Laboratory Shear Strength of Soil-STP 740

LABORATORY SHEAR STRENGTH OF SOIL A symposium sponsored by ASTM Committee D-18 on Soil and Rock for Engineering Purposes AMERICAN SOCIETY FOR TESTING AND MATERIALS Chicago, III., 25 June 1980 ASTM SPECIAL TECHNICAL PUBLICATION 740 R. N. Yong, McGill University, and F. C. Townsend, University of Florida, editors ASTM Publication Code Number (PCN) 04-740000-38

m

AMERICAN SOCIETY FOR TESTING AND MATERIALS 1916 Race Street, Philadelphia, Pa. 19103

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Copyright© by AMERICAN SOCIETY FOR TESTING AND MATERIALS 1981 Library of Congress Catalog Card Number: 80-71002

NOTE The Society is not responsible, as a body, for the statements and opinions advanced in this publication.

Printed in Baltimore, Md. September 1981

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Foreword The symposium on Laboratory Shear Strength of Soil was held in Chicago, 111., on 25 June 1980. The symposium was sponsored by the American Society for Testing and Materials through its Committee D-18 on Soil and Rock for Engineering Purposes. R. N. Yong, McGill University, and F. C. Townsend, University of Florida, presided as symposium chairmen and served as editors of this publication.

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Related ASTM Publications Behavior of Deep Foundations, STP 670 (1979), $49.50, 04-670000-38 Dynamic Geotechnical Testing, STP 654 (1978), $34.50, 04-654000-38 Dispersive Clays, Related Piping, and Erosion in Geotechnical Projects, STP 623 (1977), $40.75, 04-623000-38 Soil Specimen Preparation for Laboratory Testing, STP 599 (1976), $35.00, 04-599000-38 Field Testing and Instrumentation of Rock, STP 554 (1974), $18.75, 04-554000-38 Concrete Pipe and the Soil Structure System, STP 630 (1977), $14.00, 04-630000-07 Performance Monitoring for Geotechnical Construction, STP 584 (1975), $14.00, 04-584000-38 Laboratory Shear Testing of Soils, STP 361 (1964), $24.50, 04-361000-38 Evaluation of Relative Density and its Role in Geotechnical Projects Involving Cohesionless Soils, STP 523 (1973), $30.75, 04-523000-38

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A Note of Appreciation to Reviewers This publication is made possible by the authors and, also, the unheralded efforts of the reviewers. This body of technical experts whose dedication, sacrifice of time and effort, and collective wisdom in reviewing the papers must be acknowledged. The quality level of ASTM publications is a direct function of their respected opinions. On behalf of ASTM we acknowledge with appreciation their contribution.

ASTM Committee on Publications

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Editorial Staff Jane B. Wheeler, Managing Editor Helen M. Hoersch, Senior Associate Editor Helen P. Mahy, Senior Assistant Editor Allan S. Kleinberg, Assistant Editor

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Contents Introduction

1 STRENGTH TESTING METHODS AND REQUIREMENTS

State of the Art: Laboratoiy Strength Testing of Soils—A. S. SAADA AND F. C. TOWNSEND

7

Comparison of Varions Methods for Determining A^o— MOSAID AL-HUSSAINI

78

Apparatus and Techniques for Static Triaxial Testing of Ballast— J. E. ALVA-HURTADO, D. R. MCMAHON, AND H. E. STEWART

94

Mechanical Behavior and Testing Methods of Unsaturated Soils— T. B. EDIL, S. E. MOTAN, AND F. X. TOHA

114

Determination of Tensile Strength of Soils by Unconfined-Penetration Test—H. Y. FANG AND JOSEPH FERNANDEZ

130

Torsion Shear Apparatus for Soil Testing—P. V. LADE

145

A Servo System for ControUed Stress Path Tests—K. T. LAW

164

A New Control System for Soils Testuig—R. J. MITCHELL

180

Lateral Stress Measurements in Direct Simple Shear Device— R. DYVIK, T. F. Z I M M I E , AND C. H. L. FLOESS

191

Tensile Properties of Compacted Soils—MOSAID AL-HUSSAINI

207

Effect of Organic Material on Soil Shear Strength— O. B. ANDERSLAND, A. S. KHATTAK, AND A. W. N. AL-KHAFAJI

226

Effect of Shearing Strain-Rate on the Undrained Strength of Clay— R. Y. K. CHENG

243

Undrained Shear Behavior of a Marine Clay—D. C. KOUTSOFTAS

254

Shearing Behavior of Compacted Clay after Saturation—c. w. LOVELL A N D J. M. JOHNSON Copyright Downloaded/printed University

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Plane-Strain Testing of Sand—N.

DEAN MARACHI, J. M. DUNCAN,

C. K. CHAN, AND H. B. SEED

294

Effect of End Membrane Tliiclcness on the Strength of "Frictionless" Cap and Base Tests—G. M. NORRIS

303

Field Density, Gradation, and Triaxial Testing of Large-Size Roclcfill for Little Blue Run Dam—G. R. TRIERS AND T. D. DONOVAN 315 DATA REDUCTION AND APPLICATION OF MEASUREMENTS FOR ANALYTICAL MODELING

State of the Art; Data Reduction and Application for Analytical Modeling—HON-YiM KO AND STEIN STURE

Normalized Stress-Strain for Undrained Shear Tests—v.

329 P. DRNEVICH

The Critical-State Pore Pressure Parameter from ConsolidatedUndrained Shear Tests—p. w. MAYNE AND P. G. SWANSON Nonlinear Anisotropic Stress-Strain-Strength Behavior of Soils— J. H. PREVOST

387

410 431

A General Time-Related Soil Friction Increase Phenomenon— J. H. SCHMERTMANN

456

On the Random Aspect of Shear Strength—R. N. YONG AND M. M. TABBA

485

Preconsolidation Pressure Predicted Using s„/p Ratio— T. C. ANDERSON AND R. G. LUKAS

502

Stress Path Tests with Controlled Rotation of Principal Stress Dhections—i. R. F. ARTHUR, S. BEKENSTEIN, J. T. GERMAINE, AND C. C. LADD

516

Shear Strength of Cohesionless Soils from Incremental Creep Test Data—GILBERT Y. BALADI, R. W. LENTZ, T. GOITOM, AND T. D. BOKER

541

Comparison of Shear Strength Values Derived from Laboratory Triaxial, Borehole Shear, and Cone Penetration Tests— J. R. LAMBRECHTS AND J. J. RIXNER

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Borehole Shear Test in Geotechnical Investigations— A. J. LUTENEGGER AND G. R. HALLBERG

566

Concepts for a Shear-Normal Gage to Estimate In Situ SoO Strength and Strength Angle—R. L. MCNEILL AND S.

L. GREEN

579

Residual Shear Strength Determination of Overconsolidated Nespelem Clay—DAVID MIEDEMA, JACK BYERS, AND RICHARD MCNEARNY

594

The Need for Pore Pressure Information from Shear Tests— D. H. SHIELDS AND N. A. SKERMER

610

Behavior of an Overconsolidated Sensitive Clay in Drained KgTriaxial Tests—VINCENZO SILVESTRI

619

DISCUSSIONS

Discussion of "State of the Art: Laboratory Strength Testuig of Soils" —SUZANNE LACASSE AND MLADEN VUCETIC

633

Discussion of "State of the Art; Laboratory Strength Testhig of Soils" —J. T. CHRISTIAN

638

PANELISTS' REPORTS

Discussion on Laboratory Shear Devices—c. c. LADD

643

Limitations of Duect Simple Shear Test Devices— PIERRE LA ROCHELLE

Discussion of Soil Testing Practices—s.

653

659

T. POULOS

Some Aspects of Clay Behavior and Thefa- Consequences on Modeling Techniques—FRAN(?OIS TAVENAS

667

Development, Testing Requhements, and Fitting Procedure of ElasticPlastic Models—GEORGE Y. B A L A D I

678

A Qualitative Stress-Strafai (Time) Model for Soft Clays— J. H. A. C R O O K S

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SUMMARY

Swmnaiy

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Index

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STP740-EB/Sep.1981

Introduction

The increasing demand for better means and reliability for prediction of the yield or failure in soils, coupled with the ever present need to provide more realistic generalized stress-strain relationships of soils in design calculations and general analyses, make it very important that the geotechnical engineering profession be provided with an up-to-date appreciation of test techniques for measurement of shear strength and procedures for evaluation and reduction of measurements obtained from relevant test techniques. It has been at least 17 years since the last full documentation and evaluation of laboratory shear strength of soil has occurred {Laboratory Shear Testing of Soils. ASTM STP 361. American Society for Testing and Materials, 1964). There is a need for the profession to re-examine its position on the problems of yield and failure and to document the advances that have been made in the long intervening period in the development of new test techniques and methods for evaluation of the laboratory shear strength of soil. In the organization of this ASTM Symposium on Laboratory Shear Strength of Soil, advantage has been taken of the fact that two other companion exercises have been developed to complement this present study on laboratory test techniques for evaluation of shear strength. The many finer details of plasticity theory and generalized stress-strain relationships have been covered in the NSF/NSERC sponsored Workshop on Plasticity and Generalized Stress-Strain held at McGill University in May 1980, whilst the application of the theories to generalized practice was presented at an ASCE Symposium in October 1980. This ASTM symposium covers the very much needed study of laboratory techniques for evaluation of shear strength of soil. The object was (a) to meet the requirements for determination and assessment of the shearing resistance of soils, (b) to determine the kinds of strength parameters that can be derived from the various test techniques, (c) to assess the relevance of the various techniques presently available, (d) to establish the rationality of the test techniques, and (e) to examine the viability of the various models used for data reduction and the methods of application of data and measurements for assessment of shear strength of soils. There have been great advances made not only in equipment and instrumentation, but also in methods of tests and degree of sophistication of test techniques. In addition, advances have been made in methods of analysis, particularly with reference to the application of the measurements. The symposium was developed as a two-session presentation, each session Copyright by Downloaded/printed Copyright 1981 University of

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LABORATORY SHEAR STRENGTH OF SOIL

consisting of a state-of-the-art report and panel presentation. The program format and participants are given as follows: Session I—Strength Testing Methods and Requirements Chairman State-of-the-Art Speaker State-of-the-Art Report Panel Discussion Moderator Panelists

E. T. Selig, University of Massachusetts at Amherst A. S. Saada, Case Western Reserve University, Cleveland A. S. Saada, Case Western Reserve University, Cleveland, and F. C. Townsend, University of Florida, Gainesville

F. C. Townsend, University of Florida, Gainesville C. C. Ladd, Massachusetts Institute of Technology, Cambridge P. LaRochelle, Laval University, Quebec City S. Wright, Texas University at Austin S. Poulos, Geotechnical Engineers, Inc., Winchester, Mass.

Session II—Data Reduction and Application of Measurements for Analytical Modeling Chairman State-of-the-Art Speaker State-of-the-Art Report Panel Discussion Moderator Panelists

E. T. Selig, University of Massachusetts at Amherst H. Y. Ko, University of Colorado at Boulder H. Y. Ko and S. Store, University of Colorado at Boulder

R. N. Yong, McGill University, Montreal F. Tavenas, Quebec City J. H. A. Crooks, Golder Associates, Mississauga, Ontario George Y. Baladi, Waterways Experiment Station, Corps of Engineers, Dept. of the Army, Vicksburg, Miss. R. J. Krizek, Northwestern University, Evanston, III.

The contributions made by these participants and by the audience are gratefully acknowledged. The papers submitted to the symposium were divided into the two sessions, and were examined, evaluated, and discussed as part of the session presentation. These papers are organized in this STP as they appeared in each session. They provide the extension of the various test techniques and methods of analyses to specific examples of tests for various problem soil materials, new test techniques and applications, and particular methods of application of data reduction and evaluation. They serve as a means for demonstrating the wide range of applicability of test measurements and techniques. The editors also acknowledge the input and assistance

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INTRODUCTION

provided by Professors H. Y. Ko, K. Y. Lo, H. W. Olsen, A. S. Saada, and E. T. Selig, who functioned as an ad hoc Task Committee.

R. N. Yong Geotechnical Research Center, McGill University, Montreal, Canada H3A 2K6; symposium co-chairman and co-editor

F. C. Townsend Department of Civil Engineering, University of Florida, Gainesville, Fla. 32611; symposium co-chairman and co-editor

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Strength Testing Methods and Requu^ments

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A. S. Saada^ andF. C. Townsend^

State of the Art: Laboratory Strength Testing of Soils

REFERENCE: Saada, A. S. and Townsend, F. C , "State of the Art: Laboratoiy Strength Testing of Soils," Laboratory Shear Strength of Soil. ASTM STP 740. R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 7-77. ABSTRACT: A review and evaluation of the advantages and limitations of laboratory equipment for measuring the shear strength of soils are presented. Equipment evaluated include direct shear, torsional shear, simple shear, triaxial, multiaxial (true triaxial), plane strain, hollow cylinder triaxial, and directional shear devices. The evaluation indicates that the impetus to obtain parameters for constitutive equations and modeling has resulted in the development of improved equipment and testing techniques; specifically, the development of multiaxial (true triaxial) and hollow cylinder triaxial test equipment. Although these devices are more versatile, the conventional solid cylinder triaxial test is still the most popular. The evaluation suggests that direct shear and simple shear devices are best utilized by designers who have gained experience applying the results from such tests to structures that have behaved satisfactorily. Proper consideration must be given to the effects of membrane penetration, end restraint saturation and consolidation procedures, and rates of loading in any testing program. KEY WORDS: soils, shear strength, laboratory testing equipment, triaxial tests, direct shear, simple shear, torsional shear, hollow cylinder, true triaxial, anisotropy

The object of laboratory testing is to study the behavior of a given soil under conditions similar to those encountered in the field and to obtain those parameters which describe this behavior in a set of constitutive equations. In a laboratory test the specimen is intended and generally assumed to represent a single point in a soil medium. The validity of this assumption depends on the uniformity of stress and strain distributions within the soil samples. The uniformity will depend on the configuration of the specimen and the control and measurement of stress and strain on its surface. Separate measurements are often made for the soil phase, the water phase, and sometimes the air ' Professor and Chairman, Department of Civil Engineering, Case Institute of Technology, Case Western Reserve University, Cleveland, Ohio 44106. ^Professor of Civil Engineering, University of Florida, Gainesville, Fla. 32611.

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LABORATORY SHEAR STRENGTH OF SOIL

phase of the specimen in order to relate its contribution to the strength of the mass. While the data needed in design may be less extensive than those required for the development of constitutive equations, the present trend is to obtain as complete a record as possible. Constitutive equations are an indispensable ingredient in the application of the finite-element method to geotechnical problems; and the increased availability of computers has resulted in increased pressure for the development of testing equipment capable of covering the whole stress and strain spectra. Consequently, the last ten years have seen an explosion in the number of tools aimed at better measurements, better recording, and better processing of data obtained during laboratory testing. Testing units conceived many years ago but whose implementation was quite difficult are being used nearly on a routine basis. Automation, both electronic and fluidic, has taken most of the drudgery out of the stressing or straining systems. In this paper the various apparatuses in operation in soil laboratories for research or routine purposes are reviewed and their advantages and disadvantages are discussed. While it is advisable to have a uniform notation and sign convention in a given paper, such a uniformity is difficult to achieve when reference is made to so many publications, each with its own set of conventions. Therefore, when not specifically indicated, the sign convention used in this paper is shown in Fig. 1, where compression is positive and the arrows point in a direction opposite to that used in classical elasticity [1.2].^ For future reference the following definitions are in order [3]: The term "deviator" is used in conjunction with a state of stress or a state of strain (otherwise known as stress and strain tensors). It is a state in which the trace of the matrix representing stress or strain is equal to zero. In this paper the "difference between principal stresses" (aj — 02, for example) will be called the "principal stress difference". The term "pure shear", when used with a state of stresses at a point, is a special deviator in which two principal stresses are equal in magnitude and opposite in sign and the third one is equal to zero. Thus (Fig. 2a) a

0

0

0

-ff

0

0

0

0

represents a state of pure shear. The components here are given in the principal system of axes at Point 0. If we now rotate the system of axes by 45 deg to X-Y and use this new system as our reference (Fig. 2b), the previous matrix becomes •'The italic numbers in brackets refer to the list of references appended to this paper.

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SAADA AND TOWNSEND ON STATE OF THE ART

0

-T

-T 0

0'

0

0

0

0

Notice that the small square element represents a point through which any plane can pass; on this plane any of the two previous matrices will give the same "stress vector". A state of plane strain is a state in which the three orthogonal displacements (M, V, and w) are such and u = uix.y), v = vix,y), and w = 0. Such displacements lead to a strain matrix of the form

y.y

0

0

0

yxy

0

The z-direction is a principal direction. The term "pure shear", when used with relation to a state of strain at a point, is a state of plane strain which consists of a uniform extension in the jc-direction, say, and a uniform contraction in the j^-direction of such an

FIG. 1—Sign convention for stresses.

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10

LABORATORY SHEAR STRENGTH OF SOIL

o-cr 0

o -r o -V o o

O O 0

0 0 0

(TOO

FIG. 2—(a) Pure shear stresses at a point; coincident axes: (b) Pure shear stresses at a point; axes rotated by 45 deg.

amount that the volume remains unchanged. In this case (Fig. 3), a rhombus ABCD is distorted under a strain into a congruent rhombus A 'B 'C 'D' in which the acute and the obtuse angles have been interchanged. The three components of the displacement in this case are u = ex.

V —

= 0

1+c

where c is the strain e^. For small deformations in which c is small compared with unity, it can be neglected in the denominator of the value of v. The term "simple shear" refers strictly to a state of strain and not to a state of stress. It is a state of plane strain in which the points are displaced only in one direction (parallel to the x-axis, say) such that M =

cy.

0,

= 0

where c is the shear strain jj^y shown in Fig. 4. In this case all planes parallel to the jcz-plane slide in the direction of the x-axis without changing their distance from each other, and the displacements are proportional to their distance from the xz-plane. Like the case of pure shear it is a constant

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SAADA AND TOWNSEND ON STATE OF THE ART

m

11

^X

D

F//^AL

/A/IT/AL

l/ = CX

l/^—£- y FIG. 3—Pure shear strain conditions.

T /

^1 / / /

'/ill

i 1 1 1 1 -X /Nt '7-/>iL.

f=/A/Al. U= CV yv= 0

FIG. 4—Simple shear strain conditions.

volume deformation. Simple shear is equal to pure shear plus a rotation. Finally, it is to be noticed that a uniform state of strain does not necessarily mean that the state of stress is uniform. A Brief Histoiy of SoU Strength Testing [4a] It appears that the first real soil shear test was described by Collin in 1846 [4b]. In this test a long specimen of clay 4 cm square in cross section was loaded transversely at its center until it failed in double direct shear (Fig. 5). Leygue in 1885 [5] tilted a shear box full of cohesionless soil until the top slid across the bottom. It is not known when the direct shear apparatus was invented and if Coulomb, whose formula it uses, had anything to do with it. In its present form, credited to Krey, Terzaghi, and Casagrande, the direct Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

12

LABORATORY SHEAR STRENGTH OF SOIL

i

A

FIG. 5—Double direct shear test of Collin [4a].

shear test employs a circular or a rectangular specimen encased in a split box (Fig. 6). A normal force, W, is applied to the top of the box after which a shearing force, 5, forces the top across the bottom, causing the soil to shear along the plane defined by the split between the two parts of the box. The double direct shear test, which seems to be the earliest true shear test for soils [4b], is still in use in its original form [6] or with normal forces applied at its ends (Fig. 7). The states of stress and strain in the aforementioned direct shear devices are not uniform, and the cross section of soil common to the two parts of the box changes continuously. Torsional direct shear machines with solid and hollow specimens were designed [7] to overcome part of the problem (Fig. 8). The Swedish Geotechnical Institute [8] developed an apparatus where the soil is confined laterally by a rubber membrane and a series of evenly spaced rings (Fig. 9). Roscoe [9] used rigid but hinged plates for the ends of his shear box (Fig. 10); these tilt so as to maintain a constant specimen length parallel to the direction of shear. Peltier [10] introduced a shear box (Fig. 11) with movable sides through which forces can be applied on the intermediate principal plane. The Norwegian Geotechnical Institute (NGI) modified the Swedish device by replacing the rings by a wire embedded in the rubber membrane [11]. Triaxial testing of soils seems to have evolved simultaneously in Germany [12], the Netherlands [13], and the United States [14,15] (Fig. 12). In Germany a machine was built at the Prussian Waterways Experimental Station for the purpose of studying the consolidation of clays under conditions of negligible side friction; the surrounding liquid was entirely confined and temperature and leakage had to be closely controlled. Several investigators recognized that the apparatus could be used to measure the ratio of the axial ^

-£E3L FIG. d—Direct shear test 14a].

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SAADA AND TOWNSEND ON STATE OF THE ART

13

FIG. 7—Double direct shear test |4a|.

FIG. 8—Torsional direct shear test |4a].

-C0MF/Ay/A/<5

/?/A/
FIG. 9—Swedish Geotechnical Institute's simple shear device [9].

/y

FIG. 10—Roscoe simple shear box [9].

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14

LABORATORY SHEAR STRENGTH OF SOIL


FIG. U—Direct shear box of Peltier (4a, 10].

eucmc

p/srofi/ COA/£/A//A/G

P0/?£

P/?£5SUf?£ 7^AmUC£/?-

/VI£MB^AMa PO/?OC/S D/S/C

FIG. 12—Triaxial cell apparatus.

and lateral pressure prior to and at failure, the first results appearing to be those of Stanton and Hveem [15], Positive control over the lateral pressure was developed independently by Rendulic [16] and Housel [14]. A larger variety of stress paths can be applied in the triaxial cell with the limitation that two of the three principal stresses are always equal. The volume of the confining fluid may remain fixed [17] or may vary. In their classical treatise on the triaxial test [18] Bishop and Henkel cover in great detail all aspects of this test. The main shortcoming of the triaxial test and its special case, the unconfined compression test, is that two of three principal stresses are always equal. Recognizing that conditions in the field are often of the plane strain type and are seldom axially symmetric, researchers sought different specimen configurations to simulate a variety of field conditions. Square or rectangular prismatic specimens and hollow circular cylinders were the obvious choices. As early as 1936, Kjellman [19] reported test results on cubical specimens on which the three principal stresses could be varied independently. In the last few years several devices involving automated control of the principal stresses and strains applied to prismatic specimens have appeared. They differ in sophistication and accuracy but they all have the same goal. Hollow circular cylinders (Fig. 13) subjected to different internal and external pressures as well as to axial and torsional pressure are also in use.

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SAADA AND TOWNSEND ON STATE OF THE ART

^

15

^

^^^r-^'"^

FIG. 13—Hollow cvlinder triaxial.

Among the earliest investigations in soil mechanics taking advantage of this last configuration are those of Cooling and Smith [20] and Geuze and Tan [21].

There are other types of devices which have been used at one time or another in the laboratory to study the shear strength of soils: the squeeze test [22] described by Jurgensen, the vane test, the cone penetration test, the bending test, the punching shear test, the double punch test, etc. These devices are not in common use and will not be discussed in this paper. Table 1 lists the devices described in this state-of-the-art paper. Direct Shear Tests Direct shear tests are tests in which a specimen is laterally confined by solid rings or frames and caused to rupture on a plane by translatory or rotary motion. In translatory tests the speciment is solid, while in a rotary test it can be either solid or hollow. Translatory Direct Shear Test The most commonly used direct shear test is the box shear test (Fig. 6) in which a relatively thin soil sample is confined between two rigid frames. A normal force is applied to the soil through a piston and a rough porous stone or dentated plates in the upper half of the box, after which a horizontal force causes the two halves to move with respect to each other. The shearing forces are transmitted to the soil in part as normal pressures between soil and frames but primarily as tangential forces by means of the porous stone or dentated plates. The upper frame is generally raised a little before the start of the test in order to eliminate friction between the frames as well as the effect of side-wall friction on the normal stresses acting on the plane of failure. Before any shearing force is applied the principal stresses are as shown in Fig. 11. The major principal stress is applied to the top and bottom of the specimen, and is assumed to be uniform in spite of the ridigity of the loading Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

16

LABORATORY SHEAR STRENGTH OF SOIL

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SAADA AND TOWNSEND ON STATE OF THE ART

17

blocks. The intermediate and minor principal stresses are assumed to act on the sides of the box and to be uniformly distributed and equal; their magnitude is unknown however. When the shear load is applied the major and minor principal stresses rotate as shown in Fig. 14, while the intermediate principal stress is assumed to remain uniform and to continue acting on the sides of the box that are parallel to the direction of shear. This assumption is strictly true only if those sides are perfectly smooth. The deformation in the direction of the normal load is either uniform or tilting (Fig. 15), depending on whether the loading block is not or is allowed to rotate. The deformation in the intermediate direction is zero. While one can measure the shearing deformation, the distribution of the shearing strains within the soil is extremely nonuniform. There exists at the front and the rear edges a condition of physical cutting of the specimen which results in considerable stress concentration there. This condition gives rise to progressive failure along the plane of shearing so that the full shearing strength is not mobilized simultaneously along the entire length of the shearing plane. Furthermore, the strain restraint that forces the plane of shearing failure to occur in a particular direction introduces unknown conditions upon the soil specimen. This restraint probably tends to produce a line of thrust from the rear of the upper box to the front of the lower box obliquely across the plane of shearing, which results in a nonuniform distribution and a change in magnitude of the applied normal stress across the plane of shearing of an unknown amount. Finally, the teeth of the dentated porous stones will cause disturbance of the soil structure close to the plane of failure. Hvorslev [23], in a series of photographs, shows the effect of the dentated plates on the internal deformation and the failure of specimens of Vienna clay tested in a direct shear box (Fig. 16). Roscoe [9] also published a series of photographs comparing the deformations of specimens of plasticine tested in direct shear and in simple shear. The photographs are self-explanatory when it comes to /

il

fit! FIG. 14—Rotation of principal stresses in direct shear test.

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18

LABORATORY SHEAR STRENGTH OF SOI|.

Pi?//VC/PAL PL A A/a OF fA/LC//?£

S£CO/^DARy PtAA/ES

D/SP/.AC£M£A/rOF

l/£/^r/CAl

OFFA/LU/?£

l-/A/£

FIG. 15—Deformations in direct shear

Center

Side

p = 2

p = 2

test.

T_ = 76

H = 2.0

AL = 4.0

A L ' = 6.1

Tg=76

H =T 2.0

AL — 4.0

A L ' ~ 0.1

p = normal stress, kg/cm^ 7"^ = equivalent duration of shear test, min H = specimen thickness, cm

AL = displacement at failure, mm AL ' = displacement at end of test, mm

FIG. 16—Failure in direct shear [23].

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SAADA AND TOWNSEND ON STATE OF THE ART

19

studying the uniformity of stresses and strains in the translational direct shear test. A modification of the direct shear test to evaluate the undrained strength of soils was introduced by O'Neil [24.25] based upon Taylor's research [26]. The concept was to maintain a constant specimen volume during shear by adjusting the normal stress. The apparatus required precise measurement of the specimen thickness during shear [0.0025 mm (0.0001 in.)] and sufficient rigidity so that accurate measurements could be made. Equivalent pore pressures are determined based upon magnitude of normal stress changes. While this modification extends the applications of the direct shear test, the other limitations still exist. In spite of its drawbacks this test is still popular among many practitioners. It is simple to perform and its drainage facilities are good; consequently, primary consolidation can be accomplished and drained tests performed in relatively short periods of time. With clays, this test is generally conducted to obtain the residual strength, and an area correction is applied when the two parts of the box move substantially with respect to each other. Circular specimens are often used. The stress distribution in such cases is more complex and totally indeterminate. Torsional Direct Shear Tests The obvious advantages of any type of torsional direct shear devices are that there is no change in the area of the cross section of the shear plane as the test proceeds and that the sample can be sheared through an uninterrupted displacement of any magnitude; thus the shearing resistance can be investigated at large displacements. This type of test is conducted either on a solid or a hollow cylindrical specimen. In 1971 Bishop and his co-workers [27] presented a short review of the various torsional direct shear devices and summarized their features in Figs. 17 and 18. In their summary they primarily refer to the paper by Hvorslev [7] which in 1939 described in great detail the advantages and disadvantages of the devices then available. Notice that in Fig. 18 the apparatus of Cooling and Smith [20] is more nearly a hollow cylinder test and fits better in the later section on Triaxial Testing on Hollow Circular Specimens. Bishop et al [27] describe, in addition to other operational and measuring improvements, a new apparatus similar to that of Hvorslev and Kaufman, but with a better ratio of internal to external diameter (2/3 as opposed to 1/2) and a controllable gap between the upper and lower confining rings. Torsional Direct Shear Tests on Solid Specimens—In torsional shear tests on solid shallow cylindrical specimens the shearing stresses and strains vary from zero at the center to a maximum at the periphery. Also, since soils undergo change in volume when subjected to shear, the volumetric strains will vary in a similar manner; and since the piston which applies the vertical Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

20

LABORATORY SHEAR STRENGTH OF SOIL

SHAfE o r FAILURE SUtFACE

LOADING

CIRCLE

lli> • - ^ I I i o - - l

SYSTEM

i_.

SAMPLE TYPE

SOLID CYLINDER LOADED NORMALLY, LOWER PLATEN TWISTED

A.S.C.E. (1917)

SOLID CYLINDER LOADED NORMALLY 6 TWISTED

STIECK (1921) FRANZIUS ET AL.C1929) ( ( • « HVORSLEV, I 9 M )

SOLID CYLINDER LOADED NORMALLY 6 TWISTED

([••

SOLID DISC

SEMIENELLI (

LOADED NORMALLY

RAMIREZ ( l < 6 t )

I TWISTED

LA OATTA 1170

LANCEI (i93B) HVORSLEV, 1939)

U—IOCMJ SOLID OR DIVIDED CONFININC RINGS O-Ici

i 11111 i I—7t.-4

ANNULUS

t'6ci

M'm i

^ ^ ^ ^ ^ ^ ^ ^ ^ / ^ ^ 7 |

SOLID DISC LOADED NORMALLY, ANNULUS TWISTED

TIEDEMANN(|4S4

( l » HVORSLEV, l9Jt)

ROTATE I MCASURI T 14 ca •

n t

T MEASURED

Ajlt^tl.tltttitYtl.

SOLID DISC LOADED NORMALLY

CHANI

(l«6b)

6 TWISTED

CASACRANDE t HOLLOW CYLINDER LOADED RADIALLY e TWISTED

U.S.ENCINEtR OFFICC, •OSTON, MASS. ( » • HVORSUV,l4S4)

HEICHT'lii

FIG. 17—Summary of torsional direct shear devices-solid cylinder or disc or hollow cylinder [27].

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SAADA AND TOWNSEND ON STATE OF THE ART

SHAPE

21

OF LOADING

FAILURE

SAMPLE

SYSTEM

TYPE

SURFACE

UNCONFINED

EUJ

ANNULAR COOLING

DISC

6

LOADED SMITH

NORMALLY

(1935,1936)

(t

TWISTED

iSiJLiai

ANNULAR LOADED

DISC

C R U N E t t> HAEFELI

(<934)

HAEFELl

(1931)

NORMALLY

(r T W I S T E D

( i < c HVOflSLEV, 1939)

-I6<«-

ANNULAR lOADtD

DISC NORMALLY

TIEDEMANN(|937)

(lie

HVORSLEV, 1939}

fc TWISTED

ANNUIAII

I

2CM

r

LOADED l

DISC NORMALLY

TWISTED

U-tca-J

HV0«SLEV(H37, HJ?) NVOISLEV

(,

KAUFMAN

(19SI)

HEtlMANNC

WOLFSKILL

(1966) SOLID

OR

DIVIDED

OUTER

CONFINING RINGS

ANNULAR

DISC

0 1 en LOADED 2'Sci

V

NORMALLY

LA CATTA

(1970)

TWISTED

ANNULAR LOADED

DISC NOHMALLY

NOVOSAD (1964)

fc T W I S T E D

ANNULAR

DISC CARR

LOADED 6

6

NORMALLY

TWISTED

WALKER

(f96S]

• lOin

MEASURED ANNULAR LOADED t lOTATE

DISC

SCARLETT

t

NORMALLY

TWISTED

TODD

(19M)

TOGETHER

FIG. 18—Summary of torsional direct shear devices-annular disc (27].

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22

LABORATORY SHEAR STRENGTH OF SOIL

normal forces is rigid, there will be a nonuniform and unknown distribution of vertical normal stresses on the plane of failure. The variation in stress and volume changes makes it difficult to correlate the observed vertical movements of the piston with the stresses and volume changes in the zone of failure. The horizontal, external, normal pressure exerted by the rings cannot be controlled or determined. As in the case of the translatoty test there is a zone of weakness along the exposed surface of the sample and the danger of soft soil being squeezed out into the narrow space between the rings. A concentration of shearing stresses will take place in the soil close to the edges of the rings and may exert a large influence on the test results because of its large moment arm. The teeth of the porous stones will cause disturbance in the soil. In reducing the data it is customary to assume that the normal stress, a„, and the shearing stress, T, are uniformly distributed. The average displacement is computed using a mean radius as given by

_

Jo

"~

w

2r2

3

(1)

The average shear stress, T, is given by M T —

[^ lirrj^dr

3M 2irr2^

(2)

Jo In the previous operations, r2 is the outer radius of the cylinder and M is the twisting moment. Additional information on normal and shear stress distributions on the plane of failure are given in the next section. Torsional Direct Shear Testing on Annular Disks (also called Ring-Shear Test)—Some of the difficulties encountered in twisting solid cylinders can be partly overcome through the use of annular specimens (Fig. 19). The differences between the maximum and minimum values of the shearing stresses can be very substantially reduced and with them the nonuniformity in the normal stress distribution on the plane of failure. Since the specimen is confined between annular side walls the full normal force may not be transmitted to the plane of failure, and whatever reaches it may not result in a uniform distribution of the normal stresses. In Bishop's apparatus [27] there exists the possibility of measuring the side friction, and the gap between the confining rings is controlled (Fig. 20). The direct results of a ring shear test are corresponding values of a total normal load, W, a total torque, M, and an angular displacement, 6. As

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SAADA AND TOWNSEND ON STATE OF THE ART

23

Plane of reloUve rofary moHon

FIG. 19—Ring shear test sample.

stated by Bishop there are a number of alternative assumptions that can be made with respect to the normal and shear stress distributions: 1. The normal stress, a„', and the shear stress, T, are uniformly distributed across the plane of relative rotary motion. 2. The normal stress, a„', has a specified form of variation and the shear stress, T, has a correspondingly similar distribution. 3. The normal stress, a,,', is uniformly distributed whereas the shear stress, T, varies linearly with the radius. 4. The normal stress a„', is uniformly distributed whereas the shear stress, T, is a function of the strain. Alternative 1 is the most realistic choice. It is the simplest and assumes the soil to be plastic, as does Alternative 2. Under Alternative 2, several normal stress distributions can be analyzed to determine their effect on the computed value of <>'. Table 2 from Ref 27 gives the equation for angles of shearing resistance 0' obtained from drained ring shear tests assuming different normal stress distributions. With the dimensions of his device Bishop shows that the error in assuming a uniform stress distribution is less than ±2 percent for 0' <20 deg even for the most unlikely form of distribution. Alternative 3 is theoretically untenable. Alternative 4 is similar to Alternative 3 and requires a semi-graphical solution [7]. In Alternative 1 the average displacement is computed using a mean radius given by "'•2

2wr^dr

Ar2^ -

r,2)

2(r2^ 3(r2^

n') n')

(3)

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24

LABORATORY SHEAR STRENGTH OF SOIL

•1.

0 0

i^

r

00

Ir

M

9

0

s|»

^* •« *

6

S f

•

n < •

n A

1 £: "

o

si» N #1

o

o

X-N

c-

I 11

i!
^

!i

% •

,^

•

4

+

t-

V Nt-

vt _•

e

2

^'•

v ^

^1* ^ s

1

o

If

&

••

C

»r

e

.S/

'J*

l\»

»

r-

n

«

1 ail • •

Tc" 1

I

KO.-^

H s= ! 5 O

z

1

1

a

a

<

•

T-

a.

^ a.

•

» o •* e

M

o

3

3 _.UJ

..,..

w J -

t^.J

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SAADA AND TOWNSEND ON STATE OF THE ART

25

1

« » 6

0 0

O

z ~ 2!»

2|»

^l»

si»

« « 6

6

*^^ •

» 6

*

n

9

V

+

>-> +

4

+

iT

k

^.^ V

#»

n

^^

•

s -2.

HI I rt

rt n

•f

+

* - * •

•

6 -'-^

6

4N

^«/

i\*

2l>

o

0 0 n

n r* n

M

, ^i>

03

< 7"^ /'•^ 1 t 0.

S—(f

•>^ --^ 1 1

tT

^

1

^ ^^ 1

/-^ s-**

v^

^

>s ••

1

a

a

1

1

t.

1 vt/

n v^

a.

p-a-i-1

a

U^ ^

s

e «•

W

u

u

" o A

0 A

0 Ji O

o

O O.-

o a

ot> o a.

o o 0.

jj

0

^*'— >

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26

LABORATORY SHEAR STRENGTH OF SOIL

I

.^

.a

I I

I Si

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SAADA AND TOWNSEND ON STATE OF THE ART

27

T h e average shear stress, T, is given by M n

2>M 27r(r2^-r,3)

(4)

iTtr'-dr

ri and r^ are the inner and outer radii of the hollow cylinder. There is no doubt that it is more difficult to install a specimen of undisturbed soil in a ring shear device than it is in a direct shear device for solid cylinders. However, instrumentation developed by Hvorslev and Kaufman \2S\ and by Bishop et al \2T\ appears to have been quite successful. It certainly is not more complicated than what is routinely used today in simple shear tests or triaxial tests, both static and dynamic. General Remarks on Direct Shear Tests As stated in the introduction, ideally a test specimen is assumed to be a point at which a state of stress (or stress tensor) is acting. This assumption is only valid if the state of stress in the specimen and on its boundaries is uniform. Considering the size of the samples in direct shear tests and the boundary conditions it is impossible to make this assumption. There is no room for St. Venant's principle to take hold, and load-deformation (or torque-rotation) curves cannot be used to establish accurate constitutive equations for the behavior of soils. At every point inside the specimen and along the plane of relative motion there is a different state of stress with different principal stresses and different principal planes. As the shearing force is applied, the principal stresses rotate, and at every point they vary both in magnitude and direction. An average stress-strain curve obtained from measurements of the shearing force and the shearing displacement cannot be depended upon to provide a true stress-strain picture for the assumed stress conditions; it could only possibly be used in comparative studies of various soils tested under the same conditions. This indeed has been done for years by practitioners whose structures have performed satisfactorily. Two quantities are frequently obtained from direct shear tests: the peak angle of friction, p', and the residual angle of friction, /. Both are computed from the value of the "stress vector" acting on the plane of relative motion. At the peak, the soil is assumed to have reached a condition of plasticity governed by Coulomb's Law at all points of this plane at the same time. This is obviously impossible because of the nonuniformity of the state of stress in the specimen and the fact that the principal stresses do not have the same direction. The residual strength and its corresponding <j)/ is perhaps the only reasonably reliable quantity that can be obtained from a direct shear test. It

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28

LABORATORY SHEAR STRENGTH OF SOIL

does, however, require a very large displacement which often cannot be obtained in the translational device. Skemptom [29] described a technique of using multiple reversals to accumulate large displacements. This technique is based upon the concept that at residual strength the shear zone is entirely remolded and the previous fabric obliterated. Townsend and Gilbert [30] have shown in comparative tests on heavily overconsolidated clay shales that the residual strength measured by reversal direct shear and ring shear tests on intact and remolded specimens for practical purposes is the same. Multiple reversal tests have been conducted to simulate large displacements for softer materials, but they have been shown to give results which vary substantially from those obtained in the ring shear test. As noticed by La Gatta [31] and Bishop et al [27], the fundamental difference between the two tests lies in the failure of the multiple reversal direct shear box test to simulate the field condition of a large relative displacement uninterrupted by changes in direction. Such changes in direction cause rotation of the stresses and reorientation of the soil particles so as to result in different values of the measured parameters. Recent studies on the cyclic behavior of soils, and the observed changes in the fabric, the pore water pressures, and the dilatancy characteristics that occur upon reversal of the stresses, support Bishop's remark that the multiple reversal direct shear box test and the ring shear test cannot claim to be an acceptable way of measuring the same parameter. Finally, it is the opinion of the authors that direct shear tests are valuable tools to obtain the residual strength. The work of Hvorslev and Bishop show without doubt that when this quantity is needed, a ring shear test without reversal is quite appropriate. The details they give make it relatively easy for any laboratory to build similar devices. Translatory shear boxes will obviously remain in use. The hope is that if they are, only the square type will be used, and, with the exception of heavily overconsolidated clay shales, only for materials that do not require reversal to attain their residual strength.

Simple Shear Tests Because of the shortcomings of the direct shear devices mentioned in the last sections various attempts were made to modify them in the hope of imposing a uniform condition of simple shear to the soil specimens. One of the earliest attempts was made by Kjellman [8]. This apparatus, which is shown in Fig. 9, uses a cylindrical specimen laterally confined by a rubber membrane and a series of thin and evenly spaced rings. Roscoe in 1953 [9] used a square specimen in a box with hinged ends (Fig. 10), and while such a box may present improvements on Kjellman's apparatus, it still has many of its drawbacks. In 1966 the Norwegian Geotechnical Institute (NGI) refined Kjellman's device by replacing the rings with thin wires embedded in the rubber membrane [//].

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SAADA AND TOWNSEND ON STATE OF THE ART

29

It is interesting to note that Roscoe attempted to improve on Kjeliman's sample configuration using a square rather than a circular cross section. He also recognized that it was not likely that any apparatus could be made which would impose uniform pure shear stress to a specimen, because of what he called the "complementary shearing stresses" that have to be imposed on the lateral faces so that one can indeed have a condition of pure shear (Fig. 2b). He therefore imposed on the specimen a condition of simple shear strain leaving to the rigid faces of his apparatus the task of providing the necessary boundary stresses. In a series of photographs Roscoe [9] showed that a condition of uniform strain could be obtained under large normal loads, and, as pointed out in the introduction, this uniform state of strain certainly did not result in a uniform state of stress. Later [32] his device was instrumented to measure those boundary stresses. The NGI apparatus offers practical operational improvements over Kjeliman's. The Roscoe and NGI devices have been used very extensively in studying the static behavior of soils. More recently they have been modified for cyclic loading. Their critical appraisal is therefore quite warranted. Commenting on the Kjellman device Hvorslev said [28]: "The resultant of the vertical forces on the upper and lower end surfaces of the test specimen must form a couple in order to balance the moment produced by the shearing or tangential forces. Neither the vertical normal stresses nor the shearing stresses are uniformly distributed. This non-uniformity of stress distribution increases with increasing deformations, and the shearing resistance characteristics after initial failure can be investigated only to a limited extent". Such comments did not prevent this apparatus from being mechanically modified and used in I%6 [//]. It became quite popular because designers and some researchers needed "ease of use and convenience" or "a ball park value". The enormous proliferation of data generated by both static and dynamic tests made it very difficult to question its value. Both the Roscoe and the NGI devices claim a condition of plane strain; the second also claims reasonably uniform stress distributions. Whether the material can be in a state of plane strain in either can be "investigated" with the solution of the St. Venant problem of the fixed end beam of square or circular cross section subjected to an end load P. The solution is based on the theory of elasticity, and the boundary conditions are not exactly the same as in simple shear devices. Whenever the theory of elasticity is used in soil mechanics, the opinion is often voiced that, soils not being elastic, analyses based on such a theory are invalid. It would be unjustified to expect the magnitudes of the stresses given by elasticity to be the correct ones. However, a clear picture can be obtained regarding the components of the state of stress that come into play, their relative magnitude, and the validity of the plane strain assumption. Known elastic solutions, theoretical or experimental such as obtained from photoelasticity, are of vital importance in finding answers and making logical assumptions in soil mechanics. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

30

LABORATORY SHEAR STRENGTH OF SOIL

Analyses of Tests on Solid Square Specimens For a square cross section, the St. Venant solution [33] is shown in Fig. 21; Tyj. is the shearing stress in the direction of the applied shearing force and T^. is the perpendicular to it. To make the analysis more concrete, numerical values were chosen corresponding to actual cross sections of specimens used in practice, v has been chosen equal to 0.49, the cross section equal to 50 cm^ (7.79 in.2), a = 35.7 mm (1.40 in.), and the average shear stress P/A — 0.13P (psi). Fig. 21c shows the distribution of the shearing stress Ty^ along the line jc = 0; it is seen that there is a 38 percent difference between the center and the edge. Fig lib shows the parabolic distribution for z = 0 and z = a. Fig. 2ld shows the distribution of T^^ along z = ±0.6a as well as along the edges. Comparing the magnitudes of the shearing stresses (which are given in terms of P) in Fig. 21, we notice that T^, is very small compared with T„ except close to the edges. Neglecting Ty, seems to be quite acceptable and reduces the plane normal to the z-axis to a principal plane; smooth lateral restraint can then justify the assumption of plane strain. In the analytical solution of Roscoe [9] and later of Prevost [34] a plane strain condition is assumed and, as just demonstrated, legitimately so. The stress function type of solution brings in the normal stress components a^ that the St. Venant analysis does not. In addition, the normal stress components Oy are not linearly distributed. This is to be expected since in the St. Venant problem the lateral faces of the beam are free from restraint and the end effects are neglected. Roscoe's solution shows that, at best, only the middle third of the specimen can be considered in a state of uniform stress. In addition, in an actual test, high compressive stresses are required to overcome the tensile stresses that develop at the end platens (Fig. 22). The solution also involves the existence of tensile and compressive stresses on the sides, and it is hard to visualize how those tensile stresses can be developed by the rigid flaps of the Roscoe device. The analysis of Prevost [34] goes further and shows that if there is a small amount of slippage at the ends even this middle third area of uniformity completely disappears; the side effects, both tensile and compressive, that the device has to develop to satisfy the theory become quite preponderant (Fig. 22). In summary, we see that while the assumption of plane strain is reasonably justified, the solutions of both Roscoe and Prevost require boundary conditions that the device physically cannot achieve. Even if the required boundary conditions were satisfied, the stress distribution inside the specimen would still be totally nonuniform. The properties measured would not be those of the soil alone, but rather a combination of the properties of both soil and test apparatus; different sizes would give different results [35] and hard-to-interpret average pore pressure values if such measurements were made. Finite-element analyses have been made to study the distribution of stresses in the Roscoe device using nonlinear constitutive equations [36].

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SAADA AND TOWNSEND ON STATE OF THE ART

31

>^

f O

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32

LABORATORY SHEAR STRENGTH OF SOIL

FIG. 22—Stresses on the upper and lower faces of a simple shear sample [after Ref 34].

Such analyses confirm the nonuniformities of the stresses that the closedform elastic solutions exhibit. Analysis of Tests on Solid Circular Specimens The St. Venant solution for a circular cross section is shown in Fig. 23; along the boundary every T^^. needs a T^^ SO that the resultant of the two is tangent to the periphery, v was chosen equal to 0.49 and the area equal to 50 cm^ (7.7912 in.2). Thus the radius is 40 mm (1.5748 in.) and the average shear stress P/A = 0.128P (psi). Figure 23b shows the distribution of T^^ along the line x = 0; it is seen that there is practically no difference between the center and the edge. Figure 23a shows the distribution of T^^ for 2 = 0, /?/V2, and z = K. It is only along the x-axis that T^^ starts and ends with a zero value. Fig. 23c shows the distribution of r^^ along the line z = ± /?/V2 as well as along the periphery. For comparison purposes the value of T„

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SAADA AND TOWNSEND ON STATE OF THE ART

!

g

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33

34

LABORATORY SHEAR STRENGTH OF SOIL

along the periphery is also shown. Notice that both T^^ and T^^ are equal on the edge for z = ± ^ / V 2 as it is necessary to make the resultant shear stress vector at this point tangent to the contour. Contrary to what was seen in the case of a square cross section, T^^^ *nd T^, are of the same order of magnitude, and neglecting Ty. to satisfy the condition of plane strain is quite unacceptable. Similar results would have been obtained using other known types of stress-strain relations. The assumption of Bjerrum and Landva [//] is thus inadmissible for a circular specimen with free lateral surfaces subjected to simple shear. If circular cross sections are to remain circular, their spirally reinforced membrane would have to apply a pattern of normal tensions and compressions varying with depth and with the angle of rotation 6 around the origin. Physically this is beyond the capability of any flexible membrane or rigid circular outside stack of rings. Lucks et al [37] studied the stress conditions in the NGI apparatus using finite elements. In a short technical note, the results of two linear elastic analyses, one referred to as the three-dimensional analysis and the other as the Fourier analysis, are presented. The boundary conditions are given in terms of displacements, and for the Fourier analysis it is clearly specified that only one mode of deformation is involved. Both analyses use a Poisson's ratio of 0.49, which is close enough to the limit where numerical difficulties may result. As expected from the St. Venant analysis, equilibrium is maintained with a pattern of high normal, axial, and radial stresses in the boundary elements, the first varying with the angle of rotation 6 and the second varying with both 9 and the depth of the specimen. Lucks et al present the values of the horizontal shear stresses, T ^ , obtained from the three-dimensional analysis, the values of the boundary stresses obtained from the Fourier analysis, and contours of maximum shear stresses from the Fourier analysis. It would have been quite beneficial to see the values of T^. since they should be of the same order of magnitude as T^. The fact that the shear stress vector must be tangent to the boundary results in a value of T^, for every given value of Tj^. In this light, the published values cannot be evaluated. Finally, Lucks et al conclude with the statement that 70 percent of the sample is found to have a remarkably uniform stress condition. This percentage seems to be based on their vertical sections showing the contours of maximum shear stress. This statement would have been true if {/) the reinforcing membrane and the end platens could apply variable combinations of high radial tensions and compressions, such that the edge elements are stressed to correspond to the assumed boundary conditions, (2) the finite element mesh was fine enough to show serious stress concentrations, and (3) the Poisson's ratio of 0.49 did not distort the results of both analyses. Hara and Kyota [38] reported a study similar to the one by Lucks et al [37]. In this study the edge elements must be subjected to normal tensile and compressive stress close to 15 kg/cm^ for the state of stress in the middle part to be uniform. This is physically impossible. In a recent paper, Shen et al Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

SAADA AND TOWNSEND ON STATE OF THE ART

35

[39] also used finite elements and took into account the confining effects of the membrane which Lucks et al had not. They concluded that the "strains" were highly nonuniform and consequently the stresses were too, although one does not necessarily imply the other. Photoelastic Studies [40] In order to examine experimentally the elastic stress distribution in simple shear models of the NGI and Roscoe types, with boundary conditions closer to reality than those of the St. Venant solution, the three-dimensional photoelastic method was chosen. Three-dimensional stress analyses may be made by the frozen-stress method, in which a model made of an annealable material is subjected to a heating and cooling cycle while under load, thus locking in the load-induced strains and the accompanying optical birefringence. Careful slicing of the model will then permit observation of the interference pattern from which the stress states may be determined. A special loading fixture was designed for this study; details can be found in Ref 40. End restraints were simulated by massive blocks of the same epoxy material used for the models. In fact, the models were machined each from one piece to the shapes shown in Fig. 24. The results of this study are quite revealing. Figure 25 shows the shear stress distribution on the center plane of a square specimen simulating the Roscoe test. Figure 26 shows the same shear stress but on an NGI round specimen. Such stress distributions are far from being uniform. Indeed, they can change by as much as 47 percent whether one moves in the direction of the applied shear force (x-axis) or normal to it (z-axis). Figure 27 shows experimentally determined normal stresses, a^ and a^, close to the top of the specimen in its central slice. Figure 28 shows the ratio of the shear stress T^, in the direction normal to that in which the shearing force is applied to the shear stress T„ in the direction of the shear force, in

5HEAe

FIG. 24—Photoelastic models of circular and square simple shear specimens [40].

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36

LABORATORY SHEAR STRENGTH OF SOIL

1

[

1

-.85 .4

\\

0.44

_

- L/ ,?|.

y4

0.B

- ki

w

M

1

v! - 2 a = 1.361

1

1

1

FIG. 25—Shear stress from photoelastic analysis of square simple shear for y = 0 [40).

,1=0,60

-N,

I I UlNITE ELEMENT N ^ « - v ^ « ° ° ' f . - » C ^ '

FIG. 26—Shear stresses from photoelastic analysis of the central slice of round simple shear model [40].

the central plane of the specimen, at a distance of 15.2 mm (0.6 in.) from the jc-axis. For comparison the results of St. Venant for the cantilever beam are also shown. As can be seen, Ty. is of the same order of magnitude as T„. Essentially the photoelastic study lends support to the theoretical analysis of St. Venant and indeed complements it in those areas where the boundary conditions are different.

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SAADA AND TOWNSEND ON STATE OF THE ART

37

oUH

FIG. 27—Normal stresses from photoelastic analysis of the central slice of round simple shear model [40].

General Remarks on Simple Shear Tests Simple shear devices have very serious deficiencies that cannot be brushed off as unimportant or ignored for the salce of simplicity and the "ball park value" argument. In addition to the nonuniformities mentioned previously and which appear when shearing forces are applied to the device, additional difficulties appear when normal forces act on the loading plates. Such plates must be perfectly rough, as indicated by Finn and his co-workers [41]. This roughness will automatically contribute to additional normal confining pressures of the radial and hoop types acting on vertical planes. There are no theoretical or experimental studies giving an order of magnitude for those pressures in the simple shear apparatus, but studies conducted on triaxial specimens and hollow cylinders show that in the vicinity of the end plates they are of the same order of magnitude as the applied vertical stresses. One usually moves away from the loading plates and counts on St. Venant's principle to dismiss their effects. However, St. Venant is of no help at all when the thickness of the specimen is one third of the size of the loading plate. In addition, as simple shear takes place, additional couples are applied by the normal vertical stresses because of the increasing eccentricity. The analyses previously discussed involve nothing but linear elastic

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38

LABORATORY SHEAR STRENGTH OF SOIL

APPLIED SHEAR

P' •yz

1.4

1

1.2

-

i 1.0

--

0.8

-

Vi^-SAINT

—

VENANT

\\ \\-PHOTOELASTICITy

0.6

-

0.4

-

0.2

—

\

-1.0

\ \

\

X

\

^^--^v

1 -0.5

—

—>

FIG. 28—Variation of Tyz along the line y = 0, z = 0.6 from photoetastic analysis of the round simple shear model [40].

assumptions with no coupling between normal and shear stresses and strain. This is only true for infinitesimal strain of the type obtained in resonant columns. Even there, at 10~^ strain, coupling has been noticed on saturated clays by the senior author. In soil mechanics even small shearing stresses cause normal strains, which increase as the shearing strains increase. As has been pointed out in the section on Torsional Direct Shear Tests on Solid Specimens, the volumetric strains resulting from nonuniform shearing stress will also be nonuniform; and since the porous stone through which the vertical stress is applied is rigid, there will be a nonuniform and unknown distribution of vertical normal stresses in response to this tendency for

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SAADA AND TOWNSEND ON STATE OF THE ART

39

volume change. Those nonuniformities are, of course, to be added to those deduced through the use of linear elasticity. Tests are sometimes conducted with the vertical load being changed such that the volume remains constant. For saturated soils these changes in the vertical load divided by the area (in other words, the average change in the vertical stress) are assumed to be equal to the excess pore pressure buildup. In view of the aforementioned analyses the pore pressure cannot be uniform and equal to the average normal stress for soils of low permeability. For sands, while uniformity of the water pressure can be expected, the distribution of the effective normal stresses is far from being uniform. The wirereinforcementin the NGI membrane is also used as a strain gage to measure KQ during the consolidation phase of the test. As indicated by Dyvik et al [42] the calibration is quite tedious. Any attempt to measure the lateral stresses during the shear phase would lead to meaningless results, since it was shown that such stresses vary with the height as well as with the circumferential position as one moves around the perimeter of the sample. When one looks at Hvorslev's evaluation of Kjellman's device [28], Roscoe's experimental and theoretical work [9], the discussion of DeJosselin de Jong [43] of the paper by Roscoe et al [32], the re-analysis of Prevost and Hoeg [34], the photoelastic study of Wright et al [40], the fact that more than half of the components of the state of stress are ignored, and the miracles that results of finite-element analyses [37,38] demand that the edge elements perform, one is bound to be cautious when evaluating the data simple shear devices yield. Inclined specimens of anisotropic soils have also been tested with them [44], adding to an already untractable state of stress the complexities of stress and strain analyses of anisotropic materials. The whole simple shear device is now placed inside a cell and pressurized; and here again, because of the closeness of the loading plates and their roughness, the lateral and circumferential stresses, a^ and og, within the body of the sample cannot be assumed equal to the outside confining stress [45a]. Indeed, a simple axially symmetric finite element analysis conducted on a triaxial test specimen of the size used in the simple shear device has shown that, for rigid perfectly frictional platens, only a very thin layer on the outer lateral surface actually "sees" the lateral cell pressure. Depending on Poisson's ratio, a^ and ae vary with the radius and can become nearly equal to the vertical stress at the center [45b]. Simple shear devices have been introduced as an improvement over direct shear devices. Are they? Though direct shear tests have recognized weaknesses, today what is expected from them is to give residual strengths; this they doreasonablywell, especially in the Hvorslev-type ring shear device [23.27]. Simple shear devices, on the other hand, cannot claim to yield either reliable stress-strain relations or absolute failure values. At best they can be exploited in comparing descriptively similar soils. Perhaps their proper place today is in the hands of designers who have already conducted a large Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

40

LABORATORY SHEAR STRENGTH OF SOIL

number of such tests and built structures which behaved satisfactorily. There, experience and data from other types of tests go together and yield acceptable design parameters. Triaxial Tests on Solid Circular Cylinders In the triaxial test shown in Fig. 12, the specimen is under a state of spherical stress to which is added an axial force. The fluid pressure provides two of the principal stresses while the third one (the axial one) is provided by both the fluid pressure and the axial force imposed by the piston. This axial force can be either compressive or tensile, and the axial stress can be either the major or the minor principal stress. The force is transmitted to the specimen by rigid porous plates which permit fluid flow in and out of the soil during loading. The specimen is generally encased in a flexible membrane, although other types of encasements such as paraffin have been used. Draining strips of filter paper placed on the lateral surface help speed the radial flow of water during consolidation and decrease the pore pressure gradients. Threads of wool along the axis of the specimen have also been used for the same purpose. The axial deformation of the specimen is measured directly by monitoring the movement of the end plates or that of the piston which is in solid contact with them. The lateral deformation is irregular due to bulging and can be measured by placing extensometers or transducers inside the cell [18]. Micrometers with their stem passing through the Lucite chamber have been successfully used [46]; with proper calibration optical methods can also be used [47]. Pore pressures can be measured manually [7^], but transducers seem to have replaced manual devices nearly completely. A wide variety of tests can be conducted in the triaxial cell, and Bishop and Henkel [18] give the necessary details on how to conduct them. Compression of the specimen can be induced by increasing the axial stress, decreasing the lateral stress, or both; in extension, the opposite is done. Consolidation can proceed spherically or at any given ratio of axial-to-lateral stress. By measuring lateral displacement and by controlling the pressure in the cell to maintain zero lateral displacement, a /To-consolidation can be induced. Shearing tests can be conducted at any ratio of principal stresses as well as keeping the mean stress constant. Pneumatic [48,49] and electronic feedback systems are routinely used to obtain a wide variety of stress paths. In addition to the restriction that two out of the three principal stresses must be equal, the results obtained from tests conducted in the triaxial cell are affected by the loading end plates; their smoothness, size, and permeability; by the flexible membrane surrounding the specimen; by the filter paper used; and, of course, by the measuring system. Nonuniform stress distributions and the bulging of the specimen are the most noticeable aspects of those unwanted effects. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

SAADA AND TOWNSEND ON STATE OF THE ART

41

Theoretical Stress Distribution in Triaxial Tests The nonuniformities of the stress distributions within the specimen are primarily due to the effects of the friction on the end plates. The problem of the influence of end restraint during uniaxial or unconfined compression of cylinders has been under consideration since the latter part of the nineteenth century. In 1902 Filon [50] published his classical elastic solution in which he made the assumption that the ends of the cylinder were kept plane and that no point on the ends could move in a radial direction, as if the ends were glued. He was unable to meet exactly these boundary conditions. Pickett [51] solved this problem using a multiple Fourier technique. His graphical solution appears to be correct, with possibly some numerical inaccuracies due to the slowly converging infinite series and the difficulty in hand computation. D'Appolonia and Newmark [52] used a framework analogy, and while their solution agrees reasonably well with Pickett's solution, it does not exactly meet all the boundary conditions. Assuming slightly different boundary conditions, Balla [53] solved a similar problem. He considered that the cylinder ends remained plane and that the radial displacement on the periphery at both ends varied inversely with a friction factor. The end shear stress distribution was found to be linear, and when the friction factor was at its maximum value the radial displacement at the periphery was zero. The aforementioned solutions, except Balla's, considered an elastic material with a Poisson ratio of 1/4; Balla used 1/3. Using finite differences, Moore [45a] solved the problem of unconfined cylinders for six Poisson ratios varying between 0.15 and 0.48 and height to diameter ratios of 1 and 2. He also obtained solutions for confined cylinders, three Poisson ratios, and a ratio of height to diameter of 2. A feature that is common to all elastic solutions is the drop in the normal contact-stress as one moves towards the center of the specimen, and a very high concentration on the edges (Fig. 29). The values of the normal radial and circumferential stresses, a^ and a^, as well as the shearing stress, r^j, vary from author to author depending on how well the boundary conditions have been satisfied. Since the sides are free from shearing stresses, T^^ must be equal to zero at the top and bottom edges of the specimens. Yet except for Filon's all the solutions involve a relatively high value for T^^ there. The same is true for a^. Iti addition, Moore found that this concentration of stresses on the edges was quite sensitive to the chosen value of Poisson's ratio. Using finite elements, Girijavallabhan [54] obtained results practically identical to Pickett's [51]. While all the previous solutions dealt with a linear elastic material, Perloff and Pombo [55] considered materials with nonlinear constitutive equations of both the strain-hardening and strain-softening types. Using finite elements, they reached the conclusion that the effects of the end restraint on the observed axial stress-strain curve depends on the constitutive law of the Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

42

LABORATORY SHEAR STRENGTH OF SOIL

^^^i» D

O £1. •a

c

gtib3

=§

lb*-

ki JO X

Si

•b''

b^

i

« •

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SAADA AND TOWNSEND ON STATE OF THE ART

43

soil; the influence of those restraints being more important for brittle materials. It is proper to remark at this point that this conclusion most surely applies to the simple shear test where end restraints are more pronounced than in the triaxial test. Experimental Observations on the Effects of the End Plates Experimental studies of the effects of end restraints during compression tests can be found in the literature of every engineering material. In soils it was brought to the forefront with the emergence of the triaxial test. The experimental work by Taylor [26] in the 1940s, summarized by Rutledge [56] in 1947, led to the conclusion that reliable results could be obtained with soil specimens between usual platens, provided the length to diameter ratio was in the range of 1.5 to 3.0. On the basis of these early studies, triaxial specimens for soils have been more or less standardized using regular ends with a length to diameter ratio of 2.0 to 2.5. In 1960 Shockley and Ahlvin [57\ conducted an investigation on the nonuniform conditions in the triaxial test. They found that on tests on dry sands there was a volume increase in the middle third or failure zone of specimens over a density from dense to loose and that a volume decrease occurs at the ends of the test specimens. A similar change occurred in saturated sand specimens subjected to axial strain under constant confining conditions. For clays, based on moisture content changes, they found a volume decrease in the zone of shear and a volume increase at the ends of the specimens. Tests on large triaxial specimens of dry sand showed higher than average values of both vertical stress and vertical strain in the portion of the mass near the vertical axis just below midheight where the maximum bulge takes place with lesser values toward the edges and the ends. Rowe [58] was apparently the first to use a combination of rubber sheeting and silicone grease to develop frictionless ends for triaxial compression test specimens. The Rowe and Barden [59] grease rubber system is the popular method of minimizing end restraints (Fig. 30). Sometimes a short porous dowel is used at the center of the platens to avoid side-slipping of the sample. The paper by Rowe and Barden [59] produced interesting discussions [60-62] and started a wave of research to bring out the advantages and disadvantages of oversized lubricated end plates. Barden and McDermott [63] tested compacted clays as well as remolded normally consolidated and overconsolidated clays with lubricated and nonlubricated platens. They concluded that lubricated ends markedly reduced the vertical and radial pore pressure gradients together with the moisture migration. Barrelling was minimized but the effective strength parameters were not altered when the results were compared with specimens with a length to diameter ratio of 2 tested between ordinary platens. Bishop and Green [64] tested one type of sand and reached the same conclusion regarding the maximum angle of

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44

0-ring

LABORATORY SHEAR STRENGTH OF SOIL

c seals

greased membrane

H' diam. porous disc

A. ,araldite

I.

joint

FIG. 30—Enlarged frictionless end platen with central drainage for triaxial tests [after Ref 59].

shearing. Short samples with lubricated ends show larger axial strains and a larger dilation at failure than long samples without lubrication. Harden and Khayatt [65] refer to the necking encountered during extension tests, and show that the use of lubricated ends goes a long way in increasing uniformity. Kirkpatrick and Belshaw [66] used X-ray techniques to study the radial and circumferential strains during drained triaxial compression tests on large diameter triaxial samples of medium dense sand in which the end plates were either rough or lubricated. They found that the assumption of equality between the radial and the tangential strains is valid for lubricated samples but largely inadmissible for samples tested with rough platens. Rough platens were found to cause nonuniform strain conditions throughout the sample which are produced by the formation of quasi-rigid zones at both ends of the specimen. Kirkpatrick and Belshaw draw attention to the fact that while homogeneous strain conditions may result in homogeneous stress conditions, this was not necessarily true. In a subsequent study, axial strains were examined by Kirkpatrick and Younger [67\ and found to follow the same pattern. Duncan and Dunlop [68] tested undisturbed clay, and reached the conclusion that unless it was necessary to measure volumetric strains in drained tests on sand, the advantages gained from the use of lubrication were not worth the additional bother. Roy and Lx) [69] ran comparative drained triaxial tests at high confining pressures on strong-grained and weak-grained granular material with ordinary and lubricated ends. They found that the stress-strain relations were significantly influenced by the end conditions. For high-pressure tests, lubrication resulted in a much more uniform strain, volume change, and crushing of particles throughout the samples. Raju et al [70] found that, while the well-known failure plane develops in specimens of dense sand tested in compression between ordinary plates, no such plane occurred if the plates were lubricated. They deduced that the oc-

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SAADA AND TOWNSEND ON STATE OF THE ART

45

currence of this plane was not a property of the sand but was due to the testing procedure. Kirkpatrick et al [71], using dense and loose sand, measured the stress at the platens by means of diaphragm gages and found that lubricated platens lead to a reasonably uniform stress distribution, while nonlubricated platens resulted in nonuniformities which became more severe as the strains increased. In this last case the distribution of the normal stress bears great resemblance to the ones obtained in the theoretical elastic analysis. Finally, Lee [72] reviewed most of the aforementioned research and extended it to undrained sand. He concluded that for medium-to-dense sand there was a significant increase in static undrained strength with lubricated ends as compared with tests using regular ends. The effect was found to be significantly greater than observed for other studies pertaining to drained tests on sands and undrained tests on clays. He relates the influence of the friction to the tendency of the material to change volume, thus explaining why Duncan and Dunlop did not find much difference in their results using regular and lubricated platens.

Testing Procedures Backpressure Saturation—Since Lowe and Johnson's investigations [73], saturation of specimens by applying backpressure has become a widely used technique. The methods and magnitudes of backpressure required to saturate specimens are provided by various authors [18,74]. Lee and Black [75] provide theoretical and experimental data for the time and magnitude of backpressure to dissolve air bubbles. The procedure that has generally been adopted for backpressure saturation is to incrementally increase the chamber pressure and pore pressure simultaneously, allowing equalization at each increment. After equalization, the value of B{B = Au/Aa3) is measured before applying an additional increment. However, several variables are involved in this general technique; namely (/) the magnitude and duration of the backpressure increment, (2) the magnitude of effective consolidation pressure during saturation which may or may not permit the specimen to swell, (3) the magnitude of chamber pressure increase when checking the 5-parameter, and (4) the magnitude of back pressure applied obviously must never pre-stress the specimen, that is, apply an effective confining pressure greater than that under which the specimen is to be sheared. In this context, Donaghe and Townsend [76] suggest that the magnitude of backpressure increment and effective consolidation pressure during saturation be kept below the effective confining stress throughout the saturation procedure. Likewise, when checking the 5-parameter, the magnitude of pore pressure should be observed as the chamber pressure is increased to avoid pre-stressing. They also report that

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46

LABORATORY SHEAR STRENGTH OF SOIL

for tests on a CL and a CH soil the magnitude of backpressure applied did not affect the principal stress difference or the induced pore pressures. However, a practical problem concerning the magnitude of backpressure can arise in the case of dilative soils. If the magnitude of backpressure is significantly higher than the anticipated neutral stresses in the field, then the amount of induced negative pore pressure before cavitation will cause excessively high measured principal stress differences, which most likely will not occur in the field. To minimize the use of backpressure, techniques of differential vacuum saturation consisting of applying a full vacuum to the specimen with a highly soluble gas (for example, CO2) have also been used [77]. Anisotropic Consolidation—Although in situ stress conditions are usually anisotropic, that is, a^ > 03, isotropic stress conditions are generally used in routine triaxial tests. The reason usually given for this testing inconsistency is that anisotropic consolidation requires more time and complicated procedures and constant-stress equipment capabilities. In addition, it was thought formerly that the angle of shearing resistance in terms of effective stress was not significantly affected by method of consolidation; however, this is not the case for all soils. Early work by Rutledge [56] suggested that the water content after consolidation and the undrained strength were independent of consolidation ratio, kc, provided the vertical consolidation stress, 0,^, is the same. A comparison of literature-reported data by Donaghe and Townsend [78] observed that this suggestion is valid for compacted soils; however, for undisturbed or slurry prepared soils the assumption does not hold. For tests on slurry consolidated specimens, they observed that the water contents after consolidation were not a unique function of ffic but were related to values of aod and Toct during consolidation. Anisotropically consolidated specimens had higher water contents than isotropically consolidated specimens for the same cj^. For any given ffi^-value, the maximum (ffrffj) decreased for increasing values of anisotropic consolidation, thus causing a decrease in values of 4)'. There is general agreement in the literature [78-81] that induced pore pressures and axial strain values at failure are considerably reduced for anisotropically consolidated specimens. In this context, development of constitutive relationship parameters will be greatly influenced by consolidation conditions. The reduction in axial strain at failure due to anisotropic consolidation means that the time to failure is also reduced compared with isotropically consolidated specimens. This time reduction presents the testing detail if time to failure is significantly important to warrant altering the strain rate to compare anisotropically and isotropically consolidated specimens. More recently, Saada and his co-workers [82,83], within the context of their study of anisotropic clays, have shown that /ko^consolidated slurries of clays were extremely brittle in compression, but very ductile in extension; and Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

SAADA AND TOWNSEND ON STATE OF THE ART

47

while for normally consolidated clay the strength in compression is higher than in extension, the reverse is true for overconsolidated clays. Rates of Loading—It is common knowledge that rates of loading significantly affect the magnitude of shear strength. Increased rates of loading produce increased strengths and in the case of extremely slow loading rates creep movements will cause lower measured strengths. If saturated specimens are tested, then the loading rate selected must be slow enough so that excess pore pressures do not develop in the case of drained tests, and the pore pressures are equalized throughout the specimen for undrained ones. The selection of loading rate is of considerable practical importance as the time to perform a test is directly related to cost. Bishop and Henkel [18] propose that in drained tests 95 percent pore pressure dissipation will occur if 20H2

^'~

«C

where r , = time to failure, H — '/2 the specimen height, Cy — coefficient of consolidation, and M = a drainage boundary condition. In the case of undrained tests, it has been found [84] that for contractive soils, in the extreme, creep leads to failure without an increase in strength and thus modulus values as well as strength are low. In the case of dilative soils, it has been found [78,84] that the strength is not greatly affected by loading rate; however, modulus values may be. For normally consolidated (contractive) soils, Donaghe [85] reports a 5 percent decrease in strength per tenfold increase in time to failure. Various Corrections in the Triaxial Test—The measured strength of soils in a triaxial test is influenced by the membrane surrounding the sample as well as by the filter paper used to facilitate drainage. Bishop and Henkel [18] and Olson and Kiefer [86a] give ways to measure and correct for these effects. Conforth [86b] noticed that side drainage ceases to be effective in assisting drainage when the soil permeability is approximately 10"*" cm/s. When the residual strength is measured by means of a triaxial test, corrections must be made for soils shearing along a plane. Webb [87\ and Pachakis [88] studied this problem and recommended corrective operations. Duncan and Seed [89] reviewed the various errors that occur during triaxial testing and recommended corrections. Such corrections must be made when comparing results of different tests or trying to determine strength parameters. Piston friction has also been extensively studied, and its effects have been reduced to a negligible amount or totally bypassed through the use of ingenious bearings [90] or transducers placed inside the cell. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

48

LABORATORY SHEAR STRENGTH OF SOIL

In addition to its small but obvious confining effects the membrane, because of its penetration of granular materials, affects the measurement of volume changes in drained tests and of pore water pressures in undrained ones; effective stress paths and strength parameters are therefore modified. Newland and Allely [91] were the first to draw attention to the problem of membrane penetration. Assuming the soil to be isotropic, they suggested it can be evaluated for loading under spherical pressure as the difference between observed volumetric strain and three times the measured axial strain. Roscoe et al [92] used two methods for evaluating the membrane effects in sand specimens. The first was similar to that of Newland and Allely, the second consisted of testing under ambient pressure condition a 38.1-mm (1.5-in.)-diameter triaxial specimen containing a central brass rod throughout the height of the sample. Rod diameters varying between 6.35 and 35mm ('/4 and P/s in.) were used. The membrane penetration was obtained for each value of ambient pressure by plotting volume change measured against rod diameter and extrapolating the resulting straight line to obtain a volume change value corresponding to a rod diameter of 38.1mm (1.5 in.). While Roscoe et al [92] considered the first method to be more reliable, El-Sobhy [93] suggested that the second method was the one to use. Raju and Sadaswan [94] showed that the relation between the volume changes of a hollow cylindrical specimen and the diameter of the inserted brass rod was not linear and therefore the linear extrapolation of Roscoe was incorrect. Furthermore, they pointed out that the vertical stress of the specimen around the brass rod will not be the same as the radial stress. So they modified the top platen to achieve a spherical loading. Frydman et al [95] used hollow cylinders of glass spheres. They conducted tests with hydrostatic loading and varied the internal diameter of the cylinders. For a given stress, the various internal diameters yielded points for the measured volumetric strain which lay on a straight line. This line cut the volumetric strain axis at the true volumetric strain of the sand specimen and had a slope equal to the membrane penetration. They give semi-logarithmic relations between the penetration and D50 (the diameter of the particle corresponding to 50 percent passing in a sieve analysis). Kiekbusch and Schuppener [96] confirmed the relation of Frydman et al and found that by spreading a thin layer of liquid rubber on the membrane they could reduce the penetration by up to 85 percent. Using this technique in undrained triaxial compression tests on sands, they recorded pore water pressures 100 percent higher than in tests with normal membranes. Triaxial Tests on Anisotropic Materials Recent interest in the behavior of anisotropic /if o-consolidated clays has led many investigators to cut inclined specimens and test them in compression in the triaxial cell. Figure 31 shows specimens at various inclinations to the

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SAADA AND TOWNSEND ON STATE OF THE ART

49

direction of consolidation; Fig. 32 shows tlie bending moments and shearing forces that are generated at the ends when an inclined specimen is tested between two rigid platens [97\. Such end effects invalidate whatever information is obtained from the test. In order to illustrate that this is indeed what happens Saada [98] conducted a series of unconfined compression tests on specimens at various inclinations to the direction of consolidation, once between frictional plates and once between lubricated plates. The results are shown in Fig. 33. Unless the samples are totally free to deform, those extraneous effects will occur. Presently, the only way to study the behavior of cross anisotropic clays is to incline the principal stresses rather than incline the specimen. This will be discussed at length in the sections on Triaxial Testing on Solid Prismatic Specimens and Triaxial Testing on Hollow Circular Specimens; these examine the thin, long, hollow cylinder subjected to combinations of axial and torsional stresses. Torsional tests have been conducted on solid soil specimens by Habib [99], but their use is not recommended since the shearing stresses vary from zero

consolidation pressure

f

'-iiiJ i

»•

'^

2' /O

2

•^0

VERTICAL

2

y

INCLINED

!il_ 0 2 HORIZONTAL

FIG. 31—Orientation of triaxial compression specimens to investigate anisotropy.

y—piston

\—bushing

IM / 1^2

O^'^'CRIT. C

/-—

y-deformedi •^specimen ' -b^so «CfliT.*»«90'

FIG. 32—Bending moments and shearing forces introduced by testing inclined anisotropic specimens [97].

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50

LABORATORY SHEAR STRENGTH OF SOIL

FIG. 33—Deformation of inclined specimens of an anisotropic clay [981.

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SAADA AND TOWNSEND ON STATE OF THE ART

51

at the center to their maximum value on the outer boundary. At best they can be used to study the behavior of iineariiy elastic materials prior to failure. General Remarks on the Standard Triaxial Test The more one studies the triaxial test, the more one seems to realize its shortcomings. Yet of all the soil tests today it is the one which is the most popular. It is quite versatile and offers one the opportunity to study a wide range of parameters with relative ease. The corrections mentioned in the previous subsections are themselves often of doubtful value. Nonetheless, it is an improvement over both direct shear and simple shear tests. With or without corrections it is an excellent test for comparative studies of various soils, and there exist correlations between the results obtained by it and by field measurements that make it an excellent design tool. It is obvious from the previous discussions that any study involving materials with high volume change tendencies should use lubricated end platens. Also, if one is to test coarse sands in an undrained way, membrane penetration should be taken into account. One has also to consider the accuracies of the measuring equipment, the effects of backpressures, and the relative flexibilities of the soil and the pore pressure devices used [18]. Whether one runs a constant rate of deformation or a constant rate of stress depends more often than not on convenience. It is obvious, however, that constant rates of deformation tests are mandatory if information beyond the peak is required. Triaxial Testing on Solid Prismatic Specimens Devices Primarily Designed for Plane Strain Testing The fact that many practical problems in soil mechanics can be approximated by plane strain conditions led to the development of plane strain testing devices where the specimen is a cube or a rectangular parallelepiped. Two faces of the prism are prevented from moving while pressures are applied on the two other pairs of faces. The stationary faces are the intermediate principal planes; this means that no shearing stresses are acting on them. The intermediate principal directions of stress and strain must coincide (Fig. 34). The obvious next step was to introduce means of changing the intermediate principal stress at will, rather than just preventing the faces from moving, and measuring the resulting stresses. In any of the new apparatuses which can apply three different principal stresses or strains on a prismatic element, a way can always be found to fix two faces and operate in plane strain [100]. However, the difficulties involved in devices in which the three stresses or strains can be freely changed are much larger than those encountered when just two faces are to be kept in place. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

52

LABORATORY SHEAR STRENGTH OF SOIL

f^

\v^

F/X£0

F/X£D 0-3

^ ^ FIG. 34—Stresses in plane strain conditions.

Al-Husseini [101] has reviewed the various apparatuses as of 1971. In many the minor principal stress is the triaxial chamber pressure when such a chamber is used. Table 3 lists most of the plane strain devices that have been built by various institutions. To this list one must add the hollow cylinder with fixed length used by Whitman and Luscher [102]. Figure 35 shows a section through the WES apparatus whose configuration is similar to that of many in Table 3. The application of the pressure is made through a mixture of rigid and flexible boundaries. Figure 36 shows the principle on which Hambly's [103] device works. There the displacements are applied by rigid plates and the pressure, as measured by a set of transducers, is found to be quite uniform with a minimum of shearing restraint [104]. Some of the machines in Table 3 have been or could easily be modified to accommodate /^o-consolidation conditions [105]. The aforementioned devices apply normal pressures on the faces of the soil specimen. The soil must be isotropic; or the stresses must be applied along axes of symmetry by unrestricting surfaces to avoid the undesirable end effects illustrated in the section on Triaxial Tests on Solid Circular Cylinders. Recognizing the need for a device capable of rotating continuously the principal stresses, Arthur et al [106a] designed the directional shear cell (DSC) in which a cube is subjected to normal and shearing stresses on four of its faces while two others are not allowed to deform (Fig. 37). By varying a^,CT^,and T„ the major principal stress can be rotated without the sudden jump of 11/2 that takes place in the cyclic triaxial and simple shear tests. The behavior of anisotropic soils can be studied in this device. Some of its limitations, notably that the boundary shear stresses are limited to approximately 48.3 kPa (7 psi), are pointed out in a recent study conducted on sand materials [106b]. Multiaxial or True Triaxial Testing Devices There are three ways of applying normal stresses to a prismatic specimen of cubic or parallelepiped shape: either via rigid flat platens or flexible membranes, or a combination of both. Early attempts to test sands by Kjellman Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

SAADA AND TOWNSEND ON STATE OF THE ART

53

TABLE 3—Summary of plane strain shear devices as of 1971. Designer

Location

Reference

Lorenz et al Bjerrum and Kummencji Christensen Leussink and Wittke Marsal et al Duncan and Seed Wood Dickey et al Al-Husseini and Wade Al-Husseini Hambly Campanella and Vaid Ichihara and Matsuzawa

Technische Universitat, Berlin NGI DGl Technical University of Karlsruhe Comision Federal de Electricedad, Mexico University of California Imperial College MIT Georgia Institute of Technology WES Cambridge University University of British Columbia Nagoya University

138 139 140 141 142 143 144 145 101 146 103 147 148

[79] and Jakobson [107] are of limited applicability due to basic mechanical difficulties. By using principles developed by Hambly [103], Pearce built a true triaxial apparatus [108] where the loads are applied by means of rigid plates. Using the proper grease between the rubber membranes and the plates apparently resulted in uniform normal stresses and negligible shear stresses on the plates (Fig. 38) [104]. The second method of using flexible membranes on each of the three pairs of faces was used for tests on sand by Ko and Scott [109]. Because of comer problems [110-112] this apparatus was modified by Arthur and Menzies [110] using specially reinforced multiple rubber bags to load the sand sample. Ramamurthy [113] used rubber balloons inside metallic guides to apply principal stresses to a cubical specimen; he prevented penetration of the balloons' edges into neighboring chambers and distortion of the edges by inserting prismatic pieces of sponge inside the balloons along the edges. Ko and Scott's device has been improved by Sture [114] and by Berends and Ko [115] who used Teflon tapes and sheets as well as aluminum foil to minimize intrusion of one pressure bag into another (Fig. 39). Various combinations of flexible and rigid or rigid-lubricated boundaries on two pairs of faces have been tried. Generally the third stress was applied by the cell pressure acting on the membrane surrounding the sample. Axial rigid platens and a lateral pair of rubber bags were used by Lenoe [116], Shibata and Karube [117], Bell [118], Yong and McKyes [119], Bennett [120], Mesdary [121], and Sutherland and Mesdary [122]. This method is satisfactory, provided the problems associated with the rubber bags can be overcome. Axial rigid platens and another pair of lateral rigid platens were used by Green [123a], Mitchell [100], and Lade and Duncan [123b]. Green used what he termed the ISC belt and managed to keep a small gap between the axial and lateral rigid plates; Mitchell used compressible side plates Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

54

LABORATORY SHEAR STRENGTH OF SOIL

9.

^ y

I I d

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SAADA AND TOWNSEND ON STATE OF THE ART

55

FIG. 36—Principle of Hambly's pUme strain device (1031.

T Reinforced rubber pulling sheets.

Rigid backing plate, /, Pressure bag Pressure bog retaining vones

rubber strips

%V///////////////^

(^

50mm

0

I T ^ X area

SCALE FIG. 37—Diagram of method used to apply normal and shear stresses in the DSC 1106).

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56

LABORATORY SHEAR STRENGTH OF SOIL

FIG. 38—True triaxial apparatus using rigid platens.

MtT*UWlll*llM

FIG. 39—Cross-sectional view of assembled multiaxial cubical apparatus [114]. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

SAADA AND TOWNSEND ON STATE OF THE ART

57

made of solid blocks connected by springs and covered with brass sliders; Lade and Duncan used side plates made of steel and balsa wood laminae proportioned so that the plates could be compressed about 20 percent in the vertical direction without excessive axial force (Fig. 40). It is obvious that no simple type of apparatus is most suitable for testing all types of soils over a wide range of stress levels and stress paths. Sture and Desai [124] in Table 4 summarize the advantages and disadvantages of the various types of devices. Most of them are mechanically complex and require special care in the preparation and placing of the specimen. Most will remain, at least for the near future, research tools to be used in the development of constitutive equations and the determination of soil properties. Table 4 is self-explanatory.

Triaxial Testing on Hollow Circular Specimens As early as 1936 Cooling and Smith [20] used a hollow cylinder laterally unconfined and subjected to torque to obtain the resistance of soils in pure shear. In 1952 Geuze and Tan [21] studied the rheology of clays on thin, long, hollow cylinders subjected to torque. Later, hollow cylinders were placed in a cell and pressurized in an effort to generate a wide variety of stress paths. Two approaches were used. In the first, the inner and outer pressures are different and in addition the specimen is subjected to axial loading. In the second, the inner and outer pressures are identical and in addition the specimen is subjected to axial and torsional loading.

State of Stress in the Hollow Cylinder If the internal and external pressures are different, the stress distribution across the thickness is necessarily nonuniform. Kirkpatrick [125] assumed the validity of the Mohr-Coulomb criterion and averaged the values of the radial stress, a^, and the circumferential stress, a^, across the thickness. Wu et al [126a] made a more complete analysis based on plasticity theory and also averaged the values across the thickness. If the internal and external pressures are equal, the stress distribution across the thickness due to these pressures is uniform, provided there are no end effects. In the hollow cylinder, geometry affects the uniformity of the stress distribution. Radial frictional forces are developed at the ends of the specimen if it has a tendency to expand or contract. This tendency is always present when there is volume change or a change in length at constant volume. The radial frictional forces are self-equilibrating and their influence vanishes as one moves away from the end platens. St. Venant's principle, which is often invoked to dismiss the effects of end platens, demands a certain minimum distance to become operative. In the triaxial test on solid circular cylinders, it is customary to consider that a length-to-diameter ratio of Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

58

LABORATORY SHEAR STRENGTH OF SOIL

0 FRAME FOR COMPRESSING HORIZONTAL LOADING PLATES

- HORIZONTAL LOADING SYSTEM

FIG. 40~Cubical triaxial apparatus [after Ref 123b].

2.5 to 1 is adequate for routine testing. For hollow cylinders, in addition to the thickness, the mean radius plays an extremely important part in the determination of the proper dimensions. The radial factional forces that are imposed upon the specimen by the platens cause circumferential normal forces (hoop forces), shearing forces, and bending moments whose magnitude decreases rapidly as one moves away from the ends. Using the equations of the theory of thin elastic cylindrical shells, it is possible to gain insight concerning the relative magnitude of the stresses and their relation to the generating frictional force [33]. Consider a thin hollow cylinder of length I, mean radius a, and thickness h subjected to a tangential force F per unit length at both its ends (Fig. 41). Equations for the radial displacement w^, the bending moment per unit length M,, the shearing force per unit length Q^, and the normal hoop force per unit length Ng can be found in Refs / and 33. All the equations are expressed in terms of a constant, i3 = [3(1 — v^)/a'^h'^Y'*, where v is Poisson's ratio. With these expressions, the state of stress can be computed at any point of the cylinder. Thus one can compute the proper ratios among length, mean diameter, and thickness so that the end effects are reduced to a minimum. The distance beyond which the various stresses caused by F become negligible can be estimated from the equations derived for a very long cylinder.

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SAADA AND TOWNSEND ON STATE OF THE ART

fill

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60

LABORATORY SHEAR STRENGTH OF SOIL

h>-h

2_1 Z FIG. 41—Hollow cylinder geometry showing end forces.

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SAADA AND TOWNSEND ON STATE OF THE ART

61

For example [126b], let us consider the case of a hollow cylinder with outer and inner diameters of 22 and 18 cm, respectively, and a height of 5 cm. For these dimensions and a Poisson's ratio of 0.25, /S = 0.2896 cm~' and, in terms of F, (iV,)ends = 4.5673i^kg/cm

(MJcenter = " 1.202 i^^ kg/cm

(^(»)cen,er = 3.6823 Fkg/cm

((2,)a,z=f/4 = -0.4710Fkg/cm

The previous values allow us to compute the hoop stresses, a^, the normal stresses due to bending, a., and the shear stresses in terms of F: ('^o)ends = 2.2836 F kg/cm2

(r,,),=o = 0.75 F kg/cm^

(<^9)cemer = 1-8412 F kg/cm^

(T,,),=f/4 = 0.3533 F kg/cm^

(a-).,r„ center =

± 1.8030 F k g / c m ^

Those stresses are shown in Fig. 42. They are all of the same order of magnitude, and one cannot correct for one and ignore the others. It is obvious that the value of F depends on the tendency to expand radially, and that there is no direct way of evaluating its magnitude. The equations for long cylinders indicated that Ng is equal to zero for 0z = ir/2. This means that for the cross section shown in Fig. 42 the hoop stresses would vanish at 5.43 cm from the end; beyond that, they change sign and have a negligible value. On the other hand, the moments M, and consequently a. need /3z = TT to vanish, so that a distance z = 10.85 cm is required before they can be neglected. This indicates that the end effects completely overlap, and a specimen with these dimensions tested in simple triaxial compression leads to data which are impossible to interpret. The radial and circumferential normal stresses, a^ and og, cannot be assumed both equal to the cell pressure; consequently the corresponding strains, e^ and e^, cannot be considered equal. In Ref 127 a hollow cylinder with outer and inner diameters of 10 cm and 6 cm, respectively, and a height of 7 cm is used. In this case (3 = 0.46 c m ^ ' . For the hoop stresses to vanish one should be at 3.4 cm from the ends, and twice as far for the normal stresses due to bending to disappear. A specimen with outer and inner diameters of 71.1 and 50.8 mm (2.8 and 2 in.), respectively, and a height of 160 mm (6.3 in.) is used in Ref 128. In this case 0 = 1.87 in.~'. The hoop stresses vanish at 21.3 mm (0.84 in.) from the ends; 42.7 mm (1.68 in.) are needed for the normal stresses due to bending to disappear. To study the influence of F, Frydman et al [129] conducted tests from which an estimate of the hoop stresses could be made. Their hollow cylinders had outer and inner diameters of 101.6 and 50.8 mm (4 and 2 in.), respectively, and a height of 203.2 mm (8 in.). With these dimensions the value of /3 is 1.06 in.~'. The hoop stresses need 37.6 mm (1.48 in.) and the normal Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

62

UBORATORY SHEAR STRENGTH OF SOIL

:9cm

cr^ DUE TO M^ AT CENTER o

^r^ AT THE TOP FIG. n—Bending and shear stresses due to end effects for the configuration of Ref 126b.

stresses 75.2 mm (2.96 in.) to vanish. We thus have 50.8 mm (2 in.) left at the center of the specimen with no effects from the ends. Under triaxial compression they found that the measured values of e^ and e^ were nearly equal for loose sand, showing that both a, and og were equal to the cell pressure. For large axial strains, differences were found between e^ and eg in dense sand. The hoop stresses were held responsible for the fact that e^ was larger in magnitude than eg, both being in tension. To this, one has to add the effect of the normal stresses due to bending. Those normal stresses relieve the axially imposed ones on the outer half of the specimen and increase them on the inner half (Fig. 42). This could have an important effect on e, and eg for a frictional material. Notice that the measurements were averaged over the whole specimen and not only over the part in which the ends have no effect. It is estimated that an additional inch in the length of the specimen used in Ref 129 would have brought the values of e^ and eg for dense sand quite close together. A special geometry was adopted by Yoshinu and Ohoka [130] and Sherif [131] in order to obtain a uniform distribution of the shearing strains under

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SAADA AND TOWNSEND ON STATE OF THE ART

63

torque (Fig. 43). While the uniformity of the torsional shearing strain has been achieved by keeping the ratio of the height to the distance from the center constant, it is clear that the axial normal strains have to be nonuniform because of the rigidity of the end platens and the drastic change in height as one moves from the inner to the outer radius [130]. In addition, the small size of the specimen and the boundary stresses make it impossible to find a substantial zone where the state of stress could be uniform. If for any reason, such as the application of compressive stress, the sample has a tendency to change cross section, radial shearing forces will be generated; because of the small height of the specimen their effect will be quite substantial. In an elastic hollow cylinder subjected to a torque T, the shearing stress T^varies linearly with the radius. The assumption of a uniform distribution leads to a maximum relative difference in the shearing stress of ('•fc)max ~ ('•fc) av«

ire,) avg

1 = n 1 +n2

(5)

where n = r/r^. The higher this ratio, the better the approximation of a uniform torsional stress distribution. In the aforementioned four examples the values of n are 0.82, 0.6, 0.71, 0.5, respectively. It is obvious that the cylinders examined in the previous example hardly qualify as thin cylinders, so that the theory applied is at best a simplification of the conditions at hand. It does, however, help identify the various components of the state of stress due to end restraints and give an idea about their relative order of magnitude. Since specimens of soil cannot be infinitely long and thin, it is suggested that there be a central zone free from the effects

FIG. 43—Hollow cylinder triaxial specimen geometry of Ref 131.

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64

LABORATORY SHEAR STRENGTH OF SOIL

which should be at least equal in length to the zone influenced by a platen. The total length, (, would thus be 2>-K/0. A ratio n = 0.65 would lead to a maximum relative difference in the distribution of the torsional sharing stresses of 16 percent, which seems quite acceptable. This relative difference, however, drops very quickly as one moves toward the mean radius and as the material yields. In the expression of j3 a change in the value of v from 0.25 to 0.5 has a very minor effect. Choosing v — 0.5 and n — 0.65 leads to the following criteria for the dimensions of hollow cylinders under a system of axial, torsional, and hydrostatic stresses: f > 5.44 Vr„2 - r} and n =— > 0.65

(6)

Hollow Cylinder Under Axial and Torsional Stresses (Same Inner and Outer Pressure) The idea of combining axial and torsional stresses in thin, long, hollow cylinders is certainly not new. In 1932 Schmidt [132] used it to vary the principal stresses and maintain a constant ratio between them. More recently, Haythomthwaite [133] and Broms and Casbarian [134] used it to study the strength of soils and the effects of the rotation of the principal stresses on the various parameters. In 1963 the senior author was involved in the study of the directional properties of graphite, a cross anisotropic material, and the end effects illustrated in the section on Triaxial Tests on Solid Circular Cylinders were intensely discussed. Rather than cutting test specimens at various inclinations to the axis of symmetry and testing them in simple tension or compression, he advanced the idea of keeping the specimens along the axes of symmetry and inclining the principal stresses. To make for meaningful strain measurements, this inclination had to be kept constant, while the principal strains could take any directions they wished. This can be achieved by keeping the ratio of the axial to torsional stresses constant during a test. Indeed, for a thin, long, hollow cylinder subjected to the same inner and outer pressure in the triaxial cell, as well as to additional axial and torsional stresses, the change in principal stresses and their directions are given by (Fig. 44): ACT, + ACT^ I Aa,=^^±^+J(^^^)VA.,.2 j(-.^)V,,,

(7)

A.3 - ^ ^+2 ^ ^ -^. P ^ ^ P ^ V W

(8)

ACT,

ACT^

— tan 2i3 =

A7-9,

(9)

ACT, — ACTA

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SAADA AND TOWNSEND ON STATE OF THE ART

65

NOTATION

FIG. 44—Notation and sign convention for hollow cylinder triaxial specimens.

The major and minor principal stresses are always in the vertical plane and equal to the values of Eq 7 and 8 plus the cell pressure. The intermediate principal stress, aj = a^, is always radial, never changes direction, and is equal to a^; both being equal to the pressure in the cell. If the pressure in the cell changes so will aj, o^ and a^, in addition, of course, to a.. If the pressure in the cell remains constant and the axial and torsional stresses are changes so that their ratio remains constant, Eq 9 gives 1

tan2|3

Aa,

K

(10)

showing that j3 remains constant; the cell pressure acting equally in all directions has no effect on the direction ^. Eqs 7 and 8 become ACT,

ACT,

= ^ - ^ (1 + V r + AK^)

ACT3 =

ACT, —^(1

ACT2 =

0

-

Vl

+

4^2)

(11)

(12) (13)

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66

LABORATORY SHEAR STRENGTH OF SOIL

Under those conditions, the tests would not only proceed at a constant inclination offf,,CT2oj, but also at a constant ratio Aai:Aa2:Aff3; all fixed by choice of K. If the pressure in the cell changes by an amount which is also proportional to the change in the axial stress the properties stated earlier still hold. Consider, for example, a test in which the mean stress is to remain constant. In this case the cell pressure is decreased, say, and the axial pressure increased in the ratio of 2 to 1. Eq 9 gives - tan 20 = 2

^ Aa- H

Aa, -^

-

, "- = K 3 —- Aa. 2

(14)

Equations 7 and 8 become

Aa, = ^

('Y

+YVrn^ ]

Aa. Aa3 = - ; ^ ( y - y V l

Aa2 =

Aa, r^

+ AK^ ]

(15)

(16)

(17)

Here again, the test will proceed at a constant inclination of O], a-^, a^, and at a constant ratio Aa,: Aa2: Aa3, all fixed by the value of K. The possibilities offered by the use of thin hollow cylinder subjected combinations of axial, torsional, and spherical stresses are practically unlimited. For example, two identical tests with the same inclination of principal stresses on the axis of symmetry can be conducted, one at a constant a2 and the other with a variable one; this, to study the effects of the intermediate principal stress. An examination of Eqs 11 to 17 shows that the two tests would have the same b = a2 — aj/aj — a^ in spite of the fact that in one a2 is constant and in the other a2 varies continuously [135]. It is obvious that automatic controls are needed to change the axial, torsional, and cell pressures simultaneously with fixed ratios. Such controls can be primarily electronic of fluidic. Figure 45 shows the most recent version of the SPAC apparatus used at Case Institute of Technology since 1965. The fluidic pneumatic analog computer is set in advance for the ratios of principal stresses and inclinations to be maintained, and the stresses are subsequently

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SAADA AND TOWNSEND ON STATE OF THE ART

67

FIG. 4S—Testing thin. long, hollow cylinders using the SAADA pneumatic analog computer.

applied automatically. Figure 46 shows photographs of thin, hollow cylinders tested at various inclinations of the principal stresses at various stages of deformation and at failure [136]. Hundreds of tests were conducted by Saada and his co-workers in their investigation of A'o-consolidated cross anisotropic clays [82,83.128.136]. In those references details are given about instrumentation and techniques of conducting tests on hollow clay cylinders, from sample preparation to result evaluation. While this study does not cover dynamic testing, it was mentioned in the section on Triaxial Testing on Solid Prismatic Specimens that some authors felt a need for a capability of rotating the principal stresses in a continuous fashion during a cyclic loading of soil sample. The combination of axial and torsional stresses on a thin hollow cylinder is the ideal way for creating this condition without the problems associated with the lack of complementary stresses ever present in the simple shear devices. Consider, for example, a thin hollow cylinder subjected to a constant torsional stress. The stresses on an element are shown in Fig. 47a together with the directions of the principal stresses and principal planes. If a combination of compressive stresses and torsional stress in a direction opposite to the original constant one is slowly applied to the specimen, the principal stresses will rotate as shown in Fig. 476. This combination can be at any desired ratio. There will come a moment when the torsional stresses will cancel each other; the result is shown in Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

68

LABORATORY SHEAR STRENGTH OF SOIL

Torsion

Gen.Comp. Torsion

Gen.Comp. Torsion

3^^! Comp. ^

HU. Aba—Deformation and failure of thin, long, hollow cylinders tested in SPAC [136].

