit area was 22 kPa.
Figure 8. Average negative frictional resistance measured from pile ZH5. Table 4.
4.2 Analysis of testing data of negative frictional resistance of cast-in-place piles in loess In this paper, two kinds of methods were used to measure the results of negative frictional resistance and the in-situ immersed testing data of the cast-in-place piles in loess at several locations as well as the negative frictional resistance data recommended by the Code for building construction in collapsible regions, being listed in Table 4. It is worth paying more attention to the following 4 points: 1. It can be seen from the comparison of testing results measured by the two methods that the numerical values measured by the suspension method are liable to be small. The main reason is probably that the testing time of the suspended pile is so short that the collapsibility conditions of self-weight collapsible loess layer can not be fully reflected. In addition, the rigidity of the steel beam itself is used to fix suspended piles so that the steel beam is bound to produce the slight disturbance, whereby the measured and tested results of negative frictional resistance are affected. 2. The numerical values of negative frictional resistance obtained from tests in different regions are greatly different from each other and rather dispersed so that it is hard to obtain any laws, however the negative frictional resistance values measured at each different work-site are all higher than those
Negative frictional resistance of filling piles in loess. Negative friction/kPa
Testing place
Testing state
Maximum
Gansu Dongguang Gansu Hekou Puchen Power Plant
Suspension consolidation Constant loading consolidation Constant loading consolidation No-loading consolidation Baoji 2nd power Plant In immersion Consolidation period 2004 recommended values by code for building construction in collapsible loess regions Ningxia Yanghuang ZH4 consolidation Ningxia Yanghuang ZH5 consolidation
28 52.3 57.6
Average
Neutral point position LN /LO
18 20 27 44 35.7 30.4
0.34 ∼ 0.50 0.60 ∼ 0.71 0.85 0.85
10/15∗ 33.1 22
0.54
∗ Suggestions
by Code for building construction in collapsible loess regions: When the calculated values of self-weight collapsible amount is 70–200 mm, the pile side average negative frictional resistance feature values of the filling piles can take 10 kPa, but when over 200 mm, 15 kPa can be taken. Table 5.
Immersed settlement of points labeled and data for settlement of large pre-immersion area.
Testing point settlement/cm A1
B15
B15
B17
C1–7
C2–7
C3–7
C4–7
Pre-immersion
48.5
39.9
43.9
40.0
0.5
0.2
0.5
0.1
215.1
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values suggested by the Loess Specifications (See note in Table 4). The suggestions of the Code for Building Construction in Collapsible Regions are based on pile test results in 3 locations at Xi’an, Lanzhou and Qinghai in the 1970s, where the thickness of self-weight collapsible loess layer in these three locations was small (8–11 m), the pile length was shorter; and the negative frictional resistance was measured by the suspension method, which is no longer popular. 