Fig. 47c. If the torsional stress keeps increasing while the axial decreases, one passes through the stages of Figs. 47d and 47e. The superposition of a spherical stress in the cell will of course result in all the stresses being compressive. The pneumatic analog computer (SPAC) presently in use at Case Institute can easily provide automatically all the phases shown in Fig. 47. The rotation of the principal stresses just described, while very appealing for demonstration purposes, is generally quite useless in the case where meaningful strain measurements are to be made in order to generate constitutive equations. The idea of rotating principal stresses is aimed at studying anisotropy either inherent due to fabric or induced due to stress and strains. Under such conditions the directions of the principal stresses and strains do not coincide. Rotating the principal stresses constantly results in strains

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SAADA AND TOWNSEND ON STATE OF THE ART

n-45

aso

258

69

aoo

FIG. 46fc—Deformation and failure of thin, long, hollow cylinders tested in SPAC [136].

whose rotations are due to both anisotropy and the changes in the direction of the stress; with no possibilities of separating them. It is only by maintaining either the direction of the stresses constant and measuring that of the strains, or vice versa, that one can hope to shed Hght on this problem.

General Comments on Hollow Cylinder Testing The thin, long, hollow cylinder subjected to a combination of axial and torsional stresses in addition to spherical stresses is a very valuable tool to study cross anisotropic materials, whether this anisotropy is intrinsic to the material or stress induced. The applied system of stress is symmetric with respect to the axis of symmetry, and the ends are not subjected to unwanted bending and shears. The principal stresses can be controlled, inclined, and rotated at will. Their magnitude is practically unlimited. The fact that the specimen is circular ensures under torsion a condition of pure shear. If the material does not change volume and the length is fixed, torsion applied and the vertical forces measured, a condition of plane strain is ensured. The fact that the walls are thin and that the same pressure acts on both sides practically guarantees (away from the ends) the equality of a^ and a^ to the cell Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

70

LABORATORY SHEAR STRENGTH OF SOIL

\m/ABl£ nnD\

\f/ifm

\m/ABL£ \mmBl£

\ tfpilt ifpt

VAmB/.£ pi59|

^

FIG. 47—Continuous rotation of the principal stresses during cyclic loading.

pressure across the thickness. There is no assurance that such uniform conditions exist in the case of the solid cylinder. The shearing stress due to torsion varies across the thickness but this variation can be minimized by making the walls as thin as possible; more importantly the amount of variation can be reasonably well estimated and decreases as the test proceeds. End effects can be minimized by using long cylinders. The proportions given in Eq 6 are very satisfactory and were used by Saada and his co-workers for clays during the last 15 years. More recently they were found to be as satisfactory for sand specimens [137]. When tested in extension under controlled rate of stress, clay specimens seem to deform quite uniformly until failure takes place. Necking seems to occur at the instant of failure, which is of course catastrophic in nature as in all controlled stress tests. While the preparation of test specimens is slightly more complicated than that of the standard triaxial test, it does not offer any difficulty. Special molds allow the preparation of sand specimens, and any clay that can be cut with a piano wire will easily provide a hollow specimen. Based on Hvorslev's technique [28] the senior author has developed molds that can be used to cut, accurately and with a minimum of disturbance, a round core from a solid cylindrical specimen [136]. It is obvious that hollow cylinders cannot be obtained when the soil at hand is an undisturbed cohesive soil with inclusions of gravel, sand, and silt. While the running of the test often involves using automatic controls, manual controls can be used and are routinely available in most soils laboratories. A standard triaxial cell can be modified at reasonable cost to accommodate hollow cylinders.

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SAADA AND TOWNSEND ON STATE OF THE ART

71

Conclusions Based on the information presented herein and the experience of the authors, the following conclusions concerning the relative utility of the various apparatuses and tests are drawn: For many years the direct shear test had been the main tool used by engineers in foundations design. They recognized its weaknesses and adjusted their estimates accordingly. The ring shear test, while not used frequently, is a valuable tool in obtaining residual strengths. Devices of the Hvorslev type which do not necessitate reversal are possibly the best available today in obtaining this quantity. It is the opinion of the authors that simple shear tests are of no value for research purposes. In practice they can be used in comparative studies but intrinsically they cannot pretend to give material properties. Because of the enormous amount of data accumulated with these devices, their proper place is in the hands of designers who have calibrated their thinking in terms of the results of those tests and have successfully applied those results in their practice. The standard triaxial test is an improvement over direct shear and simple shear. It is clear, however, that if it is to lead to meaningful information, lubricated platens should be used for soils where one expects high volume changes or high volume change tendencies. Membrane penetration has to be reduced when granular soils are tested in an undrained condition, since it appears that the pore water pressures could easily differ by a factor of two if such precautions are not taken. Tests on prismatic specimens offer the opportunity to study general behavior and generate constitutive equations. The devices differ in capability and complexity, but the spread of automatic controls have made possible stress and strain paths considered impossible a few years ago. At present most seem to be in a development stage and their main attraction is that conceptually they are simple to grasp: A force is divided by an area and one has a stress that can in theory be changed at will. Where the stresses are applied through rigid boundaries, what happens inside the specimen will always remain subject to questioning since St. Venant's principle has no room to take hold. In the flexible boundary DSC the principal stresses can be rotated and anisotropy studied, but radiography is needed to measure the strain distribution. The thin, long, hollow cylinder with the same inner and outer pressure and a combination of axial and torsional stress has been in routine use for a number of years. It allows one to incline the principal stresses and change them practically at will. It is a tool with which anisotropy can be investigated with very little or no restrictions on the size of the specimen and the magnitude of the stresses. The small approximation involved regarding the

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distribution of the shear stress can be estimated with reasonable accuracy and this accuracy improves as the test proceeds. St. Venant's principle can be taken advantage of to minimize undesirable end effects should they become present. The thinness of the specimen and the fact that the same normal pressures act on the inner and outer faces increase our confidence that the normal radial and circumferential stresses are uniformly distributed inside the material. Acknowledgments The critical examination of the various testing apparatuses started in 1975 during a summer the senior author spent at the Waterways Experiment station. The authors wish to thank Messrs. S. Johnson, L. McAnear, and M. AlHusseini for the stimulating discussions which formed the bases of this state of the art. The photoelastic study of the simple shear devices was sponsored by the Waterways Experiment Station and conducted by Professor D. K. Wright at Case Institute of Technology. The work related to hollow cylinders is part of research sponsored over the last 15 years at Case by the National Science Foundation. Drs. S. Poulos and C. Ladd reviewed the manuscript and made valuable suggestions. To all, the authors wish to express their deepest gratitude.

References (/) Saada, A. S., Elasticity, Theory and Applications. Pergamon, Elmsford, N.Y., 1974. [2] Scott, R. F., Principles of Soil Mechanics. Addison-Wesley, Reading, Mass.. 1963. [3] Nadai, A., Theory oj Flow and Fracture of Solids, Vol. 1, McGraw-Hill, New York, 1950. [4a\ Sowers, G. F. in Laboratory Shear Testing of Materials, ASTM STP 361, American Society for Testing and Materials [hereafter cited as ASTM], 1965, pp. 3-21. \4b] Collin, A., Experimental Investigation on Sliding of Clay Slopes, Paris, 1846 (translated by W. R. Schriever, University of Toronto Press, 1956). [5] Leygues, M. L., "La Poussee des Terres," Ann. des Ponts et Chaussees, Sixth Serv., Vol. 10, 1885, p. 788. |61 Housel, W. S., Procedures for Testing Soils, ASTM, 1958, p. 360. [7] Hvorslev, M. J. in Proceedings, ASTM, Vol. 39, 1939, pp. 999-1022. [«] Kjellman, W., Geotechnique, Vol. 2, No. 3, 1951, pp. 225-235. [9] Roscoe, K. H. in Proceedings, 3rd International Conference on Soil Mechanics and Foundation Engineering [hereafter cited as ICSMFE], Zurich, Vol. 1, 1953, p. 186. [10] Peltier, M. R. in Proceedings, 4th ICSMFE, London, Vol. 1, 1957, p. 179. [//[ Bjerrum, L. and Landva, A., Geotechnique, Vol. 16, No. 1, 1966, pp. 1-20. 112] Seiffert, R., "Untersuchungsmetod um Festzustellen ob Sich Ein Gegebenes Baumaterial fur den Bau Eines Erddammes Eignet," les Congres des Grands Barrages, Vol. 3, 1933, p. 47. [13] Buissman, A. S. K., "Proefaderuindelyke Bepaling Van de Greas Van Inwendig Evenwient van een Grandmassa," De Ingenieur, Vol. 49, Part B, 29 June 1934. [14] Housel, W. S. in Proceedings. ASTM, Vol. 36, Part 11, 1936. pp. 426-468. 1/5] Stanton, T. E. and Hveem, F. N. in Proceedings, 14th Annual Meeting of the Highway Research Bulletin, Vol. 14, Part II, 1934, pp. 14-54. [16] Rendulic, L. in Proceedings. 1st ICSMFE, Cambridge, Vol. 3, 1936, pp. 48-51. [17] DeBeer, E., Geotechnique. Vol. 2, No. 2, 1950, p. 162.

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118] Bishop, A. W. and Henkel, D. J., The Measurement of Soil Properties in the Triaxial Test, 2nd ed., Arnold, London, 1%2. [19] Kjellman, W. in Proceedings, 1st ICSMFE, Cambridge, Vol. 2, 1936, p. 16. [20] Cooling, L. F. and Smith, D. B., Journal of the Institution of Civil Engineers, Vol. 3, 1935, pp. 333-343. [21] Geuze, E. C. W. A. and Tan, T. T. in Proceedings. 2nd International Congress on Rheology, Harrison, Ed., Oxford, 1953. [22] Jurgensen, L., "Shearing Resistance of Soils," Journal of the Boston Society of Civil Engineers, July 1934. [23] Hvorslev, M. J., "On the Strength Properties of Remolded Cohesive Soils," Ph.D. thesis. 1937, (translated in June 1963 by United States Army Engineers [hereafter cited as USAE], Waterways Experiment Station, Vicksburg, Miss.). [24] O'Neil, H. M., Journal of the Soil Mechanics and Foundations Division, American Society of Corrosion Engineers (hereafter cited as ASCE], Vol. 88, No. SM4, 1962, pp. 109-137. [25] Gilbert, P. A., "Evaluation of the O'Neil Shear-o-Meter for Performing Constant Volume Direct Shear Tests," Misc. Paper S-74-11, USAE, Waterways Experiment Station, Vicksburg, Miss., 1974. ]26] Taylor, D. W., "Seventh Progress Report on Shear Research to U.S. Engineers," MIT Publication, Massachusetts Institute of Technology, Cambridge, Mass., 1941. ]27[ Bishop, A. W., Green, G. E., Garga, V. K., Andersen, A., and Brown, J. D., Geotechnique. Vol. 21, No. 4, 1971, pp. 273-328. [28] Hvorslev, M. J. and Kaufman, R. I., "Torsion Shear Apparatus and Testing Procedures," Bulletin No. 38, USAE, Waterways Experiment Station, Vicksburg, Miss., 1952. [29] Skempton, A. W., Geotechnique. Vol. 14, No. 2, June 1964, p. 77. [30] Townsend, F. C. and Gilbert, P. A. in Soil Specimen Preparation for Laboratory Testing. ASTM STP599. ASTM 1975, pp. 43-65. [31] La Gatta, D. P., "Residual Strength of Clays and Clay-Shales by Rotation Shear Tests," Contract Report S-70-5, USAE, Waterways Experiment Station, CE, Vicksburg, Miss., June 1970; also in Harvard Soil Mechanics Series, No. 86, July 1970. [32] Roscoe, K. H., Bassett, R. H., and Cole, E. R. L. m Proceedings. Geotechnical Engineering Conference, Oslo, Vol. 1, 1967, pp. 231-237. [33] Timoshenko, S. P. and Goodier, J. N., Theory of Elasticity. McGraw-Hill, New York, 1970. [34] Prevost, J. H. and Hoeg, K., "Reanalysis of Simple Shear and Liquefaction Testing," Canadian Geotechnical Journal. Vol. 13, No. 4, 1976. [35] Kovacs, W. D. in Proceedings. Symposium on Earth and Earth Structures under Earthquake and Dynamic Loads, India, 1972, pp. 82-86. [36] Duncan, J. M. and Dunlop, P. in Proceedings. 7th ICSMFE, Mexico, Vol. 1, 1969, pp. 101-109. [37] Lucks, A. S., Christian, J. T., Brandow, G. E., and Hoeg, K., Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 98, No. SMI, 1972, pp. 155-160. [38] Hara, A. and Kyota, Y. in Proceedings, 9th ICSMFE, Tokyo, Vol. 2, 1977, pp. 247-250. ]39] Shen, C. K., Saddigh, K., and Herrmann, L. R. in Dynamic Geotechnical Testing, ASTM STP 654, ASTM, 1978, pp. 148-162. ]40] Wright, D. K., Gilbert, P. A., and Saada, A. S. in Proceedings, ASCE Specialty Conference on Earthquake Engineering and Soil Dynamics, Vol. 2, 1978, pp. 1056-1075. ]41] Finn, W. D. L., Pickering, D. J., and Bransby, P. L., Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 97, No. SM4, 1971, pp. 639-659. [42] Dyvik, R., Zimmie, T. F., and Floess, C. H. L., this publication, pp. 000-000. [43[ DeJosselin de Jong, G., "Statics and Kinematics in the Failable Zone of a Granular Material," thesis. Delft, 1959. [44] Soydemir, C , "Strength Anisotropy Observed Through Simple Shear Tests," Bjerrum Memorial Volume, 1976. [45a] Moore, W. M., Highway Research Record, No. 108, 1965, pp. 19-25. ]45b\ Saada, A. S., "A Discussion on the Strength of Soils," in Proceedings, International Conference on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, University of Missouri, Rolla, Mo., Vol. 3, 1981. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

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[46] Khera, R. P. and Krizek, R. J., Materials Research and Standards. Vol. 7, No. 9, 1%7, pp. 392-296. [47] Escario, V. in Proceedings. 5th ICSMFE, Paris, Vol. 3, 1961, p. 124. [48] Saada, A. S., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 93, No. SM6, 1967, pp. 61-78. [49] Saada, A. S., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 96, No. SM3, 1970, pp. 1085-1089. [50] Filon, L. N. G., "The Elastic Equilibrium of Circular Cylinders under Certain Practical Systems of Load," Philosophical Transactions of the Royal Society of London. Series A, Vol. 198. 1902. [51] Pickett, G., "Application of the Fourier Method to the Solution of Certain Boundary Problems in the Theory of Elasticity," Journal of Applied Mechanics, Vol. 2, 1944. [52[ D'Appolonia, E. and Newmark, N. M. in Proceedings. 1st U.S. National Conference of Applied Mechanics, American Society of Mechanical Engineers (ASME), 1951. [53] Balla, A., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 86, No. SM6, Dec. 1960. [54] Girijavallabhan, C. V., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 98, No. SM2, 1970, pp. 783-787. [55] Perloff, W. H. and Pombo, L. E. in Proceedings. 7th ICSMFE, Mexico, Vol. 1, 1969, pp. 327-333. [56] Rutledge, P. C , "Cooperative Triaxial Shear Research Program," Progress Report on Soil Mechanics Fact Finding Survey, USAE, Waterways Experiment Station, Vicksburg, Miss., 1947. [57] Shockley, W. G. and Ahlvin, R. G., "Non-Uniform Conditions in Triaxial Test Specimens," Research Conference on Shear Strength on Cohesive Soils, ASCE, Boulder, Colo., 1961, p. 341. [58] Rowe, P. W., Proceedings of the Royal Society of London. Series A, Vol. 269, 1%2, pp. 500-527. [59] Rowe, P. W. and Barden, L., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 90, No. SMI, 1964, pp. 1-27. [60] Lee, K. L. and Seed, H. B., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 90, No. SM6, 1964, pp. 173-175. [61[ Olson, R. E. and Campbell, L. M., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 90, No. SM6, 1964, pp. 167-173. [62] Tumbull, J. M., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 90, No. SM6, 1964, pp. 175-177. [63] Barden, L. and McDermott, J. W., "The Use of Free Ends in Triaxial Testing of Clays," Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 91, No. SM6, Nov. 1965. [64] Bishop, A. W. and Green, G. E., Geotechnique. Vol. 15, No. 3, 1965, pp. 243-266. [65] Barden, L. and Khayatt, A. J., Geotechnique. Vol. 16, No. 4, 1966, pp. 338-357. [66] Kirkpatrick, W. M. and Belshaw, D. J., Geotechnique. Vol. 18, No. 3, 1968, pp. 336350. [67] Kirkpatrick, W. M. and Younger, J. S., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. %, No. SMS, 1970, pp. 1683-1695. [68] Duncan, J. M. and Dunlop, P., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 44, No. SMI, 1%8, pp. 271-290. [691 Roy, M. and Lo, K. Y., Canadian Geotechnical Journal. Vol. 8, No. 4, 1971, pp. 579-588. [70] Raju, J. S., Sadaswan, S. K., and Venkataraman, M., Soil and Foundations. Japanese Society of Soil Mechanics and Foundation Engineering, Vol. 12, No. 4, 1972, pp. 25-43. [71] Kirkpatrick, W. M., Seals, R. M., and Newman, F. B., Journal of the Soil Mechanics and Foundations Division. ASCE. Vol. 100, No. SM2, Feb. 1974, pp. 190-196. [72] Lee, K. L.. Journal of the Geotechnical Engineering Division. ASCE, Vol. 104, No. GT6, 1978, pp. 687-704. [73] Lowe, John and Johnson, T. C. in Proceedings. ASCE Research Conference on Shear Strength of Soils, Boulder, Colo., 1960, p. 819. [74] "Laboratory Soil Testing," EM 1110-2-1906, Department of the Army, Washington, D.C., 1976.

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175] Lee, K. L. and Black, D. K., "Time to Dissolve Air Bubble in Drain Line," Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 98, No. SM2, Feb. 1972. [76] Donaghe, R. T. and Townsend, F. C , "Effect of Backpressure Saturation Techniques on Results of /J-Triaxial Compression Tests," WES MP GL-79-12, Vicksburg, Miss., May 1979. [77] Mulilis, J. P., Chan, C. K., and Seed, H. B., "The Effects of Methods of Sample Preparation on the Cyclic Stress-Strain Behavior of Sands," EERC Report No. 75-18, University of California, Berkeley, Calif., July 1975. \78] Donaghe, R. T. and Townsend, F. C , "Effects of Anisotropic Consolidation in Consolidated Undrained Triaxial Compression Tests of Cohesive Soils," Geotechnical Testing Journal. Vol. 1, No, 4, Dec. 1978. [79] Henkel, D. J. and Sowa, V. A. in Laboratory Shear Testing of Soils, ASTM STP 361, ASTM, 1964, pp. 280-294. [80] Udd, C. C. in Proceedings, 6th ICSMFE, Vol. 1, London, 1965, p. 282. [81] Lee, K. L., Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 96, No. SM6, Nov. 1970, p. 2025. [82] Saada, A. S. and Ou, C. D., Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 99, No. SM12, 1973, pp. 1091, 1111. [83] Saada, A. S. and Bianchini, G. B., Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 101, No. G T l l , 1975, pp. 1151-1164. [84] Casagrande, A. and Poulos, S. J., "Investigation of Stress-Deformation and Strength Characteristics of Compacted Clays," Harvard Soil Mechanics Series,, No. 7A, Oct. 1964. [85] Donaghe, R. J., "Effect of Strain Rate in Consolidated Undrained Triaxial Compression Tests of Cohesive Soil, Report 2, Vicksburg Buckshot Clay (CH)," WES MP S-70-8, May 1971, Vicksburg, Miss. [86a] Olson, R. E. and Kiefer, M. L. in Laboratory Shear Testing of Soils, ASTM STP 361, ASTM, 1964, pp. 482-491. [86b] Conforth, D. H., "Discussion on Side Filter Drains," in Proceedings, 5th ICSMFE, Paris, Vol. 3, 1961, pp. 121-122. [87] Webb, D. L., "The Mechanical ftoperties of Undisturbed Samples of London Clay and Perre Shale," Ph.D. thesis. University of London, 1%7. [88] Pachakis, M. D., Geotechnique, Vol. 26, No. 1, 1976, pp. 226-230. [89] Duncan, J. M. and Seed, H. B., "Errors in Strength Tests and Recommended Corrections," Report, University of California, Berkeley; submitted to USAE, Waterways Experiment Station, Vicksburg, Miss., 1965. [90] Olson, R. E. and Campbell, L. M., Materials Research and Standards. Vol. 7, No. 2, 1%7, pp. 45-52. 19/] Newland, P. L. and Allely, B. H., Geotechnique, Vol. 9, 1959, pp. 174-182. 192] Roscoe, K. H., Schofield, A. N., and Thurairajah, A. in Laboratory Shear Testing of Soils. ASTM STP 361. ASTM, 1964, pp. 111-128. [93] El-Sobhy, M., "The Behavior of Particulate Materials Under Stress," Ph.D. thesis. University of Manchester, 1964. [94] Raju, V. S. and Sadaswan, S. K., Journal of the Geotechnical Engineering Division. ASCE, Vol. 100, No. GTA, 1974, pp. 482-489. [95] Frydman, S., Zeitlin, I. G., Alpan, \., Journal of Testing and Evaluation. Vol. 1, No. 1, 1973, pp. 37-41. [96] Kiekbusch, M. and Schuppener, B., Journal of the Geotechnical Engineering Division. ASCE, Vol. 103, No. G T l l , 1977, pp. 1267-1279. [97] Saada, A. S., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. %, No. SMS, 1970, pp. 1847-1852. [98] Saada, A. S. and Bianchini, G. B., Journal of the Geotechnical Engineering Division. ASCE, Vol. 103, No. GT6, 1977, pp. 655-660. [99] Habib, P., "La Resistance au Cisaillement des Sols," Ph.D. thesis. University of Paris, 1953. [100] Mitchell, R. ] . , "An Apparatus for Plane Strain and True Triaxial Testing of Undisturbed Soil Samples," Canadian Geotechnical Journal. Vol. 10, 1973, pp. 520-527. [101] Al-Husseini, M. M., "Investigation of Plane Strain Shear Testing," Report No. 1, Tech. Rep. 5-71-2, USAE, Waterways Experiment Station, Vicksburg, Miss., March 1971.

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[102] Whitman, R. V. and Lusher, U., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 88, No. SM6, 1962, pp. 135-167. [103] Hambly, E. C. and Roscoe, K. H. in Proceedings. 7th ICSMFE, Mexico, Vol. 2, 1%9, pp. 173-181. [104] Sketchly, C. J. in Stress and Strain Behavior of Soils. Proceedings of the Roscoe Memorial Symposium, Foulis and Co., 1971, pp. 391-396. [105] Al-Hussaini, M. M., this publication, pp. 78-93. [106a] Arthur, J. R. F., Chua, K. S., and Dunstan, T., Geotechnique, Vol. 27, No. 1, 1977, pp. 1-30. [106h] Arthur, J. R. F., Bekenstein, S., Germaine, J. J., and Ladd, C. C , this publication, pp. 516-540. 1/07] Jakobson, B. in Proceedings. 4th ICSMFE, London, Vol. 1, 1957, pp. 167-171. [108\ Pearce, J. A. in Stress and Strain Behavior of Soils. Proceedings of the Roscoe Memorial Symposium. Foulis and Co., 1971, pp. 330-339. [109] Ko, H. Y. and Scott, R. F., Geotechnique. Vol. 17, No. 1, 1967, pp. 40-57. [110] Arthur, J. R. E. and Menzies, B. K., Geotechnique. Vol. 18, No. 2. 1968, pp. 271-272. [///] Bell, T. M., Geotechnique. Vol. 18, No. 2, 1968, pp. 267-271. [112] Green, G. E., Geotechnique. Vol. 176, No. 3, 1967, p. 295. [113] Ramamurthy, T., Journal of Soil Mechanics and Foundation Engineering of India. Vol. 9, No. 3, 1970, pp. 251-269. [114] Sture, S., "An Improved Multiaxial Cubical Cell and its Application to the Testing of Anisotropic Materials," M.S. thesis. University of Colorado, Boulder, Colo., 1973. [115] Berends, B. E. and Ko, H. Y., "Cubical Multiaxial Cell for Testing Cohesive Soils," Journal of the Geotechnical Engineering Division. ASCE, Vol. 106, No. GTl, Jan. 1980. [116] Lenoe, E. M., Experimental Mechanics. Feb. 1966, pp. 99-104. [117] Shibata, T. and Karube, D. in Proceedings. 6th ICSMFE, Montreal, Vol. 1, 1965, pp. 359-363. [118] Bell, J. M., "Stress-Strain Characteristics of Cohesionless Granular Materials Subjected to Statically Applied Homogeneous Load in an Open System," Ph.D. thesis, California Institute of Technology, 1965. [119] Yong, R. N. and McKyes, E. in Proceedings. 3rd Pan-American Conference Soil Mechanics and Foundations Engineering, Caracas, Vol. 1, 1967, pp. 131-143. [120] Bennett, D. H. in Proceedings. 7th ICSMFE, Mexico, Vol. 3, 1969, p. 519. [121] Mesdary, M. S., "The Shearing Behavior of Granular Material under a General Stress System," Ph.D. thesis. University of Glasgow, 1969. [122] Sutherland, H. B. and Mesdary, M. S. in Proceedings. 7th ICSMFE, Mexico, Vol. 1, 1%9, pp. 391-399. [123a] Green, G. E. in Stress and Strain Behavior of Soils. Proceedings of the Roscoe Memorial Symposium. Foulis and Co., 1971, pp. 285-323. [123b] Lade, P. and Duncan, J., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 99, No. SMIO, 1973, pp. 793-812. [124] Sture, S. and Desai, C. S., Geotechnical Testing Journal. Vol. 2, No. 1, 1979, pp. 20-33. [125] Kirkpatrick, W. M. in Proceedings. 4th ICSMFE, London, Vol. 1, 1957, pp. 172-178. [126a] Wu, T. H., Loh, A. K., and Malvern, L. R., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 89, No. SMI, 1963, pp. 145-181. [126b] Lade, P. V., "Torsion Shear Test on Cohesionless Soil," in Proceedings, 5th PanAmerican Conference on Soil Mechanics and Foundations Engineering, Buenos Aires, 1975. [127] Ishihara, K. and Yasuda, S., Soils and Foundations. Vol. 15, No. 1, 1975, pp. 45-59. [128] Saada, A. S. and Zamani, K. K. in Proceedings. 7th ICSMFE, Mexico, Vol. 1, 1969, pp. 351-359. [129] Frydman, S., Alpan, I., and Zeitlin, I. G. in Proceedings, 4th Asian Conference on Soil Mechanics and Foundations Engineering, Bangkok, 1971, pp. 17-23. [130] Yoshinu, Y. and Ohoka, H. in Proceedings. 8th ICSMFE, Moscow, Vol. 1.2, 1973, pp. 501-506. [131] Sherif, M. A. and Ishibashi, I., Journal of the Geotechnical Engineering Division. ASCE. Vol. 100, No. GT8, 1974, pp. 871-888.

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SAADA AND TOWNSEND ON STATE OF THE ART

77

1132] Schmidt, R., "Dissertation Gottingen," 1932. [133] Haythomthwaite, R. M. in Plasticity. Pergamon Press, London, 1960, pp. 185-193. [134] Broms, B. B. and Casbarian, A. O. in Proceedings. 6th ICSMFE, Montreal, Vol. 1, 1965, pp. 179-183. [135] Saada, A. S. and Bianchini, G. B., Journal of the Geotechnical Engineering Division. ASCE, Vol. 104, No. GT12, 1978, pp. 1537-1540. [136] Saada, A. S. and Baah, A. K. in Proceedings. 3rd Pan-American Conference on Soil Mechanics and Foundations Engineering, Caracas, Vol. 1, 1967, pp. 67-88. [137] Lade, P. V., this publication, pp. 145-163. [138] Lorenz, H., Neumeure, H., and Gudehus, G. in Proceedings. 6th ICSMFE, Montreal, Vol. 1, 1965, pp. 293-297. [139] Bjerrum, L. and Kumimencje, 0 . , "Shearing Resistance of Sand Samples of Circular and Rectangular Cross Section," Bulletin 44, Norwegian Geotechnical Institute, 1961. [140] Christensen, N. H., "Model Test of Plane Active Earth Pressure in Sand," Bulletin No. 10, Danish Geotechnical Institute, 1%1. [141] Leussink, H. and Wittke, W. in Laboratory Shear Testing of Soils. ASTM STP 361. ASTM, 1964, pp. 77-89. [142] Marsal, R. J., DeArellano, L. P., and Numez, G. A. in Proceedings, 3rd Pan-American Conference on Soil Mechanics and Foundations Engineering, Caracas, 1967, pp. 249270. [143] Duncan, J. M. and Seed, H. B., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 92, No. SM6, 1966, pp. 81-104. [144] Wood, C. C , "Shear Strength and Volume Change Characteristics of Compacted Soil under Conditions of Plane Strain," Ph.D. thesis. University of London, 1958. [145] Dickey, J. W., Ladd, C. C , and Rixner, J. J., "A Plane Strain Shear Device for Testing Clays," Research in Earth Physics, Phase Report No. 10, Massachusetts Institute of Technology, Cambridge, Mass., submitted to USAE, Waterways Experiment Station, Vicksburg, Miss., 1968. [146] Al-Husseini, M. M., "The Behavior of Sand Under Plane Strain Conditions," Ph.D. thesis, Georgia Institute of Technology, 1968. [147] Campanella, R. J. and Vaid, Y. P. in Proceedings. 8th ICSMFE, Moscow. Vol. 1.1, 1973, pp. 85-92. ]148] Ichihara, M. and Matsuzawa, H. in Proceedings. 8th ICSMFE, Moscow, Vol. 1.1, 1973, pp. 185-190.

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Mosaid Al-Hussaini^

Comparison of Various IVIethods for Determining Ko

REFERENCE: Al-Hussaini, Mosaid, ASTM STP 740. "Comparison of Various Methods for Determining A'o," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 78-93. ABSTRACT: A series of tests were conducted on sands to determine the value of the coefficient of earth pressure at rest (/CQ) and the factors which influence its magnitude. Four laboratory techniques were used to determine the value of K^ and the stress-strain relationship for Reid-Bedford sand at dense, medium, and loose states. Test results indicated that the value of KQ for the sand tested is not significantly influenced by the testing equipment or the technique used. Results show that KQ increases with decreasing relative density, increasing stress level, and number of loading cycles. On the first loading cycle, the value of KQ agreed well with Jaky equation KQ= I — sin . The constrained modulus D increased with increasing relative density, increasing stress level, and increasing number of loading cycles, but remained almost the same for all unloading cycles. KEY WORDS: soil tests, coefficient of earth pressure, sands, density (mass/volume), compression tests, soil properties

Many naturally occurring sediments as well as man-made fills are deposited and compacted in horizontal layers where no lateral yielding occurs. Under such conditions the ratio of lateral to vertical stresses is known as the coefficient of earth pressure at rest and is denoted by the symbol KQ. For elastic isotropic material under first loading, the value of KQ can be expressed directly in terms of Poisson's ratio (c); for example, KQ = i>/(l — v). Hence the value of KQ and stress-strain response of soils under /^o-conditions are important for engineering problems involving settlement of widespread fills, lateral pressure on nonyielding retaining walls, excavations, and other problems where lateral yielding is restricted. Furthermore, since KQ is treated as an elastic soil parameter, a knowledge of Kg could be applied to static problems and some dynamic problems such as the displacement in laterally confined strata due to one-dimensional wave propagation. 'Associate professor and chairman. Department of Civil Engineering. College of Engineering and Petroleum, Kuwait University, Kuwait.

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AL-HUSSAINI ON METHODS FOR DETERMINING KQ

79

Many methods and testing devices have been developed for determining the value of Ko and the stress-strain condition under one-dimensional compression. A comprehensive review of the laboratory and field techniques for determining KQ has been presented elsewhere [/].^ The problem is to determine which method and technique provide the best estimate of Kg and what factors significantly affect the measured values. The purpose of this study was to examine various experimental and analytical methods used in evaluating A'o, and to determine the various factors which affect its magnitude. Because it is practically impossible to study the performance of every device developed for measuring KQ in the laboratory, only four typical devices were selected for comparison. Material Used in Experimentation The Reid-Bedford sand used in the test program was originally obtained from the Campbell swamp area along the Mississippi River about 15 miles south of Vicksburg, Mississippi. It is a uniform sand (Fig. 1) with a grain shape varying from subrounded to subangular; a very small amount of the material is finer than the No. 200 U.S. standard sieve. Other physical properties of the Reid-Bedford sand as determined in accordance with ASTM standards are as follows: specific gravity (Gj) is 2.66, maximum void ratio is 0.903, minimum void ratio is 0.593, mean grain diameter is 0.125 mm, coefficient of uniformity is 1.5, and the sand is classified as SP in accordance with the Unified Soil Classification. Laboratory Testing Equipment The main laboratory testing equipment used in this study was a conventional triaxial apparatus with enlarged low-friction cap and base that can test soil specimens with a 71.1 mm (2.8 in.) diameter and a 152.4 mm (6 in.) height. However, four different methods for sensing the lateral deformation of the specimen and adjusting the lateral pressure to obtain zero lateral strain during Kg-test were employed. LVDT Clamp Lateral Strain Sensor Method The lateral strain sensor consisted of two 4.76-mm (^/i6-in.)-thick curved aluminum strips connected by a low-friction hinge. A soft steel spring at the other end provided tension for holding the clamp-bearing surface snugly against the specimen. A small amount of rubber cement between the bearing surface and specimen membrane assisted in holding the clamp in position. The geometry of the lateral strain sensor and position of the linear variable dif^The italic numbers in brackets refer to the list of references appended to this paper.

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80

LABORATORY SHEAR STRENGTH OF SOIL

U. S. S T A N D A R D S I E V E NUMBERS

.H

3

4

6

e 10 1416 20 30 40 30 70 WO 140 200

iin I' • T " T r T T T " loor 1 1 r " iT- i

1 I I III • fm^ i if—r- • 'ii - "t—Tn-iTr-i ^

1 1 1

1—!

N;

1 1 1

V \ \ \ \

,

t . t_ ^_ - H1 0--10

vt-^..-

5

1

0.5

GRAIN SIZE MILLIMETtllS

FIG. 1—Gradation curve for Reid-Beclford sand.

ferential transformer (LVDT) were such that the sensor indicated radial deformations which were twice the actual radial deformations of the soil specimen. After the soil was compacted at the desired density, the lateral strain sensor was placed horizontally around the midheight of the Specimen (Fig. 2). Strain-Gaged A^oBelt Method This lateral strain sensor, called the /Co-belt, has been fully described in a previous study [2]; the description herein is limited to the essential parts. The /Cfl-belt consists of a thin brass alloy band welded to a short piece of hose clamp with an adjustable thumbscrew. The two ends of the belt and a small pin form a hinge, which can be engaged and disengaged very easily. Four strain gages were mounted on the brass foil band. Two active gages were placed along the circumference; the other two were dummy gages placed along the vertical axis on the portion of the band which projected above and below the main band. Figure 3 shows the /Co-belt in position on a specimen. Swinging-Anns Lateral Strain Sensor Metliod The lateral sensor with swinging arms was originally developed by Holtz [3]. The device (Fig. 4) consists of three components: two arms, two posts, and the LVDT holder. Each arm consists of an aluminum plate 108 mm (4 'A in.) long.

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AL-HUSSAINI ON METHODS FOR DETERMINING KQ

81

FIG. 2—Lateral sensor with LVDT clamp around the specimen.

50.8 mm (2.0 in.) wide, and 6.3 mm ('A in.) thick, with a 6.3-mm ('/4 in.)-diameter hole drilled 15.8 mm (Vs in.) deep to accommodate the post. Two identical stainless steel posts were made, each 171.6 mm (6^4 in.) long and 7.9 mm (-/\b in.) in diameter reduced to 6.3 mm (V4 in.) at the ends to facilitate proper fit with other components of the device. The LVDT holder consisted of two aluminum plates, 127 mm (5 in.) long, 31.7 mm (l'/4 in.) wide, and 12.6 mm (Vi in.) thick, with one plate to hold the LVDT in position and the other its core. Two modifications were made on the original triaxial cell; the first was to drill two holes in the base to allow the passage of the posts through the magnetic seal and ball race bushings seated within the holes. The second modification was to mount the triaxial cell on four stainless steel foundation posts. Each post was 25.4 mm (1.0 in.) in diameter and 76.2 mm (3.0 in.) in length, threaded at the top to the base of the triaxial cell, and connected at the bottom to a square aluminum base plate 203 mm (8.0 in.) wide and 12.6 mm ('/2 in.) thick. The outstanding feature of this device is that the LVDT which senses the deformation of the specimen is isolated from any detrimental

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82

LABORATORY SHEAR STRENGTH OF SOIL

FIG. 3—Kfi-belt mounted on the triaxial specimen.

chamber fluids, while the LVDT clamp sensor and the ATo-belt require that air or silicon oil be used as the chamber fluid. The magnetic seal was found to offer negligible resistance to the rotation of the post in the horizontal plane; however, any slight tilting of the post from the vertical position may break the seal and cause leakage of the chamber fluid.

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AL-HUSSAINI ON METHODS FOR DETERMINING KQ

83

FIG. 4—Lutenil strain sensor with swinging arms.

Indirect or Burette Method This method, first employed by Bishop and Eldin [4], utilizes the volume change of the soil specimen to indicate whether or not zero lateral strain conditions were maintained during A'o-tests. The test method and equipment (Fig. 5) were based on the assumption that the volumetric strain of the specimen during one-dimensional compression is equal to the axial strain. In other words, the ratio of the change in volume to the change in height is constant

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84

LABORATORY SHEAR STRENGTH OF SOIL

PRESSURE

GAG£~

BACK PRESSURE SUPPLY PRESSURE REGULATOR

RELEASE

VALVES

VOLUME

CELL PRESSURE SUPPLy AIR-WATER INTERFACE

CHANGE

BURETTE

TANK

FIG. 5—General layout of the hydraulic system for the burette method.

and equal to the initial area of the specimen. Therefore, if the initial area of the soil specimen and the change in height of the specimen are known, it is possible to adjust the cell pressure so that the volume change indicated by the burette is equivalent to the calculated volume change. Test Procedure All specimens except those tested by the indirect burette method were tested dry; the burette method specimens were saturated by placing the specimens under de-aired water and subjecting them to a vacuum to remove the air prior to testing. The test procedure used in consolidating the specimen under A'o'Condition was about the same whether the lateral sensor was instrumented with an internal LVDT or external LVDT or strain gages. A null reading was established on the readout system connected to the lateral strain sensor used for the particular test. Both axial load and confining pressure were increased simultaneously so that a null condition was maintained during the entire test. Readings of axial load and axial deformation were recorded at every 10-psi increment of confining pressure.^ The procedure used in the indirect method was slightly different from the test procedure used in the other methods since no null point was needed in this test. First, a correlation was computed between the change in height of the observed volume of the specimen under no lateral yielding, and then the axial load and cell pressure were increased as dictated by the computer correlation. The procedure was slow and tedious and required continuous adjustment of the cell pressure; readings were taken whenever the collected test data fell on the established volume change versus axial deformation relationship. ^1 psi = 6.9 kPa.

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AL-HUSSAINI ON METHODS FOR DETERMINING Kn

85

Test Results and Discussion The stress-strain curves for the Reid-Bedford sand tested using the LVDT clamp, the swinging arms, the Kg-helt with strain gages, and the burette method are shown in Figs. 6, 7, 8, and 9, respectively. The upper portion of these figures shows the relationship between the radial and axial stress; the bottom portion shows the relationship between the axial stress and axial strain. It is apparent from these graphs that the relationship between a^ and a„ can be approximated by a straight line passing through the origin; consequently KQ can be expressed as the ratio of a^ to a,,. Values of KQ for the sand tested using the LVDT clamp, swinging arms, the /^o't'^'t with strain gages, and the burette method are presented in terms of initial relative densities in Table 1. Table 1 shows that, at any given range of density, the value of KQ has the same order of magnitude for all testing methods selected for restraining radial

ISOi

1
1-7

-1

< — ^

16

SO

100

ISO ?00 AXIAL STRESS ^ , » « i

ISO

300

iW

FIG. 6—Stress-strain relationships for Reid-Bedford sand under Kfi-condition using LVDT clamp.

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86

LABORATORY SHEAR STRENGTH OF SOIL

Too

iio

5oo"

Jsr

AXIAL STRESS % , » t l

FIG. 7—Stress-strain relationships for Reid-Bedford sand under K/j-condition using swinging arms (1 in. = 25.4 mm: I psi = 6.9 kPa).

deformations in this study. This indicated that all four methods provide the same acceptable degree of accuracy in measuring KQ, and the preference for one method over the others in obtaining KQ may be a matter of convenience rather than the accuracy of the result. It must be pointed out that the Ko-he\t with strain gages tends to give the highest value of KQ, while the swingingarms sensor tends to yield the lowest. The LVDT clamp method was found to be the most convenient method in determining the behavior of sand under cycling loading, and has been used to generate the remaining test data presented in this paper. Figure 10 shows that KQ decreases with increasing relative density. For isotropic elastic materials the value of Poisson's ratio (i*) may be expressed as KQ

1+KQ

(1)

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AL-HUSSAINI ON METHODS FOR DETERMINING KQ

87

2Mr

AXrAL STNfSS 4 ^ ^ FIG. 8—Stress-strain relationships for Reid-Bedford sand under K/j-condition using Kfi-belt with strain gages II in. = 25.4 mm: I psi = 6.9 kPa).

The variation of v as calculated from KQ with respect to the initial relative density of the Reid-Bedford sand is also presented in Fig. 10. Theoretical Evaluation of A^o As far as is known to the author, only two successful attempts are available for predicting KQ analytically. The first theoretical approach was derived by Jaky [5] and the second was derived by Hendron [6\. Jaky [5] postulated that a semi-infinite granular mass can be divided into Rankine zone and transitional zone, as shown in Fig. 11, and that the shear distribution on any horizontal plane is parabolic. Based on these assumptions Jaky was able to express the coefficient of earth pressure K^ with the angle of internal friction by A:o = ( l - s i n 0 ' )

(2)

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88

LABORATORY SHEAR STRENGTH OF SOIL

?-4

"50

io5

ISO i» fso !M AXIAL smess ^ , > « i

ite

Z8o

FIG. 9—Stress-strain relationships for Reid-Bedford sand under K„-condilioii using burette method (I in. = 25.4 mm: I psi = 6.9 kPa).

08

V O • *

06

LEGEND AVERAGE lyOT CLAMP SWINGING ARMS STRAIN GAGE BURETTE METHOD

h o.i.

V= ^ , 0.2

70 ^0 INITIAL RELATIVE

60 SO DENSITY Dr'/.

100

FIG. 10—Relationship between K^. f. and D^for Reid-Bedford sand.

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AL-HUSSAINI ON METHODS FOR DETERMINING Kn

89

TABLE 1—Values of Kufor the sand tested using the LVDT clamp, swinging arms, the Kg-belt with strain gages, and the burette method in terms of initial relative densities. LVDT Clamps

Swinging-Arms

ATo-Belt

Burette Method

Relative Density, D, % /Co

Relative Density,

Relative Density,

Relative Density,

25.6 72.1 99.5

26.9 72.9 96.5

30,9 75.1 94.0

0.53 0.45 0.39

0.51 0.42 0.39

0.55 0.48 0.42

n

36.0 69.3 96.8

0.52 0.44 0.39

I = RANKINE ZONE = TRANSITIONAL ZONE

FIG. 11—Rankine and transitional zones as assumed bv Jakv.

The theoretical derivation of Hendron is based on the assumption that a uniform, well-rounded, dense sand can be approximated by a face-centered array of equiradii spheres. If the array of spheres were subjected to onedimensional compression, then the value of K^ can be expressed as

1 + — - 3 ( ^ — 1 sin
(3) 1

—h 3 —— sm (j)

Comparison Between Theory and Experiment In an effort to verify Jaky's [5] and Hendron's [6] relationships between the angle of internal friction (<^') and ATg, data from a series of consolidateddrained direct shear tests (Fig. 12) were used for comparison. Using the data presented in Figs. 10 and 12, the relationship between ' and KQ obtained for Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

90

UBORATORY SHEAR STRENGTH OF SOIL

RELATIVE DENSITY O r , ^o

FIG. 12—Consolidated-drained direct shear test for Reid-Bedford sand.

the Reid-Bedford sand was established and presented in Fig. 13. The experimental results conform closely to the relationship suggested by Jaky [5] but are higher than the one suggested by Hendron [6]. Effect of Unloading and Reloading The relationship between the radial and axial stress for Reid-Bedford sand under repeated load and unload cycles is shown in Fig. 14. The relationship for the first loading cycle may be approximated by a straight line. However, upon unloading, the relationship becomes nonlinear with a flatter curvature at the

$ , DEGREES

FIG. 13—Experimental and theoretical relationships between K.y and for Reid-Bedford sand.

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AL-HUSSAINI ON METHODS FOR DETERMINING Kn

AXIAL

91

STRESS

FIG. 14—Radial versus axial stress for Reid-Bedford sand under Kn-condition using LVDT clamp (I in. = 25.4 mm: 1 psi = 6.9 kPa).

higher stress level, which then becomes concave downward with increasing slope as unloading continues. The relationship during first reloading is also nonlinear but concave upward with slope much flatter than the first loading cycle. This trend was similar for the dense specimen that exhibited a flatter slope than the loose specimen for any particular loading or unloading cycle. These results also indicate that the value of ATQ is always lower on loading than unloading. It also indicates that the secant ATo-value increases with increasing number of cycles, which implies that KQ is dependent on stress history. The influence of over-consolidation ratio (OCR) and stress level on /To-values of Reid-Bedford sand have been presented elsewhere [7\. The uniaxial stress-strain relationship for Reid-Bedford sand under loading and unloading cycles is shown in Fig. 15. This figure shows clearly that the slope of the curve which defines the constrained modulus D is much higher on unloading than loading, and while D is increasing with increasing number of Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

92

LABORATORY SHEAR STRENGTH OF SOIL

RELATIVE

DENSITY

J AXIAL STRAIN

\ «, ,

Dr- = ZS %

L "7.

FIG. \h—Axial stress-strain relationship for Reid-Bedford sand under Ky-condition using LVDT clamp (I in. = 25.4 mm: I psi = 6.9 kPa).

loading cycles, upon loading it almost has the same value for all reloading cycles. The constrained modulus for any loading or unloading cycles is much higher for dense than loose specimens. Conclusions The data show that the value of KQ for Reid-Bedford sand was found to be practically the same irrespective of the method used in maintaining no radial deformations of the specimen. The LVDT clamp, /Co-belt, swinging-arms lateral strain sensors, and the indirect burette method all produced comparable Xo-values for relative densities ranging from 25 to 99 percent. The /Co-belt tended to give the highest ATo-values, while the swinging-arms lateral strain sensor indicated the lowest values. The LVDT clamp is preferred for laboratory testing since it is easier to use and maintain and also provides reliable results.

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AL-HUSSAINI ON METHODS FOR DETERMINING KQ

93

The experimentally derived A^o-values agree well with the Jaky theoretical equation; on the other hand, the Hendron equation underestimates the experimental values. It is found that the values of A^o are lower on loading than unloading and increase with increasing number of loading and unloading cycles. The constrained modulus increases with increasing number of loading cycles, yet is practically the same for unloading cycles and is higher for unloading than loading. Acknowledgments The test described and the resulting data presented herein were obtained from research conducted at Waterways Experiment Station, Vicksburg, Miss., under sponsorship of the Office, Chief of Engineers. Valuable suggestions provided by Dr. F. C. Townsend during the conduct of the study are appreciated. References (/] Al-Hussaini, Mosaid and Townsend, F. C , "Investigation of Kg Testing In Cohesionless Soils," Technical Report S-75-16, USAE Waterways Experiment Station. Vicksburg, Miss.. Dec. 1975. |2| Al-Hussaini. Mosaid, "The Influence of End Restraint and Method of Consolidation on the Drained Triaxial Compressive Strength of Crushed Napa Basalt." Miscellaneous Paper S-70-18, USAE Waterways Experiment Station, Vicksburg, Miss., June 1970. [3] Holtz, R., personal communications, 1975. [4] Bishop. A. W. and Eldin. A. K., "The Effect of Stress History on the Relation Between KQ and Porosity in Sand," Third International Conference on Soil Mechanics and Fracture Engineering, Vol. I, 1953. pp. 100-105. \5\ Jaky, J., "The Coefficient of Earth Pressure at Re%t." Joiinial of the Society of Hungarian Architects and Engineers, Budapest, Hungary, 1944, pp. 355-358. [6| Hendron, A. J.. "The Behavior of Sand in One-Dimensional Compressions," Ph.D. thesis. University of Illinois. Urbana. III., 1963, [71 Al-Hussaini. Mosaid and Townsend. F. C . "Stress-Deformation of Sand Under A^o Conditions," 5th Pan-American Conference on Soil Mechanics and Foundation Engineering. Buenos Aires. Argentina, 1975.

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J. E. Alva-Hurtado,'

D. R. McMahon, ^ and H. E. Stewart^

Apparatus and Techniques for Static Triaxial Testing of Ballast

REFERENCE: Alva-Hurtado, J. E., McMahon, D. R., and Stewart, H. E., "Appatatut and Techniques for SUtic Triaxial Testing of Ballast," Laboratory Shear Strength of Soil, ASTMSTP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 94-113. ABSTRACT: Railroad tracks are constructed on a layer of ballast overlying the roadbed subgrade. The ballast is a coarse-aggregate-sized, noncohesive, granular material with angular panicles and usually with a uniform gradation. In order to evaluate the geotechnical performance of railroad tracks, representative stress-strain-volume change and strength properties of the ballast ate needed. Because ballast consists primarily of large [up to 76.2 mm (3-in.)} angular particles, conventional triaxial testing equipment is not appropriate. Therefore a large triaxial cell was designed and constructed. The apparatus used in the static ballast testing, and the sample preparation techniques developed, are presented. Triaxial compression test results on the granite ballast for two different density states are shown. Mohr-Coulomb strength parameters are presented, and the typical stressstrain-volume change behavior is shown. The hyperbolic parameters calculated from the static tests are also shown. The static test results using the new apparatus and sample preparation techniques indicate that railroad ballast possesses many characteristics common to granular materials. KEY WORDS: railroad ballast, triaxial apparatus, testing procedures, laboratory testing, static testing

Methods are being currently developed to predict the elastic and residual deformation behavior of railroad-track systems [1,2].* The prediction methodology requires properties obtained from laboratory testing of the ballast and roadbed materials under static and repeated load conditions equivalent to those imposed in the field by the passing trains. This paper is concerned with the static triaxial testing of ballast. 'Consulting engineer, Lima, Peru. ^Geotechnical engineer, Goldberg, Zoino and Associates of New York, Buffalo, N.Y. 14203. ^Graduate research assistant, Department of Civil Engineering, University of Massachusetts, Amherst, Mass. 01003. •"The italic numbers in brackets refer to the list of references appended to this paper.

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ALVA-HURTADO ET AL ON STATIC TRIAXIAL TESTING

95

A large triaxial cell was designed and built that was suitable for both static and cyclic ballast testing. Specimen preparation methods were established for the laboratory triaxial samples in order to simulate field conditions. These took into account the fact that problems relating to the boundary conditions in the ballast samples cause systematic errors in determining the sample densities. The apparatus and procedures developed for the testing of railroad ballast are presented. To illustrate the use of this equipment test results are given for a typical ballast material. These static tests were performed drained after isotropic consolidation to low effective confining pressures. Mohr-Coulomb strength parameters and hyperbolic stress-strain-volume change parameters are shown. Apparatus The apparatus for the static triaxial testing of railroad ballast consists of the triaxial cell, pressure controls, a volume-change device, and a universal compression machine. A schematic of the apparatus layout is shown in Fig. 1. Triaxial Cell Because a suitable triaxial cell was not available commercially, a cell was designed with the following specifications: 1. 152.4-mm (6-in.) minimum diameter specimen size. 2. Capability for loading in extension or compression. 3. Low-friction seal resistance between loading piston and the top of the cell chamber. 4. Provision for accurate alignment of the specimen with the top cap and the piston rod. A diagram of the triaxial cell is presented in Fig. 2. The cylindrical acrylic chamber is 304.8 mm (12 in.) in outside diameter, 12.7 mm (0.5 in.) thick, and 609.6 mm (24 in.) long. Neoprene 0-rings are used in the seal between the 50.8-mm (2-in.)-thick, anodized aluminum top and base plate and the acrylic chamber. The cell was designed for a maximum internal pressure of 1103 kPa (160 psi) and for 152.4-mm (6-in.) and 203.2-mm (8-in.)-diameter soil specimens with height-to-diameter ratios from 2 to 2.5. Six 19.05-mm (0.75-in.)-diameter stainless steel tension rods are used to compress the 0-rings between the acrylic chamber and the plates. The top of the chamber is divided into two parts: (/) a top plate connected to the tension rods, and (2) a top collar for the acrylic chamber which is fixed to the top plate with six screws. The specimen base pedestal and top cap are made of stainless steel and are screwed to the base plate and piston rod, respectively. Two zero-volume-change ball valves are mounted on the top collar control Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

96

LABORATORY SHEAR STRENGTH OF SOIL

PRESSURE TO AIR COMPRESSOR CELL PRESSURE REGULATOR

CONTROL

W^

'•*'*'*

BACK PRESSURE REGULATOR ATMOSPHERIC • PRESSURE

VOLUME CHANGE DEVICE

FIG. 1—THaxial testing system.

openings which pass through the top plate. Valve VT-1 provides an air-water interface inside the cell, which becomes necessary during cyclic testing. Valve VT-2 vents the cell interior while the cell is being filled with water. Four ball valves are mounted on the base plate. Valve VB-1 is connected to the base pedestal inside the specimen to permit flushing any air entrapped in the sample and pore pressure lines. During flushing, Valve VB-4 provides top drainage to the sample through a connection between the top cap and base plate. Valve VB-1 also provides the application of back pressure to the specimen and is used for bottom drainage of the sample. Valves VB-2 and VB-4 measure pore pressures at the bottom and top of the sample during drained or undrained shear. Valve VB-3 transmits the cell pressure to the specimen. The specimen is sealed from the cell water by enclosing it in two latex membranes. The membranes are sealed to the base pedestal and top loading cap with neoprene 0-rings. The tension rods are incorporated inside of the removable cylindrical acrylic chamber in order to allow proper top cap alignment with the specimen [3] while the specimen is still in the compaction mold. A piston clamping system holds the piston in any desired vertical position. Another important feature of the triaxial cell is the special ball bushing assembly which provides low piston friction and chamber sealing. This assembly is a modified version of that presented by Chan [4]. The ball bushing assembly and floating seal are made of brass; the ball bushings are made of stainless steel. An aluminum bar is rigidly fastened to the piston above the ball bushing assembly. A 76.2-mm (3-in.) dial indicator in contact with the top collar is attached to the aluminum bar to measure vertical deformations. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

ALVA-HURTADO ET AL ON STATIC TRIAXIAL TESTING

97

PIS'^ON ROD ---PISTON CLAMP BALL BUSHING ASSEi/BLY V'T-I TO AIR PRESSURE SUPPLY VT-2 " 0 BLEED OFF AIR

RYLIC CHAWBER

TOP PLATi TENSION RODS -—

i

LATEX MEMBRANE

BASE PEDESTAL

BASE PLATE

VB-4 TOP DRAINAGE

CELL PRESSURE V B - 3 M BACK PRESSURE V B a l - ' r I

VB-2 MEASURE PORE PRESSURE

FIG. 2—Triaxial cell features (I in. — 25.4 mm).

Pressure Controls The cell and back pressures applied to the specimen during testing are provided by an air compressor through air-water interfaces created in the pressure reservoirs. The reservoirs have been designed for a maximum pressure of 1103 kPa (160 psi). With the use of the reservoirs, it is possible to quickly pressurize the cell with de-aired water. The pressures can be accurately maintained for any desired period of time using air pressure regulators that maintain the desired pressures regardless of minor fluctuations in the line pressure. The air pressure regulators used have a maximum capacity of 1103 kPa (160 psi) and will maintain the pressure constant to within 0.069 kPa (0.01 psi). All connecting lines on the pressure control panel are made of 6.35-mm (0.25-in.)-diameter copper tubing; the valves employed are zero-volumechange ball valves. Two high-precision Bourdon gages measure the cell and back pressures. The connections from the control panel to the reservoirs and the triaxial cell are made of high-pressure plastic tubing. There are two valves on the panel by which atmospheric or vacuum pressure can be applied to the reservoirs to release pressure or to de-air the water. The connections from the control panel and reservoirs to the triaxial cell are made with "quick connects". Pore pressure is measured at the base or the top of the specimen through bronze porous disks using a pressure transducer. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

98

LABORATORY SHEAR STRENGTH OF SOIL

Volume-Change Device Volume change of a fully saturated sample can occur due to changes in cell pressure or axial load, provided water is permitted to flow into or out of the sample through Valve VB-1 on the cell. The measurement of volume change has been accomplished by the use of burettes. A volume-change device constructed (Fig. 3) is similar to that presented in Ref 5. In this particular design, the burette is replaced with nylon tubing, and bright colored oil is used to create a meniscus that can be clearly seen through the translucent tubing. The volume-change measurements are obtained by mounting a scale adjacent to the tubing to measure the movement of the meniscus. A four-way ball valve reverses the direction of movement of the pore fluid when the limit of the volume-change scale is reached, thus eliminating the necessity for resetting the volume change reading when measuring large volumes. This volume-change device has a sensitivity of 0.16 cm^ (0.01 in.^).

Universal Compression Machine The universal compression machine used is capable of providing various constant rates of strain. The constant rate of strain used in the ballast static tests was 0.02 mm/s (0.05 in./min), which was the slowest possible rate with this machine. The capacity of the loading frame is 53.4 kN (12 0(X) lb). The loads, measured by the load cell built into the testing machine, are registered on a dial incorporated in the machine. The triaxial cell setup in the universal compression machine is shown in Fig. 4. Testing Procedures Density Determination Ballast is a coarse-aggregate-sized, noncohesive, granular material usually with a uniform gradation. The angular particles can be up to 76.2-mm (3-in.) in size. The granite ballast used in these tests had particles ranging in size from 5 to 30 mm (0.2 to 1.2 in.), with a D50 size of 20 mm (0.8 in.) and a uniformity coefficient of 2. A previous study [6] shows that the sample boundary conditions for railroad ballast materials play a crucial role in determining the accuracy of the calculated sample densities. The problem is caused by the difficulty in defining the volume of the large boundary voids which should be excluded from the sample volume. Still further research is necessary to establish a density correlation between the laboratory and the field measurements. Rather than match the field density values, laboratory sample preparation techniques were developed to represent the observed range of ballast density conditions

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ALVA-HURTADO ET AL ON STATIC TRIAXIAL TESTING

99

FIG. 3—Volume-change device.

found in the field. A study of the variation of the in situ ballast density [/] showed that a difference of up to 0.16 Mg/m^ (10 Ib/ft^) exists under the tie in the ballast layer. The rubber-tipped impact-hammer com'Jjaction method developed by Yoo et a! [6] was chosen to prepare the laboratory triaxial samples. To establish the effort required for the compacted state, samples were prepared in a 152.4-mm (6-in.)-diameter by 304.8-mm (12-in.)-high container in three equal layers varying the number of blows per layer. The compactive effort was calculated from E=

n W.EiN

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100

LABORATORY SHEAR STRENGTH OF SOIL

FIG. 4—Assembled triaxial cell with ballast sample.

where E W, D n N Vc

= = = = = =

compactive effort in ft •lb/ft-' (nrkN/m^), drop weight = 0.0347 kN (7.8 lb), drop height = 0.43 m (1.42 ft), number of layer — 3, number of blows per layer, and ballast sample volume in the container — 0.00556 m^ (0.196 ft-').

Figure 5 presents the resulting relationship between dry density and compactive effort for the granite ballast.

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ALVA-HURTADO ET AL ON STATIC TRIAXIAL TESTING

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In order to represent the observed range of in situ ballast density states, a lower bound density state was established by preparing laboratory samples without compaction. The upper bound density state was established by using a compactive effort of 161 m-kN/m^ (3400 ft-lb/ft^) provided by 20 blows per layer in 3 layers. This is the effort in Fig. 5 at which the curve starts to level off. Sample Preparation The specimens were prepared in a specially developed split mold that was clamped together and fitted around the base pedestal. The acrylic chamber, cell top, bushing assembly, and the two front tension rods were removed during the sample preparation process. A 0.64-mm (0.025-in.)-thick latex membrane was stretched inside the mold and fixed to the base pedestal with 0-rings. The mold has two holes in the wall, which allows a vacuum to be applied to hold the membrane against the mold (Fig. 6). After the sample is prepared and before connecting the top cap and piston assembly to the sample, the ballast particles were rearranged at the top of the mold to provide a level seat for the piston top cap (Fig. 7). The membrane was next fixed to the top cap with 0-rings, and the top drainage line was connected from the top cap to the cell base plate. Then a partial vacuum of about 13.8 kPa (2 psi) was applied to the specimen to produce a confining pressure giving some strength to the specimen. After the compaction mold was removed, a second 0.30-mm (0.012-in.)thick latex membrane was rolled down over the specimen because the original membrane was often punctured during sample compaction by the sharp edges of the ballast particles (Figs. 8 and 9). Both membranes were sealed by additional 0-rings at the top and bottom. To complete the specimen setup the two front rods of the cell were replaced (Fig. 10) and the initial specimen height and diameter measurements were taken. Finally, the acrylic chamber of the triaxial cell was put in place, and the cell was sealed by screwing down the top collar to the top plate (Fig. 11). The triaxial cell was then moved to its test position in the loading frame. After the cell was filled with water and a small confining pressure applied, the vacuum in the sample was released, which allowed water from the back pressure reservoir to enter and eventually saturate the sample. Using the bottom and top drainage, the water was flushed through the specimen in order to eliminate trapped air bubbles. Once enough water was circulated, cell and back pressures were simultaneously applied in order not to impose any effective confining stresses greater than approximately 20.7 kPa (3 psi). With the sample saturated, the B pore pressure parameter, defined as B = Au/Aa, was measured. It was necessary in the majority of the tests to apply a back pressure of 137.9 kPa (20 psi) to get a fi-value greater than 0.96. Once a high B-value was achieved, the sample was isotropically consolidated to the desired effective stress. After consolidation, the specimen was sheared in the Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

102

LABORATORY SHEAR STRENGTH OF SOIL

Compoctive Effort

0

(m-kN/ni3

2000 4000 6000 8000 10000 Compaclive Ef f o r t , E ( I b - f 1 / f t ^ )

12000

FIG. 5—Laboratory density test results for granite ballast sample.

FIG. 6—Sample in compaction mold with vacuum applied to outside of latex membrane. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

ALVA-HURTADO ET AL ON STATIC TRIAXIAL TESTING

103

FIG. 7—Piston and top cap aligned with sample by bushing and rod system.

compression machine. The axial loads, vertical deformations, pore pressures, and volume changes were monitored. Testing Results Eleven static triaxial compression tests with constant confining pressures [34.5 to 137.9 kPa (5 to 20 psi)] were performed on the granite ballast. All the static triaxial samples were saturated under back pressure, isotropically consolidated, and tested in a drained state. The main reason for saturating the samples was to permit measurement of volume changes. Both uncompacted and compacted sample states were tested. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

104

LABORATORY SHEAR STRENGTH OF SOIL

FIG. S—Sample under partial vacuum with one membrane after removal of compaction mold. Cell pressure and back pressure reservoirs in background.

Parameters for the Mohr-Coulomb failure criteria were determined for the loose and dense sample physical states. Hyperbolic fitting techniques were applied to characterize the stress-strain and volume-change behavior. The influence of the ballast density state on the failure parameters and on the stress-strain and volume-change behavior was determined. Stress-Strain and Strength The average dry unit weight of the six uncompacted specimens was 1.53 Mg/m'' (95.6 Ib/ft^) with a coefficient of variation of 2.0 percent and a range

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ALVA-HURTADO ET AL ON STATIC TRIAXIAL TESTING

105

FIG. 9~Rollmg down of second membrane.

from 1.49 to 1.58 Mg/iri'' (93.3 to 98.4 Ib/ft^). The average dry unit weight of the five compacted samples was 1.62 Mg/m^ (101.2 Ib/ft^) with a coefficient of variation of 0.5 percent and a range from 1.61 to 1.63 Mg/m-' (100.6 to 101.9 Ib/ft^). The fact that the coefficient of variation for each of the two density states was low demonstrates that the preparation techniques used gave reproducible results. The dry unit weights were calculated using the dry sample weights and the initial sample heights and diameters. No corrections for the previously mentioned boundary effects were made. Assuming a specific gravity of 2.67 [7], the average initial void ratio (e„) was 0.65 for the compacted samples and 0.74 for the uncompacted samples. The effective angle of internal friction (4>) was calculated for each test asCopyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

106

UBORATORY SHEAR STRENGTH OF SOIL

FIG. 10—Removable rods being reinstalled.

suming that the value of cohesion (c) was equal to zero. When the confining pressure was increased, these values decreased for both compacted and uncompacted samples. The value was always higher for compacted samples than for uncompacted samples at the corresponding confining pressures. This difference in 4> increased with an increase in the confining pressure. Performance of replicate tests proved that this strength parameter was reproducible. The p-q stress paths are shown for the uncompacted specimens in Fig. 12 and for the compacted specimens in Fig. 13. These stress paths enable the Kf-Wne (failure line in p-q coordinates) to be determined. Using the relationCopyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

ALVA-HURTADO ET AL ON STATIC TRIAXIAL TESTING

107

FIG. II—Acrylic chamber being positioned.

ship sin $ = tan a, the average ^-value was determined for both types of specimens. The average <> / value for the compacted samples was 44.4 deg and for the uncompacted samples was 37.8 deg. From the construction of the A^-line, it can be seen that for both sample types the q'-intercept (a) was not equal to zero. The apparent cohesion value for the uncompacted samples (c = o/cos0) was 33.1 kPa (4.8 psi), and the value for the compacted samples was 19.3 kPa (2.8 psi). It is believed that this apparent cohesion was due to particle interlocking. This hypothesis has also been presented by Raymond and Davies [8]. The stress-strain and volume change relationships for the uncompacted Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

108

LABORATORY SHEAR STRENGTH OF SOIL

CID GRANITE BALLAST UNCOMPACTED SAMPLE

FIG. 12—Strength envelope for uncornpacted ballast samples (I psi = 6.89 kPa).

P

(PSI)

FIG. 13—Strength envelope for compacted ballast samples (I psi — 6.89 kPa).

and compacted samples are shown in Figs. 14 and 15, respectively. These stress-strain figures show that the static test results followed the expected trends. As confining pressure was increased, the deviator stress at failure increased. Also, the deviator stress at failure was greater for the compacted samples than for the uncornpacted samples. This difference in deviator stress at failure between compacted and uncornpacted samples increased with increasing confining pressure. This fact was also pointed out by Raymond and Davies [8].

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ALVA-HURTADO ET AL ON STATIC TRIAXIAL TESTING

109

?3 = 20 02 psi

X^

^^'

^

^ ^ 3

.

„

faj-

= 15 05 PS.

= 10,16 P5

501 psi

FIG. 14—Stress-straiii-volume change behavior for uitcompucted ballast samples (I psi — 6.89 kPal.

As the confining pressure was increased, the vertical strain at which the sample failed also increased. The compacted samples reached greater vertical strains at failure than did uncompacted samples at confining pressures lower than 103.4 kPa (15 psi). It is important to point out that, near failure, particle slippage was noticed, which made an accurate determination of the axial strain at failure difficult. The volumetric strain plots show that the ballast followed the well-established behavior trends for granular material. Volumetric strain was defined as positive when the total specimen volume decreased and negative when the volume increased. As the confining pressure was increased, the tendency for sample dilation decreased. The compacted samples tended to dilate at smaller vertical strains than did uncompacted samples at corresponding confining pressures. These observations indicate that the behavior of granular materials under low confining pressures, as in the case of railroad ballast, is different from that under high confining pressures.

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110

LABORATORY SHEAR STRENGTH OF SOIL

6" =l4 79psi

STRAIN (%)

e" 3= 5,01

psi

§" =10 01 psi ^ 5 5 - e j = 14,79 PS

< ttr K

5

^''^r::!;^!^-^ ' STRAIN (%)

IJ

15

S O

FIG. 15—Stress-strain-votume change behavior for compacted ballast samples II psi ~ 6.89 kPa>.

Hyperbolic Parameters The hyperbolic transformations [9] were applied to the stress-strain and volume change-strain data obtained from the ballast static triaxial tests. A typical plot of the stress-strain data in linearized hyperbolic form indicated that this behavior was approximately hyperbolic. However, the volume change relationship was not. Dilation plays a major role in this type of behavior. Replicate tests showed good reproducibility for the initial tangent modulus, Ej, and the ultimate deviator stress, {<j\-a3\\f The values of Rf [{oi-ai)f/ (ai-a3)uit)] from 0.74 to 0.98. These values are in agreement with the values given by Raymond and Davies {8\. The results of the hyperbolic fitting techniques are shown in Table 1. The logarithm of the initial tangent modulus (£,) as computed from the hyperbolic model is plotted in Fig. 16 as a function of the logarithm of the effective confining pressure (aj) for both compacted and uncompacted samples.

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ALVA-HURTADO ET AL ON STATIC TRIAXIAL TESTING

111

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SC9

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112

UBORATORY SHEAR STRENGTH OF SOIL

50,000

E, = 3000 o;

g o

6,000 _ 0.46

E.= 1500 o ;

O COMPACTED SAMPLES A UNCOMPACTED

1,00 0

•

SAMPLES

•

5 CONFINING

•

I — I — I

I

10 P R E S S U R E : , O",

(PS!)

FIG. 16—Variation of initial Young's modulus with confining pressure (I psi = 6.S9 kPu).

Naturally, the compacted samples has a greater initial tangent modulus than did the uncompacted samples. Generally, the relationship between these two can be represented asi', = K{ai)". A regression analysis using this functional relationship gave the following parameter values: Ei and a^ in psi units^

Compacted samples k n Uncompacted samples k It

3000 0.46 1500 0.46

Poisson's ratio is defined as the ratio of horizontal to vertical strain. The initial Poisson's ratio, (v,) and the final Poisson's ratio {v/) for both uncompacted and compacted samples are presented in Table 1. Although there was scatter in the data, the general trends were that both initial and final Poisson's ratios decreased with increasing confining pressures, and the initial Poisson's ratio was not affected by the ballast density. ^1 psi = 6.89 kPa.

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ALVA-HURTADO ET AL ON STATIC TRIAXIAL TESTING

113

Summary This paper presented the apparatus and techniques developed for static triaxial testing of railroad ballast. A large triaxial cell was designed and built. Laboratory sample preparation and setup techniques were also developed. Results using this equipment were presented for a typical railroad ballast. The results indicate that the ballast possesses many characteristics common to granular materials. Strength and hyperbolic parameters for the stressstrain-volume change behavior of the granite railroad ballast were determined based on test results obtained using the apparatus and techniques developed. Acknowledgments The study described in this paper is part of a research program dealing with track maintenance life prediction currently underway at the University of Massachusetts at Amherst under the direction of Prof. E. T. Selig. The research was supported by funds from the Office of University Research of the U.S. Department of Transportation. Phillip Mattson was the technical monitor. References |/1 Alva-Hurtado, J. E., "A Methodology to Predict the Elastic and Inelastic Behavior of Railroad Ballast," Ph.D. dissertation, Department of Civil Engineering, University of Massachusetts at Amherst, 1980. (2) Alva-Hurtado, J. E. and Selig, E. T., "Static and Dynamic Properties of Railroad Ballast," Proceedings. Sixth Pan-American Conference of Soil Mechanics and Foundation Engineering, Lima, Peru, 1979. |J| Silva-Tulla. F., "Predicting Settlement of Clay Foundations Subjected to Cyclic Loading," D.Sc. thesis. Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Mass., 1977. [4] Chan, C. K.. Journal of the Geotechnical Engineering Division. Vol. 101, GT 9, September 1975, pp. 991-995. [5] Chan, C. K. and Duncan, J. M., Materials Research and Standards. Vol. 7, No. 7, Julv 1967, pp. 312-314. [6] Yoo, T. S., Chen, H. M., and Selig, E. T., Geotechnical Testing Journal. Vol. 1, No. 1, March 1978, pp. 41-54. [7] Thompson, M. R., "FAST Ballast and Subgrade Materials Evaluation," Ballast and Foundation Materials Research Program, University of Illinois at Urbana-Champaign. for U.S. Federal Railroad Administration, Report No. FRA/ORD-77/32, December 1977. |(^] Raymond G. P. and Davies, J. R., Journal of the Geotechnical Engineering Division. Vol. 104, GT 6, June 1978, pp. 737-751. [9] Duncan, J. M. and Chang, C. Y., Journal of the Soil Mechanics and Foundation Division. Vol, 96, SM 5, September 1970, pp. 1629-1653.

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T. B. Edil,' S. E. Motan,' and F. X. Toha'

Mechanical Behavior and Testing IVIethods of Unsaturated Soils

REFERENCE: Edil, T. B., Motan, S. E., and Toha, F. X., "Mechanical Behavior and Testing Methods of Unsaturated Soils," Laboratory Shear Strength of Soil. ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 114-129. ABSTRACT: The mechanical behavior of unsaturated cohesive soils under different common stress conditions, that is, static compression, dynamic shear, and repetitive compression, is considered as a function of induced initial matrix suction by desorption from the initially saturated state. The hysteresis of moisture retention is considered outside the scope of this work. The test results suggest that the moisture regime can be expressed most suitably in terms of matrix suction. The data suggest that a rather definite change in stress-strain response takes place at a critical value of the matrix suction with modulus values, in general, dropping beyond the critical suction. The direct measurement of the total soil suctio;n in the laboratory in connection with the triaxial compression test is sought by use of thermocouple psychrometers. The total suction of the soil decreases as the applied stresses increase; the quantitative relationship is complicated by a number of factors. The matrix suction appears to be the fundamental suction component controlling the mechanical behavior during a desorption schedule. This implies certain limitations for the use of psychrometers alone in indexing the mechanical behavior of soils, especially if they have a significant osmotic suction component. KEY WORDS: unsaturated soils, soil suction, modulus, strength, repetitive loading, unconfined compression, laboratory tests, psychrometer, ceramic plate extractor, Poisson's ratio, residual strain, resonant column test

As the water table is drawn below the ground surface, decreasing porewater pressure and evapo-transpiration result in desaturation of the soil above the water table. Such a desiccated natural soil is subject to changing environmental conditions which produce a wide variety of pore-water pressure distributions in the soil above the groundwater table. In addition to desiccated natural soils, compacted soils are also unsaturated due to insufficient water on the dry side and trapped air bubbles on the wet side of the optimum moisture content. The mechanics of the unsaturated soils, unlike the 'Professor of Civil and Environmental Engineering and Engineering Mechanics, graduate student, and graduate student, respectively, University of Wisconsin-Madison, 53706.

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EDIL ET AL ON BEHAVIOR AND TESTING OF UNSATURATED SOILS

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saturated soils, has not been fully developed because of the difficulties in defining the stress conditions and in relating them to the observed behavior [1].^ Unsaturated soils exhibit basic differences from saturated soils in mechanical behavior and have been receiving more attention in recent years. The results of an experimental study of the mechanical behavior of unsaturated soils under different stress conditions and the methods of testing unsaturated soils are presented herein. Soil Suction Unsaturated soil is a multiphase material consisting of a particulate solid phase and pores which are filled with liquid and gas. There occurs specific interaction of these phases which, in turn, defines the overall mechanical integrity of the soil in terms of the interparticle forces. Numerous "effective stress" equations have been proposed for unsaturated soils [2-8] in order to relate the observed mechanical behavior to the stress conditions. The stress variables, in general, include total stress (a), pore-water pressure (M„,), and pore-air pressure (M„). The proposed relationship of these stresses to an "effective stress", a conceptual normal stress that can be shown to control the mechanical behavior, as in the case of saturated soils, is at best tentative at this time. Effective stress in unsaturated soils is controlled, among other factors [2], by the difference between pore-air and pore-water pressures, («„ — u„), which is called the matrix suction. Matrix suction is therefore the negative gage pressure at a point in the soil-water relative to the external gas pressure. It may be considered as equivalent to the work required to transfer a unit volume of soil-solution from a reference pool at the same elevation and temperature as the soil to the point in the soil. It results from the capillary and adsorptive surface forces arising from the soil matrix. When expressed as energy per unit volume, it reduces to a pressure unit. From thermodynamic or total energy considerations of the pore water, its total suction (^,) can be subdivided into a matrix suction component i\l/,„) and an osmotic (or solute) component (^i-J [5] such that ^, = ^m + \^s = (W« - W«.) + ^I's Osmotic suction arises from the differences in the ion concentration of soilwater at different points in a soil. The main postulate of this paper is that soil suction can be considered to include implicitly the net effect of all the individual interparticle forces (with the exception of cementation bonds) that influence the stress-strain and strength characteristics of the unsaturated soil. In other words, soil suction may be considered an important stress variable which controls the "effective stress" and therefore the mechanical behavior. ^The italic numbers in brackets refer to the list of references appended to this paper.

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116

LABORATORY SHEAR STRENGTH OF SOIL

Measurement of Soil Suction It is difficult to measure matrix suction in the field due to cavitation of the measuring system at pore-water pressures approaching 100 kPa negative. In the laboratory, matrix suctions in excess of this value (up to 1500 kPa) can be induced in soil specimens by placing them in a ceramic plate soil-moisture extractor [9]. The soil-moisture extractor consists of a pressure chamber containing a porous ceramic plate with a sheet-rubber backing, as shown schematically in Fig. 1. A metal screen provides space under the plate for bulk water, which is kept at atmospheric pressure by the tubular connection to the atmosphere. The bubbling pressure (that is, the pressure at which the menisci in the pores of the ceramic plate break and let air pass through) can be as high as 1500 kPa. Various matrix suction values can be induced in a specimen placed on the ceramic plate by applying an equivalent air pressure in the chamber under isothermal conditions and, thus, driving that portion of the soil-water at an energy state less than this value out of the specimens. This axis-translation technique induces matrix suction since the ceramic plate is permeable to solutes in the soil, and the soil-water is in equilibrium with a solution of the same concentration (that is, itself) in the burette. Recently psychrometers, which measure total suction, have received increased usage in measuring the suction of a soil in the laboratory and the field (Fig. 2). The low cost of psychrometers and the measuring equipment makes them attractive for engineering usage. Their use is restricted to soil suctions greater than 100 kPa. The psychrometer makes use of the Peltier effect to condense water from the air in the psychrometer chamber onto the measuring junction of a thermocouple formed commonly by fine copper and constantan wires welded together [10]. As the condensed water on the junction begins to evaporate, a potential difference is created between this junction and a reference junction resulting in an electrical current. This small potential difference can be measured by a microvoltmeter. The magnitude of this current depends, among some other factors, on the rate of evaporation, which in turn depends on the relative humidity of the air in the psychrometer chamber. If this air is in equilibrium with soil pore-air, then total soil-water potential, that is, total suction (i/-,), can be inferred from the measured relative humidity at any given temperature T from the relationship RT rP, = - ^

log P/P,

where R = V = Pg = P =

universal gas constant, specific volume of water, vapor pressure of pure water in the reference state, and vapor pressure of soil-water.

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EDIL ET AL ON BEHAVIOR AND TESTING OF UNSATURATED SOILS

\rubbcr bJckinq

117

^cerdmic plate

FIG. 1—Ceramic-plate extractor.

Mechanical Behavior—Soil Suction Relations Proceeding from the premise that soil suction is a fundamental state variable controlling overall mechanical integrity of soils, a series of tests corresponding to different loading conditions was undertaken at different initial suctions. Deformability and Strength Response in Uniaxial Compression Uniaxial compression (unconfined compression) tests were performed on specimens from laboratory consolidated samples of a kaolinitic clay [//]. Test specimens with varying fabrics (microstructures) were brought to equilibrium at various matrix suctions in a ceramic-plate extractor. Only variations from the initially saturated state were studied by means of a desorption schedule. After a particular specimen was brought to equilibrium in the extractor, it was taken out and tested in unconfined compression. The lateral deformations at the midheight were also measured during the test at three points spaced 120 deg apart by use of micrometers. The stress-strain response is essentially strain-softening for matrix suctions less than a critical value, termed ^i'^., which appears to be in the range of 500 to 700 kPa. For ^,„ > iZ-^., the stress-strain response is essentially linear with a constant modulus E, after which a strain-softening phenomenon prevails. For \l/,„ < xp^, the stress-strain response is described by a hyperbolic equation [12] and a parameter which represents the inverse of the initial tangent modulus is empirically determined. Figure 3 shows the range of values for the initial tangent modulus E, (which becomes equal to the constant modulus E for !/-„, > \t^) as a function of the initial matrix suction; it is seen that Ej generally increases with increasing 4/,,, up to a critical value, beyond which it

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118

LABORATORY SHEAR STRENGTH OF SOIL

.ceramic bulb

airline

thermocouple

(A)

(B)

FIG. 2—(a) Thermocouple psychrometer: (b) Psychrometers placed in the cap and base for use with compression test.

exhibits a decrease. As shown in Fig. 4, the unconfined strength increases rapidly with increasing values of \j/„ without any noticeable change in behavior at or above the critical suction as noted in Fig. 3. The radial deformations (average of three readings 120 deg apart) at the midheight of each specimen were used in conjunction with the axial deformations and the specimen dimensions to determine values of Poisson's ratio. Typical values of Poisson's ratio corresponding to axial strain levels of 0.01 and 0.05 are given in Fig. 5 for a range of initial matrix suctions. Poisson's ratios, in general, increased with increasing values of axial strain approaching a value of 0.5 at large axial strains. In general, as the initial matrix suction increases, the value of Poisson's ratio at a given axial strain becomes smaller, dropping to less than 0.1 at an initial matrix suction of 1500 kPa.

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EDIL ET AL ON BEHAVIOR AND TESTING OF UNSATURATED SOILS

119

S highly oriented fabric (H highly random fabric

_l

102

initial

I . I I I I II io3 matrix suction, t|J^(kP8)

FIG. 3—Modulus as a function of initial matrix suction.

14 0

highly oriented fabric

Q highly random fdbric

' 'I

V'

lo-' initial m a t r i x •uctlor\\^) (kPa)

FIG. 4—Unconfined compressive strength as a function of initial matrix suction.

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120

LABORATORY SHEAR STRENGTH OF SOIL

0 V at axial strain = 5% B W at axial strain. 1 %

I

I

I

' ' I I

initial matrix suction, 1(1 (kPa)

FIG. 5—Poisson's ratio as a function of initial matrix suction.

Dynamic Response The dynamic properties (shear modulus and damping capacity) of this kaolinitic clay were also determined using resonant column test after equilibrating specimens to various matrix suctions [13]. In Fig. 6, reference shear modulus G„ (defined as the modulus at a shear strain amplitude of 2.5 X 10~^ radians) is given as a function of initial matrix suction for two samples with distinctly different fabrics. G„ increases sharply with increasing suction up to a critical suction, \l/c = 400 kPa; thereafter it drops as the matrix suction increases, in a manner similar to the one observed in the case of the static modulus (Fig. 4). This response was typical of other specimens tested. Such a drop beyond this critical suction value was not observed with respect to the damping capacity. Response Under Repetitive Loading The important input parameters to a design program for asphaltic concrete pavements include subgrade resilient modulus (E^) and residual strain (e,,). Resilient modulus is defined as the ratio of the repeated axial stress (or the repeated principal stress difference) to that portion of the total strain that is recovered after the repeated axial load is removed. Residual or plastic strain is that portion of the total strain that is not recovered after the repeated axial load is removed. Fatigue prediction is highly sensitive to changes in subgrade resilient modulus which, in turn, varies with the

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EDIL ET AL ON BEHAVIOR AND TESTING OF UNSATURATED SOILS

O

highly orientad fabric

•

highly random fabric

121

-^^ a°,

\ is 6-

\

„

•

initial matrix suction, LjJ^ (kPa)

FIG. 6—Reference ilynamic shear modulus as a function of initial matrix suction.

moisture regime of the subgrade throughout the year. Moisture regime has special significance in highway pavement systems because such structures are generally associated with the surficial boundaries of the terrain where large moisture content variations are likely to occur throughout the year in response to changes in environmental conditions. Soil suction is a fundamental soil parameter that can reflect the influence of climate on the moisture regime, since it can be correlated with a climatic moisture index such as Thornthwaite moisture index [14], Because of these considerations, soil suction is conceived as the most appropriate parameter for characterizing the subgrade moisture regime [75], and tests were carried out to study the relationship of Er and e,, with soil suction using compacted specimens of a silt loam soil (Fig. 7). Er does not change appreciably up to i/-,,, = 100 kPa. Thereafter there is generally a sharp increase in E^ with increasing suction except at \l/,„ = 1500 kPa. The critical suction value at which the change in behavior occurs cannot be precisely determined; however, it probably has a value slightly in excess of 800 kPa. This change in mechanical behavior at a certain critical suction is similar to the one observed in static compression and dynamic shear. Major changes in e^ take place for the suction range less than 100 kPa, beyond which irrecoverable strain stabilizes at a nearly constant value. The dependency of resilient behavior for dry, wet, and optimum samples appears similar without any distinguishable trends with respect to the compaction moisture content and the resultant fabric. The same resilient

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122

UBORATORY SHEAR STRENGTH OF SOIL

I

D d r y of optimum O optimum

lniti«l Soil Suction,!!!

A w t of optitnum

|

MVnf-]

FIG. 7—Resilient modulus and residual strain as a function

of initial matrix suction.

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EDIL ET AL ON BEHAVIOR AND TESTING OF UNSATURATED SOILS

123

parameters, when plotted as a function of water content or degree of saturation (as indices characterizing the soil moisture regime) resulted in considerable scatter of the data [15]. These indices alone are found inadequate in reflecting moisture effects accurately. Direct Measurement of Suction During Mechanical Tests In the aforementioned experiments, values of matrix suction were induced by desorption in the specimens, and the response was studied as a function of the initial suction of a specimen free of external stresses prior to loading. This is appropriate when the significance and nature of initial soil suction effects are being investigated. In order to investigate the changes in soil suction due to externally applied stresses and to study the mechanical response as a function of the resulting suction, it is desirable to measure soil suction directly during a test. Furthermore, direct measurement provides a way of relating the laboratory results to the field behavior. Therefore the adoption of thermocouple psychrometry to the compression testing of unsaturated soils was considered to be promising, as it was also used by other investigators [16.17]. In this study, psychrometers were installed and sealed in the cap and base of the triaxial specimens (Fig. 2b). Experimental Problems An important aspect of testing unsaturated soils in triaxial compression is the prevention of vapor migration from specimens caused by leakage around the end caps and by diffusion through the rubber membrane. This requirement is more critical in the case of testing the unsaturated soils than the saturated ones. Use of three very tight 0-rings for sealing three membranes against the caps and filling the triaxial chamber with a sodium chloride (NaCl) solution with an appropriate osmotic pressure (about 50 percent of the total soil suction measured 24 h after placing the specimen) were found to be effective in preventing vapor migration [18]. Pore-air pressure was measured using a pressure transducer connected by a fine line in the top cap (Fig. 2b). Thermocouple psychrometers (Wescor Model PT51-05) were placed in the middle of the caps (symmetry is important in minimizing errors resulting from temperature gradients) and sealed by injecting epoxy resin. In some cases, the ceramic tip was left on the psychrometer and placed in holes drilled at the top and the bottom of the specimen. However, better results were obtained when the ceramic tips were removed and the psychrometer junction was placed in a recess of proper volume in the cap. The time to reach equilibrium may be considerably long. For the soils used in this study, (a silt loam and Grundite clay), it was two days. If a change in stress state was effected, it took more than three days to establish a suction equilibrium inside the specimen so that an equilibrium value could be measured at the

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124

UBORATORY SHEAR STRENGTH OF SOIL

boundary (top or bottom). Lack of isothermal conditions, psychrometer junction size and shape, and presence of temperature and vapor pressure gradients contribute to the increase in time to reach equilibrium or to the inaccuracies or to both. Suction Response Under Applied Stresses In order to study changes in suction as a result of applied stresses, specimens from a low-plasticity silty clay were compacted using a Harvard miniature compactor with great care to make them as uniform in moisture distribution as possible. The specimens were subsequently placed in a modified triaxial cell as described previously. The total suction response, as measured by the top and bottom psychrometers under initially isotropic and subsequently under anisotropic applied stresses, is given in Fig. 8 as a function of time. The equilibrium suction subsequent to stress increment application was reached within 3 to 4 days. The initial suction at the top of the specimen was higher than at the bottom, and the change in suction as a result of isotropic stress changes was higher at the top than at the bottom of the specimen. Suction changes due to anisotropic stress applications were relatively small initially; as axial strains approached failure large changes in suction were observed. Equilibrium total suction is given as a function of applied mean stress a„ [a„ = (CTJ + 2CT3)/(3)] in Fig. 9. There appears to be a stress path dependency for the suction response. Furthermore, the slope of the suction-applied stress plot is not constant; it varies, in general, with stress level, stress path, and initial suction. The relationship does not appear to be a simple function of the applied stress. It should be noted, however, that the slope of the suction-applied stress curve is equal or less than unity for the most part. For the soil used, the measured total suctions approximate the matrix suctions closely, since the osmotic component is believed to be insignificant. Relationship of Suction Components One of the questions which needs clarification is to what extent the matrix component of the total suction controls the mechanical behavior of soils. Four specimens of Grundite clay were prepared by mixing the clay powder with NaCl solutions of 0, 0.1, 0.5, and 0.8 m concentrations at a moisture (solution) content of about 40 percent. These mixtures were subsequently compacted to the same density. The compacted specimens (35.6 mm in diameter and height) were placed in the ceramic-plate extractor and were equilibrated to a matrix suction of 200 kPa. Their total suction was then measured by psychrometers at the top and the bottom. Fig. 10 gives total suction as a function of NaCl concentration. The dashed line gives the

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EDIL ET A L O N BEHAVIOR A N D TESTING OF UNSATURATED SOILS

(r^* fl-J-iiJ

ff-/ "•rffj

t op bottom

•o

0 8 0 140 0 9 10 280 0 420 0 n 420 160 12 13 420 250 14 4 20 340 7 * p r t s s u r e B in k Pa

S60 420 140 !40 140 140 140

1 2 3 4 5 6

X

s

125

320 70 0 180 350 510 660

••MM**-*

i.? 10

20

30

40

50

60

70

80

t i m e , (days)

FIG. 8—Measured total suction response under applied stresses.

O

isotropic s t r e s s

D dnisotrop A dnisotropic

2

4 dDplicd mcdn stress

loading (Otidinq

ff

=420kPd .140l
6 ~^ k

FIG. 9—Equilibrium total suction as a function

of applied mean stress.

theoretical total suction which is the sum of 4/„, = 200 kPa and \l/, as given by Lang [19]. The total suction measured by the top psychrometer follows the theoretical line very closely. The discrepancy observed for the bottom psychrometer is believed to be due to dilution of the soil water at the bottom as a result of contact with the ceramic plate which was initially saturated with distilled water. It is felt that by use of the total suction measured at the top of

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126

LABORATORY SHEAR STRENGTH OF SOIL

10

20 TCfTAL SUCTION (BARS)

FIG. 10—Soil suction components.

a specimen and the known induced matrix suction, the solute suction component can be estimated during a desorption schedule. In a subsequent series of tests, sodium saturated and partly leached Grundite specimens were statically compacted at a moisture content 2 percent higher than the optimum and were brought to equilibrium at various matrix suctions in the extractor. After equilibrating, their total suction was measured and repetitive loading tests were carried out. Figure 11 gives the water retention curve (water content versus suction) for these specimens. As the matrix suction varies from 50 to 1500 kPa, effecting a desorption schedule, the total suction remains practically constant after an initial drop. The value of osmotic (solute) suction varies along the desorption curve as a consequence of the removal of dissolved salts by the soil-water extract. This variation appears to be complex and possible explanations of it are obscured by the complicated nature of the extraction of clay-water systems (salt exclusion and salt sieving during pressure extraction) [20]. The repetitive loading tests on these compacted specimens of Grundite resulted in a resilient modulus-matrix suction response qualitatively similar to the one given in Fig. 7, whereas there were no trends associated with the total suction. Therefore it appears that the matrix suction is the fundamental component of the total suction in controlling the mechanical behavior, and that measurement and use of the total suction as an index of mechanical behavior can be misleading, especially for those soils with significant osmotic suction component.

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EDIL ET AL ON BEHAVIOR AND TESTING OF UNSATURATED SOILS

127

SUCTION,HI (kPdx10"T

FIG. 11 — Variation of soil suction components during a desorption cycle.

Discussion and Conclusions The mechanical behavior of unsaturated cohesive soils under different common stress conditions, that is, static compression, dynamic shear, and repetitive compression, has been considered as a function of induced initial matrix suction along a desorption cycle. The test results suggest that the moisture regime can be expressed most suitably in terms of matrix suction. It is an intrinsic parameter and reflects the effects of soil type and fabric, climate, and position of groundwater table on the mechanical response better than other indices such as water content or degree of saturation alone. The test data covering such a wide range of loading modes suggest that a definite change in stress-strain response takes place at a critical value of the matrix suction with modulus values, in general, dropping beyond the critical suction. The value of the critical matrix suction may vary as a function of soil type or testing mode or both; however, it was found to be always greater than 400 kPa for all soils and tests in this study. A similar change is not observed with respect to certain other properties, that is, strength, damping, and plastic strains. The cause of the change has not been identified and a consistent hypothesis is not obvious at this time. Measurement of soil suction in the laboratory in connection with the mechanical testing is very desirable. Thermocouple psychrometers, which measure the total suction, appear attractive for this purpose. Even though

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128

UBORATORY SHEAR STRENGTH OF SOIL

measurements with them require a level of care (and a relatively long time) quite above the level at which most engineering tests are ordinarily performed, it is possible to adopt and use them effectively in the laboratory and the field. The total suction of the soil decreases as the applied stresses (isotropic and anisotropic) increase; however, the relationship is not a simple one and depends on a number of factors. The matrix suction appears to be the fundamental component controlling the mechanical behavior. This would limit the use of psychrometers alone in indexing the behavior of soils, especially if they have a significant osmotic suction component. This certainly should not distract one from the use of psychrometers and the total suction concept in connection with the unsaturated flow and the soil-moisture equilibria. For a given soil, the water content versus suction curve (moisture retention curve) is not unique for absorption and desorption cycles. This effect is known as "hysteresis". In this study, only variations from the initially saturated state were studied by means of a desorption schedule. The hysteresis effects are considered important, but were outside the scope of this investigation. Acknowledgments The senior author acknowledges the role of Drs. B. P. Warkentin, R. N. Yong, and R. J. Krizek in provoking his interest in soil suction. The financial assistance of the National Science Foundation is gratefully acknowledged. Financial support was provided to F. X. Toha during the course of this investigation by a fellowship from the Agency for International Development Program. References [/) Fredlund, D, G., Canadian GeotechmcalJournal. Vol. 16, No. 1, Feb. 1979, pp. 121-139. [2] Bishop. A. W., Teknisk Ukehlad. No. 39, 1959. pp. 859-863. \3] Croney, D., Coleman, J. D., and Black, W. P. M., "The Movement and Distribution of Water in Soil in Relation to Highway Design and Performance." Highway Research Board, Special Report No. 40. 1958, pp. 226-252. \4\ Lambe, T. W. in Proceedings. Research Conference on Shear Strength of Cohesive Soils. American Society of Civil Engineers. 1960, pp. 555-580. |5] Aitchison, G. D. in Conference on Pore Pressure and Suction in Soils. Butterworth & Co., London, 1960. pp. 47-52. |6] Jennings, J. E. B. in Conference on Pore Pressure and Suction in Soils. Butterworth & Co., London, 1960, pp. 26-30 [7] Richards. B. G. in Permeability and Capillarity of Soils. ASTM STP 417. American Society for Testing and Materials, 1967. pp. 4-34. [c^l Fredlund, D. G. and Morgenstern. N. R., Journal of the Geotechnical Engineering Division. American Society of Civil Engineers, Vol. 103, No. GT. 5, May 1977. pp. 447-466. |9] Richards. L. A.. Agronomy. No. 9, Part 1, American Society of Agronomy, 1965, pp. 128-152. 1/0] Spanner. D. C. Journal of Experimental Botany. Vol. 2, No. 5, June 1951. pp. 145-168.

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EDIL ET AL ON BEHAVIOR AND TESTING OF UNSATURATED SOILS

129

III] Krizek, R. J., Edit, T. B., and Ozaydin, I. K., Engineering Geology. Vol. 9, No. 1, Jan. 1975, pp. 13-38. \I2] Kondner, R, L., Journal of the Soil Mechanics and Foundations Division. American Society of Civil Engineers, Vol. 89, No. SMI, Proc. Paper 3429, Feb. 1963, pp. 115-143. [13] Luh, G. F.. "An Experimental Study of Dynamic Behavior of Soils," Ph.D. thesis. Department of Civil and Environmental Engineering, University of Wisconsin-Madison, 1980. \I4] Thomthwaite, C. W., Geographical Review. Vol. 38, No. 1, 1948, pp. 55-94. 1/5) Edil, T. B. and Motan, S. E., "Soil-Water Potential and Resilient Behavior of Subgrade Soils," Transportation Research Record. No. 705, 1979, pp. 54-63. [/61 Johnson, L. D., "Psychrometric Measurement of Total Suction in a Triaxial Compression Test," U. S. Army Engineers Watervt'ays Experiment Station. Miscellaneous Paper S-74-19. Vicksburg.Miss., June 1974. [17] Edriss, E. v., Jr., and Lytton, R, L. in Proceedings, 9th International Conference on Soil Mechanics and Foundations Engineering, Tokyo, Vol. 2, 1977, pp. 217-224. [18] Toha, F. X., "Use of Thermocouple Psychrometers for Measuring Soil Suction in Triaxial Compression Testing," M.S. Degree Independent Study Report, Department of Civil and Environmental Engineering, University of Wisconsin-Madison, 1979. 1/9) Lang, A. R. G., Australian Journal of Chemistry. Vol. 20, 1967, pp. 2017-2023. [20] Lagerwerff, J. V., Soil Science Societv of America Proceedings. Vol. 28. 1964. pp. 502-506.

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H. Y. Fang^ and Joseph

Fernandez^

Determination of Tensile Strength of Soils by Unconfined-Penetration Test

REFERENCE: Fang, H. Y. and Fernandez, Joseph, "Determination of Tensile Strength of Soils by Unconfined-Penetration Test," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 130-144. ABSTRACT: This paper describes the factors affecting the test procedures and methods for preparation of test specimens for determination of tensile strength of soils by unconfined-penetration (UP) method. Correlation of tensile strength with other soil constants and strength parameters, such as Atterberg limits, activity, toughness index, unconfined compressive strength, cohesion, and friction angle, are presented. Theoretical explanations of this method and the conventional split-tension test by use of the limit analysis concept are discussed. KEY WORDS: materials tests, soil mechanics, tensile strength, limit analysis, plasticity, geotechnology, failure, cohesive soils

The impoitance of the tensile characteristics of soil has been pointed out by many investigators. It is especially useful to predict the cracking behavior of earth dams, highway and airfield pavement components, adhesion characteristics of various soil stabilization materials, and tension cracks in slope stability analysis. There are several methods available for measuring the tensile strength of soils—namely, Briquet Gang model [i]^ for measuring the direct tensile strength, the beam-type test, [2] and the split-tension test for measuring the indirect tensile strength. Recently, a simple and reliable test method named the unconfined-penetration (UP) test was developed at Lehigh University for measuring the indirect tensile strength of soils [3,4], rocks [5], and other nonmetallic construction materials [4,6]. The test results have been compared with the conventional split-tension test for various 'Professor of Civil Engineering and Director, and research assistant, respectively, Geotechnical Engineering Division, Fritz Engineering Laboratory, Lehigh University, Bethlehem, Pa. 18015. ^The italic numbers in brackets refer to the list of references appended to this paper.

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FANG AND FERNANDEZ ON TENSILE STRENGTH OF SOILS

131

materials including soil, concrete, mortar, bitumen, and cement-treated highway bases and rock. Good agreement between both tensile strength results has been observed. The UP test has an advantage in that the test can be conveniently performed in conjunction with routine California Bearing Ratio (CBR) and compaction tests. Various sizes and shapes can be used for the UP tests [7,8]. The other test methods mentioned measure the tensile strength across a predetermined failure plane, whereas the UP test always causes failure on the weakest plane, which results in the measurement of the true tensile strength [9,10]. The laboratory setup of the UP test is shown in Fig. 1. A brief description of the test and computation procedures follows: By using two steel disks (punches) centered on both the top and bottom surface of a cylindrical soil specimen, a vertical load is applied on the disks until the specimen reaches failure. The tensile strength of the specimen can be calculated from the maximum load by the formula

iKKbH - a^)

(1)

where a, = tensile strengh, psi, P = maximum load at failure, lb, K = constant, depending on specimen-punch size and soil type (see Table 1), b = radius of specimen, in., H = height of specimen, in., a = radius of disk (punch), in. The purpose of this paper is to further evaluate the effect of variables upon the observed tensile strength and the uniformity of the UP test results. These variables include specimen-punch size, punch alignment, and moisture conditions during the test. Correlations of the UP test results with the other soil constants and strength parameters, such as Atterberg limits, activity, toughness index, unconfined compressive strength, undrained cohesion, and friction angle are also presented. From these findings, it is possible to establish a standard test procedure for the UP test for the determination of tensile strength of soils. Theoretical Considerations The theoretical equation for tensile strength (Eq 1) is based on the plasticity theory. This theory, which was previously used for computing the bearing capacity of concrete blocks or rocks [11,12], has been extended to an application of soils and other nonmetallic construction materials [3,4]. Two major

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132

LABORATORY SHEAR STRENGTH OF SOIL

FIG. 1—Unconfined-penetration

test for determination of tensile strength of soils.

TABLE 1—Proposed value for parameter K. specimen-punch size, specimen height-diameter ratio, and rate of loading. /f-Value Specimen Size

Soil

Stabilized Soil

1.05 to 1.10 Harvard miniature compaction mold, 3.3 by 7.2 cm(lVi6by 2.81 in.) Proctor mold, 10.2 by 11.3 cm (4 by 4.6 in.) 1.0 1.2 CBR mold, 15.2 by 17.8 cm (6 by 7 in.) 0.8 1.0 Specimen-punch ratio 0.2 to 0.3 Height to diameter of specimen ratio 0.46 to 1.0 Rate of loading ASTM recommendation for axial strain at a ratio of 0.5 to 2 percent of heigfit per minute.

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FANG AND FERNANDEZ ON TENSILE STRENGTH OF SOILS

133

assumptions are made in the theory. The first is that sufficient local deformability of soils in tension and in compression does exist to permit the application of generalized theorems of limit analysis to soils idealized as a perfectly plastic material. The second is that a modified Mohr-Coulomb failure surface is postulated as a yield surface for soils. Figure 2a shows an ideal failure mechanism for a UP test on a cylindrical specimen which consists of two cone-shaped rupture surfaces directly beneath both top and bottom punches with many simple tension cracks located along the radial direction. The cone shapes move toward each other as a rigid body and displace the surrounding material sideways. Figure 2b shows the velocity field of the failure mechanism, where 6^, is denoted as relative velocity vector at each point along the cone surface with an angle 0. A^ and A^ are the horizontal and vertical components of 6^,. Based on limit analysis technique as described in Ref (12), the internal energy dissipation is found by multiplying the area of each discontinuity surface by tensile stress (a,) times horizontal components of velocity (A^). The external rate of work is equal to load (P) times vertical component of velocity (A^). Equating the external rate of work to the total rate of internal dissipation yields the value of the upper bound on the applied load P: P , TTfl^

1 - sin .^ ?„ , ^ , , ^, (bH . , , , , — + tan (a +
cot a a,

(2)

All notations are the same as in Eq 1, except that q^^ is defined as unconfined compressive strength and 0 as the undrained friction angle of soil, a is the angle of the cone (Fig. 2b). The upper bound has a minimum value when a. satisfies the condition hp"/hx = 0, which is

cot a = tan 0 -f sec <> /

1+

bH ——cos 4) a^ q„ / \ - s\n(j}\ 2

1/2

.

(3)

— sm 0

and is valid for a > tan ' (2a///). The upper-bound solution of Eq 2 can be reduced to P^p"

= TciKbH - a^)

(4)

Rearrange Eq 4 and it becomes Eq 1, where K = tan (2a + 0)

(5)

The value /f in Eq 5 depends not only on the angle of friction, but also on the compression-tensile strength ratio and specimen-punch ratio, as indicated in Eq 3. A comparative study of /C-value has been carried out

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134

LABORATORY SHEAR STRENGTH OF SOIL

i

y////A-

PUNCH (DISC)

RIGID AR

(a)

CROSS-SECTION

AR -SPECIMEN

(b)

VELOCITY REUTIONS

FIG. 2—Failure mechanism of unconfined-penetration test.

previously by using concrete [12] and soil {4\. Table 1 summarizes the proposed /^-values for the various types of soil and specimen-punch size. An examination of the horizontal and vertical strain distribution in the UP test at failure was also evaluated by use of concrete specimens and measured with strain gages [7]. This experiment showed that vertical strain distribution on the middle horizontal section of the cylindrical specimen was almost uniform. Good agreement between experimental and theoretical results was found. Other theoretical comparisons between UP tests and conventional splittension tests have been made by use of elastic solution, limit analysis, slipline, and finite-element solutions [7,12.13] Experimental Study The experimental study includes two phases. The first phase is to evaluate the test procedures and methods for preparation of test specimens. The second phase covers the correlations of tensile strength with other soil constants

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FANG AND FERNANDEZ ON TENSILE STRENGTH OF SOILS

135

and strength parameters. The effects of some of the variables, such as sample-punch size, rate of loading, and soil types, have been previously examined [3,4]. The correlation between unconfined compressive strength and split-tensile strength has been reported [4]. The present experiments include a further examination of soil types and correlation with unconfined compressive strength. The additional variables considered include punch alignment, molding water content, and moisture conditions during the tensile tests. Correlations with additional parameters, including Atterberg limits, activity, toughness index, cohesion, and friction angles, are also presented.

Soil Types The soil mixtures illustrated throughout this study are composed of silty clay (liquid limit = 30, plasticity index = 10) with various percentages of sand, bentonite, and biotite added. All samples passed No. 10 sieve and were air-dried. The standard Proctor mold was used for preparation of test specimens. For each type of mixture, the Atterberg limits, gradations, optimum moisture content, and maximum dry unit weight were determined in accordance with ASTM standard procedures.

Specimen-Punch Sizes and Punch Alignment For preparation of a tension test specimen, a standard Proctor mold is commonly used. However, for stabilized soil, such as cement-treated base material, the CBR mold may be used or, for saving soil material, the Harvard miniature compaction mold may also be used. As long as the ranges of the specimen-punch ratio stay within 0.2 to 0.3 and the height-specimen diameter ratio stays within 0.46 to 1.0, any size of specimen and punches can be used. Proposed values of K for various sizes of specimens are presented in Table 1. The UP test requires two steel punches (disks) centered at both top and bottom surfaces to penetrate into an unconfined soil specimen. The alignment of these two punches—that is, whether or not in the same plane—is important. Two cases were examined where the punches were eccentrically loaded. The first case had both punches in the same plane, but off-center of the specimen. The second case had one punch on the center of the specimen and the other off-center. From the experiments for each case, it was found that the maximum error that could be expected was 10 percent. To resolve this problem of alignment, two plastic tampers have been made. The diameter of the tamper is the same size as the soil specimen. At the center of each tamper is a hole with a diameter equal to the punch diameter. The use of these tampers should ensure proper alignment of the punches. The hardness of the punch material should also be investigated, especially

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136

LABORATORY SHEAR STRENGTH OF SOIL

for testing hard rocks or stabilized soils. The commonly used reamer blank tool steel is suitable for punch material. Correlation Study When the soil is saturated or very wet, it has very little tensile strength existing with no engineering significance. When the soil gradually reduces in moisture content, its tensile strength gradually develops. Therefore the moisture content during the tension test is extremely important. For comparison purposes, all specimens were tested at two moisture conditions, one at the optimum moisture content (OMC) and the other at air-dried condition. The test results are summarized in Tables 2 and 3. Experiments were performed to obtain Atterberg limits, activity, toughness index, unconfined compressive strength, cohesion, and friction angles. These are discussed in the following sections. Atterberg Limits, Activity, and Toughness Index As previously reported [3,4], the tensile strength increases as the plasticity index and liquid limit increase. Similar conclusions were reported by other investigators by using conventional split-tension tests [14], All previous study on test specimens for tension tests was based on the OMC. In this experiment further evaluations include correlation of the tension test results with activity and toughness index. The activity is defined as the plasticity index divided by the percent of clay [15]. In general, the activity value increases as the plasticity index and liquid limit increase. The tension tests were performed at both OMC and air-dried conditions. Six types of soil were'tested. The first group of soil specimens was molded at OMC and the tension test was performed at OMC condition. The second group of specimens was also molded at OMC, but was dried in air at room temperature for 40 h, then the tension tests were performed. Tension test results and activity values for both cases are plotted in Fig. 3. It is clearly indicated that the tensile strength increased significantly for all types of soil when they are air-dried. However, the amount and rate of increase in strength depends on the soil types. For a low-plasticity soil, the differences between two moisture conditions are more pronounced than for a high plasticity soil. The toughness index is defined as the ratio of plasticity index to the flow index [75]. The flow index is determined from the standard liquid limit test. This toughness index frequently is used as an indicator for the evaluation of soil stabilizing materials. Figure 4 shows the tensile strength test results versus toughness index for both moisture conditions. Similar trends are indicated in Figs. 3 and 4. From these results, it can be projected that there will be greater differences in strength between the two moisture conditions for a low-plasticity soil than for a high-plasticity soil.

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FANG AND FERNANDEZ ON TENSILE STRENGTH OF SOILS

137

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138

UBORATORY SHEAR STRENGTH OF SOIL

TABLE 3—Summary of tensile and undrained direct shear tests at various molding moisture contents. NOTES: (1) An asterisk indicates samples molded on wet-side of optimum moisture content (CMC). (2) CMC values for each soil type are presented in Table 2. (3) The data shown in the table are the average values of two or more tests. (4) 1 psi = 6.9 kPa.

Direct Shear Test Molding Moisture Content, %

Tensile Strength (a,), psi

Cohesion (C), psi

Friction Angle (). deg

C/ff,

A

10.8 12.9 12.9 13.0* 14.4* 15.3*

6.69 1.59 1.78 2.57 0.67 0.32

19.9 15.2 22.7 19.0 13.0 10.0

40.0 30.6 25.5 31.5 22.5 20.2

2.97 9.56 12.75 7.39 19.40 31.25

D

11.9 12.5 13.1 13.2 13.2 13.9 14.2* 15.8* 16.8*

8.18 9.48 6.78 7.94 7.93 4.79 5.25 1.54 0.68

21.5 22.5 23.4 24.3 22.5 21.0 30.0 16.8 14.0

42.5 37.6 36.2 34.2 36.7 34.5 28.1 24.6 19.2

2.62 2.37 3.45 3.06 2.84 4.38 5.71 10.91 20.59

F

13.2 16.4 18.8* 20.4* 22.4*

10.86 7.02 4.03 4.26 2.03

33.0 27.5 23.0 27.6 13.5

28.2 25.5 16.0 10.5 4.5

3.04 3.92 5.71 6.48 6.65

Soil No.

Unconfined Compressive Strength The ratio of unconfined compressive strength to tensile strength of materials is of interest to all design engineers because of its practical uses. For soils, most tests for this ratio are performed at OMC condition. A curvilinear relationship has been reported for various soil types [3,4,14,16,17]. In this experiment an investigation of how the moisture condition affects this ratio was carried out. Six soil types were investigated. One group was tested at OMC in both tension and compression tests, while the other group was molded at OMC but allowed to air-dry in room temperature for 40 h, then tested for both tension and compression. The test results are shown in Fig. 5. It is evident that for air-dried specimens, the compressive-tensile ratios for the six types of soils were relatively constant. However, for higher moisture

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FANG AND FERNANDEZ ON TENSILE STRENGTH OF SOILS

^o-

139

v s . A CURVE (AIR-DRIED)

FIG. 3—Tensile strength versus activity of two moisture contents during tension tests.

contents, the ratios increased significantly for all types of soil, especially for the low-plasticity soils. Figure 5 mainly points out that effects of moisture content and soil type on the compressive-tensile strength ratio are equally important when the plasticity index is less than 20 (see Region I). However, the effect of moisture content is predominant in Region II, where the compressive-tensile strength ratio is insensitive to variation in percent of clay and soil types, as reflected in plasticity index. Cohesion and Friction Angles in Undrained Condition The relationship between cohesion and tensile strength is also useful to the practitioner, as pointed out previously [16]. When soil is dry, the ratio of cohesion and tensile strength influences only the soil types. Further investigation Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

140

LABORATORY SHEAR STRENGTH OF SOIL

S 35

/O- VS. I^ CURVE (AIR-DRIED)

0.4

0.8

1.0 1.2 TOUGHNESS INDEX, I^

1.4

FIG. 4—Tensile strength versus toughness index of two moisture contents during tension tests.

of the moisture content effect on cohesion-tensile strength relationships is needed. The direct shear apparatus with undrained condition was used for determination of cohesion (c) and friction angle (). Various molding moisture contents were evaluated. For each molding moisture content, three samples were prepared and various normal loads applied. The values of cohesion and friction angle were obtained from Mohr circle diagrams. Six soil types were tested in the same manner. Typical plots of cohesion-tensile ratio versus molding moisture content for three different soil types are shown in Fig. 6. Curve A, with a plasticity index equaling 4.9, shows that a slight increase of the molding moisture content sharply affects the cohesion-tensile ratio, while Curve F, with a plasticity index equaling 78.2, indicates that molding moisture content has lesser effect on the cohesion-tensile ratio. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

FANG AND FERNANDEZ ON TENSILE STRENGTH OF SOILS

141

O 32.2

40

60

PIASTICITY INDEX, 1

Region I Region II

Percent of clay and moisture content, both significant. Moisture content more significant than percent of clay.

FIG. 5—Compressive-tensUe ratios versus plasticity index of two moisture contents during compression and tension tests. (Numbers beside points indicate percent passing 200 sieve. I

The curvilinear relationship between friction angle and tensile strength was observed for all six types of soils. Typical curves for three different soil types are shown in Fig. 7. It indicates that soils with higher plasticity indexes have lower friction angles. It can also be seen that at lower tensile strengths the rate of increase of the friction angle is much higher than at higher tensile strength. Sununaiy and Conclusions 1. The unconfined-penetration (UP) test is simple, easy to perform, and can be used conveniently in conjunction with routine compaction and CBR tests. 2. Good agreement between UP and conventional split-tensile tests exists. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

142

LABORATORY SHEAR STRENGTH OF SOIL

30

25

20

OMC •=

12.9%

F dp = 78.2)

OMC -

J 5

\ 10

i

\ 15

i

I 20

17.2T

L 25

30

MOLDING MOISTURE CONTENT, PERCENT

FIG. 6—Cohesive-tensile ratio versus molding moisture content with various soil types.

The UP test always causes failure on the weakest plane, which results in the measurement of the true tensile strength. 3. The constant AT-value depends on the specimen-punch ratio, heightspecimen diameter ratio, friction angle of the materials, and the compression-tensile strength ratio. This value ranges from 0.8 to 1.2. The specimenpunch ratio ranges from 0.2 to 0.3, and the height-diameter ratio of the specimen is 0.46 to 1.0. These values are summarized in Table 1. 4. The punch alignment is important. Both top and bottom punches should be at the center of the specimen and should be on the same plane. To avoid a problem, a plastic alignment tamper should be used. Hard tool steel should be used as punch material for testing hard rock or stabilized soil. 5. Six soil types and two moisture conditions were investigated. One series was conducted at optimum moisture content (OMC), while the second series, was completed on specimens air-dried in room temperature for 40 h. The

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FANG AND FERNANDEZ ON TENSILE STRENGTH OF SOILS

143

7.2)

32

o 24

z 16

2.0

4.0

6.0 8.0 TENSII£ STRENGTH, o^ PSI

12.0

FIG 7. —Friction angle versus tensile strength for various types of soil. (Solid points indicate samples at molding moisture contents on dry-side of optimum moisture condition. 1 psi = 6.9 kPa.)

significant differences of tensile strength at tliese two moisture conditions were observed. The amount and the rate of increase between the two moisture conditions depend on the soil types. For low-plasticity soil, the differences between the two moisture conditions is more pronounced than the higher plasticity soils for the activity and toughness index. 6. The compression-tensile strength ratios versus soil types with various molding moisture contents were also observed. They indicated that the influence of the molding moisture content is more significant than soil types for high-plasticity soils. For low-plasticity soils, both percent of clay and moisture are equally important (see Fig. 5). 7. Cohesion-tensile strength ratio has similar effects on the molding moisture content and soil types as does the compression-tensile strength ratio. For low-plasticity soil, it is shown that a slight increase of the molding moisture content sharply affects the cohesion-tensile strength ratio. On the other hand, the molding moisture content has less effect on higher plasticity soil. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

144

LABORATORY SHEAR STRENGTH OF SOIL

8. A curvilinear relationship between friction angle and tensile strength was observed (see Fig. 7). It indicates that as the plasticity index increases, the friction angle decreases. For lower tensile strength, the rate of increase of the friction angle is higher than at higher tensile strength. Acknowledgments The research reported herein was supported by the National Science Foundation under Grant GY-7459 awarded to Lehigh University. The authors express their thanks to N. S. Pandit for reviewing the manuscript. References [/) Tschebotarioff, G. P. and DePhilippe, A. A. in Proceedings, Third International Conference on Soil Mechanics and Foundation Engineering, Vol. 3, 1953, pp. 207-210. [2] Leonards, G. A. and Narain, J., Journal of the Soil Mechanics and Foundations Division. Proceedings of the American Society of Civil Engineers. Vol. 89. No. SM2, March 1963, pp. 47-98. [3] Fang, H. Y. and Chen. W. P., Highway Research Record. No. 354. 1971. pp. 62-68. [4] Fang. H. Y. and Chen, W. F., in Proceedings. Third Southeast Asia Conference on Soil Engineering, Hong Kong, 1972, pp. 211-215. [5] Dismuke, T. D.. Chen. W. F., and Fang, H. Y.. Rock Mechanics. Vol. 4, No. 2, Oct. 1972, pp. 70-87. [61 Cumberledge, G., Hoffman, G. L., and Bhajandas, A. C , Transportation Research Record. No. 560, 1976, pp. 21-29. 17] Chen, W. f.. Journal of the Engineering Mechanics Division. Proceedings of the American Society of Civil Engineers. Vol. 96, No. EM3, June, 1970, pp. 341-352. [H] Fang, H. Y. in Proceedings. 15th Annual Meeting of Society of Engineering Science. University of Florida, Dec. 1978, pp. 527-532. [9] Fang, H. Y., Geotechnical Engineering. Vol. 4, No. 1, June, 1973, pp. 59-60. I/O] Fang, H. Y., Soils and Foundations. Vol. 14, No. 3. Sept. 1974. pp. 81-82. (//] Chen, W. F. and Drucker, D. C , Journal of the Engineering Mechanics Division. Proceedings of the American Society of Civil Engineers. 95. No. EM4. Aug. 1969, pp. 955-978. [12] Chen. W. F.. Limit Analysis and Soil Plasticity. Elsevier Scientific, Amsterdam, 1975. \I3\ Chen, W. F. and Chang, T. Y. P., Journal of the Engineering Mechanics Division. Proceedings of the American Society of Civil Engineers. Vol. 104, No. EM3. June 1978, pp. 691-704. [14] Narain, J. and Rawat, P. C, Journal of the Soil Mechanics and Foundations Division. Proceedings of the American Society of Civil Engineers. Vol. 96, No. SM6, 1970. pp. 2185-2190. [15] Winterkorn, F. H. and Fang, H. Y., Foundation Engineering Handbook. Van Nostrand Reinhold, New York, 1975, Ch. 2, pp. 80-120. |/6) Fang, H. Y. and Hirst, T. J., Highway Research Record. No. 463, 1973, pp. 45-50. [17] Krishnayya. A. V. G., Eisenstein, Z., and Morgenstern, N. R.. Journal of the Geotechnical Engineering Division. Proceedings of the American Society of Civil Engineers. Vol. 100, No. GT9, Sept. 1974, pp. 1051-1061.

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p. y. Lade'

Torsion Shear Apparatus for Soil Testing

REFERENCE: Lade, P. V., "Toision Shear Apparatus for Soil Testing," Laboratory Shear Strength of Soil. ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 145-163. ABSTRACT; Laboratory studies of soil behavior during rotation of principal stress directions may be performed using a torsion shear apparatus. The requirements, construction, and operation principles for this apparatus are presented. The same confining pressure is applied to the inside and outside surfaces of a hollow cylindrical specimen. Both clockwise and counterclockwise shear stresses and vertical deviator stresses can be applied to the ends of the hollow cylinder. The entire setup is contained in a pressure cell, and the integrated loading system is located below the table which holds the cell. A variety of initial stress conditions may be used, and the behavior of soils during large stress reversals, as well as reorientation of principal stresses and combinations of these conditions, may be investigated in this apparatus. The loading system and the deformation measurement principles are described, and procedures for preparation of sand specimens are presented. The advantages and limitations of the torsion shear apparatus are discussed. KEY WORDS: geotechnical engineering, laboratory tests, mechanical properties, sands, shear strength, soil mechanics, strains, stresses, torsion

In order to perform laboratory tests for investigation of the behavior of soils during rotation of principal stress directions, it is necessary to apply shear stresses as well as normal stresses to the surfaces of the specimen. A brief review of several types of test equipment capable of transmitting normal and shear stresses for soil specimens has been presented by Lade [1]? Each of these equipment types presents difficulties in interpretation of test results caused by nonuniform stress distributions or the lack of ability to measure all stresses applied to the specimen, or both. A torsion shear apparatus, in which a hollow cylinder specimen is confined 'Associate professor, Mechanics and Structures Department, School of Engineering and Applied Science, University of California, Los Angeles, Calif. 90024. The italic numbers in brackets refer to the list of references appended to this paper. 145 Copyright by Downloaded/printed Copyright 1981 University of

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LABORATORY SHEAR STRENGTH OF SOIL

between inside and outside membranes and between cap and base rings, offers the advantage of individual control of vertical normal stress, cell pressure, and applied shear stress. The same confining pressure is applied to the inside and outside surfaces of the specimen. The vertical normal stress and the shear stress are transferred to the specimen through cap and base rings. The entire setup is contained in a pressure cell, and the integrated loading system is located below the table which holds the cell. An earlier version of the torsion shear apparatus employed a hollow cylinder specimen with height of 5 cm, average diameter of 20 cm, and wall thickness of 2 cm. Some of the stresses and strains observed in this apparatus were shown to be nonuniform [2]. They were caused by restraint at the ends where shear and normal stresses are transferred to the specimen through full friction surfaces. While this restraint may not be completely eliminated, its effect can be substantially reduced by employing taller specimens. The hollow cylinder specimen used in the torsion shear apparatus presented here has a height of 40 cm and the same average diameter and wall thickness as described previously. Based on theory of elasticity, Wright et al [3] presented an analysis from which the ratios among height, average diameter, and wall thickness of a hollow cylinder specimen may be obtained to achieve a minimum of effects of end restraint. Data from tests with different specimen heights presented at the end of the present paper indicate that the specimen dimensions employed in the torsion shear apparatus result in negligible effects of end restraint.

Requirements for Apparatus A torsion shear apparatus for measurement of stress-strain and strength characteristics of soils during rotation of principal stress directions should satisfy the following conditions: 1. The apparatus must be capable of accommodating normal and shear strains which are large enough so that failure can be obtained with a minimum of induced nonuniformity in the stress and strain distributions in the specimen. 2. The shear stresses must be transferred to the specimen with no slippage between the specimen and the stress application mechanisms. 3. The horizontal normal stresses on the inside and outside surfaces of the hollow cylinder specimen should be identical in order to simplify the analyses of the results and in order that unjustified assumptions about the soil behavior be avoided. 4. The dimensions of the specimen should be such that it behaves as a thinwalled tube, in which case the stress condition imposed on the specimen can be regarded as a plane stress condition.

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LADE ON TORSION SHEAR APPARATUS

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Before the torsion shear apparatus was constructed, three additional principles, mainly pertaining to simplification of the design and operation, emerged: 1. The procedure for preparing test specimens should be fairly simple. 2. The stress application mechanisms should be designed so that the applied normal and shear stresses can be measured independently of each other. 3. Moving parts that may result in friction of such magnitude that correction is necessary should be avoided if possible. While these latter principles may be less essential to the results, they do facilitate the performance of the tests. Stress Application in Torsion Shear Apparatus The torsion shear apparatus was designed and constructed to permit application of a confining pressure to a hollow cylinder specimen (the same confining pressure is applied to the inside and the outside surfaces of the specimen). Shear stresses and vertical deviator stresses can be applied to the top and bottom (the ends of the cylinder). The entire setup is contained in a pressure cell. A three-dimensional drawing of the torsion shear apparatus is shown in Fig. 1; a picture of the hollow cylinder specimen with cap plate and with clip gages mounted is shown in Fig. 2. The normal and shear stresses are applied to the specimen as follows: The confining pressure is applied through the cell water that surrounds the specimen. The vertical load is applied to the specimen through the cap. This vertical load is transferred to the specimen by a cap plate, which is connected to a shaft through the bottom of the cell. The resulting deviator stress, together with the cell pressure, provides for a vertical, normal stress larger than the confining pressure. The torque is transferred to the specimen through the center shaft and the cap plate. The shear stresses due to the torque cause reorientation of the principal stress directions and a stress state with three unequal principal stresses. If shear stresses are not applied to the specimen, the cell pressure is the minor principal stress. With torsional shear stresses applied, the cell pressure becomes the intermediate principal stress. The design and performance of the torsion shear apparatus and its integrated loading system are described in detail in the following sections. Specimen Setup Specimen, Cap, and Base Rings A vertical cross section of the specimen and apparatus is shown in Fig. 3. The hollow cylinder specimen is contained between a cap ring, a base ring.

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148

UBORATORY SHEAR STRENGTH OF SOIL

LINEAR MOTION TRANSOUCEtU

CENTER SHAFT-

V

TORSION SHEAR LOADING CYLINDER

r^

X •«-

- - VERTICAL LOADING CYLINDER

FIG. 1—Torsion shear apparatus with 5-cm-tall specimen.

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LADE ON TORSION SHEAR APPARATUS

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and a membrane along the inside and outside vertical surfaces. The apparatus can accommodate specimens with heights up to 40.0 cm. The inside and outside diameters are 18.0 cm and 22.0 cm, respectively, and the thickness of the specimen is consequently 2.0 cm. The cross section of the cap ring is designed to provide 0-ring seals between the inside and outside parts of the membrane (Fig. 3). The base ring, on which the specimens are prepared, is fastened to the bottom plate with three screws. The cap and base rings are made of stainless steel. Membrane The specimen is confined along the inside and outside vertical surfaces by one continuous membrane, in the bottom of which the base ring is placed. The cross section of the 0.028 to 0.030-cm-thick rubber membrane is U-shaped (Fig. 3). Holes are punched in the bottom of the membrane to provide for drainage lines and for the three screws with which the base ring is fastened to the bottom plate. Two grooves in the bottom plate below the base ring contain 0-rings which provide seals for the membrane along the base ring, when this is fastened to the bottom plate. The grooves are spaced to allow for the drainage lines and the screws (Fig. 3). Forming Jackets Circular forming jackets along the inside and outside surfaces of the hollow cylinder specimen support the membrane while the cohesionless soil is being placed. The inside forming jacket consists of a piece of thin aluminium tube, which fits inside the base ring and sits on the bottom plate. When the inside part of the membrane is pulled up, the Foisson effect makes it cling tightly around the forming jacket. The thin-walled tube is split parallel to the tube axis in order to facilitate its placement and removal. The outside forming jacket is designed as a regular vacuum jacket, which fits outside the base ring and sits on the bottom plate. Drainage Lines The cap and base rings are provided with three filter stones each. The filter stones, which are made of porous bronze, are countersunk in the rings 120 deg apart. Drainage lines, which allow measurement of the volume change of the specimen, are connected to the filter stones through fittings. The drainage lines consist of 0.32-cm (0.125-in.) Saran tubing, which pass through fittings in the bottom plate. The three lines from the filter stones in the cap ring are connected inside the cell to one line, which is led out through the bottom plate. The drainage lines from the base ring are connected outside the cell to one line.

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LABORATORY SHEAR STRENGTH OF SOIL

FIG. 2—Hollow cylinder specimen with cap plate and clip gages mounted.

Full Friction

Surfaces

In order to transfer shear stresses from the cap and base rings to the specimen and to avoid slippage at their interfaces, full friction surfaces are provided on the rings. The surface of the base ring that faces the specimen is coated with a layer of epoxy and pressed down in sand of the type being tested. The sand grains in the lower layer of the specimen, which is deposited on top of the base ring, interlock with the sand grains, which are glued to the ring. After the hollow cylinder specimen has been deposited, the surface of the cap ring is coated with a layer of epoxy and pressed down on top of the specimen. The upper layer of sand grains is thereby rigidly glued to the cap ring.

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LADE ON TORSION SHEAR APPARATUS

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Clip Gage

0 - R i n g Seals Cap Ring

Hollow Cylinder Specimen

H =40cm

;^^

-Membrane

fi)'22cin Dj = 18 cm

-Filter Stone Base Ring

- Drainage Line F I G . 3—Crass section

of hollow

cylinder

specimen

and

apparatus.

Torque and Vertical Load Transfer To facilitate assembly of the specimen and apparatus, the torsion shear unit is designed to be loaded from the bottom by an integrated loading system. The loading system is mounted on the reinforced frame of the cabinet on top of which the torsion shear apparatus is fastened. Both the torque and the vertical load are transferred to the stainless steel center shaft, which is maintained in its vertical position by a linear and rotary ball bearing encased in the bottom plate of the cell. A rolling diaphragm sealed against the bottom plate and the shaft (Fig. 3) provides a good seal around the shaft and ensures that the shaft is free to rotate and move vertically with negligible friction. The top part of the shaft has a square cross section, which fits in a square hole in the stainless steel cap plate (Fig. 1). This construction enables the transfer of the torque from the shaft to the cap plate. Figure 1 also shows a washer resting on the cap plate and fastened with a screw to the end of the shaft. The vertical load is transferred from the shaft through the screw and Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

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LABORATORY SHEAR STRENGTH OF SOIL

washer to the cap plate, which fits on top of the cap ring to which it is fastened with three screws (Fig. 3). The cap plate is provided with three 1.9-cni (0.75-in.) holes, which ensures that the same horizontal normal pressure is applied to the inside and outside surfaces of the specimen. One leg of each of the pair of clip gages, which measure the thickness change of the specimen, sticks through each of two of these holes, (Fig. 3). Pressure Cell The top and bottom plates are constructed of 2.5-cm (1.0-in.) and 3.18-cm (1.25-in.)-thick aluminium, respectively. The cell water is led in through a female Foster fitting in the bottom plate. A female Foster fitting in the top plate provides an outlet for the air in the cell. The inside surface of the top plate is slightly tapered in order to minimize the trapping of air bubbles when water is introduced into the cell. The vertical cell wall is made of 1.27-cm (0.50-in.)-thick Lucite plastic tube. The inside diameter of the cell is 27.9 cm (11.0 in.) and the height is 53.3 cm (21.0 in.). The bottom plate, the Lucite cell wall, and the top plate are held together by six 1.27-cm (0.5-in.)-diameter tie-rods, which are put in place after the specimen is prepared and the cell wall and top plate are installed. A small cylindrical Lucite container, which clips on one of the tie-rods, is connected to the cell by a 0.64-cm (0.25-in.) plastic tube through the bottom plate. This cylinder is filled with water to such a level that the water surface is at midheight of the specimen. After the cell has been filled with water, the cell pressure is applied by air pressure on the water surface in the small Lucite cylinder. A pressure transducer mounted at the bottom of the small cylinder measures'the cell pressure. Loading System The torsion shear apparatus is designed so that the specimen is loaded from the bottom by an integrated loading system (Fig. 1). The loading mechanisms are mounted on the reinforced frame of the cabinet on top of which the torsion shear apparatus is fastened. Both the torque and the vertical load are transferred to the center shaft below the bottom plate of the apparatus, as seen in the upper part of Fig. 4. Vertical Load The vertical load is supplied by an oil-filled pressure cylinder, which is mounted directly below the center shaft. The oil enters the pressure cylinder through a 0.64-cm (0.25-in.) plastic tube on the side of the cylinder. A load cell, which measures the vertical load applied to the specimen, is fastened to the lower end of the center shaft. The vertical load is transferred from the pressure cylinder to the load cell through a 0.467-cm (0.188-in.)-thick

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LADE ON TORSION SHEAR APPARATUS

SIDE

153

VIEW Bottom Plate of Torsion Shear Apparatus •—Center Shaft

5

1 3^—r&^—^

)ue Load C e l l — 7

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Linear and Rotary Beari Bearing

C a b l e s - l _ 3 F l ^ T o r q u e Arm h r ^ il" Inlet ^ ^ ^ : \ "^Oil Inl Vertical Load Cell Counter Balance Spring ; = - * - O i l Inlet

Vertical Loading Cylinder

Hollow Central Piston Rod

TOP VIEW Torque Loading

Cylinder—51

tt £

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#2

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N A Square Hole for Center Shaft

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-

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Vertical Load Cell

^ y~—Vertical Loading ,,/ Cylinder J l ^ ^ C a Cable ble _ ^ j _ p p

#1

# 3

^—'

^

Torque Load Cell

'

==•

FIG. 4—Schematic diagram i>j loading system for torsion shear apparatus.

stainless steel cable. This cable extends through the hollow central piston rod in the pressure cylinder and is fastened to the lower end of the piston rod, as seen in the upper part of Fig. 4. Using a long, thin cable for the load transfer ensures that the vertical loading mechanism does not induce a moment. Torque The torque is applied to the center shaft, as seen in the lower part of Fig. 4. A torque arm with two branches is mounted on the center shaft just above the vertical load cell. This part of the center shaft has a square cross section that fits in a square hole in the torque arm. This construction enables the transfer of the moment from the torque arm to the center shaft. Four oil-filled Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

154

LABORATORY SHEAR STRENGTH OF SOIL

pressure cylinders supply the horizontal loads through cables to the torque arm, the ends of which have circular shapes, as seen in the lower part of Fig. 4. The distances from the center to the ends of the torque arm are consequently maintained constant at 14.0 cm when the center shaft with the torque arm is rotated. The arrangement of the four pressure cylinders makes it possible to apply torsional shear stresses in both the clockwise and the counterclockwise directions. Opposite pressure cylinders are interconnected (No. 1 with No. 2, and No. 3 with No. 4), so that the torque arm is symmetrically loaded. This ensures that no horizontal load is applied to the linear and rotary ball bearing, which guides the center shaft. Vertical deformations of the hollow cylinder specimen will cause the torque arm to move vertically and could result in changes in the vertical load applied to the specimen. However, long cables are used to connect the pressure cylinders to the torque arm, so that the angles between the cables and the horizontal loading plane are small, and the induced vertical load is thereby made negligibly small. The four pressure cylinders are mounted outside the cabinet to make the distances from the pressure cylinders to the torque arm as long as possible. The torsional load applied to the specimen is measured by four load cells attached to the piston rod of each cylinder. Their position is seen in the lower part of Fig. 4. Stress and Strain Control The pressures for confinement of the specimen, torque, and vertical load are obtained from air pressure. Both the vertical load and the torque can be either stress or strain controlled. A schematic diagram of the stress and strain control system is shown in Fig. 5. The principle of the strain control regulators, which are used on the oil lines to the vertical loading cylinder and to the torque loading cylinders, is shown in the lower part of Fig. 5. A differential flow controller maintains a pressure drop of 3 psi (0.2 kgf/cm^ = 20 kPa) across a needle valve. A feedback line from the top of the controller is connected to the upstream side of the needle valve. The pressure drop is determined by a spring-loaded diaphragm in the controller, and is independent of the pressures in the upstream and the downstream parts of the oil line. In order for the strain control regulator to work properly, it is required that the pressure difference between the two parts of the oil line be at least 3 psi (0.2 kgf/cm^ = 20 kPa). For strain-controlled tests, the needle valve is used to regulate the rate at which oil flows through the strain control regulator. A nondisplacement shut-off valve and a strain-control regulator are installed in parallel in each of the oil lines, as seen in the upper part of Fig. 5. The shut-off valve is closed when strain-controlled loading is desired, and the strain rate is regulated by the needle valve. When stress-controlled loading is

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LADE ON TORSION SHEAR APPARATUS

To Chamber

To Vertical Loading Cylinder

To Clockwise Torque Loading Cylinders

155

To Counter -Clockwise Torque Loading Cylinders

' — A i r Pressure Su pply

Strain Control Regulator

>

I T d^:=)-*^ => - 4 \

^—Flow Controller *— Needle Valve D i r e c t i o n of Flow

FIG. 5—Schematic diagram of stress and strain control system.

desired, the shut-off valve is opened, the needle valve is closed, and air pressure is used to control the load. All air pressure lines are connected through a selector valve to a manometer so that each air pressure can be measured as desired. The oil lines to the torque loading cylinders are connected to an oil pressure manometer. The difference between the pressures in the oil line upstream and downstream from the strain control regulator can therefore be monitored and kept above 3 psi (0.2 kgf/cm^ = 20 kPa).

Counterbalance System In order to counterbalance the weights of the parts that are attached to the force-transmitting shaft, such as the cap plate, top ring, torque arm, load cell, and the center shaft itself, a spring is placed between the top plate of the vertical cylinder and the vertical load cell (Fig. 4). The spring is chosen with a Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

156

LABORATORY SHEAR STRENGTH OF SOIL

suitable spring constant to balance the excess weights before the test is started.

Maximum Stresses In order to keep the equipment to a reasonable size and cost the tests were conducted at relatively low stresses. The maximum stresses which can be applied to the specimen are limited by the strength of the Lucite cell wall and the performance of the torque arm. The maximum cell pressure used in any test to date is 400 kPa (4.0 kgf/ cm^). The vertical load cell fastened to the lower end of the center shaft is designed for a maximum load of 1000 kgf corresponding to a deviator stress of 800 kPa (8.0 kgf/cm^). The torque load cells are designed for a maximum load of 5(X) kgf each, resulting in a maximum load of 10(X) kgf in one direction, corresponding to a shear stress of 8(X) kPa (8.0 kgf/cm^).

Maximum Strains The maximum vertical deformation of the hollow cylinder specimen is limited by the maximum stroke in the vertical pressure cylinder. This movement cannot exceed approximately 3.0 cm. The 40.0-cm-tall specimen can therefore be compressed vertically about 7.5 percent. The maximum shear deformation of the specimen is limited by the maximum stroke of the pistons in the horizontal pressure cylinders. Since this stroke is approximately 5.0 cm, the maximum shear strain that can be applied to the specimen is about 12 percent.

Defonnation Measurements Vertical and Shear Deformations Both the vertical and the shear deformations are measured with linear motion transducers outside the cell. A 0.64-cm (0.25-in.) stainless steel rod is installed centrally in a socket in a small beam on top of the cap plate (Fig. 1). The rod sticks out through ball bushings encased in the top plate and sealed with an 0-ring below the ball bushings. The coil of the vertical linear motion transducer is mounted solidly directly above the rod (Fig. 1). The rod is connected with the core in the transducer, which registers the vertical deformations. A horizontal arm is mounted on the rod outside the cell. The arm, which rotates with the cap ring, has a circular section with a groove (Fig. 1). The shear deformation transducer is mounted on one of the rods on top of the cell. The transducer is pointed tangentially to the grooved circular section of the arm. The core is connected with an unstretchable radio dial cord to the

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LADE ON TORSION SHEAR APPARATUS

157

arm, so that the cord will track in the groove as shear deformations are registered by the linear motion transducer. In order to ensure a steady movement of the core and to measure shear strains during unloading and reverse loading, a string is fastened to the opposite end of the core and provided with a small weight. The string is carried over a pulley behind the transducer, and the weight keeps the string stretched, thus avoiding jumps, and pulls the core back during unloading and reverse loading. The complete setup can be seen in Fig. 6. A grid consisting of appropriately spaced vertical and horizontal lines is drawn on the outside surface of the membrane (Fig. 2), in order that the uniformity of the shear strains can be observed during and after testing.

FIG. 6—Fully assembled upparuius.

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LABORATORY SHEAR STRENGTH OF SOIL

Horizontal Deformations The horizontal deformations of the specimen are measured with clip gages. These consist of pieces of beryllium copper band on which strain gages are glued. Beryllium copper is chosen because it has a linear stress-strain relationship. A pair of clip gages measures the change in thickness of the specimen wall. The gages clip on the wall with one leg sticking inside the specimen through holes in the cap plate (Fig. 3). Each of the clip gages is made of aluminium and shaped as a narrow U with the leg sticking outside the specimen shorter than the inside leg. A beryllium copper strip is fixed to the short leg, which makes the total length of the two legs equal. Four strain gages are glued to the beryllium copper strip near the fixed end. The four gages are connected in a full bridge. The beryllium copper strip is much more flexible than the rigid aluminium frame, so that most of the bending of the clip gage due to change in wall thickness is concentrated at the strain gages on the strip. A single clip gage measures the change in the outside diameter of the specimen. This gage is made entirely of beryllium copper band, which is shaped as a half ring according to its position around the specimen. The tips of the gage clip onto the outside surface of the specimen at midheight points 180 deg apart. Four strain gages are mounted on the middle section, two on the inside and two on the outside surface. The strain gages are connected to form a full bridge. Since the tips of this horizontal clip gage barely hang on to the specimen, it is necessary to support the middle portion of the gage. A gallows, which stands on the bottom plate, is provided with a piece of copper wire in which the middle portion of the clip gage hangs. From each of the three full bridges a cable with four wires for measurement is led out of the cell through a watertight fitting in the bottom plate. The clip gages are consequently tied permanently to the bottom plate of the cell. The strain gages and the wires are thoroughly waterproofed. Each of the U-shaped clip gages measures the change in wall thickness, and the horizontal strains in the radial direction can be calculated directly from these measurements. The horizontal strains in the tangential direction can be calculated from the measurements of all the clip gages by At -

^D

A€h, -

(1)

where Af = change in thickness of the specimen wall, AD = change in outside diameter of the specimen, and D„ = average diameter of the specimen ( = 20.0 cm).

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LADE ON TORSION SHEAR APPARATUS

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Volumetric Deformations The volume change of the specimen, which is saturated with water, is measured with the volume change device designed by Chan and Duncan [4]. Correlation between Linear and Volumetric Strains Since three perpendicular normal strains are measured, the volume change measurement provides a check on the performance of the clip gages through the following relation, which is valid for small strains. fv =

fvert +

fht +

fhr

(2)

Slight amounts of bulging of the outside surface of the specimen in the horizontal, radial direction were noticed after most tests. The value of At measured with the clip gages was therefore too high and Eq 2 was not satisfied in general. Since the bulging affects the measurements of At and AD equally, the calculated value of e^t is considered to be reasonably correct. To improve the accuracy of the measurements, average values of e^^ were calculated from Eq 2 knowing e,,, e^^^, and £|,t.

Corrections Corrections to Stresses The vertical load and the torque are corrected for the load carried by the membrane. The membrane load is calculated by using Hooke's law and the elastic modulus [approximately 1400 kPa (14.5 kgf/cm^)] and Poisson's ratio ( = 0.5) for the latex rubber. In addition to the corrections due to membrane load, the vertical load measured with the load cell is corrected for the effects of cell pressure on the center shaft and the stiffness of the counter balance spring. A calibration curve relating the spring load and the instantaneous height of the specimen is established. Thus the spring load can be calculated from the specimen height measured during the test. Because the specimen is relatively tall (40 cm), the vertical stress is calculated at midheight. Thus half of the specimen weight is included in the vertical force correction. Corrections to Strains Corrections to the measured deformations were found to be negligible.

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160

LABORATORY SHEAR STRENGTH OF SOIL

Preparation of Test Setup The membrane is fitted around the base ring, and the holes for drainage lines and screws are marked and punched in the bottom of the membrane. The surface of the base ring, which faces the specimen, is coated with a layer of epoxy and pressed down in sand of the type being tested. The base ring is then placed in the bottom of the membrane and put in place on the bottom plate, so that the drainage lines fit in their respective holes. The base ring is fastened with three screws to the bottom plate, thereby sealing the membrane and the drainage lines. The total height of the top ring and the base ring with the full friction surface is measured. The forming jackets are placed, and the membrane is stretched up through and around the forming jackets. The outside part of the membrane is held in place with an 0-ring around the outside forming jacket, to which a vacuum is applied. A sieve, which fits inside the forming jackets, is put in place and a measured quantity of air-dry sand is poured inside the sieve. The sieve is lifted slowly out of the forming jackets, and the sand is deposited through the sieve in a loose state. The sand is deposited to overheight and, with the cap ring placed on top of the sand deposit, the forming jackets and the cap ring are vibrated until the desired density of the sand is obtained. The top surface is leveled, and the cap ring coated with a layer of epoxy is placed on top of the specimen. The rubber membranes are pulled up around the cap ring and sealed with 0-rings. The top drainage lines are then connected to the cap ring, and a vacuum [ ~ 30 kPa (0.3 kgf/cm^)j is applied to the specimen through a bubble chamber in order to be able to detect leaks. After removing the forming jackets, the dimensions of the specimen are measured and the void ratio of the specimen is calculated. If a leak is detected, the specimen is painted with layers of rubber latex until the leak is repaired. Each layer of rubber latex is allowed to dry before the next layer is applied. A grid consisting of appropriately spaced vertical and horizontal lines is drawn on the outside surface of the membrane. After the specimen is prepared, the cap plate and the washer are placed on the center shaft and fastened with a screw. The cap plate is then pushed down to contact with the cap ring and fastened with three screws. The large clip gage is installed, with its ends at points 180 deg apart on the outside surface of the specimen, and its middle portion suspended in a copper wire from a gallows. The gages, which measure the change in thickness of the specimen wall, are installed with one leg sticking through holes in the cap plate and clipping on the wall at midheight of the specimen. Gallows and copper wire are also used to support these clip gages. The small beam with the small center rod is fastened to the top of the cap plate, and the cell wall and the top plate are put in place and fastened with six tie-rods to the bottom plate. The linear motion transducers sitting on top of the cell are installed and connected to the small center rod sticking out through the top plate. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

LADE ON TORSION SHEAR APPARATUS

161

The cell is filled with water and a confining pressure is applied simultaneously with the release of the vacuum in the specimen. The air-dry sand specimen is saturated with water employing the CO2method described in detail in Refs 5 and 6. Influence of Specimen Height The tangential, horizontal normal stress in the cylinder wall {aj is the only stress which is not measured in the torsion shear apparatus. The value of a,. may be assumed to be equal to the cell pressure during isotropic compression. However, due to end restraint, a^ is unknown when shear stresses are applied to the specimen. In previous studies of torsion shear tests on 5-cmhigh specimens, it was shown thatCT^is nonuniform along the height of the specimen [2] and that the values of (ff^r.average/ffceii) ^t failure were about 2.7 and 1.8 for dense and loose Monterey No. 0 Sand, respectively [/]. Using the apparatus described here, two series of tests were performed on specimens of loose Santa Monica Beach Sand with heights of 10 cm and 40 cm. No vertical deviator stress was used in these tests, and failure was produced by applying torsional shear stresses. If it is assumed that the end restraint has negligible effect on the average behavior of the 40-cm-tall specimens, so that a^ = tJceii' then the calculated friction angles compare very favorably with those obtained from corresponding cubical triaxial tests on the same sand. Using the friction angles from the 40-cm-tall specimens together with the stresses measured in the 10-cm-tall specimens, the unknown values of a^ at failure may be calculated for the latter specimens. Figure 7 shows values of (^A.average/<^ceii) plotted against specimen height for loose Santa Monica Beach Sand. Monterey No. 0 Sand is similar to Santa Monica Beach Sand in many respects (particle shape and composition, uniformity coefficient, maximum and minimum void ratios, and range of friction angles). The result of a test on loose Monterey No. 0 Sand performed with the same stress path as for the other tests is shown in Fig. 7 to provide a data point corresponding to a specimen height of 5 cm. Based on the data shown in Fig. 7, it is reasonable to conclude that the effects of end restraint are negligible in 40-cm-tall specimens of loose sand, and it is likely that sufficiently uniform stress states may be achieved in specimens with heights considerably lower than 40 cm. Conclusion A torsion shear apparatus, in which a hollow cylinder specimen is confined between inside and outside membranes and between cap and base rings, is described. This apparatus offers the advantage of individual control of vertical normal stress, cell pressure, and applied shear stress. The entire setup is contained in a pressure cell, and the integrated loading system is located Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

162

LABORATORY SHEAR STRENGTH OF SOIL

2.0

I

• I

-

•

J

••

1

Q 6^..^:— Monterey No 0 Sand D, = 27 %

1.5

_

\

r—Santa Monica Beach Sand —^

1^0 • 2.0 • ' V ^ 3.8a ^ ^

„ 1.0

_

\ 2.01

fZ

> Values of Ocell ' "^ k g f / c m ^ ) aie Indicated at the Data Points

re

D

Average Dianietei = 20 cm Wall Thickness = 2cm I

I 10

1 20

S p e c i m e n Height

FIG. 7—Effects

1 3D

40

(cm)

of end restraint in torsion shear tests on hollow cylinder specimens.

below the table which holds the cell. A variety of initial stress conditions may be used, and because both clockwise and counterclockwise shear stresses can be applied to the specimen, the behavior of soils during large stress reversals, as well as reorientation of principal stresses, may be investigated. The apparatus fulfills all the stated requirements, and a study of the influence of end restraint indicates that the specimen dimensions are such that fairly uniform stress states are achieved. Acknowledgments The tests on Santa Monica Beach Sand were performed by Elisha Geiger of the School of Engineering and Applied Science at the University of California at Los Angeles. The torsion shear apparatus presented here was constructed with support from the National Science Foundation under Grant No. ENG 75-05325. References [1] Lade, P. V. in Proceedings, 5th Pan-American Conference on Soil Mechanics and Foundations Engineering, Buenos Aires, 1975, Vol. I, pp. 117-127. [2] Lade, P. V. in Proceedings. Second International Conference on Numerical Methods in Geomechanics, Blaksburg, Va., 1976, Vol. 1, pp. 381-389; errata m Journal of the Geotechnicul Engineering Division. Proceedings of the American Society of Civil Engineers. Vol. 104, No. GTl, Jan. 1978, pp. 173-174. [3] Wright, D. K., Gilbert, P. A., and Saada, A. S. in Proceedings. American Society of Civil Engineers Speciality Conference on Earthquake Engineering and Soil Dynamics, Pasadena, Calif., 1978, Vol. 2, pp. 1056-1075.

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LADE ON TORSION SHEAR APPARATUS

163

[4] Chan, C. K. and Duncan, J. M., Materials Research and Standards. Vol. 7, No. 7, July 1967, pp. 312-314. [5] Lade, P. V. and Duncan, J. M., Journal of the Soil Mechanics and Foundations Division, Proceedings of the American Society of Civil Engineers, Vol. 99, No. SMIO, Oct. 1973, pp. 793-812. 161 Lade, P. V., Geotechnical Testing Journal. Vol. I, No. 2, June 1978, pp. 93-101.

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K. T. Law^

A Servo System for Controlled Stress Path Tests

REFERENCE: Law, K. T., "A Servo System for Controlled Stress Path Tests," Laboratory Shear Strength of Soil. ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 164-179. ABSTRACT: This paper describes a servo system capable of imposing a prescribed stress path tor the study of soil behavior in the laboratory. Various conditions were examined: (/) stress paths resembling those in the field, (2) both axisymmetric and plane strain shearing, and (J) large strain or post failure (or yield) state. The servo system is composed of two main parts: A minicomputer and an electricpneumatic (E/P) transducer. The minicomputer collects and processes data while the experiment is in progress. The appropriate electrical signals are transmitted to the E/P transducer, which regulates the pressure connected to the back-pressure line of the triaxial or plane strain apparatus. With the axial load applied at a constant strain rate, it is possible to measure the complete stress-strain behavior, including that at large strains, along a prescribed stress path. A series of tests was carried out to illustrate the capability of the servo system. For the particular case of slope stability analysis, another series of tests was conducted from which peak and post-peak strength envelopes were obtained. KEY WORDS: servo system, computerized soil tests, controlled stress paths, triaxial tests, plane strain tests, strength envelopes, peak, post peak

Prediction of soil behavior under load is an essential requirement of engineering design. One way to improve such prediction is to examine the behavior of the soil by various test methods that yield results applicable under field conditions. The stress path involved in shearing soils is an important factor influencing soil behavior and is receiving growing attention. A stress path, a line drawn through points on a stress plot, denotes the sequence of stress changes experienced by a soil element during the shearing process. Under field situations it starts from the point representing the in situ stress condition and proceeds to other points, as dictated by the type of structure being considered and the geometry and characteristics of the entire subsoil. The effects of stress path 'Research Officer, National Research Council of Canada, Ottawa, Ontario, Canada. 164 Copyright by Downloaded/printed Copyright 1981 University of

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LAW ON SERVO SYSTEM FOR STRESS PATH TESTS

165

were recognized as early as 1948 when Taylor [1]^ pointed out the likelihood of being able to obtain the correct strength by reconsolidating soil specimens in the laboratory to the in situ pressures. Bozozuk and Leonards [2] and Bjerrum [3] provided evidence that such reconsolidated specimens do yield more consistent information than unconsolidated ones for estimating soil behavior under the loading condition. Following reconsolidation, shearing along different stress paths produces varying effects on different aspects of soil behavior. The general experience [4-6] has been that stress paths do not greatly influence cohesion (c') or the angle of internal friction (4>'); on the other hand [7-9], they strongly affect the deformational characteristics. Based on the second observation, Lambe [10,11] formulated the stress path method for solving deformation problems. A number of methods have been used for shearing soils under a controlled stress path condition. Some have used the triaxial cell with minor modifications [12-14]. Others [15-17] have employed a special apparatus designed and built to test certain soil types. The above test equipment, however, permits only one mode of shearing; that is, incremental loading or controlled stress loading. It is not possible to shear soil specimens under a controlled strain rate condition as is required for study of rate effect and the post-peak stress-strain relation for a brittle soil. The equipment described in Ref 16 can impose constant strain rate shearing, but the control of stress path is lost. With computer technology it is now possible to build a system that is capable of controlling the stress path under controlled strain rate conditions in the shearing of soil specimens. Such a system is described herein.

Description of Apparatus Figure 1 is a schematic diagram of the complete apparatus. Basically it consists of a servo system and a loading cell (triaxial or plane strain). The servo system is composed of two main parts: a minicomputer and an electricpneumatic (E/P) transducer. Figure 2 shows a plane strain test conducted using the servo system.

Operation Principle The principle of operation of the servo system can be illustrated by means of a constant strain rate test conducted along the stress path represented by a fourth-degree polynomial: 4

P'=

E a„q"

(1)

H=0

^The italic numbers in brackets refer to the list of references appended to this paper.

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166

LABORATORY SHEAR STRENGTH OF SOIL

VOLTAGE ji

DIVIDER

E f TRANSDUCEK

P MINI MAGNETIC

<-

COMPUTER

TAPE

DISPLACEMENT VOLUME C H A N G ; p

A

D

MEASURING DEVICE

CELL ''

t

PRESSURE

|;

^ / V ' - ' w v V ' / v >/>y'7 PORE V.ATER PRESSURE VOLUME CHANGE

FIG. 1—Schematic diagram of servo system for controlled stress path tests.

where the a's are the coefficients of the polynomial; q = ( a / - ah')/2

(2a)

p' = ( a ; + a h ' ) / 2

{2b)

and Oy and ffh' are the vertical and horizontal effective stresses. In a compression test a,' and aj,' are the major and minor effective principal stresses ffj' and a^', respectively; while in an extension test, they are a^' and a i ' , respectively. Definingp ' and q in terms of a^' and (7^' instead of a\' and (J3' gives a sign convention to q that is positive in compression shearing and negative in extension shearing. By assigning appropriate values for the coefficients in Eq 1, curved and linear stress paths can be applied to soil specimens. Some examples of compression and extension tests are shown in Table 1. The application of q on the soil specimen is achieved by straining the soil specimen at a constant rate on the load press. The horizontal effective stress, CTh', is applied using the servo system in such a way thatp ' and q closely satisfy Eq 1. In the present test system (j),' is equal to the difference between the cell and the back pressures. While the cell pressure is kept constant, the back pressure is regulated by the servo system to produce the appropriate oi,'. This procedure eliminates the need to correct for any load applied to the piston as a result of cell pressure changes. The back pressure regulation will also affect ffv' (ffy' = 2g + (Th) a i d hence/?', resulting in an actual stress path somewhat different from the prescribed one (Fig. 3). The allowable deviation e be-

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LAW ON SERVO SYSTEM FOR STRESS PATH TESTS

167

1. Load cell 2, Displacement transducer 3. Rotating bushing 4. Piston 5. Electric/pneumatic transducer 6. Volume change transducer 7. Plane strain cell 8. Hanger for anisotropic consolidation 9. Specimen 10. oj-transducer II. Pressure amplifying relay 12. Back-pressure line 13. Load press 14. Cell pressure line FIG. 2—A controlled stress path plane strain test.

tween the stress paths, however, can be reduced to a tolerable value to be given in a later section. The complete task of regulating <7(,' in accordance with Eq 1 involves three steps: (/) monitoring responses, (2) processing data, and (3) changing the back pressure. Response

Monitoring

Electrical transducers (Figs. 1 and 2) are used to monitor load, pressure, axial displacement, and volume change during the experiment. These quantities, measured in terms of voltage, are transmitted through an analogue/digital (A/D) converter to the minicomputer for processing. A load cell far more rigid than the soil specimen is used to remove possible problems arising from loading system flexibility, particularly when measuring postCopyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

168

LABORATORY SHEAR STRENGTH OF SOIL

o

+

o

+

+

+

:s n) Tt <SJ

> <j

3

"ri

a>

s"«

%J

^ x)

& •^

CS

?. co

,>! 1 II w u ^o Ul j o:

oa

<•

!-

n

,r

i

a E

a i;; o

c M •Q.

m

(/}

u u c c

«« a

•Q.

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LAW ON SERVO SYSTEM FOR STRESS PATH TESTS

169

PRESCRIBED ACTUAL

n /

-e

\

M.-r]

^^

V-^i^J ^

"

^

P'

'(q)

>^ FIG. 3—Prescribed and actual stress paths in a controlled stress path test under constant strain rate.

peak behavior. This load cell can take compressive and tensile loads so that both compression and extension tests can be carried out. The cell and back pressures are registered using pressure transducers of the unbonded strain gage type. Both transducers yield values of absolute pressure and the effect of barometric pressure changes is cancelled out because aj,' is equal to the difference in back and cell pressures. The axial displacement is recorded by means of a direct-current differential transformer (DCDT) transducer, the volume change by a float-displacement instrument as described by Mitchell and Bum [18]. Minicomputer The minicomputer performs two main tasks: (7) data acquisition and processing, and (2) transmission of a pertinent electrical signal to the E/P transducer. Raw experimental data are accepted at a certain frequency controlled by a variable to be fed into the computer. Engineering quantities such as stress and strain are computed following the standard method [12]. Values of p ' and q are deduced using Eqs 2a and 2b.These engineering quantities are displayed on a teletype or stored on a magnetic tape. Substituting q in Eq 1 yields the theoretical value p , ' required to follow the prescribed stress path. The difference between p' and p,' is evaluated and compared with the allowable limits ± e . If the difference exceeds the limits, a numerical increment ^ is added to or subtracted from the current number being sent through the digital/analogue (D/A) converter to the E/P transducer. Consequently, the pressure from the E/P transducer to the back-pressure line will be modified in accordance with the change in the current number. As the checking Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

170

LABORATORY SHEAR STRENGTH OF SOIL

for deviation from the prescribed stress path and the subsequent pressure modification (if necessary) are done sufficiently frequently, it is not necessary for the E/P transducer to behave linearly. This has proved to be very useful because usual problems such as nonlinearity, hysteresis, or minute drifting in characteristics will impose no effect on the overall performance of the servo system. Electric-Pneumatic Transducer The E/P transducer, also shown schematically in Fig. 1, is a device that regulates pressure in proportion to the voltage it receives. A voltage divider is installed between the D/A converter and the E/P transducer to reduce the voltage to an acceptable range. The basic E/P transducer delivers a pressure ranging from 20 to 100 kPa, and for practical purposes a pressure-amplifying relay is used to expand it to 80 to 400 kPa. The basic device and the relay are each supplied by a constant pressure about 30 kPa higher than the respective maximum output pressures. That from the relay is the back pressure supplied to the soil specimen via a quick connector, which facilitates switching the servo system from one shearing apparatus to another. At present three E/P transducers have been installed. Three controlled stress path tests can therefore be run at the same time, along with seven conventional triaxial or plane strain tests, all linked to the minicomputer. Operation Frequency and Other Parameters The operation of the servo system may be performed at a frequency of up to once per second. Between operations, the voltage on the E/P transducer and hence the back pressure remain at the level of the last operation. The minicomputer and the E/P transducer use an a-c power of 105 to 125 V at 50 to 60 Hz, and both are equipped with standby batteries that immediately cut in and maintain operation in the event of power failure. The frequency of operation, allowable deviation e, and numerical increment ^ (which controls the size of change in aj,') are all adjustable, depending on the behavior of the soil specimen during shear. By adjusting them together the prescribed stress path can be closely followed. In testing Leda clay, for instance, the specimen responds relatively rapidly in the early part of the test and the following have been found adequate: frequency allowable diviation e size of back pressure change

1 operation/30 s 0.25 kPa 0.3 kPa

At the later stage of testing the frequency may be reduced to once every 1 to 5 min while the other two parameters remain unchanged.

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LAW ON SERVO SYSTEM FOR STRESS PATH TESTS

171

Test Description and Results Two test series were conducted: (!) to illustrate the capability of the servo system in soil testing, and (2) to obtain strength envelopes for stiff Champlain Sea clay for natural slope stability considerations. The majority of tests in the first series were carried out along linear stress paths, although curved ones were also possible by assigning appropriate values to the coefficients of the polynomial (Eq 1). All specimens were trimmed from 127-mm-diameter Osterberg samples and were enclosed in thin Ramses rubber membranes; all were 80 mm high and 36 mm in diameter for triaxial tests, and 36 by 36 mm in cross section for plane strain tests. Side drains were provided and a strain rate of 3.5 percent axial strain per day (calculated by the method of Bishop and Henkel [12]} was used to allow adequate pore pressure equalization within the specimen. A Geonor triaxial cell with a rotating bushing to reduce piston friction was employed in the triaxial compression and extension tests. Specimen preparation and mounting were identical to preparation for an ordinary triaxial test. No cell modification was required in the compression tests, but some accessories were made for the extension tests. The arrangement for triaxial extension tests is shown schematically in Fig. 4. Fastened to the piston is a circular plate on which weights are placed to balance the cell pressure acting on the piston. The piston is screwed to the top stainless steel loading platen for application of pulling force. After consolidation, a coupling is mounted to connect the load cell to the piston, and shear can be started by lowering the load press at a constant rate. The coupling is designed to allow for possible small misalignment between the piston and the load cell. A correction of 0.75 kg is made in the data processing to account for the top platen weight and extension of the rubber membrane. The cell for performing plane strain tests has been described in detail by Bozozuk [19]. It is similar in principle to the triaxial cell except that provisions are made to maintain zero strain in the intermediate principal stress direction. This is done by mounting in the cell two side blocks that can be brought into contact with the specimen. Load cells are installed at the end of the blocks for measuring the intermediate principal stress during the test. Again, anisotropic consolidation can be applied, but only plane strain compression tests are possible. Anisotropic consolidation can be applied by different methods (Fig. 5). For vertical consolidation pressure exceeding the horizontal, the standard Geonor hanger system (Fig. 5A) may be used, but it requires frequent adjustments to keep the arm of the hanger level. It is simpler to put appropriate weights on the piston (Fig. 5B) in addition to those for balancing cell pressure. For horizontal pressure greater than the vertical, the position of the Geonor hanger system is modified (Fig. 5C) so that a pulling force can be in-

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172

LABORATORY SHEAR STRENGTH OF SOIL

CROSSBAR

XC LOAD

I

•

CELL

COUPLING

FOR

APPLYING

TENSION

-^

WEIGHTS

ROTATING BUSHIN G

STAINLESS STEEL

£

CAP

B.

FIG. 4—Arrangement for triaxial extension tests.

troduced to the piston. This method again necessitates frequent adjustment of the hanger arm. A simpler method is to take away appropriate weights from the pistons (Fig. 5D) already in use for balancing cell pressure. (It should be noted that there is one advantage in using the hanger system: larger loads can be more easily applied because of the moment arm ratio.) The tests in the first series for illustrating the capability of the servo system are summarized in Table 1, and the corresponding stress paths are shown in Fig. 6. Except for Test 8, all tests were conducted on a stiff, fissured, and brittle Champlain Sea clay from Rockcliffe, Ottawa, Canada. Its moisture content ranged from 65 to 70 percent; other detailed characteristics have been given by Mitchell [20]. In Tests 1, 4, and 6, the consolidation ratio K of the horizontal to vertical consolidation pressures was assigned a value greater or less than 1.0, with a subsequent shearing across thep'-axis. This resulted in a reversal of shear stress direction or a 90-deg rotation in principal stress. Anisotropic behavior can be studied and it is possible to simulate, in the laboratory, the stress paths corresponding to situations such as building embankments on soft clays and cutting slopes in stiff clays. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

LAW ON SERVO SYSTEM FOR STRESS PATH TESTS

173

FIG. 5—Methods of applying anisotropic consolidation pressures.

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174

LABORATORY SHEAR STRENGTH OF SOIL

PLANE

STRAIN

TRIAXIAL

+ Ve il

-ve '' FIG. 6—Examples of stress paths conducted by means of the servo system.

Test 7 is a plane strain test with the vertical stress held constant. It is applicable to a long vertical cut, either standing freely or supported by a retaining structure that allows the active pressure to develop. Test 2 is a constant a^^' compression test; Tests 3 and 4 are constant stress ratio tests in both the compression and extension stress space. All are useful for studying the fundamental behavior of the clay. Typical p'-q plots for triaxial and plane strain tests (Tests 5 and 6) are shown in Fig. 7. They are computer plots showing the entire stress path realized during the tests. Deviation from the prescribed stress path is negligible so that the objective of controlling the stress path is achieved. The same is also true of all the other tests listed in Table 1. Test 8 involved a nonlinear stress path and was performed on an undisturbed, soft, sensitive marine clay (its properties have been given by Bozozuk and Leonards [2]). This test was designed for studying the in situ behavior of clay subjected to a self-boring pressuremeter test, as described by Eden and Law [21]. The nonlinear stress path (Fig. 8) was deduced from the in situ test for the soil at the pressuremeter-soil interface, where the strains, radial pressures, and pore pressures were monitored by means of electronic transducers. In the laboratory the soil specimen was trimmed horizontally and mounted in the cell in such a way that plane strain condition was maintained in the original in situ vertical direction, as was true also in the pressuremeter test. After consolidation, appropriate values were assigned to the coefficients Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

LAW ON SERVO SYSTEM FOR STRESS PATH TESTS

175

PLONE STROIN COMPRESSION (TEST NO.61

a) a.

TRIOXIRL EXTENSION ~~^--^ (TEST NO.E)

p'

kPa

FIG. 1—Typical stress paths during tests.

in Eq 1, causing the subsequent shear to follow the nonlinear stress patn (Fig. 8). Figure 9 shows the stress-strain and volume change-strain curves for the laboratory test (Test 8). A significant volume change was found to take place. Although it is not possible to measure volume change during a pressuremeter test, the laboratory test indicates that shearing along the observed effective stress path involved some drainage. This is in contrast with the usual assumption of undrained shear for this in situ test. The deduced pressuremeter strength will therefore be generally higher than the undrained strength and will yield an unsafe design if used directly for some engineering applications. The second test series was also carried out on Rockcliffe clay. Plane strain and triaxial tests were conducted in a relatively low stress range, in which most natural slope failures occur. Various stress paths were used to simulate those possible in the field [22]. All specimens were sheared to a large strain (about 8 percent) for observing post-peak behavior. Typical stress-strain and volume change-strain curves for triaxial and plane strain tests conducted at constant p' are shown in Fig. 10. Dilatancy exists around the peak strength, which is followed by a drop to post-peak strength. The peak and post-peak values for all the tests are presented on a p '-q plot in Fig. 11. Two distinct strength envelopes can be obtained, one for peak and the other for post-peak. They do not appear to depend on the stress paths or on the mode of straining, plane strain, or axisymmetric strain. For natural slope stability considerations they can be characterized by <j>f' = 48deg, c/' = 5.5 kPa 0 / = 40deg, c / = OkPa Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

176

LABORATORY SHEAR STRENGTH OF SOIL

1 40

30

1

0

LAB

•

FIELD

PLANE

1

1

1

1

STRAIN

PRES5UREMETER

—

—

^ - - 0 — •

—

_ ^

20

i 0

10

1

i

1 '

n

0

10

1

20

1

30 p',

FIG. 8—Effective

1

40

1

50

-|

1

70

80

kPa

stress paths for laborutory and field pressuremeter

40

1

60

1

1

1

tests.

•

30 - V - ^ ^ . —

-

20

/ *=

/ /

10

-

AXIAL STRAIN, %

1

,•

2

3

4

5

1

1

I

1

-

°\.

VOLUME 1N C R E A S E ,f=

-2

-

\ 1

1

FIG. 9—Shear stress-axial strain and volumetric stress path test under plane strain condition.

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strain-axial

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1

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Dec License

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reproductions

U W ON SERVO SYSTEM FOR STRESS PATH TESTS

80

111

-

PLANE p'

STRAIN

TEST

98 kPo

TRIAXIAL

TEST

p' - 83 kPo

30

20

10

4,1J I

o 1

' ± -1 •

<

J > -(/I

0

1

L 2

3

J

L

4

5

AXIAL FIG. 10—Typical stress-strain

6

J7

8

9

10

STRAIN, %

and volume change-strain

curves.

where 0 ' and c' are the angle of internal friction and cohesion in terms of effective stresses, respectively; and subscripts/ and r refer to peak and postpeak stages. Summary and Conclusions A description is given of a servo system for shearing soil specimens along linear or curved effective stress paths, as defined by a fourth-degree polyno-

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178

UBORATORY SHEAR STRENGTH OF SOIL

120

1

1 1 1 1 1 a,

TEST

PEAK

UEG

100

TRIAXIAl

-

80 —

1

1

1 1

1

1 1

1

SYMBOL

43

O

-•1.6

o

90

D

135

a

PLANE

90

V

STRAIN

135

/

POST-PEAK.

/ /

^0

-o^""''^.

—

\> 0

'• b

^

^

$c/"

- .^p;40

_

\

Cp

20

y ^ t f l ^

• ^

/ •

"

.p^o^y^h'^

5.5 kPo

\

o

^r c;

—

0

^ " ^

-

^

1 20

1

1 40

1

1 60

1

1 80

1 1 100

1 120

1 1 140

1 160

( a ' + cr. )/2, kPa V n

FIG. II—Summary of test results of Rockcliffe clay.

mial. The servo system comprises a minicomputer and an electric-pneumatic transducer. It can be conveniently connected to the conventional triaxial and plane strain cells in such a way that compression and extension tests can be performed at constant strain rate under the axisymmetric or plane strain mode of straining. Tests on a stiff Champlain Sea clay yielded the following observations: 1. The stress paths realized closely followed the given paths. 2. The post-peak stress-strain relation was determined for this brittle clay along various stress paths. 3. Peak and post-peak strength envelopes were obtained for natural slope stability considerations. These envelopes are independent of stress paths and modes of straining. Acknowledgments The author expresses his appreciation to D. C. MacMillan, Technical Officer, for suggestions during the design of the servo system and for writing the computer program in assembly language for use in the minicomputer. This

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LAW ON SERVO SYSTEM FOR STRESS PATH TESTS

179

paper is a contribution from the Division of Building Research, National Research Council of Canada, and is published with the approval of the Director of the Division. References [/] Taylor, D. W., Fundamentals of Soil Mechanics, Wiley, New York, 1948. [2] Bozozuk, M. and Leonards, G. A. in Proceedings, Specialty Conference on Performance of Earth and Earth-Supported Structures, Purdue University, Lafayette, Ind., 1972, Vol. 1, Part 1, pp. 299-317. \3] Bjerrum, L. in Proceedings, Eighth International Conference on Soil Mechanics and Foundation Engineering, Moscow, Vol. 3, 1973, pp. 111-159. [4] Henkel, D. J. in Proceedings. American Society of Civil Engineers Research Conference on Shear Strength of Cohesive Soils, University of Colorado, Boulder, Colo., 1960, pp. 533554. [5] Lade, P. V. and Duncan, J. M., Journal of the Geotechnical Engineering Division, Proceedings, American Society of Civil Engineers, Vol. 102, No. GTl, 1976, pp. 51-68. [6] Olson, R. E., Geotechnique, Vol. 12, No. 1, 1962, pp. 23-43. [7] Campanella, R. G. and Vaid, Y. P. in Proceedings, Eighth International Conference on Soil Mechanics and Foundation Engineering, Moscow, Vol. 1, Part I, 1973, pp. 85-92. \8] Simons, N. E. in Proceedings, Roscoe Memorial Symposium, Cambridge University, 1971, pp. 241-252. [9] Yudhbir and Mathur, S. K. in Proceedings, Ninth International Conference on Soil Mechanics and Foundation Engineering, Tokyo, Vol. 1, 1977, pp. 353-356. \10] Lambe, T. W., Journal of the Soil Mechanics and Foundations Division, Proceedings, American Society of Civil Engineers, Vol. 90, SMS, 1964, pp. 43-68. [//] Lambe, T. W., Journal of the Soil Mechanics and Foundations Division, Proceedings, American Society of Civil Engineers, Vol. 93, SM6, 1967, pp. 309-332. [12] Bishop, A. W. and Henkel, D. J., The Measurement of Soil Properties in the Triaxial Test, 2nd ed., Edward Arnold Ltd., London, 1%2, 219 p. [13] Ladd, C. C. and Varallyay, J., "The Influence of Stress System on the Behavior of Saturated Clays During Undrained Shear," Research Report R65-11, Massachusetts Institute of Technology, Cambridge, Mass., Department of Civil Engineering, 1965. [14] Wong, P. K. K. and Mitchell, R. J.. Geotechnique, Vol. 25, No. 4, 1975, pp. 763-782. [15] Ko, H-Y. and Scott, R. F., Geotechnique, Vol. 17, No. 1, 1967, pp. 40-57. [16] Bishop, A. W. and Wesley, L. D., Geotechnique, Vol. 25, No. 4, 1975, pp. 657-670. [17] Wong, P. K. K., "Strength and Stress-Strain Relations of a Sensitive Clay," Ph.D thesis, "Queen's University, Kingston, Ont., Can., Department of Civil Engineering, 1972. [18] Mitchell, R. J. and Bum, K. N., Canadian Geotechnical Journal. Vol. 8, No. 2, 1971, pp. 34-345. [19] Bozozuk, M., "The Gloucester Test Fill," Ph.D thesis, Purdue University, Lafayette, Indiana, 1972. |20| Mitchell, R. J., Canadian Geotechnical Journal, Vol. 7, No. 3, 1970, pp. 297-312. [21] Eden, W. J. and Law, K. T., Canadian Geotechnical Journal, Vol. 17, No. 3, 1980, pp. 369-381. [22] Mitchell, R. J., Canadian Geotechnical Journal, Vol. 12, No. 4, 1975, pp. 447-455.

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R. J. Mitchell'

A New Control System for Soils Testing

REFERENCE: Mitchell, R. J,, "A New Control System for Soils Testing," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 180-190. ABSTRACT: In load-deformation testing of soils it is generally necessary to supply both fluid pressures and direct loads (forces) on the sample boundaries. In addition, soils are tested under both controlled load and controlled deformation. Often three separate systems exist in a standard soils laboratory: gear driven presses, dead load hangers, and a regulated fluid pressure system. This paper describes a control system that employs commercially available rolling diaphragm cylinders and micro-flow needle control valves to supply simple and economical control for soils testing. KEY WORDS: soil testing, control

The use of air pressure to replace the mercury pot system for supplying fluid pressures for soils testing has gained favor in recent years due to advantages such as ease of operation and environmental safety. The standard air system, which is composed of a compressor, storage tank, and regulator valves, is not, however, entirely reliable, since a power failure of more than a few hours can result in release of stored air and loss of test control. In addition, the bleeder type of pressure regulator, while very accurate in control, is subject to malfunction from moisture and dirt in air lines. Even when operating efficiently, many of these valves waste large volumes of compressed air to the atmosphere. The fluid pressure system described in this paper operates reliably on relatively small volumes of compressed air which can be supplied by a foot pump, a small a-c or d-c compressor, or from rental air cylinders. A fluid pressure can be converted to a constant load (force) using a commercial rolling diaphragm cylinder. These cylinders are leakage free and essentially frictionless. With the addition of a needle control valve, a controlled variable loading system, which has advantages over the gear driven 'Professor, Queen's University, Kingston, Ont. K7L 4N6. 180 Copyright by Downloaded/printed Copyright 1981 University of

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MITCHELL ON CONTROL SYSTEM FOR SOILS TESTING

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deformation control system, can be arranged. The basic systems and some of the many possible variations are discussed in this paper. Basic Load Control System This system can be most simply demonstrated with reference to the unconfined compression test, as shown schematically in Fig. 1. The air reservoir is charged to a pressure in excess of that necessary to fail the sample, and the test is carried out by opening Valve 1 and adjusting the needle valve to allow fluid flow into the cylinder at the desired testing rate. The test gage monitors the pressure in the cylinder, and the axial force applied by the piston is calculated from this pressure. The dial gage monitors the axial deformation of the sample. After a test. Valve 1 and the needle valve are closed and Valve 2 and the bypass valve are opened to allow return of the fluid to the reservoir. The reservoir is located at a lower elevation than the cylinder to provide sufficient differential pressure to return the piston to the zero position. Some of the advantages of this system are: 1. Low initial cost compared with a gear driven press and proving ring system. 2. Low power cost since the loss in air volume is minimized by having the fluid reservoir full at zero piston position. 3. The entire assembly can be made portable and a small air tank could provide the driving force for many site tests. 4. The piston returns to a zero dial gage reading at the end of each test and the adjustment piece provides contact for variable length samples. 5. Post peak decreases in shearing resistance can be monitored in brittle samples because the elastic stored energy is small. 6. The needle valve offers positive and continuous control over a wide range of loading rates. At a constant setting of the needle valve, the deformation rate is reduced as the sample assumes load. The sample is loaded more rapidly during the early linear portion of the deformation and the rate of load application reduces towards failure. This reduces the overall test time while maintaining the desired slow rate of loading in the critical plastic or brittle range of deformation. 7. Using a double-acting cylinder, the system is capable of applying extensional loading or direct tension as well as compression. 8. The system can be used for dead loading (for example, consolidation testing) by bypassing the needle valve and adjusting the air pressure at each load increment. Repeated or cyclic loading can be achieved by providing a variable reservoir pressure. Commercial rolling diaphragm cylinders are available in a variety of internal areas and stroke lengths. If an air pressure of about 700 kPa (100 psi) is available, a 0.008 m^ (12 in.2) area is suitable for most soils testing, being Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

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LABORATORY SHEAR STRENGTH OF SOIL

BYPASS
FLUID FLOW TO CYLINDER

AIR SUPPLY ^

VALVES 2i

I

AIR RESERVOIR

FLUID RESERVOIR

FIG. 1—Schematic of loading system.

equivalent to a 0.5 tonne press. By using a 0.023-m^ (36-in.^) cylinder a 1.5 tonne equivalent is obtained. Figures 2 and 3 showed two basic test systems using these two sizes. The large Bellofram air cylinder shown in Fig. 2 is single acting (compression only) with a roller rod bearing. The test gage is calibrated to read sample stress for a nominal 50-mm-diameter sample (to ± 5 kPa), and the ±0.01-mm dial gage can be read directly as axial strain for standard metric sized samples. Thus the technician can plot a stressstrain curve directly from these readings as the test proceeds. The Bellofram cylinder is powered directly by a domestic water supply (4(X) kPa pressure) and the water is wasted on the return stroke. For a nominal strain of 10 percent about 0.2 L of water is used in each test. The system shown in Fig. 3 employes a double-acting Bellofram which has an inner rod bearing and a U-cup seal (providing a virtually frictionless movement). The system is operated basically as shown in Fig. 1, except that a small positive water head is applied to the lower chamber to return the piston to its zero position. For a nominal 50-mm-diameter sample, the axial stress is accurately determined to ± 1 kPa. Both of these systems employ Circle Seal micrometer needle valves which can be precalibrated for the fluid being used (water and silicon oil have been used under normal room temperatures and anitfreeze has been used for frozen soils work). The handle of the micrometer needle valve is calibrated in Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

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FIG. 2—Large single-acting Bellofram rolling diaphragm cylinder.

microns from 0 to 300 microns. For the slow loading rates normally used in soils testing, the setting would be less than 25 microns (one full turn of the handle). In this range the flow rate through the valve is a linear function of both the valve setting, M, and the pressure difference across the valve, Ap. Thus Q = KMAp

(1)

The nominal strain rate is obtained by dividing the flow rate by the effective area of the cylinder and the nominal sample length. Then e, =- C.MAp

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LABORATORY SHEAR STRENGTH OF SOIL

FIG. 3—Smaller double-acting Bellofram rolling diaphragm cylinder.

Using 100 centistoke silicon oil at 20°C, the calibration constant for a 0.008-m^ (12-in.^) cylinder and 100-mm nominal sample height was obtained as Cf = 6.2 X 10~*/kPa-min. Thus, for example, a pressure difference of 100 kPa at a micrometer setting of 5 microns would produce a nominal strain rate of ej = 3.1 X 10~^/min (3.1 X lO"-* %/min) or approximately 4.5 percent per day. This rate can be factored, linearly, upwards or downwards by increases or decreases in either the pressure difference or the needle valve setting. In theory, this offers an infinitely variable range of reproducible loading rates. In practice, the reproducibility of the flow rate is subject to variations in room temperature and other minor variations. Test rates are chosen by using the estimated soil strength as a guide to establish a reservoir pressure that will give a nominal pressure difference (reservoir pressure minus cylinder pressure), Ap, at failure. The deformation rate at failure is then selected and the micrometer setting is obtained from the calibration constant. The rate variation during a test will depend on the value of Ap chosen. If Ap is large with respect to the cylinder pressure at failure, the deformation rate will approach a constant value throughout the test. If Ap is small compared with the cylinder pressure at failure, the initial deformation rate will be given from the calibration constant, using the reser-

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voir pressure as the initial value of Ap, and the rate will decrease to the design value at failure. As noted previously, this can shorten the test time considerably while maintaining the desired rate at failure. Control of Fluid Pressures Figure 3 shows a standard triaxial cell in place beneath the loading system. To provide a reliable cell fluid pressure and the option of pressure variation throughout a test a double reservoir fluid pressure system, as shown schematically in Fig. 4, is used. The reservoirs are charged with air pressure and there is no loss of air volume during a test. For a constant cell pressure (standard triaxial test), a single reservoir is charged with air to the desired cell pressure. With a filter to prevent dirt contamination in the reservoir, the fluid can be injected to the triaxial cell from the reservoir and returned to the reservoir after the test for re-use. A silicon oil cell fluid is often used to reduce membrane leakage and has been found to provide the necessary lubrication and cell leakage reduction when rotating bushing cells are used. The reservoir volume (the compressed air volume) should be sufficiently large to maintain the pressure within allowable tolerances for the test duration (considering expected changes in fluid volume and temperature). Volume changes are due to cell leakage, sample volume changes, and piston entry into the cell. Using a medium viscosity silicon fluid, the cell leakage can be maintained at about the same order of magnitude as the compensating volume of piston entry. For +10 percent sample volumetric strain, the effect of volume change on the reservoir air pressure can be kept to ±0.5 percent by providing a reservoir capacity of about one hundred times the sample volume. For standard 50-mm-diameter samples, a reservoir of 0.021 m^ is used and about 1 L of fluid is in the reservoir when the cell is full. The reservoirs are made from 0.3-m ID thick-walled Perspex tube of 0.3 m length with AIR SUPPLY

•CIRCLE SEAL VALVE

AJ=£ 4— —_f c»

IGAUGEL TRIAXIAL ^^CELL

t .,

« •*

' •

RESERVOIR N" I FILTER

^

/

RESERVOIR N° 2 FLOW CONTROL VALVE

FIG. 4—Schematic of basic cell pressure system.

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LABORATORY SHEAR STRENGTH OF SOIL

aluminum end plates and 0-ring seals. With a temperature of 20 ± 2°C and an overall volume change of 0.02 L of fluid, the pressure is held constant to ± 1 percent. Indeed, since a temperature change of 1°C causes an air pressure change of approximately 0.35 percent, the temperature variations are likely to be more important than reservoir fluid volume changes. Most soils laboratories are maintained at fairly constant temperature, however, due to other testing considerations. If pressure changes do occur during the course of a test, the reservoir can always be recharged from time to time. It is often desirable to vary the cell pressure during a triaxial test. For research purposes a direct control on the stress path might be desired (for example, constant octahedral stress, constant stress ratio), but for practical purposes it is sufficient to be able to diverge from the standard test. Such divergence provides additional information on the soil behavior and has been recommended by numerous researchers in conjunction with specific analyses or problems.^-' To provide this capability, a second reservoir (as shown in Fig. 4) has been incorporated into the fluid pressure system. The cell pressure is increased during a test by placing a high pressure in Reservoir 2 and controlling the fluid flow to Reservoir 1 where the decrease in air volume results in an increase in pressure. A decrease in cell pressure during the course of a test is achieved by allowing flow in the opposite direction with the second reservoir at atmospheric pressure. This can produce a reduction in the octahedral normal effective stress in a drained triaxial test, representing the case of active failure in field situations. At a constant setting of the needle valve, the flow rate decreases as the pressure difference between the reservoirs decreases. Under constant temperature the pressure in Reservoir 1, with fluid flowing to atmospheric pressure, is given as

1+ T

(3)

where P = pressure at any given time, Pg = initial pressure in Reservoir 1, r = (C Po/V„)t = a dimensionle§s time factor, C = dQ/P = flow constant, KM, obtained by setting the needle valve, Vg — initial air volume in Reservoir 1, and t = real time. By judicious choice of V„ and C, a range of different rates of decrease of cell pressure can be obtained. In all cases the cell pressure will decrease (or increase when Reservoir 2 has the higher pressure) at a faster rate during the •^Lambe, T. V/., Journal of the American Society of Civil Engineers. VoL 93, No. SM6, 1%7, pp. 309-331. •"Mitchell, R. J., Canadian GeotechnicalJournal. Vol. 12, No. 4, 1975, pp. 447-455.

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early stage of a test and the rate of change of pressure will decrease towards the end of a test. With the cylinder loading system, the axial stress will also increase at a faster rate in the early stage of a test and this rate will also decrease as the test progresses. Thus it is possible to follow stress paths where the applied stress vector Aaj/Aa, remains fairly constant throughout the duration of the test.

Design Considerations Commercial triaxial cells and loading frames are not needed with the aforementioned system, since the rolling diaphragm cylinder can be mounted directly on a cell to form a test unit. Data acquisition can be limited to two basic systems—a fluid pressure system and a fluid volume system. Fluid pressure transducers for various applications are commercially available and electronic fluid volume systems have been developed.'' A simple and inexpensive test unit for triaxial compression and extension testing is shown in Fig. 5. Three pressure transducers and two fluid volume monitoring systems are used. The pressure transducers monitor cell pressure, cylinder pressure, and sample pore water pressure. The fluid volume systems monitor the sample strains. The cell is also shown in Fig. 6 and is designed for testing samples with nominal dimensions of 75 mm diameter by 150 mm height. Volume change measurements are made by monitoring the cell fluid level change in a 25.4-mm ID Perspex tube directly connected to the cell. The 76.2-mm OD annulus around the piston rod provides a volume change capacity of about 260 cc, and the direct-current differential transformer (DCDT) is capable of discerning a level variation of 50 ± 0.02 mm. This allows sample volumetric strains of up to 40 percent to be accommodated with a measurement accuracy of ±0.015 percent. The advantage of this system is that volumetric strains can be measured on partly saturated samples. With saturated samples, the burette readings can be used as a periodic check on the overall volume change, or the sample drainage facilities may be employed to carry out permeability testing as the test progresses. The fluid level can be adjusted to give an electronic zero reading on the DCDT prior to testing. Axial deformation is monitored by the fluid level in the supply reservoir. The supply reservoir sectional area is approximately equal to that of the air cylinder and, hence, the axial deformation is determined to ±0.02 mm. The DCDT is well matched to the air cylinder, allowing 50 mm of displacement and monitoring up to 33 percent axial strain at an accuracy of ±0.001 per^Mitchell, R. J. and Bum, K. N., Canadian GeotechnicalJournal. Vol. 8, No. 2, 1971, pp. 341-345.

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LABORATORY SHEAR STRENGTH OF SOIL

EPOXY SEALED ELECTRIC CELC

AIR PRESSURl^ j

LEADS

,

I

FROM UPPER CHAMBER RESERVOIR (VOLUMETRIC CELL)

ROLLING DIAPHRAGM CYLINDER PISTON .PISTON ROD ^U-CUP SEAL

1.2 cm * POSTS ( 4 ) -DRIP PAN -PERSPEX CELL -DRAINAGE LEAD TO BURRETTE

0-RING

TO BURETTES FLUSHING SYSTEM AND PRESSURE -TRANSDUCER

FIG. 5—Sectional view of Bellofram cell.

cent. In practice this accuracy is reduced to about ±0.01 percent due to the effects of pressure changes on the cylinder, fluid, and reservoir. The pore water pressure transducer is placed at the opposite end of the sample from the drainage lead in order to monitor the gradient in the sample during drained tests (that is, to ensure Aw is sufficiently close to zero during the course of the test). The drainage lead is thick-walled 2-mm ID flexible plastic tubing which is sealed to the cell base and connected to the top loading cap after the sample is placed in the membrane. This connection uses an O-ring seal to ensure zero leakage. Two other transducers monitor the Bellofram reservoir pressure and cell pressure. For compression testing, a cone and radius seating is provided between the piston rod and the top loading cap. The cell pressure acts on the fluid reserCopyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

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FIG. 6—Bellofram triaxial equipmem.

voir for the lower chamber of the air cylinder (as well as in the top of the cell and level monitor) in order to prevent any loss of air pressure due to leakage. This also allows the upper chamber fluid to be pressurized at zero load and eliminates any zero errors in the displacement of fluid volume to this cell. The upper chamber fluid reservoir is also used for monitoring axial deformation in extension tests because of the potential for leakage through the piston rod U-cup seal. This leakage is found to be very small, however, and a small reservoir with an O-ring slip-seal is positioned conveniently on the piston rod, prior to testing, to keep this fluid leakage separate from the cell fluid. The piston rod is directly connected to the top cap for extension tests using a special end piece on the piston rod. This end piece has a steel pin which is inCopyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

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LABORATORY SHEAR STRENGTH OF SOIL

serted into the top cap through a slot and fixed in place by a small rotation of the top plate before bolting it to the tie rods. This provides a bayonet type of connection which can be disconnected at the end of a test. Conclusions This paper outlines a new method of stress control for soils testing using commercially available rolling diaphragm air cylinders and micro-flow needle valves powered, through fluid reservoirs, by small quantities of compressed air. The main requirements for reliable operation are clean fluid reservoirs and a fairly constant temperature (±2°C) for the duration of a test. While the rate of change of stresses in the system are nonlinear and the reproducibility of testing rate is not as exacting as the standard gear-driven machine, the new system offers several advantages. The main advantages are versatility, reliability, and comparatively low cost. Acknowledgments Appreciation is extended to Alf Williams for his efforts in machining various parts of the equipment and to the National Research Council of Canada for financial support.

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R. Dyvik,' T. F. Zimmie,' and C. H, L. Floess'

Lateral Stress Measurements in Direct Simple Shear Device

REFERENCE; Dyvik, R., Zimmie, T. F., and Floess, C. H. L., "Lateral Stress MeasuiemenU in Direct Simple Sliesr Device," Laboratory Shear Strength of Soil, ASTMSTP 740, R. N. Yong and F. C, Townsend, Eds., American Society for testing and Materials, 1981, pp. 191-206. ABSTRACT: Monitoring lateral stresses in a soil specimen during monotonie or cyclic shear tests significantly increases the amount of information obtained from these tests. A technique is described for interpreting lateral stress data during consolidation (the initial phase of either type of shear test) and determining the lateral stress level at the start of the shear test. In addition, the coefficient of lateral earth pressure at rest (A'o) is determined. The Norwegian Geotechnical Institute (NGI) Direct Simple Shear Device was used in this study. Lateral stress measurements were made with calibrated wire-reinforced membranes (acting as strain gages). Two undisturbed samples of soft marine clay were investigated: a Gulf of Mexico and a Gulf of Alaska sample. The samples were obtained from a depth of about one metre below the sea floor. Large vertical specimen strains were encountered even though the applied consolidation stresses were small (a maximum vertical stress of 0.518 kg/cm^). The technique described includes methods for eliminating possible sources of substantial error at these low stress levels. The values of K^ as determined from the lateral stress measurements agree well with values determined indirectly. KEY WORDS) clays, consolidation, earth pressure, lateral pressure, shear strength

Lateral stresses in direct simple shear soil specimens have seldom been measured. Roscoe et al [1]? using the Cambridge Simple Shear Device, have measured the lateral stresses in sands during static shear. Youd and Craven [2] have used Norwegian Geotechnical Institute calibrated membranes to measure lateral stresses in sand specimens during cyclic loading. This paper is primarily concerned with the techniques and considerations 'Research assistant, associate professor, and instructor, respectively, Civil Engineering Department, Rensselaer Polytechnic Institute, Troy, N.Y. 12181. M"he italic numbers in brackets refer to the list of references appended to this paper.

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LABORATORY SHEAR STRENGTH OF SOIL

involved in measuring lateral stresses in a soil specimen during the consolidation phase of a shear test (which may be either monotonic or cyclic shear). After the lateral stress level at the end of consolidation (KQ, the coefficient of lateral earth pressure at rest) has been established, further measurements of lateral stresses during the shear phase is a relatively simple matter. It is beyond the scope of this paper to present the results of the test program measuring both the static and cyclic shear resistance of clay soils. However, additional information can be found elsewhere [3-6].

Clay Investigated Two clay samples were investigated in this study. One was a Gulf of Mexico sample obtained 360 km (225 miles) east of Corpus Christi, Texas; the other was a Gulf of Alaska sample from the Copper River Prodelta. Both samples were 10.2-cm-diameter undisturbed samples obtained from the United States Geological Survey (USGS). Pertinent geotechnical data is given in Table 1. Note that the natural water contents for both clays were at or above their liquid limits. Both clay samples were obtained at shallow depths (approximately 1 m) below the seafloor, and had low effective stresses in situ. Many of the problems encountered in this test program were due to the low effective stresses, and the results reported herein represent a severe test of procedures and equipment. Thus, if the procedures recommended in this study are followed, one can be more confident of test results as the in situ effective stresses increase. These clays were stored in an environmental wet room that was kept at 4°C and 100 percent relative humidity.

Equipment Shear Device The Norwegian Geotechnical Institute (NGI) Direct Simple Shear Device was used in this investigation (Fig. 1). This device has been modified for cyclic loading capabilities. This modification includes a hanger system and hydraulic actuator which enables a cycled shear force to be applied to the soil specimen. The peak cyclic shear stress level remains constant during a test (that is, the test is stress-controlled) and is in the shape of a square wave with complete stress reversal on the horizontal plane. The device has a range of cycling periods from 2 to 198 s, with most tests performed at a 4- to 10-s period. A constant specimen volume is maintained during the shear tests (monotonic or cyclic loading tests). The change in vertical load that is applied to maintain constant volume is equivalent to the excess pore pressure buildup [3-6].