3. It can be seen from the integration of Table 1 and Table 4 that the numerical values of negative frictional resistance are not certain to rise with an increase in the amount of collapsibility and have no apparent relation with the collapsible types of the work-sites. For instance, the testing work-site of Pucheng Coal-Fired Power plant falls into the non-self-weight collapsible loess work-site, and the amount of collapsibility of the immersed testing pit is 6.3 cm; the testing work-site of Baoji Second Coal-Fired Power plant falls into the self-weight collapsible loess work-site, and an amount of collapsibility of the immersed testing pit is 8.5 cm. Though the amount of collapsibility is far less than that in Lanzhou Donggang and Lanzhou Hekou, the negative frictional resistance is much higher than that in the above two work-sites of Lanzhou, where there is self-weight collapsible loess. It can be seen from this that in the Code for Building Construction in Collapsible Loess Regions, the suggestions that the frictional resistance of greater self-weight collapsible loess take higher value are worth further discussion (with the reference to Note in Table 4). 4. Neutral point positions obtained from the tests at different work-sites or sites are of great dispersions from 0.34 to 0.85, which is beyond the range of reference values set in Technical Code for Building Pile Foundation (i.e. 0.55–0.66). 5
CONCLUSIONS
1. In a saturated state, the limited bearing force on a single pile is less than half that in the natural state, being only 4000 kN; the negative frictional resistance is 33 kPa. 2. When the length of the suspension pile is much smaller than the thickness of collapsible loess, the negative frictional resistance measured can not reflect the deformation states of collapsible loess
and the pile interactions, with their numerical values being small. Accordingly, the results measured by the frictional end bearing test pile penetrating through the complete collapsible layer represent practical conditions. 3. The negative resistance and neutral point positions and immersion process are closely related to the settlement in the process of consolidation. The variation in numerical values is large. Accordingly, based the existing data, it is difficult to obtain some related laws. 4. The neutral point positions of cast-in-place piles in several large–sized engineering project via the insitu tests and measurement are beyond the reference values provided by Technical Code for Building Pile Foundation. The real measured negative frictional resistance is far higher than the negative frictional resistance value suggested by the Code for Building Construction in Collapsible Loess Regions; and the numerical values of negative frictional resistance have had no apparent corresponding relation with the collapsibility types and the magnitudes of collapsibility at the sites. Accordingly, the negative frictional resistance in the nonself-weight collapsible loess work-site cannot be ignored completely.