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TABLE 1 —Geotechnical data for the two clays investigated \3,4\. Gulf of Mexico Clay Water content, % Average liquid limit Average plastic limit Average plasticity index Specific gravity Sensitivity (Fall Cone) Sand, % Silt. % Clay, % Consolidation history 0 ' at 2% 7 (a, = 0.518 kg/cm^). deg Visual description

100 to 120 105 30 75 2.71 2.5 2 28 70 normally consolidated 17.6 grey uniform nonstratified

Gulf of Alaska Clay 57 to 65 50 27 23 2.84 3.8 1 34 65 underconsolidated 25.8 brown uniform nonstratified

FIG. 1—NGI direct simple shear device.

Membrane Calibrated wire-reinforced rubber membranes manufactured by Geonor for the NGI device were used in this study (Fig. 2). These were the standard sized membranes with a specimen area of 50 cm^.

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LABORATORY SHEAR STRENGTH OF SOIL

FIG. 2—Calibrated wire reinforced rubber membrane.

The reinforcement in these membranes is constantan wire with a diameter of 0.015 cm, a Young's modulus of 1.55 X 10* kg/cm^, and a tensile strength of 5800 kg/cm^. The wire is wound at 20 turns per centimetre of membrane height (0.05 cm center to center spacing) [7]. The membranes must provide adequate lateral resistance to prevent crosssectional area change during consolidation and shear. The space between the wire reinforcement winding allows the membrane and specimen to strain vertically during consolidation. The calibrated membranes operate on a strain gage principle; the average lateral stress within the soil specimen is calculated from changes in the electrical resistance of the reinforcing wire due to its very small elongation. The total height of the wire windings is 3 cm. The middle third acts as the strain gage. The soil specimen height is approximately 2 cm, and therefore lateral stresses are measured at the central centimetre. The maximum allowable lateral stress in these membranes is about 1.4 kg/cm^. Several attempts were made to convert uncalibrated membranes (also manufactured by Geonor) to calibrated membranes, because uncalibrated membranes are more readily available and cost about one-quarter as much as calibrated ones. Different types of strain gages (including SR-4 strain gages) were affixed to the wire reinforcement. Problems with this method included (/) stripping away of the outer surface of latex substantially weakened Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

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the membrane (water leaks resulted), (2) the mounting surface was very small (only the top surfaces of the wires), and (3) the affixed strain gages would not allow vertical deflection of the membrane during consolidation (if they even stayed on the membrane). Attempts at isolating the central wire windings also proved fruitless as wire slippage constantly changed the calibration and the membranes were prone to water leaks (even the smallest leak produces an electrical short circuit in the strain gage bridge). Thus Geonor calibrated membranes were used for this investigation.

Data Acquisition The NGI device has been fully instrumented with appropriate linear variable differential transformers (LVDTs) and load cells, and the data are recorded on strip chart recorders. The number of cycles of applied shear stress, shear deformation, change in applied vertical load, resulting lateral stress, and change in height during consolidation of the soil specimen can therefore be continually monitored. Environmental Rooms The tests were performed in another controlled temperature and humidity environmental room. The room was kept at 20°C (68°F) in order to minimize temperature effects on the calibrated membranes. The clay samples were allowed a few hours for temperature equilibrium before the start of consolidation. These membranes have also been found to operate best under dry conditions [7], and for this reason the room was kept at a relative humidity of about 55 percent.

Procedure Membrane Calibration Geonor will supply a calibration curve with each calibrated membrane, if requested, but the authors deemed it prudent to do their own calibrations. Reasons for this included (/) good accuracy desired at the low stress levels used in this study, (2) calibrate stress directly to strip chart output (instead of microstrain readings) for convenient and continuous monitoring, and (J) eliminate possible calibration differences in using different equipment and conditions (different bridge amplifier, amplifier settings, and temperature compensating membrane). A number of membranes were calibrated by both Geonor and the authors, and the initial calibration curves agreed quite well in all instances. These calibrations are accomplished with the use of a calibration cylinder.

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LABORATORY SHEAR STRENGTH OF SOIL

This is a plexiglass cylinder which is the same diameter as the soil specimen and has a rubber bladder around its center portion (Fig. 3). The calibrated membrane is slipped over the calibration cylinder, and known air pressures are introduced into the cylinder and thus to the membrane through the bladder. Resulting readings on the strip chart recorder (from the strain gage bridge amplifier) are calibrated directly to the applied pressures. A typical membrane calibration is shown in Fig. 4. The calibration curve (reading versus stress) is a straight line but has an intercept of 0.02 to 0.03 kg/cm^ at zero reading (depending on the membrane). This is due to the fact that some of the lateral pressure is resisted by the latex in both the bladder and the membrane (other than.the reinforcing wire) and a small initial pressure is needed to seat the bladder against the membrane. The calibration curve is the average of several calibrations with increasing and decreasing pressure, before the first use of the membrane and occasionally after a few shear tests. Subsequent calibrations of the membrane may change the intercept of the calibration curve slightly, but do not significantly change the slope (curves are parallel), and, as will be explained later, only the slope is important in the lateral stress computations. Bridge Amplifier Setup A bridge amplifier along with a strip chart recorder was used in this study. They allow the continuous monitoring of lateral stresses (as opposed to discrete readings obtained from a null indicator type amplifier). The actual bridge was a two-arm wheatstone bridge comprised of an active membrane, a temperature compensating (passive) membrane, and two precision resistors inside the bridge amplifier completing the bridge. The environmental room used in these tests maintains temperature by alternating cycles of heating and cooling. For this reason, there is a 0.25° to 0.5°C fluctuation in temperature over a period of a few minutes (the average temperature remains constant). Precision wire-wound resistors of 0.05 percent accuracy (154 fl) were necessary for steady output from the bridge under these small temperature fluctuations (1 and 0.1 percent resistors yielded outputs oscillating with temperature). The electrical resistance of the membranes can vary from 138 to 167 Q. The active and passive membranes were chosen with as identical resistances as possible (usually within a few ohms). This difference in active and passive membrane resistance did not perceptibly affect the bridge output with small temperature changes. The bridge amplifier was equipped with both a variable balance resistor and zero suppression, which were necessary to obtain readings on scale. In order to avoid resistance changes in the bridge connections, the membranes were soldered to the shielded cable leading to the bridge amplifier before the first membrane calibration and remained as such until they had to be replaced. A good active membrane will typically last through five shear

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DYVIK ET AL ON LATERAL STRESS MEASUREMENTS

197

FIG. 3—Culibrared membrane mid culibratiuii cylinder.

tests (although one membrane lasted through fifteen tests). The active membrane has to be replaced after either the calibrated wire reinforcement breaks (opening the bridge circuit) or a break in the latex develops, allowing salt water from the sample to electrically short the wire reinforcement. Equipment Calibration The recorder outputs are calibrated for applied vertical load, specimen height deflection during consolidation, and shear deflection during shear testing. False deformation of the NGI device (porous stones, top and bottom specimen caps, and a set of bearings allowing lateral deflection of the top specimen cap during shear) is calibrated for both loading and unloading. This is necessary for accurate specimen height determination during consolidation loading and unloading during shear (as explained earlier). False deformation is on the order of 5 to 10 percent of the vertical deflection of these clays after the last consolidation stress (0.50 kg/cm^) and is very important in accurately determining pore pressures and resulting lateral stresses during shear. Calibration of the entire system is periodically checked. However, the input voltage to the load cell and LVDTs is checked with an accurate digital

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198

LABORATORY SHEAR STRENGTH OF SOIL

RECORDER

READING

FIG. 4—Results of five calibrations (increasing and decreasing pressure) of Membrane I.

voltmeter before and during every test. This ensures that calibration remains constant. Sample Preparation Sample preparation includes cutting the soil specimen, mounting it between the top and bottom caps, applying the calibrated membrane, and installing the assembly in the NGI simple shear device. The technique used is that suggested by NGI [7\ with only slight modifications. The trimming and

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DYVIK ET AL ON LATERAL STRESS MEASUREMENTS

199

mounting apparatus is manufactured by Geonor (Fig. 5) specifically for the NGI device. The NGI trimming device and procedures were originally developed for soft Scandinavian clays, and the same were used with the soft clays tested herein. With stiffer clays, other trimming procedures can be used. Test Procedure After the sample has been installed in the NGI simple shear device, consolidation loads are applied to the soil specimen through a 10:1 lever arm. The consolidation stress increments in this study were 0.12, 0.24, and 0.50 kg/ cm^, which brought the specimens to a normally consolidated state. The

FIG. 5—NGI specimen trimming apparatus.

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200

LABORATORY SHEAR STRENGTH OF SOIL

times for 100 percent consolidation for both clays at these three consolidation stress levels were all less than 60 min. The first two consolidation stresses were applied for about 12 h each and the last stress at least 24 h before the shear phase of the test (a total consolidation time of about 48 h). During this time vertical height and lateral stresses in the specimen were continuously monitored. Vertical load from the load cell was also monitored in order to determine when the lever arm needed leveling. Determination of A^o

Direct Determination O/KQ Before the application of the first consolidation stress (0.12 kg/cm^), the calibrated membrane reading is balanced to zero (with the specimen top cap in place). The lateral stress reading used for the computation of KQ is taken at the end of a corresponding consolidation stress increment (the sample is well into secondary consolidation and the lateral stress readings have stabilized). These readings from the calibrated membrane must be corrected for vertical strain of the specimen (the membrane strains the same amount). The lateral stress is computed by the equation

(^h--.

(1)

1 - e, where a/, = effective lateral stress, R — reading from the bridge output, C — calibration factor (slope of the curve) of the calibrated membrane, and Ej, = vertical strain of the sample \T\. In,general, it is difficult to determine when the vertical consolidation arm is exactly in contact with the top cap of the soil specimen. However, this slack at the start of consolidation is easily determined from the output of vertical specimen deflection on the recorder (a sudden, straight line). The slack and the false deformation of the system are subtracted from the vertical deflection reading for each loading increment. The corrected vertical deflection is used to calculate the vertical sample strain, e„. Since the lateral stress readings were balanced to zero with the top cap in place, the information obtained is the change in lateral stress with respect to the change in applied vertical stress (the slope of the ATo-line). For this reason, only the slope of the calibration curve for the calibrated membrane is used. That is, the intercepts of the curves for different membranes or the change of the intercept for a particular membrane in subsequent calibrations

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DYVIK ET AL ON LATERAL STRESS MEASUREMENTS

201

is not important, since the stress conditions are such that the straight line portion of the curve can be used. Considerable effort and testing were necessary to validate this observation, but this validation was necessary due to the low effective stresses in the clays tested. For soils at higher effective stresses, this would be a relatively unimportant detail. The vertical stress during consolidation versus the measured lateral stress (corrected for e^) is shown on the primed axes in Figs. 6 and 7 for the Gulf of Mexico and the Gulf of Alaska clays, respectively. A best fit straight line (least squares) was drawn for the data. The equations for these lines are

0.4

-

(2)

0.672 5„' - 0.044

Oh

%

\ /

-0.3 tf^s 0.67 (Fy) /

I o.

1

I«>

-0.2

0.2

RC

-

Ko^v,

Z

o

-0.1

N

s o I-

u

/

1

O.I /

0.0 0.0

1

1

1

0.1

0.2

0.3

1

ai

1

1

OA

1

1

1

0.2

0.3

0.4

EFFECTIVE VERTICAL STRESS, 7 ,

0.5

1

'

0.5 (kg/cm>)

FIG. 6—Results of lateral stress measurements during 15 consolidation tests at 3 vertical stresses — Gulf of Mexico clay.

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202

LABORATORY SHEAR STRENGTH OF SOIL

0.0

0.0

0.1

a2

0.3

0.4

as

? V

EFFECTIVE VERTICAL STRESS, 7^ (kg/cm^) FIG. 7—Results of lateral stress measurements during 5 consolidation tests at 3 vertical stresses — Gulf of Alaska clay.

for the Gulf of Mexico clay, and ff/,' = 0.536 CT„

0.034

(3)

for the Gulf of Alaska clay. Equations 2 and 3 are the result of 15 and 5 consolidation tests, respectively. Up to this point, the stress applied vertically to the soil specimen by the top cap and the porous stone has been ignored. This stress is 0.018 kg/cm^, and therefore the true vertical stress at each consolidation increment is 0.138, 0.258 and 0.518 kg/cm^. The true vertical stresses on the specimen and the slope of the /Co-line have been defined, and since KQ is assumed to be linear from zero stress conditions [8], the origin of the /Co-plot (a^ and a^ equal to zero) is defined as the intersection of these two knowns. This is seen as the unprimed axes in Figs. 6 and 7 for each clay.

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DYVIK ET AL ON LATERAL STRESS MEASUREMENTS

203

Lateral stress readings have been attempted using a membrane reading of zero before it is mounted over the specimen. This procedure led to unsatisfactory results primarily due to (1) the subsequent expansion of the membrane necessary to install it over the specimen, (2) incomplete specimen seating against the membrane, (3) the change between dry air and a saturated sample in the membrane, (4) the need to maintain a slight hydrostatic head (necessary to keep the specimen saturated during a test), and (5) stress conditions such that the straight line portions of the membrane calibration curves cannot be used (as discussed previously). There was also some question as to whether /Co-conditions existed when the only vertical load was the top cap. To check this, the change in lateral stresses corresponding to a a^ of 0.24 and 0.5 kg/cm^ (the last two consolidation stresses) were calculated with the measured lateral stress at the end of the first consolidation stress, 0.12 kg/cm^, taken as zero. The slope of the resulting Kg-line was identical to the slope for all three stress levels (shown in Figs. 6 and 7), thus indicating /fo'Conditions. Indirect Measurements of Kg Several different semi-empirical equations for the determination of KQ have been proposed. Jaky has proposed the following equation based on the drained friction angle of the soil [9]: Ko = 0.95 - sin <^'

(4)

Alpan [10] recommends an alternative relationship for normally consolidated clays: /i:o = 0.19 +0.233 log PI

(5)

where PI is the plasticity index, in percent. Brooker and Ireland [9] developed a chart relating/ifo' overconsolidation ratio (1.0 in this study), and plasticity index. Table 2 shows the comparison between these indirect K(,-determinations and the measured values in this study. These values were determined from data listed in Table 1. Consolidation Phase Since the lateral stress measured by the membrane is constantly recorded, a rise in lateral stress is seen at the moment of vertical load application. This is the total lateral stress, as the excess pore pressure at this instant is ideally equal to the increment of applied vertical stress. The lateral stress reading drops with time as the excess pore pressure dissipates to zero and the effective lateral soil stress rises from zero to the /fo-condition (Fig. 8).

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204

LABORATORY SHEAR STRENGTH OF SOIL

TABLE 2—Comparison of measured values of KQ and indirect determinations of K^^

Measured value of Kg KQ = 0.95 - sm' Ko = 0.19 + 0.233 log PI Brooker and Ireland /Co-chart

K

-

0.3

_

Gulf of Alaska Clay

0.67 0.65 0.63 0.70

0.54 0.52 0.51 0.56

CONSOLIDATION

TOP CAP

0.4

Gulf of Mexico Clay

.12

kg/cm'

.24 kg A m '

.50

SHEAR TEST

kg/cm'

0.4 TEST

M-IODL

0.3

E

»0.2

-

0.2

0.1

0.1

""-'

0.0 0.0

0.5

0.0 12.0

12.5

24.0

24.5

in

4B.0

TIME (HOURS)

FIG. 8—Time-dependent response during typical consolidation stage.

Initiation of Shear Test After consolidation, KQ has been determined for a particular clay. Since the soil specimen is at /Co-conditions at the start of the shear test (monotonic or cyclic shear), a true initial lateral stress reading, /?,, corresponding to zero lateral stress, can be computed from the following equation: Ri = R - Ko a,j/C

(6)

where R is the final lateral stress reading corresponding to the final applied vertical stress a^f (at the end of consolidation), and C is the membrane calibration factor. In other words, the reading, R, is made from the primed axes in Figs. 6 and 7, and therefore an initial reading, R„ must be calculated so that (/? — Ri)C equals KQ a^j (measured from the unprimed axes). No further corrections are made in the lateral stress readings for vertical strain, e^, as the specimen is kept at constant volume during shear, and €„ up to this point has been compensated for in the /Co-calculations.

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DYVIK ET AL ON LATERAL STRESS MEASUREMENTS

205

Conclusions The NGI calibrated wire-reinforced rubber membrane provides a convenient method for experimentally determining the coefficient of lateral stress at rest, Kg, of a soil specimen. The membranes performed well at the low stresses used with these soft marine clays, and this program was considered to be an extreme test of the feasibility of carrying out the lateral stress measurements. For both the Gulf of Mexico and the Gulf of Alaska clays, various indirect determinations of KQ agree well with the measured values. The procedures necessary to obtain satisfactory lateral stress measurements during consolidation have been described in this paper. These procedures can also be used during subsequent direct simple shear tests. If satisfactory lateral stress measurements are obtained prior to shear, then the measurement of lateral stresses during shear is relatively simple for static, cyclic, or combined shear tests. Typically, the measurement of lateral stress during shear is an important piece of information desired (as was the case in this test program), since this additional information allows one to define the state of stress in the sample, plot stress paths, determine the orientation and magnitude of principal stresses, determine the change in lateral stress during cyclic loading, etc. Presentation of shear test results is beyond the scope of this paper, but the data is available elsewhere [3-6], Acknowledgments Funds for this project were provided by grants from the National Science Foundation, Grant No. FFR 76-14220 (formerly ENV 76-14220) and Grant No. PFR 78-18743, sponsored by the Earthquake Engineering Program for the Directorate for Applied Science and Research Applications (ASRA) (formerly RANN). The authors wish to thank Paul Schimelfenyg, graduate student at Rensselaer Polytechnic Institute, for his valuable assistance during this project. References [/) Roscoe, K. H., Bassett, R. H., and Cole, E, R. L. in Proceedings. Geotechnical Conference, Oslo, Vol. I, 1967, pp. 231-237. [2] Youd, T. L. and Craven, T. N., Journal of the Geotechnical Division. American Society of Civil Engineers, Vol. 101, No. GT2, Feb. 1975, pp. 217-221. [3] Floess, C. H. L., "Direct Simple Shear Behavior of Fine Grained Soils Subjected to Repeated Loads," Ph.D. dissertation, Rensselaer Polytechnic Institute, Troy, N.Y., Dec. 1979. [4] Carroll, M. D., "Sample Size Effects Using the NGI Direct Simple Shear Apparatus," Masters project, Rensselaer Polytechnic Institute, Troy, N.Y., May 1979. (5) Kopal, D. J., "NGI Direct Simple Shear Tests on Concord Blue Clay," Masters project, Rensselaer Polytechnic Institute, Troy, N.Y.. Dec. 1979.

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206

LABORATORY SHEAR STRENGTH OF SOIL

[6] Zimmie, T. F. and Floess, C. H. L., "Simple Shear Behavior of Fine Grained Soils Subjected to Earthquake and Other Repeated Loading," National Science Foundation Directorate for Applied Science and Research Applications (ASRA), Final Report, Rensselaer Polytechnic Institute, Troy, N.Y., March 1979. [7] Geonor, "Description and Instruction for Use of Direct Simple Shear Apparatus Model h-12," Geonor A/S, Oslo, 1968. IS] Abdelhamid, M. S. and Krizek, R. J., Journal of the Geotechnical Engineering Division, American Society of Civil Engineers, Vol. 102, No. GT7, July 1976, pp. 721-738. [9] Brooker, E. W. and Ireland, H. O., Canadian GeotechnicalJournal, Vol. 11, No. 1, 1965, pp. 1-15. [10] Alpan, I., 5oi7 and Foundation. Japanese Society of Soil Mechanics and Foundation Engineering, Vol. 7, No. 1, 1967, pp. 31-40.

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Mosaid

Al-HussainP

Tensile Properties of Compacted Soils

REFERENCE: Al-Hussaini, Mosaid, "Tensile Propertie« of Compacted Soils," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 207-225. ABSTRACT: This investigation describes the development of a hollow cylinder testing device and the feasibility of using this equipment for determining the tensile properties of compacted cohesive soils. Hollow cylinder tests were conducted on compacted specimens of Vicksburg buckshot clay (CH), Vicksburg lean clay (CL), and a sandy clay mixture (SC) from DeGray Dam. Unconfined compression tests and indirect tension tests were also conducted to provide comparative compressive properties of the materials. With this hollow cylinder testing device it is possible to measure the radial deformation along the inner and outer surfaces of the specimen; these measurements enable the determination of the modulus of elasticity ( £ ) and Poisson's ratio (x) of the tested soils. The ratio of tensile modulus to the compression modulus, as determined by hollow-cylinder and unconfined compression tests, ranges from 2.6 to 4.4. On the other hand, approximately equal Poisson's ratio values were measured by hollow-cylinder and unconfined compression tests. Based upon results of this experimental program, the hollow cylinder test is judged to provide a reasonably accurate method for measuring the tensile properties of compacted soils. KEY WORDS; soil tests, cohesive soils, compacted soils, tensile tests, test equipment

Tensile stresses may be encountered in highway and airfield pavement systems subjected to heavy moving loads. The existence of such tensile stresses in rigid or flexible pavements is considered harmless until their intensity exceeds the tensile strength of the pavement materials. High tensile stresses are usually indicated by cracks visible at the surface layer of pavement, which in most cases endanger the performance and integrity of the structure. The increased use of stabilized subbase as an integral part of pavement systems and the desire to build crack-free highways and airfields have stimulated interest in the tensile properties of stabilized as well as unstabilized soils. Associate professor and chairman, Department of Civil Engineering, College of Engineering and Petroleum, Kuwait University, Kuwait.

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LABORATORY SHEAR STRENGTH OF SOIL

Considerable previous research for characterizing engineering materials subjected to tensile stresses has been conducted on brittle materials such as rock and concrete. However, due to the following factors, tensile characterization of soft materials such as soils has been ignored: 1. Design practices and stability analyses do not account for tensile strength of soil. 2. Suitable testing apparatus which can accurately impose and measure tensile stresses and strains are not available. 3. Reliable theories which realistically describe soil behavior under tensile stresses are not available. Increasing interest in the construction of pavement and earth structures free from cracks makes tension testing not only of academic interest but of practical necessity because only tensile tests can faithfully describe the cracking problem in soils. By fully understanding the tensile behavior of soil, it may be possible to develop a rational approach for designing pavements that will not suffer cracking during their normal life times. The purpose of this study is to determine the tensile properties of compacted soils using hollow-cylinder and indirect tension testing devices, and to compare results with those obtained by the unconfined compression test. Hollow Cylinder Testing Equipment A comparative description and history of development of a number of laboratory tension testing devices has been reported by Al-Hussaini and Townsend [/.2]^. Most of these devices can be used for testing brittle material and include direct tension tests [3.4], indirect tension or Brazilian test [5], beam test [6], and double punch test [7]. While these provide values of tensile strength, values of the elastic properties are practically impossible to obtain owing to problems of measuring strains. For this reason, a hollow cylinder apparatus capable of determining both tensile strength and elastic properties for soft materials such as soils was constructed and used in this study. This hollow cylinder apparatus (Fig. 1) is capable of testing a 101.6-mm (4-in.) inside diameter, 152.4-mm (6-in,) outside diameter, and 101.6-mm (4-in)-high hollow cylinder soil specimen. The specimen is placed between two smooth annular platens and covered from the inside and outside surfaces by two thin rubber membranes. The soil contact face of each platen has an annular recess 6.4 mm ('A in.) wide and 3.2 mm (Vs in.) deep to receive a porous stainless steel ring which acts as a filter. Each platen is provided with a drainage port for saturating the specimen as well as measuring volume change or pore pressure during testing. The specimen cover has a spherical ^The italic numbers in brackets refer to the list of references appended to this paper.

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AL-HUSSAINI ON TENSILE PROPERTIES OF COMPACTED SOILS

209

1 SOIL SPECIMEN 2 UPPER PLATEN 3 LOHER PLATEN 4 SPECIMEN COVER 5 LOAOINGRAM 6 BASE PLATE 7 RUBBER MEMBRANE 8 CAP 9 CYLINDRICAL SHELL 10 RAM HOUSING 11 FOUNDATION RING 12 FOUNDATION POST 13 LVDT FOR OUTSIDE DIAMETER 14 LVDT FOR INSIDE DIAMETER 15 TIE ROD 16 ELECTRICAL CONNECTOR

FRONT VIEW SECTION SCALE 2

0

2

4 IN

FIG. 1—Details of the hollow-cylinder apparatus II in. = 25.4 mm).

seating to receive the tip of the ram. The pressure chamber consists of a base plate, a cap, and a cylindrical shell; details of these components are presented in Ref 2. Probably the outstanding feature of the hollow cylinder tensile device is the two deformation sensors used to measure the change in the inner and outer diameters of specimens during testing. Each lateral deformation sensor consists of three linear variable differential transformers (LVDTs) connected in series and placed 120 deg apart and at equal distances from the center of the specimen (Fig. 2). A special casing houses each LVDT to provide spring loading; the casing is mounted on an L-shaped post fixed to the base of the apparatus. Before beginning the test program, the sensitivity and stability of each lateral deformation sensor were checked and an accurate deformation calibration was obtained. Small Teflon disks provided for each LVDT serve as bearing plates and prevent point contact with the soil specimen. Compressed air is used to provide confining pressure surrounding the hollow cylinder specimen. The rate of flow of air to the inner and outer peripheries of the specimen is regulated through precision regulators. Plane

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210

LABORATORY SHEAR STRENGTH OF SOIL

FIG. 2—Top view of specimen with specimen cover removed.

strain conditions (that is, no vertical deformation) are maintained by placing the loading piston in contact with the specimen cover and fixing it. An LVDT, readable to the nearest 0.254 mm (0.001 in.), is attached to the loading ram to ensure that plane strain conditions are maintained. Test Procedure A special forming mold was designed and fabricated for compacting hollow cylinder specimens. Soil was compacted in five layers using a pneumatic hand tamper provided with a special Teflon foot to ensure similar densities throughout the specimen. The soil specimen was properly placed on the base plate and upper platen, and the membranes were seated around it using O-rings. A slight vacuum was applied to the specimen to ensure close

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AL-HUSSAINI ON TENSILE PROPERTIES OF COMPACTED SOILS

211

contact between the inner membrane and the soil. The strain sensors for measuring changes in the inner and outer diameters during application of pressures were placed around the specimen (Fig. 3). The specimen cover was fastened tightly to the upper platen, thus isolating the pressure acting against the surface inside the specimen from that acting on the outside of the specimen. Finally, the ram was brought into contact with the specimen cover cap, and the pressure chamber was attached. Three tests were conducted on each soil. In the first test, the outer pressure was maintained at zero and the inner pressure was increased incrementally until failure occurred. In the second test, both the inner and the outer pressures were increased simultaneously until the confining pressure reached 12.8 kPa (2.0 psi), then the outer pressure was held constant while the internal pressure was increased incrementally until failure occurred. The third test was similar to the second test except that the outer pressure (P„) was held constant at 25.6 kPa (4.0 psi) instead of 12.8 kPa (2.0 psi). During the test, the internal pressure (P,), deformation of the inner radius (w,), and deformation of the outer radius (M„) were continuously recorded on an x-y-y recorder. Soil Properties Three soils were used in the testing program: a highly plastic clay (CH) known locally as Vicksburg Buckshot clay, a low-plastic clay (CL) known as Vicksburg silt, and a clayey sand (SC) processed from clayey sandy gravel material obtained from the borrow area at DeGray Dam in Arkansas. The tested soils were air dried, crushed, and sieved through a 6.4-mm (0.25-in.) screen prior to adding water and compacting the test specimens. The gradation curve for the material tested is shown in Fig. 4. Atterberg limits along with the maximum density and the optimum water content, using standard Proctor compaction effort but with a Corps of Engineers sliding-weight rammer, are presented in Table 1. Although the tested soils were mixed at about the optimum water content, the density for the compacted CH was 1476.8 kg/m3 (92.3 pcf), for CL was 1596.8 kg/m^ (99.8 pcf), and for SC was 1744 kg/m3(109pcf). Stiess-Defonnation Analysis The hollow cylinder test is based on the principle that when a hydrostatic pressure is applied to the internal surface of the specimen a tangential tensile stress is generated, and when this stress exceeds the tensile strength of the material the specimen fails in tension. Assuming the material to be homogeneous, elastic, and isotropic, the radial stress (a^), the tangential stress (ff,), and the radial deformation («) can be obtained using a procedure similar to that presented by Den Hartog [8] as

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212

LABORATORY SHEAR STRENGTH OF SOIL yly


P - 2 _ p.j.2 : ;

a, =

Ppr^^ - Pirl ; ;

1

r 2 - r-2

' o

21 p, _ p \

(1)

ir,^ - r,^)r'

^ r?rJ{Pi - P„) (.2W2

(2)

W - r?)r

' /

,2.2

u = E{r} - r,-2)

rir, • ( P „ - P , ) ( l + , / )

{r}P;-r}P„){\-v)

(3) where Po To Pj r, r E V

— = — = = — =

outer pressure, outer radius, inner pressure, inner radius, radial distance of the point under consideration, modulus of elasticity, and Poisson's ratio.

At the inner surface, r — r, and u = M,; thus r 2 - j - ^.2

2r„ P. -

E{r„^ - r,-2)

-Po + PPi

(4)

At the outer surface, r = r^ and u = Ug', thus '•o/'o

£•

r

2r,2

r 2 + r-2 ° ' 2

L r 2 - r,.2

2

1 ,.

' '^

(5)

Assuming K^ = {r} + r,-2)/(r„2 - r,-2), ATj = (2r,-2)/(r„2 - /•,.2), and and Xj = (2r,/)/(ro2 — r,^), and after proper substitution and solving Eqs 4 and 5 simultaneously, the values of E and v can be obtained as K2P? + E - rir^

K,P,^-2K,P,P,

r.PiUo - r^P^Ui

r A-i

V=

r>P.

Ai

(6)

(7)

Pi

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AL-HUSSAINI ON TENSILE PROPERTIES OF COMPACTED SOILS

213

FIG. 3—Assembly of the tensile testing apparatus.

Soil Parameters from the Hollow Cylinder Tests For convenience, the relationship between stresses and deformations in the hollow cylinder tests was expressed in terms of the pressure difference (/', P„) as a function of both w, and w„. These curves are depicted in Figs. 5, 6, and 7 for the CL, CH, and SC materials, respectively. The curves show that all specimens tested exhibited nonlinear behavior, which is most likely a time-dependent behavior. They also indicate that inner radial deformation

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214

LABORATORY SHEAR STRENGTH OF SOIL

U.S. STAND* IP SIEVE OPENI»4G IN INCh ES )i 1 « M H 3 4

,J

1 1

i—r-

-

«

U.S. STANOAHO SKV E N U M K I t S 6 10 t 4 1 6 20 30 4C SO 7 0 WO 140 1 1 I I I

HVDtOMRII 100

1 1 II

w

'N \ > \ \ CLH

to

" -70

-

"1

to 30

-

..L

\

30

\

40

\,

s^JN

N

1

}0

\

10

"

H-

)

-— 1

1 S0

20

\

\

^

40

"

1\^ ^

,sr

—

10 -CH

10

GKAIN

0 i SIZE AMU.W lET

ns

0.1

vj

30 70

\.

•0

ro

'

t''

1

30

003

0.01

0.003

0.001

FIG. 4—Grain-size distribution curves for soils tested.

TABLE 1—Index properties of tested soils.

Soil

Specific Gravity (Gj)

Liquid Limit (LL), %

CL CH SC

2.69 2.68 2.70

34 57 37

Maximum Dry Plasticity Index Optimum Water Density {y^^), Content (MO, % pcf" (PI). % 12 36 23

15 22 14

109.2 98.2 117.0

"1 pcf = 16kg/m''

(M,) is always larger than outer radial deformation («„) and that the ratio of the two deformations is approximately constant for any given soil type and confining pressure. Failure of the hollow cylinder specimens occurred suddenly, and they cracked radially in several places along lines parallel to the axis of the cylinder. Typical failure cracks are shown in Fig. 8. The average value of the tensile stress within the specimen at failure was usually assumed to be the tensile strength of the material [9,10]. The assumption of uniform stress within a specimen is valid for a thin-walled cylinder having a diameter-to-thickness ratio greater than 5. However, this assumption is only approximately valid for thick-walled cylinders owing to stress gradients which generate stresses of different magnitudes on the inner and outer surfaces. Accordingly, the tensile stress at the mean radius (r,„) is expressed by Hvorslev and Kaufman [//] as

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AL-HUSSAINI ON TENSILE PROPERTIES OF COMPACTED SOILS

2

215

r„'~n'

(8)

Summaries of tensile stresses at failure for the hollow cylinder tests are presented in Table 2. These tabulated results show that, although s,„s,^ increased slightly with increasing stress levels for the CL and CH materials, the s,„i„ and the s,,„ values essentially remained within a narrow range. An additional series of tests on the CH material was also conducted to show the effect of density on the tensile strength; the results are presented in Table 2 (Tests 4, 5, and 6). The results show that the tensile strength decreases with decreasing density. By measuring the radii deformations at the inner and outer radii of the specimen at any applied pressure and by assuming the validity of fundamental assumptions of the theory of elasticity, it is possible to calculate the elastic parameters of the soil under tension. Expressions for E and v, presented in Eq 6 and 7, are used to generate the data presented in Fig. 9 when soil specimens were subjected only to internal pressure (P,). This figure

^ f

0

^ P o

4 PSI

^~Po

2 PSI

0

0.001 0.002 0.003 0.004 0.005 DEFORMATION OF INNER RADIUS U|, IN.

- 4 PSI

^-Pt

^ P o

^Po

0.006

2 PSI

0

0.001 0.002 0.003 0.004 0.005 DEFORMATION OF OUTER RADIUS UQ, I N .

FIG. 5—Radial pressure—deformation relationship for CL soil (I in. = 25.4 mm, I psi = 6.9 kPa).

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216

LABORATORY SHEAR STRENGTH OF SOIL

Po - i PSU ^Po

~ 2 PSI

-0

^-P(

0.002 0.004 0.006 0.006 DEFORMATION OF INNER RADIUS U,, IN.

Po-

tP i / - ^ 2PSI

^ P a -

^^--Po

0.010

^0

0.002 0.004 0.006 0.008 DEFORMATION OF OUTER RADIUS Uo> IN.

0.010

FIG. 6—Radial pressure—deformalwn relationship for CH soil II in. = 25.4 mm. I psi 6.9 kPa). TABLE 2—Summary o) hollow-cylinder tensile test results at failure.

Material Type

Water Content (W), %

Dry Density (7do). P'^f"

Inner Pressure (P,). psi''

Outer Pressure (P„). psi''

CL-1 CL-2 CL-3 CH-1 CH-2 CH-3 SC-1 SC-2 SC-3 CH-4 CH-5 CH-6

15.4 16.4 16.0 21.2 21.3 21.6 13.S 13.5 13.5 21.0 21.1 21.5

99.8 99.9 99.7 89.8 91.8 95.2 108.7 108.5 109.9 85.8 86.3 86.4

1.6 5.2 8.3 4.3 7.1 10.5 3.2 6.0 8.6 3.5 6.4 9.7

0 2 4 0 2 4 0 2 4 0 2 4

Tensile Stress, psi'' *f max

4.17 6.09 7.00 11.0 10.90 12.44 8.09 8.12 7.76 8.85 9.25 10.54

•^t max

2.52 2.89 2.65 6.65 5.80 5.94 4.89 4.12 3.11 5.35 4.80 4.79

^im

2.95 3.90 3.93 7.93 7.41 7.99 5.90 5.38 4.49 6.46 6.12 6.52

"1 pcf = 1 6 k g / m \ ''1 psi = 6.9 kPa. 'Calculated using r = r, in Eq 2. ''Calculated using r = r„ in Eq 2. ''Calculated using r = (2/3) [(r,,-" - r/)/(/-„2 - r,2)] in Eq 8.

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AL-HUSSAINI ON TENSILE PROPERTIES OF COMPACTED SOILS

Po

4PS/~v^

^ P c

^

2 PS/

0

Po

0.001 0.002 0.003 0.004 DEFORMATION OF INNER RADIUS U;, IN

p3

217

0,005

4 PS/ ^

- Po

• Po

2 Pi

0

T O.OOI 0.002 0.003 0004 0.006 DEFORMATION OF OUTER RADIUS U Q , IN.

FIG. 7—Radial pressure—deformation relationship for SC soil II in. — 25.4 mm. I psi — 6.9 kPa).

shows that E decreased with increasing /*,, which reflects the nonUnear behavior of the soil tested. However, v varied within a very small range for each soil, and its average values were 0.20, 0.49, and 0.28 for the CL, CH, and SC materials, respectively. The interpretation of E and v for tests in which P„ equals 13.8 and 27.6 kPa (2.0 and 4.0 psi) is more difficult, since tangential stresses at the beginning of the tests were compressional and changed gradually to tensile stresses with an increase of P, over P„. Therefore values of E and v for these tests reflect both the compressive and tensile behavior of the soil tested. More complication with interpretation of the results is added by the fact that creep or viscoelastic behavior of the soil becomes more pronounced with an increasing stress level. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

218

LABORATORY SHEAR STRENGTH OF SOIL

FIG. %—Typical failure of hollow cylinder in tension test.

Unconfined Compression Tests Unconfined compression tests were conducted on 71.1-mm (2.8-in.) diameter specimens in addition to the tension tests in order to provide comparisons between soil parameters obtained from tension and compression testing. A standard triaxial compression cell with enlarged low-friction end platens was used for these tests. Direct measurement of radial deformation of the specimen was made during the tests using a lateral strain deformation sensor consisting of an LVDT attached to the specimen by a circumferential clamp at midheight of the specimen. Another LVDT attached to the loading

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AL-HUSSAINI ON TENSILE PROPERTIES OF COMPACTED SOILS

219

NNER PRESSURE P., PSI

FIG. 9—Variation of E with respect to P, for hollow cylinder test (I psi = 6.9 kPa).

piston was used to measure the axial deformation of the soil specimen. These two LVDTs enabled the measurement of the elastic parameters of the material tested (see Fig. 10). Unconfined compression stress-strain curves for the CL, CH, and SC materials (not shown for brevity) were used for determining the unconfined compressive strengths (SJ as well as the elastic constants under compression. The modulus of elasticity (E) was approximated by the initial slope of the stress-strain curve, while Poisson's ratio (v) was approximated by the ratio of the lateral strain (€3) to the axial strain (ei) for the linear portion of the stress-strain curve. A summary of the unconfined compression test data is presented in Table 3. Indirect Tension Test Apparatus The indirect tension test apparatus (Fig. 11) is used to test a cylindrical specimen 101.6 mm (4 in.) in diameter and 114.2 mm (4.5 in.) in height placed between the loading platen and the base. The base is made of a 457.2 mm (18 in.) long by 228.6 mm (9 in.) wide by 25.4 mm (1.0 in.) thick aluminum plate. Two stainless steel guide posts, 19 mm (0.75 in.) in diameter and 30.5 mm (12 in.) in height, are used to allow aligning the vertical movement of the top loading platen with respect to the base without allowing tilting. The top loading platen is made of a 457.2 mm (18 in.) long by 152 mm (6 in.) wide by 25.4 mm (1.0 in.) thick aluminum plate, and is provided with linear ball bushings to reduce friction along the guide posts. Axial

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220

LABORATORY SHEAR STRENGTH OF SOIL

FIG. 10—Unconfined compression test assembly.

TABLE 3—Summary of unconfined compression test results at failure. NOTE—1 in. = 25.4 mm, 1 psi = 6.9 kPa, and 1 pcf = 16 kg/m^.

Average Material Type CL-1 CL-2 CH-1 CH-2 SC-1 SC-2

Water Dry Content Density (VK), % (7dry)- pcf 16.0 15.7 22.0 22.4 13.9 13.9

102.0 103.4 90.7 91.7 114.6 111.9

Height in.

Diameter,

6.32 6.31 6.32 6.31 6.32 6.32

2.83 2.82 2.83 2.83 2.84 2.82

in.

Unconfined Compressive Initial Poisson's Strength Modulus Ratio (5^.), psi (£;), psi M 22.22 22.04 22.44 23.78 20.40 21.20

3600 3400 3200 3200 3600 3000

0.24 0.24 0.30 0.20 0.32 0.28

diametric load is applied to the specimen through two curved aluminum loading strips, 12.7 mm (0.5 in.) wide and 152 mm (6 in.) long, attached to the top loading platen and the base. These strips are used to distribute the applied load on an area 12.7 mm (0.5 in.) wide along the loaded surface of the specimen.

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AL-HUSSAINI ON TENSILE PROPERTIES OF COMPACTED SOILS

221

FIG. 11—Indirect tensile test apparatus.

A load cell and LVDT that can be connected to the loading platen are used for measuring and recording the applied axial load and the change in the vertical diameter of the specimen, respectively. The change in the transverse diameter is measured by using a cantilever arm system. This system consists of two cantilever arms instrumented with strain gages that read to the nearest 0.025 mm (0.001 in.). The free end of each cantilever is placed in contact with the soil specimen along its transverse diameter while the fixed ends are attached to the cantilever block adjustable block (Fig. 11). All deformations and load measurements are recorded simultaneously on a strip-chart recorder (not shown) and can be observed on a digital readout system. Indirect Tension Test Procedure and Results The material was first compacted to 95 percent of Standard Proctor density, in accordance with ASTM Methods for Moisture-Density Relations of

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222

LABORATORY SHEAR STRENGTH OF SOIL

Soils and Soil-Aggregate Mixtures Using 5.5-lb (2.49-kg) Rammer and 12-in. (305-mm) Drop (D 698-78) except that a sliding-weight rammer was used, and at a water content close to the optimum. Soil specimens were compacted, trimmed, extruded from the mold, and then measured accurately prior to testing. Each specimen was centered between the loading strips. The cantilever arms of the lateral sensors were brought in contact with the specimen, and the LVDT for measuring the vertical deformation was set in its proper position (Fig. 11). Vertical load was then applied to the specimen at a constant rate of strain. Simultaneous measurements of the axial load and diametric deformations in the axial and lateral directions were recorded on a strip-chart recorder. The tensile strength (j^) at failure may be expressed as IP irna where d ~ diameter of the specimen, P = load applied to the loading strip, and h = length of the specimen. Duplicate indirect tension tests were conducted on each soil to assure the validity of the test data; a summary of tensile strength for the material tested is shown in Table 4. Discussion of Test Results Tensile strength obtained from the hollow-cylinder and indirect tension tests are summarized in Tables 2 and 4, respectively; the compressive strength obtained from the unconfined compressive strength is presented in Table 3. Because of the difference in the initial density, water content, and TABLE 4—Summary of indirect tensile test results at failure. NOTE—1 in. = 25.4 mm, 1 psi = 6.9 kPa, and 1 pcf = 16 kg/m^.

Average Diameter W), in.

Tensile Strength

(Tdry)' P<^

Average Length (r), in.

102.0 101.8 95.9 95.4 111.5 111.6

4.56 4.57 4.57 4.56 4.58 4.59

4.0 4.0 4.0 4.0 4.0 4.0

2.12 2.32 5.79 5.82 3.94 3.94

Material Type

Water Content (W), %

Dry Density

CL-1 CL-2 CH-1 CH-2 SC-1 SC-2

15.9 16.0 20.6 20.7 13.3 13.6

(Sj), psi

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AL-HUSSAINI ON TENSILE PROPERTIES OF COMPACTED SOILS

223

stress condition of each type of test used in this study it is difficult to make a direct comparison between the results generated. It will be observed, however, that the tensile strength obtained from the indirect tension test is comparable to the minimum tensile strength obtained from the hollow cylinder test. The difference in the result may be attributed to many factors, such as assumptions used in obtaining the tensile strength, the stress gradiant within the specimens, and the state of stress at the time of failure. The unconfined compressive strength obtained was about 5 to 10 times larger than the tensile strength. For the unconfined compression tests, the value of Poisson's ratio (v) was calculated directly from the measurements of the axial and radial strains. In the hollow cylinder test an indirect method based on the measurements of the radial deformation (see Eq 7) was used in calculating v. These direct and indirect methods were applied to specimens of CL, CH, and SC material; the results are summarized in Table 5. With the exception of the CH soil, the results show that there is a general agreement in the values of v obtained from the unconfined compression and hollow cylinder tests. The modulus of elasticity (E) for the unconfined compression test was approximated by the initial slope of the stress-strain curve. However, for the hollow cylinder test, E was obtained indirectly from measurements of applied stresses and deformation using Eq 6. The variation of E with respect to the internal pressure P, for the hollow cylinder test is shown in Fig. 9. This figure shows that E is initially very high and decreases gradually with increasing P, until failure occurs. It should be noted that E for the hollow cylinder test represents the secant modulus rather than the tangent modulus, since the total deformations were considered in calculating E. Comparisons of average values of E at the beginning of the tests for soil specimens tested in the hollow-cylinder and the unconfined compression tests are shown in Table 5. The results show that the value of E obtained from the hollow cylinder was about three to four times higher than that obtained from the unconfined compression, which is much lower than that under tension. Conclusions From the data presented in this study it is apparent that the hollow cylinder apparatus is capable of testing soils under tensile stresses. The ability to measure the radial stresses and deformations allows the measurement of tensile stress, elastic modulus, and Poisson's ratio for the tested specimens. Because of the radial stress gradient, the calculated tensile strength might be different from the actual tensile strength of the material, and it is greater for the hollow-cylinder than the indirect tension test. Based on the results of the soils tested it appears that the tensile strength increases as the plasticity of the soil increases. The ratio St/Sc, based upon

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224

LABORATORY SHEAR STRENGTH OF SOIL

TABLE 5—Average values of elastic parameters. Hollow Cylinder

Unconfined Compression

Type of Soil Tested

E

II

E

p

CL CH SC

9200 13800 14700

0.20 0.49 0.28

3500 3200 3300

0.24 0.25 0.30

the hollow-cylinder and unconfined compression tests, varies from '/4 to Vio. However, the ratio of tensile modulus (£,) to compressive modulus (EJ values, as determined by hollow-cylinder and unconfined compression tests, ranged from 2.4 to 4.6. For the SC and CL soils tested, approximately equal values of Poisson's ratio were measured by the hollow-cylinder and the unconfined compression tests. It is hoped that the hollow cylinder described in this study is a first step along the road of understanding the complex nature of tensile properties of soil in the field. The use of elastic theory for an inelastic material might be justified since tensile strains at failure are very small. However, further research is needed to understand the tensile characteristics of real soil, taking into account isotropy versus anisotropy, monotonic versus cyclic loading, and effective stress versus total stress analysis. Acknowledgments The test described and resulting data presented herein were obtained from research conducted at Waterways Experiment Station, Vicksburg, Miss, under sponsorship of the Office, Chief of Engineers. Valuable suggestions provided by Dr. F. C. Townsend during the conduct of the study are appreciated. References (/) Al-Hussaini, Mosaid and Townsend, F. C , "Tensile Testing of Soils—A Literature Review," Miscellaneous Paper S-73-24, USAE Waterways Experiment Station, Vicksburg, Miss., May 1973, 12) Al-Hussaini, Mosaid and Townsend, F. C , "Investigation of Tensile Testing of Compacted Soils," Miscellaneous Paper S-74-10, USAE Waterways Experiment Station, Vicksburg, Miss,, June 1974. \3] Bishop, A. W. and Garga, V, K,, Geotechnique. Vol, XIX, No. 2, June 1969, pp. 309-312. \4] Bofinger, H, E., "The Measurement of the Tensile Properties of Soil Cement," RRL Report LR 365, Road Research Laboratory, Ministry of Transport, Crowthome, Berkshire. 1970. |5) Carneiro, F. L. L. and Barcellos, A., "Tensile Strength of Concrete." Bulletin No, 13, International Union of Testing and Research Laboratory for Material and Construction (RILEM), Paris, France, March 1953, pp, 99-125.

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AL-HUSSAINI ON TENSILE PROPERTIES OF COMPACTED SOILS

225

|6j Leonards, G. A. and Narain, J., Journal of Soil Mechanics and Foundations Division, American Society of Civil Engineers, Vol. 89, SM2, March 1963, pp. 47-95. |71 Fang, H. W. and Chen, W. F., "Double Punch Test for Tensile Strength of Soils," Fiftieth Annual Meeting on Soils and Rock Mechanics, Highway Research Board, 1971, pp. 62-67. [ff] Den Hartog, J. P., Advanced Strength of Materials. McGraw-Hill. New York, 1952. [9] Kirkpatrick, W. M. in Proceedings, Fourth International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, London, pp. 172-178, 1957. I/O] Whitman, R. V. and Luscher, U., Journal of the Soil Mechanics and Foundations Division. American Society of Civil Engineers, Vol. 88, No. SMG, December 1962, pp. 135-167. Ill] Hvorslev, M. J. and Kaufman, R. I., "Torsion Shear Apparatus and Testing Procedures," Bulletin No. 38, USAE Waterways Experiment Station, Vicksburg, Miss., 1952,

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O. B. Andersland,' A. S. Khattak,^ and A. W. N. Al-KhafajP

Effect of Organic Material on Soil Shear Strength

REFERENCE: Andersland, O. B., Khattak, A. S., and Al-Khafaji, A. W. N., "Effect of Organic Material on SoU Shear Strength," Laboratory Shear Strength of Soil. ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 226-242. ABSTRACT: The term organic soil ordinarily refers to combinations of weathered rock products and partially decayed plant matter. The organic fraction tends to dominate soil physical properties for organic contents in excess of 20 percent by weight. To simulate these materials and to include precise control over organic content, fiber type and size, and mineral type, kaolinite and pulp fibers were used to prepare model organic soils. For comparison, kaolinite and all fiber samples were included. The effect of organic material on soil shear strength is shown in terms of consolidation and stress-strain behavior, undrained shear strength, and the shear strength parameters c ' and '. Decomposition effects on vane shear strength are reported for selected soil samples and one consolidation pressure. The experimental work gives a relationship between void ratio and logarithm of pressure that is dependent on both organic content and pressure level. A small initial increase in organic (fiber) content significantly increased the compressive and vane shear strengths of the model organic soil. Higher organic contents changed the material behavior from one with a peak compressive strength at about 7 percent axial strain (kaolinite) to one with an almost straight line stress-strain curve for strains in excess of 20 percent (all fiber). Decomposition in the model organic soils led to a large decrease in vane shear strengths. An increase in organic (fiber) content increased the shear strength parameter 0 ' for both the CIU and CID triaxial tests. A failure criterion, based on the maximum ratio of shear stress to the effective normal stress (maximum obliquity), gave (^'-values intermediate to the CIU and CID values for high organic contents. KEY WORDS; fibrous soil, organic soil, shear strength, soil mechanics, strength parameters, stress-strain curves, undrained strength

The term organic soil ordinarily refers to a transported soil consisting of the products of rock weathering with an admixture of decayed plant matter [1].^ Soils containing 20 percent or less organic material by weight show 'Professor of Civil Engineering, Michigan State University, E. Lansing, Mich. 48824. ^Associate Professor of Civil Engineering, South Dakota State University, Brookings, S. Dak. 57007. •'Assistant Professor of Civil Engineering, University of Detroit, Detroit, Mich. 48221. ''The italic numbers in brackets refer to the list of references appended to this paper. 226 Copyright by Downloaded/printed Copyright 1981 University of

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ANDERSLAND ET AL ON EFFECT OF ORGANIC MATERIAL

227

physical characteristics which are influenced primarily by the mineral ingredients [2,3]. Arman indicates that these soils can be used for base or embankment materials and general foundation work [2]. With larger organic contents (20+ percent by weight) the physical properties become increasingly dominated by behavior of the organic fraction [2.4]. High organic content soils tend to be excessively compressible and to exhibit low shear strengths. This behavior has limited their use as an engineering material. The organic content of a given soil will vary with time if adequate amounts of nutrients needed by micro-organisms responsible for breakdown of the organic matter are present. An additional problem is the identity of organic matter in the soil profile since various stages of decomposition are often observed. In many cases decomposition rates are slow so that the effects relative to settlement and shear strength can be ignored and current soil properties are adequate for design purposes. In some cases, primarily manmade landfills containing nutrients added during sludge de-watering, the change in physical characteristics due to decomposition can be very significant. In either case, accurate measurement of organic content becomes important relative to prediction of soil behavior. Arman recommends that soil organic content should be determined by combustion at 440°C [2]. The weight loss, compared with that at 105°C, is taken as a measure of the organic content. Franklin et al found that burning at 400 to 450°C until constant weight was attained gave reliable organic contents [3]. Al-Khafaji recommended a similar procedure and introduced a correction factor to allow for loss of surface hydration water associated with the 400°C ignition temperature [5]. The effect of organic material on soil shear strength is complicated by changes which occur during decomposition and uncertainties regarding the current identity of organic matter in the soil profile. The two limiting conditions are represented by no decomposition and 100 percent decomposition. The more fibrous organic soils would more closely represent little decomposition. The amorphous-granular peat structure [6] and humus material found in top soils generally represent later stages in the decomposition process. The equilibrium void ratio (or water holding capacity) for a given stress level increases with increasing organic content. For higher organic contents (peat) large deformations are required to fully mobilize the shear strength [4,7]. Failure criteria based on acceptable strain levels may control in many cases. The shear strength parameter (f>' for peat or muskeg (43.5 and 48 deg, respectively) reported by Hanrahan et al [8] and Adams [9] is high compared with inorganic soils. There is a lack of information on the use of these
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228

LABORATORY SHEAR STRENGTH OF SOIL

strain behavior, undrained shear strength, and shear strength parameters. Decomposition effects on vane shear strengths are reported for selected model soil samples and one consolidation pressure. A number of conclusions summarize the effect of organic material on shear strength of the model organic soils. Experimental Work The experimental work involved preparation of model organic soil samples followed by consolidation and triaxial or vane shear tests. A brief description of the materials studied, sample preparation, and strength tests follows. Materials Studied Pulp fibers included a range of sizes with a weighted average length of 1.6 mm based on the TAPPI [10] test procedure and typical diameters of 20 fim observed in the electron microscope. Surface area measurements, using the water vapor absorption method [//], gave values close to 133 m^/g of fiber. A value of 1.54 was used for the specific gravity of the almost pure cellulose fibers. The kaolinite included particles with 100 percent passing 40 /tm, 93 percent passing 10 ftm, and 42 percent passing 1 /im. The grain-size distribution was relatively well graded. Consistency limits included a liquid limit of 47.8 percent, plastic limit of 27.5 percent, and plasticity index of 20.3 percent. The specific gravity of kaolinite particles equal to 2.70 was used in the study. Sample Preparation Pulp fiber board, after freeze drying, was separated into a fluffy mass. Selected proportions of dry kaolinite and dry fiber were mixed. Next water was added in amounts needed to form a slurry. This slurry was normally consolidated until the mass formed a soft cylinder from which smaller test specimens could be trimmed. A high-speed rotary cutting tool minimized problems with trimming the fibrous model soil. Other sluny samples were used directly for consolidation and vane shear experiments. Nutrients and seed bacteria, in predetermined proportions, were added directly to the slurry for those experiments involving decomposition. Kaolinite specimens were also formed by consolidation of a slurry followed by hand trimming of test specimens. Consolidation and Strength Tests One-dimensional consolidation, for stresses ranging from 122 kPa up to 35 MPa, was accomplished using special compression test cylinders with sample cross-sectional areas of 645 and 100 mm^ and sufficient height to permit use

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ANDERSLAND ET AL ON EFFECT OF ORGANIC MATERIAL

229

of model soils with an initial slurry consistency. Top and bottom porous stones permitted any excess water and air to escape under a small initial load. The volume of water draining from each sample under increasing incremental loads provided a check on decrease in sample thickness. A force transducer mounted below the bottom porous stone eliminated the problem of ram friction and permitted load measurement to an accuracy of ± 5 N. All-around consolidation at low pressures was conducted with standard triaxial cells. Vane shear tests were conducted only for low consolidation pressures using a miniature laboratory apparatus. Samples were prepared and consolidated in 3-L beakers. The test vane was inserted through an opening in the top porous stone, and duplicate test locations were available simply by rotating the stone. Complete remolding and return of drained fluid to the sample after each test series permitted decomposition to continue for later shear tests with more sample decomposition. The degree of decomposition, X^,, defined as suggested by Al-Khafaji [5] was

where Xj^ is the initial organic fraction and Xfj is the organic fraction after partial decomposition. Determination of Xfo and Xfj using the ignition test permits computation of the degree of decomposition Xj;. Triaxial tests, using conventional cells and procedures [72], included allaround consolidation and use of backpressures to insure a high degree of sample saturation. Both consolidated-undrained (CIU) tests, with pore pressure measurements, and consolidated-drained (CID) tests were conducted on the model organic soils, kaolinite, and all fiber samples. Sample deformation rates were selected in accordance with procedures outlined by Bishop and Henkel [12].

Consolidation Consolidation, either all-around or anisotropic, is a normal part of most triaxial tests for measurement of soil shear strength. Application of an external load causes a gradual decrease of water content. The void ratio decreases until sufficient shearing resistance is developed through interparticle contacts to resist interparticle shear forces. For a change in organic content the equilibrium void ratio-logarithm of pressure relationship was altered as shown in Fig. 1 for one-dimensional consolidation. Similar curves were obtained for all-around consolidation. Most geotechnical field problems correspond to the lower pressure range. The large void ratios together with the high water holding capacity of organic material relates to the major effect which

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230

0,

LABORATORY SHEAR STRENGTH OF SOIL

3 i-

40%F/fiO%C

iy weight V ^

I

16 %f/84 %C

? - by weight

-Kaolinite

t

10

•

1

4

1

I

6

I

I

a

-.J

t i

10

Pressure, i.Wm

2

4

I I I -I 1.1,.

6

8 10

2

FIG. 1—Void ratio-logarithm of pressure curves (one-dimensional consolidation) for several model organic soils (data from Ref I3A

organic material has on soil shear strength. The kaolinite curve was linear whereas the addition of organic material (pulp fiber) imposed a nonlinear behavior between void ratio and logarithm of pressure. Note that the experimental data in Fig. 1 show a common point of intersection for all organic contents at a pressure close to 17 MPa and a void ratio close to 0.6. Organic matter has a high absorptive capacity for water with those molecules close to the fiber more tightly held than molecules more distant. Calculations [13] showed that at a pressure of 35 MPa only about 3 or 4 water molecules remained for each cellulose unit. Since the void ratio-logarithm of pressure data for the model organic soils relates to ultimate settlement prediction, a few comments seem in order. The slope of the curves in Fig. 1 represent the compression index, C^, common to soil settlement calculations. It is evident from the curves that for a given organic content the compression index is not constant but will decrease with an increase in pressure. If any decomposition of organic material should occur during consolidation the void ratio-logarithm of pressure curve would be shifted downward. The implications relative to settlement prediction for organic soil deposits are significant. For small changes in pressure, typical of many geotechnical field problems, and no decomposition the compression index may be considered approximately constant. For larger pressure increments errors in settlement prediction would increase significantly. Questions regarding additional settlement due to loss of organic solids by decomposition lie outside the scope of this paper.

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ANDERSLAND ET AL ON EFFECT OF ORGANIC MATERIAL

231

Stress-Strain Behavior The stress-strain behavior of a soil represents the combined effect of cohesion, dilatancy, and friction. Only small strains are required to mobilize cohesion, after which it disappears. Interference between particles causes a volume increase tendency or added shear strength. After some strain and no further tendency for volume increase, the dilatancy component normally disappears. When the stress-strain curves become horizontal, only the friction component is active. The components of shear resistance—cohesion, dilatancy, and friction—are dependent on soil composition [14], The addition of organic fibers to saturated kaolinite has the initial effect of stiffening a model organic soil and increasing the ultimate strength for drained and undrained conditions. This behavior is illustrated in Fig. 2 where comparisons are shown for several model organic soils. Note that an increase in fiber content (16 percent dry weight basis) significantly increased the peak stress (271 kPa compared with 189 kPa) even though the kaolinite was consolidated under a higher pressure (343 kPa compared with 294 kPa). Horizontally oriented fibers tend to limit lateral expansion of vertically oriented compression specimens, thereby enhancing their compressive strength. Should any decomposition occur, the benefit derived from the fibers would tend to disappear. Decomposition products—including digested organic matter (humus), new microbial cells, a variety of volatile acids, methane, and water—would further reduce the shear strength. Higher organic (fiber) fractions increasingly altered the stress-strain behavior, giving an almost straight line response for all fiber samples (Fig. 2). Particle interference in the form of fiber interlocking appeared to inFiber Consol.press.

400

343 k Pa

40% fiber/ 60% kaolinite (dry wt. I Consol. press. = Z94k Pa 7

• E 300

U 200

100

0

2

4

6

FIG. 2—Stress-strain curves (undrained)

8 10 12 14 axial strain, H^, %

16

18

20

for several model organic soils (data from Ref \3).

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232

LABORATORY SHEAR STRENGTH OF SOIL

fiuence the deformation behavior. Undrained triaxial compression tests on peat [7] showed the same stress-strain behavior with the stress difference increasing for axial strains up to 30 percent and more. When unloaded, the axial strain did not return to zero but retained a significant portion of the total deformation. This same straight line approximation appears at lower organic contents for a consolidated drained triaxial test (Fig. 3). The volumetric strain (Fig. 3) changed almost linearly with axial strain. Horizontally oriented fibers again limited lateral specimen expansion so that most of the drainage involved a decrease in specimen height. For low organic contents and drained test conditions the stress-strain behavior was influenced primarily by the mineral fraction, kaolinite. Soil shear strength may be defined as the shear stress on the failure plane at failure. More often a well-defined slip surface cannot be identified, and failure is conveniently defined in terms of the maximum principal stress difference that can be mobilized. This criteria serves for organic soils with a high mineral fraction (Fig. 2). With a high organic fraction the principal stress difference continues to increase for axial strains well over 20+ percent, as shown in Fig. 2 and also reported for peat by Hanrahan and Walsh [7]. Hence it becomes necessary to define failure arbitrarily at some limiting strain, which, by more or less common consent, is often taken at 20 percent axial strain. These two criteria have been used in this study. For the undrained triaxial (CIU) tests and high organic contents the pore pressure becomes equal to the cell pressure at about 15+ percent axial strain. At this stage the undrained test becomes a semi-drained test with zero lateral effective stress. Use of a limiting 20 percent axial strain to define failure becomes meaningless at this stage when the object is to measure the shear strength parameter <^'. To circumvent this problem, failure can be defined in terms of the maximum ratio of shear stress to effective normal stress (maximum obliquity). Use of this definition for failure is illustrated in Fig. 4 for model soil samples containing 40 percent organic material (dry weight basis) and papermill sludge samples with close to the same organic fraction. The maximum ratio developed at about 8 percent axial strain. This failure criterion avoids the problem of a zero minor principal effective stress during measurement of the shear strength parameter <j>'. Pore Pressure Parameters Laboratory tests for measurement of soil shear strength include the limiting undrained condition and measurement of pore pressures to help in understanding soil behavior. After initial consolidation and closure of drainage lines, a backpressure was applied to the model soil specimens so as to ensure a degree of saturation close to 100 percent. Values for the B-parameter, ratio of observed pore pressure to an applied all-around pressure, were close to unity for most samples. In a few cases, entrapped air

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ANDERSLAND ET AL ON EFFECT OF ORGANIC MATERIAL

233

0.8^

Sample CD-CFl 40%ffber/60%kaolinlte (dry wt. Consol. press. = 44lkPa

4

—i—^ 111 1^ i4 ife I's ^0 Axial strain, ,, % 6 8 10 ^2 14 16 18 20 -I-

FIG. 3—Consolidated-drained triaxial test on a 60 percent kaolinite/40 percent fiber (dry weight basis) sample (data from Ref Yi). (a) Stress difference: (b) Volumetric strain.

and equipment problems gave lower values for B. An increase in deviator stress for the undrained condition produced the change in pore pressures shown in Fig. 5b. For a 5-value of unity and no change in cell pressure, Parameter A equals the ratio of observed pore pressures to increase in deviator stress (Fig. 5c). For all fiber samples, values of ^4 increased with axial strain up to a limiting maximum value, then decreased slightly when pore pressures approached the cell pressure. Thereafter test conditions did not satisfy pore pressure theory requirements and erroneous values of A were obtained. The deviator stress continued to increase with axial strain regardless of the zero lateral effective stresses. The /4-parameters decreased with higher organic fractions, average values ranging from about 0.75 for 16 percent organic content down to 0.68 for all fiber samples. Triaxial tests on peat with water contents of 400+ percent showed that pore pressures always attained equality with cell pressures at failure [8]. Undrained Shear Strength The undrained shear strength of normally consolidated clay soils increase linearly with overburden stress and hence linearly with depth. This behavior

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234

LABORATORY SHEAR STRENGTH OF SOIL

- Data from Khattak (1978) ^^ Tests CU-CFl through CU-CF3. 40% organic mat'l Idry wt. basis). - Data from Charlie (1975) tests U-MO through U-1-13 , , ., •^ 40 % organic mat'l (dry wt. basis).

/

i

/-Sample CU-CF3

2

35 = % axial strain 1 2 3 Effective normal stress, cT' KN/m' FIG. 4—Consolidated-undrained triaxial data presented in terms of the maximum ratio of shear stress to effective normal stress (maximum obliquity).

is not always observed in peat deposits [4] because decomposition in some layers produces a decrease in the undrained shear strength. In general, the ratio of undrained shear strength to effective overburden stress is a useful way to characterize the undrained strength of normally consolidated soils. For the model organic soils the ratio of undrained shear strength to consolidation pressure, c,/p, increased linearly with organic content (volumetric basis) from about 0.7 for kaolinite up to 1.6 for all fibers. This increase in the c,/p ratio appears to be related to the improved tensile characteristics of the model soil. Decomposition would decrease this ratio. For normally consolidated clay soils the c„/p ratio generally falls below one [15]. Undrained shear occurs in field problems when the soil void ratio and water content remain unchanged (no consolidation) during load application. The unconfined compression test is perhaps the most common method for measuring the undrained strength. The usual assumptions [1] include a perfectly undisturbed sample with no change in water content and that effective stresses in the sample remain practically unaltered from those existing before recovery from the ground. These assumptions may be approximated for those organic soils in which the mineral fraction dominates the physical properties (up to about 20 percent organic material by weight). Higher organic (fiber) fractions tend to give the soil an increasingly resilient or spongy structure, the magnitude dependent on the presence of fibers versus more amorphous-granular organic materials. This resilient behavior makes it more difficult for all-around capillary pressures [/] to replace the beforesampling effective stresses around the unconfined sample periphery. A com-

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ANDERSUND ET AL ON EFFECT OF ORGANIC MATERIAL

235

Sample CU-CF2 W fiber/60% kaolinite Wry weight basisi

0.4

ro.3 Consol. pressure = 392kPa

0.2 £ 0.1

2

4

6 8 10 12 14 Axial strain, 6,, % (a) 1

16 18 20

Axial strain, 6,, %

(c) FIG. 5—Consolidated-undrained triaxial test on a 40 percent fiber/60 percent kaolinite (dry weight basis) sample (data from Ref li). (a) Stress difference: (b) Excess pore water pressure; (c) A-parameter.

parison between unconfined compressive shear strengths and vane shear strengths are shown in Fig. 6 for a normally consolidated fibrous organic soil (papermill sludge). Sample specimens were carefully hand cut from block samples. Charlie [16] reports that the lower unconfined compressive shear strengths appeared to be due to soil expansion on unloading and physical disturbance in sampling and sample preparation for laboratory testing. Decomposition with disintegration of fibers and formation of decomposition products — digested organic matter (humus), new microbial cells, a variety of volatile acids, methane and water — should lead to a reduction in shear strength for organic soils. Structural breakdown of an organic pulp fiber is illustrated m Fig. 7 where comparison photos show no decomposition and an advanced stage of anaerobic decomposition. Colonies of rod-shaped bacteria appear on the surface of the partially decomposed fiber. Changes in

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236

LABORATORY SHEAR STRENGTH OF SOIL

391lb/ft^(18.73kN/m^l sand

/ / sludge

94 -

90

sand

/ -/ / •~ 82 sludge

sand

78 7-r?

September 7, 1972

•"0.4 0.8 1.2 1.6 2.0 vane shear strength , kgf/cm

FIG. 6—Comparison of unconfined compressive strengths and vane shear strengths for a normally consolidated papermilt sludge with an average organic content of 55 percent (after Charlie tl6]A

vane shear strength, as a result of decomposition, were observed using a model organic soil. A slurry, prepared from selected weight fractions of kaolinite and fibers with nutrients and seed bacteria added, was consolidated under a pressure of 1.14 kPa. Initial vane shear strengths were measured using a small laboratory vane (12.7 mm across by 25.4 mm long) inserted into 3-L samples through an opening in the top porous stone. Care was taken so that the vane would shear a complete cylindrical surface for each test. Pulp fibers, with an average length of 1.6 mm, were about 7 to 8 times shorter than the minimum vane dimension. The sample was then remolded to the same slurry condition (water drained during consolidation was returned to the sample) and allowed to decompose under anaerobic conditions. Consolidation to the same stress level followed by vane shear tests was repeated at several stages of decomposition. The results, summarized in Fig. 8, include data for samples with initial organic contents of 30, 60, and 80 percent by weight. Note that the initial vane shear strengths increased with higher organic contents. Decomposition reduced the vane shear strengths for the 80 percent organic content sample from about 6.3 down to 0.5 kPa, a very significant reduction. This behavior has serious implications relative to stability of man-made landfills containing organic waste material and some natural organic deposits.

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ANDERSLAND ET AL ON EFFECT OF ORGANIC MATERIAL

237

(a)

FIG 1-Organic pulp fibers, (a) No decomposition. X2000 (after Khattak [Uh- (b) Advanced stage of anaerobic decomposition. XIOOO (after Al-Khafaji [S\).

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238

LABORATORY SHEAR STRENGTH OF SOIL

Consolidation pressure Ql =1.14kPa

initial organic content /-80% (by weight)

10

15

20

25

30

35

40

45

decomposition, %

FIG. 8—Vane shear strength versus decomposition for three model organic soils Ikaolinite and pulp fiber) at a consolidation pressure of 1.14 kPa (data from Al-Khafaji [5]).

Shear Strength Parameters The Mohr-Coulomb theory of failure [/] and use of effective stresses defines soil shear strength in terms of shear strength parameters c' and <^'. These parameters were evaluated for several model organic soils using the triaxial test under drained conditions and undrained conditions with pore pressure measurements. For organic soils with a high mineral fraction failure was defined in terms of the maximum principal stress difference that was mobilized. With higher organic contents and principal stress differences continuing to increase for axial strains of 20+ percent, two definitions of failure were considered, an arbitrary limiting deformation of 20 percent axial strain and the maximum ratio of shear stress to effective normal stress (maximum obliquity). A comparison of Kj-lmes for the consolidated-undrained (CIU) and consolidated-drained (CID) triaxial tests on fiber samples (Fig. 9) gives c ' equal to zero and '-values of 80.4 and 31.0 deg, respectively. For the undrained test pore pressures attained values equal to the cell pressure at axial strains around 15 percent; hence the 80.4 deg value for <>' at 20 percent axial strain represents a semi-drained condition with zero lateral effective stresses. The principal stress difference continued to increase for axial strains greater than 20 percent. An alternative approach (Fig. 4) for the undrained test used the maximum ratio of shear stress to effective normal stress which defined failure at lower axial strains, about 8 percent. This gave 0 '-values equal to 39 deg, intermediate to 80.4 and 31.0 deg for the CIU and CID tests on all fiber samples. A summary of (^'-values for the model organic soils (Fig. 10) shows 20.1 deg for the kaolinite compared with higher <> / '-values for the organic soils.

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ANDERSLAND ET AL ON EFFECT O F ORGANIC MATERIAL

239

(a) 300r

Failure at 20% axial strain

200

100

0 ' = sin~'(tan(«,') 8S' = 8Q.4° 100

200 300 i W J +g^), kN/m^

400

(b) 800r

600^

o Mrain rate =0.079 mm/min. A Strain rate = 0.0317 mm/min. Failure at 20% axial strain.

FIG. 9—Summary of triaxial data for fiber samples (data from Ref 13A (a) Consolidatedundrained tests: (b) Consolidated-drained tests.

For organic contents below 20 percent by weight the effect on ^' was reasonably 'small. Small changes for c' (up to 20 kPa) were observed for the normally consolidated samples with intermediate organic contents. These values of c' and (^' may be compared with those reported for a remolded peat of c ' = 5.5 kPa (0.8 psi) and ' = 43.5 deg \8], and for an undisturbed peat, c ' = 0, ' = 48 deg [9]. With decomposition of the organic fraction, a decrease in 0 ' would be anticipated for the model organic soil. Jankowski [17] states that the angle of internal friction in peats decreased with an increase in the degree of decomposition. More research is needed relative to selection of the appropriate 0 '-values for field problems and the effects of decomposition on the shear strength parameters.

Conclusions Model organic soils prepared from kaolinite and pulp fibers have been studied relative to the effect organic material has on soil shear strength.

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240

UBORATORY SHEAR STRENGTH OF SOIL

Fiber, % by volume 60 80 100 Fiber, % by dry weight

lb—'"itr

FIG. 10—Fiber content versus shear strength parameter ' for model organic soils (data from Ref 13A

These conclusions are intended to reflect the findings of this investigation and are limited to the materials used and to the test procedures employed. 1. Triaxial consolidation, either isotropic or anisotropic, of model organic soils shows that the relationship between void ratio and logarithm of pressure is dependent on both organic content and pressure level. At low stress levels, high organic content soils experience large decreases in void ratio with small increases in pressure. 2. The compression index, C^., used in settlement computations varies significantly with stress level and organic content of the soil. Decomposition, in the model organic soil, also decreased the compression index and introduced questions concerning loss of soil solids and the related effect on settlement. 3. A small increase in organic (fiber) content significantly increased the compressive strength of kaolinite for both drained and undrained conditions. Higher organic contents changed the material behavior from one with a peak compressive strength at around 7 percent axial strain (kaolinite) to one with an almost straight line stress-strain curve (all fiber). For all fiber samples the principal stress difference continued to increase for axial strains greater than 20 percent, regardless of zero lateral effective stresses in the CIU test. 4. For the same consolidation pressure the undrained (vane) shear strength increased with an increase in fiber content of the model organic soils. The higher shear strengths correspond to higher water contents (greater water holding capacity due to more organic matter) and lower densities (lower specific gravity of the organic matter). 5. Decomposition in the model organic soils led to a large decrease in the undrained shear strength measured at a given consolidation pressure (constant effective stress). The strength reduction was brought about by a break-

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ANDERSLAND ET AL ON EFFECT OF ORGANIC MATERIAL

241

down of the fiber structure and the formation of decomposition productsdigested organic matter (humus), new microbial cells, a variety of volatile acids, methane and water—in the soil. 6. Consolidated-drained (CID) triaxial tests on model organic soil samples with failure based on the maximum principal stress difference or the stress at 20 percent axial strain gave '-values ranging from 20 deg for kaolinite up to 80-f- deg for all fiber samples. 7. A failure criterion, based on the maximum ratio of shear stress to effective normal stress (maximum obliquity), gave '-values intermediate to the (CIU) and CID test values for high organic content soils. This criterion avoids the problem of the minor principal effective stress going to zero for the (CIU) test at axial strains of 15 percent or more. For all fiber samples this criterion gave 4>' equal to 39 deg compared with 80+ and 31 deg for the CIU and CID tests, respectively. Acknowledgments This study was supported by National Science Foundation Grant No. ENG75-13765 and by the Division of Engineering Research, Michigan State University. The kaolinite and pulp fiber were provided by the National Council of the Paper Industry For Air and Stream Improvement, Inc. Their support is gratefully acknowledged. References [/] Terzaghi, Karl and Peck, R. B., Soil Mechanics in Engineering Practice. 2nd ed., John Wiley & Sons, New York, 1967. [2] Arman, Ara, "Engineering Classification of Organic Soils," Highway Research Record, No. 310, National Academy of Sciences-National Academy of Engineering, Washington, D.C., 1970, pp. 75-89. 1.?] Franklin, A. G., Orozeo, L. F., and Semray, R., Journal of the Soil Mechanics and Foundations Division. American Society of Civil Engineers, Vol. 99, No. SM7, 1973, pp. 541-557. [4] MacFarlane, I. C. in Muskeg Engineering Handbook. Ch. 4, I. C. MacFarlane, Ed., University of Toronto Press, Canada, 1969. [5] Al-Khafaji, A. W. N., "Decomposition Effects on Engineering Properties of Fibrous Organic Soils," unpublished PhD. thesis, Michigan State University. E. Lansing, Mich., 1979. 16] Radforth, N. W. in Muskeg Engineering Handbook. Ch. 2, I. C. MacFarlane, Ed., University of Toronto Press, Canada, l%9. [7] Hanrahan, E. T., and Walsh, J. A. in Proceedings. 6th International Conference on Soil Mechanics and Foundation Engineering, University of Toronto Press, Canada, 1965. pp. 226-230. [8] Hanrahan, E. T., Dunne, J. M., and Sodha, V. G. in Proceedings. Geotechnical Conference, Norwegian Geotechnical Institute, Oslo, Norway, 1967, pp. 193-198. [9] Adams, J. I., in Proceedings. 6th International Conference on Soil Mechanics and Foundation Engineering, University of Toronto Press, Canada, 1965, pp. 3-7.

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242

LABORATORY SHEAR STRENGTH OF SOIL

1/0] "Fiber Length of Pulp by Classification, Suggested Method T233 su-64," Technical Association of the Pulp and Paper Industry (TAPPI), Atlanta, Ga., 1964. 1//) "Instruction Manual of Perkin-Elmer Shell Model 212B Sorptometer," Instrument Divi sion, Perkin-Elmer Corporation, Norwalk, Conn., 1961. [12] Bishop, A. W. and Henkel, D. J., The Measurement of Soil Properties in the Triaxial Test 2nd ed., Edward Arnold, London, 1962. [13] Khattak, A. S., "Mechanical Behavior of Fibrous Organic Soils," unpublished PhD thesis, Michigan State University, E. Lansing, Mich., 1978. [14] Lambe, T. in Proceedings. Research Conference on Shear Strength of Cohesive Soils American Society of Civil Engineering, Boulder, Colo., 1960, pp. 555-580. [15] Lambe, T. W. and Whitman, R. V., Soil Mechanics, John Wiley & Sons, New York, 1969, [16] Charlie, W. A., "Two Cut Slopes in Fibrous Organic Soils, Behavior and Analyses," un published PhD. thesis, Michigan State University, E. Lansing, Mich., 1975. [17] Jankowski, W., "Peat Bogs as Building Sites," Polish Technical Abstracts. Vol. 1, No. 17, 1955.

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R. Y. K. Cheng'

Effect of Shearing Strain-Rate on the Undrained Strength of Clay

REFERENCE: Cheng, R. Y. K., "Effect of Shearing Strain-Rate on the Undiataied Strength of Clay," Laboratory Shear Strength of Soil. ASTM STP 740. R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 243-253. ABSTRACT; Dynamic testing method is required to determine the strength of soils for problems of dynamic loading. This paper presents an experimental technique for measuring the relationship of undrained shear strength and strain-rate of a clay. Torsion tests were performed on remolded hollow cylinder specimens. The test results show that the undrained shear strength increases initially with strain-rate from the static undrained strength, but subsequently the undrained strength reaches an ultimate value as the strain-rate increases. KEY WORDS: soil shearing strain rate, soil shear strength, dynamic soil testing

The shear stress and strain-rate relationship of soils is required to study problems involving loading. Some of these problems are those related to ground mobility, landing of aircraft on unpaved clay fields, tillage, rapid excavation of soils, and penetration of projectiles into soils. This paper presents a procedure for measuring the undrained strength of a clay specimen subjected to various straining rates. The results of the test give the relationship of the undrained strength and strain-rate of the clay. Torsion Test on Hollow Cylinder The experimental procedure herein [/]^ uses a hollow cylindrical specimen. A state of pure shear is induced in the specimen by rotating one end of the specimen at a constant rate. As this specimen will be deformed beyond its elastic limit, and as the wall of the specimen is relatively thin, the shearing stress across the wall is considered to be uniform. Geuze and Tan [2] and ' Professor of Civil Engineering, Old Dominion University, Norfolk, Va. 23508. ^The italic numbers in brackets refer to the list of references appended to this paper. 243 Copyright by Downloaded/printed Copyright"^ 1981 University of

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244

LABORATORY SHEAR STRENGTH OF SOIL

Saada and Ou [3] used hollow cylindrical specimens in their investigations of the stress-strain relations of soils. The state of stress of a hollow cylinder in torsion about the z-axis is shown in Fig. 1. The stress distribution in a hollow cylinder due to an applied torque is well established [4] for the case where the elastic limit of the material is not exceeded. Beyond the elastic limit and into the plastic range, the shear stress is considered to be constant radially across the wall of specimen (Fig. Ic). Considering the equilibrium condition that the external torque is equal to the internal twisting moment, as a result of the shear stress, yields T=\T„jdA

(1)

A

Imposing the boundary conditions with R\ and Rj as the inside and outside radius, respectively, the shear stress is related to the torque as

2x

(/?2^-/?,3)

(2)

where T„, is the ultimate undrained shear stress and T is the maximum torque. Referring to Fig. la, the shearing strain, y, is related to the angle of rotation, 0, at the top of the specimen by

Re tan where h is the specimen height and R is the mean of Rj and /?2. Taking the time derivative of y yields

h^ + RH^ J dt where 7 is the shearing strain-rate. For small values of 6, the second term in the denominator on the righthand side of Eq 3 may be neglected and the strain-rate expressed by

Torsion Apparatus Figures 2 and 3 show the torsion apparatus. The flywheel, weighing 356 N, is supported by a shaft which can rotate and move vertically. The flywheel is

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CHENG ON EFFECT OF SHEARING STRAIN-RATE ON CLAY

245

(b) Stresses On Element

(c) Stress Distribution At Maximum Torque FIG. 1—Reference axes and stresses.

driven by an air jet, and the rate of rotation is measured by a magnetic counter. At the lower end of the flywheel shaft, a spring-loaded clutch can engage the flywheel to the torsional shaft, thereby applying an instantaneous rotation on the specimen in the triaxial chamber at the same rate of rotation as the flywheel. The rate of rotation of the specimen is also measured by a magnetic counter. A standard triaxial chamber was modified to contain the specimen. The specimen was held firmly at the base, and the top of the specimen was connected to the torsional shaft, which had to be fitted precisely to the chamber housing of the triaxial cell. This tight fit, which is required to contain the hydrostatic pressure in the chamber, develops substantial friction between the chamber housing and the shaft. To eliminate the effect of the friction, the torque transducer is mounted between the shaft and the top of the specimen plate.

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246

LABORATORY SHEAR STRENGTH OF SOIL

A, B. C. D. E. F.

Turbine Flywheel Clutch Assembly Torsion Shaft Coupler Triaxial Cell

G, H. I. J. K. L.

Torque Transducer Test Specimen Loading Plate Clutch Handle Magnetic Counter Linear Ball Bearings

FIG. 2—Torsion apparatus.

Sample Preparation Unit and Procedure Mississippi Buckshot clay was used for all tests. The liquid and plastic limits are 61 and 28 percent, respectively [5]. A test specimen was prepared by consolidating a clay slurry at water content of 80 percent in a mold. The slurry was prepared by mixing dry clay powder with distilled water, and the mixture was allowed to soak for 24 h. The consolidation mold (Fig. 4) consisted of a split cylinder forming the outside mold and a solid core cylinder forming the inside mold. The base of the mold also served as the base plate for the specimen, and the top of the mold served as the top loading plate for the specimen. The inside face of the split cylinder and the surface of the solid core cylinder were lined with paper cloth which acted as a filter during consolidation by radial flow. The vertical compression of the sample was achieved by applying a vertical force on the top cap through a rigid piston driven by a pneumatic jack. By gradually varying the vertical consolidation pressure for approximately 48 h, a hollow cylindrical specimen, with the top and bottom loading plates in place, was 100 percent consolidated and was

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CHENG ON EFFECT OF SHEARING STRAIN-RATE ON CLAY

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248

LABORATORY SHEAR STRENGTH OF SOIL

!®?-=in5e-"-' * FIG. 4—Specimen mold.

ready for testing. Figure 5a shows a sample mounted on the base of the triaxial chamber with the torque transducer placed on the top loading plate. The horizontal wrinkle lines on the specimen were formed by the vertical movement of the paper cloth, but these lines did not influence the shearing resistance of the specimen. Figures 5b and 5c show various deformed shapes of the specimen after the tests. The sample used in this study was 7.62 cm high with inside and outside radii of 7.62 cm and 10.16 cm, respectively. The wall thickness was 1.27 cm. The water content of all the specimens varied from 30 to 34 percent, corresponding to dry unit weights from 14.6 to 13.7 kN/m^. The average water content of a specimen was determined at the end of test from nine samples by taking three samples each from the top, middle, and bottom of the specimens. Variation of water content in each specimen was ±1.2 percent. Testing Procedure All tests were conducted with no confining pressure. By regulating the nozzle pressure, the air turned the flywheel (Fig. 2) until it reached a steady rate of rotation indicated by signals from a magnetic pickup. The clutch was

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CHENG ON EFFECT OF SHEARING STRAIN-RATE ON CLAY

249

FIG. 5a—Specimen be/ore testing.

rapidly engaged and the specimen was subjected to an instantaneous rotation with the same rate as that of the flywheel, since the mass ratio between the flywheel and specimen was 30 to 1. A typical test result is shown in Fig. 6. Electrical outputs from the transducer and magnetic pickups were recorded on a direct-write oscillograph. The top trace indicates the rotation of the flywheel. With 80 peaks per revolution, the rate was determined from the time pulse which was set at 0.1-s intervals. The next lower trace indicated the rotation at the top of the specimen. The trace which recorded the signal of the torque transducer gives the variation of the torque, and it was determined from the calibration signals shown by the horizontal lines recorded just before and after each test. The calibration signal represented a torque of 4.86 N-m. The torque recorded for each test included the shearing resistance of the specimen and the effects of the inertia of the transducer and top loading plate. The torque measured in test without the specimen was due to the effects of the inertia of the transducer and top loading plate. The shearing stress in the specimen was determined from the difference of the maximum torques measured with and without the specimen at the same rate of rotation of the top loading plate.

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250

LABORATORY SHEAR STRENGTH OF SOIL

FIG. Sb—Low water-content specimen after testing.

Results and Analysis Since the variation of water content in each specimen was ±1.2 percent, the specimens ranging in water content from 30 to 34 percent were divided into four groups consisting of 1 percent increment of water content for each group from 30 to 34 percent. The undrained strength was determined using Eq 2 from maximum torque; the strain-rate was determined using Eq 4 from the rate of rotation of the flywheel. All test results indicated that maximum torque developed within a rotation of 0.15 rad/s. The test results plotted in Fig. 7 indicated that for each group of specimens, the undrained strength is bounded by an upper limit henceforth known as the ultimate dynamic strength, S„, which can be written as Sm = So + a

(5)

where S^ is the static undrained strength and a is the dynamic component of the ultimate dynamic strength. For strain-rate less than 15 rad/s for all tests performed, the relation between undrained strength, S, and strain-rate, y, without any confining pressure can be written as S = So + a(l-e'^y) Copyright Downloaded/printed University

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(6) ASTM

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British

CHENG ON EFFECT OF SHEARING STRAIN-RATE ON CUY

251

FIG. 5c—High water-content specimen after testing.

FIG. b—Typical recorded time history {specimen water content at 30percent: shearing strainrate at 4.8 rad/s).

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252

LABORATORY SHEAR STRENGTH OF SOIL

Specimen Water Content, % 30 < w < 31 31 < w < 32 32 < w < 33 33< w <34 Static Undroined Strengtti

Symbol 0

• A A

•

-oi5r\

10 X 10

2

4

6

8

10

12

14

16

Strain Rote, X, rad/sec FIG. 7—Relationship between undrained strength. S, and strain-rate,

y.

where /8 is a coefficient that gives the rate at which the strength approaches the ultimate dynamic strength. The values of the static undrained strength, S, shown in Table 1 and Fig. 7 were taken from Fig. 2.5B of Ref 6 which gave the unconsolidated undrained strength of the Buckshot clay. The value of the ultimate dynamic strength, S„„ for each group of specimens is the asymtote for Eq 6, and the value of a is the difference between S„, and S^. The value of /3 was next determined using the method of least squares with linear relationship of the logarithmic transformed variables.

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CHENG ON EFFECT OF SHEARING STRAIN-RATE ON CLAY

253

TABLE 1—Summary of torsion tests on Mississippi Buckshot clay. < W << 34 W << 31 31 31 31 << W W << 32 32 Specimen water content, W,% 30 <: W 32 < 14.49 14.25 13.99 Average dry unit weight, kN/m-' 0.84 0.87 0.90 Average void ratio 12.0 9.5 6.7 Ultimate undrained strength, S^. N/m^ X lO"" 4.3 3.8 3.1 Static undrained strength, S„, N/m^ X 10'' 7.7 5.7 3.6 Dynamic component, a, N/m^ X 10'' 0.15 0.20 0.30 Coefficient, 0

Conclusions The experimental technique presented in this paper can be employed to determine the relationship of rate of loading on the undrained strength of a clay. Since the undrained strength under dynamic load is always larger than the undrained strength under static load, dynamic testing procedure must be employed to determine the undrained strength and strain-rate relationship. For strain-rate less than 15 rad/s performed in this study, the undrained strength and strain-rate relation has been shown to be expressible in the form (Eq 6): S = So + a{l - e-^y) The study also shows that the ratio of the ultimate dynamic strength and the static strength, 5„,/5„, increases with dry density. Acknowledgments This research was sponsored by National Aeronautics and Space Administration Grant No. NGL47-003-012. The author is grateful for this support. References |/1 Cheng, R. Y. K., "The Effect of Shearing Strain-Rate on the Ultimate Shearing Resistance of Clay," NASA CR-2634, National Aeronautics and Space Administration, Feb. 1976. [2] Geuze, E. C. W. A. and Tan, T. K., "The Mechanical Behavior of Clays," Proceedings. 2nd International Congress of Rheology, 1954. [3] Saada, A. S. and Ou, C. D., Journal of the Soils Mechanics and Foundations Division. American Society of Civil Engineen, Vol. 99, No. SM12, Dec. 1973. [4] Timoshenko, S. P. and Gere, J. M., Mechanics of Materials, Van Nostrand Reinhold, New York, 1972. [5] Crenshaw, B. M., Butterworth, C. K., and Truesdale, W. B., "Aircraft Landing Gear Dynamic Loads from Operation on Clay and Sandy Soil," AFFDL-TR-69-51, U.S. Air Force, Feb. 1971. |6] Carroll, W. F., "Vertical Displacements of Spread Footings on Clay, Static and Impulsive Loadings," TR No. 3-599, Report 5, U.S. Army Engineers, Waterways Experiment Station, Sept. 1963.

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D. C. Koutsoftas^

Undrained Shear Behavior of a Marine Clay

REFERENCE: Koutsoftas, D. C., "Undrained Shear Behavior of a Marine Clay," Laboratory Shear Strength of Soil. ASTM STP 740. R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 254-276. ABSTRACT: A comprehensive series of undrained shear tests were performed on a lean sensitive marine clay in both the normally consolidated and overconsolidated state. The types of tests performed included triaxial compression and extension and direct simple shear tests on /fo-consolidated specimens. It was found that the clay is highly anisotropic with respect to its undrained shear strength and its stress-strain characteristics. Undrained shear strengths from compression tests were 1.7 to 1.8 times greater than from extension tests. Undrained strengths from direct simple shear tests were somewhat higher than the strengths from extension tests. Similar anisotropic behavior was also observed for undrained moduli. Failure strains were found to be influenced by the stress system during consolidation and the mode of shear. A'Q-consolidated specimens sheared in compression failed at extremely low strains and showed significant strain softening. The importance of these observations as they may relate to problems of undrained stability is discussed. KEY WORDS: anisotropy, compression, direct simple shear, extension, KQ consolidation, overconsolidation ratio, stress-strain behavior, undrained moduli, undrained shear strength

Nomenclature Types of Tests Undrained triaxial compression test with /Co-consolidation and measurement of excess pore water pressures during shear CA^oUE Undrained triaxial extension test with /Co-consolidation and measurement of excess pore water pressures during shear CAOUDSS Undrained direct simple shear test with /iLo-consolidation and measurement of excess pore water pressures during shear Prefix A indicates a change in a given quantity. CKQVC

'Senior engineer. Dames & Moore, Park Ridge, III. 60068.

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KOUTSOFTAS ON UNDRAINED SHEAR BEHAVIOR OF MARINE CLAY

Other A Af c £•„ Euso ESP Ip, PI /Co K, OCR p

q qf Su S„{H) 5„(V) w„ Wf w/ Wp 7 jf AM e

255

Symbols Skempton's/4-parameter = (Aw — Aai)/(,Aai — Aa^) /4-parameter at failure, that is, at ((Ji — (J3)max Effective cohesion intercept Undrained Young's modulus Undrained Young's modulus determined at a shear stress equal to one half the undrained shear strength Effective stress path Plasticity index Coefficient of earth pressure at rest, CTA/CTV SAHVSAV) Overconsolidation ratio '/2 (ff, + CT3)

V2 (ffi — 03) = shear stress '/2 (ai — 03) at failure Undrained shear strength Undrained shear strength from extension test Undrained shear strength from compression test Natural water content Water content at failure Liquid limit Plastic limit Shear strain Shear strain at failure Excess pore water pressure Axial strain

€y Pi a^ ffvm ^vmax

Axial strain at failure Initial settlement Vertical effective stress during consolidation Maximum past pressure determined from consolidation tests Maximum vertical consolidation stress applied to a test specimen in the triaxial apparatus oi Major principal stress oj Minor principal stress ffi Major principal effective stress 03 Minor principal effective stress a/, Horizontal effective stress CTv Vertical effective stress Ti, Horizontal shear stress Effective friction angle ksf Kips per square foot tsf Tons-force per square foot

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256

LABORATORY SHEAR STRENGTH OF SOIL

Recent experimental studies [1-12]^ have established that many soft clays exhibit anisotropic characteristics with respect to their undrained shear behavior. Recognizing the importance of strength anisotropy in problems of stability on soft ground, Bjerrum [13], Davis and Christian [14], and Ladd et al [3], among others, suggested that undrained shear strengths be obtained from tests which simulate the appropriate mode of shear under different portions of a foundation. Figure 1 demonstrates with an example the appropriate shear tests required to establish undrained shear strengths for evaluating the stability of an embankment on soft ground. Ladd et al [3] pointed out that soil anisotropy has two components, one being inherent anisotropy reflecting the depositional characteristics of the soil and the other being a stress system induced component whenever the coefficient of earth pressure at rest (KQ) is not equal to unity. Hansen and Gibson [15] predicted theoretically that for truly isotropic materials (that is, when inherent anisotropy is absent) stress system induced anisotropy leads to different shear strengths under different modes of shear. This anisotropy results from the fact that different increments of shear stress are required to produce failure as the major principal stress at failure {aif) varies between the vertical and horizontal direction. In practice one is interested in the combined anisotropy. The investigation of combined anisotropy of clays, however, requires that the test specimens be consolidated under A'o-conditions. Most of the experimental research effort concerning the anisotropic behavior of clays has, so far, focused on the behavior of normally consolidated clays but even so, published data are rather limited. There is very little published information on the stress-strain-strength characteristics of overconsolidated clays which exhibit anisotropic behavior. Furthermore, such information as is available in the literature for overconsolidated clays has usually been obtained from tests on isotropically consolidated specimens or by using artificially sedimented clays, or both. Thus there is a need for information on the stress-strain-strength characteristics of overconsolidated clays from tests which correctly simulate the initial in situ stress conditions and which simulate the proper mode of shear under different portions of clay foundations. The purpose of this paper is to present the results of a comprehensive series of shear tests conducted on undisturbed samples of an overconsolidated, slightly sensitive, marine silty clay. Stress-strain-strength characteristics are presented from triaxial compression, extension, and direct simple shear tests performed on specimens consolidated under conditions of no lateral strain, that is, under A'o-conditions. The paper discusses the anisotropic characteristics of this clay over the range of overconsolidation ratios of one to ten, and points out similarities and differences in behavior with other clays for which published data are available.

^The italic numbers in brackets refer to the list of references appended to this paper.

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KOUTSOFTAS ON UNDRAINED SHEAR BEHAVIOR OF MARINE CLAY

257

//A^^^/y/-\^^v//^'•v/A^WA^v^A*y;'/>^V//^^W

EXTENSION TEST

DIRECT SIMPLE SHEAR TEST

COMPRESSION TEST

FIG. 1—Relevance of laboratory shear tests to shear strength in the field embankment on soft ground.

Experimental Program Material The soil was obtained from a site off the coast of New Jersey located approximately 8.7 km (10 miles) northeast of Atlantic City. Water depths were about 12.2 m (40 ft). All sampling and field testing operations were performed from a jacked-up platform which stood about 18.3 m (60 ft) above the ocean floor. Undisturbed samples were obtained with a 76-mm (3.0-in.) nominal diameter piston sampler from depths below mudline ranging from about 1.0 to 3.7 m (3 to 12 ft). The soil referred to as silty clay is an inorganic marine clay with liquid limits between 25 and 45 percent and a plasticity index of 18 ± 5 percent. The Atterberg limits plot slightly above the y4-line of the plasticity chart. In situ effective overburden stresses, ff^„, ranged from 9.6 to 71.9 kPa (200 to 1500 psf), while in situ maximum past pressures {a^„) ranged from 143.8 to 277.8 kPa (3000 to 5800 psf). In situ overconsolidation ratios (OCRs) were between 5 and 9, with occasional values up to 20 for soil close to the ground surface. Most of the tests reported herein were performed on specimens whose in situ OCRs were between 5 and 10. Natural water contents were 32 ± 8 percent and typically were at about the liquid limit plus or minus three to four percent. Sensitivity ranged between 5 and 10. Koutsoftas and Fischer [16] provide detailed information on the stress history and in situ undrained shear behavior of this soil. Test Program All tests reported herein were performed on undisturbed specimens reconsolidated in the laboratory to obtain normally consolidated and overconCopyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

258

LABORATORY SHEAR STRENGTH OF SOIL

solidated specimens with known overconsolidation ratios, as recommended by Ladd and Foott [17]. The following types of tests were performed as part of this investigation: 1. Ko-consolidated undrained triaxial compression tests with pore water pressure measurements (C/CQUC)—/Co-consolidation was achieved by applying the loads in very small increments [approximately 12 kPa (0.25 kSF) per increment]. Axial and volumetric deformations were continuously monitored and the axial or lateral stresses adjusted as required to maintain zero lateral strain. All specimens were sheared at a strain rate of 0.5 percent per hour, by increasing the axial stress while maintaining the lateral stress constant. 2. K()-consolidated undrained triaxial extension tests with pore water pressure measurements (C/CQUE)—Consolidation was performed as described above for the C/TQUC tests. The specimens were sheared at a constant rate of strain of 0.5 percent per hour by decreasing the axial stress while the lateral stress was maintained constant. 3. Ko-consolidated undrained direct simple shear tests {CKQVDSS)—The tests were performed in accordance with the procedures outlined by Bjerrum and Landva [18]. The specimens were sheared at a constant shear strain rate of 5 percent per hour. /iTo-consolidation in the triaxial apparatus is a difficult and time-consuming process. The variation of the coefficient of earth pressure at rest, A"o, with overconsolidation ratio was known prior to the initiation of the C/iLoU-triaxial tests, from the results of consolidation tests performed in a special odometer which has the capability of measuring the lateral stresses during consolidation. Figure 2a shows the variation of KQ with OCR from two tests and compares the data with previous correlations reported by Brooker and Ireland [19] for clays of similar plasticity. This information was very valuable in guiding the selection of initial stress increments. However, the final stresses at each consolidation stress increment were determined on the basis of the axial and volumetric deformations measured during the test to assure no lateral strain. Figure 2b shows the variation of KQ with overconsolidation ratio obtained during /iCo-consolidation in the triaxial apparatus. Again the data compare well with the estimated ATo-values based on the Brooker and Ireland [19] correlations, and are very close to the KQ-dat& obtained from the special odometer tests. One of the difficulties in selecting appropriate consolidation stresses to take the test specimens into the virgin compression range (as recommended by Ladd and Foott [17]) relates to the fact that the specimens may undergo large volumetric and shear strains during consolidation, which may destroy the basic structure of the soil. This problem was minimized by using very small stress increments during the consolidation process and allowing approximately one day between stress increments, during which time aging of the specimen would take place and the interparticle bonds would become relatively stabilized.

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KOUTSOFTAS ON UNDRAINED SHEAR BEHAVIOR OF MARINE C U Y

it.U SVMIOL

i

Ott Gl 1.9

(fii

Wj.

1»

32.5

3« 37

IS

32.1

259

16

O K N SYMMLS ARC FDR FIRST UNLOADINC CYCLE CLOSED SYMMLS ARE FOR SECOND UNLOADINC CYCLE

w @ X

1.0

^

3 ^"-INTERPOLATED FROM •ROOKCR

•

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O 111

1

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^

• ,i 1 — U.9 1

^

* T

^

u

(K,)K' (K,)M>OCR"

w o u

• •0.42 TO 0.41 (K»>»e'O.S TO 0.93 1

0

2

3

4

9

6

7

8 9 n

OVEKCONSOLIDATION RATIO, 9v max / 7ve

(a) FROM SPECIAL OEDOMETER TEST

<

I \

X

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z

t Ul

ou I

2

3

4

9

6

7

S

9

I

0

OVERCONSOLIOATION RATIO, 7vMax^'*e

(b) FROM CK^DC TESTS FIG. 2—Coefficient

of earth pressure at rest (Kg/ versus OCR.

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260

LABORATORY SHEAR STRENGTH OF SOIL

Typically, the time required for consolidation using this procedure varied from 8 to 12 days. The last stress increment, at the maximum consolidation stress, was maintained for 3 to 5 days so that sufficient secondary compression could take place. Since the specimens were consolidated under ATo-conditions, the consolidation process in the laboratory was in essence an extension of the in situ consolidation process. Therefore it should not be expected to cause any abrupt changes in soil structure. It is recognized, however, that the water content decreased during the consolidation process by 8 ± 3 percent, and thus the soil might have become less sensitive than it otherwise would be in its in situ state. The extremely low failure strains and the large strain softening exhibited by the normally consolidated specimens (as described later) support the belief that the interparticle structure of the test specimens was not damaged by the consolidation process. Had the soil structure been altered significantly during the consolidation process it would have been detected by the development of large failure strains and by not exhibiting strain softening to the degree that it did in compression tests. Thus the test results seem to indicate that the consolidation procedure selected for this testing program was appropriate.

Test Results Stress-Strain Characteristics The stress-strain plots presented herein are normalized in the sense that the deviator stress (for triaxial tests) and the horizontal shear stress (for direct simple shear tests) are divided by the pre-shear vertical consolidation stress (a^). Figure 3 presents normalized stress-strain relations from C/CoU-compression tests. Data are shown for normally consolidated specimens and for overconsolidated specimens with overconsolidation ratios up to 11. Figure 4 shows normalized stress-strain relations from C/iToU-extension tests, for OCRs ranging from one to eight. Figure 5 presents normalized stress-strain relations from C/iToU-direct simple shear tests. Data are shown for normally consolidated specimens and for overconsolidated specimens with overconsolidation ratios up to 11. Visual examination of the data shown in Figs. 3 to 5 leads to the following observations: 1. The specimens tested in compression fail at very low axial strains especially at low overconsolidation ratios. The failure strains increase with increasing overconsolidation ratio as shown in Fig. 6, which plots shear strains versus OCR. For those specimens tested in extension or direct simple shear, failure

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KOUTSOFTAS ON UNDRAINED SHEAR BEHAVIOR OF MARINE CLAY

0.8

1

1

1 0.6

e

^

Q

1 WL

IWHOt.

T$F 34.4

no 2U

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261

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19 20 AXIAL STRMN, £a,X

29

30

(a) NORMALLY CONSOLIDATED SPECIMENS

9

10

19

20

29

30

AXIAL STRAlN.to , % (b) OVERCONSOLIDATEO SPECIMENS FIG. 3—Stress-strain relations from CK„UC tests (I tsf = 96 kPa).

takes place at large strains, usually above 7 percent. It should be noted that shear strains from triaxial tests are taken as 1.5 times the measured axial strains. 2. The normally consolidated specimens tested in compression show significant strain softening after the peak deviator stress is reached. Some strain

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262

LABORATORY SHEAR STRENGTH OF SOIL

'b* S

0 12 16 AXIAL STRAIN (%) in EXTENSION FIG. ^—Stress-strain relations from CKgUE tests II tsf = 96 kPa).

softening is also seen in the overconsolidated specimens; however, it is much smaller than for the normally consolidated specimens. The specimens tested in extension or direct simple shear show no strain softening within the strain range of interest for most practical cases (less than 10 percent). These observations are very important in the selection of appropriate shear strengths to be used in stability computations. Henkel [20] and Johnson [21] pointed out that strain compatibility along a potential failure surface must be considered and that the shear strengths selected for stability analyses must correspond to the shear strain levels developed within the foundation along the potential failure surface.

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KOUTSOFTAS ON UNDRAINED SHEAR BEHAVIOR OF MARINE CLAY

263

0.3

(0 (0 bJ K t(O

0.2 u

X M

un uf

WL (tip

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2.4

4.096

2.05

4.'I27

2.06

^—

15 20 SHEAR STRAIN, / ' , %

TSF

25

30

(a) NORMALLY CONSOLIDATED SPECIMENS

2.0

•

^^.-0CR=II.7

I :

-A.

-A——^—

19

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as

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4.07

-l.t

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r^ " 0

5

10

IS

20

25

30

SHEAR STRAIN, If ,% (b) OVERCONSOLIOATEO

SPECIMENS

FIG. 5—Normalized stress-strain relations from CKQUDSS

tests (I tsf = 96 kPa).

Undrained Shear Strength Ratios The stress-strain data presented in Figs. 3 to 5 show that the normalized undrained shear strength ratios, S^/o^^, increase with increasing overconsolidation ratio. This is true for all three types of tests. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

264

LABORATORY SHEAR STRENGTH OF SOIL

ID U

<

E m

Z

3

OVERCONSOUIDATION

4

5

6

7

8

9

10

RATIO, OCR ^ OVnKK/OVc

FIG. 6—Failure strains versus OCR.

Figure 7 shows the variation of S^fo^^ with the logarithm of overconsoiidation ratio. Data are shown from compression, extension, and direct simple shear tests. The normalized undrained shear strength ratios are highest for the compression tests and lowest for the extension tests. The results of direct simple shear tests fall between the strength ratios from compression and extension. This observation shows that the silty clay exhibits anisotropic behavior induced by the reorientation of principal stress directions during shear. This is clearly demonstrated in Fig. 8, which plots normalized strength ratios as a function of the angle of rotation of principal planes for various OCRs. The trends shown in Fig. 8 are very similar to the data presented by Soydemir [5] and by Koutsoftas and Fischer [22]. The lower portion of Fig. 7 shows K^, the ratio of normalized strengths in^xtension, Su{H)/a„, to normalized strengths from compression tests, 5'„{v)/ffvc > as a function of overconsolidation ratio. In these expressions, 5„(/f) and 5'„(v) are the undrained shear strengths with the major principal stresses in the horizontal and vertical directions, respectively, and a^^ is the vertical consolidation stress used in the test. The anisotropic strength ratio, K^. is approx-

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KOUTSOFTAS ON UNDRAINED SHEAR BEHAVIOR OF MARINE CLAY

IV?

2.0

o z

/%

UJ

oc

265

1.5

(O

CKQUC testsO)^

a:

<

111 X OT O

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(A)

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z < IT

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/

/• 0 325 Averos * of 3 test*

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0.5

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^ ! = = ^ ^

z

0.23 Avwag* of 3 tests

[^—0.175 Avarog t of 2 tests 1

3

4

3

4

5

6

7

8

9

10

9

10

1.0

0.5

I

2

5

6

7

8

OVERCONSOLIDATION RATIO, 0CR= ^ m o x / ^ , ; FIG. 1—Normalized undrained shear strengths and K, versus OCR.

imately constant within the range of OCRs of 1 to 10. This also demonstrates that the silty clay is anisotropic not only in the normally consolidated state but also in the overconsolidated state. K^ remained constant with increasing OCR. However, Ladd et al [3] presented K^ ratios for two other clays and showed that K^ was increasing with increasing OCR. Figure 9 presents the relative increase in undrained shear strength ratios with increasing overconsolidation ratio. In this figure, the normalized shear strength ratio at a particular overconsolidation ratio, (5'„/avc)oc' 's divided by the corresponding normalized shear strength ratio for the normally con-

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266

LABORATORY SHEAR STRENGTH OF SOIL

0

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ANGLE OF ROTATION OF PRINCIPAL PLANES, DEGREES FIG. 8—Undrained shear strength ratios as a function of reorientation of principal planes and OCR.

solidated soil, (5„/ff„c)Hc- The data from all three types of tests fall within a narrow range. The relationship between the ratio of normalized strengths and overconsolidation ratio may be described as suggested by Ladd et al [3] by an equation of the form OCR"

(1)

where w is a dimensionless coefficient. For the data shown in Fig. 9 the value of TO varies from 0.80 to 0.85. It is interesting to note that Ladd et al [3] reported w-values ranging from 0.75 to 0.85 from direct simple shear tests on five other clays. Effective Stress Behavior Figure 10 presents normalized effective stress paths (ESP) from CKQUcompression and C/LoU-extension tests. Figure 11 presents normalized ef-

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KOUTSOFTAS ON UNDRAINED SHEAR BEHAVIOR OF MARINE CLAY

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fective stress paths from direct simple shear tests. Examination of the effective stress paths leads to the following observations: 1. At failure, the normally consolidated specimen tested in compression showed a slight reduction in average effective stress, p = Vi (aj + 03), while the overconsolidated specimens showed a significant increase in average effective stress. The increase in effective stress becomes more pronounced as the overconsolidation ratio increases. This increase in effective stress during shear is mainly responsible for the increase in 5„/a^ ratio as the overconsolidation ratio increases. 2. During shear, normally consolidated specimens tested in extension showed a dramatic reduction in average effective stress, which explains the low Su/Oyc- As the overconsolidation ratio increases, the reduction in effecCopyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

268

LABORATORY SHEAR STRENGTH OF SOIL

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KOUTSOFTAS ON UNDRAINED SHEAR BEHAVIOR OF MARINE CLAY

269

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270

LABORATORY SHEAR STRENGTH OF SOIL

tive stress becomes smaller. Eventually at OCRs greater than two there is an increase in effective stresses during shear which again is the reason for the observed increase in S^/'o^c with increasing overconsolidation ratio. The same general behavior is also seen from the results of the direct simple shear tests. Effective stress envelopes in compression and extension are shown in Fig. 12. For compression tests, the envelope at maximum obliquity is best represented by a straight line with a small cohesion intercept. The effective stress envelope at maximum shear stress appears to be curved. For the extension tests a single straight line envelope passing through the origin fits the test data adequately, both at maximum obliquity and at maximum shear stress. The pore pressure coefficients at failure {Aj) are plotted versus overconsolidation ratio in Fig. 13. The pore pressure coefficients in extension are greater than the corresponding values from compression tests. Ladd et al [3] reported similar behavior for two other clays. It is important to note that the pore pressure coefficients remained positive even for OCRs up to 10. This behavior is in agreement with the data presented by Ladd et al [3] and by Nakase and Kobayashi [23]. It differs significantly, however, from previously published correlations established from triaxial compression tests performed on isotropically consolidated specimens. Data presented by Bishop and Henkel [24] and Duncan and Seed [9,10] showed that Aj becomes zero at about OCR of 4 and becomes negative at greater OCRs. Nakase and Kobayashi [23] compared Ay-factors from tests on isotropically consolidated and /Co-consolidated specimens. They found that >lj-factors from isotropically consolidated specimens became negative at OCRs greater than 8, while Af factors from /Co-consolidated specimens remained positive for OCRs even greater than 10. This difference in pore pressure behavior is significant and would have an important influence on predictions of pore pressures. Another important characteristic related to pore pressure generation during shear is the fact that the specimens tested in C/iToU-compression showed a large increase in positive excess pore pressure after the peak deviator stress was reached. This observation could be very important in the prediction of pore pressures in a foundation when a limited yielded zone develops as can occur at high factors of safety as described by D'Appolonia et al [25].

Undrained Moduli Table 1 summarizes undrained Young's secant moduli at an incremental shear stress level of one half of the incremental shear stress required to reach failure. At corresponding overconsolidation ratios the secant moduli in compression are two to three times greater than the moduli in extension. This im-

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KOUTSOFTAS ON UNDRAINED SHEAR BEHAVIOR OF MARINE CLAY

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plies that the silty clay is also quite anisotropic with respect to its stress-strain characteristics. Figure 14 plots normalized Young's moduli, EJS^, as a function of overconsolidation ratio for the three types of tests. The moduli were determined at an incremental shear stress level of one half of the incremental shear stress at failure. Normalized moduli, E^/Su, are often used on an empirical basis [see D'Appolonia et al [25] for estimating E^ of clays for predicting initial settlements iPi)]. The normalized moduli from compression tests are the highest, while the normalized moduli from extension and direct simple shear tests are quite close at OCRs above two. Figure 15 shows a plot of normalized Young's moduli versus overconsolidation ratio, but the moduli are normalized with respect to the preshear vertical effective stress rather than S„. The advantage of this type of plot is that it shows much more clearly the soil anisotropy with respect to moduli. It should be noted that the specimens which were tested in compression and extension were consolidated to maximum vertical stresses ranging between 479 to 574.8 kPa (10 to 12 kSF) and therefore specimens with the same OCR had similar preshear vertical consolidation stresses. Thus, when the normalized moduli from compression and extension tests are compared at the same OCR, the comparison reflects realistic differences in moduli since the vertical effective stresses would be approximately the same.

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KOUTSOFTAS ON UNDRAINED SHEAR BEHAVIOR OF MARINE CLAY

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274

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OVERCONSOLIDATION RATIO, Oymox/^vc FIG. 14—Normalized Young's moduli versus OCR from CKgUC tests on the silty clay.

Conclusions The results of a comprehensive series of undrained shear tests on KQ-COTIsolidated specimens of the silty clay lead to the following conclusions: 1. The silty clay is highly anisotropic with respect to its undrained shear strength behavior. The strengths from extension tests are only 55 to 60 percent of the strengths in compression. Direct simple shear tests gave strengths midway between the compression and extension strengths. 2. The normalized undrained strength ratios increase with increasing OCR primarily because overconsolidated specimens show significant increase in effective stress during shearing, while normally consolidated specimens show a decrease in effective stresses. 3. The silty clay is also quite anisotropic with respect to its stress-strain characteristics. Undrained moduli from compression tests are two to three times greater than moduli determined from extension tests at corresponding incremental shear-stress levels and OCRs. Direct simple shear tests gave undrained moduli which for normally consolidated specimens were slightly lower than the moduli determined from extension tests, while for overconsolidated specimens were slightly higher than corresponding values from extension tests. 4. Strains at failure were very small in compression particularly for normally consolidated specimens being on the order of 0.6 percent. However, failure in direct simple shear tests and triaxial extension tests takes place at large strains, typically greater than 7 percent. Normally consolidated specimens exhibit significant strain softening after the peak shear stress is reached in compression. Overconsolidated specimens also showed strain softening in compression although not as pronounced as for Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

KOUTSOFTAS ON UNDRAINED SHEAR BEHAVIOR OF MARINE CLAY

275

600

2

3

4

9

6

7

8

9

10

19

OVERCONSOLIDATION RATIO, OCR FIG. IS—Normalized Young's modulus versus OCR from CKQUC tests.

normally consolidated specimens. Direct simple shear tests and extension tests showed no tendency for strain softening. The strain softening coupled with the large discrepancy of failure strains under different modes of shear points out that the selection of design shear strengths must satisfy the requirement for strain compatibility along potential failure surfaces. 5. Pore pressure coefficients at failure, Af, were higher from extension tests than from compression tests. Furthermore, /l^-factors were positive within the range of overconsolidation ratios of 1 to 11. Acknowledgments The author acknowledges with appreciation the contribution of R. S. Ladd of Woodward-Clyde Consultants who supervised the triaxial extension tests. The triaxial compression tests were performed under the supervision of Walter Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

276

LABORATORY SHEAR STRENGTH OF SOIL

Jaworski of Goldberg Zoino and Associates. A number of compression tests were also performed by Geotechnical Engineers Inc., under the supervision of Gonzalo Castro. The direct simple shear tests were performed at MIT under the supervision of C. C. Ladd, who also kindly reviewed the paper and offered many useful suggestions. Dames & Moore provided financial assistance for the preparation of this paper. Colleague J. A. Fischer is acknowledged for his encouragement and constructive criticism as Principal-in-Charge for the project. R. R. Rumpf assisted with the evaluation of the test results. References [/] Bjerrum, L. in Proceedings, 8th International Conference on Soil Mechanics and Foundation Engineering (ICSMFE), Moscow, 1973, Vol. 3, pp. 109-159. [2] Ladd, C. C. in Proceedings, 8th ICSMFE, Moscow, 1973, Vol. 4.2, pp. 108-115. [3] Ladd, C. C , Foott, R., Ishihara, K., Poulos, H. G., and Schlosser, F. in Proceedings, 9th ICSMFE, Tokyo, 1977, Vol. 2, pp. 421-494. [4] Soydemir, C , "Strength Anisotropy Observed Through Simple Shear Tests," Laurits Bjerrum Memorial Volume. 1976, pp. 99-113. |5] Soydemir, C , Journal of the Geotechnical Engineering Division. American Society of Civil Engineers (ASCE), Vol'. 103, No. GT4, 1977, pp. 360-361. [6] Bishop, A. W. and Wesley, L. D., Geotechnique. Vol. 25, No. 4, 1975, pp. 657-670. [7] Vaid, Y. P. and Campanella. R. G., Journal of the Geotechnial Engineering Division. ASCE, Vol. 100, No. GT3, 1974, pp. 207-224. [8] Caincross, A. M. and James, R. G., Geotechnique. Vol. 27, No. 1, 1977, pp. 31-36. [9| Duncan, J. M. and Seed, H. B., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 92, No. SMS, 1966, pp. 21-50. [10] Duncan, J. M. and Seed. H. B., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 92, No. SM6, 1966. pp. 81-104. [//] Henkel, D. J. and Wade, N. H., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 92, No. SM6, 1966, pp. 67-80. [12] Amerasinghe. S. F. and Parry. R. H., Journal of the Geotechnical Engineering Division. ASCE, Vol. 101, No. GT12, Dec. 1975, pp. 1277-1293. [13] Bjerrum, L. in Proceedings, ASCE Specialty Conference on Performance of Earth and Earth-Supported Structures, Lafayette, Ind., 1972, Vol. II, pp. 1-54. ]14] Davis, E. H. and Christian, J. J., Journal oj the Soil Mechanics and Foundations Division. ASCE. Vol. 97, No. SMS, 1971, pp. 753-769. 1/5] Hansen, J. Brinch and Gibson, R. E., Geotechnique. Vol. 1, No. 3, 1949. pp. 189-204. [/61 Koutsoftas, D. C. and Fischer, J. A., Journal of the Geotechnical Engineering Division. ASCE, Vol. 102, No. GT9, Sept. 1976, pp. 989-1005. [17] Ladd, C. C. and Foott, R., Journal of the Geotechnial Engineering Division, ASCE, Vol. 100, N0.GT7, 1974, pp. 763-786. [IS] Bjerrum, L. and Landva, A., Geotechnique. Vol. 16. No. 1, 1966,, pp. 1-20. [19] Brooker, E. W. and Ireland, H. O., Canadian Geotechnical Journal. Vol. 2. No. 1, Feb. 1965, pp. 49-53. [201 Henkel, D. J. in Proceedings, ASCE Specialty Conference on Lateral Stresses and EarthRetaining Structures, Ithaca, N. Y., 1970, p. 1049. [21] Johnson, S. D. in Proceedings. ASCE Specialty Conference on Analysis and Design in Geotechnical Engineering, Austin, Tex.. 1975. Vol. II, p. 1048. ]22] Koutsoftas, D. C. and Fischer, J. A.. Journal of the Geotechnical Engineering Division. ASCE, Vol. 103. No. GT12, Dec. 1977, pp. 1462-1463. [23] Nakase, N. and Kobayashi, M. in Proceedings. 4th Asian Regional Conference, Bangkok, 1971, Vol. 1, pp. 147-150. [24] Bishop, A. W. and Henkel, D. J., The Measurement of Soil Properties in the Triaxial Test. 2nd ed., Edward Arnold, London, 1962. [251 D'Apolonia, D. J., Poulos, H. G., and Ladd, C. C., Journal of the Soil Mechanics and Foundations Division. Vol. 97, No. SMIO, 1971, pp. 1359-1377. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

C. W. Lovell^ and J. M. Johnson^

Shearing Behavior of Compacted Clay after Saturation

REFERENCE: Lovell, C. W. and Johnson, J. M., "Shearing Behavior of Compacted Ctoy alter Saturation," Laboratory Shear Strength of Soil. ASTM STP 740. R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 277-293. ABSTRACT: The purpose of this investigation was to ascertain the relationships among the compaction conditions (dry density moisture content and compaction energy) and the shearing behavior after saturation for a kneading compacted, highly plastic clay. The effective stress strength and pore pressure parameters were evaluated for various compaction conditions through the performance of consolidated undrained triaxial tests with pore water pressure measurement (CU) at a constant rate of strain. Long-term environmental effects were approximated prior to shear with backpressure saturation followed by consolidation to an isotropic state of stress representing the vertical load applied by succeeding lifts of an embankment. The results of the testing program showed that the effective stress friction angle is relatively invariate for the range of compaction conditions investigated. The magnitude and range of variation of the measured values of the effective stress strength intercept were small. However, the volumetric strain upon saturation and the values of Skempton's /1-parameter at failure were strongly affected by compaction conditions. Accordingly, the undrained strength of the compacted clay was significantly altered by the details of compaction. Statistical analyses were performed to construct prediction equations based on the compaction variables for percent volume change due to saturation and consolidation. Skempton's y4-parameter at failure, and the effective stress strength intercept. The equations obtained for percent volume change due to saturation and consolidation and Skempton's /4-parameter at failure indicate that as-compacted dry density, initial degree of saturation, and consolidation pressure are the critical variables influencing behavior. The equation for the effective stress strength intercept indicates that initial void ratio and compaction moisture content are the significant variables. These equations will aid efforts to predict and modify the long-term shear behavior of compacted cohesive soils. KEY WORDS; compaction, shear strength, effective stress, saturation, pore pressure parameters, statistical analyses

'Professor, School of Civil Engineering, Purdue University, W. Lafayette, Ind. 47906. ^Geotechnical engineer, Klohn-Leonoff Consultants, Inc., Denver, Colo. 55614.

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LABORATORY SHEAR STRENGTH OF SOIL

The extensive use of soil in highway embankments and earth dams is attributed to the satisfactory engineering properties which can be imparted to a soil mass through compaction. Compaction densifies the soil through the expulsion of pore air at constant moisture content and produces greater shear strength, lower compressibility, and lower permeability. The satisfactory performance of a compacted soil structure over the long term requires knowledge of the relationships among the compaction variables, which can be controlled during construction, and the engineering properties of the soil mass after loading and wetting. Compacted soil properties have received attention from distinguished researchers over several decades. However, this paper focuses on the relatively limited attention given to the development of statistically valid equations relating the compaction variables to the properties of the compacted soil. In this regard, DiBemardo [1]^ studies the compressibility of laboratory compacted Saint Croix clay (CH) in its as-compacted condition and after saturation under load. The ascompacted shear behavior of Saint Croix clay under various confining pressures was studied by Weitzel [2]. The shear behavior of laboratory compacted Saint Croix clay after saturation and consolidation under various confining pressures was the subject of the research discussed in this paper. Parameters for the long-term analysis of embankment stability were obtained from samples tested in the consolidated undrained mode with pore water pressure measurements (CU). The samples were formed in the laboratory with a kneading compactor and were later trimmed to the desired dimensions. Prior to shear they were back pressure saturated and consolidated under isotropic states of stress which approximated the loading applied by succeeding lifts of an embankment. The ultimate purpose of this testing program was the development of statistically valid prediction equations for percent volume change due to saturation and consolidation (AV/VQ, %), Skempton's /4-parameter at failure (Af), and the effective stress parameters (c ' and <(>') based on the laboratory compaction variables. After completion of a similar study on field compacted samples, the prediction equations will be correlated with those obtained for the field compaction case. This correlation will provide the engineer with valuable understanding of how long-term shear behavior can be modified through appropriate specification of initial compaction. Background Fabric of Compacted Fine-Grained Soils Barden and Sides [3\ utilized scanning electron microscopy and a battery of soil behavior measurements to arrive at an aggregate model of compacted The italic numbers in brackets refer to the list of references appended to this paper.

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LOVELL AND JOHNSON ON SHEARING BEHAVIOR OF CLAY

279

soil fabric. Prior to compaction the packets of soil particles, or domains, were clustered into aggregates of visible and varying proportions. After compaction, a significant difference was observed at low magnifications between the fabrics of soil compacted somewhat wet and dry of the line of optimums. After compaction somewhat dry of the line of optimums, the distinct packets or domains were still visible with large pores intervening. However, for compaction wet of the line of optimums, the individual domains and pores were no longer visible. High magnification revealed no significant differences between the particle level fabrics of "wet" and "dry" samples. The authors postulated that moisture contents dry of optimum produce soil packets and aggregations with sufficient strength to resist distortion during compaction and leave large interaggregate pore spaces. Higher moisture contents weaken the packets and aggregations, allowing them to deform under load and reduce the volume of the large pores. Hodek [4] arrived at an aggregate model of compacted soil fabric independently of Harden and Sides. He verified his "deformable aggregate" model by first investigating the particle orientation and strength of kaolin aggregates of varying moisture content and size. He then investigated the compaction characteristics of the aggregates and the swell characteristics of the compacted samples. It is now generally concluded that aggregate models, like those cited above, provide an explanation of engineering behavior superior to that of the particle level model popular some 20 years ago [5].

Long-Term Behavior of Compacted Fine-Grained Materials Knowledge of the relationships between the compaction conditions (dry density, moisture content, and compaction energy) and the long-term volume change and strength behavior of compacted soils is potentially quite valuable. However, the published data are limited, particularly with respect to the formulation of statistical relations. Table 1 shows that the effective stress parameters (c', 0') are only slightly affected by compaction conditions. Abeyesekera et al [6] reached a similar conclusion for New Providence (Indiana) shale, although loosely placed shale had a decidedly reduced <> / '-value. Compacted shale samples with high initial void ratios displayed net volumetric compression after saturation and consolidation, while samples with low initial void ratios expanded. The variation in void ratio was therefore much smaller after saturation and consolidation than in the as-compacted condition. Abeyesekera [7] further found that pore pressures and the Skempton .4-factor were very much affected by the initial compaction variables and the confinement under which the compacted samples were saturated. An orderly arrangement of the data was apparent when the compaction pressure was interpreted as a potential prestressing value. Differences in

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280

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LOVELL AND JOHNSON ON SHEARING BEHAVIOR OF CLAY

281

pore pressure response were then explained in terms of an overconsolidation ratio analogy. Apparatus and Procedure The soil utilized in this study was obtained from the side of a knoll near Saint Croix, Indiana. The results of classification tests on the soil are shown in Table 2. X-ray diffraction analysis revealed that kaolinite is the predominent clay mineral and that traces of montmorillonite are also present [/]. The parent materials of this residual clay are believed to be sandstone and shale. An automatic kneading compactor of the type usually employed for bituminous mixes was utilized in this study to produce samples 101.6 mm (4.0 in.) in diameter and 116.8 mm (4.6 in.) high in a standard Proctor mold. Kneading-type compaction was chosen to approximate actual field compaction more closely than possible with either impact or static laboratory compaction. The soil was placed and compacted in the mold in five lifts of approximately equal thickness. Each lift was subjected to 30 tamps of the compaction foot. Kneading foot pressures were chosen to fit moisture content versus dry density relationships obtained from impact compaction tests at three energy levels. The highest energy level was the modified Proctor compaction test (AASHTO T 180-70) and the intermediate level was the standard Proctor compaction test (AASHTO T 99-70). The lowest energy level was obtained by running an impact-type compaction test with only fifteen blows on each of the three layers. A deviation from standard compaction procedures was the use of a new soil sample for each compaction point. After weighing the compacted sample and mold for a density determination, the sample was extruded from the compaction mold using a hydraulic jack. The extruded sample was then placed in a split mold which was tightened in preparation for sampling. Three samples were desired from each large sample of compacted soil. Sharpened, thin-walled stainless steel tubes were used exclusively for the high and intermediate density samples, as the soil strength was too great for wire saw trimming. The sampling tube dimensions, 81.3 mm (3.2 in.) long, 38.1 mm (1.5 in.) in outside diameter, and a wall thickness of 2.5 mm (0.098 in.), were determined on the basis of a two to TABLE 2—Classification test results for Saint Croix clay. Liquid limit, % Plastic limit, % Plasticity index, % Natural moisture content, % Specific gravity of solids Unified soil classification AASHTO soil classification

53 22 31 18 to 20 2.80 CH A-7-6

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282

LABORATORY SHEAR STRENGTH OF SOIL

one sample aspect ratio, with an excess for end trimming. The sampling procedure used for the high and intermediate density samples was found to be too strenuous for the low-density samples, as sample disturbance was evidenced by significant density increases during sampling. Wire saw trimming, commonly employed with soft clays, was found to be adequate for the low-density samples. The samples were cured for from one half to three days after compaction to minimize the effects of thixotropy on swell and consolidation [8,9]. The samples were wrapped with longitudinal filter paper drains to shorten the drainage path and accelerate backpressure saturation, consolidation, and pore pressure equalization [10].

Backpressure Saturation Total pressure supply was limited by the 1034 kPa (150 psi) capacity of the air compressor. Consolidation pressures of 69, 138, and 276 kPa (10, 20, and 40 psi) left 965, 896, and 758 kPa (140, 130, and 110 psi), respectively, available for backpressure. The procedure for simultaneously increasing the cell pressure and backpressure to achieve saturation without excessive cyclic loading of the samples is described by Lowe and Johnson [//]. Two methods of checking saturation, one quantitative and one qualitative, were employed during backpressuring. The quantitative method was the familiar B-parameter check [10], The qualitative check involved monitoring the water level in the backpressure line after closing the cell pressure line and increasing the backpressure [7,12].

Consolidation and Undrained Shear After saturation had been achieved, generally within 30 h, the back pressure was maintained constant while the cell pressure was increased to create a differential equal to the desired final consolidation pressure: 69, 138, 207, or 276 kPa (10, 20, 30, or 40 psi). The consolidation process was monitored by recording the amount of water flow from each sample until primary consolidation was complete and secondary compression was evidenced. Following consolidation the value to the back pressure line was closed and the sample was axially compressed at a constant rate of strain. Pore water pressures were measured with a single pressure transducer attached to the triaxial cell base. Axial compression was continued until slightly past the load peak or to 20 percent strain if no peak occurred. It was necessary to select a strain rate which allowed pore water pressure equalization throughout the sample volume. A deformation rate of 0.0635 mm (0.0025 in.)/min was chosen, which translates to approximately 0.09

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LOVELL AND JOHNSON ON SHEARING BEHAVIOR OF GUY

283

percent strain per minute. At this rate, 20 percent strain is achieved in 3.5 to 4h. Results and Discussion of Results Compaction The dry density versus moisture content relationships were determined from impact compaction tests at three levels of gross input energy. The test specifications for each energy level are listed in Table 3. To attain dry density values on the impact compaction curves for each moisture content by kneading compaction, it was necessary to experimentally vary the compaction foot pressure. Moisture contents ranged from 3 percent dry of optimum to 3 percent wet of optimum at each energy level, and effectively bracketed the practical range of compaction conditions. Each sample was assigned a name based on compaction conditions and consolidation pressure. Firstly, each sample was assigned a letter to signify to which dry density versus moisture content curve it corresponded. M, S, and L stood for modified Proctor, standard Proctor, and low-energy Proctor, respectively. Next, a D, O, or W was assigned to signify compaction dry, at, or wet of optimum, respectively. A number from 1 to 7 was then assigned to differentiate each sample from the others with the identical compaction conditions. Last of all, the consolidation pressure in kilopascals was enclosed in parentheses and placed after the first three symbols. For example, the first sample compacted dry of optimum on the modified Proctor curve and consolidated to 69 kPa would appear as MDl (69). Over 40 samples were compacted and tested. Volume Change Due to Saturation and Consolidation Lx)ng-term conditions within a compacted embankment include changes in void ratio from the as-compacted condition in response to wetting and the TABLE 3—Specifications for impact compaction tests.

Test Series

Volume of Mold, nr^ (ft^)

Height of Hammer Drop, mm (in.)

Modified Proctor Standard Proctor Low Energy Proctor

0.000944 (1/30) 0.000944 (1/30) 0.000944 (1/30)

457 (18) 305 (12) 305 (12)

Weight of Number Number Hammer, N of Blows (Ibf) per Layer of Layers 5 3 3

44.5 (10) 24.5 (5.5) 24.5 (5.5)

25 25 15

Gross Energy, kj m' (ft-lb/ft^) 2693 (56250) 594 (12400) 356 (7400)

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284

LABORATORY SHEAR STRENGTH OF SOIL

load imposed by succeeding lifts. The mechanisms by which the volume changes occur are consolidation, swell, and collapse. For this study, longterm conditions were approximated in the laboratory by back pressure saturation of the compacted samples prior to consolidation under an isotropic state of stress [13]. The volume changes which occur in response to wetting and loading are very important in terms of the successful long-term performance of the compacted embankment. Firstly, the settlement of the embankment due to internal compression must lie within the limits imposed by the design assumptions and acceptability criteria. Secondly, the strength of the soil at a given confining pressure is greatly altered by changes in void ratio and must be modified for use in stability analyses. Figure 1 shows for example, the saturated-consolidated responses obtained from only the optimum moisture content sample of this study. These 1850

1800

ZERO AIR VOIDa

1750 O COMPACTED CONDITION

E

1700

•

9

-

1650

(

SATURATED CONSOLIDATED CONDITION ) CONSOLIDATION . PRESSURE I k N / m ' )

«

Z UJ

o > o

1600

1550

1500

1450

10

12

14

16

18

20

22

MOISTURE CONTENT,

24

26

28

30

w(%)

FIG. 1—Moisture content and dry density values before and after saturation and consolidation (compaction wet of optimum moisture content).

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LOVELL AND JOHNSON ON SHEARING BEHAVIOR OF CLAY

285

samples exhibited either net swell or net compression, depending upon the consolidation pressure. Considering all samples, as the as-compacted void ratio increased (dry density decreased) for a given consolidation pressure, the percent volume change due to saturation and consolidation increased (less net swell or greater net compression). As expected, increases in consolidation pressure resulted in higher values of percent volume change (less net swell or greater net compression). For compaction conditions not susceptible to collapse, an increase in compaction moisture content resulted in an increase in percent volume change (less net swell or more net compression). Stress-Strain and Pore Water Pressure Response The stress versus strain and pore water pressure versus strain curves for samples compacted to standard Proctor dry densities at optimum are shown in Fig. 2. Seed and Chan [14] found that samples compacted to different initial conditions and saturated and consolidated to common values of dry density, moisture content, and consolidation pressure, failed at approximately the same principal stress difference. This conclusion was also valid for the data of this study [13]. Effective Stress Strength Parameters Examples of stress paths and failure envelopes are shown in Fig. 3 for standard Proctor optimum samples. The values of the effective stress strength parameters are shown for all the various compaction conditions in Table 4. The effective stress angles of friction measured in this study range from 18.9 to 21.4 deg. The effective stress strength intercept, c', ranged from 7 to 24 kPa. For a constant value of consolidation pressure, c ' increased as final void ratio decreased. Statistical Analysis Statistical relationships between dependent and independent variables were constructed through the use of linear regression analysis. The Statistical Package for the Social Sciences (SPSS) [15] provided the programs used to identify meaningful variables and utilize them in linear regression analyses. The procedures, as well as the criteria for statistical acceptance, are discussed in detail in Johnson [13]. Percent volume change due to saturation and consolidation (AV/V„, %), Skempton's/1-parameter at failure (/If), and the effective stress strength parameters (c' and 0') were treated as dependent variables. Since the hypothesis of this study stated that at least some of these dependent variables could be modified by the specifics of compaction, the independent variables are those of the initial rather than the final soil condition.

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286

LABORATORY SHEAR STRENGTH OF SOIL

AS03 (276) OS04 (239)

lit

m .00

.04

.08

.12

Axial Strain, c,

FIG. 2—CIU results—Tests SOI to S04.

Prediction Model for Volume Change Due to Saturation and Consolidation Equation 1 was the most satisfactory relationship produced for this dependent variable: AWV„ (%) = 28.48 - 0.0000136 pj2 + 0.0077

5,N/5V

(1)

where A V'/Vo(%) = estimated value of percent volume change due to saturation and consolidation, %, pj = as-compacted dry density, kg/m^,

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LOVELL AND JOHNSON ON SHEARING BEHAVIOR OF CLAY

287

Sj = initial degree of saturation, %, and a'c = isotropic consolidation pressure, IcPa. All statistical criteria were satisfied, including a coefficient of determination (/?2) of 0.95. (The criteria applied, in addition to the distribution of residuals, are shown by the example in Table 5). Figure 4 shows that for a constant value of saturation AV/V„ (%) decreases (more net swell or less net compression) as dry density increases. This is a result of the greater swell

DSOI (69) 250.0-

OS02 (1381 a S03 (276) OS04 (239)

200.0 • E z a

150.0cu

100.0tr

50.0

0.00.0

500

100.0

150.0

2000 p °

250 0 '

'

300.0

35O0

400.0

450.0

(kN/m')

FIG. 3—Effective stress paths—Tests SOI to S04.

TABLE 4—Measured values of the effective stress strength parameters.

Test Series

Effective Stress Strength Intercept (c'), kPa

Effective Stress Friction Angle (*'), deg

MDl (69) to MD4 (276) MOl (69) to M04 (69) MWl (85) to MW3 (276) MW4 (76) to MW6 (276) SDl (69) to SD3 (276) SD4(l38)toSD7(138) SOI (69) to S04 (239) SWl (69) to SW4 (138) LDl (69) to LD4 (69) LOl (69) to L03 (276) L04 (69) to L06 (276) LWl (69) to LW3 (276)

11 15 24 16 15 9 17 13 9 12 10 7

21.1 20.4 19.2 21.3 19.0 18.9 19.4 21.4 20.6 20.0 20.6 21.3

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288

LABORATORY SHEAR STRENGTH OF SOIL TABLE 5—Statistical data of the prediction equation for percent volume change due to saturation and consolidation, AV/Vp (%).

Statistical Criteria Coefficient of multiple determination {R^) Adjusted coefficient of multiple determination (R/) Overall f-test Partial f-test ""', 5,Va/ Coefficient of correlation (R) Coefficient of partial determination

rU^V/V,-p/S.^/^) rHA^/V„-Si^p/)

Value 0.95 0.95 412.49 674.39 155.39 0.01 0.94 0.89

"r^ (K • X| Xj) = coefficient of partial determination between Y and X, when X2 is in the equation.

potential of compacted fine-grained soils at higher densities. Figure 4 also shows that for constant values of dry density and initial degree of saturation, AV/V„ (%) increases (less net swell or more net compression) as consolidation pressure increases. Prediction Model for Skempton's k-Parameter at Failure—Equation 2 was the most satisfactory relationship produced during the statistical analysis oiAf. Af = 1.79 - 0.00011 Pd-JSi^ \2%a\/pa

(2)

where Af Pj 5, o\

— estimated value of Skempton's y4-parameter at failure, — as-compacted dry density, kg/m^, = initial degree of saturation, %, and — isotropic consolidation pressure, kPa.

The statistical data for this equation are all satisfactory, although the /?^-value of 0.71 is marginal. Figure 5 shows that for constant values of consolidation pressure and initial degree of saturation, Af decreases as dry density increases. Figure 5 also shows for constant values of consolidation pressure and as-compacted dry density that an increase in initial degree of saturation produces a decrease in Af. This trend can be attributed to the decreasing swell potential obtained with higher percent saturation. For two samples compacted to equal dry densities and unequal degrees of saturation, the one with the low degree of saturation will swell more (or compress less) for a given consolidation pressure and be more likely to compress during shear. It will therefore produce a higher value of A, than the sample compacted to a higher degree of saturation.

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LOVELL AND JOHNSON ON SHEARING BEHAVIOR OF CLAY

289

kN/m'-

1500

1550

1600

1650

1700

1750

1800

leso

DRY DENSITY. />,(kg/m*) FIG. 4—Prediction of percent volume change due to saturation and consolidation for an initial saturation of 80 percent.

1850 DRY DENSITY, /)^(kg/m') FIG. 5- -Prediction of Skempton s A-parameter at failure for a consolidation pressure of 170 kPa.

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290

LABORATORY SHEAR STRENGTH OF SOIL

Prediction Models for the Effective Stress Strength Parameters 4>' and c '—Equation 3 was the most satisfactory relationship produced during the analysis of (/>',
(3)

while Eq 4 was the most satisfactory one for c '. c ' = 1.71 — 3.83 w log e„

(4)

where c' = estimated value of the effective stress strength intercept, kPa, w — compaction moisture content, %, and e„ = initial void ratio. The statistical data for Eq 4 are satisfactory, although the /i^-value of 0.63 is marginal. Figure 6 shows that for a constant value of compaction moisture content, an increase in initial void ratio produces a decrease in c'. Figure 6 also shows for a constant value of initial void ratio that an increase in the compaction moisture content produces an increase in c'. This behavior can be attributed to the greater swell potential of the samples compacted to the lower compaction moisture contents. As the compaction moisture content increases, the final void ratio attained for a given consolidation pressure decreases. A lower void ratio implies a higher overconsolidation ratio or a higher maximum past pressure and a higher value of c'.

13

14

15

16

17

IB

19

20

21

22

23

24

25

26

27

COMPACTION MOISTURE CONTENT, w(%) FIG. 6—Prediction of effective stress strength paramter c'.

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LOVELL AND JOHNSON ON SHEARING BEHAVIOR OF CLAY

291

Conclusions Based upon the laboratory studies reported herein, the following principal conclusions were reached: (1) The long-term volume change behavior of compacted Saint Croix clay is largely a function of the swell potential of its as-compacted condition, with depth of overburden (consolidation pressure) exerting a large but secondary influence. This is borne out by the following trends: (a) An increase in as-compacted dry density (p^) for constant values of initial degree of saturation (5,) and consolidation pressure (a \) produces a decrease in percent volume change (AV/VQ, %) due to saturation and consolidation (more net swell or less net compression). (b) With the exception of two collapse-prone compaction conditions, an increase in the value of 5, for constant values of pj and a \ produces an increase in AV/V„ (%). These trends show agreement with the results of swell tests presented by Holtz and Gibbs [16] and Parcher and Liu [77]. (2) Skempton's/4-parameter at failure {Af) is largely a function of the final void ratio (ej) attained with the selected consolidation pressure, and is probably related to the degree of overconsolidation produced by compaction. Since cy is a function of the percent volume change due to saturation and consolidation (AV/V(,, %}, Aj is greatly affected by the swell potential of the ascompacted condition. The following trends were observed: (a) A decrease in the initial void ratio (e,,) for constant values of initial degree of saturation {S,) and consolidation pressure ('. for the range of compaction conditions investigated for the Saint Croix clay, is essentially a constant value with an average of 20.1 deg and a range of ± 1.3 deg. (4) The effective stress strength intercept, c', is largely a function of the final void ratio (ej) attained with a selected consolidation pressure, and is probably related to overconsolidation ratio and the maximum past pressure created in the soil by compaction. Since ej is a function of the percent volume change due to saturation and consolidation, c', is greatly affected by the swell potential of the as-compacted condition. (5) Equations 1, 2, and 4, obtained through the use of linear regression

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292

LABORATORY SHEAR STRENGTH OF SOIL

analysis, were determined to be the best predictive equations for volume change due to saturation and consolidation, Skempton's y4-parameter at failure, and the effective stress strength intercept. They are, of course, restricted to the data combinations experimentally examined by Johnson

im. Acknowledgments The Indiana State Highway Commission and the Federal Highway Administration provided the financial support for this study. The Joint Highway Research Project, Purdue University, W. Lafayette, Indiana, administered the project. References l/j DiBernardo, A., "The Effect of Laboratory Compaction on the Compressibility of a Compacted Highly Plastic Clay," MSCE thesis, Purdue University, W. Lafayette. Ind. May 1979; also Joint Highway Research Project Report No. 79-3. \2] Weitzel, D. W., "The Effect of Laboratory Compaction on the Unconsolidated-Undrained Strength Behavior of a Highly Plastic Clay," MSCE thesis, Purdue University, W. Lafayette, Ind., August 1979; also Joint Highway Research Project Report No. 79-11. [3] Barden, L. and Sides, G. R., Journal of the Soil Mechanics and Foundations Division, American Society of Civil Engineers [hereafter cited as ASCE], Vol. 96, No. SM4, 1970, pp. 1171-1200. [4] Hodek, R. J., "Mechanism for the Compaction and Response of Kaolinite," Ph.D. thesis, Purdue University, W. Lafayette, Ind., Dec. 1972; also Joint Highway Research Project Report No. 72-36. [5] Lambe, T. W., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 84, No. SM2, 1958, pp. 16S4-1 to 1654-33. [6] Abeyesekera, R. A., Lovell, C. W., and Wood, L. E., "Stress-Deformation and Strength Characteristics of a Compacted Shale," Papers of the Conference on Clay Fills, Institution of Civil Engineers, London, England, Nov. 1978, pp. 1-14. [7] Abeyesekera, R. A., "Stress Deformation and Strength Characteristics of a Compacted Shale," Ph.D. thesis, Purdue University, W. Lafayette, Ind., May 1978; also Joint Highway Research Project Report No. 77-24. [8] Seed, H. B. and Chan, C. K., "The Thixotropic Characteristics of Compacted Clays," Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 83, No. SM4, 1957. pp. 1427-1435. 19] Gray. D. H. and Kashmeeri, N. A., "Thixotropic Behavior of Compacted C\ay%," Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 97, No. SMI, 1971, pp. 193-207. [10] Bishop, A. W. and Henkel, D. J., The Measurement of Soil Properties in the Triaxial Test. 2nd ed., Edward Arnold, London, 1962. [//] Lowe, J. and Johnson, T. C , "Use of Back Pressure to Increase Degree of Saturation of Triaxial Test Specimens," Research Conference on Shear Strength of Cohesive Soils, ASCE, Boulder, Colo., 1960, pp. 819-836. [12] Lee, K. L., Morrison, R. A., and Haley, S. C. in Proceedings. Seventh International Conference on Soil Mechanics and Foundation Engineering, Mexico, 1969. Vol. 1, pp. 231-238. [13] Johnson, J. M., "The Effect of Laboratory Compaction on the Shear Behavior of a Highly Plastic Clay after Saturation and Consolidation," MSCE thesis, Purdue University, W. Lafayette, Ind., August 1979; also Joint Highway Research Project Report No. 79-7.

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LOVELL AND JOHNSON ON SHEARING BEHAVIOR OF CLAY

293

[14] Seed, H. B. and Chan, C. K., Journal of the Soil Mechanics and Foundations Division. ASCE. Vol. 85, No. SM6, 1959. pp. 31-47. |/5] Nie, N. H., Hull, C. H., Jenkins, J. G., Steinbrenner, K., and Bent, D. H., Statistical Package for the Social Science. 2nd ed., McGraw-Hill, New York, 1975. |/6) HoKz. W. G. and Gibbs, H. J.. "Engineering Properties of Expansive Clays." Transactions. ASCE. Paper No. 2814, 1956, pp. 641-663. |/7) Parcher. J. V. and Liu, P. C Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 91, No. SM3, 1965, pp. 1-17. [18] Linell, K. A. and Shea, H. P., "Strength and Deformation Characteristics of Various Glacial Tills in New England," Research Conference on Shear Strength of Cohesive Soils, ASCE, Boulder, Colo., 1960, pp. 275-314. 1/9] Bazett, D. J. and Bell, E. S. in Laboratory Shear Testing of Soils. ASTM STP 361. American Society for Testing and Materials, 1963, pp. 423-434.

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N. Dean MarachVJ. M. Duncan,^ C. K. Chan,^andH. B. Seed^

Plane-Strain Testing of Sand

REFERENCE: Marachi, N. Dean, Duncan, J. M., Chan, C. K., and Seed, H. B., "Plane-Strain Testing of Sand," Laboratory Shear Strength of Soil. ASTM STP 740. R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 294-302. ABSTRACT: Sand was tested under triaxial conditions, plane strain conditions, and conditions where the intermediate principal strain ((2) varied between the limits for triaxial and plane strain. Tests were performed using a variety of specimen sizes and shapes, a range of densities from loose to dense, and a range of confining pressures from 70 to 3450 kN/m^ (10 to 500 psi). The results of these tests provide useful guidelines for plane strain testing of cohesionless soils: (/) Plane strain and triaxial test results differ most for dense specimens tested at low pressures, (2) Plane strain equipment need not be elaborate. Specimens with square cross sections and simple lubricated end plates can be used for plane strain tests, and (.3) The end plates need not enforce a condition of perfect plane strain. Tests with values of (2 ^ larg^ as 40 percent of the axial strain at failure result in essentially the same value of the angle of internal friction (0) as do perfect plane strain tests. KEY WORDS: soil strength, strain, soil properties, soil testing, sands, plane strain testing

Strength tests on granular materials are often performed under triaxial conditions in order to simplify equipment requirements and test procedures, even though (/) the field application for which the tests are performed may correspond more closely to plane strain than to triaxial conditions, and (2) the stress-strain and strength behavior under plane strain conditions may be considerably different from those measured under triaxial conditions. Theoretical considerations [1,2]^ and experimental data [3-9] indicate that the strength and deformation characteristics of granular materials in plane strain may be considerably different from those for triaxial conditions. A dense specimen of sand tested in plane strain has higher strength and smaller strain at failure than a triaxial specimen tested at the same confining pressure. The object of this investigation was to examine the effects of density, effective confining pressure, specimen size, specimen shape, and intermediate 'Vice President, Converse Ward Davis Dixon, San Francisco, Calif. 94105. ^Professor of Civil Engineering, research engineer and lecturer, and Professor of Civil Engineering, respectively, University of California, Berkeley, Calif. 94720. The italic numbers in brackets refer to the list of references appended to this paper. 294 Copyright by Downloaded/printed Copyright 1981 University of

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MARACHI ET AL ON PLANE-STRAIN TESTING OF SAND

295

principal strain (^2) on plane strain test results, and to use this information to provide answers to a number of unresolved questions concerning the testing of granular materials under plane strain conditions. Those questions are: 1. How do triaxial and plane strain test results compare at high confining pressures? 2. Are plane strain test results affected by specimen shape or size? 3. How are plane strain test results affected if the ideal condition of no longitudinal strain (e2 = 0) is not satisfied? Monterey Sand All of the tests were conducted on Monterey No. 20 sand, a uniformly graded sand classified as SP in the Unified System. The particles were rounded to subrounded and were hard, consisting predominantly of quartz, with a smaller amount of feldspars and other minerals. D^ for the material was 0.55 mm (0.022 in.), coefficient of uniformity was 1.25, and coefficient of curvature was about unity. The maximum void ratio (e) was 0.83 and the minimum was 0.53. Test specimens were prepared to initial void ratios (e„) of 0.75, 0.65 and 0.55, corresponding to relative densities of 27, 60, and 90 percent, respectively. Testing Equipment The plane strain specimens tested were rectangular and had lubricated steel end plates to restrict deformation in the longitudinal direction (Fig. 1). The tie rods were stiff enough to limit the longitudinal strains (£2) to less than 0.1 percent, even in tests at high confining pressures. As discussed subsequently, it was found that longitudinal strains of this magnitude have no appreciable effect on the test results, and it is thus unnecessary to adhere strictly to the ideal condition of €2 — 0. In some tests rubber washers were used beneath the tie rod nuts to permit varying amounts of longitudinal strain. These strains were measured using dial gages (in vacuum tests) and electrical clip gages (in tests performed inside a pressure chamber to measure lateral deflections to 0.01 mm). The values of oi were not measured. Rectangular specimens of six different sizes and shapes were tested (Table 1). Tests were also performed on cylindrical triaxial specimens 7.1 cm in diameter by 17.8 cm high. The specimens were placed loosely inside a forming jacket by dropping the sand from a low height, and were then vibrated to the desired density. All of the specimens were tested in the air-dry condition. Initial void ratios were measured with the specimens subjected to 70 kPa (10 psi) effective confinement by vacuum. All tests performed were drained, and hence all references to pressures and test parameters herein are for effective stress conditions. A thin layer of silicone grease was used to reduce the frictional drag between

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296

LABORATORY SHEAR STRENGTH OF SOIL

INTERFACE LUBRICATED WITH GREASE

STEEL TIE RODS

m

RUBBER MEMBRANE

w

m

B-B

-

CAP

STEEL END PLATES

w

AXIAL LOAD

1

SAND

B BASE

^^

1 -DRAINAGE LINE

FIG. \—Plane strain specimen (2.5 cm wide by 2L6 cm long by 10.1 cm high).

TABLE \—Dimensions of plane strain specimens. Width, cm

Length, cm

Height, cm

Length/Width Ratio

2.5 2.5 4.6 11.4 11.9

21.6 14.0 11.4 28.4 11.9

10.1 10.1 11.4 28.4 29.2

8.5 5.5 2.5 2.5 1.0

the end plates and the rubber membrane around the specimen. In some of the tests the end plates were supported on load cells so that the frictional drag could be measured, and it was found that this was on the order of 0.05 percent of the axial load. In order to prevent formation of a gap between the end plates and the specimens at the higher confining pressures greater than 70 kPa (10 psi). the axial load was increased simultaneously as the confining pressure increased above 70 kPa (10 psi), thus consolidating the specimens under a condition of no lateral strain. The same procedure was used in the triaxial tests. The range of possible experimental error was estimated by analyzing the accuracy of all of the quantities measured in the testing program. It was found that the maximum experimental error in the measured value of <^ was ±0.4 deg for the tests performed using 03 = 70 kPa (10 psi) and ±0.5 deg for tests performed using 03 = 550 kPa (80 psi) and 3450 kPa (500 psi). Comparison of Plane Strain and Triaxial Test Results Stress-strain curves for plane strain and triaxial tests performed using 70 kPa (10 psi) confining pressure are shown in Fig. 2. It may be noted that:

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MARACHI ET AL ON PLANE-STRAIN TESTING OF SAND

297

1. The plane strain specimens reach higher values of maximum principal stress ratio (CTi/aj)/ than do triaxial specimens with the same initial void ratio. 2. The plane strain specimens fail (reach the maximum principal stress ratio) at smaller values of axial strain (e,) than the triaxial specimens. 3. The maximum principal stress ratios for both the triaxial and the plane strain tests decrease as the initial void ratio increases. 4. The difference between the maximum principal stress ratios for the plane strain and triaxial tests decreases as the initial void ratio increases. Variations of 0 with initial void ratio are shown in Fig. 3. It may be seen that the value of <{> for plane strain exceeds the value of 0 for triaxial by about 7 deg for tests conducted with initial void ratios of 0.55. For tests with initial void ratios of 0.75, the difference is about 4 deg. Leussink and Wittke [2] found even greater differences (about 11 deg) between values of 0 measured in plane strain and triaxial tests on dense uniformsize glass spheres tested at an effective confining pressure of 70 kPa (10 psi). Comforth [4] found smaller differences (4 to 5 deg) for tests on dense sand performed at 200 kN/m^ (30 psi) confining pressure. Variations of 0 with confining pressure for tests on Monterey sand are shown in Fig. 4. As the confining pressure increases, the difference between the values of 0 for plane strains and triaxial conditions decreases. With a confining pressure of 3450 kPa (500 psi) the difference is about 1 deg. These results show clearly that the difference between values of 0 measured in plane strain and triaxial conditions is greatest for dense specimens at low 9

[

/"\

DENSE eo=0.55

MEDIUM DENSE 60=0.65 PLANE STRAIN • ROUND TRIAXIAL •

0

6

'

o 1-

{\ ku

X <

r

tn

"> » cc

tn (-1 < a.

o S 3 cc a.

\ 1

I

'

1

0

I

1 2 3 4 AXIAL STRAIN, %

5

FIG. 2—Stress-Strain relationship for plane strain and triaxial specimen /03 = 70 kPa (10 psi)].

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298

LABORATORY SHEAR STRENGTH OF SOIL

O3 = 70kN/m2 (lOpsI)

^

fe% -

o.a

t:"' \i%^

0.7 INITIAL VOID RATIO

FIG. 3—Angle of internal friction—void ratio relationship for plane strain and triaxiai tests at a, = 70 kPu (10 psi).

30

100 psi CONFINING PRESSURE

SOO

1000

FIG. 4—Variations of angle of internal friction with confining pressure.

confining pressures. As the initial density of the sand decreases, and as the confining pressure increases, the difference between values of <> / from plane strain and triaxial tests decreases. These relationships provide insight with respect to the degree of conservation involved in using triaxial test results for analysis of plane strain conditions in the field. The degree of conservation is very large if the sand is dense and the confining pressure is small. When the

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MARACHI ET AL ON PLANE-STRAIN TESTING OF SAND

299

sand is loose and the confining pressure is large, little conservatism is involved in using triaxial test results for analysis of plane strain conditions. Values of axial strain at failure (€//) for triaxial and plane strain tests are shown in Fig. 5. It may be seen that the values of eij are always smaller for plane strain than for triaxial tests. In both types of tests the values of e/y are larger for loose specimens than for dense specimens, and the values of e/^ are larger for high confining pressure than they are for low confining pressures. Effect of Specimen Shape on Plane Strain Test Results Plane strain tests have usually been performed using rectangular specimens with lengths several times as large as their widths [3,4,9]. It has been shown [3,8] that if the length/width ratio of the specimen is sufficiently large ( > 15) no end plates are needed because the longitudinal restraint afforded by the cap and base is sufficient to reduce the longitudinal strain to a value close to zero, resulting in behavior essentially the same as plane strain. However, when lubricated end plates are used to limit longitudinal strain, there is no advantage to be gained by using specimens with large ratios of length/width. As shown in Fig. 6, the values of 0 measured in plane strain tests with lubricated end plates are the same for square or rectangular specimens. The results in Fig. 6 also show that the size of the specimen has no effect on the results, as would be expected. The values of for all of the specimen sizes and shapes exhibit the same consistent variation with void ratio. The use of square plane strain specimens has two very important practical advantages over the use of long rectangular specimens: 1. A thicker plane strain specimen, with a larger height and greater volume, may be tested in a cylindrical pressure chamber of any given size if the specimen cross section is square than if the cross section is rectangular. 2. The cap and base of a square plane strain specimen can be constructed very readily with a transition in shape from square to round, which makes it possible to seal the membrane in the same way as is done for triaxial specimens, with an 0-ring clamping the membrane against the round section. This is considerably easier than designing an effective means of sealing a membrane on a rectangular shape. Caps and bases for rectangular specimens can also be constructed with transitions to round shapes, if desired, although the resulting shape is more awkward than for a square specimen and a longer transition length is necessary. Effect of Longitudinal Strain on Plane Strain Test Results Theoretically, it is incorrect to describe as "plane strain" any condition where the intermediate principal strain (62) is not equal to zero. However, as the data in Fig. 7 show, some amount of longitudinal strain is tolerable in

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300

LABORATORY SHEAR STRENGTH OF SOIL

O3=550kN/m' (SOpsI)

0.55

0.65

0.75

0.55 0.65 0.75 INITIAL VOID RATIO

0.55

0.65

0.75

FIG. 5—Axial strain at failure for plane strain and triaxial tests.

2.5 X 21.6 X 10.1 cm 2.5 X 14.0 X 10.1 cm 4.6 X 11.4 X 11.4 cm 11.4 x28.4x 28.4 cm 11.9x 11.9x 29.2cm

0.6

0.7 INITIAL VOID RATIO

FIG. ()—Variations of with e„ for different shape plane strain specimens.

"plane strain" tests because the measured value of <> / is practically unaffected by small values of ej- This is an important finding because it shows that the tie rods which connect lubricated end plates need not be extremely stiff, nor is it necessary to use a null system such as that employed by Comforth [4] to compensate for the strain in the tie rods. While these measures enhance the purity of this test condition, they have no significant influence on the test results. The data in Fig. 6 has been replotted in Fig. 8 together with data from tests at confining pressures of 550 kPa (80 psi) and 3450 kPa (500 psi). It may be

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M A R A C H I ET A L ON PLANE-STRAIN TESTING OF S A N D

301

cc a m a z' o I-

o

z

< 03 = 70 kN/niMlOpsi) I

I

1

2

Co AT FAILURE

FIG. 7—Variations of (t> with (2^-

• a c — --~^_

1

3450 kN/m^ (SOOpsi)

\

550 kN Im' l,(80psi

'•..•

i-03 = 7 OkN/m^ >

(10

psi)

•\ S o '"•

•

am 0.55 to 0.75

0.2

0.4 0.6 Cj/c, AT FAILURE

0.8

1.0

FIG. 8—Significance of strain condition at failure.

seen that as long as the ratio of the longitudinal strain to the axial strain at failure is less than 0.4, the value of 0 measured in such an "imperfect" plane strain test differs by less than 1 deg from the value for "perfect" plane strain test.

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302

LABORATORY SHEAR STRENGTH OF SOIL

Conclusions Based on the results of plane strain and triaxial tests on Monterey No. 20 sand, the following conclusions may be drawn: 1. The value of <> / for plane strain conditions is higher than for triaxial conditions, and the strain at failure is smaller. The greatest differences occur for dense specimens tested at low confining pressures. As the initial void ratio or the confining pressure increases, the difference between plane strain and triaxial test behavior diminishes. With ^3 = 3450 kPa (500 psi) the difference in the values of 0 measured in triaxial and plane strain tests is about 1 deg. 2. The shape of plane strain specimens with lubricated end plates has no effect on the test results. Therefore square specimens may be used with considerable practical advantage as compared with the use of long rectangular specimens. 3. The tie rods which connect the lubricated end plates need not be extremely stiff, and it is unnecessary to employ a null system to ensure that ^i = 0. Provided that the value of €2 is less than about 40 percent of the axial strain at failure, the value of 0 will differ by no more than 1 deg from the value for perfect plane strain conditions. Acknowledgments The studies described in this paper were performed in the laboratories of the University of California in Berkeley under the sponsorship of the State of California Department of Water Resources. References 1/] Finn, W. D. L. and Mittal, H. K. in Laboratory Shear Testing of Soils. ASTM STP 361. American Society for Testing and Materials, 1964, pp. 42-51. [2] Leussink, H. and Wittke, W. in Laboratory Shear Testing of Soils. ASTM STP 361. American Society for Testing and Materials, 1964, pp. 77-89. \3] Bjerrum, L. and Kummeneje, C , "Shearing Resistance of Sand Samples with Circular and Rectangular Cross Sections," Norewegian Geotechnical Institute, Publication No. 44, 1961, pp. 1-7. [4] Comforth, D. H., Geotechnique. Vol. 14, 1964, pp. 143-167. [51 Finn, W. D. L., Wade, N. H., and Lee, K. h., Journal of the Soil Mechanics and Foundations Division. American Society of Civil Engineers, November 1967, pp. 297-308. [6] Habib, P. in Proceedings, Third International Conference on Soil Mechanics and Foundation Engineering, Vol. I, 1953, pp. 131-136. [7] Lenoe, E. M., Experimental Mechanics. February 1%6, pp. 99-104. [8\ Marachi, N. Dean, "Strength and Deformation Characteristics of Rockfill Materials," Ph.D. thesis, University of California, Berkeley, Calif., 1969. [9] Sultan, H. A. and Seed, H. B., Journal of the Soil Mechanics and Foundations Division. American Society of Civil Engineers, Vol. 93, SM4, 1967, pp. 45-67.

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G. M. Morris^

Effect of End Membrane Thickness on the Strength of 'Trictionless" Cap and Base Tests

REFERENCE: Norris, G. M., "Effect of End Membrane Thickness on the Strength of "Frictionless" Cap and Base Tests," Laboratory Shear Strength qfSoU, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 303-314. ABSTRACT: Considerable effort has been devoted to assessing differences in behavior between the conventional triaxial test (// = 2 to 2'/2 D) with end restraint and the "frictionless" cap and base test {H = D) with greased end membranes. While it is generally acknowledged that a minimal end membrane thickness is required for a frictionless test on sand to prevent effective bearing of particles through end membranes and into cap and base, it has not been recognized that beyond some optimal thickness a Poisson's effect dominates, causing an artificial reduction in sand strength. Therefore sand strength decreases gradually as end membrane thickness increases, first as end restraint is reduced and then as the Poisson's effect takes over. With the aid of stacks of multiple greased membranes, the optimum end membrane thickness (thickness where end restraint and Poisson's effect are near minimum values and counterbalance each other) can be established and the Poisson's effect avoided. Given that optimum end membrane thickness for the frictionless test on sand varies with sample height and confining pressure as well as particle size, and that the frictionless test requires correction or central measurement of sample deformation (overall deformation includes sand, membranes, extruding grease, etc.), the conventional test is preferable whenever feasible. Certainly the conventional test can be used when strength alone is required, since it yields a strength comparable to that of the frictionless test with optimum end membrane thickness on sand. KEY WORDS: frictionless cap and base test, conventional triaxial test, end restraint, end membrane thickness, optimum thickness, Poisson's effect, sand

'Assistant professor. Civil and Environmental Engineering Department, Clarkson College of Technology, Potsdam, N.Y. 13676; formerly assistant professor. Civil Engineering Department, University of Nevada-Reno, Nev. 89557.

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304

LABORATORY SHEAR STRENGTH OF SOIL

Recently, Lee presented two papers on the effects of end restraint on static and cyclic triaxial tests.^ While concentrating on undrained static and cyclic tests on sand, he also summarized the literature regarding drained static tests on sand and undrained static tests on clay. While it was Lee's desire to conclude research and discussion on the effects of end restraint, another matter with respect to so-called "frictionless" cap and base tests must be considered, namely, the influence of end membrane thickness relative to tests on sands. During the course of a study of the shear strength of sands as related to particle characteristics,^ the author had occasion to run drained static tests on sands of four uniform but different sizes. In order to obtain stress-strain and strength results free of the influence of end effects, it was deemed necessary to employ specimens with a length-to-diameter ratio of one with end membranes and high vacuum silicone grease between membranes and cap and base, after Rowe and Harden.'' In order to determine the appropriate minimal end membrane thickness to use with a sand of a particular size, preliminary tests were run on Monterey No. 0 sand with the intention of using the minimal membrane thickness to particle size ratio so determined to establish minimal thicknesses for other size sands. While it was recognized that a minimal end membrane thickness would be required to prevent effective bearing of individual particles through the rubber membrane (causing an undesirable degree of frictional end restraint), it was not known what effect an added thickness in excess of the minimal value would have. Since different size sands were to be used in the subsequent test program, the question of the effect of additional thickness was deemed important given the desirability of testing with a single size membrane (equal to the minimal thickness for the coarsest sand). Two series of tests were conducted on Monterey No. 0 sand,^ one series using progressively thicker membranes or a progressively thicker stack of membranes and a second series using a progressively thicker stack of greased membranes (greased between membranes as well as between end membrane and cap and base) as shown in Fig. 1. These tests were conducted on speci^Lee, K. L., Journal of the Geotechnical Engineering Division. American Society of Civil Engineers, Vol. 104, No. GT6, Paper 13838, June 1978, pp. 687-704; and Lee, K. L. and Vernese, F. J., Journal of the Geotechnical Engineering Division, American Society of Civil Engineers, Vol. 104, No. GT6, Paper 13839, June 1978, pp. 705-719. •'Norris, G. M., "The Drained Shear Strength of Uniform Quartz Sand as Related to Particle Size and Natural Variation in Particle Shape and Surface Roughness," thesis presented to the University of California, Berkeley, 1977, in partial fulfillment of the requirement for the degree of Doctor of Philosophy. ''Rowe, P. W. and Barden, L., Journal of the Soil Mechanics and Foundations Division, American Society of Civil Engineers, Vol. 90, No. SMI, Paper 3753, Jan. 1964, pp. 1-27. "'Monterey No. 0 is a uniform medium sand, most of which passes the No. 30 sieve and is retained on the No. 50 sieve. Each batch of Monterey No. 0 sand varies slightly in the amount of undersize and oversize materials present. The sand used in this study exhibited a C„ = 1.4 and a D50 = 0.42 mm.

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NORRIS ON END MEMBRANE THICKNESS

y^

305

membrane

ymmammaMmmfmmmC ^ grease (thickness )immm.mhhMmUmmmi(y^

greatly exaggerated)

FIG. 1—Multiple greased end membranes.

mens 50.8 mm (2.0 in.) in diameter by 50.8 mm (2.0 in.) high, with deformation, and therefore strain, measured over the central 30 mm (1.15 in.) with linear variable differential transformers (LVDTs) mounted on split ring holders as shown in Fig. 2.^ In addition, a conventional specimen 35.6 mm (1.4 in.) in diameter by 88.9 mm (3.5 in.) high was tested. All tests were conducted on dense sand {D^ = 90 percent) at 118 kPa (1.20 kg/cm^) confining pressure. The trend in test results for frictionless cap and base tests with a height-todiameter ratio of one as end membrane thickness increases up to the minimal value (relative to the sand, sample height, and confining pressure used) is shown conceptually in Fig. 3. This trend in thin membrane tests remains the same whether or not grease is used between stacked end membranes. It simply indicates a progressive reduction in effective particle penetration through end membranes into cap and base, and hence a reduction in end restraint, with increased thickness. Effective particle penetration causes shear stress transfer between greased or ungreased stacked membranes, such that the combined thickness, acting as a single unit, expands with the sample and slips relative to the cap and base at the greased cap and base interface. The effect of thickness of single or stacked membranes (ungreased between layers) on behavior as thickness increases beyond the minimal value is shown conceptually in Fig. 4. The corresponding pattern of sample deformation observed in thick end membrane tests is shown conceptually in Fig. 5. This deformation pattern for strains near failure indicates that the membranes, acting as a single unit, expand more than the sand (under the same axial load), and by this Poisson's effect a reduced strength results; the greater the end membrane thickness, the greater the reduction in strength. Note that the Poisson's effect results from the greater vertical com''Separating sand deformation from overall deformation (sand, membranes, extruding grease, etc.) is a significant problem, particularly with the smaller 50.8-mm (2-in.)-high specimen used here. The problem was resolved by taking central measurements of deformation with an influence-free, split-ring LVDT device.

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306

LABORATORY SHEAR STRENGTH OF SOIL

rubber band clamp guides

upper split clamp, cut to an inner diameter o£ 2.30"

LVDT coll upper clamp LVDT core 1.15 + .01" centerto-center spacing. (1.00 + .01" clear spacing) lover clamp

FIG. 2—Split ring device (I in. = 25.4 mm).

pressibility of the membranes; that is, even if the end membranes have the same Poisson's ratio as the sand, they undergo greater vertical deformation and therefore greater lateral expansion than the sand under the same axial load. Furthermore, the relative significance of the Poisson's effect is a function of sample height; that is the greater the sample height, the thicker the end membrane required to cause the same relative strength reduction. If one considers Figs. 3 and 4 together, there is a progressive decrease in strength with continued increase in end membrane thickness. An "optimum" end membrane thickness, fopt. for ^ particular sand, sample height, and confining pressure is that value where end restraint and Poisson's

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NORRIS ON END MEMBRANE THICKNESS

307

increasing thickness

min

"frictionless" cap and base tests; helght-to-dlaraeter ratio of one

Axial Strain* £FIG. 3—Effect membrane tests.

of end membrane thickness on stress-strain and strength behavior for thin

effect are near minimal values and counterbalance each other. ^ However, without subsequent tests on stacks of multiple greased membranes, it would be impossible to distinguish the optimum membrane thickness from the trend in Figs. 3 and 4 combined. Thin and thick membrane test results spEnning either side of f^pt are shown in Fig. 6. (As will be shown subsequently from multiple greased membrane tests, topt — 0.64 mm.) Note that two 0.20 mm-thick membranes, with no grease between them, were used to obtain an equivalent single membrane 0.40 mm thick; likewise two and three membranes 0.64 mm thick were used to obtain the 1.28 and 1.92 mm thicknesses, respectively. With no grease between layers, there is no relative slip between membranes and the behavior is that of an equivalent single membrane of the combined thickness; hence the 'Recognize that minimal thicknesses for end restraint and Poisson's effect considered separately are thicknesses for which said effects are reduced to an arbitrarily set small absolute value and that they need not coincide. (For instance, at a given confining pressure, the minimal thickness for end restraint increases with increasing particle size, while the minimal thickness for the Poisson's effect decreases with increasing sample height.) An optimum thickness is therefore an intermediate value where end restraint and Poisson's effects offset each other.

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308

LABORATORY SHEAR STRENGTH OF SOIL

increasing thickness (of single membranes)

FIG. ^—Effect of end membrane thickness on stress-strain and strength behavior for thick membrane tests.

end membrane (exaggerated thickness)

FIG. 5—Sample deformation of thick end membrane tests.

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NORRIS ON END MEMBRANE THICKNESS

309

l(0.40imn)

l(0.64imii) l(1.28iran) l(1.92min)

Axial Strain, e

(%)

FIG. 6—Fricthnless cap and base test stress-strain curves for single or equivalent single membrane series (1 kg/cm^ = 98.1 kPa).

designations 1(0.40 mm), 1(1.28 mm), and 1(1.92 mm), which reflect single equivalent thicknesses of the indicated values. The 0.30 and 0.64 mm thicknesses were uncombined single membranes designated 1(0.30 mm) and 1(0.64 mm), respectively, in Fig. 6. As can be seen from these results, strength decreases continuously with increased single (or equivalent single) membrane thickness as characterized in the preceding paragraph. The type of results from tests with successively thicker stacks of greased membranes is shown conceptually in Fig. 7. In this case, if the optimum thickness is assumed to be four times the incremental membrane thickness, tx, then tests on stacks up to 4?, thick show a progressive reduction in strength. Tests on stacks greater than At\ yield results identical to those for 4f| because only the four membranes adjacent to the sand sample ends ex-

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310

LABORATORY SHEAR STRENGTH OF SOIL

4t

1

( = t

opt

),5t,,6t,,... 1 1

FIG. 7—Effect of end membrane thickness on stress-strain and strength behavior for multiple greased membrane tests.

pand and deform with the specimen. Because effective particle penetration is only four membranes deep, that is, fopt, and because of the lubricated interface at this level, slip occurs between the membranes at fop, as pictured in Fig. 8. (Note that underlying layers expand more than the optimum thickness in direct contact with the specimen ends.) This type of behavior was observed in tests with thick stacks of multiple greased membranes and was accompanied by uniform specimen deformation in contrast with the nonuniform Poisson affected deformation of the thick single membrane tests. The results of the multiple greased membrane tests are shown in Fig. 9 along with the 1(0.64 mm) single membrane test for reference. The membrane designations used in this figure refer to the number and thickness of greased membranes employed in the stack on each end of the specimen. Hence 3(0.64 mm) signifies three 0.64-mm-thick greased membranes having a combined thickness of 1.92 mm. Note that within experimental error all stress-strain curves appear to be one and the same. This indicates that optimum thickness for the given sand and test conditions is approximately 0.60 to 0.64 mm; that is, the membranes for the 3(0.20 mm) and 2(0.30 mm) tests

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NORRIS ON END MEMBRANE THICKNESS

311

A number of layers, of combined thickness equal to t, a unit with the particles; the unit expands radially by sliding on the greased surface of the ^uppermost layer below.

FIG. 8—Behavior of multiple greased end membranes of combined thickness greater than

act as single units equal to the optimum thickness, while the innermost 0.64 mm thickness of the 2(0.64 mm) and 3(0.64 mm) tests slips relative to the outer layers as described in the preceding paragraph. Had the optimum thickness been smaller, say 0.40 mm, then the innermost 0.40 mm of the 3(0.20 mm) test would have acted as a single unit and given a stress-strain curve higher than the others and identical to that of the 1(0.40 mm) single membrane test. On the other hand, had the optimum thickness been greater, say 1.28 mm, the 3(0.20 mm), 2(0.30 mm), and 1(0.64 mm) curves would have been the same, greater than the 2(0.64 mm) and 3(0.64 mm) curves, which would have been identical to the 1(1.28 mm) single membrane test curve. Note that the optimum end membrane thickness of 0.60 to 0.64 mm corresponding to the sand and test conditions employed is approximately one and a half times the D^ size of the sand. The value of this multiple will increase with increased confining pressure and sample height, and most likely will decrease with increased spread in the grain size curve. The combined results of all frictionless cap and base tests are shown in Fig. 10, data points omitted, along with the stress-strain curve from the conventional triaxial test on dense Monterey No. 0 sand. Note that the conventional triaxial test strength is comparable to, though somewhat greater than, the frictionless cap and base test employing optimum end membrane thickness. Therefore it would seem that when strength alone is required, the conventional test is sufficiently accurate for most practical applications. In addition, note that based on deformation and strain measurements taken centrally (to avoid inaccurate corrections for membrane and grease effects).

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312

LABORATORY SHEAR STRENGTH OF SOIL

•

3(0.2Cliran)

O

2(0.30mm)

O

1(0.64mm)

A

2(0.64mm)

•

3(0.64mn)

T 5 Axial S t r a i n , r

r 7

(.7.)

FIG. 9—FrictUmless cap and base test stress-strain curves for multiple greased membrane series (1 kg/cm^ = 98.1 kPa).

the same initial tangent modulus results for all frictionless tests. Only at a stress level greater than 30 to 40 percent of maximum deviator stress is there sufficient lateral expansion for differences in end restraint effects to reflect differences in stress-strain behavior. The corresponding range in volume response for all frictionless cap and base tests as determined from burette readings is shown in Fig. 11 along with the volume change curve from the conventional test. The frictionless cap and base test range should be further corrected for end membrane penetration during shear, which would further accentuate the difference in dilatant behavior of the frictionless cap and base test versus the conventional test.

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NORRIS ON END MEMBRANE THICKNESS

313

conventional test

3(0.20mm) ^ 2 (0.64mm) 1(0.64mm), 3(0.64mm)

Monterey No. 0 Sand ' 907. r •' = 1 . 2 0 kg/cm2

D

Axial Strain, r (%)

FIG. 10—Frictionless and conventional test stress-strain curves (1 kg/cm^ = 98.1 kPa).

Summary and Conclusions The current set of tests indicates that significant variation in sand strength can result from frictionless cap and base tests, depending on the end membrane thickness employed. To obtain a value of strength indicative of the sand, the optimum end membrane thickness should be used, or alternatively, thin multiple greased membranes with a combined thickness greater than (or equal to) the optimum thickness. Based on tests on dense Monterey No. 0 sand (JDSO - 0.42 mm) at 118 kPa (1.20 kg/cm^) and a sample height of 50.8 mm (2.0 in.), an initial estimate of optimum end membrane thickness might be taken as one and a half the mean particle size of the material being tested. The value of this multiple will increase with confining pressure and sample height, and most likely will decrease with increased spread in the grain size curve.

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314

LABORATORY SHEAR STRENGTH OF SOIL

6

.

5

-

conventional test 3

^

-

2

FIG. II — Volume change response.

Given the necessity of establishing optimum end membrane thickness (or testing with stacks of multiple greased membranes in excess of optimum thickness) and employing central measurement of sample deformation with the frictionless test on sand, the conventional test is preferable whenever feasible, certainly when strength alone is required, since it yields strengths comparable to (though slightly larger than) frictionless tests with optimum end membrane thickness.

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G. R. Thiers^ and T. D. Donovan^

Field Density, Gradation, and Triaxlal Testing of Large-Size Rockfill for Little Blue Run Dam

REFERENCE: Thiers, G. R. and Donovan, T. D., "Field D e n ^ , Giadatton, and TriazU Teitlng of Latse-Size RockflU for LitOe Blue Ron Dam," Laboratory Shear Strength of SoU, ASTM STP 740. R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 315-325. ABSTRACT: The results of field density and gradation tests mvolving large-size compacted rockfill (sedimentary rocks) were used to establish gradation and compaction requirements for large-size (38-cm-diameter) and conventional (15-cm-diameter) triaxial tests. The gradation requirements were that the gradation curves for triaxial test materials should be parallel to the corresponding field gradation curve, except for minor modifications to avoid excessive inclusion of fines. The angle of mtemal friction decreased as maximum particle size increased, in a manner similar to that reported by others. Extrapolation was used to check the 0-values used in design. KEY WORDS: triaxial tests, gravel, rockfill dams, internal friction, density, grain size

Rock particles as large as 76.2-cm (30-in.) in diameter are used as a major component of many earth-rock dams. If the shear strength of such rockfill at placement gradation and density can be determined, embankment slopes can be optimized. The purpose of this paper is to summarize the application and adjustment of existing procedures for determining field density, gradation, and shear strength for large size rockfill at a particular earth-rock dam (Little Blue Run Dam). Guidelines for future application of these procedures are also presented. 'Senior staff engineer and vice president, respectively, Consultants, Inc., Monroeville, Pa. 15146.

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LABORATORY SHEAR STRENGTH OF SOIL

Procedures Used to Determine Field Density, Gradation, and Shear Strengtli of Rockfill Field Density and Gradation The plan view and design cross-section for Little Blue Run Dam located in southwestern Pennsylvania near the tip of the West Virginia panhandle^ are shown in Figs. 1 and 2. The expected rockfill densities, assumed before construction, are listed in Table 1. Following Stephenson,^ large-size samples of 27 to 54 kN (3 to 6 tons) were excavated by backhoe from 1.5- to 1.8-m (5- to 6-ft)-diameter test pits at the locations .designated in Figs. 1 and 2.^ The excavated material was placed in a truck and weighed on a truck scale. Each pit was lined with plastic and filled with water to obtain the pit volume used for density calculations. Water contents were determined by measuring the water contents of representative portions of the finer material, and then

TEST POINTS

FIG. 1—Plan location of test points. ^Thiers, G. R,, Lobdell, L. W., and Mihalcin, B. M., "Foundation Treatment for Little Blue Run Dam," Proceedings, Rock Engineering for Foundations and Slopes, Vol. 1, American Society of Civil Engineers Specialty Conference, Boulder, Colo., Aug. 1967. ^Stephenson, R. J. in Evaluation of Relative Density and Its Role in Geotechnical Projects Involving Cohesionless Soils, ASTM STP 523, American Society for Testing and Materials, 1973, pp. 234-247. •"Final trimming of test pits was done by hand. The size of sample obtained at a given location was determined by the requirement that the volume of the largest particle sampled must comprise less than 10 percent of the corresponding total sample of volume.

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THIERS AND DONOVAN ON LITTLE BLUE RUN DAM

Q Z lU

o us

(z o EL 10) UJ t-

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317

318

LABORATORY SHEAR STRENGTH OF SOIL

TABLE 1—Rockfill parameters assumed before construction.

Type of Material

Zone No. 2 3 4

Random fill Resistant sandstone Semiresistant rockfill

Unit Weight, kN/m^

Angle of Internal Friction, deg

21.2 (135 pcf) 18.9 (120 pcf) 18.9 (120 pcf)

30 40 37

calculating the overall water content using the gradation results and assuming negligible water in the coarser fraction. The densities and water contents are listed in Table 2, along with a description of each material tested. The gradation of five of the samples was established by measuring and weighing individual large pieces' and successively screening representative portions of the remaining material. The gradation curve for Sample 1 is shown in Fig. 3, along with the range of gradation curves obtained. Gradation parameters Dio, Cc and C„ are presented in Table 2. Shear Strength A procedure for determining the angle of internal friction of large size rockfill has been presented by Marachi et al.^ The procedure involves the testing of mixtures having different maximum particle sizes (say, 2, 8, and 30-cm), but having gradation curves which are parallel to the field gradation curve. Plotting angle of internal friction against maximum particle size permits extrapolation to determine the angle of internal friction corresponding to the maximum particle size expected in the field. The ideal "parallel" gradation curve for material from Test Point 1 adjusted to have 6.35 cm (2.5 in.) as the maximum particle size is presented in Fig. 3. (Specimens with 6.35 cm as the maximum particle size were used in 38-cm-diameter triaxial shear tests.) For the ideal curve shown, the amount passing the No. 2(X) sieve is approximately 8 percent. Because of the difficulties involved in accumulating the volume of material passing the No. 2(X) sieve corresponding to 8 percent for the 38-cm-diameter triaxial specimens [approximately 180 N (40 lb) of minus 200 material for each specimen], mixtures having gradation curves matching compromise gradation curves as indicated in Fig. 3 were prepared and used in 38- and 15-cm (15- and 6-in.)-diameter tests. This greatly reduced the volume of minus 200 material required. Corresponding ideally graded 15-cm-diameter specimens were tested for comparison purposes. ^Marachi, N. D., Chan, C. K., and Seed, H. ^., Journal of the Soil Mechanics andFountfotions Division. American Society of Civil Engineers, Vol. 98, No. SMI, Proc. Paper 8672, Jan. 1972, pp. 95-114.

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THIERS AND DONOVAN ON LITTLE BLUE RUN DAM

319

S 2 • M g 5?

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320

LABORATORY SHEAR STRENGTH OF SOIL

X C3 lU

>m E

ui

z

z o a lU

Q.

1

0.1

0.01

PARTICLE DIAMETER IN METRES

1.0

0.1

0.01

PARTICLE DIAMETER IN mm

FIG. 3—Gradation curves.

The density values for the triaxial test samples are listed in Table 3, along with the effective confining pressures applied and an indication of whether samples were tested under "moist" or "saturated" conditions. Each compaction water content was approximately equal to the corresponding field water content. The 38-cm-diameter tests were performed by personnel of the South Atlantic Division Laboratory of the U.S. Army Corps of Engineers under R. J. Stephenson, Director. The 15-cm-diameter tests were performed by personnel of the soils laboratory of GAI Consultants, Inc., under P. E. Glogowski, Laboratory Director. Results of Testing Program Four types of rock were involved in the test program: shale, claystone, siltstone, and sandstone. The shale and claystone and a soft siltstone, were found in various combinations in Zone 2, the "nonresistant" portion of the embankment (nonresistant meaning "having low resistance to weathering"). Three samples from Zone 2, one from Zone 4 (semiresistant siltstone and

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THIERS AND DONOVAN ON LITTLE BLUE RUN DAM

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321

322

LABORATORY SHEAR STRENGTH OF SOIL

sandstone) and two from Zone 3 (resistant sandstone) were tested. Representative stress-strain curves and failure circles (Mohr diagrams) are presented in Figs. 4 and 5 along with c = 0 failure envelopes obtained by "least squares" fit (assuming c = 0 to conform to preconstruction assumptions). The resulting (^-values are listed in Table 3 and plotted against maximum particle size in Fig. 6.^ Because the maximum particle size tested was 6.35 cm, curves developed by Becker et af for medium hard (Venato) sandstone were used to guide extrapolation to field conditions (30 cm maximum size in Zone 2; 76 cm in Zones 3 and 4). Even though the Zone 3 and Zone 4 tests were run at confining pressures of 0.32 to 0.34 MPa (47 to 49 Ib/in.^), the 38-cm data for these

ffj

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ffj

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•O.ZMPa

e 2 O " 1

1

1

AXIAL STRAIN,%

0.4

0.8

1.2

NORMAL STRESS. (7

1.6 (MPt)

FIG. 4—Stress-Strain curves and Mohr's circles at failure for 0.38-m (15-in.)-diameter triaxial test of material from Test Point 1. *The -values for 15-cm-diameter samples of "compromise" gradation material were less than the corresponding results for "ideal" gradation material, which indicates that the use of the compromise curves is conservative. ^Becker, E., Chan, C. K., and Seed, H. B., "Strength and Deformation Characteristics of Rockfill Materials in Plane Strain and Triaxial Compression Tests," Report No. TE-72-3 to State of California Department of Water Resources, Geotechnical Engineering Division, Department of Civil Engineering, University of California, Berkeley, Calif., Oct. 1972.

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THIERS AND DONOVAN ON LITTLE BLUE RUN DAM

0

10

323

20

AXIAL STRAIN,%

NORMAL STRESS,
FIG. 5—Stress-Strain curves and Mohr's circles at failure for 0.38-m (I5-in.)-diameter triaxial test of material from Test Point 4.

zones plot on or slightly above the 0.21-MPa curve obtained by Becker et al. On this basis, the 0.21-MPa curve was used to guide extrapolation of the Zone 3 and 4 curves to the 76-cm particle size, giving a -value obtained for Zone 2 was approximately 36 deg, which is well above the 30-deg value assumed in design.) Soinmaiy and Conclusions The results of large-size field density and gradation tests involving compacted rockfill (sedimentary rocks) were used to establish gradation and Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

324

LABORATORY SHEAR STRENGTH OF SOIL

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THIERS AND DONOVAN ON LITTLE BLUE RUN DAM

325

compactkwi requirements for large-size (38-cm-diameter) and conventional (15-cm-diameter) triaxial tests. Gradation requirements were based on Marachi et al (gradation curves for triaxial test materials parallel to corresponding field gradation curve), with modifications of the lower portions of the curves to avoid excessive inclusion of fines. The angle of internal friction decreased as maximum particle size increased, in a manner similar to that reported by others. Extrapolation was used to check the (^-values used in design. Goidebies for Fntuie Testing 1. In determining field density of rockfiH it is recommended that pit volume be at least 10 times the volume of the largest particle removed. 2. In applying the "parallel gradation" method presented by Marachi et al to materials having more than 5 percent passing the No. 16 sieve it is recommended that consideration be given to relaxation of the "parallelism" requirement for the lower portion of the gradation curve to avoid excessive "fines" requirements (see Fig. 3). 3. In estimating (^-values for large size rockfill the use of the 0-particle size curves developed by Becker et al is recommended. Acknowledgments This study was conducted for Dravo Corporation of Pittsburgh, Pa., in conjunction with construction of Little Blue Run Dam. The cooperation and support of Dravo Corporation is gratefully acknowledged.

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Data Reduction and Application of Measurements for Analytical Modeling

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Hon- Yim Ko' and Stein Sture

State of the Art: Data Reduction and Application for Analytical Modeling

REFERENCE: Ko, Hon-Yim and Sture, Stein, "State of the Art: Data Reduction and Application for Analytical Modeling," Laboratory Shear Strength of Soil. ASTM STP 740. R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 329-386. ABSTRACT: Due to the availability of large digital computers and advances in computational analysis techniques, it has become feasible to perform stress analyses of geoteehnieal structures involving complex geometries and material behavior. A key element in such analyses is the proper modeling of the constitutive behavior of soils. Intensive research in recent years has led to a proliferation of constitutive models which have been postulated to represent soil behavior under general loading conditions. In this paper some of these models are reviewed regarding their basic assumptions and the requirement of input data for their characterization. A classification of constitutive models is given on the basis of basic approaches to relating stress and strain. Representative models from each class are selected for detailed examination, with the hyperbolic model, the elastic—perfectly plastic model, the Cam-Clay model, the cap model. Lade's model, Prevost's model, and the endochronic model being selected. Finally, a comparison is made of these models regarding their range of applicability. KEY WORDS: soil engineering properties, constitutive models, model classification, comparison, input data requirements, laboratory testing

For many years, since the beginning of modem soil mechanics in the 1920s, when a soil engineer was faced with a design situation involving the prediction of movement of soil masses, the traditional approach had been to treat it as either a stability or a deformation problem and to proceed to seek solutions by assuming rigid plasticity or linear elasticity for the soil behavior. This approach had been necessitated primarily by the helplessness one felt if the realistic material behavior was used in formulating the field equations for the stresses and deformations, since the nonlinear, inelastic, anisotropic, and time-dependent soil response invariably leads to a highly complex set of equations to be solved. Thus, the simplifications in terms of rigid plasticity 'Professor of Civil Engineering and Assistant Professor of Civil Engineering, respectively. Department of Civil Engineering, University of Colorado, Boulder, Colo. 80309.

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330

LABORATORY SHEAR STRENGTH OF SOIL

and linear elasticity had been justified in view of the need for solutions, even though they might be crude. Such solutions, when coupled with judgement based on the experience of the user, have been used to various degrees of success in soil engineering analysis. In the last two decades, the development of computational analysis techniques and the availability of large digital computers have removed a majority of the barriers to the tracking and solution of large problems with complex geometries and material behavior. These developments have precipitated a surge of interest in modeling the constitutive behavior of soils. In order to represent the stress-strain properties of soils correctly in computations of structural response, it is necessary not only to have a model that predicts the correct pattern of behavior under general three-dimensional loadings (that is, identify the parameters), but also to have quantitative determinations of the constants that appear in the model. Thus, along with the theoretical formulation of constitutive models, many test devices have been developed for studying the behavior of soils and measuring their response to loads in three-dimensional stress space. The emphasis in soil testing is no longer placed entirely on determining the shear strength of soils, as indicated by the theme of the 1960 ASCE Conference on Shear Strength of Soils [/],2 but increasing attention is now paid to the evaluation of the stressstrain behavior before and after failure. Since it is realized that there is an intimate interaction between stiffness and strength for soils, one often talks about stress-strain-strength behavior. The purpose of this symposium was to focus on new developments in test methods and on procedures for evaluating the test data for constitutive modeling of soil behavior. The first session focused on the test methods; the state-of-the-art paper by Saada and Townsend reviewed the various existing test methods, and discussed the advantages and disadvantages of various devices.-' In this paper we will assume that the necessary precautions have been taken by the experimenter and model developer in using any of these devices to measure soil properties, so that the stress-strain curves obtained are accurate representations of the soil behavior. Thus, given the capability of measuring accurately the response of soil, the following questions arise: (7) What experiments should be conducted? and (2) How should the data be analyzed? The answer to both questions is that it depends on the constitutive model that is intended to be used to model the behavior, since in the analysis of soil structural response a model must be input as part of the description of the system. Therefore we will address these questions by examining some of the constitutive models commonly in use by the geotechnical engineering profession and focus on the input data requirements in each model. ^The italic numbers in brackets refer to the list of references appended to this paper. •'This publication, pp. 7-77.

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KO AND STURE ON STATE OF THE ART

331

It is not intended in this paper to give the individual models a rigorous theoretical analysis. The object is rather to describe the analytical treatment in simple terms that reflect the usefulness for the general practitioner. Classification of Constitutive Models Given a set of laboratory data, one should be able to examine the general response "behavior" of the soil and deduce that certain qualitative behavioral patterns, such as for volume change and ultimate strength, exist. Many investigations on soil behavior have stopped at this point, and the experimenters have in turn been content to have gained an understanding of the phenomenological response of the soil to the special type of loading that was used in generating the experimental data. For the purposes of applying such understanding to the solution of field problems in which the deformations, stress distributions, and stability of the soil mass are sought, one must be able to quantify such qualitative understanding into a form that can be used in rational analysis. The advances in computational techniques that have been made during the last two decades demand material characterization in forms that describe the response of the soil in general stress-strain relations, rather than in specialized constrained conditions such as axially symmetric uniaxial strain or plane strain loading. As pointed out by Saada and Townsend in their state-of-the-art paper, only those devices that subject the test specimen to arbitrary three-dimensional stress states are, straightly speaking, suitable for obtaining data for constitutive modeling. This is equivalent to saying that it is easier to specialize from the most general case than to make generalizations on the basis of specialized circumstances. While three-dimensional stress-strain data are required to gain a complete understanding of the constitutive behavior of any material, the notion of basing one's constitutive model on simple test results and then verifying that the model will also make adequate predictions along more complicated loading conditions has been inherited from metal plasticity. The findings from the North American Workshop on Generalized Stress-Strain and Plasticity Theories for Soils (1980) indicate that this approach has produced results with varying degrees of success, depending on the complexity of the model being applied for the predictions. Therefore, given the same laboratory data set, different modeling techniques may produce totally different representations of the soil response. Thus it is important for the engineer saddled with the task of constitutive modeling to understand the implications of choosing a certain model over others, especially with respect to the trade-off between predictive power and simplicity of input requirements. It has generally been accepted that the behavior of soils is too complex to be modeled adequately by linear elasticity. The inherent nonlinear and inelastic nature of soil's behavior makes it necessary to use more complex theories for modeling.