REFERENCES Li Dazhan, Teng Yanjing, He Yihua, Sui Guoxiu. 1994. Vertical bearing behaviour of large diameter belled pile in collapse loess. Chinese Journal of Geotechnical Engineering 16(2): 11–21. Liu Jinli. 1990. Design and calculation of pile foundations. Beijing: China Architecture and Building Press. Liu Limin, Shu Xiang, Xing Juhua. 2002. Theory advances and engineering practice of pile foundations. Beijing: China Architectural Material Press. Liu Mingzhen. 1999. A calculation method of negative skin friction on the pile group in the self-weight collapsible loess stratum. Chinese Journal of Geotechnical Engineering 21(6): 749–752. Liu Zudian. 1997. Mechanics and engineering of loess. Shaan-xi: Science and Technology Press. Qian Hongjing, Luo Yusheng et al. 1985. Collapsed loess foundation. Beijing: China Architecture and Building Press. Wang Guolie, Ming Wenshan. 2001. Immersion deformation of collapse loess and Engineering technologies. Research and Engineering of Collapsed Loess. Beijing: China Architecture and Building Press.
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Unsaturated Soils: Advances in Geo-Engineering – Toll et al. (eds) © 2008 Taylor & Francis Group, London, ISBN 978-0-415-47692-8
Author index
Abbo, A.J. 705 Abdallah, A. 847 Addenbrooke, T.I. 773 Agus, S.S. 305 Air`o Farulla, C. 321 Ali, N. 811 Ali Rahman, Z. 435 Al-Najjar, M.M. 873 Alonso, E.E. 3, 341, 487 Amraoui, N. 959 Anderson, M.G. 675 Arduino, P. 721 Arson, C. 695 Ashayeri, I. 235, 355 Augarde, C.E. 145, 213, 219, 417, 765 Azari, B. 791 Bardanis, M.E. 263, 381, 589 Barnel, N. 369 Becker, R. 181, 189 Bieberstein, A. 189 Biglari, M. 235, 355 Bilotta, E. 349 Bilsel, H. 335 Blatz, J.A. 855 Blight, G.E. 883, 889, 895 Brown, J.L. 361 Caicedo, B. 117, 135 Cardoso, R. 487 Casini, F. 609 Cecconi, M. 271 Chai, H.Y. 647 Chao, K.C. 243, 389 Charlier, R. 459, 779 Chen, Z.H. 979 Cherubini, Claudia 761 Cheuk, C.Y. 835 Collin, F. 633, 779 Colmenares, J.E. 511 Congreve, A. 145 Costa, S. 159 Crouch, R.S. 727 Cui, Y.J. 229, 249, 369, 647 Cui, Y.-J. 625
Cuisinier, O. 327 Cumbers, J.M. 243, 389 Datcheva, M. 797 Davies, O.C. 817 de Campos, T.M.P. 747 De Gennaro, V. 123, 151, 283, 633, 713, 841 De Vos, M. 459 Delage, P. 33, 229, 249, 283, 633 Delalain, P. 151 Delaure, E. 123 Deneele, D. 327 Desideri, A. 609 Dewoolkar, M.M. 97 Dodagoudar, G.R. 861 d’Onofrio, A. 531 D’Onza, F. 531 Duffy, W.P. 973 Dye, H.B. 805 Dyer, M. 465 Ebrahimi-Birang, N. 129 El Youssoufi, M.S. 683 Elkassas, A.S.I. 755 Estabragh, A.R. 449, 575 Evangelista, A. 909, 917 Evans, F.D. 145, 213 Fang, X.W. 979 Feng, H. 735 Feret, M.J. 959 Firgi, T. 299 Foresta, V. 349 François, B. 63, 539 Fredlund, D.G. 129, 375 Gallipoli, D. 145, 213, 219, 435, 727, 765 Gatmiri, B. 453, 695, 785, 791, 841 Gavin, K. 823 Gens, A. 53, 229, 547, 667 George, L.A. 97 Georgiadis, K. 581 Gerard, P. 779
987
Ghezzehei, T.A. 761 Giordano, G. 205 Glendinning, S. 817 Gómez-Espina, R. 257, 667 Grove, S.M. 675 Guimarães, L. do N. 53 Guo, J.F. 979 Haghighi, A. 841 Hamid, T.B. 429 He, Y.X. 953 Hemmati, S. 785, 791 Hoffmann, C. 291, 967 Hofmann, M. 597 Hofstetter, G. 597 Houston, S.L. 805 Houston, W.N. 805 Hoyos, L.R. 83, 721 Hu, L.B. 653 Huang, X.F. 979 Huebner, C. 181, 189 Hueckel, T. 653 Imre, E. 299 Iravanian, A. 335 Jaquin, P.A. 417 Javadi, A.A. 449, 575, 755, 873 Jommi, C. 617 Jotisankasa, A. 901 Karam, J.P. 647 Karstunen, M. 567 Karthikeyan, M. 829 Kavvadas, M.J. 263, 381, 589 Kenny, M. 465 Khalili, N. 659 Khire, M.V. 867 Khoury, C.N. 141 Kimoto, S. 735 Ko, H.-Y. 495 Kodaka, T. 735 Kodikara, J. 159, 375 Kohler, R. 597 Koliji, A. 63, 641