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332

LABORATORY SHEAR STRENGTH OF SOIL

Many models have been proposed during the last two decades which advance beyond Hooke's law. It is advantageous for later discussion to classify these models according to the nature of their inherent assumptions. In this classification of constitutive models it is necessary to draw the distinction between modeling of soil behavior and the applications to analysis. In applications to analysis, there are currently in use iterative and incremental methods for nonlinear analysis. In the iterative schemes, which broadly can be categorized as initial stress and strain methods, a stress distribution and a strain distribution are sought that satisfy not only equilibrium, compatibility, and boundary conditions, but also the constitutive relations. This only works if the stress-strain relationship is represented as deformation theory in which the stress is related to the strain, as opposed to the case where the constitutive relation is expressed in terms of increments of stress and of strain. On the other hand, the incremental method of analysis seeks a stepby-step approximation to the loading process, and requires the strain increments be calculated as the results of incremental loading. Thus the relation between the stress and strain increments is required for the computations, which could be obtained directly from an incremental constitutive theory, or by determining the "tangent" modulus from a deformation theory. Although an overwhelming majority of the nonlinear analytical techniques employ the incremental approach, the constitutive model used in the analysis need not necessarily be of the incremental nature. We will therefore base the following classification of constitutive models solely on the basis of their representation of soil behavior, without any regard to the method of analysis for which the constitutive model serves as an input. A wide range of constitutive models has been proposed and used for the response of soils. These models generally fall into one of the following basic categories: Deformation Theory Incremental Theory Perfect and Incremental Plasticity Endochronic Theory A brief description of each of these types is given for later reference. Deformation Theories A deformation theory is one in which a relation between the stress and strain tensors is assumed to exist. For soils, the stresses could either be the total or effective stresses, representing undrained or drained responses. In the former case, a separate or auxiliary procedure is needed to calculate the pore pressures generated unless the constitutive model is incorporated into the coupled Biot theory [2]. The equations in a deformation theory usually appear as

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KO AND STURE ON STATE OF THE ART

333

Sij = 2G(g,e)eij

(1)

aj.^ = 3K(q,e)eki,

(2)

and Sjj and e,, are the deviators of the stress tensor g = [CT,y] and the strain tensor e = [e,y], and G and K are the secant shear and bulk moduli, respectively. Here the equations are written for an isotropic material, and the moduli can be made stress or strain dependent in order to represent nonlinear behavior. Because of isotropy, the moduli can also be written in terms of invariants of the stress and strain tensors. Hyperelasticity [3] can be classified as a deformation theory. There the number of material constants appearing in the model goes up according to the order of the model, for example, five and nine constants for the secondorder and third-order models, respectively. The hyperbolic model [4] can also be put into this category, and will be discussed in detail in a later section. Incremental Theories In incremental theories, the stress and strain increments are related by coefficients which can be either constant or dependent on the stress or strain states. Hypoelasticity is an example of an incremental theory, with the relation expressed as ^"(i ~ Cijkiiq,e)dtki

(3)

d^ii - Dijki{q,e)dai,i

(4)

or where C and D are the tangent stiffness and compliance tensors, respectively. Because the stiffness or the compliance tensor is dependent on the stress and strain states and not on their history, and because these incremental theories do not have the power to model the unloading behavior, they are seldom applied to soils. Perfect and Incremental Plasticity Incremental plasticity leads to relations similar to those in Eqs 3 and 4. The functions Q^/ or I^ijki i" this case are more complicated, being derived from potential functions which are strain-history dependent. Although some authors [5] have classified incremental plasticity as a special case of hypoelasticity, the similarity applies only to the form of the stress incrementstrain increment relations and not in the implicit assumptions and the method of their derivation. Incremental plasticity applied to soils usually includes the following basic elements: (7) The strain increment c?€,y can be decomposed into the elastic

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334

LABORATORY SHEAR STRENGTH OF SOIL

and plastic parts, dejf and deyP. (2) The elastic strain increment can be calculated as dtif = Cij^idaij, where Cy^/ is the elastic constitutive tensor. (3) There exists a yield surface/((TJ,, H) = 0, representing the boundary of all states in stress space that are reachable from the current stress state elastically. (4) When the stress state reaches the yield surface, the plastic strain increments are defined by a plastic potential ^(CT;,, H*) = 0 such that

deifP = \-f-

(5)

where X is a scalar multiplier, whose determination will be based on the basic elements (1) to (4) and a consistency relation. In this description of incremental plasticity, the yield function / and the plastic potential g depend on the hardening parameters H and H*, which reflect the plastic strain history. If such dependence is absent, then ideal plasticity is obtained. (5) The consistency condition, df = 0[6] ensures that the stress state does not leave the yield surface when stress states follow the expansion of the yield surface. (6) Strain or work-hardening materials require a hardening rule. The flow rule in Eq 5 which allows for the calculation of the plastic strain increments can be further classified as either associated or nonassociated. In the case of an associated flow rule, with/ = g, the plastic strain increments calculated from Eq 5 are normal to the yield surface, and Drucker's postulate [ 7] for a stable material applies. However, it is easy to see why it is not appropriate to insist on normality, since strain-softening (and hence unstable) behavior does exist for soils, and since the volumetric strains predicted from an associated flow rule are usually too large compared with experimental observations. Thus several constitutive models have been proposed for soils in which nonassociated flow rules are employed. These will be discussed in later sections. Based on the pioneering work of Drucker et al [8], several hardening plasticity theories have been advanced to describe the consolidation and yielding behavior of soils. The basic differences among these models lie in the description of the yield surface and the manner in which the hardening parameter H enters into the yield function. Thus isotropic hardening plasticity models specify the yield surfaces to expand or contract isotropically about the hydrostatic axis in principal stress space, as exemplified by the Cam-Clay model [9], the Weidlinger Cap model [10], and Lade's model [//]. On the other hand, anisotropic hardening models, exemplified by Prevost [12] and Mroz et al [13], prescribe a set of nesting yield surfaces that translate as well as expand in stress space, from which yielding can be defined. The bounding surface model of Dafalias and Herrman [14] is also a useful tool for incorporating path dependent behavior.

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KO AND STURE ON STATE OF THE ART

335

Endochronic Theory In recent years, a different approach has been proposed to represent the inelastic behavior of materials based on the concept of intrinsic time, that is, a nondecreasing scalar variable, which is equal to the path length traced in deviatoric strain space for time independent materials. This endochronic theory involves no yield surfaces, and the inelastic behavior of the material is followed by empirical expressions representing the strain-hardening or softening responses as well as the volume dilatancy. These empirical expressions can be evaluated to any degree of accuracy depending on the amount of data available. As the sophistication of the models increases so that the complex soil behavior can be represented, the data input requirements for these models to work properly become more stringent. A compromise is often necessary between these two conflicting demands. As shown by the conclusions of the Montreal Workshop, some of the constitutive models currently in use require much more data input than is generated by conventional soil testing. On the other hand, these models are not capable of representing the inherent and stress induced anisotropy of most soils. It is obviously impossible, or impractical, to review all the models that have been proposed to represent the constitutive behavior of soils. We will therefore concentrate on those representative models of each category that have been used extensively and whose implementation in analysis have demonstrated their ability to model soil response adequately. In the following sections, we will describe these selected models, discuss their advantages and disadvantages, and review the methods of analyzing laboratory soil test data for calibrating these models.

Hyperbolic Stress-Strain Model Description Perhaps the most widely used constitutive model for soils is the hyperbolic model, first proposed by Kondner [15], Kondner and Zelasko [16], and subsequently amplified by Duncan and Chang [4]. Kondner based the model on the observation that the stress-strain curve of soil tested in triaxial conditions with a constant confining stress resembles a hyperbola (Fig. 1) whose equation is

''•""^ = 7 1 ^ = 1 Ei

' (ff, -

(^> aj)^ It

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336

LABORATORY SHEAR STRENGTH OF SOIL

The axial stress versus axial strain curves obtained under various values of confining pressure are related to a family of hyperbolas defined by five coefficients: modulus number, K\ modulus exponent, «; failure ratio [17], Rf\ and the two Mohr-Coulomb strength parameters: the cohesion intercept, c; and the friction angle, 4>- Thus, the tangent modulus, £ , , is given by Rf{\ — sin 4>){a\ — a^) E,

1 -

2c cos
(7)

'

<

where /?„ is the atmospheric pressure. Although the work of Duncan and Chang [4] only dealt with the axial stress-strain behavior and assumed a constant Poisson's ratio p, subsequent extensions allow for the nonlinear volumetric strains to be modeled. One of the following two procedures is used for this purpose. In the first, developed by Kulhawy and Duncan [18], the variation of the tangent values of Poisson's ratio, v„ with confining pressure, is modeled by G -

Flog^ Pa

d{a\

/?/(ffi -

KpJ-

(8)

- CT3)

gjKl - sin (j))

2c cos (/) + 2 a3 sin 0

\Pa

where G is the value of the initial Poisson's ratio c, (at zero strain or zero deviator stress) when the confining pressure 03 is one atmosphere, F is the reduction in c, for a ten-fold increase in a3, and d is the rate of change in the Poisson's ratio v with the radial strain. With the tangent values E, and v, defined from Eqs 7 and 8, respectively, the rest of the response upon loading is determined by assuming isotropic elasticity. In the second procedure, proposed by Duncan et al [19], the bulk modulus of the soil B is assumed to depend only on cj^ and is independent of the value of (CTI — 03). The value of B is related to that of 03 by B

""AT.

(9)

where Kh is the bulk modulus number and m is the bulk modulus exponent. From B and E„ the tangent value of the Poisson's ratio can be calculated from elasticity considerations. The original model of Duncan and Chang has also been extended to incorporate the soil behavior observed upon unloading. This behavior is assumed to be elastic for unloading and reloading, with the value of Young's modulus E^j dependent only on the confining pressure, as in

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337

(10)

^urPa

where ATyr is the unloading-reloading modulus number, ''his, then, completes the description of the hyperbolic stress-strain model. Limitations and Advantages There are some significant limitations inherent in this model. It is based on the generalized Hooke's law for isotropic behavior and does not have provisions for anisotropic, either inherent or stress induced, responses. By the same token, shear dilatancy is not modeled. It is also only capable of modeling the pre-peak response, whereas the strain-softening behavior is not represented. The parameters that are used to characterize the model in Eqs 7, 8, 9, and 10 are determined by fitting the model to triaxiai test data, and, if the loading path deviates greatly from that of triaxiai compression, the strains predicted by the model may not be accurate. It is conceivable that the model can be fitted for triaxiai extension conditions. However, there are important advantages of this model, among which are that the parameters have easily understood physical significance and coefficients are easily evaluated from standard laboratory tests. In addition, the

Rf/b

FIG. 1—Hyperbolic fit to stress-strain curve at constant

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widespread use of the model in many applications has culminated in a wealth of information on the range of values of the model constants for a variety of soil types under both drained and undrained conditions. Evaluation of Material Constants To evaluate the constants in this model, only conventional triaxial compression test data will be required. A series of tests, conducted in the range of confining pressure of interest and with volume change measurements, will provide the necessary data basis for such evaluation. The Mohr-Coulomb strength coefficients c and <> / can be determined by any conventional procedure. Two methods are commonly used. The first method involves plotting the Mohr circle of stresses at failure and measuring the intercept and the angle of inclination of the linearized portion of the failure envelope over the stress range of interest. In the second method, the values at failure of '/2(ai — a3)j are plotted versus those of V2(a| + 03)^. The intercept, a, and the slope angle, a, of the best-fit line are used to calculate c and <j) according to (t> — sin ~' (tan a) and

(11) c = cos (t)

Two steps are involved in evaluating the modulus coefficients K and n, which prescribe the variation of the initial tangent modulus E, with the confining pressure according to

r,-^P„(^)"

(12)

The first step is to determine E/ for each test, and is best executed by plotting £/(ai — 03) versus e (Fig. 2). The reciprocal of the intercept of the straight line (1/a) is equal to E,, whereas the inverse slope of the line (1/6) is equal to (ai — a3)uit, which incidentally defines the failure ratio Rf = [(a, — 03)/]/l(o\ ~ ff3)uitl- The second step is to plot E/ versus 03 from each test on a log-log scale, using the slope and the intercept of the data line to evaluate n and K in Eq 12, (Fig. 3). It is usually assumed that n in Eq 10 for unloading and reloading is equal to that determined for Eq 12 for primary loading, and therefore only one unloading curve will be required to evaluate the unloading modulus E^r, from which K^^ can be calculated from Eq 10. The Poisson's ratio coefficients (G, F, and d) are evaluated in a two-step procedure. The first is to determine the value of the initial Poisson's ratio, v,-,

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FIG. 2—Transformed plot of hyperbola.

03=1

Log a , FIG. 3—Evaluation of some of the coefficients in the hyperbolic model.

and then to determine d representing the rate of increase of the Poisson's ratio with respect to the radial strain. Then the values of c, from several tests are plotted against the logarithm of 03 in order to evaluate F and G from V: = G — F log

(13)

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If the bulk modulus B (Eq 9) is chosen instead of v to represent the volumetric strain behavior, the coefficients K^ and w in Eq 9 are evaluated in the same manner as described for K and n in Eq 12. Incremental Plasticity Models In conventional foundation and earth structure design, soils have traditionally been modeled as rigid plastic materials for the purpose of estimating the collapse load or ascertaining the onset of instability. However, there is no unified agreement regarding which failure criterion should be used to describe the strength data obtained from soil testing. Research in the last two decades using true triaxial test equipment has demonstrated the influence of the intermediate principal stress on the failure strength of soils, especially granular soils, and the nonlinearity of the failure envelope has always been apparent. These features have provided the motivation for more sophisticated mathematical description of the failure conditions than the MohrCoulomb criterion. However, the latter remains the most widely used failure model because of the vast experience accumulated from using the limiting equilibrium design methods that have been developed on the basis of the Mohr-Coulomb criterion. The simplicity of the criterion, requiring only two parameters c and <^, is also an important reason for its popular use. In limiting equilibrium analysis, due to the indeterminacy in the problem, it is usually necessary to make assumptions for the stress distribution. In the sense of the limit theorems [20], this makes the collapse loads calculated by limiting equilibrium methods neither the upper bound nor the lower bound. Limit analysis is also based on the assumption of perfect plasticity, but it further assumes that at yield, the deformations are governed by a flow rule to be derived from a plastic potential. In the case of an associated flow rule, the plastic potential coincides with the yield function, so that plastic strain increment vectors are normal to the yield surface. Thus, with this normality assumption, powerful limit theorems have been derived to bound the collapse loads calculated. In limit analysis, any failure criterion or yield surface can be utilized, although there are certain restrictions regarding convexity and smoothness of the surface. This theory was originally developed for metal plasticity, but later developments extended it to deal with frictional materials also [21]. In order to account for the effect of three-dimensional stress states, the Drucker-Prager or extended Von Mises criterion is usually assumed. Both the Mohr-Coulomb and the extended Von Mises failure surfaces appear as cones in principal stress space, but with different shapes for the cross section on the deviatoric planes (Figs. 4 and 5). Under the assumption of the normality flow rule, they both predict a volume expansion of the soil at failure, which is much larger than those observed during experiments on soils. This in turn raised strenuous objections from the soil mechanicians.

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341

^<jr°z'"3

Drucker-Prager JZ c cot*

FIG. 4—Failure surfaces in principal stress space.

AAsn M!ses/

Drucker-Proger Mohr-Coulomb

FIG. 5—Cross section of failure surfaces on deviatoric plane.

Mostly because of this objection to using perfect plasticity for soil behavior, a series of work-hardening plasticity models have been developed. They can all be traced to the pioneering work of Drucker et al [8] in which two important features were noted that set the stage for recognizing soils as work-hardening materials. The first is that the consolidation curve, with the usual virgin compression and unloading/reloading branches, constitutes a clear indication of work-hardening behavior, and the second is the feature associated with the

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LABORATORY SHEAR STRENGTH OF SOIL

preconsolidation stress corresponding to a yield surface which, when reached by subsequent loading, will indicate the onset of irreversible deformations. The yield surface as postulated by Drucker et al consists of two portions: the Mohr-Coulomb surface and a cap which passes through the isotropic compression axis. The cap translates along that axis, with the position determined by the preconsolidation stress. The relationship between this stress and the void ratio is governed by a hardening rule. The plastic strain increments would then be given by the normality flow rule, treating the composite yield surface as the plastic potential. From this concept of "capped" work-hardening plasticity have sprung several models with various modifications. The most notable of these are the Cambridge Cam-Clay models and the Weidlinger cap model, which will be described later. Drucker-Prager Model Description In this model the yield surface is identified with the failure surface given by fUx,J2D) = oiJ^+^D-k

= 0

(14)

where J\ is the first stress invariant of the stress tensor a^^, and JJD is the second invariant of the deviatoric stress tensor (l/2)(sj,5„). The material coefficients a and k are related to the internal angle of friction and cohesion for the material. The implementation of these constants in analysis requires an evaluation of the type of analysis to be performed in conjunction with the boundary value problem formulation. For instance, if a plane strain analysis is to be conducted, where the Mohr-Coulomb condition is to be matched in compression, the constants are tan
(15a)

* = V9 + ?2tan^,^

<^^*^

If, on the other hand, an axisymmetric situation is considered, the constants for triaxial compression (CT) > 02 = 0;^) are 2 sin (^ a = -f^-7z r—: v3 (3 — sm 0)

,,, . (16a)

6 C cos 0 v3 (3 — sm (p)

MAI,\

and

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343

and for triaxial extension (ffj =CT2> ''a)2 sin V3 (3 + sin )

(16c)

and _

6 c cos <> / v3 (3 + Sin 0)

Equations 15 and 16 clearly show that a proper definition of the coefficients a and it are required in order to perform realistic analyses. Normality is assumed so that, at yield, the incremental plastic stress-strain relationship can be written as 6,y'' = ^ | ^

(17)

where superscript p denotes the plastic component of the strain tensor e,, due to the increment in the stress tensor (T,,, and superdot denotes the increment (or rate). X is an arbitrary non-negative scalar parameter to be determined as a function of the strain rate tensor. The total strain rate e^, is the sum of the elastic and plastic components i/f and e,,''; that is. 'J iii = eif + ii/

(18)

The relation between the stress and elastic strain rate is given by Hooke's law as

where E is Young's modulus, v is Poisson's ratio, 6/, is the Kronecker delta. Combining Eqs 18 and 19, we obtain the relation between the stress rate and the total strain rate as a,-," = 1 + .;

..._xi^U_J^r...-xJ/ ^tr. daj +T^i;A^^^-^i^ 1 - 2v V ** da. h

(20)

Jkk

In order to determine X, we observe that during plastic loading the stresses must lie on the yield surface, / = 0, and furthermore, as the stress state changes, the yield surface must correspond to this change [6]: df

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LABORATORY SHEAR STRENGTH OF SOIL

Since dJ doij

dan

I 2

yn^Im bay (21) -1/2 ,

Then, combining Eqs 20 and 21, we obtain

#=0=[ia6, + i / , , - . , ] ^ ('

£//

:

:

Si

+ 1 Ijv (^** ~ ^"/ ^''

(22)

X can be obtained from Eq 22 as X=

GJ2D ^'^Spqipg + B ikk G + ap

(23)

where 2(1 + ,)

(24)

and B =

2aG ( \ + V 1 - 2v

(25)

Thus, with X determined, the stress rate-strain rate relation can be obtained from Eqs 20 and 21 in terms of the current stress state. These incremental relations assume isotropic behavior and non-work-hardening perfect plasticity. Determination of Material Constants The elastic material constants appearing in the Drucker-Prager model (Eq 19) are Young's modulus E and Poisson's ratio v, which, of course, could be expressed in terms of the bulk modulus K and the shear modulus G. These moduli can be determined from the unloading curves from the isotropic consolidation and drained triaxial tests, respectively, conducted over the range of loading that is of interest. The constants, a and k, appearing in the yield function (Eq 14), can be determined from failure stress data, which usually are expressed in terms of c and 4> from which a and k can be calculated from Eqs 15 and 16.

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Limitations of Model Because the failure envelope, expressed in linear form in Eq 14, is also used as the plastic potential, the plastic volumetric strains predicted are usually much greater than those observed in laboratory tests. This contradicts the concept of critical void ratio, which represents the state reached at relatively large, plastic shear strains. In addition, because the failure envelope represented by Eq 14 does not cross the hydrostatic 7]-axis when plotted in principal stress space, the model does not predict the irreversible volumetric strains observed under isotropic consolidation of normally consolidated clays. As mentioned before, these limitations led to the development of the cap models, which will be described next. Cam-Clay Model The Cam-Clay model is a work-hardening plasticity model based on the work of Drucker et al [8], with two important points of difference. The first is the introduction of the concept of critical states corresponding to critical void ratio versus stress locus, proposed by Roscoe et al [22], which suggests that all shear tests on a soil will produce end conditions which lie on a critical state line in the space of p, q. and e (Fig. 6), which for the conditions of triaxial compression are defined as p=i:(ax-\-

02 + Oi) = -z(a\+2ai)

(26)

q = a^-

(27)

Gi

and e = void ratio where a represents effective stresses. Thus the Mohr-Coulomb envelope, or any other surface that has been used to connect failure stress data, is just a collection of such end points, and therefore is not a complete yield locus. It is the yield surface at ultimate strength. The second point of difference lies in the formulation of a basic energy dissipation expression in order to develop an equation for the yield surface. Roscoe et al [23] assumed that there is no recoverable component in the shear distortion of wet clay and derived the Cam-Clay model, which was described in detail by Schofield and Wroth [24]. The original Cam-Clay constitutive equations overpredicted the observed values of the strain increments at small shear stress levels. This was presumably due to the original assumption regarding zero recoverable shear strain. The original "bullet" shaped cap, moreover, predicted shear strains in isotropic compression. Burland [25] and Roscoe and Burland [9] have suggested a modified ver-

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LABORATORY SHEAR STRENGTH OF SOIL

q=<j|-a3

Critical State Line 'In q-p Plane Critical State Line In Space Elastic Wall

Yield Surfaces In q - p Plane

Swelling Line

IMormol Consolidation in p^e Plane

Critical State Line In p ~ e Plane

FIG. 6—State boundary surface in p-q-e space.

sion of the Cam-Clay model, which we will describe in the next section. Many other versions of the original and modified Cam-Clay models have been forwarded over the years. For the sake of brevity and simplicity we shall direct our attention to the first modified version. Description The Cam-Clay model developed for axially symmetric stress conditions on the basis of experimental observations in the "triaxial" compression tests can best be described in relation to a three-dimensional p-q-e (state boundary) space from which sections can be shown for further delineation. Based on isotropy, two components of strains are defined as v = ei + 2 63, and e — (2/3)(6| — €3). The isotrppic consolidation line in the e ~ Inp plane has a slope of —X analogous to the compression index C^, while the elastic rebound and reloading curve has a slope of — K analogous to the swelling index Cj (Fig. 7). For a soil in the virgin compression state, the irreversible volumetric strain rate from .4 to fi is given by vP =

(X - K) p \ + eo p

(28)

where eo is the void ratio corresponding to the current hydrostatic stress p, and p is the increment or rate. This stress fraction is the source for the natural logarithm mentioned earlier. The elastic volumetric strain recovered during rebound from B to C is Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

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(29)

I + Co p

The plastic volumetric strain expression given in Eq 28 governs the change of the compaction state of the soil and controls the strain-hardening. Thus the soil had passed through a succession of yield surfaces from A to B. When a shear stress q is applied, a point can be plotted in p-q-e space representing the state of the sample. Therefore the state boundary surface represents the convergence of all state paths, and it separates the admissible and inadmissible state points. On this surface we find the critical state line representing the end points of the state paths, where no further change in the stress state or the void ratio of the soil will take place under continual, large shear strain. The projection of the critical state line on the p-q plane is linear and has the equation q — Mp

(30)

where M is the frictional constant, equal to 6 sin 7(3 — sin ') in triaxial compression and 6 sin 7(3 + sin 0') in triaxial extension. Subscripts C and E are often added to the coefficient M to characterize these respective conditions. The projection of the critical state line onto the e ~ \x\p plane is also a straight line parallel to the virgin compression curve, with equation e — Br

Xlnp

(31)

where e^ is the void ratio when p = 1. A soil is "wet" when its state corresponds to a point between the critical state line and the virgin compression curve, and will strain-harden when loaded in shear until it reaches critical state. "Wet" soils are therefore those that are normally or lightly overcon-

g^

A

^Normol

Consolidation Line

Critical - A . State Line ^ -AK

* \ *

\

'dry' \ w e t ' \ es

C

"

~" X — ^ ^ e-ei- Kin p

P'l

mp FIG. 7—Isotropic consolidation

and swelling

behavior.

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LABORATORY SHEAR STRENGTH OF SOIL

solidated. A soil is "dry" when its state corresponds to a point on the dense side of the critical state line. For a wet soil, the strain-hardening effects can be described in terms of a succession of yield surfaces. For the modified Cam-Clay model, Roscoe and Burland derived the following expression for the yield surface: 9

(32)

where po is the strain-hardening parameter or isotropic consolidation stress representing the hydrostatic pressure at the point where the rebound curve containing the projection of the state would intersection the virgin compression curve in e ~ \np plane. This, of course, is the same as the preconsolidation pressure, if no shear stress has been involved. Eq 32 represents an elliptical yield curve in the p — q plane, as shown in Fig. 8, where the critical state line intersects the ellipse at its maximum point. As the soil strainhardens, the strain-hardening parameter po increases by an amount po given by Eq 28 as

1+eo Po =

(33)

PovP

Compression (3|>02=CT3)

Yield Surfaces: Original Com - Cloy Modified Cam-Clay

Po

p= 1/3(01+253)

Extension (o, < ^3 • 03)

FIG. 8—Yield surfaces in Cam-Clay models.

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where VP remains to be calculated by using an assumed associated flow rule in conjunction with the yield function in Eq 32. Thus the critical state line in p — q plane is not a yield locus in itself, but is the termination of yield loci where they have horizontal slopes, and therefore, under the normality rule, predicts zero plastic volumetric strain increment at critical state (that is, shearing at constant volume). With the aforementioned description of the yield function/ and the strain hardening parameter po. the strain increments due to any stress increment (,p,q) under an existing stress state (p,q) can be calculated as 1 1 + e

(X-/C)

2l/7j

M^ + r{^

(X-/C)

2T;7J

1 + e

M2 + r,2

e = iP

+ X^

(35)

+

2v

X- K

(34)

1 + e \ M 2 -

IJV

\M^

l-qi] + ^p + n^

(36)

where rj = q/p. In this version of the model the elastic shear strain ^ is assumed zero. More recent formulations include elastic shear strain where ^ = q/3G. Determination of Material Constants The four material constants appearing in the modified Cam-Clay model are easily determined from conventional triaxial tests. The constants X and K are the compression and swelling indices based on isotropic consolidation tests. If an isotropic consolidation test is used, the compression and swelling indices from that test, C^j and Q , can be used to compute X and K as X = Cei/2.303

(37)

K = Csi/2.303

(38)

where In 10 = 2.303. The elastic constants A^(bulk modulus), £'(Young's modulus), and G(shear modulus) can be determined from

K =

pa+ eo)

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LABORATORY SHEAR STRENGTH OF SOIL

^ 3p{l + eo)(l E =

2P)

^ ^ 3(1 - 2v) p 2(1 + v) K The frictional constant M can be determined by carrying out triaxial compression (Mc) or extension (ME) tests to ultimate loading. The ratio of q/p at ultimate loading when critical void ratio is reached is then equal to M. Such a test also provides the information necessary to calculate e^ defining the critical state line. Limitations of Model The modified Cam-Clay model in the form just described was originally developed for representing soil behavior under axially symmetrical, triaxial compression loading. The extension of the model to triaxial extension and plane strain loadings was described by Roscoe and Burland [9] and good agreement was obtained. In order to further extend this theory to truly threedimensional loading, it is necessary to replace the shear stress q in the triaxial case by \ ( ^ , where J2D is the second invariant of the deviatoric stress tensor. The modified Cam-Clay model was originally developed for "wet" clays that are normally or lightly overconsolidated, and which strain-harden, that is, contract in volume, when sheared. The model has not been successfully applied to heavily overconsolidated clays which strain-soften, and a large part of the reason for this lack of correlation between theory and experimental data is due to the heterogeneity in deformation developed during shearing of overconsolidated clays. The model performs best for clays that have initially experienced isotropic consolidation. A /Co-consolidation history frequently results in yield loci which seem to be centered on the A'o-line rather than the/j-axis. Such behavior can only be modeled by anisotropic hardening models.

Weidlinger C ^ Model Description A series of constitutive models with a capped yield surface has been developed for use in large finite element analysis codes for ground shock computations, as described by DiMaggio and Sandler [10], Sandler et al [26], Sandler and Baron [27], and Baladi and Rohani [28]. These models have also been applied in analyses of static problems. This particular cap

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model concept, which is frequently termed the Weidlinger model after the company affiliation of the original developers, is in many respects quite different from most conventional critical-state soil mechanics cap models. It resembles more closely the MIT model described by Christian [29] and Tang and H6eg [30]. The model is based on classical incremental elasto-plastic strainhardening theory. Besides a hardening rule, a flow rule, and the constitutive parameters characterizing the material's elastic component behavior, the model consists of a stationary ultimate strength or failure surface, which also serves as the bounding yield surface, and a strain-hardening moving cap that is situated between the ultimate strength surface and the hydrostatic stress axis (Fig. 9). Stress states on any one instantaneous surface are characterized by a common single value of a strain parameter such as volumetric plastic strain, which in turn appears as the state parameter in the hardening rule. This hardening parameter is therefore the characteristic that governs the movement of the cap surface according to a semi-empirically developed hardening rule. The yield surface is symmetric about the hydrostatic compression axis, and the moving hardening plastic cap intersects the hydrostatic axis at right angles at X. The comer region resulting from the intersection between the moving cap and the stationary ultimate strength surface is arranged in such a way that the tangent to the cap at this point is always parallel to the hydrostatic axis. This feature assists in securing that no volume change occurs when the stress state arrives at the ultimate strength surface by route of the moving cap. The flow rule continues to be expressed in terms of the equation of the cap at the comer point. The ultimate strength surface serves in those instances merely as the end point of the loading process. In these respects, this cap model is very similar to the Cam-Clay model described earlier. However, the ultimate strength surface is curved as opposed to the straight line surface used to characterize the Cambridge and MIT models. The curved surface in conjunction with the translating cap is used to control dilatant behavior at higher stress levels commensurate with observed behavior of real soils. It is composed of a combination of normal and extended Von Mises criteria in conjunction with a transition surface that links these. The extended Von Mises or Drucker-Prager conical surface bounds the yielding behavior at lower stress levels, and the Von Mises cylindrical surface bounds the yielding behavior at higher stress levels, as seen in Fig. 9. This ultimate strength criterion was devised in order to provide a better control on the amount of dilatancy predicted by conventional models at higher levels of mean stress. The transition surface in Fig. 9 is fitted in such a way that its end points approach asymptotically the Dmcker-Prager or extended Von Mises criterion at very low mean stress levels and the normal Von Mises criterion at the higher mean stress levels. The derivation of the comCopyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

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LABORATORY SHEAR STRENGTH OF SOIL

J^Di.

Drucker - Prager ^^ Line X

I

^^ Mises Line

\ Retracted i ' L

i

^

\ \

Elliptical Cap f (Jl.JzD.K)

X

•*J,

FIG. 9—Ultimate strength and yield surfaces in cap model.

plete bounding or ultimate strength surface is based on conventional laboratory shear tests to be described later. The moving position of the yield surface or the cap has been given an elliptical shape with constant eccentricity. This concept is therefore similar to the Modified Cam-Clay yield criterion of Roscoe and Burland. The convex cap extending from the ultimate strength surface to the hydrostatic stress axis constitutes one quadrant of the ellipse; this is the only portion of the yield surface that is used to describe the material's behavior. Stress states on the ultimate strength surface situated behind the intersection of the moving and stationary surfaces normally produce strain-softening responses in conventional critical state soil mechanics models. However, the Weidlinger cap model is restricted to strain-hardening plasticity, since strain-softening behavior is neither envisioned in the materials for which the model was developed nor accounted for in the model theory. The cap expands monotonically as the volumetric plastic strain increases. Unloading under the ultimate strength surface in most instances leaves the cap fixed at its outermost position, and such stress paths therefore result only in elastic deformation. Interpretation of nonlinear stress-strain behavior in unloading and reloading under the current yield surface has frequently been devised by introducing nonlinear elastic moduli. A partial contraction of the cap has been incorporated in some versions of the model, especially those developed for rocks, in those instances where the ultimate strength surface is reached prior to attaining a preconsolidated position of the cap. The normality condition on the ultimate strength surface subsequently results in

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353

volume expansion which is often observed in fracturing rocks. In these cases the retracted cap has often served the purpose of controlling such volume expansions. In conventional critical state models, the lower intersection of the elliptical cap and the hydrostatic axis remains fixed. In fact, most models place the lower extreme stress state of the ellipse right at the origin, and in a few instances a small penetration of the ellipse into the tensile regime is used to characterize tensile behavior. On the other hand, the Weidlinger cap models do not possess this restriction, since the entire cap translates in such a way that neither the lower extreme of the ellipse nor any other point on the cap is tied down to any particular location on the hydrostatic stress axis. The instantaneous position and the translational behavior of the cap are controlled entirely by a hardening rule, which usually is characterized in terms of volumetric plastic strain, in addition to the geometric condition that the intersection point between cap and ultimate strength surface bisects the ellipse. As mentioned previously, the ratio between the major and minor ellipse axes is ordinarily assumed constant for all stress states and yield surfaces. Baladi and Rohani [28] have suggested means for changing this ratio depending on the stress path. Although the models do not explicitly account for path dependent effects and other features of anisotropic hardening plasticity, such phenomena can to a limited extent be simulated by the features described previously. A recently developed version of the model, described by Sandler and Baron [27], introduces kinematic hardening, which enables the prediction of hysteresis in repeated loading and unloading cycles. The Weidlinger model belongs essentially to the class of isotropic hardening, incremental elasto-plastic constitutive models. The cap models satisfy nearly all the original requirements for continuity and uniqueness put forward by Drucker in the definition of stable plastic materials. These conditions lead to associated plastic flow and, thus, normality conditions. In addition to the conditions which were originally devised for metal plasticity, many aspects of realistic soil behavior have also been incorporated into the cap models, such as dilatancy, hysteresis, and densification in isotropic compression. The strain-hardening and volume change characteristics are controlled by volumetric strain rather than void ratio terms, which frequently appear as state variables and moduli in many critical state models, although the relationship between volumetric strain and void ratio change is obvious. Analytical Description In describing the Weidlinger-type cap models emphasis is put on those versions which have seen widest application in the literature. We will begin with a description of the ultimate strength surface, the hardening capped yield surface, and the hardening rule. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

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UBORATORY SHEAR STRENGTH OF SOIL

The composite ultimate strength surface consists, as earlier mentioned, of a Drucker-Prager and a Von Mises surface. The Drucker-Prager criterion is characterized as //(DC) — ^ / ^ — aJi — ki — 0

(39)

and the Von Mises criterion is described as

-kj^O

//(VlM)

(40)

where /j is the first invariant of stress, and JID is the second invariant of stress deviator. The constants ki and A: 2 characterize strength contributions from cohesion. The analytical forms of these criteria have been discussed in previous sections. The term a is a coefficient which is directly related to the internal angle of friction for the soil, it also denotes the angle of the DruckerPrager cone. The ultimate strength or failure surface ff has also frequently been described in the literature as the/i-surface. The complete transition surface is described in terms of linear and exponential terms as ffiJuJio)

= ho"^ -A

(41)

+ C-BJ^ = 0

where A, B, and C are material constants. The evaluation of these will be discussed later. This ultimate strength surface degenerates to the DruckerPrager criterion for/j approaching zero where in turn k\— A — C. When/j becomes sufficiently large relative to B, the exponential term becomes insignificant and the regulating expression approaches asymptotically the Von Mises criterion. In this case, k2 = A. The elliptically shaped yield surface that constitutes the cap is often described by

fcUx,hD^'\li) =

Ji X{K)

UK)

- L{K)

1 2

12

+

A - Ce-^^*"'

1= 0 (42)

or as fciJuho^'^, x) = R^ho + Ui - UK)? - RV

=0

(43)

where the subscript c in /<, denotes the capped yield surface (which is sometimes referred to in the literature as the/2-surface), and K is an internal state variable which characterizes the hardening process as a function of the plastic volumetric strain history. A further description of K and the associated

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355

hardening rule follows. L denotes the value of /j where the elliptical surface intersects the ultimate strength surface. This point also describes the center of the ellipse. X denotes the value of/i at the intersection between the ellipse and the/j-axis, which occurs at right angles. X is therefore the extreme value of/i for a given yield surface, and corresponds to the isotropic preconsolidation stress. The parameter R is the ratio between the major and minor ellipse axes, and it is normally constant. Recent attempts at modeling path dependent behavior have utilized varying R. The parameter b is the ^JTID value when JI — L.\t describes the minor ellipse axis where X — L or Rb constitutes the major ellipse axis. The isotropic stress states X and L are related as X{K) = UK) +R[A-

Ce-Bi-M]

(44)

since the expression inside the bracket is the value b. In other words, it is sufficient to specify either XorL for describing the instantaneous location of the cap. The hardening rule which has been used most frequently derives from the volumetric stress-strain response behavior of the material subjected to isotropic compression, with the plastic volumetric strain assumed to have the form €/ = W[l - e-°^(«']

(45)

where D and W are additional material constants. W denotes a maximum volumetric plastic strain measure which can be obtained in isotropic compression relative to a certain initial condition. Increased isotropic consolidation stress denoted by X results in material compaction, and the ultimate state is theoretically the condition where no further void space exists. The soil has essentially been compacted to solid rock. In practice, it is not feasible to carry out such a complete description. It is in most applications sufficient to carry out isotropic compression tests to a stress level which is higher than the mean stress level expected in the prototype operation. The parameters D and W are in turn fitted to that condition. The initial cap position corresponds to an initial preconsolidation stress, which must be carefully evaluated from the in situ condition prior to model implementation and parameter assignment, since the laboratory evaluation will identify e/ as being zero at the initial state. In the early model development, the hardening parameter K was set equal to the plastic volumetric strain: K = €/

(46)

However, the hardening parameter has recently been taken as a stress measure [27] such that

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356

LABORATORY SHEAR STRENGTH OF SOIL

L{K)

=

K

if K < 0

(47)

L{K)

<

K

if K > 0

(48)

or

The hardening parameter K is implicitly defined as the functional of the plastic volumetric strain e/ = £/[VK, D. X{K)] described previously. The strain history dependent functional is therefore only characterized along the isotropic compression stress axis. A more complex relationship controlling the volumetric plastic strain has been described by Sandler et al [26]. Limitations and Advantages Although a recent version of the model allows the introduction of kinematic hardening into the failure envelope and cap surface [27], where J2D is replaced by a new parameter Q2D i" the original expressions (Eqs 41 and 43), the definition of such behavior has not yet been linked to relevant laboratory test procedures. Q2D is defined as the second invariant of the tensor (Sij — ay), where Sy is the deviator stress tensor and ay is a kinematic hardening tensor reflecting earlier stress history. Difficulties may arise in cases where the principal stress state rotates in the course of nonproportional loading, which in turn produces varied stress-strain-strength responses in the material. The current hardening rule appears to be very restrictive and may not adequately represent stress paths that diverge pronouncedly from the isotropic stress axis. Calibration of the model and the evaluation of the constants rely on straight line proportional loading tests or conventional triaxial compression tests. Since the stress paths of conventional triaxial compression and extension tests nearly overlap, and all shear stress paths at constant mean stress overlap in the/2D ~ Ji space, the models may not adequately distinguish between differences in ultimate strength as well as the prior yielding behavior for such extreme states as compression and extension. The third stress invariant {J^) may be needed in these situations. The ultimate and cap surfaces are currently rotationally symmetric about the/i-axis in/2D ~ Ji space. Strain-softening predictive capabilities have intentionally been excluded from the models, while the current models except for the version described by Baladi and Rohani [28] are not capable of predicting the generation of pore water pressure. The models are apparently intended to simulate behavior of a wide range of geological materials where cyclic loading and unloading effects along specific stress paths are significant. The model coefficients are relatively few and readily obtained from conventional tests in those instances where simple load path histories are to be modeled. Along these paths, the predictive capability of the models is good.

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Evaluation of Material Constants At least eight constants are needed for the model description, and in order to evaluate these, data from conventional triaxial compression, uniaxial strain, and isotropic compression tests are needed. The uniaxial strain or /ifo-tests are not necessary, but such information would greatly improve the accuracy of computed elastic bulk and shear moduli. The models have also been fitted from data obtained in proportional loading and direct shear tests. The first stage in the data reduction and fitting procedure is to utilize the unloading portions of the available results in the determination of the elastic moduli. In some instances average or secant unloading moduli are computed, while in other instances only the initial portion of the unloading stress-strain curve is used in conjunction with nonlinear elastic unloadingreloading schemes or for the recently developed anisotropic hardening versions. The bulk modulus K is readily obtained from isotropic compression tests, and the shear modulus G is readily obtained from triaxial shear tests, whereas the uniaxial strain tests will produce the combination K + (4/3)G. This last test is especially helpful in evaluating Poisson's ratio if such information is needed. The following analytical statements describe the moduli: dJi = 3KdIi'

(49)

dsy = 2Gdef

(50)

and

where K and G can be described as AT = K{Ji, e/), and G = G{J2D, e/) if nonlinearrepresentationsare needed. The ultimate strength or failure envelope can only be fitted from shear tests such as conventional triaxial compression and proportional loading tests. Stress points at failure from many such tests are marked in the72D ~ Ji plane. The coefficients A, B, and C in Eq 41 have the dimensions of stress, (stress)"', and stress,respectively.A-C is equal to the cohesive intercept, that is, the/jo'^^ value when/j = 0. If sufficient data are available to ascertain the position of the bounding Von Mises envelope, then /2D''^^ (max) is equal to A. The constant B describes the rapidity with which the transition surface approaches the Von Mises envelope, and B is validated by trial-and-error attempts at certain key points along the surface. The cap surface has been designated a priori to have an elliptical shape. The object of the data fitting is to modify the ellipse shape by manipulating the governing constants in such a way that the resulting expression corresponds as closely as possible to the test results. This must be done in conjunction with the hardening rule. Both cap shape and hardening rule are varied at the same time in order to obtain such a fit. Each cap surface devised Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

358

LABORATORY SHEAR STRENGTH OF SOIL

for monotonic compression corresponds to a certain measure of accumulated volumetric plastic strain. This strain is constant on the entire cap. Whereas the description of the hardening rule is confined to the/j-axis, the change in volumetric plastic strain upon shearing can be monitored in triaxial tests originating from an isotropic stress state. Certain stress points and the associated total volumetric plastic strain can be discretely marked along given stress paths diverging from the Jj-axis. Numerous sets of such tests and families of experiments will provide the information needed to describe the evolving elliptical caps. In fitting the eUipses great care must be exercised to maintain constant eccentricity. During this procedure new sets of trial constants are utilized to validate the adequacy of the surface and the hardening rule. The parameters D and W, which have dimensions (stress)"' and strain, respectively, have been described previously (Eq 45). They are obtained from isotropic compression tests by fitting Eq 45 to the plastic volumetric strain data. R is obtained from developed ellipse geometry as the ratio of the major to minor axes. The midpoint of the ellipse L is determined in conjunction with the isotropic compression or consolidation stress X which in turn is related to the total volumetric plastic strain that appears in the hardening rule. It is conceivable that such fitting procedures can best be methodically done by using special data reduction computer programs. Attempts have been made to evaluate R from elastic considerations. Yamada and Abou-Sayed [31] introduced the concept of a constant complementary energy surface which was postulated to be equivalent to the cap surface, and this in turn resulted in the following expression for R: ^

^ 9^6(1 + .) G l-2v

^^^'

which conforms closely to resuhs obtained by different model developers. Elasto-Plastic Stress-Strain Model of Lade Description An elasto-plastic constitutive model for three-dimensional stress-deformation analysis for monotonic loading only was developed by Lade and Duncan [//]. The analytical description of the model is based on conventional workhardening incremental plasticity theory. A semi-empirically developed workhardening rule was incorporated into the yield function in the model. The resulting constitutive equation relates rates of effective stress to total strain rates. The model contains essential features from the classical MohrCoulomb strength criterion, which distinguishes this scheme from many other elasto-plastic work hardening models for soils. Yet, unlike the Mohr-

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359

Coulomb strength criterion, it incorporates the influence of the intermediate principal stress in a consistent manner. The conventional shear strength parameters c and do not appear explicitly in the formulation of the ultimate strength surface, or in the yield and potential functions. It should be noted that the theory does not model soils that exhibit cohesive properties or tensile strength. The stress-strain-strength model has been developed for sands and normally consolidated, remodeled cohesive soils. The model is to a great extent characterized by combination of stress invariants. The ultimate strength surface which remains stationary in stress space during loading and unloading has the appearance of the irregularly shaped hexagonal pyramid described by conventional Mohr-Coulomb theory (Fig. 10). However, the functional description of the surface, which derives from the ratio between the cube of the first stress invariant and the third stress invariant {J\^/JT}, provides for smoothly rounded edges in a fashion that conforms to experimental evidence. The model has proceeded through several stages of development; the most recent version presented by Lade [32] includes curved yield and ultimate strength surfaces, independent evaluation, and utilization of yield and potential functions which allow for associated or nonassociated flow rules. Although the initial model development focused on the description of sand, later descriptions treat normally consolidated clay equally well. Test results for sand and normally consolidated clay suggest that the directions of the strain increment vectors at ultimate strength form acute angles with the - Ultimate Strength Surface -Expansive Yield

Surface

('l£'")o

"V Yield ^ \ Surfaces Ultimate Strength Surface

(b)

y§a2=^03

FIG. 10—Ultimate strength and yield surfaces in Lade's model.

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360

LABORATORY SHEAR STRENGTH OF SOIL

ultimate strength surface in principal stress space or in the triaxial plane. On the other hand, the projections of these increments on the octahedral plane are perpendicular to the ultimate strength surface boundaries on that plane. These observations assist in describing the ways the inelastic strain increments are formulated. The plastic strain component of the total strain increment is divided into separate plastic collapse and plastic expansive strain terms, which are modeled separately. The plastic expansive strain is described by conventional plasticity theory by means of an expanding yield surface. This surface may or may not be equal to a plastic potential surface that in turn will result in associated or nonassociated plastic flow rules. The plastic collapse strain accounts for a part of the volumetric strain, and is introduced in order to predict hysteretic unloading and reloading features which are especially pronounced at low isotropic effective stress levels. Figure 11 shows a schematic illustration of the elastic-plastic collapse, and plastic-expansive strain components versus principal stress difference, and how these strain components relate to the volumetric strain. The model is capable of predicting drained as well as undrained behavior. In the model development the elastic strains are determined by linear isotropic elasticity through Hooke's law. The unloading-reloading Young's modulus is obtained from triaxial tests, and varies with isotropic pressure confinement according to £ur = ^ u r P a ( - ^ )

(52)

where K^^ is a constant modulus number for the unloading-reloading characteristics of a particular soil, and the exponent n is determined from triaxial compression tests and data reduction on a log-log graph, a^ is the confining pressure and Pa is the atmospheric pressure that is introduced in order to render the fraction nondimensional. Poisson's ratio v has up to this stage of development been assumed to be independent of density and level of confinement, and has been set constant, with V — 0.2 for sands and c = / (PI) for normally consolidated clays [33]. The ultimate strength or failure surface has currently a curved hexagonalconical shape, which was introduced to account for the decrease in strength observed at high stress levels. The ultimate strength surface is defined by the function

/p = VI

(54)

at ultimate strength. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

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361

(compression)

FIG. 11—Strain components in Lade's model.

The yield surface which defines the boundary between states of stress where both elastic and plastic deformations take place and those where only elastic deformations occur has the same general shape as the ultimate strength envelope. It is initially centered above the hydrostatic stress axis, and expands symmetrically or uniformly from this state with increased deviator stresses or as the yield function increases. The ultimate strength envelope is its outermost limit and the two surfaces coincide at this stage. The movement and the geometry of the yield surface are independent of stress path and stress history. This in turn renders this model an isotropic hardening model. The determination of the yield criterion and its role in the analytical development is not based on an a priori decision with regard to normality. This is a significant deviation from the conventional characterization of many other elasto-plastic work-hardening stress-strain relationships, including the original and modified Cam-Clay models where the yield function and the ensuing constitutive relations are determined by assuming normality at the outset of the development. The yield surface is ff-

27

(55) Pa

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362

LABORATORY SHEAR STRENGTH OF SOIL

and its ultimate position is / / =fp = ^1

(56)

The yield surface remains stationary during neutral loading and unloading. Equation 55 describes the more recent curved expansive yield surface. The straight surface of the earlier model is obtained if m = 0. The previous theory also predicted elastic behavior under proportional loading along stress paths that coincided mih the expansive yield surface, which in turn resulted in loading tangential to the yield surface. A plastic potential function for the expansive surface is developed independently of the yield function through the observation of inelastic strain increments vector directions of selected points in stress space relative to given yield surfaces. Comparisons between the yield and potential functions would establish whether the material requires description according to an associated or nonassociated flow rule. The analytical expression for the potential function is quite similar to an aforementioned ultimate strength and yield function: (57)

where rj2 is a constant dependent on the value of the yield function of the particular point in stress space and on the mean confining stress. The fitting of the potential surface is done in such a manner that the surface at every point intersects the field of experimentally determined plastic strain increments at right angles. The relationship between the plastic strain increment and the potential function is given by deiiP^\-f^

(58)

Two parameters are involved in the stress-strain relationship, r/j and \p. \p characterizes the magnitude of the plastic strain increment, and 172 determines the directions of strain increments in those planes that are perpendicular to the octahedral plane. A translating cap has been introduced in the later version of the model in order to describe the collapse strain and to control the plastic volumetric strain magnitude [32]. The cap is centered around the hydrostatic stress axis, and the cap surface intersects this axis at right angles. The yield function and the potential function are equal in this case as a result of the arguments presented earlier {g^ =fc)The collapse strain yield cap is given in terms of stress invariants as /,=/,2+2/2

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KO AND STURE ON STATE OF THE ART

363

Increments of collapse strains are produced as the value of/^ increases. Since equal strains are produced in an isotropic material under isotropic compression, the yield and potential functions should produce an equal collapse strain in this state, which is described by c/e,/ = X , 4 ^

(60)

where X,- is a coefficient to be determined from the work-hardening law. The total description of the collapse strain increment is done in conjunction with the total differentials of the yield function, the consistency condition, and Hooke's law. The earlier version of the model predicted that only elastic strains would develop during proportional loading situations; however, the introduction of the collapse cap surface and the curved expansive yield surface ensures that nonlinear stress-strain responses also occur along such paths. It should be realized that the growth of/<. alone does not lead to an ultimate strength condition. The interplay between the collapse cap and the expansive surface is illustrated in Fig. 10. In the course of increased compression and deviator stress both surfaces expand, and they are linked by the stress point at the location of their intersection. The plastic collapse strain increment vector and the plastic expansive strain increment vector are added vectorially to give the plastic strain increment. One such vector is shown in Fig. 10. The elastic and inelastic constants describing the model can be determined from simple and conventional experiments such as triaxial and isotropic compression tests. However, an accurate description of the soil's yielding and volume change behavior necessitates testing along more complex stress paths that are of a kind that can only be conducted in a true triaxial cubical apparatus. The initial development of the model was based on such test procedures carried out on a sand [//]. In addition to the aforementioned tests, several tests along proportional loading straight line stress paths ranging from triaxial compression to triaxial extension were carried out. The results were depicted on successive octahedral planes characterized by the increased mean stress which in turn facilitated the study of the material's yielding behavior. Multiple sets of loading and unloading stress-strain curves depicting triaxial deviator stress versus major and volumetric strains form the basis for the investigation of the elastic behavior and for fitting of curved yield surfaces. The investigators observed that for the same mean stress levels the workhardening relationship remained approximately constant irrespective of the relative magnitudes of the principal stresses. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

364

LABORATORY SHEAR STRENGTH OF SOIL

Limitations and Advantages The current model is based on isotropic plastic hardening behavior; therefore it should not be expected that the model will provide adequate predictions for situations where stress reversals or large changes in the stress path under loading or unloading take place. Inherent or induced anisotropy cannot be handled by the model. The model has been fitted for overconsolidated clays or dense sands that show strain-softening behavior. The model is cast entirely in terms of effective stresses, and prediction of responses during undrained conditions will in turn require inclusion of a pore water pressure expression or require that e^ = 0 for each increment of stress [33,34].

The constitutive matrix that evolves from the nonassociated flow rule characterization is not symmetric, and this in turn results in nonsymmetrical element and global stiffness matrices for implementation in analysis. The solution of a nonsymmetric global stiffness matrix together with force and displacement vectors requires special equation solver routines. The incremental elasto-plastic constitutive theory models quite well many important aspects of soil behavior encountered in laboratory investigations, such as stress-path dependency, shear dilatancy, influence of the intermediate principal stress, and influence of mean effective stress levels. The constitutive matrix provides coupling between shear stresses and normal strains as well as between normal stresses and shear strains. Evaluation of Material Constants Only conventional triaxial and isotropic compression test results are needed to generate data for the determination of the constants of this model. At least two triaxial tests conducted at different confining stress levels are needed in order to obtain best-fitted curves for constants to be described later in this section. Although Lade has shown that more elaborate test procedures do not produce significantly more information for many sands, it is believed that tests should be conducted over a wide range of confining stress levels, as well as with variation of the intermediate principal stress. Axial and volumetric strain measurements are needed. The variation of the unloading and reloading Young's modulus is determined as part of a two-step procedure, as discussed earlier in the section on the hyperbolic model. E,r = K,,p,{-^^

(61)

The first step involves the determination of £•„ for various unloadingreloading confining stress levels (Fig. 11). The second step involves plotting

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KO AND STURE ON STATE OF THE ART

365

£'ur versusCT3from each test conducted at different stress levels on a log-log graph. The resulting slope and the intercept of the fitted line with a^ = I defines the exponent n and modulus number K^^- It should be noted that E^^ or A^ur does not correspond to the Ei and K for the Duncan-Chang hyperbolic model, since the latter pertains to a composite elasto-plastic tangent modulus. The coefficients r)i and m, which define the ultimate strength surface, are determined by plotting the expression log {J\^/J3 — 27) versus log (Pa/Ji) at specimen failure on a log-log graph (Fig. 12). The factor rjj is deduced from the intercept of the fitted straight line at the ratio log iPa/J\) = 1. The factor m is the slope of the fitted straight line in the log-log plot. The apex angle of the rounded hexagonal pyramid/cone increases with the value of rji, and the curvature of the ultimate strength surface becomes more pronounced with increased values of m. As noted earlier, m = 0 produces a straight conical surface. At this stage, it is worthwhile to note that sands and drained normally consolidated clays behave quite differently in some important respects. The yielding and ultimate strength characteristics of sands are highly dependent on the initial density, which in turn influences the internal friction angle. Therefore it can be stated that any given sand will possess many different ultimate strength surfaces whose locations are dependent on the initial density. On the other hand, there is no conclusive evidence that normally consolidated clays behave in this manner. Thus it can be stated that only one position of the ultimate strength surface exists for a normally consolidated clay. The plastic potential function gp is a function of rjj and m. The factor m has already been described. The factor r)2 is determined from the experimentally obtained directions of the plastic strain increments plotted in the triaxial-Rendulic plane. In order to describe ri2 it is first necessary to determine an incremental "plastic" Poisson's ratio

"" = - T ^

(62)

This value is subsequently substituted into Eq 63, which was developed by combining Eq 62 for the incremental plastic Poisson's ratio and the flow rule expressed by the plastic potential gradient.

3(1 + vP)Ji2 - 27a3(ai + VPOJ) '" ^

'Pari , I , , — 1 / a3(a, + VP03)

'^'

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>n(l + .P)7,2\——

(63)

/,(^)+27

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(al

366

LABORATORY SHEAR STRENGTH OF SOIL

n Actual Data at Failure

"'

o

. ».

[m

C3»

^

1

Po/Ji'i

\ log(pg/J|) FIG. 12—Evaluation of coefficients in Lade's model.

As described earlier, experimental evidence suggests that conventional triaxial compression tests at certain stress levels will produce the necessary information. The expansive yield function ff appears as a variable in the expression for 7/2- A graph is produced by plotting the computed expression for »j2 as a function of^ for a given triaxial cell confining stress. A typical graph is shown in Fig. 13. The incremental "plastic" Poisson's ratio is determined from triaxial tests by subtracting the elastic and the collapse strain increments from the total strain increment. de/jP = deij - de,/ - de,/

(64)

It is usually observed that rj2 is almost a linear function otff in spite of the elaborate expression (Eq 63) relating the two terms. Furthermore, it appears as if the slopes of the straight lines pertaining to certain confining stress levels are identical, although the intercept of the lines with the 7/2 axis is dependent onff3.Lade has suggested that ri2 can be expressed by (65)

where S is the slope of the straight fitted lines, and the two last terms characterize the intercept. The coefficients R and S are obtained from the diagram shown in Fig. 14. Lade [32] has elaborated further on the characteristics of 1J2 and/^. The work-hardening law is characterized by a semi-empirical procedure. It is obtained by fitting curves to experimental data relating plastic work to the degree of hardening. It is described in part by the proportionality \p which after an appropriate analytical operation can be expressed as Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

KO AND STURE ON STATE OF THE ART

X„ =

367

AW„ Pa

3gn + mi)2

(66)

where AWp is the increment in plastic work corresponding to an increase in the stress level characterized by A/j. In order to derive a semi-empirical expression for the parameter Xp, it is necessary to describe an increment in plastic work per unit volume, AWp, by means of known quantities. Experimental evidence suggests that the yield function fy can be expressed in terms of the plastic work as /W„\i/i

f'="-'^'{7:)

(67)

where ^ > 0.

Increasing 03

Intercepts at

ff • 0

FIG. 13—Evaluation of coefficients in Lade's model.

J'3/Pa FIG. 14—Evaluation of coefficients in Lade's model.

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LABORATORY SHEAR STRENGTH OF SOIL

In this expression the coefficients a, b, and q are constant for a given triaxial confining pressure a^. The constant a is determined by

"~''Mw

]

^^^^

V'^p peak/

where e is the base for the Napier logarithms and Wp peak is the value of Wp at peak ultimate strength. The constant q is discussed subsequently. The constant b is determined by 1 q^p

(69) peak

The plastic work at peak strength varies with the confining stress, and the relationship can be investigated further by plotting the variables in a log-log diagram (Fig. 15). W'ppeak=^/'a(y-)

(70)

The constants P and t are determined as the value when (oz/pa) = 1 and the slope of the fitted straight line in the diagram, respectively. The constant q is formally defined as

" p peak


(71)

60/

where the functional combinations {Wp (^,fp «>) and (Wp ^^i,, T/J) constitute two sets of corresponding values on a curve where {Wp/pJ is plotted versus fp. In principle, it can be stated that any two points on the given curve can be used for defining q, but Lade found that the optimum curve fit was achieved when the peak point value of the curve and the point value corresponding to 60 percent of r/j on the pre-peak work-hardening part of the curve were utilized. This particular scheme for evaluating q is performed for a certain confining stress level. The variation of q with confining stress can be plotted in a separate diagram (Fig. 16); the relationship often appears to be linear.

. = a + ^(g)

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where a and 0 are the intercept between the straight line and the ^-axis where (aj/j?,,) = 0, and the slope of the straight line, respectively. Lade has discussed certain details pertaining to the distinction between workhardening and work-softening parts in the Wp versus/) relationship [32]. Anisotropic Elasto-PIastic Model of Prevost Description A set of elasto-plastic anisotropic hardening models for characterizing many categories of soil responses ranging from undrained behavior of

I /

'

p

FIG. 15—Evaluation of coefficients in Lade's model.

0

<'3/PQ

FIG. 16—Evaluation of coefficients in Lade's model.

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370

UBORATORY SHEAR STRENGTH OF SOIL

saturated clays to drained behavior of sands has been developed by Prevost [12,35-37], An improved version has recently been developed for predicting stress-strain-strength behavior under drained conditions in conjunction with Biot consolidation theory [38], The models have evolved from the observation that the stress-strain history has a pronounced influence on the constitutive behavior of soils, and the realization that this feature, which is related to induced anisotropy, may be of primary importance in the development of constitutive theories. Prevost has utilized anisotropic hardening concepts forwarded by Mroz [39] to obtain a model which can simulate realistically the plastic behavior of soils upon reversed loading. The object is to describe the influence of inherent as well as induced anisotropic elasto-plastic, hysteretic, and path-dependent stressstrain behavior as accurately as possible. This is achieved by merging concepts from isotropic and kinematic hardening plasticity theories [40,41], It is often observed that most soils can exhibit behavior of either category depending on the initial conditions and the type of loading subsequently applied to the soil. Soils that are initially subjected to isotropic or anisotropic consolidation behave differently when sheared under proportional and monotonic loading, with the differences in stress-strain-strength behavior becoming pronounced when the load history is more complex. The current model was developed on the premise that repeated load cycles and nonproportional loading require formulations which allow for the description of induced anisotropy as well as inherent anisotropy. The model appears to be especially well suited for irregular loading paths in the deviatoric subspace. The anisotropic hardening behavior is described by means of a field of plastic shear moduli associated with a corresponding set of nesting yield surfaces in stress space. Models that use nesting surfaces have been described in great detail by Mroz [39,42], Individual plastic moduli are constant on their particular surfaces, but the complete description of the constitutive behavior is dependent on the stress path between the surfaces and the relative configuration of these. Such a description was achieved in the original model through the assumption of associated flow properties, a flow rule, and a hardening rule in conjunction with the standard procedures for deriving stress-strain relations in incremental hardening plasticity. The newer model development, which incorporates drained soil behavior, includes a nonassociated flow rule on the yield surfaces enclosed within the ultimate or bounding surface, and it prescribes an associated flow rule on this extreme surface. The yield surfaces are allowed to translate in stress space while they at the same time change in size. The deformation rates associated with an incremental stress state are determined by the translation and the change in size of particular yield surfaces. In the implementation of the theory it is assumed that the stress increment for a short increment follows a straight line in stress space as well as in the stress-strain plots. This feature simplifies

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KO AND STURE ON STATE OF THE ART

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the theoretical formulation of the model as well as its implementation in computational schemes. A set of piecewise linear stress increments constitute the stress path; in the limit this path can be visualized as being smooth and of arbitrary shape. Each nesting surface is described by plastic shear and bulk moduli and a diiatancy parameter in the case of the newer model. It should be noted that the material constants which are connected with each step on the stress path are described by the nesting yield surface that was most recently penetrated. This again shows that refined predictions are obtained by including a sufficient number of nesting surfaces in order to both smooth the stress path and to update the material variables. Since the loading in the original model takes place under undrained conditions, the yielding of the clay is independent of the imposed octahedral normal total stress. Therefore only deviatoric stresses appear in the general yield function. The isotropic undrained behavior of clays has in the past been successfully modeled by the Von Mises criterion [43]. This yield criterion is therefore the nucleus of the current model, but some modifications have necessarily been introduced in order to extract the anisotropic and path dependent performance from the model. The yield condition pertaining to one particular stage (m) of the evolving surface has the form 3 Jm

— ^-a/'))(5^-a^("'>)

[^(m)]2 = 0

(73a)

The parameters a,,''"' characterize the material's memory of past loading or unloading events, and represent the center coordinates for the current yield surface, /„,, which appears as a circle when projected on the octahedral plane. The parameter k^"'^ constitutes the current size or radius of the yield surface, which appears as a right circular cylinder in stress space with its axis parallel to the hydrostatic line. Since the model is stated in terms of deviatoric stresses, it is realistic to introduce an outermost or bounding yield surface that also serves the part of an ultimate strength surface, outside which no stress state is admissible. In the new model version, which incorporates the effect of the mean normal stress, the piecewise evolving surface has the form /„_ = - | [s.. - a,y<"''][5,y - «,/'">] + C\p-

/3<"'']2 - [A:("')]2 = 0

(73fc)

where p is the mean effective stress and |8<"'* is the center coordinate of the wth surface along the/>-axis. The surfaces described in Eq. 13b are ellipsoids of revolution with the major principal axis initially coaxial with the isotropic stress axis for an initially isotropic material. A general description of these surfaces is shown in Fig. 17, which includes

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372

LABORATORY SHEAR STRENGTH OF SOIL

Path of movement of nested surfaces

p= l/3(oy+2o,:

(a)

In p-q

Plane

(b) In Transformed

Plane

FIG. 17—Nesting yield surfaces in Prevost s model generalized to three-dimensional loading.

definitions in the triaxial compression as well as extension regimes. It is interesting to note that circular projections in the deviatoric subspace or octahedral plane are indicated in spite of the separate compression and extension descriptions. Drained soil behavior would probably exhibit hexagonal yield surface features on such planes. Ease of model representation is achieved by introducing a new parameter Cp for the mean effective stress axis, where C is termed the yield surface axis ratio, which in turn gives the yield surfaces a circular shape instead of the more cumbersome elliptical shape [38]. The new and old model theories have many common features; for the sake

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KO AND STURE ON STATE OF THE ART

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of brevity emphasis will here be put on the old model. Readers are referred to the quoted references. During the course of loading or unloading, the constitutive relationships are governed by the expansion or contraction as well as translatory features of the yield surfaces and by the associated hardening rule. The initial position of the yield surfaces prior to a loading and unloading program is prescribed by the preconsolidation state. An isotropically consolidated specimen would be represented by a stress point on a surface of infinitesimal magnitude located at the center and coinciding with the hydrostatic axis, whereas an anisotropically consolidated specimen would produce a stress point on a surface displaced asymmetrically with respect to the hydrostatic axis (Fig. 18). The preconsolidation stress axis describes the initial position, and since the parameters a,y*"'' may be different from each other and not equal to zero, the yielding is anisotropic (Fig. 17). If the material is inherently anisotropic-orthotropic and consolidated in such a way that the principal material axes are oriented differently from the global system axes, it is to be expected that all a//"'* ^ 0. But if the principal material axes and the system axes coincide, then the mixed terms, a^/'"' = a.^S"''' = «,,*'"' = 0 prior to applied loading. The more ideal case of complete isotropy is encountered for axe'""' — a^'""' = a.^^"'^. A A^Q-consolidation, for example, would result in a displaced circular yield surface which would be located on the particular vertical stress axis. It is therefore important to maintain a physical reference axis system independent of material axis systems. Movement of the stress point from the initial position in loading is defined by the field of plastic moduli, which in turn are defined in stress space by a collection of yield surfaces/o,/i,/2, •••,/„,. • •• ./p. where/,, is the bounding surface, with respective circle sizes, A:*"* < fc'" < kS^^ . . . < A:'''' and center positions a;,", a//", a^/^', . . . , a^/P* (Figs. 17 and 18). The yield surfaces are said to be nesting because they do not intersect. The surfaces are translated by the stress point and under certain conditions may move to new positions, as if they were pushing each other on common tangent planes. The expression describing the geometric features under these conditions is

A:(0)

-

^(1)

-

• •• -

pj)

(74)

During loading and in those instances where the deviatoric stress increment vector is directed out from the current yield surface,/„,, the total deviatoric strain increment is given by dei^ = de^f + def

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(75)

by

ASTM by

of

British

374

LABORATORY SHEAR STRENGTH OF SOIL

dsii

de,:

2G

+ HJ

m)12 [*<"•)]

(*W -

oikl'"^)dSki

(76)

which reflect the flow rule. The plastic shear modulus H„,' for the yield surface/„,, and the associated flow rule, are used to describe the plastic strain, while G is the elastic shear modulus that prescribes the elastic strain. The elasto-plastic shear modulus associated with the yield surface /„, can therefore be stated as

-H„,- -2G +H„, —

(77)

It is observed that H„,' is allowed to be zero or less than zero on the outer surface only. A scalar parameter X is used to characterize both k^'"^ and H„,'. It increases monotonically during loading as well as in unloading, and is described by the length of the plastic deviatoric strain path as

X = 1 {J defdeifl

(78a)

It should be mentioned that the pressure-sensitive model version also uses the function e„"

dt,:P

mb)

FIG. 18—Nesting surfaces in Prevost's model obtained from triaxial testing.

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375

to characterize Jfc*'"' and H„'. eaP reflects directly volumetric hardening characteristics. In the event unloading takes place, the stress increment vector is directed inwards from the current yield surface. The plastic modulus H,„' associated with/„, must therefore have an infinite magnitude, which results in initially elastic behavior for the first step of unloading. H„,' also has an infinite magnitude at the initial stage/o, with size fc"" = 0 associated with an infinitesimal yield surface. Reverse yielding takes place from the point of stress increment reversal or unloading. The proximity of the new / ) -surface from the new /g-surface located at a point on the old outermost touched nesting surface defines the extent of the elastic range. The inward piecewise evolution of the nesting surfaces appears quite similar to the one described during primary loading. Within the framework of incremental plasticity theory it is more convenient to write the deviatoric stress increment in terms of the deviatoric total strain increment as 2

« . . — «• ••('")

dsij = 2G - 2 (2G - //„,)

'j^(,„)j2

[s,i - «,/"•>] de„

(79)

In order to describe this relationship completely the hardening rule must be incorporated. The hardening is reflected in the yield surface's position coordinates a,,''"'. So, if the stress point currently associated with yield surface /„, moves to surface /„,+], the translation of the nesting load surface is characterized by the increment or change in position of coordinates c/a,/'"' by

da,/'"* = ^^ I

k^)

) ^(7 - [—

(80)

^ii^

where the scalars A:'"'' and *;<"'+') denote the instantaneous sizes of the yield surfaces/„, and/„,+i, respectively. Likewise the tensors «,,*'"> and a,;/"'+" denote the location of these surfaces along the deviator stress axis. These parameters are associated with a certain value of the hardening parameter X defined in Eq 78. The parameter d/x is obtained from the consistency condition df = 0, which specifies that the stress point cannot leave the yield surface during loading.

dn =

^H„,(sii - aii^'"^)deii - k^"'^dk<-^ ± _ _ • ;t(m + l)^(m) _ | (^^.. _ „ J".+ l))(s.. -

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„Jm))

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EST No

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reproductions

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LABORATORY SHEAR STRENGTH OF SOIL

where dSij = H„,deij

(82)

The various categories of material models and their capabilities can be summarized as follows: 1. Model with Isotropic Hardening and Softening Rules—The yield surfaces do not translate in this case, but they increase in size concentrically as the loading proceeds. The plastic stress-strain-strength behavior is independent of the mean effective normal stress. Strain-softening behavior can be activated in one model version when the extreme yield surface is reached. The elasto-plastic shear modulus takes on a definite negative value. 2. Model with Kinematic Hardening and Softening Rule—For this model category the yield surfaces do not change in size, but are translated in stress space by the stress point, which is the conventional feature in some metal plasticity kinematic hardening models. A strain-softening rule can be activated also in this case when the outermost yield surface is reached. 3. Model with Combined Kinematic and Isotropic Hardening and Softening for Pressure Insensitive Soil—This model category is mainly intended for simulating situations involving undrained clay behavior. The yield surfaces change in size and translate by the stress point at the same time. This is the model described in Eqs 74 to 82. 4. Model with Combined Kinematic and Isotropic Hardening and Softening for Pressure Sensitive Soil—This model represents the most universal application of Prevost's theory. The yield surface is described in Eq 73b. Many of the model variables and constants vary with volumetric strain or mean effective stress [38]. This completes the description of the anisotropic hardening stress-strain model. Limitations and Advantages Although the later version of the model includes drained behavior, the model which is generally most familiar to users is only valid for undrained situations. In this model it is assumed that associated plastic flow takes place on all surfaces, which is a reasonable assumption that has often been verified experimentally. The new model utilizes a nonassociated flow rule on the internal nesting surfaces, whereas an associated flow rule is introduced on the ultimate strength or bounding surface. It is asserted that the material behavior information needed to predict complex loading events can be obtained from simple tests, which are described subsequently. However, load reversals or other dramatic deviations from straight-line load paths will change the material constitution, and they may in fact erase newly created fabric features. The influence of a rotating

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377

principal stress field is accounted for in the analysis and theory of the model, but such refinements may become clouded since the laboratory data input are of a very conventional character. If the memory is erased to some extent during a prototype operation, this will not be detected by the model since laboratory information is lacking and there is no avenue for incorporating such features in the model. Far more complex stress path tests may be needed to validate the model. The model may appear intractable and too complex to many practitioners. But stress-induced anisotropy is accounted for in a realistic manner, and this model may still be the simplest and most complete analytical statement on elasto-plastic anisotropic hardening theory. Similar descriptions have been described by Mroz et al [13,44]. Evaluation of Model Constants The evaluation of the model constants requires the assessment of the initial positions and sizes of relevant yield surfaces from consolidation or precompression data, prior to undrained loading. The user must select a priori how many nesting surfaces are necessary for defining the stress-strain traces in a piecewise manner and how these surfaces should be spaced. Triaxial compression and triaxial extension tests in the octahedral plane at a given mean stress level provide sufficient information for the description of the undrained soil model versions, whereas more than two test sets at various mean stress are needed for describing the pressure-sensitive models. The associated plastic moduli are also computed, and it is determined how they change as the loading continues. The ultimate strength surface is determined by conducting conventional triaxial compression and extension tests on identical soil samples. The elastic shear (G) and bulk (B) moduli are derived by conventional means, which may involve the evaluation of early initial tangents or early unloading tangents in shear stress versus strain tests and initial unloading slopes in isotropic compression tests. Endochronic Theory A new approach has been developed in the last decade for describing the history-dependent response of inelastic materials. The fact that this approach, called the endochronic theory, does not require identification of a yield surface or the definition of loading and unloading makes it particularly attractive for soils which develop plastic strains from the onset of loading. To the uninitiated reader or user the endochronic models may appear as a hybrid between linear visco-elasticity and ideal plasticity. What sets this model apart from elasto-visco-plastic models is the introduction of the concept of "endochronic time" or "intrinsic time" in place of real time. The model has been found to be an invaluable tool in simulating behavior of

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378

LABORATORY SHEAR STRENGTH OF SOIL

metals and concrete, since it reproduces well strain-hardening as well as strain-softening, and other characteristics of plasticity in predominantly uniaxial stress fields. The endochronic theory, developed by Valanis [45], has been applied to modeling soil behavior by Bazant and Krizek [46], Cuellar et al [47], Ansal et al [48,49], Bazant et al [50], and Valanis and Read [51]. This theory is under vigorous development and we will attempt to summarize the essential features of the basic approach. Description of Theory The volumetric and deviatoric strains are treated separately. The deviatoric strain increments are expressed as the sum of the elastic and inelastic components as rfe,, = dei/ + de,f (83) dsu

=

Sjj

2G+1G''

(84)

where Sy is the stress deviator, G is the shear modulus which depends on the stress level, and z is the intrinsic time whose increment dz is defined by

where zi and T\ are material constants, dt is the real-time increment, and the parameter f is utilized to represent phenomenologically the accumulation of mjcrostructural changes as deformations develop, and can be used to represent strain hardening or softening behavior. For time-independent materials, Eq 85 reduces to dz = —

(86)

The increment d^is assumed to be a function of only the current stress state a, strain state e, and the cumulative value of f. Thus df can be rewritten as d^ = F(€,g,nd^

(87)

where f is the distortion measure, with d^ defined as d^ = V Vide/jdeij

(88)

The function F, representing hardening and softening behavior, must be determined semi-empirically from experimental data. It is convenient to consider F as & composite function in which

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KO AND STURE ON STATE OF THE ART 379

m

F{t, o, t)d^ =

F,(€, a)

di

(89)

The function F^ is chosen to represent the effects of the stress and strain states, and / is chosen to reflect the stress history. For example, Ansal et al [49] proposed the forms

P,=

a +

l-fl,/,|(l-KM2D) 0.01 + 02

(90)

Pa

and ^1

fi-n) = 1 +

1 + ^2';

(91)

where a, ai, 02, a^, fii, and ^2 ^^ constants, p„ is atmospheric pressure, 7] and /] are the first stress and strain invariants, and IID is the second invariant of the strain deviator. The material constant z 1, appearing in Eq 85, is called the plasticity coefficient, and is chosen to account for the rigidity and deformability of the soil and for clays is given by Ansal et al [49] as a function of the product of the initial void ratio CQ and the consolidation pressure OQ. The volumetric strain increments are also expressed as the sum of the elastic and inelastic components: de = de' + deP da' 3K

+ d\

(92)

where a' = effective volumetric stress, and d\ = densification-dilatancy measure, d\^Lie,g,\)d^

(93)

The function L plays the same role in controlling the inelastic volume changes as F did in controlling the hardening-softening behavior under deviatoric stress. Similar to the development leading to Eq 90, Ansal et al [49] postulated that for clays

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LABORATORY SHEAR STRENGTH OF SOIL

Co[l + C,/|] -^ '-^

L(i, a, X) -

1+ -^)(1 » Pa /

+C3/2B)(1

(94) +C4X)

where the C's are material constants. Thus the endochronic theory describes soil behavior on the basis of two material variables, the intrinsic time f, and the densification-dilatancy measure X. Semi-empirical functions, examples of which are given in Eqs 90, 91, and 94, are used to represent the dependence of these variables upon the stress and strain states. In addition, the strain-history effect is accounted for by the distortion measure ^, Eq 88, which is coupled with the functions for f and X to reproduce the volumetric and shear response along any stress and strain path. Limitations and Advantages The fact that a yield surface is not required in the formulation of the endochronic theory is attractive, since there is no need for an argument regarding normality of the flow rule. The inelastic response of soil to volumetric and shear loading is modeled directly by semi-empirical functions. The desired degree of accuracy can be obtained by increasing the complexity of these functions, although it has been shown that a few constants (for example, five) may be sufficient for adequately representing clay behavior. Further, it appears that if sufficient experience has been gathered in applying this theory, and if meaningful correlations can be established to express the material constants in terms of some index properties of a large variety of soils, then the need of extensive soil testing could be bypassed. However, due to the nonuniqueness of the curve-fitting procedures, one can never be sure that the set of constants assigned for a particular type of soil can adequately represent the response under general three-dimensional stress paths, especially along paths that differ markedly from those used in the curve fitting. Nor is it safe at this stage of theory development to make extrapolations beyond the range of soil types for which satisfactory experience has been obtained. Evaluation of Material Constants The number of constants appearing in the semi-empirical functions depends on the accuracy desired in matching experimental data. Two approaches are possible in evaluating these constants for a given clay. The first involves performing a relatively simple stress-strain test on the given soil, such as the triaxial test, and determining the constants by an optimization technique. This evaluation requires the integration, by trial and error, of the

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KO AND STURE ON STATE OF THE ART

381

incremental equations in the theory, and curve-fitting the equations to the experimental data. As usually is the case, there is no unique set of values for the constants that will give a perfect match to the data. Thus the correspondence between the equations and the data can only be optimized locally adjacent to the initial guesses of the values of the constants. Obviously, the experience of the modeler plays an important role in the success of this first approach. The second approach is to establish correlations for each constant to the basic properties of clays, such as the Atterberg limits, and the consolidation pressure. By assembling these correlations over a wide range of clay types and over a wide range of stress and strain history, it is possible to determine the values for a particular soil by using its index properties, without having to perform any testing. These two approaches were demonstrated by Ansal et al [49]. General Discussion The constitutive models discussed in the previous sections are presently in common use for the analysis of stresses and deformations of soil structures. They have been selected for review as examples of various types of models whose input requirements for calibration present different approaches to laboratory data reduction. These models are summarized in Table 1 with respect to the characteristic features, capabilities, and data requirements. One surprising common thread running through this wide variety of models is that they all require laboratory tests no more complicated than the conventional triaxial compression test. This could be due to the unavailability to the model developer of more sophisticated test equipment, such as the hollow cylindrical torsional shear device or the cubical true triaxial test device, that Saada and Townsend have reviewed. One exception to this is the case of Lade, who did calibrate his model against true triaxial test data, but who still falls back on the reliance of the more conventional and more readily accessible triaxial test. It is indeed fortuitous that these models require such relatively simple tests for generating the data base for their calibration, because it leads directly to the widespread use of such models by the practitioners in geotechnical engineering. On the other hand, it has not been conclusively established that constitutive models that have been calibrated with data from the highly specialized triaxial test could successfully predict the response under more general three-dimensional and nonproportional loading. Considering the fact that all models start with the explicit or implied assumption of isotropic behavior, and the fact that no special provisions were made in the model formulation to account for stress-induced anisotropy, one is led to suspect that such dominant characteristics of soil response are not within the reach of the predictive capabilities of existing constitutive theories. The problem of stress-history effects occupies a central position in the study

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LABORATORY SHEAR STRENGTH OF SOIL

TABLE 1—Summary of constitutive

S 3

«_

< [2

c5 X ^

E Z « 1 z

o

Hyperbolic (DuncanChang) DruckerPrager

deformation theory

3

elastic—perfectly plastic (isotropic)

4

Cam-Clay

elastic-hardening plastic (isotropic)

6

Cap elastic-hardening (Weidlinger) plastic (isotropic)

8

Lade

elastic-hardening plastic (isotropic)

14

Prevosl

elastic-hardening plastic (isotropic)

Endochronic

incremental plasticity without a yield surface

more than 4 18

s -s 3 fl 3 conventional triaxiat compression tests at different 03 2 conventional triaxial compression tests at different 03 1 isotropic consolidation and swelling test. 1 conventional triaxial compression test 1 isotropic compression test with at least 1 u n load ing- re loading cycle, 3 conventional triaxial compression tests at different 03 3 conventional triaxial compression tests at different 03 1 triaxial compression and 1 triaxial extension test requirements go up according to desired accuracy

in general, yes. curve fitting procedures well defined yes

yes

yes. location of CSL is involved

yes

in general, no

in general, no. although procedures well defmed yes. hardening function difficult to evaluate no

yes

in general, yes

yes

in general, yes

in general, no

N.A. = not applicable.

of soil behavior and its mathematical modeling. However, its full understanding still awaits much further research. There appears to be some confusion among the constitutive model developers and users on the question of coaxiality, anisotropy, and normality. It is essential to clarify such issues, since their understanding is central to the further developments of these or new models, as well as to the manner in which laboratory data should be analyzed. If the applied principal stress axes are aligned with the principal material axes, then it is expected that the resulting principal strain axes would be coincident (coaxial) with the stress axes, irrespective of the anisotropy of the material. For an isotropy material, coaxiality is automatically obtained, while noncoaxiality of stresses and strains is a direct consequence of anisotropy. It is easy to visualize that, since shear strains are developed in an orthotropic material in those principal stress directions which are not coincident with the axes of orthotropy, the noncoaxiality of principal stresses and strains is the rule. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

KO AND STURE ON STATE OF THE ART

383

models and their capabilities.

illl

111

ill

•£•8-si

N.A."

yes. often quoted in literature

associated

yes, dynamic shock wave propagation

yes

in general, no

in general, no

yes

yes

associated

in general, no

associated

in general, no

associated/non-

no

associated

in general no, no anisotropic hardening included

yes

no

yes

associated/non-

no

yes

no

yes, anisotropic harden-

associated

yes

in general, no

yes

N.A.

ing features partially included

It is common practice to analyze laboratory test data in terms of stress and strain invariants since, as demonstrated in the constitutive models described in this paper, many of the models are formulated on the basis of such invariants. It is not sufficient to keep track of only the stress and strain magnitudes in terms of the invariants; their directions are also important. If measured strains are analyzed to derive plastic strains, and if their increment vectors are plotted and superposed on the stress space where the yield surface is also plotted in order to verify normality, one would expect again that normality would not be obtained as a rule for anisotropic materials. Even if normality is shown for certain circumstances, there still exist doubts on the overall validity of such conclusions, since only partial data (magnitudes and not directions) are being used. On the other hand, if only loading in the direction of the principal materials axes is used, as in conventional triaxial testing of cylindrical samples whose axes are either perpendicular or parallel to the bedding planes, the resulting principal stress and strain axes are auto-

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LABORATORY SHEAR STRENGTH OF SOIL

maticaliy coaxiaL But it is rare in practice to find such coincidence of applied stresses with the material layering. It is perhaps appropriate to point out the difficulties to be expected in attempting to accurately model soil response. For anisotropic materials, it is necessary to keep track of the stress directions as well as the stress magnitudes. Thus at least six quantities are required (for example, the three principal stresses and their orientations with respect to the material reference axes) to specify the applied stress state. The specification of the three stress invariants is not sufficient for such purposes. This automatically points to the deficiency of those models that currently require only the stress invariants for representing soil behavior. This includes all the models that have been reviewed in this paper. Although some of these models do have the capability of incorporating kinematic hardening behavior, such representation is always carried out with the implicit assumption of nonrotating principal stress directions. There are several reasons for the lack of such considerations in the constitutive modeling of soil behavior. The primary reason is the obvious mathematical complexities which must accompany the incorporation of effects of rotating stress states on the behavior of anisotropic materials. A second reason equally responsible for inhibiting such developments is the lack of test equipment that will provide for such stress rotations. The hollow cylinder torsional shear test and the cubical test in the direct shear cell, both of which were reviewed and evaluated by Saada and Townsend, are both recent developments that could potentially provide the answer to the need for valid laboratory test data, but they have not received widespread utilization to the point where there is a data bank accumulated from which model developers can draw information regarding the appropriate features to put into their theories. As mentioned at the beginning of this paper, any constitutive model must be capable of qualitatively representing the right pattern of behavior before it can be quantitatively calibrated. Both the qualitative and the quantitative aspects require good quality laboratory data. Conclusions At the beginning of the 1970s there existed a large gap between the availability of powerful analytical techniques for the calculations of stresses and deformations in soil masses and the ability to model the constitutive behavior of soils. This has motivated the development and refinement of the models described in this paper, which have been selected for inclusion as representative of the various classes of models. Many others that have been proposed are not considered here, obviously to avoid duplication. The level of activities in such research development has been very high, and has led to some very sophisticated formulations for the complex behavior of soils. However, at the same time, it has come to be realized that these constitutive models have not

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KO AND STURE ON STATE OF THE ART

385

been fully validated for their performance under certain types of loadings. This is due primarily to the lack of quality laboratory data that point to the influence of such effects as described earlier, although it is not difficult to accept intuitively the existence of these effects. The authors feel that in order to close this new gap it is imperative that laboratory test procedures be developed to study these effects. The feedback from laboratory studies will provide the basis for further validating existing and new models. The collection of good laboratory data under a variety of loading conditions to form a data bank, from which future theoretical developments can draw, appears to be an important step that can be readily accomplished to provide the impetus for continued evolution of constitutive modeling.

References [/] Research Conference on Shear Strength of Cohesive Soils, American Society of Civil Engineers (ASCE), Boulder, Colo., June 1960. [2] Biot, M. A., Journal of Applied Physics, Vol. 12, Feb. 1941, pp. 155-164. |J] Masson, R. M. and Ko, H. Y. in Proceedings, Second International Conference on Numerical Methods in Geomechanics, Blacksburg, Va., June 1976, pp. 294-305. [4] Duncan, J. M. and Chang, C. Y., Journal of I he Soil Mechanics and Foundation Division, ASCE, Vol. %, No. SM 5, Sept. 1970, pp. 1629-1653. (5) Vagneron, J., Lade, P. V., and Lee, K. L. in Proceedings, Second International Conference on Numerical Methods in Geomechanics, Blacksburg, Va., Vol. 3, 1976, pp. 1329-1351. [6] Prager, Vi., Journal of Applied Physics, Vol. 20, 1949, pp. 235-241. (7) Drucker, D. C , Quarterly Applied Mathematics. Vol. 7, No. 4, 1950, pp. 411-418. [8] Drucker, D. C , Gibson, R. E., and Henkel, D. J., Transactions, ASCE, Vol. 122, 1957, p. 338. [9] Roscoe, K. H., and Burland, J. B. in Engineering Plasticity, Cambridge University Press, London, 1968, pp. 535-609. [10] DiMaggio, F. L. and Sandler, I. S., Journal of the Engineering Mechanics Division, ASCE, Vol. 97, No. EM 3, June 1971, pp. 935-950. |//1 Lade, P. V. and Duncan, J. M., Journal of the Geotechnical Engineering Division, ASCE, Vol. 101, No. GT 10, Oct. 1975, pp. 1037-1053. \I2\ Prevost, J. H., International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 1, No. 2, 1977, pp. 195-216. \13\ Mroz, Z., Norris, V. A., and Zienkiewicz, O. C , International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 2, 1978, pp. 203-221. [14] Dafalias, Y. F. and Herrman, L. R. in Proceedings, International Symposium on Soils under Cyclic and Transient Loading, Swansea, U.K., 1980, pp. 335-345. [15] Kondner, R. L., Journal of the Soil Mechanics and Foundation Division, ASCE, Vol. 89, No. SM 1, Feb. 1963, pp. 115-143. [16] Kondner, R. L. and Zelasko, J. S. in Proceedings, Second Pan-American Conference on Soil Mechanics and Foundation Engineering, Vol. I, 1%3, pp. 289-333. [17] Janbu, Nilmar, in Proceedings, European Conference on Soil Mechanics and Foundation Engineering, Wiesbaden, West Germany, 1963, Vol. 1, pp. 19-25. [18] Kulhawy, F. H. and Duncan, J. M., Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 98, No. SM 7, July 1972, pp. 653-665. 1/9] Duncan, J. M., Byrne, P., Wong, Kai S., and Mabry, P., "Strength Stress-Strain and Bulk Modulus Parameters for Finite Element Analysis of Stresses and Movements in Soil Masses," Geotechnical Engineering Report, University of California, Berkeley, 1979. [20] Drucker, D. C , Prager, W., and Greenberg, H. J., Quarterly Applied Mathematics, Vol. 9, pp. 381-389, 1952.

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LABORATORY SHEAR STRENGTH OF SOIL

[2/1 Dnicker, D. C. and Prager, W., Quarterly Applied Mathematics, Vol. 10, No. 2, 1952, pp. 157-165. [22] Roscoe, K. H., Schofield, A. N., and Wroth, C. P., Geotechnique, Vol. 8, No. 1, 1958, pp. 25-53. [23\ Roscoe, K. H., Schofield, A. N., and Thurairajah, A., Geotechnique, Vol. 13, No. 3, 1%3, pp. 211-240. [24] Schofield, A. N. and Wroth, C. P., Critical State Soil Mechanics, McGraw-Hill, London, 1968. [25] Burland, J. B., "Deformation of Soft-Clay," Ph.D. thesis, Cambridge University, 1%7. [26] Sandler, I. S., DiMaggio, F. L., and Baladi, G. \., Journal of the Geotechnical Engineering Division, ASCE, Vol. 102, No. GT 7, July 1976, pp. 683-699. [27] Sandler, I. S. and Baron, M. L. in Proceedings, Third International Conference on Numerical Methods in Geomechanics, Aachen, West Germany, Vol. 1, 1979, pp. 363-376. [28] Baladi, G. Y. and Rohani, B., Journal of the Geotechnical Engineering Division, ASCE, Vol. 105, No. GT 4, April 1979, pp. 465-480. 129] Christian, J. T., "Plane Strain Deformation Analysis of Soils," Ph.D. thesis. Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Mass., 1966. [30] Tang, W. H. and Hoeg, K., "Plane Strain Loading of a Strain-Hardening Soil," Contract Report No. 3-129, Report 5, Contract DA-22-079-ENG-471, Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Mass., March 1968. [31] Yamada, S. E. and Abou-Sayed, A. S., Journal of the Geotechnical Engineering Division, ASCE, Vol. 105, No. GT 2, Feb. 1979, pp. 183-200. [32] Lade, P. V., International Journal of Solids and Structure, Vol. 13, 1977, pp. 1019-1035. [33] Lade, P. V. in Proceedings, Third International Conference on Numerical Methods in Geomechanics, Aachen, West Germany, April 1979, pp. 1325-1337. [34] Lade, P. \., Journal of the Geotechnical Engineering Division, ASCE, Vol. 104, No. GT 6, June 1978, pp. 721-735. [35] Prevost, J. H., Journal of the Geotechnical Engineering Division, ASCE, No. GT 8, Aug. 1978, pp. 1075-1090. [36] Prevost, J. H., Journal of the Engineering Mechanics Division, ASCE, EM 5, Oct. 1978, pp. 1177-1194. [37] Prevost, J. H. in Proceedings, Third International Conference on Numerical Methods in Geomechanics, Aachen, West Germany, Vol. 1, 1979, pp. 347-361. [38] Prevost, J. H., "Nonlinear Anisotropic Stress-Strain-Strength Behavior of Soils," Department of Civil Engineering, Princeton University, Princeton, N.J., 1980. 139] Mroz, Z., Journal of Mechanics and Physics of Solids, Vol. 15, 1%7, pp. 163-175. [401 Hill, R., The Mathematical Theory of Plasticity, Clarendon Press, Oxford, 1950. [41] Prager, W., Journal of Applied Mechanics, Transactions of the American Society of Mechanical Engineers, Vol. 78, Series E, 1956, p. 493. [42] Mroz, Z., Acta Mechanica, Vol. 7, 1%9, pp. 169-212. [43] HOeg, K., Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 98, 1972, pp. 43-58. [44] Mroz, Z., Norris, V. A., and Zienkiewicz, O. C , Geotechnique, Vol. 29, No. 1, 1979, pp. 1-34. [45] Valanis, K. C , "A Theory of Viscoplasticity without a Yield Surface," Archives of Mechanics, Vol. 23, 1971, pp. 517-551. [46] Bazant, Z. P. and Krizek, R. J., Journal of the Engineering Mechanics Division, ASCE, Vol. 102, No. EM 2, 1976, pp. 225-238. [47] Cuellar, V., Bazant, Z. P., Krizek, R. J., and Silver, M. h.. Journal of the Geotechnical Engineering Division, ASCE, Vol. 103, No. GT 5, May 1977, pp. 399-416. [48] Ansal, A. M., Bazant, Z. P., and Krizek, R. J., "Constitutive Relation for Isotropically Consolidated Clays," Report 77-12/643/1, Department of Civil Engineering, Northwestern University, Evanston, HI., Dec. 1977. [49] Ansal, A. M., Bazant, Z. P., and Krizek, R. h. Journal of the Geotechnical Engineering Division, ASCE, Vol. 105, No. GT 4. April 1979, pp. 519-537. [50] Bazant, Z. P., Ansal, A. M., and Krizek, R. J., Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM 4, Aug. 1979, pp. 549-565. [5/1 Valanis, K. C. and Read, H. E., Journal of Computers and Structures, Vol. 8, 1978, p. 503. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

V. p. Dmevich'

Normalized Stress-Strain for Undrained Shear Tests

REFERENCE: Drnevich, V. P., "NomuUzed Stress-Strain for Undrained Shear Tests," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 387-409. ABSTRACT: Normalized stress-strain curves are obtained by use of maximum shearing stress to normalize shear stress and reference strain to normalize shear strain. Reference strain is defined by initial tangent shear modulus and maximum shearing stress. This paper defines initial tangent shear modulus and maximum shearing stress to be functions of effective stress state. Consequently, the normalizing parameters vary with stress points along the stress path. An incremental procedure is established whereby normalized stress-strain curves can be obtained. These curves are relatively independent of effective stress path and are nearly identical to those obtained from drained tests. This method shows promise for correlating results from drained and undrained triaxial tests with results from other types of shear tests. KEY WORDS: stress-strain, stress paths, simple shear tests, triaxial compression tests, shear modulus, normalization techniques, soils, sample disturbance, laboratory tests, data analysis

Many types of shear tests are being used to determine parameters and coefficients for constitutive equations describing shear behavior. Among these tests are the triaxial compression test, direct simple shear test, and the torsional simple shear test. If a given soil were tested in each of these apparatus, the resulting shear stress-shear strain behavior would depend significantly on the apparatus used, particularly if the soil were saturated and the testing were done without allowing drainage. Some of the differences in behavior would be due to the boundary conditions imposed by a given apparatus—for example, end platen restraint, reinforced membrane, membrane penetration, etc. Others would be due to shortcomings of the theories used for data reduction. This is particularly true when elastic relationships are used to obtain shear data from axial compression data. 'Professor of Civil Engineering. University of Kentucky, Lexington, Ky. 40506.

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Even for a given test apparatus, there is difficulty in reconciling stressstrain data from tests on the same soil but tested at different confining stresses or tested at different anisotropic states of stress. Presented herein is an incremental procedure for normalization of stressstrain data from laboratory shear tests. The procedure accounts for effects of shear strength, confining stress, consolidation at anisotropic stresses, void ratio changes, and effective stress path. A curve of normalized shear stress versus normalized shear strain results. Details of the procedure for drained and undrained simple shear and triaxial compression tests are given. Normalization of both shear stress and shear strain was proposed by Hardin and Dmevich [1].^ The process involved (/) calculating a maximum applied shear stress, T^I,^; (2) normalizing the applied shear stress, r, with 7n,ax' {3) determining an initial tangent shear modulus, Gmax'. i'f) calculating a reference strain, y^, from T^ax and Gmax; and (5) normalizing the shear strain, y, with reference strain, y^. Thus for a given test, single values of Tmax' Gmaxi and y^ were used to normalize all data. This procedure was applied to quasistatic as well as dynamic loadings of all types of soils [/]. For undrained shear tests on saturated or nearly saturated soils, the effective stress path will most likely be different from the total stress path. The value of applied shear stress at failure will then be different from the value of Tmax which is Calculated assuming a simple shear (vertical) stress path and shear strength in terms of effective stress. Also, if one tries to use the undrained shear strength for T^^^, the normalized stress-strain curve will be different for drained and undrained tests at the low applied stress levels even though no excess pore pressures are generated. The actual stress-strain curves should be identical at these low stress levels, and it is reasonable to expect that the normalized curves should also be identical. The normalization process suggested by Hardin and Dmevich [/] also does not apply to triaxial compression type shear tests. On the other hand, the incremental procedure proposed herein applies to any shear test where the effective stress path is predominately one of shear. This includes triaxial, direct simple shear, and torsional simple shear tests. Hardin [2] suggested that different classes of loading be considered with Class 1 Loadings, as described in Fig. 1, being those whose effective stress paths are within ± 4 5 deg to the vertical. It is suggested that the incremental procedure proposed herein be applicable to all Class 1 Loadings. The concepts of the incremental normalization process are presented first, then the detailed procedures are outlined for special loadings. Some examples of normalized data are given, and a brief discussion is presented on the method and its use for generating stress-strain behavior for in situ conditions. ^The italic numbers in brackets refer to the list of references appended to this paper.

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DRNEVICH ON NORMALIZED STRESS-STRAIN

389

sin 0 '

Range of Effective Stress Poths For Class I Loadings qj"^\

c' cos 0' %'

Pi'

Initial State of Stress

o-v'

FIG. I—Range of effective stress paths for Class 1 loadings.

Basic Concepts of Incremental Nonnalization Consider an effective stress path as shown in Fig. 2a. The specimen has been anisotropically consolidated prior to the application of the shear loading phase. The stress point labeled a defines the normal and shear stresses for this condition. It is assumed that the shear strength of the soil is defined by the Mohr-Coulomb parameters c' and (^'. On the stress path diagram, the intercept of the Kf-line is given by c' co&<j>' and the slope by sin (^'. Next, consider some increment b-c along the stress path. This increment is shown in larger scale in Fig. 2b. The vertical component of this increment b-d, corresponds to an increment of shear stress. If this increment of shear stress were associated with a drained simple shear test having a vertical stress path, then the value of T^^^ and Gmax would be known and constant. From these, the reference strain, 7^, would be calculated from

By Eq 1, reference strain would also be constant. In a manner analogous to the stress path diagram, it is possible to construct a strain path diagram (from the Mohr's circles for strain). The vertical component of the associated strain path increment would be one half the shear strain increment. If the shear strain increment is divided by the value of reference strain, 7^, a value of incremental normalized shear strain is obtained. This incremental normalized shear strain is assumed to be independent of the direction of the stress path increment or the direction of the strain path increment. The total normalized shear strain for the end of the stress path increment (Point c in this example) is obtained from

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390

LABORATORY SHEAR STRENGTH OF SOIL

(7/7r), = (7/7r),-l + (A7/7r> (2) where J and j — 1 are the 7th and {j — l)th stress points, respectively, along the stress path. The corresponding normalized shear stress for each point along the stress path is obtained from the value of T associated with that stress point divided by the value of T^ax associated with the assumed vertical effective stress path for pure shear. The initial portions of incrementally normalized stress-strain curves, where little or no excess pore pressures are generated, will be consistent for both drained and undrained loadings. Furthermore, at failure, the value of T/Tjaax wiU be Unity for both drained and undrained loadings. Techniques for Special Loadings General Two types of tests are addressed in this section: simple shear and triaxial compression. The loading phase for each may be drained or undrained. Specimens may be isotropically or anisotropically consolidated. The former (a)

q ,

c cos 0

(b)

Actual Stress Path Increment

Associated Sttear Stress Increment

FIG. 2—(a) Typical stress path increment: (b) Enlarged view of stress path increment.

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391

is considered a special case of the latter. For anisotropically consolidated specimens, the normalized shear stress and the normalized shear strains do not include shear stresses or shear strains associated with the consolidation process but only those associated with the loadings applied after consolidation. Simple Shear Tests Anisotropic consolidation can be achieved in both direct simple shear tests and in torsional simple shear tests. In the former, the lateral effective consolidation stresses are related to the vertical effective stresses by the coefficient of lateral earth pressure at rest, KQ. In torsional simple shear tests, anisotropic consolidation stresses are achieved by applying axial stresses (positive or negative) in addition to the isotropic confining stresses. Nearly any principal stress ratio, less than that required for failure, may be achieved. In Fig. 3a, the stress point with coordinates (p,', q,) is associated with anisotropic consolidation. The corresponding Mohr's circle is the small dashed half circle passing through this point. The point in Fig. 3a marked (aj'), corresponds to the horizontal planes in the specimen which are major principal planes. The shearing stresses applied during the shear loading phase of the tests are applied to this plane. The vertical vector, labeled T, represents the applied shear stress. For a given value of shear stress applied during a drained test, the major and minor principal stresses change and may be established by means of a new Mohr's circle which is the solid half circle in Fig. 3a. The stress path associated with the value of T for drained loadings goes from the point with coordinates (p,', ^,) to the point (p,', q). Additional shear stress could be applied until the stress path intersects the Kf line. The value of the stress point ordinate at failure is defined as qf, and the head of this vector is shown in Fig. 3a. The Mohr's circle corresponding to failure is shown in Fig. 3a by the dashed partial circle passing through the point (p,', qj). Note that the applied shear stress associated with failure is given by 7^,3, with the head of this vector also shown in Fig. 3a. By geometry, it can be shown that ^max = K p ' s i n . / , ' + C' C0S
(q.)^O.i

(3)

where for drained loadings: p ' = p , ' = 0 . 5 [ ( a , ' ) , + (a3'),], 9,-= 0.5[(a,'),--(03'),], ' = angle of shearing resistance in terms of effective stress, and c' — cohesion in terms of effective stress. Note that T^a, 's not the absolute maximum shear stress but the maximum applied stress. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

392

LABORATORY SHEAR STRENGTH OF SOIL

(a)

/>^^^^

c' cos 0'

^max\

/^"fq^ T \ / /"tq^N / / ri

(b)

:' cos 0

FIG. 3—(a) Stress path diagram for anisotropic consolidation and drained simple shear loading; (b) Stress path diagram for anisotropic consolidation and undrained simple shear loading.

The situation is slightly different for undrained conditions when a shear stress is applied. Due to dilation (positive or negative), excess pore pressures will be generated. If they are positive, they will cause all abscissa values to be shifted to the left by the amount of the excess pore pressure. The shift will be to the right for negative excess pore pressures. The case with positive excess pore pressures is demonstrated in Fig. 36. The effective stress path is the dotted line from a to b. The center of Mohr's circle moves from p , ' to />', a distance equal to the excess pore pressure. Likewise, the effective vertical stress is reduced by the excess pore pressure and the vector T represents the applied shear stress. For the normalization process proposed herein, the value of T^ax for point b in Fig. 3Z) would be the value of applied shear stress required for a simple

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DRNEVICH ON NORMALIZED STRESS-STRAIN

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shear loading through point b to the Ay-line. The large dashed portion of a circle intersecting the A^-line would be the corresponding Mohr's circle; the value of Tmax (with head of vector shown in Fig. 3b) associated with this circle is calculated from Eq 3. The value of p ' in Eq 3 for this case isp,' minus the excess pore pressure. It is plain to see that the value of r^ax varies with the excess pore pressure generated and that each undrained stress path increment will have a different value of r^^^. The next item needed for the normalization process is the initial tangent shear modulus, Gmax- It can be measured at the onset of applied shear loadings. Typically, these measurements should be made at shear strains of 0.001 percent or less. Ultra sensitive static tests or resonant column tests can be used. Both give essentially the same values [3,4]. For stress path increments after the first, the value of G^ax for the normalization process may change due to changes in a variety of parameters, most of which were discussed by Hardin and Black [5]. The most significant parameters are accounted for in the Hardin Equation. An improved version of this equation (Hardin [2]) is

""-=

625 (OCR)'^ , 0.3 + 0.7e^ ^^"-" ^ "

^'^

where e = void ratio of the soil, OCR — Over Consolidation Ratio, K — coefficient based on plasticity index from Table 1, Pa = atmospheric pressure in same units as a„' and Gmax- and = mean effective confining stress. The ideal way to obtain G„,ax-data for each stress path increment would be to use wave propagation techniques (resonant column or ultrasonics) in conjunction with the applied shear stress. However, this would be quite cumbersome and impractical for most situations. It is recommended that either precise static measurements or wave propagation techniques be used to get [GmaxJi for the first stress path increment. In lieu of this, values of [Gmaxl/ may be estimated from Eq 4. For subsequent stress path increments, values of [Gmax]. may be adjusted to account for changes in void ratio and mean effective confining stress according to the following equation which is based on Eq4.

Gmax = [Gmax]/ Q J + ^QJ^^l

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LABORATORY SHEAR STRENGTH OF SOIL

TABLE \—Coefficients

K/orEq4.

K

Plasticity Index

0 20 40 60 80

0 0.18 0.30 0.41 0.48 0.50

> = 100

For simple shear type loadings, it can be shown that [a„'/(a„'),] = [{p'-

qi/3)/(p,'

- q,/3)]

(6)

where each of the parameters are defined in Fig. 3b. Note that for drained simple shear loadings, p' = Pi' for all stress path increments and Eq 5 becomes only a function of void ratio. The initial void ratio can be calculated from measurements made at the specimen at the beginning of the test. These will have to be adjusted for volume changes associated with consolidation to get the void ratio at the time of shear loading. Volume changes associated with drained shear loading may be measured by monitoring the pore water entering or leaving the specimen. However, the initial tangent shear modulus is not too sensitive to changes in void ratio. This is demonstrated in Fig. 4 for different initial values of void ratio from 0.2 to greater than 1. Preliminary results have shown that volumetric strains due to applied simple shear are usually less than 2 percent. From Fig. 4 this would mean that volume changes due to applied simple shear loading would cause less than a 5 percent change in initial tangent shear modulus. Consequently, for drained simple shear tests, the initial tangent shear modulus may be constant. For undrained simple shear tests, only the portion of Eq 5 associated with mean effective confining stress needs to be applied and Eq 5 with Eq 6 becomes Gn,ax = [Gmax],- Kp ' '

9,/3)/(p,' -

9,/3)]0-5

(7)

where the parameters are defined in Fig. 3b. In summary, for simple shear tests, it can be said that the incremental normalization process is identical for both the direct simple shear and the torsional simple shear. If these tests are drained during the application of shear, the stress path is vertical, Tn,ax and G^ax are both constant for all stress path increments. Hence, for this case, the incremental process is not needed. For undrained simple shear loadings, the process for each stress path increment consists of determining a value of r^ax by use of Eq 3 and adjusting Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

DRNEVICH ON NORMALIZED STRESS-STRAIN

Gmox

395

1.0

[^maxli

-5

0

5

Volumetric Strain (%) FIG. 4—Effects

of volumetric strain on G„„„..

tlie value of [G„ax\i by Eq 7. Henceforth the procedure is as outlined in the section on Basic Concepts on Incremental Normalization. Triaxial Compression Tests Consolidation PAa^e—Specimens in the triaxial test may be consolidated isotropically or anisotropically. The state of stress and the stress path diagram for these tests are identical to those for simple shear. The stress point associated with the consolidated specimen has coordinates (p,', 9,). Axial Loading Phase—The total and effective stress paths associated with the axial loading phase of the triaxial compression test are shown in Fig. 5. For drained tests, the two stress paths will be identical and have a slope of unity. The horizontal differences between the total and effective stress paths is a measure of the excess pore pressure generated by the axial loading. The procedure for normalizing these data is similar to the procedure for normalizing the data from simple shear tests in that for each stress point on the effective stress path, values of T^^^, G^ax. and 7^ must be determined. In addition, values of axial stress and axial strain must be converted to values of shear stress, T, and shear strain, 7. In triaxial tests, the vertical and horizontal planes in the specimen always remain principal planes. Application of axial load increases the major principal stress which in turn causes the radius of the Mohr's circle to increase Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

396

LABORATORY SHEAR STRENGTH OF SOIL

q

1

^ ^^'l^^^-^^^ ^^^^'--^^^^-Excess Pore Pressure

^-'*C1 /

^ ' ' ^ ESP\

/ /TSP

''i 1

1

1

p. p FIG. 5—Total and effective stress paths for iiiidrained triaxial compression test on anisotropically consolidated specimen.

and hence causes the shear stress to increase. In Fig. 6a, the small dashed circle represents the condition at the end of the consolidation phase and the solid circle represents some point on the stress path for a drained axial loading. It can be shown by geometry that the value of r is related to agxiai by 9

= 0.5 a.axial

(8)

where a^^^^\ = axial stress applied in addition to consolidation stress. The value of q^^^^ associated with drained triaxial loadings is the shear stress associated with the large dashed Mohr's circle shown in Fig. 6a. The head of the vector representing q^^x is also shown in this figure. The magnitude of ^niax is given by c' cos 4>' + p' sin 4>'

(9)

The value of 7n,ax used for normalizing r is the portion of q^^^ due to the applied axial load and is the difference between q ^ and qj. Hence, the value of 'max is given by c ' cos 0 ' + /J' sin 0 ' — qr, (10) Note that values of q„^^ and r„^^ vary continuously with applied axial stress. At failure, the value of q^^,^ is equal to the shear strength and the value of r/Tmax equals unity. For undrained triaxial loadings, the procedure for obtaining T and Tma, is exactly the same as for drained loadings and Eqs 8 and 10 apply without modification. The corresponding Mohr's circles, stress path, and vectors are shown in Fig. 66. At failure, the value of ^^ax will equal the undrained shear strength and the value of T/T^ax will again equal unity. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

DRNEVICH ON NORMALIZED STRESS-STRAIN

397

(a)

(b)

FIG. 6—(a) Stress path diagram for anisotropic consolidation and drained triaxial compression loading: (b) Stress path diagram for anisotropic consolidation and undrained triaxial compression loading.

Values of Gmax for normalization may be obtained from torsional resonant column tests on the specimen after consolidation is complete. Use of the Hardin apparatus [6] is ideally suited for this because values of G^ax can be measured continuously during the axial loading phase. If this apparatus is not used, data from resonant column tests on similar specimens consolidated at the same mean effective confining stress may be used to obtain values of [CJ'max]/ for use in the data reduction process. If no test data are available, the value of [Gmax], may be estimated by use of Eq 4. Equation 5 is then used to adjust values of [G^^^]j for changes in volume and mean effective confining stress. For the situations where volume changes are small (less than 2 percent) and for undrained tests, Eq 5 reduces to Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

398

UBORATORY SHEAR STRENGTH OF SOIL

C?max -

[Gn,ax],- Hp' '

q/^ViPi

'

?,/3)]«-5

(H)

where the parameters are defined in Figs, ba and bb. Values of reference strain for each point on the triaxial compression test stress path are calculated by means of Eq 1 using the values of T^a, and G^ax determined by use of Eqs 10 and 11. The last items needed for normalization of triaxial compression data are values of shear strain associated with a given stress point. For drained tests and for undrained tests on partially saturated soils, measurement of specimen volume changes or of lateral deformation is important if accurate normalized data are to be obtained from the triaxial test. If specimen volume changes are measured, the equivalent shear strain for the jth stress point is calculated from 7,- = 7,_, + 1.5 (e,- - e,-,) + 0.5 (V,. - V,_,)/V

(12)

where 7,-1 €,, 6,-1 V;- Vj-i V

= equivalent shear strain for {j — l)th stress point, = axial strain for thejth and {j — l)th stress points, — specimen volumes for thejth and (j — l)th stress points, and = initial specimen volume.

If lateral deformation measurements are made, the equivalent shear strain for the jth stress point is calculated from 7,- = 7/-, + (6/ - €,-i) - [(e,),- - (e,),-i]

(13)

where (e^);, (er),-i = radial strains for the./th and {j — l)th stress points, respectively. The development of Eqs 12 and 13 is based on the discussion of plastic dilation by Hardin [2] and on the use of the Mohr diagram for strain. The process is analogous to calculating a tangent Poisson's ratio and applying it to the axial strain increment to determine a shear strain increment. The total shear strain for that stress point is the shear strain for the previous stress point plus the increment in shear strain. Once the shear strain values are established, the procedure for obtaining normalized behavior is identical to that for the previous cases. Examples of Normalized Stress-Strain General Torsional simple shear tests and triaxial compression tests were conducted on a variety of undisturbed and on one laboratory remolded and compacted soil as part of a recently conducted research program [4]. Results of tests on Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

DRNEVICH ON NORMALIZED STRESS-STRAIN

399

the laboratory compacted soil are presented herein to demonstrate the nature of the normalization process and to compare the results from one type of test to another. A description of the soil tested is given in Table 2. Torsional Simple Shear Tests A special torsional simple shear apparatus was used for conducting these tests. This apparatus, described in Ref 4, 7. and 9, had a shear strain resolution better than 0.001 percent and was capable of applying strains greater than 4 percent. Both torque-controlled and rotation-controlled tests could be performed. The tests reported herein were performed on isotropically consolidated and saturated specimens that were 5 cm (2 in.) in diameter by 7.5 cm (3 in.) long. The shear loading was done with the apparatus set for rotation control. Two tests were performed with drained conditions prevailing and two were performed with undrained conditions. The effective stress paths for these tests are given in Fig. 7 and the conventional shear stress-shear strain curves are given in Fig. 8. Incrementally normalized shear stress-shear strain curves are given in Fig. 9 for all four tests. From this figure, it is evident that a single curve can be used to represent this soil. Triaxial Compression Tests The triaxial apparatus that was used for these tests incorporated a Hardin resonant column oscillator [6] that made it possible to measure values of in-

TABLE 2—Summary of soil properties. Liquid limit Plastic limit Specific gravity

21 15 2.68

Particle Size Analysis % passing 100 79 57 Clay Fraction < 0.002 mm 20% Classification Unified CL-ML AASHTO A4(5) Textural Clay-sand Average compacted density 2085 kg/m3 Mean void ratio 0.521 18.4 % Mean water content Sieve No. 10 40 200

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400

LABORATORY SHEAR STRENGTH OF SOIL

S.

40

60

80

100

120

140

p'(kPa) FIG. 7—Stress paths for torsional simple shear tests on remolded soil.

Shear Strain (%) FIG. 8—Shear stress versus shear strain for both drained and undrained torsional simple shear tests on remolded cohesive soil. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

DRNEVICH ON NORMALIZED STRESS-STRAIN

401

1.25

0.00 ••

20

40

60

80

100

120

140

Norm. Shear Strain FIG. 9—Normalized shear stress-shear strain for both drained and undrained torsional simple shear tests on remolded cohesive soil.

itial tangent shear modulus during the entire testing operation from consolidation through axial loading to failure. Seven tests on the laboratory compacted soil were performed on specimens that were 5 cm (2 in.) in diameter by 10 cm (4 in.) in length. All specimens were isotropically consolidated and back pressure saturated. The effective stress paths for the three undrained tests are given in Fig. 10 and those for the four drained tests are given in Fig. 11. The Kj-lme (shear strength parameters) was the same for both types of tests. The conventional axial stress-axial strain curves for the undrained tests are given in Fig. 12 and those for the drained tests are given in Fig. 13. The incrementally normalized shear stress-shear strain curves for the undrained tests are given in Fig. 14 and those for the drained tests are given in Fig. 15. In both Figs. 14 and 15, the incremental normalization process appears to do a reasonable job of collapsing the data onto a single curve. It is of interest to compare the normalized curves of both the drained and undrained triaxial tests with each other and with the normalized curves from the torsional simple shear tests. This is done in Fig. 16 where the data points correspond to the mean values from Figs. 9, 14, and 15. Examination of Fig. 16 reveals that there is better agreement between the incrementally normalized torsional simple shear data and the undrained triaxial test data than there is between the drained and undrained triaxial data. Part of the disparity of the drained Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

402

LABORATORY SHEAR STRENGTH OF SOIL

200 I I I I I I I I I I I I I I I I I I I I I I I I I

150

100

150

200

250

p' (kPa) FIG. 10—Effective cohesive soil.

200

stress paths for undrained triuxial compression tests on remolded

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

I

100 FIG. 11—Effective soil.

I '

150 p' (kPa)

I I

I I I

200

I ' ' I

250

I I ' I

300

stress paths for drained triaxial compression tests on remolded cohesive

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DRNEVICH ON NORMALIZED STRESS-STRAIN

250 I

200

£ '

150

403

r

-

-

100

4

10

6

Axial Strain (%) FIG. 12—Stress-strain curves for undrained triaxial compression tests on remolded cohesive soil. 400

4

6

8

10

12

Axial Strain (%) FIG. 13—Axial stress-axial strain curves for drained triaxial compression tests on remolded cohesive soil.

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404

LABORATORY SHEAR STRENGTH OF SOIL

100

200

Norm. Shear Strain FIG. 14—Normalized shear stress-shear strain curves for undrainecl triaxial compression tests on remolded cohesive soil.

and undrained triaxial data may be due to differences in the rate of testing. The rate for the drained tests was approximately one third of the undrained. Two additional undrained tests were performed at these slower rates. Results for these tests showed some rate effects, but were still very close to the faster undrained tests. Part of the difference may also be due to the differences in the distribution of axial strains within the triaxial test specimens. This topic is currently undergoing further study. One very interesting sidelight to these triaxial tests is the comparison of the values of G^^^ measured by the Hardin apparatus with those calculated by Eq 11. Data for these comparisons are presented in Fig. 17 for the undrained tests consolidated to 100 kPa (14.5 psi) and in Fig. 18 for the drained tests consolidated to 75 kPa (10.9 psi). In each figure, the data points denoted by circles are the measured values. Those denoted with the diamonds are those determined by use of Eq 11 where the value of [Gmax]/ was the value measured just prior to the initiation of axial loading and reflected the increase in shear modulus associated with about one log-cycie-of-time in secondary compression. The triangular data points utilize the value of initial tangent modulus measured at the end of primary consolidation for the value of [Gmax], and are closer to the actually measured values. The most probable reason for this is that the axial loading process destroys a large portion of the

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DRNEVICH ON NORMALIZED STRESS-STRAIN

100

405

200

Norm. Shear Strain FIG. 15—Normalized shear stress-shear strain curves from drained triaxial compression tests on remolded cohesive soil.

stiffness gained during secondary compression. It is recommended that the value of initial tangent shear modulus measured at the end of primary consolidation be used in the incremental normalization process. Use of Normalized Stress-Strain Curves A detailed presentation on the use of incrementally normalized stressstrain data is beyond the scope of this paper. This aspect is addressed to some extent in Refs 4 and 9 and is the subject of continued study. However, it is appropriate to give a brief overview of applications. In order to obtain stress-strain curves of shear behavior for in situ conditions from normalized stress-strain curves, the initial tangent shear modulus and the shear strength are needed along with some estimate of the loading stress path. With this information, the inverse of the normalization process is performed to get the desired stress-strain behavior. It was shown in Refs 4 and 9 that the normalized stress-strain curves were relatively independent of sample disturbance. Hence, curves generated from tests on "undisturbed" specimens should be quite applicable to in situ conditions even though some inevitable disturbance occurs due to stress release and other causes. It is suggested that the normalized curves define the sense

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406

LABORATORY SHEAR STRENGTH OF SOIL

?—I—I—I—I—r

Slow Undrained Triaxial and Slow Drained and Undralned Torsional Simple Shear in

Very Slow Drained Triaxial Tests

J

I

I

I

I

_i

u

50

150

100

I

I

L.

200

Normalized Shear Strain

FIG. 16—Comparison of normalized data from triaxial compression tests and torsional simple shear tests, both on remolded cohesive soil.

150

Measured

o

o E

50

I 4

6

ID

Axial Strain (%) FIG. 17—Variation of initial tangent shear modulus versus axial strain for undrained triaxial compression tests on remolded cohesive soil.

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DRNEVICH ON NORMALIZED STRESS-STRAIN

200

'

\

407

^

Calculated Based on End of Primary & Secondary

-OOi

-AC Calculated Based on End of Primary Consolidation

50

Axial Strain (%) FIG. 18—Variation of initial tangent shear modulus versus axial strain for drained triaxial compression tests on remolded cohesive soil.

of soil behavior. Values of initial tangent shear modulus and shear strength measured in situ provide the scaling factors which are applied to the normalized stress-strain curves in the deconvolution process. It is also suggested that the incremental normalization process would be beneficial in the study of some of the lesser understood parameters affecting stress-strain behavior, such as creep, overconsolidation, and secondary compression effects. The normalization process accounts for the prime parameters and would permit their effects to be removed. Hence these effects could be studied much more efficiently. Summary and Conclusions An incremental normalization procedure is proposed and outlined. The procedure is applicable to simple shear and triaxial compression tests and may be used for drained as well as undrained tests. Typical test results on a given soil were presented, and it was shown that the incrementally normalized data from different types of tests are relatively independent of the test used. The process is based on the use of effective stress and requires that the initial tangent shear modulus be measured. For cases where this cannot be done, an equation is given which may be used to estimate this modulus. It was shown

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408

LABORATORY SHEAR STRENGTH OF SOIL

that the initial tangent shear modulus varies with changes in void ratio and mean effective confining stress, but is relatively independent of the applied shear stress; this is a confirmation of the findings of Hardin and Black [5]. The normalized stress-strain concept should be helpful in the study of the effects of less dominant parameters on stress-strain because the process of normalization removes the effects of most major parameters. This concept should also be useful in analytical programs that require the stress-strain behavior for a wide variety of initial conditions and stress paths. The process used in the programs would be the inverse of the process used to obtain the normalized curves and would make use of initial tangent modulus, strength data, and effective stress paths which may be different from those used in generating the normalized curves. This feature, plus the fact that the normalized curves appear to be relatively insensitive to effects of sample disturbance, makes the method attractive for accurately describing in situ shear stress-shear strain behavior. Acknowledgments This work was sponsored by a cooperative effort among the University of Kentucky Research Foundation, the Department of Civil Engineering at the University of Kentucky, and the U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., Contract No. DACW39-78-C-0046. The author is grateful for this support. He also wishes to acknowledge the helpful suggestions of his colleague, B. O. Hardin, and the Army's technical monitor, W. F. Marcuson, III. Two graduate students, J. P. Koester and S. H. Bickel, were actively involved through most of the period. Each has written an M.S. degree thesis on his portion of the work. The hard work, long hours, and contributions of these gentlemen are most appreciated. Two additional graduate students, Johnson Toritsemotse and C. A. Rivette, assisted with the data reduction aspects of this work. Their patience and diligence is to be commended. Finally, the author wishes to acknowledge the ingenuity and resourcefulness of the Laboratory Technician, W. W. Thurman, who designed and constructed many of the accessories for the test apparatus. References [/) Hardin, B. O. and Dmevich, V. P., Journal of the Soil Mechanics and Foundations Division, American Society of Civil Engineers, Vol. 98, No. SM7, July 1972, pp. 667-692. [21 Hardin, B. O. in Proceedings, Specialty Conference on Earthquake Engineering and Soil Dynamics, Vol. 1, American Society of Civil Engineers, 1978, pp. 3-90. [3\ Tseng, Richard Jau Yu, "A Study of Liquefaction of Sand by Torsion Shear Test," a dissertation submitted in partial fulfillment of the requirements for the degree Doctor of Philosophy at the University of Kentucky, Lexington, Ky., 1974. [4] Dmevich, V. P., "Evaluation of Sample Disturbance on Soils Using the Concept of

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DRNEVICH ON NORMALIZED STRESS-STRAIN

[5] [6] [7]

[S]

|9]

409

'Reference Strain'," Final Report submitted to U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., on Contract No. DACW39-78-C-0046, May 1979. Hardin, B. O. and Black, W. L., Journal of the Soil Mechanics and Foundations Division. American Society of Civil Engineers, Vol. 94, No. SM2, March 1968, pp. 353-369. Hardin, B. O. in Special Procedures for Testing Soil and Rock for Engineering Purposes, ASTM STP 479, American Society for Testing and Materials, 1970, pp. 516-529. Koester, J. P., "Strain-Control Torsional Simple Shear Investigation of Sample Disturbance Using the Concept of Reference Strain," submitted to the Graduate School, University of Kentucky, Lexington, Ky., in partial fulfillment of the M.S. degree requirements, 1979. Biekel, S. H., "Examination of the Concept of Reference Strain Utilizing Triaxial/Resonant Column Tests on Remolded Cohesive Samples," submitted to the Graduate School, University of Kentucky, Lexington, Ky., in partial fulfillment of the M.S. degree requirements, 1980. Dmevich, V. P. and Massarsch, K. R., Journal of the Geotechnical Engineering Division. American Society of Civil Engineers, Vol. 105, No. GT9, Sept. 1979, pp. 1001-1016.

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p. W. Mayne' and P. G. Swanson'

The Critical-State Pore Pressure Parameter from ConsolidatedUndrained Shear Tests

REFERENCE: Mayne, P. W. and Swanson, P. G., "The Critical-State Pore Pressure Parameter from Consolidated-Undrained Shear Tests," Laboratory Shear Strength of SoU. ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 410-430. ABSTRACT: The results of isotropic and anisotropic consolidated-undrained shear tests (CIU, C/fo, U) are used to determine the critical-state pore pressure parameter (A„). The relative advantages of using the critical-state parameter (A„) over Skempton's pore pressure parameter (^4) and Henkel's parameter (a) are discussed. The effects of overconsolidation ratio (OCR) and initial stress state (Ka) on both Henkel's and Skempton's pore pressure parameters can significantly alter effective stress predictions of undrained strength. The critical-state parameter is independent of OCR, Ka, and level of shear to failure, thus requiring only two basic soil constants in order to predict undrained strength: (/) the effective stress friction angle ('), and (2) the critical-state pore pressure parameter (A„). An "extended" critical-state model is developed using the equivalent pressure concept for overconsolidated states. The method then provides a simple analytical representation of undrained stress-strain behavior and pore pressure response for clays with different values of OCR. One additional soil constant (C,.: the virgin compression index) is required in order to model stress-strain behavior. The validity of the critical-state theory is substantiated by data from over ninety different clay and silt soils reported in the geotechnical literature. Furthermore, the criticalstate concepts are shown to encompass both total stress and effective stress methods under one unified theory. KEY WORDS: clays, effective stresses, overconsolidation, strength, strain, total stresses, triaxial shear tests

pore pressure, shear

Effective stress methods have shown the importance of pore pressures on shear strength and stress-strain behavior of clay soils [l-95\.^ The pore pressures developed during undrained shear depend on several primary fac' Geotechnical engineer and senior geotechnical engineer, respectively. Law Engineering Testing Company, Washington, D.C. 22101. ^The italic numbers in brackets refer to the list of references appended to this paper.

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MAYNE AND SWANSON ON PORE PRESSURE PARAMETER

411

tors: (/) the initial effective vertical stress {a^o'), (2) the degree of overconsolidation (OCR), (3) the initial stress state {KQ), and (4) the applied level of shear stress (or strain). Numerous empirical, experimental, and theoretical methods of representing the undrained response of clay and silt soils during loading have been proposed. The geotechnical community needs a reliable and theoretically sound predictive method which can accurately model the undrained behavior of clay soils from a variety of depositional environments and stress histories. Whether or not a method is applied in practice depends upon its versatility and simplicity. In addition, a good predictive method should require a minimal amount of field and/or laboratory testing and use basic soil constants which are currently recognized by practicing geotechnical engineers. This paper discusses the application of the critical-state pore pressure parameter in a simplified method of predicting undrained stress-strain behavior. The natural variations of the parameter are studied by reviewing data from over 90 different clay and silt soils reported throughout the geotechnical literature. The data are analyzed in terms of total stresses and effective stresses. Critical-state concepts presented by Schofield and Wroth [96] and Roscoe and Burland [97\ are used to incorporate total stresses and effective stresses into one rational theroy. Undrained shear behavior is described using only three soil constants: (i) the critical-state pore pressure parameter (Ao), (2) the effective stress friction angle (<^'), and (3) the virgin compression index (C,,). Present Definitions of Pore Pressure Parameters The concept of a pore pressure parameter was first proposed by Skempton [98] to relate the change in total stress to the effective stress state. Skempton postulated that the pore pressure (AM) which generated as a result of a change in total stress be defined as Aw = B [Aaj + A (Aa, - Aaj)]

(1)

where the parameter B is an indirect measure of the sample saturation, and A is Skempton's pore pressure parameter. For a saturated triaxial compression test (5 = 1), the equation reduces to Au=A (Aq)

(2)

where q is the principal stress difference (a^ — 03). Henkel and Wade [99] subsequently improved upon the equation to include stress invariants such that A« = AP + |(Ar„„) Copyright Downloaded/printed University

by

(3) ASTM

Int'l

British

Columbi

by of

412

LABORATORY SHEAR STRENGTH OF SOIL

where TQCI is the octahedral shear stress, P is the mean normal effective stress, and a is Henkel's parameter. The simplicity of these equations would appear to ensure their use in general geotechnical practice. However, researchers \l,22^3,44,68,84,96,100] have shown that the commonly accepted /4-parameter varies with OCR, A'o, confining pressure, and shear stress level. Henkel's parameter (a) does not vary with confining pressure, but is dependent on OCR, Ku, and shear stress level. The Cam-Clay theory presented by Schofield and Wroth [96] follows the basic physical laws governing conservation of energy. The concepts of work and stored energy are applied using principles of recoverable (elastic) and irrecoverable (plastic) strains. A discussion of yield surfaces applied to this theory has been presented elsewhere [64,96,9A- For an isotropically consolidated soil, the Cam-Clay theory predicts that the pore pressure at failure (M^) is given by

«/ = J ^ T ^ ^

+ P / [1 -

(C - ' 0 C R ) A » ]

(4)

where <^' is the effective stress friction angle, and A^ is the critical-state pore pressure parameter. In the following sections, it will be shown that A„ is a basic soil constant which is independent of initial confining pressure, OCR, A'o, and shear to failure. Critical-State Pore Pressure Parameter The critical-state concepts can be used to represent the undrained strength characteristics of overconsolidated soils. Atkinson and Bransby [101] have derived an expression for the undrained strength of an overconsolidation (O.C.) soil in terms of its normally consolidated (n.c.) strength times OCR raised to a power function. This equation can be expressed in a normalized fashion for an overconsolidated soil which has experienced simple rebound such that 5„/a,„

'(O.C.)

= S,yo„ '(n.c.) OCR^-

(5)

where S„/ay^ ' is the normalized strength to overburden ratio (classically the c/P ratio), and A„ is defined by A„ = 1 - C / C

(6)

where C^ and Cj are the isotropic virgin compression and swelling/recompression indices, respectively. Numerous investigators [101-103] have shown that C^ is in fact a variable with OCR and is different during loading than for reloading. The appropriate "average" value of C^ to use in analysis has been investigated by Egan [47], Pender [103], and Van Eekelen and Potts [50]. In order to avoid this Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

MAYNE AND SWANSON ON PORE PRESSURE PARAMETER

413

problem in the present study, the critical-state pore pressure parameter (A„), has been redefined in terms of overconsolidated strength data:

^^

_ log[5»/g,;(o.c.)] - log[5,/g^'(n.c.)] log [OCR]

Ladd et al [100] and Mayne [104,105] have reported typical values of A„ for several soil types. This definition of A„ is still applicable should the recent method of analyzing consolidation data as presented by Butterfield [106] prove to be valid. Butterfield postulates that Cj is linear for a log [1 + e„] versus log [P'] relationship. It has been previously demonstrated by Ladd and Foott [6] that normalized strengths (S„/a„i') are a function of OCR. The authors have used this approach to review shear strength data from many different sources. The undrained strengths generally refer to peak strengths, since the critical-state strengths were not reported by the experimenters who provided the data. The "critical-state failure" described by Schofield and Wroth [96] is defined as the stress level at which continuous deformation occurs at no change in volume. An actual determination of the "critical-state failure" is difficult, if not impossible, for many natural soils. Instead, it was hoped that the basic concepts proposed by the theory would be valid if applied to undrained peak strength data. Therefore, for simplicity, "failure" has been defined as the undrained strength at maximum deviator stress. Egan [47] explains in more detail the relative positions of the "peak" and "critical" states of failure for soils. Figure 1 is a graphical representation of undrained peak strength to overburden ratios versus OCR for over 90 different clay and silt soils reported throughout the geotechnical literature. The references for each of the soils are listed in Table 1 along with a summary of some relevant soil characteristics. The clay soils have been tested under many different conditions, including type of shear test (triaxial, direct simple shear, etc.), initial stress states (CIU, CAU, C/C„U), testing rates, different researchers and laboratories, soil structure (undisturbed, remolded, compacted), etc. A closer examination of Fig. 1 shows several interesting features: 1. The overconsolidated shear strength—overburden ratio {S„/a^,„') has been normalized to the S^/a,^' ratio for normally consolidated conditions (OCR = 1). This is to force the linear relationship between (S„/a„') and OCR on a log-log plot through the origin, thus allowing a clearer presentation of data. 2. The slope of each relationship is the critical-state pore pressure parameter (A„) of that soil. Values of A,, for each soil have been determined from linear regression analyses and are included in Table 1 for all the soils considered. For clarity, individual data points are not presented; however, samCopyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

414

LABORATORY SHEAR STRENGTH OF SOIL

1

'

'

1

'

'

' • 1

'

'

'

y

_ Note; Numerals correspond to soils and references listed in Table 1. Dashed lines indicate extrapolated data.

20 "-

/ / /

/ 1

10 --

/

A<*?^

"

T3

'5 P 5 •o o O o in >% t: o a u E a> w > O o c "o

~

c/^2 > < ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ - ^ ^ ^ ' y ^ H B S ^ ^ ^ ^ ^ = = = ^ ^=rs^=':l-=«=^°"~

^

,

,

1

r

.

,

,

_ — — '«'

1

1

10

20

.

OCR FIG. 1 — Variation of undrained strength with OCR for over 90 different clay soils.

TABLE \~Soil Reference No.

properties.

SJa^' Soil

1 Weald 2 Kaolin CIU C/iToU 3 San Francisco Bay Mud 4 London Clay 5 Keuper Marl 6 Portland 7 Illite 8 Boston Blue 9 Bangkok 10 Oslo 11 Bradwell

'

Ao

r

(n.c.)

Reference

22.0

0.531

0.994

0.279

Henkel, I960

23.5 22.0 35.2 18.4 25.9 32.0 24.6 26.8 25.4 27.0 20.0

0.398 0.319 0.568 0.384 0.758 0.767 0.491 0.752 0.727 0.618 0.376

0.985 0.984 0.983 0.970 0.999 0.999 0.993 0.998 0.998 0.988 0.959

0.313 0.308 0.432 0.250 0.256 0.300 0.341 0.200 0.270 0.380 0.300

Amerasinghe and Parry, 1975 Mitchell, 1976 Henkel, 1%0 Brown et al, 1975 Ladd and Foott, 1974 France and Sangrey, 1977 Ladd and Foott, 1974 Ladd and Foott, 1974 Simons, 1960 Skempton, 1961

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MAYNE AND SWANSON ON PORE PRESSURE PARAMETER

415

TABLE I—{Continued). Reference No.

Su^O-m'

Soil

0'

A„

r

(n.c.)

Reference

12 Bentler 13 Shellhaven

22.7 23.0

0.590 0.779

0.999 0.994

0.310 0.205

Togrol, 1965 Skempton and Henkel. 1953

14 Calcium Montmorillonite 15 Newfield 16 Vienna 17 Virginia Coastal 18 Spestone Kaolin

12.5 30.5 25.8 30.1 22.6

0.193 0.505 0.671 0.482 0.704

0.919 0.999 0.997 0.955 0.992

0.221 0.475 0.356 0.409 0.210

19 20 21 22 23 24 25 26 27 28 29 30 31

33.7 21.0 21.0 20.0 23.0 24.2 47.0 28.0 22.2 28.3 21.0 37.0 32.9

0.727 0.454 0.772 0.653 0.630 0.590 0.788 0.875 0.641 1.007 0.709 0.671 0.714

1.000 0.967 0.998 0.992 0.995 0.999 0.997 0.972 0.998 0.941 0.994 0.982 0.999

0.400 0.320 0.240 0.255 0.333 0.250 0.430 0.310 0.280 0.265 0.230 0.360 0.335

32 Ghana

20.8

0.290

0.974

0.380

33 34 35 36 37 38

Halloysite Simple Clay Seattle Rang de Fleuve Sodium lllite Grundite

34.3 23.1 28.8 28.6 20.7 32.3

0.835 0.550 0.515 0.920 0.369 0.413

0.992 0.998 0.997 0.995 0.954 0.997

0.418 0.290 0.372 0.378 0.340 0.356

39 40 41 42 43 44 45 46 47 48 49 50

Terra Roxa Amuay Scott Connecticut Varved Toledo Kawasaki Tjipanundjang Weirton Colluvium Concord Blue Agnew Lagunillas Drammen

29.2 29.9 33.4 20.9 20.0 35.9 35.0 19.0 24.8 25.0 26.5 30.7

0.872 0.5% 0.922 0.724 0.619 0.842 0.469 0.498 0.684 0.491 0.589 0.781

0.978 0.993 1,000 0.998 1.000 0.994 1.000 0.982 0.998 0.973 0.992 0.9%

0.313 0.342 0.231 0.163 0.200 0.370 N/A N/A 0.355 0.308 0.305 0.285

51 52 53 54 55 56

Liskeard Vicksburg Massachusetts Moose River Muskeg Ottawa Estuarine Lilla Edet

26.1 25.9 30.5 47.7 35.3 24.3

0.847 0.729 0.223 0.541 0.828 0.372

0.990 1.000 0.999 0.9% 0.9% 0.997

0.298 0.287 0.416 0.683 0.300 0.290

Mesri and Olson, 1970 Sangrey et al, 1969 Hvorslev, 1960 Swanson and Brown, 1977 Parry and Nadarajah, 1973 Shibata and Karube, 1969 Hvorslev, 1960 U d d and Foott, 1974 Moh et al, 1969 Croce et al, 1969 Olson, 1962 Lo, 1962 Simons, 1960 Whitman, 1960 Raymond, 1972 Simon et al, 1974 Gibbs et al, 1960 Koutsoftas and Fischer, 1976 de Graft-Johnson et al, 1969 Taylor and Bacchus, 1969 Ladd, 1964 Sheriff et al, 1972 Tavenas et al, 1978 Olson and Hardin, 1963 Perloff and Osterberg, 1%3 da Cruz, 1963 Lambe, 1963 Landanyi et al, 1965 Ladd and Foott, 1974 Wu et al, 1978 Ladd and Lambe. 1963 Wesley, 1974 D'Appolonia et al, 1966 Egan, 1977 Egan, 1977 Ladd and Lambe, 1963 Van Eekelen and Potts, 1978 Raymond, 1973 Ladd,1962 Wissa et al, 1965 Adams, 1967 Kenney and Watson, 1961 Bjerrum and Simons, 1960

Japanese Little Belt Atchafalaya Soft Bangkok Milazzo Calcium lllite Mexico Volcanic Drammen Backswamp Kars Leda Portsmouth Willard Bay Plastic Holocene

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416

LABORATORY SHEAR STRENGTH OF SOIL

TABLE I—(Continued). Reference No.

Soil

57 New York Varved 58 Khor-AI-Zubair 59 Texcoco

^J^J (n.c.)

Reference

0.990 0.999 0.941

0.328 0.360 0.420

Leathers and Ladd. 1978 Hanzawa, 1977 Alberro and Santoyo. 1973

0.787 0.765

0.999 0.997

0.420 0.400

Mitachi and Kitago. 1976

35.1 34.9

0.851 0.795

0.999 0.998

0.362 0.361

Mitachi and Kitago, 1976

36.1 34.0 36.9 27.0 29.0

0.791 0.786 0.584 0.972 0.662

0.997 0.998 0.999 0.994 0.999

0.410 0.360 0.530 0.290 0.295

Mitachi and Kitago, 1976

0'

A„

r

N/A 27.3 34.0

0.620 0.684 0.725

37.2 35.1

60

Hokkaido Silt A CIU CKoV 61 Hokkaido Silt B CIU CAToU 62 Hokkaido Clay CIU CKoV 63 Fao 64 Saint Alban 65 Kanpur Clay

Hanzawa, 1977 Tavenas et al, 1978 Yudhbir and Varadarajah, 1974 Yudhbir and Varadarajah, 1974 Sketchley and Bransby. 1973 Broms and Casbarian, 1965 Ladd, 1976 Montgomery, 1978 Fischer et al, 1978 Korhonen, 1977 Wu et al, 1962 Broms and Ratnam, 1963 Karlsson and Pusch, 1967

66

Rann of Kutch

26.0

0.454

0.995

0.326

67

Spestone Kaolin

17.2

0.740

0.999

0.184

68

Kaolinite

29.2

0.130

0.999

0.492

69 70 71 72 73 74 75 76

New England Ohio Silt Drammen Clay Lansisalmi Sault Ste Marie Bath Kaolinite Modndal Bangalore Monmorillonite Bangalore Kaolinite Kinnegar Calcutta Regina

32.0 32.9 25.1 19.5 28.9 24.5 27.0

0.715 0.709 0.880 0.364 0.743 0.431 0.720

0.999 0.993 0.999 0.957 0.887 0.996 0.993

0.325 N/A 0.218 0.215 0.327 0.425 0.254

12.5 25.5 27.0 30.2 20.0

0.166 0.326 0.857 0.544 0.556

1.000 1.000 0.944 0.984 0.999

0.211 0.422 0.338 0.342 0.308

81 Long Island Coastal 82 Hackensack Varved 83 New Providence 84 Alaska Gulf 85 East Atchafalaya Kc - 1.00 Kc = 0.67 K, = 0.50 86 Buckshot Clay /fc = 1.00 Kc = 0.67 Kc = 0.50 87 Kyoto 88 Guanabara Bay 89 Kodiak Island 90 Winnepeg Clay

22.8 19.0 30.5 34.5

0.482 0.760 0.720 0.698

0.951 0.986 0.998 0.999

0.271 0.158 N/A 0.408

21.7 18.8 21.5

0.599 0.516 0.488

0.993 0.997 0.998

0.282 0.258 0.281

Donaghe and Townsend, 1978

26.7 22.1 24.9 32.5 25.1 42.2 12.8

0.685 0.730 0.703 0.211 0.880 0.672 0.556

0.992 0.996 0.997 0.999 0.935 0.979 0.997

0.335 0.305 0.320 0.530 0.253 0.510 0.211

Donaghe and Townsend, 1978

77 78 79 80

Sridharan et al, 1971 Sridharan et al, 1971 Crooks and Graham, 1976 Gangopadhyay et al, 1974 Widger and Fredlund, 1979 Swanson and Brown, 1977 Saxena et al, 1978 Abeyesekera, 1979 Singh and Gardner, 1979

Akai and Adachi, 1965 Costa Filho et al, 1977 Sparrow et al, 1978 Crawford, 1964

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MAYNE AND SWANSON ON PORE PRESSURE PARAMETER

417

TABLE I—(Continued). Reference No. 91 92

•^ii/^vo'

Soil

Sydney Kaolin Weald Clay CIU C/CoU 93 Kaolinite Vertical Horizontal 94 Kaolin 95 Beaumont Clay

Reference

Ao

r

(n.c.)

30.7

0.704

0.972

0.410

Poulos, 1978

25.9 25.0

0.683 0.696

0.999 0.998

0.323 0.256

Henkel and Sowa, 1964

27.8 29.2 24.7 24.0

0.736 0.673 0.673 0.624

0.991 0.984 0.991 0.988

N/A N/A 0.238 0.267

Duncan and Seed, 1966

'

Wroth and Loudon, 1967 Mahar and Ingram, 1979

pie correlation coefficients (r) from the linear regression studies are generally high (r > 0.98), indicating an excellent fit. (Note: r = 0 indicates no correlation; r = I indicates a perfect fit). 3. The critical-state theory predicts by conservation of energy that a limiting condition exists (Ao(max) = 1), whereby the work dissipated in the soil must either be equal to or less than the energy input. The soils included in this study lie within the theoretically acceptable boundaries. In fact, the variation of A„ may be approximated as a normal distribution having a mean of 0.64 and standard deviation of 0.18. It should be noted that highly sensitive clays and cemented soils may prove exceptions to this upper limit. It is also observed that those soils in Fig. 1 which exhibit high values of A„ (greater than 0.9) are sensitive clays. 4. The relationships shown in Fig. 1 are from total stress strength data. No direct pore pressure measurements have been used in the analyses. Although most soils encountered in nature are overconsolidated to some degree, the OCR is not often known during testing unless supplementary consolidation testing is conducted or a SHANSEP [6] approach is employed. The parameter A^, may also be determined from the results of consolidatedundrained shear tests conducted at confining pressures less than the maximum preconsolidation pressure (a'^max) without knowledge of the OCR. The critical-state pore pressure parameter is then defined by the absolute value of the slope of a linear relationship between log [S^/a^'io.c.)] and log ( a ^ ' ) , as shown in Fig. 2. The parameter A„ has been defined in terms of initial vertical effective stresses ( a ^ ' ) . Therefore no distinction has been made between isotropic and anisotropic states of stress. A comparison A^ determined from both isotropic and anisotropic stress conditions is shown in Fig. 3. There appears to be little difference between A^ determined from these different test conditions. Mitachi and Kitago [60] have also supported these findings. In general, Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

418

LABORATORY SHEAR STRENGTH OF SOIL

i°g('%

.)

logl

y

/

/

/

/

/

^ A ,

C/

/

/

/

S 'a/u /

/

/

-A

/

6..

Note;

,("c.)

CTVO'

0"

1^0"!

" vo

\

"vmox.

log (OCR)

FIG. 2—Definitions of critical-state pore pressure parameter from undrained strength data.

however, the soils shown in Fig. 3 are laboratory-prepared materials; therefore these conclusions may not be relevant to natural anisotropic clays. In the preceding sections, it has been shown that the critical-state pore pressure parameter is a soil constant. The pore pressure parameter can be used to predict undrained shear strengths for various stress histories and initial stress conditions. The application of the pore pressure parameter is best presented in its relationship with the critical-state theory. The remainder of the paper describes the relatively simple analytical equations which use the pore pressure parameter to predict undrained behavior. Effective Sttess Theories

The normally consolidated undrained strength of a clay soil can be determined from the relationship between log [S„/a„,'] and log [OCR] as the intercept at OCR = 1, as shown in Fig. 2. Alternatively, an effective stress approach by Schofield and Wroth [96] proposes that the undrained stress path to failure for an isotropically normally consolidated soil is given by (?//") = ^ l o g e ( P „ ' / i " )

(8)

where A/ = (6 sin 0 ')/(3 — sin ') is the slope of the failure line m q — p space, and P„' and P' are the initial and current values of mean normal effective stress, respectively. Further derivation gives the Cam-Clay prediction of undrained shear strength for normally consolidated soils as Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

MAYNE AND SWANSON ON PORE PRESSURE PARAMETER

J„/(7^'(n.c.) = 0.5Mexp(— A„)

419

(9)

Measured and predicted values of S^/a^ '(n.c.) are compared in Fig. 4. The results of this study show that for all the soils considered with no adjustments made for test type, sample disturbance, testing rate, anisotropy, or inhomogeneity, a best fit straight line relationship with no intercept is S„/(j„'(n.c.) = 1.114[0.5Mexp(- A„)]

(10)

having a sample correlation coefficient r = 0.83. These findings suggest that the Cam-Clay theory of Schofield and Wroth [96], in general, underpredicts the undrained shear strength by approximately 11 to 12 percent. A similar linear regression study conducted solely on the anisotropic test data (CAU and C/C„U tests) indicated an underprediction of about 7 to 8 percent {r = 0.85). Equations 5 and 9 can be combined to represent the undrained strength for a clay soil over a range of OCR: S,/a^'{o.c.)

= 0.5M(e-' OCR)^"

0.5

(11)

1.0

AoO'sofropi'cJ FIG. 3—Comparison of Ao determined from CAU tests and CIU tests.

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420

LABORATORY SHEAR STRENGTH OF SOIL

0.7

1

,

.

.^

...

.

J

1

,

.

,_

,_

•54

Legend 0.6

•

c m TESTS

•

CAU/CKoU TESTS

r

\r7 .63

Ai •89

0.5 •15

:s

0.4

./^

,74 .3/i J3V59 "77 y's *91. '84 / 10 ,,19*60 / •36 • ••^'^Ki.35^4 47i.58 64A^^ / ^ , 3 n • »16 f 4 0 / '•^ OR'

-

*68

X

53

.

-

!BR'B6 69iv«1

^26 " f p o s ^ e •64 f J '^tffe ^

0.3

*»^\, • 1 4 . ^ < 9 4 „ , 41 •90 760*^8 8^* . F"43 °^

0.2

Xf

/82

0.1

1

1

1

1

0.1

0.2

0.3

0.4

1

1

0.5

0.6

0.7

3 sin^' 3 -mf' FIG. 4—Measured and predicted values of Su/(Jvo'("c.) bv Cam-Clay theory of Schofield and Wroth (961.

Another version of the critical-state model, known as "modified CamClay", has been presented by Roscoe and Burland [97]. For normally consolidated behavior, their theory predicts that 5„/a,/(n.c.) = 0.5M(2-M

(12)

which is shown in Fig. 5 for the data included in this study. Linear regression analyses indicate the model slightly overpredicts the undrained strength by about 6 percent. A best fit line (b = 0) is found to be 5,,/a^'(n.c.) = 0.938 (0.5 Ml-"")

(13)

having a sample correlation coefficient r = 0.84.

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MAYNE AND SWANSON ON PORE PRESSURE PARAMETER

421

0.7 Legend

0.6 ~

.

CIU

»

CAU/CKoU

c&K

TESTS

^ TESTS

^ ^ .63y

.87

"ts 0.5 -

I

74. ^^J^.m

\o.4 Q

JS. r .10 /

^

•'

„ *^

44

-

^"^ ^

/ ™ *'• &

-

*e

/ H 7

/

/

•«?

*«

01 -

1

0./

I

Oi'

1

1

1

0.3

0.4

0.5

1

0.6

07

FIG. 5—Measured and predicted values of Su/avo'(M.o.) by modified Cam-Clay theory of Roscoe and Burland [97].

The statistical results can be used to empirically adjust the theoretical relationships in one of several ways: (/) inclusion of a cohesion intercept term (c '), (2) inclusion of an attraction term (a ') as proposed by Van Eekelen and Potts [50\, or {3) adjusting the value of the friction parameter M (alter ' by approximately 2 or 3 deg) as suggested by Schofield and Wroth [96]. It should also be noted that the majority of the undrained strengths were measured using the triaxial apparatus. The commonly accepted method of determining shearing rates as proposed by Bishop and Henkel [107\ assume only 95 percent of pore pressure equalization at failure. Possibly, the theory is correct and the experimental data are in error.

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422

LABORATORY SHEAR STRENGTH OF SOIL

Stress-Strain Behavior The Cam-Clay models also provide simple analytical representations of undrained shear behavior to failure for normally consolidated soils. Soils which occur at stress states below the current yield surface are assumed to deform as elastic materials. The model presented in this paper deviates from the original theories in that plastic strain concepts are also assumed to apply during overconsolidated conditions. For isotropic consolidation, the stress ratio {q/P') to failure as a function of strain (e) is assumed to be unique for a given soil, independent of OCR. By adopting the expression presented by Schofield and Wroth [96] and substituting an average value of C^ = C^. (1 — A^) from Eq 6, the stress ratio varies with axial strain by -exp

^/^' = M H

M(l+e)log,(10) C,A„(1-A„) '

(14)

where e is the void ratio prior to shear. The current value of mean normal effective stress (P') is determined by extending Eq 8 to represent overconsolidated behavior: P ' = />„ '(e-' OCR)'^" exp A„(l - log, OCR)

(«?/P') M

(15)

The deviator stress q = (ai — a3) may then be expressed as a function of strain by q^iq/P')P'

(16)

The stress-strain function can be obtained in closed-form solution by substituting Eq 14 into Eq 15, and then Eqs 14 and 15 into Eq 16. This "extended Cam-Clay" model can be used to represent the undrained stressstrain behavior for clays as well as provide simplified stress paths to failure. Only three soil constants are required to model this behavior: 0', Cf, and A„. q^ MP/OCR^"exp{A„l(l

- lnOCR)(exp7?6) - 1]}(1 -expRe)

(17)

where ^ ~

Mil +ejln,(10) CrA„(A„ - 1)

The application of the "extended" model to predict undrained stressstrain response is illustrated in Figs. 6 and 7 for several different soils. The model is shown to give very reasonable representations of the deformational characteristics of clay soils using only a minimal amount of information. In Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

MAYNE AND SWANSON ON PORE PRESSURE PARAMETER

q(kPa)

SPeSTONE KAOLIN [18] Ao'0.704 0' 'tS.S'

BOSTON BLUE [8] A,'0.703

0' =ie. f

400

423

Cc

C, =0M$

=0.693

zoo xperimehtal data

o q(kPa)

WEALD [105] A, =0.485 0' = 22.8' Cc =0.114

EAST ATCHAFALAYA [85] A.'0.580 f 'SI.7' Cf =0.445

400

200

15

€/%) FIG. 6—Undrained stress-strain behavior for Boston Blue Clay, Spestone Kaolin, East Atchafalaya, and Weald Clay using extended Cam-Clay theory; experimental (solid lines) and predicted {dotted lines).

general, an "attraction" of approximately 11 percent was added to the value of P ' to account for experimental-theoretical differences. Pore Pressure Response The versatility of the critical-state pore pressure parameter for both total and effective stress analyses has been demonstrated. The "extended" theory can also be used to give a simplified representation of pore pressure response during undrained shear to failure for isotropically consolidated soils: u=P'

+ P'

(q/P')

- 1

(18)

as shown in Fig. 8 for Newfield Clay [15]. By substituting Eqs 14 and 15 into Eq 18, the pore pressure is predicted as a function of strain. The authors believe that a more rational and promising critical-state theory which can Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

424

LABORATORY SHEAR STRENGTH OF SOIL

qfkPa) 400

200 0

q(kPa) 400

KAWASAKI I ^t'0.842 g'=35S' Cc =0.668

ILLITE [7]

[44]

A, = 0.491 g'=Z4.S' Cc =0.408 OCR

200

— a

10

15

0

e,(%)

10

15

€,(%)

FIG. 7—Undrained stress-strain behavior for Simple clay, Keuper Marl, Kawasaki, and lllite using extended Cam-Clay theory; experimental {solid lines) and predicted (dotted lines).

better model the pore pressure behavior of overconsolidated soils has been presented by Pender [103]. The approach by Pender, however, is more sophisticated, thus requiring a computer to facilitate computations. The statistical findings presented herein can be used to estimate P' at the criticalstate failure (Pes') for use in Pender's model. The critical-state parameter A^ can also be used to predict the effective stress friction angle (') from total stress strength data. Returning to the theory of Schofield and Wroth [96], it is derived that sin 0 ' = {1/3 + [5'„/ff^'(n.c.)exp(A„)]-'}-'

(19)

Based on the available data, the prediction is again different from experimental values by approximately 12 percent. A linear regression best fit line (b = 0) for the relationship shown in Fig. 9 is 0 '(measured) = 0.871 0 '(predicted)

(20)

with r = 0.82. The recommended procedure for determining the value of A^ for a specific Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

MAYNE AND SWANSON ON PORE PRESSURE PARAMETER

425

250 ii(kPa) 200 OCR = I equation

150

(18)

A/

100

Newfield Clay [15] after Sangrey, Henkel aEsrig (1959)

/

-I

10 w Q. (I> w. O Q.

50

7

f 0

•^

• OCR = 6

-50

6,(%) -100 0

1

2

3

4

5

6

7

8

axial strain FIG. 8—Measured and predicted pore pressure response for Newfield Clay.

clay or silt soil is illustrated by Fig. 2. A set of two or more consolidatedundrained shear tests, conducted at different confining stress levels where a'„ < a\max 's required for this approach. Alternatively, if a SHANSEP approach is employed, the results of only one CIU or CK„\J test are required: logJ(2/M)(5„/a,/(o.c.))] logJOCR] - 1

(21)

An average "attraction" of about 11 percent should be added to a\„ to account for the observed differences between experimental results and CamClay theory. Conclusions The critical-state pore pressure parameter has been shown to be independent of OCR, KQ test conditions, and level of shear to failure, and thus should be considered a basic soil constant. The critical-state parameter has been statistically verified as versatile and applicable to general geotechnical engineering practice. Simple analytical expressions requiring only two soil constants (A,, and 0') can be used to accurately predict the undrained strength of normally consolidated and overconsolidated clay soils. One addiCopyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

426

LABORATORY SHEAR STRENGTH OF SOIL

60 Note; Numerals correspond to soils and references listed in Table I.

50

40

30

20 •Q.

10 -best fit line ( b=o) r = 0.82

60

30

0' predicted

from total stress dota

FIG. 9- -Relufionship between experimental and predicted values of the effective stress frictiim angle.

tional constant (C^) is needed in order to provide reasonable stress-strain relationships and pore pressure response during undrained shear to failure. Acknowledgments The authors extend gratitude to C. Peter Wroth, University of Oxford, for his inspiration, and to Donna Reese and Anne Bethoun, Law Engineering Testing Company, for their assistance in preparing this study. Refefences [I] Henkel, D. J. in Shear Strength of Cohesive Soils, American Society of Civil Engineers (ASCE), New York, 1960, pp. 533-554.

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MAYNE AND SWANSON ON PORE PRESSURE PARAMETER

427

[2] Amerasinghe, S. F. and Parry, R. H., Journal of the Geotechnical Engineering Division, ASCE, Vol. 101. No. GT 12, Dec. 1975, pp. 1277-1293. [3] Mitchell, J. K., Fundamentals of Soil Behavior. Wiley, New York, 1976, pp. 283-339. HI See Ref/. 15] Brown, S. F., Lashine, A. and Hyde, A., Geotechnique. Vol. 25, No. 1, March 1975, pp. 95-114. [6] Ladd, C. C. and Foott, R., Journal of the Geotechnical Engineering Division, ASCE, Vol. 100, No. GT 7, July 1974, pp. 786-793. |7] France, J. and Sangrey, D. A.. Journal of the Geotechnical Engineering Division, ASCE, Vol. 103, No. GT 7, July 1977. pp. 769-785. [S] See Ref 6. 191 See Ref 6. [10] Simons, N. E. in Shear Strength of Cohesive Soils, ASCE. New York. 1960. pp. 744-763. [11] Skempton, A. W. in Proceedings, 5th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Dunod Press, Paris, 1961, pp. 351-357. 1/21 Togrol, E. in Proceedings, 6th International Conference on Soil Mechanics and Foundation Engineering, Vol. 2, University of Toronto Press, 1965, pp. 382-384. 1/Jl Skempton, A. W. and Henkel, D. J. in Proceedings, 3rd International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Swiss Organizing Committee, Zurich, 1953, pp. 302-312. 1/41 Mesri, G. and Olson, R., Geotechnique, Vol. 20, No. 3, Sept. 1970, pp. 261-270. 1/51 Sangrey, D. A., Henkel, D. J., and Esrig, M. I., Canadian Geotechnical Journal, Vol. 6, No. 3, Aug. 1%9, pp. 241-252. 1/61 Hvorslev, M. J. in Shear Strength of Cohesive Soils, ASCE. New York, 1960, pp. 169-273. 1/71 Swanson, P. G. and Brown, R. E.. "Triaxial and Consolidation Testing of Cores from the 1976 Atlantic Margin Coring Project," Open File Report No. 78-124 to the United States Geological Survey, Law Engineering Testing Company, Washington, D.C., Nov. 1977. [IS] Parry, R. H. and Nadarajah, V., Geotechnique, Vol. 24, No. 3. March 1973. pp. 345-358. 1/9] Shibata, T. and Karube, D. in Proceedings, 7th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Sociedad Mexicana de Mecanica de Suelos, Mexico, 1969, pp. 361-368. 1201 See Ref 16. [21] See Ref 6. 1221 Moh, Z., Nelson, J., and Brand. E. in Proceedings. 7th International Conference on Soil Mechanics and Foundation Engineering. Vol. 1. Sociedad Mexicana de Mecanica de Suelos, Mexico, 1969, pp. 287-295. [23] Croce, A., Japelli, R., Pellegrino, A., and Viggiani, C. in Proceedings. 7th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Sociedad Mexicana de Mecanica de Suelos, Mexico, 1969, pp. 81-89. 1241 Olson, R., Geotechnique, Vol. 12, No. I, March 1%2, pp. 23-43. 125] Lo, K. Y.. Geotechnique, Vol. 12. No. 4. Dec. 1962, pp. 303-318. 1261 Simons. N. E. in Shear Strength of Cohesive Soils, ASCE. New York. 1960, pp. 727-745. 127] Whitman, R. V. in Shear Strength of Cohesive Soils, ASCE, New York, 1960. pp. 581-614. [28] Raymond, G. P. \n Performance of Earth and Earth-Supported Structures, Vol. 1, Part 1, ASCE, New York, 1972, pp. 319-340. 129] Simon. R. M., Christian, J. T. and Ladd, C. C. in Analysis and Design in Geotechnical Engineering, Vol. I. ASCE. New York. June 1974, pp. 51-84. [30] Gibbs. H. J. et al in Shear Strength of Cohesive Soils, ASCE, New York, 1960. pp. 102-115. [31] Koutsoftas. D., Fischer. J.. Dette, J., and Singh, H., "Evaluation of the Vibracorer as a Tool for Underwater Geotechnical Explorations," Offshore Technology Conference. OTC Paper 2629, Houston, May 1976. 1J21 deGraft-Johnson, J. W. S., Bhatia, H. S., and Gidigasu, D. M. in Proceedings, 7th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Sociedad Mexicana de Mecanica de Suelos, Mexico, 1969, pp. 165-172. [33] Taylor, P. and Bacchus. D. in Proceedings, 7th International Conference on Soil

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428

UBORATORY SHEAR STRENGTH OF SOIL

Mechanics and Foundation Engineering, Vol. 1, Sociedad Mexicana de Mecanica de Suelos. Mexico, 1969, pp. 401-409. \34\ Ladd, C. C , "Stress-Strain Behavior of Saturated Clay and Basic Strength Principles," Report No. R64-17 to the U.S. Army Engineer Waterways Experiment Station, Vicksburg, Miss., April 1964. [35] Sherif, M. A., Wu, M. J., and Bostrum, R. C , "Reduction in Soil Strength Due to Dynamic Loading," Microzonatioii Conference. Vol. II, National Science Foundation and ASCE, Nov. 1972, pp. 439-454. [36] Tavenas, F., Blanchet, R., Garneau, R., and Leroueil, S., Canadian GeotechnicalJournal, Vol. 15, No. 2, May 1978, pp. 283-305. \37\ Olson, R. and Hardin, J. in Proceedings. 2nd Panamerican Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Sociedad Mexicana de Mecanica de Suelos, Mexico, 1963. pp. 204-218. \38\ Perloff, W. H. and Osterberg, J. O. in Proceedings. 2nd Panamerican Conference on Soil Mechancis and Foundation Engineering, Vol. I, Sociedad Mexicana de Mecanica de Suelos, Mexico, 1963, pp. 103-128. [39] daCruz, P. T. in Proceedings, 2nd Panamerican Conference on Soil Mechanics and Foundation Engineering, Vol. I, Sociedad Mexicana de Mecanica de Suelos, Mexico, 1963, pp. 73-102. \40] Lambe, T. W. in Proceedings, 2nd Panamerican Conference on Soil Mechanics and Foundation Engineering, Vol. H. Sociedad Mexicana de Mecanica de Suelos, Mexico, 1963, pp. 257-308, [41] Ladanyi, B. et al, Canadian GeotechniculJoumal. Vol. 2, No. 2, May 1965, pp. 60-89. [42] See Ref 6. [43] Wu, T. H., Chang, N., and Ali, E. M., Journal of the Geotechnical Engineering Division, ASCE, Vol. 104, No. GT 7, July 1978, pp. 889-905. [44] Ladd, C. C. and Lambe, T. W. in Laboratory Shear Testing of Soils, ASTM STP 361, American Society for Testing and Materials, 1963, pp. 342-371. [45[ Wesley, L. D., Journal of the Geotechnical Engineering Division, ASCE, Vol. 100, No. GT 5, May 1974, pp. 503-522. [46] D'Appolonia, E. D., Alperstein, R., and D'Appolonia, D. J. in Performance of Slopes and Embankments, ASCE, New York, 1966, pp. 489-518. [47] Egan, J. A., "A Critical State Model for the Cyclic Loading Pore Pressure Response of Soils," Ph.D. thesis, Cornell University, Ithaca, New York, June 1977. [48] See Ref 47. [49] See Ref 44. [50] Van Eekelen, H. and Potts, D. M., Geotechnique. Vol. 28, No. 2, May 1978, pp. 173-196. [51] Raymond, G. P., Highway Research Board Bulletin. No. 463, 1973, pp. 1-17. [52] Ladd, C. C , discussion on "Use of Stress Loci for Determination of Effective Stress Parameters" by R. Yong and E. Vey, Highway Research Board Bulletin. No. 342, 1962, pp. 49-51. [53] Wissa, A,, Ladd, C. C , and Lambe, T. W. in Proceedings, 6th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, University of Toronto Press, 1965, pp. 412-416. [54] Adams, J. in Proceedings, 6th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, University of Toronto Press, 1965, pp. 3-7. 155] Kenney, T. and Watson, G. in Proceedings, 5th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Dunod Press, Paris, 1961, pp. 191-195. [56] Bjerrum, L. and Simons, N. in Shear Strength of Cohesive Soils, ASCE, New York, 1%0, pp. 711-726. [57] Leathers, F. D. and Ladd, C. C , Canadian Geotechnical Journal. Vol. 15, No. 2, May 1978, pp. 250-268. |5«1 Hanzawa, H., Soils and Foundations, Vol. 17, No. 4, Dec. 1977, pp. 17-30. [59] Alberro, J. and Santoyo, E. in Proceedings, 8th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1.1, USSR National Society on Soil Mechanics and Foundation Engineering, Moscow, 1973, pp. 1-9.

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429

\60] Mitachi. T. and Kitago, S., Soils and Foundations. Vol. 16, No. 1, March 1976, pp. 45-58. [6/] See Ref 60. [62] See Ref 60. \b3\ Hanzawa, H., Soils and Foundations, Vol. 17, No. 4, Dec. 1977, pp. 1-15. [64] Tavenas, F., Leroueil, S., LaRochelle, P., and Roy, M., Canadian Geotechnicid Journal. Vol. 15, No. 3, Aug. 1978, pp. 402-423. {64b] Tavenas, F. A. et al in In Situ Measurement of Soil Properties, Vol. 1, ASCE, New York, 1975, pp. 450-476. 165) Yudhbir and Varadarajah, A., Soils and Foundations, Vol. 14, No. 4, Dec. 1974, pp. 1-12. 166) See Ref 65. |67] Sketchley, C. J. and Bransby, P. L. in Proceedings, 8th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, USSR National Society on Soil Mechanics and Foundation Engineering, Moscow, 1973. pp. 377-384. [68] Broms, B. and Casbarian, A. in Proceedings, 6th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, University of Toronto Press, 1965, pp. 179-183. 169] Ladd, C. C , "Laboratory Determination of Soil Parameters for Excavation and Shallow Foundations," Field and Laboratory Determinations of Soil Parameters, ASCE, National Capital Section, Washington, D.C., 1976. ]70] Montgomery, M. W., "Geotechnical Investigation - Gas Centrifuge Enrichment Plant. Portsmouth, Ohio," Law Engineering Testing Company, Report No. MK 7502, April 1978. [71] Fischer, K. P., Anderson, K. H., and Mourn, J., Canadian Geotechnical Journal, Vol. 15, No. 3, Aug. 1978, pp. 322-331. [72] Korhonen, K. H. in Proceedings, 9th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Japanese Society of Soil Mechanics and Foundation Engineering, Tokyo, 1977, pp. 165-168. [73] Wu, T., Douglas, A. and Goughnour, R., Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 90, No. SM 3, June 1962, pp. 1-32. [74] Broms, B. and Ratnam, M., Journal of the Soils Mechanics and Foundations Division, ASCE, Vol. 89, No. SM 6, Nov. 1963, pp. 1-26. 175] Karlsson, R. and Pusch, R. in Proceedings, Geotechnical Conference, Oslo, Vol. 1, Norwegian Geotechnical Institute, 1967, pp. 35-42. 176] Sridharan, A., Rao, Narasimha S. and Rao, Venkatappa, G., Soils and Foundations, Vol. 11, No. 3. Sept. 1971, pp. 1-22. 177] See Ref 76. [78] Crooks. J. H. and Graham, J., Geotechnique, Vol. 26, No. 2, 1976, pp. 293-315. [79] Gangopadhyay, C , Som, N. and Roy, S., Indian Geotechnical Journal, Vol. 4, No. 2, Jan. 1974, pp. 140-160. [80] Widger, R, A. and Fredlund, D. G., Canadian Geotechnical Journal, Vol. 16, No. 1, Feb. 1979, pp. 140-151. [81] Swanson, P. G. and Brown, R. E., "Triaxial and Consolidation Testing of Cores from the 1976 Atlantic Margin Coring Project," Open File Report No. 78-124 to the United States Geological Survey, Law Engineering Testing Company, Nov. 1977. ]82] Saxena, S., Hedberg, J. and Ladd, C. C , Geotechnical Testing Journal. Vol. 1, No. 3. Sept. 1978, pp. 148-161. [83] Abeyesekera, R. A., Geotechnical Testing Journal, Vol. 2, No. 1, March 1979, pp. 11-19. [84] Singh, Ram and Gardner, William in Soil Dynamics in the Marine Environment. Proceedings of ASCE, Preprint 3604, April 1979. [85] Donaghe, R. T. and Townsend, F. C., Geotechnical Testing Journal. Vol. 1, No. 4, Dec. 1978, pp. 173-189. [86] See Ref 85. [87] Akai, K. and Adachi, J. in Proceedings. 6th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, University of Toronto Press, 1965, pp. 146-150. [88] Costa Filho, L., Wemeck, M., and Collet, H. in Proceedings. 9th International Con-

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LABORATORY SHEAR STRENGTH OF SOIL

ference on Soil Mechanics and Foundation Engineering, Vol. I, Japanese Society of Soil Mechanics and Foundation Engineering, Tokyo, 1977, pp. 69-72. \S9] Sparrow, R. W., Swanson, P. G.. and Brown, R. E., "Report of Laboratory Testing of Gulf of Alaska Cores," Open File Report to the United States Geological Survey, Law Engineering Testing Company, March 1979. [90] Crawford, C , Canadian GeotechnicalJournal, Vol. 1, No. 4, Nov. 1964, pp. Ill-US. [91] Poulos, H. G., Geutechnical Testing Journal, Vol. I, No. 2, June 1978, pp. 102-106. [92] Henkel, D. J. and Sowa, V. A. in Laboratory Testing of Soils. ASTM STP36I, American Society for Testing and Materials, 1964, pp. 280-291. [93] Duncan, J. M. and Seed, H. B., Journal of Soil Mechanics and Foundations Division. ASCE, Vol. 92, No. SM 5, May 1966, pp. 21-50. [94] Wroth, C. P. and Loudon, P. A. in Proceedings. Geotechnical Conference, Oslo, Vol. 1, 1%7, pp. 159-163. [95] Mahar, L. J. and Ingram, W. B.. "Geotechnical Investigation for a Field Study of Pile Group Action," FUGRO GULF, Inc., Report No. 78-161-1 for the Federal Highway Administration, Oct. 1979. [96] Schofield, A. N. and Wroth, C. P., Critical-State Soil Mechanics, McGraw-Hill, London, 1968, pp. 134-206. ]97] Roscoe, K. H. and Burland, J. B. in Engineering Plasticity, Cambridge University Press, 1%8, pp. 535-609. [98] Skempton, A. W., Geotechnique, Vol. 4, 1954, pp. 143-147. [99] Henkel, D. J. and Wade, N. H., Journal oj Soil Mechanics and Foundations Division, ASCE. Vol. 92, No. SM 6, June 1%6, pp. 67-80. [100] Ladd, C. C , Foott, R., Ishihara, K., Schlosser, F., and Poulos, H. G. in Proceedings, 9th International Conference on Soil Mechanics and Foundation Engineering, Vol. 2, Tokyo, 1977, pp. 421-495. [lOI] Atkinson, J. H. and Bransby, P. L., The Mechanics of Soils, McGraw-Hill, London, 1968, pp. 329-333. ]I02] Mesri, G., Ullrich, C . and Choi, Y., Geotechnique, Vol. 28, No. 3, Aug. 1978, pp. 281-307. [103] Pender, M. J., Geotechnique, Vol. 28, No. 1, March 1978, pp. 1-25. [104] Mayne, P. W., Geotechnical Testing Journal, Vol. 2, No. 2, June 1979, pp. 118-121. [105] Mayne, P. W., Journal of the Geotechnical Engineering Division, ASCE, Vol. 106, No. GTU.Nov. 1980, pp. 1219-1242. [106] Butterfield, R., Geotechnique, Vol. 29, No. 4, Dec. 1979, pp. 469-479. [107] Bishop, A, W. and Henkel, D. J., The Measurement of Soil Properties in the Triaxial Test, Edward Arnold, London, 1957.

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J. H. Prevost^

Nonlinear Anisotropic Stress-StrainStrength Behavior of Soils

REFERENCE: Prevost. J. H., "Nonlinear Anisotropic Stress-Strain-Strengtii Beliavior of Soils," Laboratory Shear Strength of Soil. ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 431-455. ABSTRACT: Soils consist of an assemblage of particles witli different sizes and shapes which form a skeleton whose voids are filled with various fluids. The stresses carried by the soil skeleton are conventionally termed "effective stresses" in the soil mechanics literature, and those in the fluid are called the "pore-fluid pressures". In cases in which some flow of the pore fluid can take place, there is an interaction between the skeleton strains and the pore-fluid flow. The solution of these problems therefore requires that soil behavior be analyzed by incorporating the effects of the flow (transient or steady) of the pore fluid through the voids, and thus requires that a multiphase continuum formulation be available for soils. Such a theory was first developed by Biot (1955) for an elastic porous skeleton. However, it is observed experimentally that the stress-strain behavior of the soil skeleton is strongly nonlinear, anisotropic, elastoplastic, and path-dependent. An extension of Biot's theory into the nonlinear anelastic range is therefore necessary in order to analyze the transient response of soil deposits. Such an extension of Biot's formulation is proposed herein by viewing soil as a multiphase medium consisting of an anelastic porous skeleton and viscous fluids, and by using the modem theories of mixtures developed by Green and Naghdi (1965) and Eringen and Ingram (1965). In order to relate the changes in effective stresses carried by the soil skeleton to the solid rate of deformation tensor, a general analytical model is used which describes the nonlinear, anisotropic, elastoplastic, stress and strain dependent, stress-strain-strength properties of the soil skeleton when subjected to complicated three-dimensional and, in particular, cyclic loading paths. The theory falls within the general framework of the formalism of classical plasticity theory. It combines properties of isotropic and kinematic plasticity, and allows for the adjustment of the plastic hardening rate to any kind of experimental hardening law by using a collection of nested yield surfaces. It is shown that the model parameters required to characterize the behavior of any given soil can be derived entirely from the results of conventional soil tests. The model's extreme versatility and accuracy is demonstrated by applying it to represent the behavior of both cohesive and cohesionless soils under both drained and undrained, monotonic and cyclic loading conditions. The use of the proposed formulation for solving boundary value problems of interest in soil mechanics is illustrated. KEY WORDS; consolidation, constitutive equations, diffusion, finite elements, geotechnical engineering, plasticity, porous media 'Assistant Professor of Civil Engineering, Princeton University, Princeton, N.J. 08544.

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LABORATORY SHEAR STRENGTH OF SOIL

Soil consists of an assemblage of particles with different sizes and shapes which form a skeleton whose voids are filled with various fluids. The stresses carried by the soil skeleton are conventionally termed "effective stresses" [1]^ in the soil mechanics literature, and those in the fluids are called the "porefluid pressures". In cases in which some flow of the pore fluids takes place, there is an interaction between the skeleton strains and the pore-fluid flow. The solution of these problems therefore requires that soil behavior be analyzed by incorporating the effects of the flow (transient or steady) of the pore fluids through the voids, and thus requires that a multiphase continuum formulation be available for soils. Such a theory was first developed by Biot [2] for an elastic porous skeleton. However, it is observed experimentally that the stress-strain behavior of the soil skeleton is strongly nonlinear, anisotropic, elasto-plastic, and path-dependent. An extension of Biot's theory into the nonlinear anelastic range is therefore necessary in order to analyze the transient response of soil deposits. Such an extension of Biot's formulation [3] is adopted herein. The resulting coupled field equations [3] obtained by viewing soil as a multiphase medium consisting of an anelastic porous skeleton and viscous fluids, and by using the modem theories of mixtures developed by Green and Naghdi [4] and Eringen and Ingram [5], are presented. In order to relate the changes in effective stresses carried by the soil skeleton to the skeleton rate of deformations, a general analytical model is used [6] which describes the nonlinear, anisotropic, elastoplastic, stress and strain dependent, stress-strain-strength properties of the soil skeleton when subjected to complicated three-dimensional and, in particular, cyclic loading paths [7]. A brief summary of the model's basic principle is included and the constitutive equations are provided. It is shown that the model parameters required to characterize the behavior of any given soil can be derived entirely from the results of conventional soil tests. The model's extreme versatility and accuracy are demonstrated by applying it to represent the behavior of both cohesive and cohesionless soils under both drained and undrained, monotonic and cyclic loading conditions. The use of the proposed formulation for solving boundary value problems of interest in soil mechanics is thereafter illustrated by applying it to analyze (7) the one-dimensional and two-dimensional consolidation of a linear elastic porous medium, and (2) the time-dependent response of a rigid footing resting on top of a soil deposit and loaded at various loading rates.

Field Equations For a saturated soil consisting of a macroscopically perfect fluid and a piecewise-linear time-independent porous skeleton wherein both the pore ^The italic numbers in brackets refer to the list of references appended to this paper.

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PREVOST ON NONLINEAR ANISOTROPIC BEHAVIOR OF SOILS

433

fluid and the solid grains are incompressible, the coupled field equations take the following forms [3]: div[ff'' + a'' div v^] - div[(p„, + p„, div v^l] + div[D : L'] + p„,divv^b - a") + pb = p'a' + p"'a»' (1) •k"'^ • (grad/j„, - p„,b + p^a") + div v» = 0

— div

(2)

Pw

where D ahcd

1 [<^hcl ^ac

Cad ^hc

<^ur ^hd ~ '^bc ^ad\

(3)

is a tensor arising from geometric changes, (4) is the total stress tensor [J], (5) «"• = (1 — «")divv'

(6)

p^ = (1 - «")p,

(7)

p = p^ ^- TV^'P^.

(8)

and the subscripts s and w refer to the solid and fluid phases, respectively. In Eqs 1 and 2: a'' = effective Cauchy stress tensor; p^, = pore-fluid pressure; V" = velocity of a-phase; a" = acceleration of a-phase; d" and w" = symmetric and skew-symmetric parts of the velocity gradient L", respectively; fcws = permeability tensor; p„ = microscopic mass density of a-phase; n" = porosity; b = body force density per unit mass; and a superimposed dot indicates the material derivative following the motion of the solid skeleton. In Eq 1, o'^ denotes the Jaumann derivative, namely. ^•s -

if's ^_ „'s

. ^ s _ ^s . ^ '

(9)

When neglecting inertia effects in both the solid and fluid phases, Eqs 1 and 2 simplify to div[^'^ + ff'Mivv^] - div[(p„. +p„,divv^)l] + div[D:Ln+p„divv^b + pb = 0 (10) — div

•k-^ • (gradp„, - p„, b) -f div V' = 0

(11)

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434

UBORATORY SHEAR STRENGTH OF SOIL

In its linearized form, Eq 10 simplifies to dw[&'' - p„ 1] + p„ div y'b + ph = Q

(12)

Of particular importance in soil mechanics are fully drained and undrained loading conditions. Clearly, both of these conditions are special cases of the aforementioned general equations, and the corresponding field equations can be derived from Eqs 10 and 11 as shown in the following three sections. Undrained (Instantaneous) Loading Condition In that case, k"'* = 0 relative to the rate of loading, no drainage of the fluid phase can take place, and the pore fluid follows the motion of the solid skeleton. In that case, v* = v"'. «"• = 0, and div v^ = div v*" = 0, and Eq 10 simplifies to div[J'^ - p„, 1] + div[D : V] + ph = 0

(13)

Fully Drained (Slow) Loading Conditions In that case, k"'* = oo relative to the rate of loading, no excess pore-fluid pressure builds up (that is, p„ = 0), and Eqs 10 and 11 then simplify to div[^ " + (ff '^ - p„ 1) div v^] + div[D : V] + p„, div v^ b + pb = 0 -gradp,.

+ p„,h = 0

(14) (15)

Fully Drained Steady-State Conditions When the skeleton stresses and strains have reached constant values, v* = 0, and the pore-fluid flow has reached steady p„ = 0 and dv^'/dt — 0, Eq 11 then simplifies to k"^ • (gradp„. - p„, b)

div

= 0

(16)

P«.

Constitutive Equations The constitutive equations for the solid skeleton are written in one of the following forms: ''c'ah'' CahctI '^c/

small deformations (17)

— '^

finite K.^ah '^ + (^ah '^ Vc.c deformations

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PREVOST ON NONLINEAR ANISOTROPIC BEHAVIOR OF SOILS

435

Cabcd is an (objective) tensor valued function of, possibly, Oab '^ and the deformation gradients. Many nonlinear material models of interest can be put in the above form (for example, all nonlinear elastic materials and many elastoplastic materials). The finite deformation form of the constitutive Eq 17 was first proposed by Hill [8] in the context of plasticity theory and has been advocated by McMeeking and Rice [9]. For soil media, the form of the C-tensor is given as [6] C = E - j ^ +Q.E.p(E:P)(Q:E)

(18)

where H' is the plastic modulus; P and Q are symmetric second-order tensors, such that P gives the direction of plastic deformations and Q the outer normal to the active yield surface; and E is the fourth-order tensor of elastic moduli, assumed isotropic for the particular class of material models implemented. The plastic potential is selected such that, in agreement with experimental observations, the plastic deviatoric rate of deformation vector remains normal to the projection of the yield surface onto the deviatoric stress subspace; that is, P - — (trace P)l = Q - ~

(trace Q)l = Q '

(19fl)

traceP = traceQ + A -

^{Q':Q'}'^^

(1%)

where .4 is a material parameter which measures the departure from an associative flow rule. When >1 = 0, P = Q; consequently the C-tensor possesses the major symmetry. The yield function is selected of the form [6] / = ^ ( s ^ - a) : (s^ -a)

+ C^(p'» - ^)2 - ^2 = 0

(20)

where s* is the deviatoric stress tensor (that is, s* = a '^ — p '* 1, p '* = '/3 trace a ' 0 ; a and |3 are the coordinates of the center of the yield surface in the deviatoric stress space and along the hydrostatic stress axis, respectively; k is the size of the yield surface; and C is a material parameter called the yield surface axis ratio. In order to allow for the adjustment of the plastic hardening rule to any kind of experimental data (for example, data obtained from axial or simple shear soil tests) a collection of nested yield surfaces is used. A plastic modulus is associated with each of the yield surfaces, and

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436

LABORATORY SHEAR STRENGTH OF SOIL

where h ' is the plastic shear modulus, and {h' + B') and (h' — B') are the plastic bulk moduli associated with / which are mobilized in consolidation tests upon loading and unloading, respectively. The projections of the yield surfaces onto the deviatoric stress subspace thus define regions of constant plastic shear moduli. The yield surfaces' initial positions and sizes reflect the past stress-strain history of the soil skeleton, and in particular their initial positions are a direct expression of the material "memory" of its past loading history. Because the a's are not necessarily all equal to zero, the yielding of the material is anisotropic. Direction is therefore of great importance and the physical reference axes ix,y,z) are fixed with respect to the material element and specified to coincide with the reference axes of consolidation. For a soil element whose anisotropy initially exhibits rotational symmetry about the j-axis, a^ = a^ = — a^/2, and Eq 20 simplifies to [{a, •' - a, •') - aY + C^ (p '' - &Y - k^ = 0

(22)

where a = 3a^/2. The yield surfaces then plot as ellipses in the axisymmetric stress plane {a^'^ — a,'^) as shown in Fig. 1. Points C and E on the outermost yield surface define the critical state conditions (that is, H ' = 0) for axial compression and extension loading conditions, respectively. It is assumed that the slopes of the critical state lines OC and OE remain constant during yielding. The yield surfaces are allowed to change in size as well as to be translated

(a;-a;)

3p'»(aj;*2a;)

FIG. I—Field of yield surfaces in axial stress plane.

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PREVOST ON NONLINEAR ANISOTROPIC BEHAVIOR OF SOILS

437

by the stress point. Their associated plastic moduli are also allowed to vary and, in general, both k and H' are functions of the plastic strain history. They are conveniently taken as functions of invariant measures of the amount of plastic volumetric strains and/or plastic shear distortions, respectively [7]. Complete specification of the model parameters requires the determination of (1) the initial positions and sizes of the yield surfaces together with their associated plastic moduli, (2) their size or plastic modulus, or both, change as loading proceeds, and (3) the elastic shear, G, and bulk, B, moduli. The soil's anisotropy originally develops during its deposition and subsequent consolidation which, in most practical cases, occurs under no lateral deformations. In the following, the >'-axis is vertical and coincides with the direction of consolidation; the horizontal jcz-plane is thus a plane of material's isotropy and the material's anisotropy initially exhibits rotational symmetry about the vertical ji-axis. The model parameters required to characterize the behavior of any given soil can then be derived entirely from the results of conventional monotonic axial and cyclic strain-controlled simple shear soil tests [6.7.10,11]. This will now be explained and further discussed. Determination of Model Parameters In order to follow common usage in soil mechanics, compressive stresses and strains are considered positive. All stresses are effective stresses unless otherwise specified and, in order to simplify the notation, the superscript s is omitted hereafter. As explained previously, for a material which initially exhibits crossanisotropy about the vertical j-axis, the initial position in stress space of the yield surfaces is defined by the sole determination of the two parameters a*"'' andfi^"'^(m — 1, . . . , p), and Eq 22 simplifies to \q - a'""]^ + C2 [p ' - /^("•'p - [A;("'>]2 = 0

(23)

for axial loading conditions (that is, a^' = oj and i^ = T^, = j ^ — 0), where q — {Oy' — a^'). The yield surfaces then plot as circles in the q versus £p ' plane (referred to as the axial stress plane hereafter) as shown in Fig. 2. A^hen the stress point reaches the yield surface,/„,, q = a*"'' + ;fc*"'> sin d

(24a)

p ' = /3<"'' + ——- cos e

(24fc)

where d is defined in Fig. 2, and Eq 18 simplifies to ^ 1 , 1 — = -T;;r + -T7-r sin 6> ( s i n e + C7 cos 0) q Copyright by Downloaded/printed University of

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LABORATORY SHEAR STRENGTH OF SOIL

FIG. 2—Field of yield surfaces in q versus C„ ' plane.

-7T = ~r-^ B

-TTT(2ccose H„,

+ A„, V6cos^|tane\)—— (sin6 + Cy cos9) 37

(25A) where (from Eq 21) h,„'+B„/cose

(26)

e„ = trace d = i^ + 2i^

(27)

H,„' = and

(28) (29)

7 =

where G = elastic shear modulus, B — elastic bulk modulus, and C = 3/V2. The dependence of the model parameters upon the effective mean normal stress and volumetric strain are assumed to be of the forms X =

(30)

Xj

Pi

and y =3;iexp(XeJ

(31)

respectively, where x = B. G. h„,'. B„,';y = a*"'', /3'"'', *''">; X and n are experimental parameters (n = 0.5 for most cohesionless soils [12], and n = 1

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439

for most cohesive soils); P i ' = initial effective mean normal stress (that is, at e^ = 0); e^ = (vj — v)/vi where v = current volume and v, = initial volume (that is, a t p ' = pi' and q = 9,) of the soil specimen. When the stress point reaches the outermost yield surface, fp, the soil specimen is in a normally consolidated state. It is assumed that the consoHdation soil test results then plot as a straight line parallel to the projections of critical state lines on the e,, versus Ln p ' plane [13]. The parameter X is then simply determined from the results of /Co-consolidation soil test results; that is,

X=- V ^

(32)

iv

PK

where the subscript/superscript K refers to /Cg-loading conditions. Interpretation of Monotonic Drained Axial Compression and Extension Soil Test Results Let dc and BE denote the values of 6 (Eq 24) when the stress point reaches the yield surface,/„,, in axial compression and extension loading conditions, respectively. Combining Eqs 24 to 31, one finds that 1 tan dc

,

1 tan $£

1 2C

3 7c

(33)

J- 3 7£ yc

yE .

cos Oc — cos BE= RcE (sin 6c ~ sin 6^)

(34)

where n

_ ^ P c ' - P E ' exp[X(e,^ - e / ) ] qc - 9£exp[X(€„'' - e / ) ] 1

_ / pc' y

t

xc

\ P\' /

q

1 - ( Pc' \" t yc

\ Pi'

/

p

2G, 1 B'1

(36)

(37)

and similarly for :c£ andj^^, where the subscripts C and E refer to axial compression and extension loading conditions, respectively. In Eq 33, the plus sign ( + ) is to be used when tan dc tan BE < 0, and the minus sign ( —), when tan dc tan 6^ > 0. The smooth experimental stress-strain curves obtained in axial tests are now to be approximated by linear segments along which the tangent (or

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440

LABORATORY SHEAR STRENGTH OF SOIL

secant) modulus is constant. Evidently, the degree of accuracy achieved by such a representation of the experimental curves is directly dependent upon the number of linear segments used. The model parameters associated with the yield surface/„, are determined by the condition that the slopes q/I&re to be the same in axial compression and extension tests when the stress point has reached the yield surface/„,. The corresponding values OQ and ^^ are determined by combining Eqs 33 and 34. For that purpose, note that Eq 34 is more conveniently rewritten as

tan 6c

tan ^£- /

1 — RCE^

\ tan 6c tan 6^

Once 6c and 6^ have been determined, the model parameters associated with f„ are simply obtained by combining Eqs. 24 and 25; namely, „ , xc sin 6c TC — Xp sin 6r TE B„,' = — ^ ^-r-^

(39)

cos 6c ~~ cos »£•

h„' =Xcsm6cTC-B„'cos6c A„,^f6=

^

I tan e,

37c ^ ^ tan ^ c - 2C yc

k^On) = g c e x p ( - X f / ) - g g e x p ( - X 6 / ) sin 6c -~ sin 6^ «/'"' = 9 c e x p ( - Xe^C) - ki^"''> sin 6c

(40) (41)

^^^^

(43)

t (m)

/3,»"')=pc'exp(-Xe,C)

^cos^c

(44)

where TC = sin 6c + Cyc cos 6c

(45a)

TE = sin 6E + CyE cos 6^

(4Sb)

The yield surface,/], is chosen as a degenerate yield surface of size A / " = 0. Further, in order to get a smooth transition from the elastic into the plastic regime, ^ i ' = oo; so that the material behavior inside/2 is elastic. The elastic shear, Gi, and bulk, 5 ) , moduli are then determined from the steepest slopes observed at the origin of the plots q versus e, andp ' versus e^ of the axial compression/extension soil test results, respectively. At the critical state, Xc = x^ = 0; and the stress point is on the outermost yield surface/^. From Eqs 39 and 40, it is apparent that ftp' = 0 in that case.

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Interpretation of Monotonic Unchained Axial Compression and Extension Soil Test Results In undrained tests, 4^ = 0, and (from Eq 37)yc= yg — " B\ in that case. The model parameters associated with the yield surface /„, are again determined by the condition that the slopes q/T are to be the same in axial compression and extension tests when the stress point has reached the yield surface /„,. As noted previously, the corresponding values dc and d^ are determined from Eqs 33 and 34, in which RCE-C''''''''

(46)

Knowing B^ and B^, the model parameters associated with /„, are computed using Eqs 39 to 45 in which e^^ = e,,^ = 0. Note that the sole use of undrained axial soil test results for the determination of the model parameters does not allow the determination of the parameter \ . Interpretation of Simple Shear Soil Test Results In simple shear soil tests, e^ = e^ — e^ = 0. The necessary algebra for the determination of the model parameters is considerably simplified in that case if the elastic contributions to the normal strains are neglected. Equations 17 to 21 then yield a^' — a.',

«('") = ( a / - a / )

(48)

fc<'"> = \ / 3 T ^

(49)

/3('.')=p/ = a / - - | ( a / - a / )

(50)

The model parameters associated with the yield surface/„, are then simply determined from the aforementioned equations and a piecewise linear representation of the shear stress-strain curves obtained by a simple shear test. Note that the sole use of simple shear test results does not allow the determination of the parameters X, B„,', and A„,. On the other hand, it is apparent from Eqs 47 and 49 that the degradation of the mechanical properties of the material under cyclic shear loading conditions, that is,

k^"'He)hJ{e)

Copyright Downloaded/printed University

by

(51)

ASTM by

of

British

442

LABORATORY SHEAR STRENGTH OF SOIL

with e " = j | Y d ' : d ' ] d ' = d - ^(trace d)6

(52)

where the integration is carried along the strain path, are most conveniently determined from the results of cyclic strain-controlled simple shear tests (e = \ I/V3 171 in that case). This is explained and further discussed in Ref 7. The aforementioned procedures for the determination of the model parameters may be easily coded, and a simple computer code has been written for that purpose. This code is available to interested readers. Application to Characterization of Soil Stress-Strain-Strength Behavior As an illustration. Tables 1 and 2 give the parameter-values for the Cook's Bayou sand [14] and the Drammen clay [15], These parameters were determined by using solely the results of axial compression/extension soil tests. Figures 3 and 4 show the model predictions for both axial compression and consolidation/swelling tests, respectively, performed on the Cook's Bayou sand. They agree very well with the experimental test results for all cases. Figures 5 and 6 show the model predictions for both undrained axial and simple shear tests, respectively, performed on the Drammen clay. They agree very well with the experimental test results for all cases (in Fig. 6, T/, denotes the average horizontal shear stress measured experimentally). Figure 7 shows the model predictions for cyclic stress-controlled and strain-controlled simple

TABLE 1 —Cook s Bayou sand lOy,,' = 50 psi) model parameters IG, = 2000psi. B, = 22 920psi. n = 0.5, X = I4S.I). a*™*, psi"

/S*"',

*<"-'.

^m'

m

psi

psi

psi

psi

'4/11

2 3 4 5 6 7 8 9 10 11 12 13 14 15

24.00 28.07 32.16 37.28 41.54 46.05 45.68 42.95 45.78 44.31 48.00 66.66 87.23 122.60

60.24 60.91 61.39 60.68 61.57 62.47 61.66 65.29 68.33 74.75 85.24 93.18 109.50 131.50

32.36 36.39 40.23 43.63 48.25 53.10 64.61 77.47 88.34 105.80 127.90 153.00 196.30 261.50

27640.00 23870.00 20300.00 14830.00 12870.00 10550.00 6476.00 5005.00 3599.00 2617.00 2011.00 1379.00 619.70 0.00

-4865.00 -5724.00 -5892.00 -5041.00 -4588.00 -3879.00 -2485.00 -1896.00 -1475.00 -1234.00 -909.90 -574.20 -286.60 0.00

-0.1384 -0.2380 -0.3446 -0.6810 -0.7750 -0.8636 -1.020 -0.9069 -0.9391 -0.8995 -0.8694 -1.062 -1.068 -1.113

BJ,

"1 psi = 6.9 kPa.

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443

TABLE 1—Drammen clay (OCR = 4) model parameters

m

a*"'Va„,.'

**"''/a„. •

''-./"vc '

2 3 4 5 6 7 8 9 10 11 12 13 14 15

0.100 0.150 0.300 0.400 0.475 0.525 0.550 0.575 0.600 0.575 0.550 0.550 0.525 0.467

0.300 0.350 0.600 0.700 0.775 0.875 0.950 1.025 1.050 1.125 1.200 1.250 1.275 1.373

266.667 133.333 100.000 73.333 54.667 40.000 31.000 24.333 17.333 13.333 10.000 6.667 3.333 0.000

shear and axial tests performed on the Drammen clay. They agree very well with the experimental test results [15] for all cases. Application to Solution of Boundaiy Value Problems Attention is restricted in the following to "quasi-static" loading conditions. The finite element formulation of the aforementioned governing equations (Eqs 10, 11, 17 to 21) is performed by using the Galerkin procedure (see, for example, Ref 16). The class of constitutive equations assumed leads directly to the definition of tangent stiffness matrix (see, for example, Refs 9 and 17). A simple backward difference scheme is adopted for the numerical time integration [18] in transient analysis. Further, in order to increase its accuracy, a predictor-corrector type algorithm is used at each time step (see Ref 17 for further details). The element and material model libraries are modularized and may be easily expanded without alteration of the main code. The present element library contains a two-dimensional element with plane stress/plane strain options and a three-dimensional element. Full finite deformation effects may be accounted for. A contact element is also available for two-dimensional and three-dimensional analysis. The present material library contains a linear elastic model and various elastoplastic and soil models. Some features which are available in the program are (/) both symmetric and nonsymmetric matrix equation solvers, and (2) reduced/ selective integration procedures, for effective treatment of incompressibility constraints [79] which arise in undrained loading cases. A number of examples are now presented which demonstrate the versatility and accuracy of the proposed formulation in solving boundary value problems of interest in soil mechanics. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

444

UBORATORY SHEAR STRENGTH OF SOIL

o Measured —

Predicted (Cy-Cx)(%) 2.

(a) Shear stress-strain behavior (b) Volumetric stress-strain behavior FIG. 3—Cook s Bayou sand — calculated and measured stress-strain behavior in drained axial compression soil test.

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445

5. PV»v

0 Measured _

Predicted

Cu (%)

.0

0.25

0.50

0.75

FIG. 4—Cook's Bayou sand — predicted and measured stress-strain behavior in Kf^-consolidalion/swelling tests.

One-Dimensional Elastic Consolidation [18] The finite element mesh and problem description are shown in Fig. 8a. The traction, h, is appHed instantaneously to the top surface at time, t = 0, and thereafter held constant with drainage occurring only at the top (or bottom) surface. The gravity load is set equal to zero (that is, b = 0 in Eqs 10 and 11). Under these conditions, a closed-form solution in the small deformation regime, for the pore-fluid pressure dissipation as a function of time, can be obtained (see, for example, Ref 20) and is shown in Fig. Sb. H is the initial depth of the layer, C^ is the one-dimensional consolidation coefficient [C^ = («"'/p„)ft:''HX' + 2^0 where X^ and n' = Lame's constants], and U is the degree of consolidation. The numerical results shown in Fig. Sb were ob-

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446

UBORATORY SHEAR STRENGTH OF SOIL

•c—c

ComprBSSlon

A^^ * I' y |£y 0'

Extension

-.8 0

1 2 3 VERTICAL STRAIN

A V.