Kulsawan, B. 901 Kurucuk, N. 375
Noyer, M.L. 959 Nuth, M. 63, 559
Laikram, A. 83 Lakshmikantha, M.R. 405 Laloui, L. 63, 539, 559, 641, 653 Laufer, I. 299 Le, T.T. 229 Ledesma, A. 405 Legrand, L. 417 Li, X.L. 229 Lima, A. 229, 519 Liu, J.K. 471 Lloret, A. 667 Lloret, M. 567 Lourenço, S.D.N. 145, 213 Lutenegger, A.J. 411
Oh, W.T. 441, 503 Oka, F. 735 Oldecop, L. 925 Overton, D.D. 243, 389
Machard de Gramont, H. 959 Maertens, J. 459 Mancuso, C. 103, 205, 531, 609 Marcial, D. 249 Mašín, D. 659 Masrouri, F. 847 Massoudi, N. 495 Mayor, P.A. 947 McCartney, J. 173 McCloskey, G. 465 Meca, T. 423 Medero, G.M. 213 Medina, C. 743 Mendes, J. 219 Merchán, V. 423 Migliaro, G. 349 Miller, G.A. 141 Mirzaii, A. 453 Moncada, M.P.H. 747 Mongiovì, L. 89 Monroy, R. 315 Montrasio, L. 933 Mrad, M. 847 Mu˜noz, J.J. 123 Mukherjee, M. 867 Murillo, C. 135 Murray, B.J. 553 Murray, E.J. 553 Nelson, J.D. 243, 389 Ng, C.W.W. 481, 525 Nguyen, H.D. 151, 283 Nicotera, M.V. 909, 917 Nishimura, T. 441 Nowamooz, H. 847
Pacheco, R.R. 925 Pagano, L. 111, 205 Papa, R. 909, 917 Passeggio, G. 205 Pedroso, D. 705 Peng, L.Y. 471 Pereira, J.M. 647 Peron, H. 63, 653 Phoon, K.K. 829 Pineda, J.A. 511, 519 Pinyol, N.M. 3 Potts, D.M. 581, 773 Pozzato, A. 165, 173 Prat, P.C. 405 Praveen Kumar, R. 861 Priol, G. 633 Puppala, A.J. 83, 503 Qin, B. 979 Rahardjo, H. 901 Rajkai, K. 299 Ramon, A. 341 Rao, B.N. 861 Rees, S.W. 811 Ridley, A. 315 Robelin, C. 959 Rojas, J.C. 103, 205 Romero, E. 33, 229, 423, 519, 617 Romero, E.E. 341, 511 Rouainia, M. 817 Rubin, A. 411 Russo, G. 271, 277 Saix, C. 683 Salager, S. 683 Salinas, L.M. 475 Samarasekera, L. 129 Samat, S. 547 Sanchez, M. 465, 567, 667 Sánchez, M. 53 Schanz, T. 305, 797 Scheuermann, A. 181, 189, 197, 299 Schlaeger, S. 181, 189 Semprich, S. 747 Shafiee, A. 235, 355
988
Sheng, D. 53 Sheng, D.C. 705 Siemens, G.A. 855 Sivakumar, V. 361, 553 Smart, T. 145 Smith, P.G. 773 Solowski, W.T. 727 Sorgi, C. 151, 283 Springman, S.M. 941, 947 Steger, G. 747 Stropeit, K. 625 Sture, S. 495 Su, G.W. 761 Sultan, N. 841 Suzuki, H. 735 Ta, A.N. 647 Tamagnini, R. 713 Tang, A.M. 229, 369 Tapia, J. 405 Tarantino, A. 33, 89, 165, 173, 291, 603, 967 Tedesco, D.V. 277 Telekes, G. 299 Teysseire, P. 947 Tham, L.G. 835 Thielen, A. 941 Thusyanthan, N.I. 159 To, E.C.Y. 835 Toll, D.G. 145, 213, 219, 435, 829, 901 Tombolato, S. 89, 603 Tomboy, O. 459 Toyota, H. 441 Triantafyllidis, Th. 189 Tristancho, J. 117 Tse, E.Y.M. 481 Ulloa, J.C. 135 Urciuoli, G. 909, 917 Valentino, R. 933 Vanapalli, S.K. 441, 503 Vargas Jr., E. 747 Vasquez, J.V. 475 Vassallo, R. 609 Vaunat, J. 423, 547 Verbrugge, J.-C. 459
Villar, M.V. 257, 667 Vinale, F. 103, 111 Vulliet, L. 641 Wagner, N. 181, 189 Walthall, S. 973 Wang, Y. 675 Wei, C. 97 Wheeler, S. 567 Wheeler, S.J. 625 Whenham, V. 459
Wu, G. 675 Wuilleumier, A. 959 Xu, J. 525 Xue, J.F. 823 Yang, H.P. 397, 953 Yasrebi, S.S. 453 Yung, S.Y. 525 Zandarín, M.T. 925
989
Zdravkovic, L. 315, 581 Zeghal, M. 743 Zhang, R. 397 Zhang, Y. 765 Zheng, J.L. 397, 953 Zhou, J. 689 Zhou, Y.D. 835 Zimmerer, M. 797 Zingariello, M.C. 111, 205 Zornberg, J. 173