FIG. 5—Drammen clay (OCR = 4) — calculated and measured stress-strain behavior in undrained axial soil tests.

tained by taking At„ = j8Af„_i with /8 = 1.5 and 2,5, respectively, and AT, = 10-'' (that is. At, = 0.250 for V = 0.83, n' = 0.38, H = 10, n"- = 0.3, and k"*' = 10"'). Numerical agreement with the analytical solution is shown in Fig. 8b. Note that complete consolidation is achieved in only 12 or 24 steps when /3 = 2.5 and 1.5, respectively. These results demonstrate the accuracy and stability of the numerical scheme. Fig. 8c shows the settlement, 5, of the top surface as a function of the dimensionless time, T, for various h/E^ ratio (E^ — Young's modulus) for the case v' — Poisson's ratio = 0.3. The curves show that the larger the h/E" ratio, the more drastic is the difference between finite and small deformation results. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

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0

2 SHEAR

4

6

STRAIN

447

8 V. — Predicted

Legend 0 ^ Measured

FIG. 6—Drammen clay (OCR = 4) — predicted and measured stress-strain behavior in simple shear soil test.

Two-Dimensional Elastic Consolidation [18] The finite element mesh and problem description are shown in Fig. 9a. A strip load of width 2B with a uniform intensity, h, is applied instantaneously at time f = 0 to the top surface, and thereafter held constant with drainage occurring only at the top surface. The gravity load is again set equal to zero. Fig. 9b shows the computed dimensionless excess pore-fluid pressure as a function of the dimensionless time factor T — Cy t/B^ where C,, = 2 ^^«"fc"V p„. The results are presented as ratios with the initial excess pore-fluid pressure, and A//i^ = 0.1 in Fig. 9b. The numerical results shown in Fig. 9b were obtained by taking At„ = 0 At„_i with /3 = 1.5, so that complete consolidation could be achieved in only 34 steps. A closed-form solution, in the small deformation regime, for the excess pore-fluid pressure dissipation as a function of time is available for the case of an infinite elastic half space [21]. Numerical agreement with this analytical solution is shown in Fig. 9b. The

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448

LABORATORY SHEAR STRENGTH OF SOIL

• 2«

-~"i S

1• i «5 •—

w

E S

<E <J S

/ Xwi"

S c » 5

-

If*'''

• a

• -

u

'

>•

11a. ui

s«

S*

u

m

•1

>• >-

«iM

o-

a

s «

AT

1L:

iiT.

M

-

3

I

Wj/Mj

I 1 p< ^

o

1

&. ^ "^

-S o s

s1 sg ^3 )w

1 1

•c

1 £

1 »Mj/Mi

p

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449

•.^US/CP

I u >o '-

O

oa

ffi

s z

11 ^l

.•|M»i4
OS

»fpe/C*»-*»)

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450

LABORATORY SHEAR STRENGTH OF SOIL

°

11

1.0

0

0

c

— a

11-U)

_ _ _ ^ ^ "'

I

•

^N^

.8

Finite Elements >v

a

H

'

0

0

0

—

0• c—

—

•

-

o 1=1.5

0

0

0

I

0

.6\ j

Analyticol

.4 --

-

0 0

.2

-

\ ^

0

1 10-3

5—i

10-2

10-1 b

4

r^^ lot

lOl

T-Cv^:

H»

8/H

(a) Finite element mesh (b) Degree of consolidation versus time (c) Settlement versus time FIG. 8—One-dimensional elastic consolidation.

numerical solution accurately predicts the increase in excess pore-fluid pressure which occurs at the early times of consolidation. This phenomenon is characteristic of the coupled theory [2.21-24] and is referred to as the Mandel-Cryer effect. Figure 9c shows the computed dimensionless settlement, 6, of the center point of the strip load as a function of the dimensionless time, T, for various h/fi^ ratio. The curves again show that the larger the h/n" ratio, the more drastic is the difference between finite and small deformation results. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

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451

Hh 111 nil

K.I. ((.(•RaflKUd louKMrir

T.eyt/B* y».o

10-3

lO-J

10-1

lOO

lOt

102

(a) Finite element mesh (b) Pore-fluid pressure versus time at depth Z = B/2 (c) Midpoint settlement versus time FIG. 9—Two-dimensional elastic consolidation. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

452

LABORATORY SHEAR STRENGTH OF SOIL

•2 ^

00

m

cd a:

V)

ziiin 1 I '

\

y ••

e

o c

II ^

•o

t4 I

3 o ffi T3

^ 01

H CD

ir

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o

PREVOST ON NONLINEAR ANISOTROPIC BEHAVIOR OF SOILS

453

Two-Dimensional Elasto-Plastic Consolidation [18] The finite element mesh and problem description are shown in Fig. 10a. A rigid permeable strip footing of width IB is resting on the surface of a soil layer with drainage occurring at the top surface only. The mechanical properties of the soil to be considered in this example are described by the axial compression and hydrostatic consolidation stress-strain curves shown in Figs. 3 and 4. Table 1 gives the model parameter values which characterize the behavior of this soil. The parameter values have been normalized by dividing them by a^^ '^ — vertical effective consolidation stress. The soil deposit is assumed to be normally consolidated, and &„. ''^ = y '^z where z is the depth measured from the top surface of the deposit and 7'^ = (1 — «»)p,. Here «»' = 0.7, p/p„. - 2.82, andfe™= 2.10'*'. The transient response of soil deposit under the footing load is dependent upon the rate of loading, w,

^^

1 dh H' dT

where T = Cj/B^ as previously, and n^ is selected to be the initial (at time f = 0) shear modulus at depth Z = 5 / 2 , (that is, /x* = 120.0). At very slow loading rates (that is, w -> 0) the soil deposit's response is fully drained, whereas when the loading rate becomes large (that is, w — 00), the deposit behaves in an undrained (that is, constant volume) fashion. This is illustrated in Fig. lOb, which shows the computed load/settlement curves for various loading rates. These calculations were performed by neglecting changes in geometry (that is, small strains/displacement) and by including the effects of gravity. The numerical results shown in Fig. \0b were obtained by taking At,, = ^ Ar„_, with jS = 1.1, so that loading could be achieved in 16 steps only. Use of the proposed formulation for solving other boundary value problems of interest in soil mechanics has also been demonstrated by applying it to analyze the interaction of an offshore gravity structure with its soil foundation when subjected to cyclic wave forces [25,26], the penetration of marine pipelines into their soil foundation [26], and the localization of deformations into shear bands in soil media [27].

Smnmary and Ctmclusions The coupled field equations that govern the behavior of anelastic porous media are presented. A general analytical model that describes the nonlinear, anisotropic, hysteretic stress-strain behavior of the soil skeleton is proposed. The accuracy and versatility of the model are demonstrated. The

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454

LABORATORY SHEAR STRENGTH OF SOIL

use of the proposed formulation in solving boundary value problems of interest in soil mechanics is demonstrated. Acknowledgments Computer time was provided by Princeton University Computer Center. References [/] Terzaghi, K., Theoretical Soil Mechanics, Wiley, New York, 1943. [2] Biot, M. A., Journal of Applied Physics, Vol. 26, 1955, pp. 182-185. [3] Prevost, J. H., International Journal of Engineering Science, Vol. 18, No. 5, 1980, pp. 787-800. [4\ Green, A. C. and Naghdi, P. M., International Journal of Engineering Science. Vol. 3, 1%5, pp. 231-241. [5] Eringen, A. C. and Ingram, J. D., International Journal of Engineering Science. Vol. 3, 1965, pp. 197-212, and Vol. 5, 1967, pp. 289-322. [6] Prevost, J. H., Journal of the Engineering Mechanics Division, American Society of Civil Engineers, Vol. 104, No. EMS, 1978, pp. 1177-1194. [7) Prevost, J. H., International Journal of Numerical Analytical Methods in Geomechanics, Vol. 1, No. 2, 1977, pp. 195-216. [8\ Hill, R., Journal of the Mechanics and Physics of Solids, Vol. 6, 1958, pp. 236-249. [9] McMeeking, R. M. and Rice, J. R., International Journal of Solids and Structures, Vol. 11, 1975, pp. 601-616. [10] Prevost, J. H., Journal of the Geotechnical Engineering Division. American Society of Civil Engineers, Vol. 104, No. GTS, 1978, pp. 1075-1090. [//] Prevost, J. H. in Proceedings, 3rd International Conference on Numerical Methods in Geomechanics, Aachen, Germany, Vol. 1, 1979, pp. 347-361. [12] Richard, F. E., Woods, R. D., and Hall, J. R., Vibrations of Soils and Foundations. Prentice-Hall, Englewood Cliffs, N.J., 1970. \I3] Roscoe, K. H. and Burland, J. B. in Engineering Plasticity. Heyman and Leckis, Eds., Cambridge University Press, Cambridge, England, 1%8, pp. 535-609. [14] Forrest, J. H. et al, "Experimental Relationships between Moduli for Soil Layers Beneath Concrete Pavements," Report No. FAA-RD-76-206, 1976. [15] Anderson, K. H. in Proceedings. BOSS 76 Conference, Tronheim, Norway, Vol. 1, 1976, pp. 392-403. [16] Zienkiewicz, O. C , The Finite Element Method. McGraw-Hill, New York, 1977. [IT] Hughes, T. J. R. and Prevost, J. H., "DIRT II — A Nonlinear Quasi-static Finite Element Analysis Program," California Institute of Technology, Pasadena, Calif., August 1979. [18] Prevost, J. H., Journal of the Engineering Mechanics Division. American Society of Civil Engineers, Vol. 107, No. EMI, 1981, pp. 169-186. [19] Malkus, D. S. and Hughes, T. I. R., Computer Methods of Applied Mechanical Engineering. Vol. 15, No. 1, 1978, pp. 63-81. [20] Scott, R. F., Principles of Soil Mechanics. Addison-Wesley, New York. 1963. [21] Chen, A. T. -F., "Plane Strain and Axi-Symmetric Primary Consolidation of Saturated Clays," Ph.D. thesis, Rensselaer Polytechnic Institute, Troy, N.Y., 1%6. [22] Cryer, C. W., Quarterly Journal of Mechanics and Applied Mathematics. Vol. 16, 1963, pp. 401-412. [23] Mandel, J., "Etude Mathematique de la Consolidation des Sols," Actes du Colloque International de Mechanique. Poitier, France, Vol. 4, 1950. pp. 9-19. [24] Mandel, J., Geotechnique. Vol. 3, 1953, pp. 287-299. [25] Prevost, i. H., Hughes, T. J. R., and Cohen, M. F., "Analysis of Gravity Offshore Structure Foundations,"/owrna/o/Perrotewm Technology, Feb. 1980, pp. 199-209.

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455

\26] Prevost, J. H. and Hughes, T. J. R., "Finite Element Solution of Boundary Value Problems in Soil Mechanics," in Proceedings. International Symposium on Soil under Cyclic and Transient Loading, Swansea, U.K., Jan. 1980, pp. 263-276. 127\ Prevost, J. H. and Hughes, T. J. R., Journal of Applied Mechanics, American Society of Mechanical Engineers, Vol. 48, No. 1, 1981, pp. 69-74.

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/. H. Schmertmann^

A General Time-Related Soil Friction Increase Phenomenon

REFERENCE: Schmertmann, J. H., "A General Time-Related SoU Friction Increase Phenomenon," Laboratory Shear Strength of Soil. ASTM STP 740, R. N. Yong and P. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 456-484. ABSTRACT: Various laboratory treatments of clay specimens produced an increase in the frictional component of their ability to mobilize shear resistance. These treatments included compression after isotropic normal consolidation, compression after isotropic overconsolidation, anisotropic normal consolidation, chemically induced dispersion, changing pore fluid, decreasing rate-of-strain, increasing time for secondary compression, and allowing time for creep. The paper shows how increasing clay fabric dispersion in these treatments relates directly to an increased friction capability. The author then suggests that the dispersion shifts the external shear load to stiffer and stronger aggregates of particles in the fabric. This produces a stiffer and stronger clay due to its increased frictional capability. The practical aspects of this behavior include a better understanding of various laboratory specimen aging effects such as increasing modulus and the quasi-preconsolidation effect, recognizing it as a frictional and not a bonding behavior, and the desirability of including such behavior in the laboratory or computer simulation of in situ performance. KEY WORDS: soils, soil tests, shear properties, clays, fabric, compressibility, aging, time effects, friction

Nomenclature A Ag c' Cf c/j D E

Pore pressure parameter = [AM/A(CTI ' — oj')] Net value of A during quasi-preconsolidation (2-4 ESP in Fig. 12) Empirical Mohr-Coulomb cohesion intercept in terms of effective stress Early notation for /^ Alternative expression for the D-component, = AT/ACT' Component of mobilized shear resistance seemingly linearly dependent on effective stress, a', at constant structure Young's modulus

'Principal, Schmertmann and Crapps, Inc., Gainesville, Fla. 32601.

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SCHMERTMANN ON TIME-RELATED SOIL FRICTION INCREASE

ESP G Gj iNC iOC / /f IDS-test /„, IQ KQ NC OC Pc Po Apcq PI R ^2 S4 u wi Wp Wj X^ j3 A 6 a a' ai' oi' 03' <Ti 'h Oi'( T

457

Effective stress path Shear modulus Specific gravity of soil solids Isotropically normally consolidated Isotropically overconsolidated Component of mobilized shear resistance seemingly independent of effective stress, a', at constant structure. Note I + D — T Notation for / to emphasize that component is a function of strain, value of / at strain e Experimental procedure for determining the / and D components of T as functions of strain. Usually done with e and u control Maximum value of / determined from a graph of / versus strain Mobilized shear resistance when a ' = 0, the bond shear resistance Ratio of (J3 Vffi' during virgin consolidation Normally consolidated Overconsolidated Preconsolidation pressure Normal consolidation pressure Increment of apparent p^. due to quasi-preconsolidation effect Atterberg plasticity index Overconsolidation ratio Value of [(1 — Ko)/{l + KQ)] before secondary compression aging Value of [(1 — /Co)/(I + KQ)] at start of new increment of virgin consolidation Pore water pressure Atterberg liquid limit Atterberg plastic limit Atterberg shrinkage limit Fraction of /3-strength increase mobilized during secondary aging Parameter relating /-component to effective stress [1]^ Denotes "an increment of" Strain Total normal stress Effective normal stress, = a — u Major principal effective stress Average value of a^' (bar denotes average value) Minor principal effective stress Higher effective stress level in an IDS-test Lower effective stress level in an /D5-test Mobilized shear resistance

The italic numbers in brackets refer to the list of references appended to this paper.

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458

(j>'
UBORATORY SHEAR STRENGTH OF SOIL

Empirical soil friction strength angle in terms of effective stress Early notation for Z)-component, = tan^'rf^ Part of ' actually mobilized

The Bjerrum Memorial Volume (BMV) contains a paper by the author [/] that presents a detailed summary of laboratory research aimed at contributing towards a better understanding of the frictional and bond components of shear strength behavior in all soils. Parts of Ref / describe a seemingly very common and not generally appreciated shear phenomenon in cohesive soils. This paper extracts and organizes these parts from the parent BMV reference so as to focus on the evidence that relates to and describes this phenomenon. Any conventional Mohr-Coulomb shear strength envelope shows the combined effects of changes in effective stress and the changes in the soil structure or fabric associated with such changes in effective stress. Reference 1 describes some special experimental methods for separating these effects. Extensive use of these methods, as described herein, shows how the mobilized components of shear strength change with changes in fabric, and how the changes in these components with time indicate a dispersive change in structure with time. This dispersion then leads to a fabric stress transfer behavior which usually produces a stronger and stiffer clay due to increased friction-type strength. This work seems to offer a nonbond explanation for the "aging" effects, such as "quasi-preconsolidation", sometimes observed in lab clay specimens. Understanding this phenomenon first requires a brief explanation of the special soil shear resistance components used by the author, and the laboratory test method used to determine them. The (/.-Component and the /Z)5-Test Geotechnical engineers usually find it convenient to separate the shear strength of soil into components. The most common set of such components results from the linear approximation of the Mohr-Coulomb failure envelope, giving the friction (slope) and cohesion (intercept) components. However, the apparently linear or nearly linear envelope often determined from conventional series of consolidated-undrained or drained shear tests represents only an empirical result for the convenience of engineering analysis. The empiricism results from both the linear approximation and from the fact that the envelope combines the effects of changes in stress and the laboratory changes in soil structure resulting from the changes in stress. Many investigators, including the author in the BMV, have shown that the Mohr-Coulomb shear strength envelope has significant curvature. This curvature becomes especially apparent when the investigator determines the

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SCHMERTMANN ON TIME-RELATED SOIL FRICTION INCREASE

459

envelope from a series of shear tests designed to maintain the structure of the soil as nearly constant as possible while testing over the required range of effective stress [/]. Consider the general case of a curved envelope as shown by x-y-z in Fig. 1. This figure also illustrates one way of representing the shear strength of any point y on the envelope by means of the sum of the two components labeled / and D in the figure. The first step to obtain these components at point 3^ requires constructing a tangent to the curve at that point. This tangent then intercepts theCT' = 0 axis at point c. Thus we can say that the illustrated soil behaves at point y as if it had an effective stress independent component of / and an effective stress dependent component of D. The ratio of (D/ff' )y denotes the shear strength sensitivity of the soil at point y to varying the effective stress. It thus gives a point value of fabric friction capability. The author has given this ratio the symbol d^ as shown in Eq 1. The e-subscript emphasizes that the mobilization of d depends on strain. AT

'^^'7'' Ao'

(1)

Note that the intercept /-component does not represent the correct value of a' = 0 intercept strength that the Fig. 1 soil could actually mobilize, /Q and not c represents the correct intercept strength. For ordinary envelope curvatures for clay the value of / can considerably exceed the value of IQ. In fact, Ref 1 shows that noncemented clays often have negligible values of /Q. Thus / does not designate a physical cohesion or bond strength for the soil illustrated in Fig. 1. Instead it represents an intercept obtained by extrapolating a tangent to the envelope curve. The BMV paper shows that the /-component has a surprisingly constant and unique behavior that appears related to the radii of the edges of the particles in contact and therefore to a

EFFECTIVE STRESS

FIG. I—Curved Mohr constant-structure envelope showing the definition of the 1- and D-components of mobilized shear strength.

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460

LABORATORY SHEAR STRENGTH OF SOIL

soil's grain size and mineralogical distribution. This aspect of/-behavior falls beyond the scope of this paper. However, this paper will subsequently show some of the uniqueness of the /-component in conjunction with discussions of rff-behavior. While the profession normally uses the Mohr-Coulomb envelope for a defined failure condition, such as maximum shear or maximum stress ratio, in principle one can construct such an envelope for any defined mobilized shear strength condition such as that mobilized at a given value of test sample strain. Other envelopes could represent the mobilized strength at other values of strain. The investigator could then plot the variation of the / and D strength components as functions of strain at any constant magnitude of effective stress, such asCT,,' in Fig. 1. The author has accomplished the separation of the / and D components as functions of 5'train by means of a laboratory testing procedure appropriately designated the IDS-itst. The BMV reference [/] describes this test in detail, as do Schmertmann and Osterberg [2] and Schmertmann [3,4]. Briefly, the test consists of subjecting a soil to a nondestructive change in effective stress conditions cycled between two constant reference states, such as two constant values of (Ti', which the investigator maintains constant by appropriate control of pore pressure over the complete strain range of the test. By interpolation the investigator obtains two complete stress-strain curves, one for each effective stress level. From these he or she can show how the / and D components varied with strain. The previous references give many examples of the results from this type of testing. By this method one can determine the effective stress sensitivity of the mobilized shear strength, the value of d^ in Eq 1, as a function of strain simply by dividing the ZJ-component at each strain by the current average value of effective stress.

Soil Treatments that Produce an Increase in d^ As part of his shear strength research the author subjected soil samples to a variety of stress, chemical, and time-related treatments, and studied their effects on the strain mobilization of the / and D components of shear resistance. Many of these treatments produced important changes in maximum shear resistance or the strain rate of mobilization of resistance, or both. But, to the author's great surprise at the time, the /-component remained constant during most of these treatments. The changes in mobilized shear resistance behavior resulted almost entirely from changes in the D-component and therefore in d^. This section discusses the various treatments and their effects on these strength components and on fabric dispersion. This section will also make use of the term "dispersion" with the soil fabric or soil structure meaning first suggested by Lambe [5].

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SCHMERTMANN ON TIME-RELATED SOIL FRICTION INCREASE

461

Fabric Dispersion The initial formation and structure of clays with their platy-shaped particles, or aggregates of such particles, involves many edge-to-face or edge-toedge contacts. Lambe [5] referred to clays with a large proportion of such contacts as having a "flocculent" fabric or structure, which tends to produce a random orientation of particles. Distortions or other modifications of this structure which reduce the number of such contacts tend to produce a more oriented and parallel arrangement between the clay particles or aggregates of such particles. Lambe referred to this type of fabric or structure modification as "dispersion". When a clay reaches the state of having a predominantly parallel fabric, he referred to it as "dispersed". The following eight sections will show that mobilizing d^ appears to correlate with dispersion. Note that dispersion under undrained conditions tends to decrease stiffness and strength, as usually happens when remolding an undisturbed clay at constant water content. However, dispersion with drainage may have an entirely different effect. A typical IDS-test cycles between two constant-ai' conditions and allows whatever drainage required to maintainCT]' constant during the strain. Compression of isotropically. Normally Consolidated (iNC) Clay At the very beginning of the research in developing and using the IDS-test \2] the author discovered that after the typical, one-day, isotropic, normal consolidation a clay would fully mobilize its /-component at 1 percent or less axial strain but only gradually mobilize its D-component. Figure 2 and the solid lines in the lower half of Figs. 3 and 4 illustrate such test results from two clays. Table 1 lists some of the mineralogical properties of these and the other clays involved in this paper. Note the very rapid rise, probably essentially elastic, in the /-component compared with the much more gradual development of d^. It appears that mobilizing d^ requires significant axial strain. This strain implies significant shear strain and significant movement between soil particles. We know that shear strain tends to disperse structure. In the extreme of the very high strain, residual state, we have a high degree of dispersion in the planes of shear movement. We thus have the first connection between d^ and dispersion—both increase with strain. The final, 10 percent strain components in Fig. 2 reinforce this connection. At a strain between 6 and 10 percent this sample developed a distinct shear plane, which produced an otherwise unusual abrupt drop in / and a corresponding increase in D and d^. We associate the shear plane and its high shear strains with locally increased soil structure dispersion, and thus have this test to connect more directly an increasing df with increasing dispersion. See Ref 2, p. 665, for more details about this test.

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462

LABORATORY SHEAR STRENGTH OF SOIL

'U 0-6 risr ^-"n 0.5 .E O.U -

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Compression After One Cycle of isotropic Overconsolidation HOC) Figures 3 and 4 also show the stress-strain curves (top half of figure) and the component mobilization curves (bottom half of figure) after one-cycle overconsolidation by ratios of 4 and 3, respectively. Note that this overconsolidation produces a large increase in shear strength, greatest at low strain and diminishing with additional strain. Note also that this increase occurs while maintaining effective stress levels approximately the same as those used in the similar IDS-test on the comparative iNC sample. The component curves show that essentially the entire strength increase from overconsolidation results from a large increase in d^. The strain mobilization of the /-component remains essentially the same as for the iNC clay. The process of overconsolidation not only increases the density of particle packing but on the micro-fabric level the densification process reduces void space and therefore must force the platy particles into a more parallel orientation. Overconsolidation tends to disperse structure. We thus have further evidence that dispersion has the net effect of increasing d^. Anisotropic Consolidation Schmertmann and Hall [6] investigated the effect of anisotropic consolidation at various K ' = Oi '/a^', ratios but using the same Oi' magnitude at each K '. Figure 5 shows some of the results from their comparative testing. They found that the subsequent compressive strength of both kaolinite and Boston blue clay increased as the normal consolidation K '-ratio increased. This occurred despite the reduced consolidation oj' magnitude as K' in-

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SCHMERTMANN ON TIME-RELATED SOIL FRICTION INCREASE

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creased. Note that once again the after-consoHdation compressive strain mobilization of the /-component did not change. The strength mobilization increases due to anisotropic consolidation appeared due entirely to increases in the Z)-component. These increases gradually reduced with increasing compressive strain, but they still had a significant magnitude at 5 percent compressive strain in the IDS-Xesi that followed the K '-consolidation. Increasing the K '-ratio during normal consolidation produced successively increased vertical strain during that consolidation. As discussed in the section on Compression of iNC Clay, more strain might mean more disper-

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464

LABORATORY SHEAR STRENGTH OF SOIL

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FIG. 4—Comparisons of shear component mobilization in NC and OC (R = 3) extruded kaolinite clay II kg/cm^ = 98 kPa = 1.02 tsf).

sion and therefore help explain the greater d^ at the beginning of the compression test that followed the consolidation. Chemically Induced Dispersion The addition of small amounts of chemicals to a cohesive soil can sometimes cause dramatic changes in its fabric. The author added sodium phosphate dispersants to kaolinite and Boston blue clays (BBC) before machine remolding and extruding some of the triaxial test specimens. These dispersants had the effect of reducing the shrinkage limit and plasticity index

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SCHMERTMANN ON TIME-RELATED SOIL FRICTION INCREASE

465

TABLE 1—Plasticity and mineralogy of clays tested.

Remolded Clay

PL

0.002 mm,

%

%

Activity

Clay Minerals

4 9

60 20

0.07 0.45

14 19

13 53

1.08 0.36

21 105

60 85

0.35 1.24

Kaolinite—99% Kaolinite—15% Ulite—10% Montmorillonite—10% lllite—45% Chlorite—25% Kaolinite—99% Montmorillonite—85% lllite-5%

Dispersed kaolinite (0-EPK) Enid (residual) Jacksonville Boston blue Kaolinite Lake Wauberg

All / ^ results from constant-a|' /D5-tests using: isotropic consolidation to 3.50 kg/cm^, "i • high = 3.30 kg/cm^ o r low = 2.60kg/cm^ 1 kg/cm^ = 98 kPa = 1.02 tsf.

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FIG. 5—Strain mobilization of the I and D components after about 20-h anisotropic secondary consolidation <1 kg/cm^ = 98 kPa = 1.02 tsf I [6].

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466

UBORATORY SHEAR STRENGTH OF SOIL

of each clay, and progressively reducing the equilibrium void ratio at a given effective stress (Table 2a). These progressive effects followed from the presumed progressive increase in clay fabric dispersion resulting from adding a more powerful dispersant chemical. Table 2a also shows that such progressive dispersion had essentially no effect on the maximum value of the /-component, /,„. In contrast, Table 2b lists a dramatic increase in d^ at the selected representative compressive strains of I and 3 percent. This appears to offer direct evidence of the unique connection between increased clay fabric dispersion and increased d^—at least at low relative (to residual state) shear strain. Changing a Clay's Pore Fluid Starting with a still hot, oven-dried kaolinite powder, the author prepared dry triaxial test specimens and then vacuum-saturated them with five different pore fluids ranging in viscosity from dry nitrogen to a 25 percent glycerine and 75 percent water mixture. Table 3 lists information about these samples. After near-saturation of the kaolinite with these various fluids, the author performed an ordinary IDS-test of the constant-a,' type, using the same effective stress levels for all the comparative tests. Figure 6 shows the comparative strength component results as a function of strain. Once again, the /-component behavior seems about the same for all the tests. Also once again, the c/^-values show dramatic differences. The less the viscosity of the pore fluid, the greater the value of d^ mobilized at a given strain. It appears that for the same rate-of-strain conditions in this series of comparative tests that more movement between particles can take place within a given time or strain interval as the pore fluid viscosity decreases. This seems reasonable because the lower the viscosity the more easily the pore fluid can move out of the way and not retard the particle movements. One can also explain this by saying that a lower viscosity allows more dispersion per unit strain and therefore a more rapid mobilization of d^. Note that the increase in d^ with decreasing viscosity took place despite a large increase in test void ratio with this decreased viscosity. Such a void ratio increase by itself should reduce particle inference effects and therefore reduce d^. It appears that an even larger viscosity effect dominated the combined behavior. Decreasing Rate of Strain In their closure in 1962 Schmertmann and Hall [7] presented the results from a series of IDS-tests on duplicate specimens of extruded kaolinite in which all variables remained constant except rate-of-strain. This rate varied by a factor of over 5000 for the seven tests involved in this comparative series. Figure 7, copied from this discussion, shows the comparative high-ff]' stress-

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468

LABORATORY SHEAR STRENGTH OF SOIL

TABLE 2b—Effects of chemical dispersion on plasticity, void ratio, and mobilized shear strength components: Examples of pre-dispersion of soil structure increasing strain-rate of d^-mobilization. Average tan""' rf, (deg) at IDS-Test Axial Compressive Extruded Soil Kaolinite (DW-EPK) N*-EPK 0*-EPK Boston blue clay (BBC) 0*-BBC

e, = 1.0%

t, = 3.0%

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•Denotes addition of sodium phosphate dispersant prior to extrusion.

strain curves and also the comparative / and D components of mobilized shear resistance. Once again, the /-component remains approximately constant. But the strain-mobilization of d^ increases significantly with decreasing rate-ofstrain. It appears that reducing the rate-of-strain allows the soil particles more time to interact with each other and therefore to develop a higher value of c?j at a given strain. This would also follow from the previous concept of decreasing viscosity allowing greater soil structure dispersion. Increasing the time at a constant pore fluid viscosity should have the same effect as decreasing viscosity while time remains constant. These data now begin to show how increasing time produces a larger d^component. Other examples now follow. Increasing Time for Secondary Compression A series of tests in which the author allowed progressively increasing times for secondary compression (under constant effective stress conditions) proved informative. Figure 8 shows the IDS-test components obtained from this comparative series, again on remolded kaolinite, with all other test conditions the same. Note again that /„, remains about the same with any differences probably due mostly to experimental variations. Again, in contrast, there occurs a dramatic increase in the rate of d^-mobilization with strain, especially at low strains. This dramatic increase occurred despite the fact that this kaolinite had a typical very low coefficient of secondary compression. The effect of time seems most pronounced at the beginning strains of the IDS compression tests following the secondary consolidation. It decreases with additional strain and appears destroyed in this soil after about 3 percent compressive strain. The heavy line in Fig. 8 shows, again for comparative purposes, the /Detest c?j-component from the same kaolinite clay, but deliberately dispersed Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

SCHMERTMANN ON TIME-RELATED SOIL FRICTION INCREASE

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470

LABORATORY SHEAR STRENGTH OF SOIL

1

2

3

4

AXIAL COMPRESSIVE STRAIN, in p«r cent

FIG. 6—Effect of different pore fluids on I and D mobilization in compacted dry. then saturated, kaolinite powder (see Table 3) II kg/cm^ = 98 kPa = 1.02 tsf).

before machine extrusion (see Q-EPK in Table 2a). The reader can see that the initial 0.4 percent strain mobilization of d^ by the undispersed kaolinite after five weeks of secondary consolidation appears about the same as that of the deliberately dispersed kaolinite following only one day of secondary consolidation. It thus appears that the effect of time may allow the clay structure to develop a more dispersed type of particle arrangement by internal particle adjustments with very little overall strain. Here we have an apparent link between fabric-time effects, clay dispersion, and increasing d^. Note that Table 2a also shows that the Q-EPK dispersion did not change /„, compared with the DWEPK I„,-values in Fig. 8. Although not demonstrated directly at this point in the paper, a constant /-component behavior with strain combined with an increased D (or d^) component means that the stiffness of the soil as measured by an initial shear modulus, G, or Young's modulus, E, must also increase compared with the same clay without the £)-component increase. Thus successively increasing times in secondary consolidation must also successively increase G and E. Schmertmann [8] presented direct evidence of this. Figure 9 and Table 4 come from Ref 8. The undrained, initial moduli from these tests using kaolinite increased by a factor of about 10 with increased secondary time from about 2 h to 25 days, apparently with very little if any difference in void ratio or gross pore pressure behavior. Engineers working in the soil dynamics Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

SCHMERTMANN ON TIME-RELATED SOIL FRICTION INCREASE

0

1 2 3 AXIAL COMPRESSIVE STRAIN, 6,, in percent

471

4

FIG. 7—Effect of rate of compressive strain on the \DS-test results obtained from duplicate specimens of remolded, saturated kaolinite clay II kg/cm^ = 98 kPa = 1.02 tsf).

specialty have also recognized the clay structure stiffening effect from secondary consolidation. For example, see Anderson and Woods [9]. This fact has introduced the need for a correction factor of about 1.5 to 3.5 before using lab-determined G-values for the in situ clay. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

472

LABORATORY SHEAR STRENGTH OF SOIL

1 2 3 4 5 AXIAL COMPRESSIVE STRAIN, In per cent

FIG. 8—Effect of secondary isotropic consolidation times on I and D in extruded kaolinite clay II kg/cm' = 98 kPa = 1.02 tsf).

These results suggest that small differences in clay fabric can have large consequences. They also suggest an explanation for the quasi-preconsolidation effect. Figure 8 shows that the stiffening of the structure with increasing secondary time results from the low-strain increase in d^. Figures 3 and 4 and the discussion in the section on Compression after One Cycle of Isotropic Overconsolidation show the same increase in d^ with overconsolidation. Hence for a small increment of additional strain following secondary consolidation the clay will behave as an overconsolidated clay. A later section of this paper quantitatively discusses the quasi-preconsolidation effect. Time for Undrained Creep Bea [10] performed a series of undrained creep tests following isotropic, normal consolidation of both kaolinite and remolded and undisturbed samples of Boston blue clay. These samples strained slowly with time under a constant axial compressive deviator stress. After such creep he performed IDS-tests in which he forced a controlled strain rate upon the clay greater than the prior creep strain rate. He used the IDS-tests to separate the components of mobilized shear strength over the additional /D5-test strains,

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SCHMERTMANN ON TIME-RELATED SOIL FRICTION INCREASE

473

All four pore pressure curves 3re_^ within shaded area, without order

0

1

2 3 Axial compressive strain, (^, in %

4

5

FIG. 9—Example of secondary shear strength behavior: consolidated-undrained compression of machine extruded and saturated kaolinite {I kg/cm^ = 98 kPa = /. 02 tsf).

and, by back-extrapolation, also at the end of creep. He then compared these results with the component separations from duplicate specimens not subjected to such creep. Figure 10 presents some of his results from kaolinite, and Fig. 11 and Table 5 from Boston blue clay. The explanations now given should help the reader to understand the unavoidably complex Figs. 10 and 11. Figure 10 first shows the no-prior-creep reference /- and D-component strain mobilization curves from replicate tests H-13 and B-1. These tests produced mobilization curves that almost coincide—the solid lines for / and the dashed lines for D. Bea then superposed the component mobilization results from IDS-tests performed after allowing three samples of the same clay to undergo different values of compressive strain during creep under constant deviator stress. Creep test No. 2 had a constant deviator stress of 1.12 kg/cm^

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474

LABORATORY SHEAR STRENGTH OF SOIL

TABLE 4—Details of comparative tests shown in Fig. 9. Computed

Test No.

Time in Secondary, min

Void Ratio

Degree of Saturation

200 201 204 203

35600 9920 1310 115

0.882 0.879 0.880 0.883

99.5 99.8 99.7 100.0

Initial Tangent Modulus, £,',

kg/cmVn, % 90 insufficient data 35 9

Initial void ratio = 1.013. Isotropic consolidation, 1-increment, 0 to 3.5 kg/cm^ End of primary (Casa. construction) = 85 min. Strain rate approximately 1 % in 6 h. Constant triaxial cell pressure = 3.5 kg/cm^. G, = 2.609, Wi = 52 %, w^, = 31 %, w, = 25 %, 60 %—2 microns. The initial tangent modulus is the average modulus between the first and third data points obtained during the compression (after the 0-0 point; the deviator stress at these points was 0.1 and 0.5 kg/cml 1 kg/cm^ = 98 kPa = 1.02 tsf.

for 9 days,^ which produced an axial compressive strain of 0.7 percent. The subsequent IDS-test obtained the /-component data shown by the solid square points and the D-component data shown by the + symbols. Comparison with the reference mobilization curves shows almost no change in /-component mobilization, but does show the large increase in D-component mobilization illustrated by the cross hatching beginning at 0.7 percent strain. Similarly in Fig 10, creep test No. 3 under the greater deviator stress of 1.68 kg/cm^ produced 1.7 percent axial strain during 10 days of creep. The subsequent /D5-test produced the solid triangles for the /-component determinations and the open circles for the Z)-component determinations. One can again see almost no change in /-component mobilization as a result of the prior creep, but can easily see the large increase in £)-component mobilization illustrated by the different cross hatching beginning at 1.7 percent strain. Again in Fig. 10, creep test No. 4 under the still greater constant 1.96 kg/cm^ deviator stress produced a strain of 5.0 percent during 11 days of creep. The subsequent IDS-test produced the /-component determinations shown by the solid circles and the D-component determinations shown by the X symbol. One can again see only minor change in /-component mobilization as a result of the prior creep, but can easily see the increase in D-component mobilization illustrated by the cross hatching beginning at 5.0 percent strain. The reader will see that for the first 1 to 2 percent of additional and forced M kg/cm^ = 98 kPa = 1.02 tsf.

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SCHMERTMANN ON TIME-RELATED SOIL FRICTION INCREASE

0

2

4

6

8

475

10

AXIAL COMPRESSIVE STRAIN, € „ in •/.

FIG. 10—Effect of undrained creep on shear component mobilization in remolded kaolinite II kg/cn? = 98 kPa = 1.02 tsf) (10).

~ 0.8 6 E, at end|;\ p O of creep. ^«»

AT END OF UNDRAINED CREEP NO. I D S TEST "; DAYS 1high •15 4.69 3.09 17 3.42 -16 4.44 3.04 19 3 43 R .o I-DAY ISOTROPIC CONSOL ' " TO 3.65 NO CREEP ' BEGAN UNDRAINED CREEP AT ISOTROPIC 3.65

Of*

-0.6

0.4 = 8-18

ft 1

0.2 -

'8

19

20

21

22

30

26 a

22

±

0.0

3A

18 23

AXIAL COMPRESSIVE STRAIN £, in 7 .

FIG. 11—Example of excess D-component mobilization after undrained creep in remolded Boston blue clay II kg/cm^ = 98 kPa = 1.02 tsf) [10].

Strain following the creep, forced at a constant rate, this machine-extruded kaolinite clay considerably increased its t/j-mobilization compared with the same clay without prior creep. Also note that after only a very small IDS-test strain the value of the /-component becomes equal to that for the same clay but without the prior creep. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

476

LABORATORY SHEAR STRENGTH OF SOIL

TABLE 5—Effect

of creep on the I and D components in undisturbed BBC (stresses in kg/cm^l."

Creep

At End of Creep

Test

(a, — Oj)

Days

B-13 B-14

2.02 2.00

11 3

f|,

%

2.50 2.00

Without Creep

t a n " ' d^

/

15.0 deg 15.1 deg

0.31 0.27

tan"'

rf,

11.0 deg 9.5 deg

/ 0.51 0.54

"1 kg/cm^ = 98kPa = 1.02 tsf.

Figure 11 shows the same type of behavior noted for the Fig. 10 kaolinite, but this time after creep-straining the remolded Boston blue clay to the comparatively high value of about 19 percent axial strain. Test B-18 data provide the no-creep reference for comparison to the with-creep tests B-15 and B-16. Again, the cross hatching beginning at the strain at the end of creep shows the large increase in mobilized D-component following the creep. In this case the tan"' d^-component increased about 8 deg as a result of the soil structure adjustments that took place during the 17 to 19 day creep. Table 5 shows that a similar dramatic increase in the D-component occurred after subjecting two undisturbed samples of Boston blue clay to creep. The similarity between the changes in the strain mobilization of the D-component due to secondary consolidation and due to undrained creep suggests a similar cause. The section on Increasing Time for Secondary Compression suggested clay fabric dispersion as the cause for secondary consolidation. It therefore appears plausible that such dispersion also produces the creep effects discussed in this section. Hypothesis for Dispersion Producing Increased Friction Resistance Summary of Dispersion-df Behavior A simple forced strain, or simple isotropic consolidation, or anisotropic consolidation with increasing stress ratios, or changing a clay's pore fluid in the direction of reduced viscosity, or inducing prior dispersion by chemical additives: each produced the similar effects of increasing a cohesive soil's subsequent shear resistance sensitivity to a change in effective stress (increasing df). These common effects suggest a common cause. In each case the cause seems related to soil fabric dispersion. Decreasing the rate of strain in a strain-controlled compression test, or increasing the time for one-dimensional secondary consolidation, or increasing the time for anisotropic stress creep behavior also have the common effect of increasing a soil's subsequent c?f-component of strength, but sometimes for only a very limited strain interval in the subsequent forced increased rate of Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

SCHMERTMANN ON TIME-RELATED SOIL FRICTION INCREASE

477

strain IDS compression test. These similar time-related behaviors also suggest a common cause. It seemed possible, for each case, to relate the cause to soil fabric dispersion. Hypothesis for Dispersion-d^ Behavior The multitude of treatments discussed previously all produce essentially the same effect in terms of the / and D strength components, thus strongly suggesting that this behavior involves something fundamental in soil fabric response. The author hypothesizes the following behavior: A clay can and will slowly readjust its fabric under drained conditions, such as during long periods of time at constant stress. The more easily dispersed (moved) particles or aggregates of particles yield by particle-to-particle slippages to those particles or aggregates of particles with more rigidity and which probably also have more strength and more resistance to dispersion. Such slippage and consequent yielding produces secondary compression in one-dimensional or isotropic consolidation, or creep if the soil can develop shear strain. With time the soil becomes stronger and stiffer as a result of the yield-transfer of applied shear to those stiffer and stronger aggregates. This transfer shows up as a decrease in the rate of volume change or creep movement. These stronger particle aggregates now find themselves closer to failure, with a greater mobilization of particle friction and interference effects. These effects depend primarily on the magnitude of effective stress. Thus, with the increased strength and stiffness resulting from the load transfer necessitated by dispersive particle movements, we also get an increase in the shear sensitivity of the soil to changes in effective stress, and d^ increases. A new increment of strain will accompany each subsequent full mobilization of the increased shear resistance capability of the new, more dispersed fabric. When achieving this mobilization in an /D5-test the forced strain of the test does not permit the re-occurrence of the dispersive behavior that caused the strengthening to occur. Instead the particle load transfer and strengthening effects that resulted from fabric dispersion break down with the newly forced strain, and the mobilized shear resistance behavior returns to that which would have occurred had the time interval with constant stress and drained dispersion not happened; the data in Figs. 10 and 11 provide examples. Dispersion-d^ Phenomenon Affects All Soils The data and discussions in this paper have included only cohesive soils because of the more dramatic effects associated with their more complicated fabric and to limit the length of this paper. However, study of Ref / will show that the phenomenon probably occurs in all soils. For example, we tacitly admit the existence of a quasi-preconsolidation effect (see the section on In-

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478

UBORATORY SHEAR STRENGTH OF SOIL

creasing Time for Secondary Compression and the following section) in sands when we use the common assumption of neglecting settlement when the vertical stress increase becomes less than 10 percent of the in situ vertical stress. A Practical Application—The Quasi-PieconsoUdation Effect Leonards and Altschaeffl [//] documented in 1964 that after allowing much longer than customary secondary compression aging times following primary consolidation in the laboratory, an otherwise normally consolidated clay behaved as if it had a preconsolidation stress, p^, greater than the normal consolidation pressure, PQ. They denoted the difference (pc — Po) = Apc, as the quasi-preconsolidation effect, and reported that all the clays they tested to that time had shown this effect, with an average ratio of Ap^g/po — 0.40. A 40 percent overconsolidation can sometimes have a very important practical value. For example, it might reduce footing settlements to acceptable values and eliminate the need for piles. But many engineers still remain uncertain about the cause and magnitude of this quasi-preconsolidation effect. This section does not present a complete discussion of the subject. Rather, it should show the reader one possibility for a physical and quantitative explanation of the quasi-preconsolidation effect based on the shear strength research results discussed in this paper. The section on Increasing Time for Secondary Compression has already discussed a possible, perhaps even a probable, cause for this effect involving the similar increase-in-c?j behavior from secondary compression aging and overconsolidation. The author will now attempt a quantitative analysis to determine the magnitude Ap^^, using the experimental results presented herein and in the parent reference [/]. Please refer to Fig. 12 to aid this analysis. The effective stress path (ESP) 1-2 shows a clay undergoing an increment of normal consolidation along the appropriate /To-line, reaching the vertical principle stress consolidation pressure of poi- The clay then ages in secondary compression and increases in strength due to the increase-in-d^ behavior detailed in this paper. By the time the clay again experiences primary consolidation due to an increment of external loading it will have increased its frictional shear strength. But the well-known formula KQ — I — sin <^; suggests that any increase in <^ will reduce KQ. Assuming the formula applies, then the next increment of consolidation will begin along some new /Cfl-line as shown in Figs. 12a and I2b. The ESP of the clay must somehow move from Point 2 to a point on the new KQ-line. It may begin this move during the volume change associated with the secondary compression aging under a constant /Jo2 effective stress condition. Figure I2b illustrates this change. Figure 12a shows various constant-y4 ESPs radiating from point 2, where ^ = Au/A{a^' — a^') as usual.

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SCHMERTMANN ON TIME-RELATED SOIL FRICTION INCREASE

(a)

K(|-UNE DURING ^ E X T CONSOLIDATION

(cr-T-)ESP lU-USTRATED FOR H'^-X' 0'O.Z X,= 0.5

^A=0 |A»05

NA=:

\\

1°

/

/ y ^

/

^ ^ m A L K^-LINE

1 y ^

\

479

^^-^l(l-K^

"^''^^><^^'''*-y^

.

DUE TO d j INCREASE-

ISP*

Pa

Jiq__^ '04 03

(b) ((^,-V)ESP

SECONGARY"

.,., 3

A»0

4

CONSOLIDATION cr, =n,

FIG. 12—Effective

stress paths before, during, and after the quasi-preconsolidation process.

Because of the constant po2, the clay ESP must follow an >4 = +1 or — 1 path until it reaches point 3 (illustrated fori4 = +1) at the end of secondary compression aging. After this aging we subject the clay to an increase in ai, which tests for the quasi-preconsolidation effect. This effect reaches its maximum when the ESP reaches point 4. After reaching point 4, the additional volume and shear strains associated with further increasing effective stresses gradually destroy the special fabric dispersion effects that increased ' during the 2-3 aging, and the ESP eventually returns to the initial Ko-line at some point 5. Figure 12a arbitrarily shows the 4-5 ESP as horizontal (con-

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480

UBORATORY SHEAR STRENGTH OF SOIL

stant T). Figure I2b shows the 4-5 ESP as returning at point 5 to the virgin compression curve applicable to the initial Ko-line because the fabric has now completely lost the special fabric friction-increase effects from the 2-3 aging. To simplify this discussion, let us imagine the ESP from 3-4 as occurring along another constant-/! path. The 3-4 part of the ESP will likely produce little or no volume change. If this path produced no volume change, then the pore pressures generated in a triaxial compression test would equal zero, which in turn would mean that A = 0 from 3-4. Figure 12a illustrates an assumed A = 0, and a^' = constant, path from 3 to 4 for the actual onedimensional compression test. Figure lib illustrates the no volume change. The clay at Point 4 will now have an equivalent consolidation pressure of />04, which, as Fig. 12 shows, may considerably exceed the previous po2 and Po3- The difference (po4 ~ ^02) represents the quasi-preconsolidation effect Apcg. The author has derived a formula for the Ap^g increase ratio from the geometry in Fig. 12a. After denoting the [(1 — /Co)/(l + KQ)] slopes of the /fo-lines as ^2 for the before-secondary aging condition and as ^4 for the after-secondary aging, he then obtained Eq 2: Apc, ^ 2(1 - A,)iS, - S2) po [1 - (1 - 2Ag)S,] (1 + S2)

^^

where A^ = the net effect value of A over the entire 2-4 ESP of the quasipreconsolidation process. The author next developed an expression fory4^ for substitution into Eq 2, using a new term X^, which denotes the fraction of the 2-4 ESP increase in strength mobilization that occurs during the 2-3 ESP, A = + 1 or — 1, time in secondary compression. Use a negative Xs for a 2-3 ESP along an /4 = — 1 path. The remaining fraction of mobilized strength increase then occurs during the assumed 3-4 ESP, A = 0, quasi-preconsolidation interval of stress increase. To accomplish the expression for A^ also required the assumption that the conventional c ' = 0. In addition the writer needed an alternative expression for the increase in mobilized strength, expressed to this point as (^4 — ^2). As shown in Figs. 5, 10, and 11, and as detailed further in Reference /, during times of rest at constant stress the fabric dispersion causes the /-component of applied and mobilized shear to reduce to near-0 with a matching increase in the D-component to still carry the applied shear. Subsequent forced strain then remobilizes the same /-component with very little additional strain, while the increased D-component still remains effective for a longer interval of additional strain. Thus the total mobilized shear resistance of the clay increases by the magnitude of the /-component for a small interval of strain at increased strain rate following a time interval of aging or creep strain rate. However, the increased shear resistance occurs as an increase in d^. Reference / demonstrates that the value of the /-component in Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

SCHMERTMANN ON TIME-RELATED SOIL FRICTION INCREASE

481

a clay depends primarily on the magnitude of effective stress, with a proportionality constant denoted jS. Thus, the tan <^„,' along ^2 can increase by jS along S4. Making use of all the above, plus the geometry shown in Fig. 12a, allowed the derivation (after much manipulation) of the Eq 3 expression for>l„ ' « •

i [, _ [d - 2^,) + (52 + g)1 ]

A, = ^ ) i - \ :

2(

. ,.\,,:,: , ;j ( [l+il2X,)(S2 + /3)J j

(3)

Substituting Eq 3 into Eq 2 produced (after much manipulation) Eq 4 as an alternative expression for the Ap^^-ratio.

po

(1 - 52 - /3)(1 + 52)

^'

Equation 4 shows that the relative magnitude of the quasi-preconsolidation effect depends primarily on /S and X^. But Ref / also shows that |S has an approximately constant value averaging about 0.185 for the clays tested. As explained previously, X, depends on the relative strength increase mobilization along the Fig. 12a 2-3 ESP compared with the 2-4 ESP. Substituting into Eq 4 then gives the quasi-preconsolidation effect predictions from this theory. Assuming (KQ = 1 — sin (^') gives [52 = sin '/ (2 — sin ')]. Assume that 13 = 0.185. We now come to the question of what sign (and magnitude) to use for .Yj! + , —, or zero?—which the writer considers a fascinating question and one with almost no answer in the technical literature. The writer found only the experimental work of Newlin [12] in which he showed that X^ ~ 0 over about two log cycles of secondary compression time to 500 min, for three clays with PI from 5 to 16 percent and with the clays in undisturbed, remolded, and compacted conditions. For lack of any other data, assume that X^ = 0. Then Eq 4 predicts a quasi-preconsolidation effect of 48 percent for 0 ' = 15 deg to 64 percent for <^' = 35 deg. However, the author believes that more plastic clays and longer secondary aging times than investigated by Newlin [12] would show a positive A2.3 and therefore a positive Xj. The quasi-preconsolidation decreases to 36 to 50 percent if X^ = 0.25 and to 24 to 32 percent if X, = 0.5 (illustrated in Fig. 12a). These values all check approximately with the average of 40 percent (from laboratory data) suggested by Leonards and AlschaeffI [//]. One can also imaginje circumstances where the present theory will predict a A/j^.^-effect less than the aforementioned 24 to 64 percent. If the fabric of the clay lacks the ability for the dispersion increase-in-dj behavior, then no strength increase will occur, 54 will = S2, P = 0, and Apc, will = 0. The writer has found no instance of such a lack and it seems unlikely for most clays. More likely, a clay might have such a sensitive fabric that it tends to Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

482

LABORATORY SHEAR STRENGTH OF SOIL

collapse during secondary compression and causes the 2-3 ESP in Fig. 12a to go directly to the new virgin consolidation /^o-line. A^ and X^ would then both = 1, and Eqs 2 and 4 then predict ^p^q — 0. The Ottawa clay described by Crawford and Bum [13] probably behaves with ^4, = 1. The author has now proposed a physical phenomenon to explain the shear strength increase associated with aging, and shown quantitatively how this applies to produce the quasi-preconsolidation effect. This effect depends on the fabric-dispersion increase-in-d^ behavior together with a sufficiently insensitive fabric to produce low A^ and X^ values. Other Practical Aspects of Dispersion-c/; Behavior Dynamic Modulus Correction As noted in the section on Increasing Time for Secondary Compression, engineers have discovered that they must increase the dynamic values of E and G determined from undisturbed samples and laboratory reconsolidation of the clay in order to match in situ data. Anderson and Woods [9] note typical correction factors of about 1.5 to 3.5, depending on the relative secondary compression ages of the laboratory and in situ clay. The need for the correction probably results from the in situ clay having experienced a much longer secondary aging than the reconsolidated laboratory samples, giving more time for the time-dispersion-df transfer and thus producing a stiffer fabric in the in situ clay. Need to Age Laboratory Samples The aforementioned modulus correction also suggests the need for a possible aging correction to laboratory shear strength data, or the appropriate aging of laboratory test samples, or a combination. The same longer in situ secondary times can increase the ordinary quasi-static shear test moduli (see Fig. 9) and strengths. It seems clear that laboratory samples will better duplicate in situ behavior if the clay in the samples better duplicates the fabric of the clay in situ. For some clays, and perhaps most clays, producing an adequately similar fabric in the laboratory samples would require long aging times at constant stress under drained conditions. Engineers do not commonly do this at present, but perhaps they should move in this direction. Need for Stress-Rest Control Testing The application of loads on cohesive soils in the field often involves a slow rate with interspersed periods of rest. Such application should allow time for a possibly significant dispersion-c/j clay fabric stress transfer to occur, with the consequent reduced clay compressibility and increased strength. When

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SCHMERTMANN ON TIME-RELATED SOIL FRICTION INCREASE

483

modeling a loading sequence in the laboratory, say by the stress path simulation method, the engineer should for best results also allow the appropriate changes in fabric to occur in the laboratory sample. This requires stresscontrolled testing, with appropriate rest stops at constant stress. Such testing can perhaps duplicate in the sample the clay fabric changes that would occur in situ. The research outlined in this paper has shown that testing with ordinary constant strain rates does not allow the dispersion-c?^ transfer and strengthening phenomenon to occur, or at least to occur fully. Because this transfer has a potentially important effect, engineers should sometimes consider giving up the convenience of strain-control testing and go back to the "old fashioned" stress control methods. Aging Strength Not Due to Clay Bonding Many engineers have assumed, and some have attempted to prove, that the clay strength increases from constant-stress aging in the laboratory result from increased bond formation between the clay particles. This probably occurs over geologic time intervals, as when clay turns to claystone and shale. However, the research outlined in this paper leads to the opposite conclusion that these strength increases have nothing to do with bond formation over the range of typical laboratory aging times. Figure 1 shows that the /o-intercept, which equals that shear resistance not dependent on effective stress and therefore due to internal bonding, forms a part of the larger /-component. Any increase in /g should usually show as an increase in /, but the /-component stayed remarkably constant during the various clay treatments that increased the total clay shear strength. The D-component always increased to account for the total strength increase. It seems clear from these results that the /Q bond strength did not increase measurably with laboratory aging and that d^ increased greatly. The realization that the rf^-component increase produces the strength increases during laboratory aging led the author to consider how this could happen, which in turn led to the hypothesis given in the section on Hypothesis for Dispersiondf Behavior. A more general recognition that aging over laboratory aging times, and probably also over engineering project life spans, involves a fabric dispersion and stress transfer adjustment rather than a bonding phenomenon should save some further false starts and help the profession to more quickly reach a better understanding of clay particle mechanics and clay fabric and structure, and particularly how these change with engineering time. Conclusions 1. A variety of laboratory experimental studies, which involved special shear strength component testing in several clays that had undergone various Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

484

LABORATORY SHEAR STRENGTH OF SOIL

chemical, stress, and time treatments, all resulted in an increase in the frictional component of shear resistance with no measurable change in the bond component. 2. This paper suggests a clay fabric modification process to explain the friction increase behavior. This process involves a pervasive, continuing fabric dispersion with an associated transfer of shear load to stiffer and stronger particle aggregates within the fabric. 3. A better recognition of the dispersion-friction process may produce some important practical results. Among these the author quantitatively describes the quasi-preconsolidation effect and notes how to best duplicate or otherwise take advantage of the clay "aging" effects that can both increase subsequent shear modulus and reduce compressibility. Acknowledgments Dr. Frank Townsend, Professor of Civil Engineering at the University of Florida, kindly reviewed several drafts of this paper and made important suggestions. References (/] Schmertmann, J. H. in Laurils Bjerrum Memorial Volume. Norwegian Geotechnical Institute, Oslo. 1976, pp. 65-98. [2] Schmertmann, J. H. and Osterberg, J. O. in Proceedings, Research Conference on Shear Strength of Cohesive Soils, American Society of Civil Engineers [hereafter cited as ASCE], Boulder, Colo., 1961, pp. 643-694. \3\ Schmertmann, J. H., "An Experimental Study of the Development of Cohesion and Friction with Axial Strain in Saturated Cohesive Soils," Ph.D. dissertation, Northwestern University, Evanston, 111., June 1962. [4\ Schmertmann, J. H., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 88, No. SM6, 1962, pp. 169-205. [5) Lambe, T. W., The Structure of Organic Soil. ASCE, Proceedings. Vol. 79, Separate No. 315, 1953. [6] Schmertmann, J. H. and Hall, J. R., Jr., in Transactions. ASCE, Vol. 128, Part I, 1961, pp. 949-981; also published in Journal of the Soil Mechanics and Foundations Division. ASCE. Proceedings Paper 2881. Aug. 1961. [7] Schmertmann, J. H. and Hall, J. R., Jr., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 88. No. SM4, 1962, pp. 163-167; also in Ref 6, pp. 976-981. \8] Schmertmann, J. H., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 91, No. SM2, Part 1, 1965, pp. 131-315. [9] Anderson. D. G. and Woods, R. D., Journal of the Geotechnical Engineering Division. ASCE, Vol. 102, No. GTS. May 1976, pp. 525-537. [10] Bea, R. G.. Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 89, No. SMI, 1963, pp. 268-277. [II] Leonards, G. A. and Altschaeffl, M., Journal of the Soil Mechanics and Foundations Division. ASCE, Vol. 90, No. SMS, Sept. 1964, p. 148. [12] Newlin, C. W., "A Laboratory Investigation of Lateral Stresses during One-Dimensional Consolidation," Ph.D. dissertation, Northwestern University, Evanston, 111., June 1965. [13] Crawford, C. B. and Bum, K. N. in Laurits Bjerrum Memorial Volume. Norwegian Geotechnical Institute, Oslo, 1976, pp. 117-124.

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R. N. Yong^ andM. M. Tabba^

On the Random Aspect of Shear Strength

REFERENCE: Yong, R. N. and Tabba, M. M., "On the Random Aspect of Shear Stiei%th," Laboratory Shear Strength of Soil. ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 485-501. ABSTRACT: This paper discusses the random nature of shear strength of soils as opposed to the customary deterministic approach, where shear strength is thought of as a property that attains a specific value. In this approach uncertainty resulting from the intrinsic nature of the soil, as well as from the sampling and testing techniques (STT), is identified and supported by actual data. Implications of the random character of shear strength are discussed insofar as they affect present concepts of soil plasticity. This paper advances the notion that currently used yield criteria are merely theoretical models which fit available data to some extent and could actually be violated. An analytical model of mapping and prediction of shear strength is introduced, where one, two, or more sets of measurements corresponding to various STT are analyzed and could be combined to enable prediction of the mean, variance, and covariance of shear strength at desired locations. KEY WORDS: soils, shear strength, random, modeling, mapping, prediction, design, statistical analysis, sampling, testing

It has long been recognized that identical tests on apparently identical soil samples from the same source may often yield different shear strength values. When several identical tests are performed, it is not unusual to note disagreement, scatter, and uncertainty associated with the test results obtained. Measured shear strength values vary between higher and lower bounds in identical tests, with some values being more likely than others. This random aspect suggests that shear strength values using the same test technique could be represented by a histogram or a probability density function rather than by a specific value. This problem becomes more evident 'William Scott Professor of Civil Engineering and Applied Mechanics, and Director, Geotechnical Research Centre, McGill University, Montreal, Quebec, Canada. Geotechnical project engineer, National Boring and Sounding Inc., Group Lavalin, Montreal, Quebec, Canada, and Auxiliary professor. Department of Civil Engineering and Applied Mechanics, McGill University, Montreal, Quebec, Canada.

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LABORATORY SHEAR STRENGTH OF SOIL

when different sampling and testing techniques are used to measure shear strength, since in all probability disagreement of results will be even greater. Undrained shear strength values from field vane tests, for example, would in all likelihood differ from those of laboratory vane tests or unconfined compression tests. The degree of scatter depends on the nature and conditions of the soil as well as on the sampling and testing techniques. In general current practice, the commonly used deterministic approach of choosing a specific value or yield surface to represent shear strength of the soil at hand neglects the random aspect of soil strength and other properties. It is not uncommon for the engineer, guided by his judgement and experience, to pick up these values with no clear rules to follow. The values chosen will sometimes correspond to a lower bound and sometimes to the mean value. In almost all cases the confidence level associated with the chosen values is indeterminate. Uncertainty Associated with Shear Strength Although several types of test techniques are used to obtain the shear strength of soils (for example, undrained, consolidated undrained, and drained shear strength), scatter of test results or uncertainty is common to all of them. The discussions and developments presented herein pertain to all types of shear strength measurements. In the present context the question of whether shear strength is an intrinsic property or a resistance induced by testing becomes irrelevant. The scatter of measured shear strength may be attributed to several sources, namely, the intrinsic nature of the soil, and sampling and testing techniques. Intrinsic Nature As has been noted previously in numerous studies, for example, Lumb [/]•', Schultze [2], and Alonso [3], natural soil deposits, by and large, lack macroscopic and microscopic homogeneity. Both regional variations and variations within the same profile reflect the results of irregular geologic, climatic, environmental, and perhaps man-made conditions. Local variations within the same layer reflect irregularity of source materials, methods of deposition, and response to ensuing environment. Thus variations with locations of the soil element in the vertical and horizontal directions, herein termed as "spatial trends", are expected and can actually be observed on graphical plots of shear strength records. Note that scatter of shear strength measurements with respect to the spatial trend could also be present, as could be seen •'The italic numbers in brackets refer to the list of references appended to this paper.

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YONG AND TABBA ON RANDOM ASPECT OF SHEAR STRENGTH

487

if one performed tests on block samples, since the spatial trend is equal in all such measurements. To demonstrate the preceding observations, some unconfined compression test results obtained from tests on specimens from the same block are shown in Fig. 1. This figure shows the stress-strain curves from strain-controlled, unconfined compression tests on 38 by 76 mm (1.5 by 3.0 in.) cylinders trimmed from an undisturbed soil block of sensitive clay from St. Jean Vianney, Quebec. This was one of several soil blocks recovered from a trench dug below the failure surface of the May 1971 landslide reported by Tavenas et al [4]. The curves shown in Fig. 1 give an example of scatter in the undrained shear strength measurements for specimens derived from the same soil block. Thus, although visual examination suggested that the block was homogene-

UNCONFINEO COMPRESSION psi

kPa

BLOCK SAMPLE

ri

80 •500

/

1

70

60•*°°

\

\

*

\

\

0

00-9

\ 1

\

\

D

00-10

/ /

h

\

^

00-11

U 1•

50-

40-

1 / / /

\> K\

««t 00-4

it \ V •Hix \ ^ ^ ^ ^

30-

20-

I \ j^

10-

f

L

strain rate ( = 0.055/inin

~^^---^--. 2

3

4

5

6

8

t.%

Axial Strain

FIG. 1—Stress-strain curves of unconfined compression tests on undisturbed block specimens.

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488

LABORATORY SHEAR STRENGTH OF SOIL

ous and the tests are essentially identical, the scatter of results is obvious for both peak and residual axial stresses. Other sets of identical strain-controlled, consolidated undrained (CU) triaxial tests were carried out on 53 by 106 mm (2.1 by 4.2 in.) specimens obtained from the same block and other companion blocks from St. Jean Vianney. Such tests furnished less scattered results, as may be seen in Fig. 2, corresponding to a confining cell pressure of 137.8 kPa (20 psi). Sampling and Testing Techniques (STT) Apart from identical tests, it is known [5,6] that different sampling and testing techniques (STT) used to measure shear strength generally provide test results which show significant differences or disagreements. Random scatter due to STT itself is superposed and coupled with scatter resulting from the intrinsic nature of the soil, as has been shown, for example, by Tabba and Yong {7\. This can be attributed to such factors as soil type and conditions, test technique, created stress field or stress path utilized in the testing procedure, prevailing stress field, strain rate, stress relief, scale effects, drainage conditions, storage of samples, etc. It is not realistic on the one hand to attempt to evaluate the effects of these factors on each STT while overlooking on the other hand the random nature of shear strength. However, overall comparisons (termed calibrations) may be made on the basis of an agreed-upon set of standard measurements corresponding to various STT. The calibration of data would allow one to quantify the relative bias of two or more STT and would permit adjustment of available data sets. Table 1, from Ladd [5], shows an example of mean bias of undrained shear strength from various tests at several locations. The ratio of undrained shear strength from unconfined compression (UC) or unconsolidated undrained, (UU) triaxial tests to the strength measured by field vane is shown in the left-hand column; the right-hand column shows the ratio of strength from UC or UU to that from consolidated undrained (CU) triaxial tests (consolidated to the overburden pressure). The differences and variations in the ratios of undrained strengths are evident, as noted previously by Ladd, depending on the STT used as well as on the soil and site. These ratios reflect the mean of a systematic bias of the measurements or, simply, the ratio of means of the two STT considered in the ratio. It is useful to observe that the spatial trend component of the shear strength is implicit in both means of the measurements given in the numerator and denominator of the strength ratios given in Table 1. Note that the spatial trend is defined as a deterministic component of shear strength that depends on the physical location of the soil element within the same soil layer. It would be desirable, however, to exclude the trend component and compare only the relative bias of two STT. From the preceding, it is clear that wide variations and uncertainty of shear strength measurements do exist depending on the STT used. In the

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YONG AND TABBA ON RANDOM ASPECT OF SHEAR STRENGTH

489

CONSOLIDATED UNDRAINED TRIAXIAL TESTS- BLOCK SAMPLE

6

8

10

Axial Strain f,%

FIG. 2—Stress-Strain curves ofCU triaxial tests on the undisturbed block specimens from St. Jean Vianney, Quebec.

next section the conflict between present concepts of soil plasticity and the random aspect of shear strength is examined. Plasticity versus Uncertainty Conflict Analyses of soils subject to complex states of stress have traditionally been conducted either as stability problems or problems associated with loadCopyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

490

LABORATORY SHEAR STRENGTH OF SOIL

TABLE 1—Comparison of undrained shear strength from various test methods at different sites. NOTE—This table is a very slightly altered version of a table by C. C. Ladd [5] and is reprinted by his permission. Ratio of Undrained Strengths UC or UU Location

Soil

Gulf of Mexico soft clay (CH) M.I.T. Campus N.C. Boston blue clay Mexico City Mexico City clay Kawasaki, N.C. clays Japan (CL and CH) Lagunillas, N.C. clay (CH) Venezuela Skabo, Norway N.C. clay (5, = 5) quick clay Manglerud, Norway (5, > 100) Ottawa, leda clay Canada

Depth, m

Field Vane

UC or UU Triaxial CU'' Type of Sample

0to6 29

0.54 0.55

0.85 0.34*

Shelby 3 in. piston

20 to 45

0.64 0.67

0.74 0.58

3 in. Shelby

0.81

0.82

2.8 in. Shelby

10 to 16

1.04

0.88

N.G.I.'

6.5 to 10

1.4

0.82

N.G.I.

6

17

1.91 -1.0

0.98 -0.95

block piston

"For confining pressure = overburden pressure. */C„-consolidation for triaxial CU. 'N.G.L = Norwegian Geotechnical Institute.

deformation response. By and large, soil stability problems are examined with the aid of limit equilibrium principles, regardless of the stress-strain behavior below the yield/failure point or the prevailing state of stress. The general framework of the analyses which utilize limiting equilibrium principles does not as a rule consider the stress-strain properties of the soil material below the yield/failure "point". These analyses require the definition or specification of an admissible stress field in addition to an appropriate yield or failure criterion. The important role of a valid and representative yield or failure criterion cannot be overemphasized. Present Concepts of Plasticity and Failure In spite of the numerous and bewildering spectra of yield and failure criteria available to the geotechnical engineer, only a few are currently used in the application or implementation of limit equilibrium techniques for solution of stability problems. The more common ones favored are the extended Tresca, the extended Von Mises, and the Mohr-Coulomb criteria [8]. While other criteria may be applied in a few cases or may still be in the development stage, it is pertinent to observe that the yield or failure criterion chosen for implementation in the overall analysis must model the Soil behavior. The use of a chosen yield or failure criterion implicitly requires that certain

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YONG AND TABBA ON RANDOM ASPECT OF SHEAR STRENGTH

491

expectations concerning predicted soil behavior be met, since the criterion in essence models the soil behavior. This, however, may not be a totally valid representation of the overall response performance of the soil being studied. Thus, for example, the adoption of a perfectly plastic behavior response of the soil beyond yield might in actual fact contradict the behavior of a workhardening or strain-softening performance of the soil. In addition, one should note that the adoption of a yield or failure criterion which implicitly assumes material isotropy will not be applicable to a soil which is in actual fact anisotropic. This material property distinction cannot be overemphasized. In purely frictional or purely cohesive soils, only one shear strength parameter, that is, the friction angle <j) or cohesion c, respectively, is used in the specification of any of the three preceding criteria. In soils which are neither purely frictional nor purely cohesive, if resistance to shear is by a combination of cohesion and friction mechanisms, then it is noted that the shear strength parameters c and <j> are needed. Note that c and <> / are shear strength parameters that are obtained through the application of the two-parameter failure theory. Their direct relationship to the actual physics of the problem (that is, shear resistance mechanisms) is obtained when the soil response performance is properly modelled. In other soils where overconsolidation effects or strong bonding forces, or both, exist, it has been observed that in several instances the application of a simple yield or failure criterion, normally used for c-<j> soils, may not adequately represent the actual situation. An example of such an inadequacy is shown in Fig. 3 where a bonded sensitive clay from St. Jean Vianney is tested at effective normal pressures/?' below the preconsolidation pressure PciPc ~ 100 psi = 689.5 kPa). The shear strength s = (a| - (Tj)/! from consolidated undrained (CU) triaxial tests is shown at peak and residual levels. It may be seen that a curved envelope would better fit peak shear strength as opposed to a straight Mohr-Coulomb envelope. Further discussion of this problem is given later in the section on Conflict Resolution. Violations of Fitted Criteria It is not unusual to observe some deviations between predicted shear strength and response performance from an analytical model on the one hand and measured strength and observed performance on the other hand. When such deviations or disagreements occur, one might observe that the fitted criterion, in a deterministic context, could be violated. Violations may be attributed either to shortcomings of the analytical model or to inadequacy of the STT. In the second-order envelope fitted to peak shear strength in Fig. 3, for example, this envelope represents the average shear strength s mobilized at a given p '. The actual measurements obtained show violations both on the safe and unsafe sides of the fitted failure envelope. Note that the unsafe side Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

492

LABORATORY SHEAR STRENGTH OF SOIL

-^

c

:::) u

I ^ .^

0:0

q, e / (Si) -

, s 4)6u9j(s

Jesi(5

Ol

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YONG AND TABBA ON RANDOM ASPECT OF SHEAR STRENGTH

493

is in actual fact inadmissible or imaginary from the theoretical point of view, since points in this region cannot exist. Violations due to shortcomings of the analytical model are expected in the following cases: 1. When anisotropic soils are represented by isotropic analytic models. 2. When a strain-softening or work-hardening soil is represented by models assuming perfectly plastic behavior. 3. When the velocity field is assumed normal to the stress-increment field using plasticity analyses. 4. Extrapolation of fitted yield criterion beyond the range of available data, as, for example, at the lower end of the envelopes of Fig. 3. This is a well-known phenomenon in regression analysis, where the confidence level in the mean is reduced towards the two extremities of the data range [9]. Violations due to the inadequacy of the sampling and testing techniques (STT) can occur under the following circumstances: 1. If biased shear strength measurements are used for prediction without the necessary corrections for inherent bias, as shown by Tabba and Yong [7]. Such bias might be due to the created stress field and boundary conditions, sample orientation, sample disturbance and storage, stress relief, scale effects, strain rate, drainage conditions, pore-pressure development, volume change, etc. 2. When sample size (that is, number of tests) is too small to warrant prediction with reasonable confidence levels. 3. Where measurements are improperly distributed within the zone of interest to the project. Conflict Resolution It is apparent from the preceding discussions that two main drawbacks may be cited with regard to the present practice: 1. Failure to accommodate the random aspect of soil shear strength, including the spatial trend and scatter associated with a certain sampling and testing technique STT. This is a direct consequence of use of deterministic yield/failure criteria. 2. Failure to compare and/or combine test results belonging to different STT. It is noted that in addition to better and more careful testing techniques, improvement in one's capability for prediction of shear strength must also rely on the resolution of the aforementioned deficiencies. The wide range of soil types encountered in practice, and the increasingly numerous sampling and testing techniques available to the profession, require that proper attention Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

494

LABORATORY SHEAR STRENGTH OF SOIL

be paid to the recognition of the aforementioned deficiencies and to a resolution of the "conflict". Modelling of Shear Strength The basic requirement for resolution of the aforementioned conflict recognizes the random aspect of shear strength. The simplest representation of such a random phenomenon will identify the spatial trend as well as the scatter with respect to it, plus any autocorrelation that may exist in the data. Probabilistic modelling procedures of shear strength have been proposed earlier by several researchers, Wu and Kraft [10], Alonso [3], Lumb [//], Yucemen et al [12], Yong et al [13], Van Marcke [14], among others. Many of these models, however, are by and large difficult to use in practical situations where data points are few, are irregularly spaced, and come from different STT. For practical purposes, it suffices to deal with first-order probability approximation, where the random shear strength at each point in the soil deposit is represented by its mean, variance, and covariance. Higher-order probability parameters will not be useful in general, since a limited number of data points does not allow for any meaningful estimation of such parameters. An analytical model of mapping and prediction of random soil properties was suggested by Tabba and Yong [7], where the measured property (shear strength) Pj at any point i was resolved into a deterministic spatial trend component Pfand a random scatter component e, with respect to Pf, or Pi = P*+ e,

(1)

It was shown that the random scatter component denoted by e, combined uncertainty due to the soil's intrinsic nature with that due to the sampling and testing techniques. Two types of data are distinguished depending on the sampling technique used: block sampling which denotes a cluster of data at one point in space, and borehole sampling which denotes one piece of data at each point sampled. Distinction is also made according to the testing technique used between biased and unbiased data. The unbiased data set is defined as that which corresponds to the STT judged to be the most appropriate or accurate as a measurement of shear strength. Note that the judgement of "accuracy" of test result as a means of comparison of test information from two or more tests is purely one of relative measure of level of confidence in the test result obtained. The higher one's level of confidence in a particular test technique and the results obtained thereby, the greater is one's assessment of the "accuracy" of the results. It follows then that other types of STT providing a lesser degree of confidence in accuracy of measurements would be considered as biased data. Note that different test and research laboratories might differ

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YONG AND TABBA ON RANDOM ASPECT OF SHEAR STRENGTH

495

insofar as "good sophisticated" test equipment and techniques are concerned. Thus, while one laboratory might consider the triaxial test to produce unbiased test results, another might consider the unconfined compression test or the direct shear test as "unbiased". With a set of measurements -P, from a borehole sampling program, irregularly distributed within the zone of interest to the project, one can associate each Pi with the physical location of point / (x,, yij, Zj) with respect to a global coordinates system (x.y.z). A trend function is then fitted to data points i = 1, 2, . . . n, using matrix formulation of the Maximum Likelihood theorem [15], Residuals are examined and their variance and autocorrelation function are derived. When two or more data sets, corresponding to biased and unbiased STT, are available for the same soil deposit, calibration is carried out to evaluate various parameters characterizing the spatial trend and scatter of shear strength. Of particular interest to this study are two parameters e and X, defined by Tabba and Yong [7] in the following manner: !• e, defined as the mean bias, represents the average relative bias of the biased data set with respect to the unbiased one. In other words, it is the average amount of bias by which biased shear strength measurements are different from the unbiased ones, the latter being considered as datum for comparison purposes. 2. X, defined as the bias of variance, is the ratio between variances of the biased and the unbiased shear strength measurements, which represent the amount of bias in the variance of scatter e, brought about by the biased STT as compared with the unbiased STT. Both e and X exclude the effect of spatial trend and can be calculated for a variety of mapping situations. To illustrate the application of biased and unbiased test results, reflecting one's assessment of the level of confidence of test measurements obtained, the analytical model of mapping and prediction was applied by Tabba and Yong [16] to the analysis of a landslide at St. Jean Vianney, Quebec, Canada [4], Mapping of undrained shear strength of the landslide area was carried out using four data sets corresponding to different STT, namely, field vane, laboratory vane, UC on recovered borehole samples, and UC from undisturbed blocks identical to those mentioned earlier. Various mapping combinations were calibrated and the amounts of bias e and X calculated. Considering the UC results from borehole samples as unbiased data set (see footnote to Table 2), e and X associated with the other three STT are shown in Table 2. It is seen, for example, that undrained shear strength measurements using field vane are on the average higher than those of UC (borehole) by 68.2 kPa (1425 psf), and the associated scatter is also higher by a ratio of 2.35 to 1.0. Thus UC on undisturbed block samples provides, on the average, the highest shear strength \e = 124.1 kPa (2590 psf)] of the four STT while it maintains a low scatter (X = 1.03). Meanwhile, the

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496

LABORATORY SHEAR STRENGTH OF SOIL

TABLE 2—Comparison of undraimd shear strength from different samioling and testing techniques. Sensitive clay - St. Jean Vianney. Quebec [from Tabba and Yong IRef 16)]. Unbiased Test"

Mean bias e, psf kPa Bias of variance X

Biased Tests

UC Borehole''

Laboratory Vane''

Field Vane''

UC Blocks''

0 0 1

1025 49.1 2.0

1425 68.2 2.35

2590 124.1 1.03

"The choice of UC resuHs from borehole samples as unbiased data is used here for comparison purposes only and does not reflect any belief by the authors that it is the most appropriate or accurate method to measure the undrained shear strength of sensitive clays. *Unconfined compression on disturbed borehole samples using Shelby tubes, sample size 38 by 76 mm (1.5 by 3 in.). "•Laboratory vane on disturbed borehole samples using Shelby tubes, vane size 13 by 13 mm ('/2 by '/2 in.) down to 30 m (100 ft) depth, then 17 by 8.5 mm (2/3 by '/3 in.) downward. ''Field vane in boreholes, vane size 51 by 102 mm (2 by 4 in.). ••Unconfined compression on undisturbed blocks recovered from Trench T2, sample size 38 by 76 mm (1.5 by 3 in.). For sample stress-strain curves see Fig. 1.

lowest shear strength measurements are obtained from UC on borehole samples (e = 0), which provided the lowest variance of the four STT as well (X = 1.0). These results regarding the mean bias e are in general agreement with published data given by La Rochelle and Lefebvre [6] for sensitive clays of eastern Canada, and reflect the degree of disturbance due to the STT. One can conclude that for the St. Jean Vianney sensitive clay, UC on borehole samples created the highest disturbance while the lowest is offered by UC from block samples; the scatter of results is kept as low as possible in both techniques. On the other hand, field and laboratory vane created medium disturbance, but caused more scatter in test results. To implement shear strength mapping, one, two, or more parameters are needed to define the yield or failure criteria at each point in the soil deposit. As in the example of St. Jean Vianney cited here, the undrained shear strength of cohesive soils may be adequately described by one parameter s„ as in the Tresca yield criterion 5„ = •/2(a, - (T3)

(2)

Therefore, in such cases, mapping is carried out using individual measurements Sui at various points i. In cases where the shear strength is attributed to pure friction, s may be assumed as the product of the effective normal pressure p ' = '/2((Ji' + a^) and tan (/>, the friction coefficient. For soils where shear resistance is obtained through a combination of cohesion and friction, utilization of the Mohr-Coulomb failure criterion as s =" c + p' tan
Copyright Downloaded/printed University

by

(3)

ASTM

Int'l

British

Columb

by of

YONG AND TABBA ON RANDOM ASPECT OF SHEAR STRENGTH

497

will yield the shear strength parameters identified as c and (f). When mapping the shear strength of such soils, it it necessary to split the measured shear strength into two components c and tan (/> at each point in space, using Eq 3. This would require a minimum of two tests at each point in space, and provide two sets of data pertaining to c and tan 0, thus allowing for mapping to be performed on each set separately. The correlation between c and tan 0 expressed as the covariance COV (c, tan (jy) or correlation coefficient p^. t^„ ^ needs to be evaluated. Tabba [17] has shown that the Mohr-Coulomb failure criterion generally implies a negative correlation between c and tan ; namely, positive deviations from the mean value of cohesion are counterbalanced by negative deviations from the mean value of friction. This negative correlation has been confirmed experimentally by other researchers 118.19]; for the St. Jean Vianney blocks mentioned earlier, a correlation coefficient of p^ f^„ ^ = —0.586 has been found. In practical terms this tends to reduce scatter in shear strength and furnishes a second source of strength if the first is reduced. Prediction of Shear Strength The ultimate purpose of geotechnical exploration programs, including sampling, testing, and mapping, is to enable more accurate predictions of the random soil property at required locations. Therefore, referring to the previous definitions, one is interested in predicting Pf, the unbiased shear strength at point./ of known coordinate (jc,, yj. z,). By the same token, P, could be broken into a trend component P*and an unbiased scatter component e* or p. = p*+ e*

(4)

From this prediction model, one can find the means, variances, and covariances of shear strength at desired locations./. Clearly, the terms on the righthand side of Eq 4 have to be evaluated from the mapping model as explained before, and that requires at least one data set of unbiased shear strength measurements. The methodology used in this respect was presented by Tabba and Yong [7]. Design Shear Strength In the analysis of some geotechnical problems, such as risk analysis of slope stability [13], it is sufficient to predict the means, variances, and covariances of shear strength at certain points. However, in design situations, such as foundations design, it is awkward to work with several values representing various characteristics of the random shear strength. It is desirable therefore to use a single value, termed design shear strength, that engineers could use

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498

LABORATORY SHEAR STRENGTH OF SOIL

in a deterministic context. A similar problem has been encountered in structural reliability when devising probabilistic design formats [20]. Although several such formats exist, the general idea of a design shear strength is to reduce the mean value of shear strength by an amount proportional to the variance so that it would correspond to a certain probability of being exceeded by design loads. It is suggested here that the following simple formula be used to obtain the design shear strength Sj, given the mean E{s) and standard deviation a^ of the predicted shear strength at the desired location (Fig. 4a): Sj - Eis) - (vai)

(5)

where i; is a design constant. Equation 5 is similar to those proposed by Cornell [21] and Ang and Amin [22], The design constant i; is to be determined such that P„, the probability of violation of Sj on the left, will not exceed a certain acceptable level. The value of P^ is therefore equal to the area under the probability curve below Sj (Fig. 4a). Naturally, violations of sj may be point or zonal violations or both. At present, prediction of shear strength is performed using second-order moment probability (that is, free of any probability distribution). Thus one has to assume a certain probability distribution to be able to calculate P^. An upperbound estimate of P^, may be obtained using the Chebyshev inequality without knowing the probability distribution function [9]. The Chebyshev inequality may be written as P[E{s) + va; s s < E{s) - u(7j-] < —

(6)

which is shown graphically in Fig. 4b; in addition, the plot of P^ versus i; is shown for the normal distribution. Clearly, the difference between the two curves is considerable, particularly for low values of v, which may be attributed to the very conservative estimate of the Chebyshev upperbound, since it covers the probability of symmetrical violation on the right as well (Eq 6). Meanwhile, P„ estimate from the normal distribution is closer to reality, but still in error due to the negative range of s included. Other estimates which take care of this error, such as from the lognormal distribution (Fig. 4fl), may be used. If one chooses, for example, an sj lower than the predicted mean of shear strength by three standard deviations, then this design shear strength will stand a probability of 0.0013 of being violated according to the normal distribution, and such probability could never exceed 0.111 according to the Chebyshev upperbound. Concluding Remarks The intrinsic nature of soil deposits is a major source of uncertainty associated with shear strength, as witnessed from identical tests on apparently

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YONG AND TABBA ON RANDOM ASPECT OF SHEAR STRENGTH

499

Area below Sj = Pv . Normal

Log Normal

(a) E(i) Shear Strength

Chebyshev's Upper Bound

1

2

3

4

5

6

7

tj

No. of Std. Deviations From The Mean Els) FIG. 4—Probability of violation of nominal design shear strength s^.

identical soil samples. The other major source of uncertainty is due to the sampling and testing technique (STT) used to measure shear strength. Examples were given for different soils using various STT, and the associated contradiction of results was discussed. The conflict between present concepts of plasticity and failure on the one hand and uncertainty of shear strength data on the other hand can be illustrated by noting that the fitted yield or failure criteria may be violated due to shortcomings of the analjrtical model as well as the inadequacy of the sampl-

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500

LABORATORY SHEAR STRENGTH OF SOIL

ing and testing techniques. Resolution of the conflict can be obtained through an analytical model of mapping and prediction of shear strength where the measured shear strength at any point is resolved into a deterministic spatial trend and a random scatter. Note that distinction is made between various kinds of sampling methods and between biased and unbiased data depending on the accuracy of the STT. A mapping model such as the one used by Tabba and Yong [ 7,16] can analyze and calibrate shear strength data belonging to different STT. In this model it is postulated that various STT have one common purpose, namely, to measure the shear strength of the soil. Hence, comparisons of measured values are justified, despite the fact that boundary conditions and stress paths are generally different from one STT to another. It should be noted that the random nature of measured shear strength does indeed exist and that this causes problems in association with fitted yield or failure criteria. While yield/failure criteria may be found deficient, numerical evaluations of the deficiencies are vital to a rational design procedure. Undoubtedly, further research is needed in this regard. References [/] Lumb, P., Canadian GeotechnicalJournal. VoL 3, 1966, pp. 74-97. [2] Schultze, E. In Proceedings, First International Conference on Applications of Statistics and Probability to Soil and Structural Engineering, Hong Kong, 1971, pp. 372-387. [3] Alonso, E. E., "Application of Random Function Theory to Settlement Problems in Soil Engineering," Ph.D. thesis, Northwestern University, 1973. [4] Tavenas, F., Chagnon, J. Y., and La Rochelle, P., Canadian GeotechnicalJournal, Vol. 8, 1971, pp. 463-478. 15] Ladd, C. C. in Proceedings uf the Geotechnical Conference. Oslo, Vol. 2, 1967, pp. 112115 (discussion). 16] La Rochelle, P. and Lefebvre, G. in Sampling of Soil and Rock. ASTM STP 483. American Society for Testing and Materials, 1971, pp. 143-163. [7] Tabba, M. M. and Yong, R. N., "Mapping and Predicting Soil Properties, Part 1— Theory," Journal of the Engineering Mechanics Division, Proceedings of the American Society of Civil Engineers, to appear in Oct. 1981. [8] Yong, R. N. and Warkentin, B. P., Soil Properties and Behaviour. Elsevier-North Holland, New York, 1975. [9] Benjamin, J. R. and Cornell, C. A., Probability. Statistics and Decisions for Civil Engineers. McGraw-Hill, New York, 1970. [10] Wu, T. H. and Kraft, L. M., Journal of the Soil Mechanics and Foundations Division. Proceedings of the American Society of Civil Engineers. Vol. 96, SM2, 1970, pp. 609-630. (//] Lumb, P. in Proceedings. Second International Conference on Applications of Statistics and Probability to Soil and Structural Engineering, Aachen, 1975, pp. 397-421. [12] Yucemen, M. S., Tang, W. H., and Ang, A. H. S., "A Probabilistic Study of Safety and Design of Earth Slopes," Structural Research Series No. 402, Department of Civil Engineering, University of Illinois, Urbana, HI., 1973. [13] Yong, R. N., Alonso, E. E., Tabba, M. M., and Fransham, P. B., Canadian Geotechnical Journal. Vol. 14, 1977, pp. 540-553. [14] Van Marcke, E. H., Journal of the Geotechnical Engineering Division. Proceedings of the American Society of Civil Engineers. Vol. 103, GTU, 1977, pp. 1227-1246. 1/5] Tabba, M. M. and Yong, R. N. in Proceedings. Third ASCE/EMD Specialty Conference, Austin, Tex., Sept. 1979, pp. 331-334.

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YONG AND TABBA ON RANDOM ASPECT OF SHEAR STRENGTH

501

[16] Tabba, M. M. and Yong, R. N., "Mapping and Predicting Soil Properties, Part II—Applications," Journal of the Engineering Mechanics Division, Proceedings of the American Society of Civil Engineers, to appear in Oct. 1981. [17] Tabba, M. M., "Risk Analysis of Slope Stability with Special Reference to Canadian Sensitive Clays," Ph.D. thesis. Department of Civil Engineering and Applied Mechanics, McGill University, 1978. ]I8] Lumb, P., Canadian CeotechnicalJournal. Vol. 7, 1970, pp. 225-242. [19] Matsuo, M., "Reliability in Embankment Design," Publication No. R76-33, Department of Civil Engineering, Massachusetts Institute of Technology, 1976. [20] Turkstra, C. J., "Theory of Structural Design Decisions," Study No. 2, Solid Mechanics Division, University of Waterloo, Ontario, 1972. 12/) Cornell, C. A., "A Probability Based Code Format," presented at American Concrete Institute fall convention, Memphis, Tenn., Nov. 1968. [22] Ang, A. H. S. and Amin, M., Journal of the Structural Division, Proceedings of the American Society of Civil Engineers. Vol. 95, ST7, 1%9, pp. 1389-1405.

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T. C. Anderson^ and R. G. Lukas^

Preconsolidation Pressure Predicted Using s^/p Ratio

REFERENCE: Anderson, T. C. and Lukas, R. G., "Preconsolidation Pressure Predicted Using sj p Ratio," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 502-515. ABSTRACT: This paper illustrates the use of Skempton's i , / p relationship along with the undrained shear strength for predicting the preconsolidation pressure for lightly overconsolidated clays. The validity of this prediction procedure is demonstrated by test results on soils from the Chicago area. A good correlation was found between predicted versus measured preconsolidation pressure. The relationship between liquidity index and measured preconsolidation pressure was also evaluated and found to be rather poor for the Chicago area soils studied. KEY WORDS: consolidation, clays, shear strength, preconsolidation pressure, settlement

Nomenclature e OCR ff„c

p p Pc Pc'

PI Su

s,/ CCD

Void ratio Overconsolidation ratio Vertical consolidation stress Pressure Effective vertical overburden pressure Most probable preconsolidation pressure (measured) Predicted preconsolidation pressure Plasticity index Undrained shear strength Predicted undrained shear strength Chicago City datum

'Senior geotechnical engineer. Engineers Testing Laboratories, Inc., Phoenix, Ariz. 85040; formerly senior project engineer. Soil Testing Services, Inc., Northbrook, HI. 60062. ^Senior vice president. Soil Testing Services, Inc., Northbrook, 111. 60062.

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ANDERSON AND LUKAS ON PREGONSOLIDATION PRESSURE

503

In 1957, Skempton established the following empirical correlation for normally consolidated clays [/]•' based on field vane test results: s„/p = 0.11+ 0.0037(PI)

(1)

where Su = undrained shear strength, p = effective vertical overburden pressure, and PI = plasticity index in percent. This statistical relationship has been found to be broadly valid over a wide range of types of sedimented clays [2]. Use is usually made of this relationship to estimate the undrained shear strength of samples from Atterberg limit tests, if the deposit is known to^be normally consolidated. In addition, if values of 5„ and PI have been determined, the correlation is also utilized to evaluate whether a deposit is preconsolidated. A unique relationship exists between the undrained shear strength and water content at failure for normally consolidated clay samples [3,4]. As shown in Fig. 1, the curve for undrained shear strength (5„) is approximately parallel to the curve for effective consolidation pressure. The latter curve is the same as the pressure-void ratio curve from a one-dimensional consolidation test. As a clay deposit consolidates under the maximum effective applied pressure, a reduction in water content and a corresponding increase in shear strength occurs. The soil deposit can be considered to be normally consolidated under the maximum effective applied pressure, and there is a definite relation between preconsolidation pressure and undrained shear strength. When the maximum effective pressure is reduced to a lesser effective pressure, the undrained shear strength of the deposit is retained at about the same value corresponding to the maximum effective applied pressure. Actually a slight reduction in undrained shear strength will probably occur, since the void ratio will increase slightly as the effective pressure decreases. Therefore it should be possible to roughly predict the preconsolidation pressure for lightly overconsolidated clays, if the undrained shear strength is known [5,6]. The predicted value of the preconsolidation pressure {p^) is then p/ = —^

(2)

where {s,/p) is computed from Eq 1. It is the intent of this paper to show the validity of this empirical prediction procedure through the use of test results on lightly overconsolidated soils from the Chicago area. ^The italic numbers in brackets refer to the list of references appended to this paper.

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504

LABORATORY SHEAR STRENGTH OF SOIL

Hii i6.\—i HUifi—i

Hiiii6—a

»«'*'

UNDRAINED SHEAR STRENGTH <Su)OR EFFECTIVE CONSOLIDATION PRESSURE (Pc) FIG. 1—Relationship between undrained shear strength or effective consolidation pressure and water content lor void ratio).

Presentation and Discussion of Test Results Field and Laboratory Procedures All of the data presented herein were obtained from a total of 46 samples. Relatively undisturbed samples were obtained by 7.5 and 13 mm (3 and 5 in.) thin-walled push tube (Shelby) or Osterberg-type piston samplers. Water content, Atterberg limits, consolidation and undrained shear strength tests were made on each sample. Consolidation tests were performed upon 6.5-mm (2.5-in.)-diameter specimens trimmed from the larger diameter samples. The most probable preconsolidation pressure {pc) was determined using the Casagrande method. The undrained shear strength on a majority of the samples was determined by unconfined compression tests. In some cases, the undrained shear strength was determined through the use of unconsolidated-undrained triaxial compression or in situ vane shear tests. The results of the tests performed are shown in Table 1. Geologic Origin of Samples In Table 1, Samples 1 to 7 are from post-glacial lacustrine deposits from suburban areas around Chicago. Samples 8 to 30, with the exception of Samples 10 and 25, represent the lake border glacial till deposits, commonly

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ANDERSON AND LUKAS ON PRECONSOLIDATION PRESSURE

505

known as the "soft Chicago clay." Some of these samples are of medium to stiff consistency, being stiffer zones within the soft clay deposit. Samples 10 and 25 are from lacustrine deposits situated above the glacial till. Samples 31 to 46, with the exception of Sample 35, represent stiff to very stiff consistency glacial till layers located below the lake border soft clay deposit or near ground surface where the soft clay is absent. Sample 35 is from a glaciolacustrine layer interbedded with the stiffer till deposits. The geologic origins of these samples represent a good cross section of the various types of clay deposits which exist in and around the Chicago area. The plasticity index for the samples range from 8 to 184 percent, but are generally below 45 percent.

Overconsolidation and Sy/p Ratios The overconsolidation ratios (OCR) shown in Column 10 of Table 1 generally range from 1.1 to 8.7, which indicates that the samples are primarily overconsolidated. An OCR of 26.7 is indicated for Sample 10, which is from a very shallow depth below the bottom of Lake Michigan. The high degree of overconsolidation in relation to the very low existing effective overburden pressure is probably the result of erosion of previous beach deposits or desiccation. Comparison of the present s^p ratio with the ratio predicted by Eq 1 can be used for an evaluation of whether a sample has been preloaded and, in a qualitative way, the degree of overconsolidation [2]. The ratio of undrained shear strength {s„) divided by the present effective overburden pressure (p) is presented in Column 12, while the s„/p ratios computed from Eq 1 are given in Column 13. It should be noted that the values shown in Column 12 are greater than those in Column 13 for all samples, which further suggests that all samples are overconsolidated. The ratio of the values from Column 12 to Column 13 is given in Column 14; it should be noted that this ratio is of roughly the same magnitude as the corresponding overconsolidation ratio shown in Column 10.

Comparison Between Predicted and Measured Preconsolidation Pressure In Table 1, the measured preconsolidation pressure is shown in Column 8, while the predicted value based on Eq 2 is indicated in Column 15. The ratio of predicted to measured preconsolidation pressure is shown in Column 16, while a plot of the measured versus predicted preconsolidation pressures is presented in Fig. 2. As can be seen, there is a good correlation between the predicted and measured values below a pressure of approximately 575 kPa (6 tons-force/ft^). Considering the problems with sample disturbance and determining the most

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506

LABORATORY SHEAR STRENGTH OF SOIL

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ANDERSON AND LUKAS ON PRECONSOLIDATION PRESSURE

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508

LABORATORY SHEAR STRENGTH OF SOIL

r-f4 PREDICTED PRECONSOLIDATION PRESSURE, P,; , TONS/ FT"

FIG. 2—Measured versus predicted preconsolidation pressure II tons-force/ft^ = 95.8 kPa).

probable preconsolidation pressure from a consolidation test curve, the correlation is quite satisfactory. Above the 575 kPa (6 tons-force/ft^) pressure, the predicted values are consistently higher than the measured preconsolidation pressures. These results are for the stiffer consistency samples and the consolidation test curves are relatively flat, without any distinct break in the area of maximum past preconsolidation pressure. In addition, these samples were rarely loaded to high enough pressures to accurately establish the slope of the straight line portion of the virgin consolidation curve. These factors make it very difficult to determine the most probable preconsolidation pressure. Relationship Between Measured Preconsolidation Pressure and Liquidity Index The liquidity index values for the samples are shown in Column 7 of Table 1. Figure 3 is a plot of liquidity index versus measured preconsolidation pressure. As can be seen by the scatter of data points in this figure, the correlation between liquidity index and preconsolidation pressure is rather poor. The upper and lower limit curves indicated in NAVFAC DM-7 [4], which

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ANDERSON AND LUKAS ON PRECONSOLIDATION PRESSURE

r^

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FIG. ^—Liquidity index versus measured preconsolidation pressure II tons-force/ft^ 95.8 kPa).

relate liquidity index to effective consolidation pressure for a range of soil sensitivity, have also been plotted in Fig. 3. A number of the data points plot outside the curves and especially above the upper curve. Thus the data do not fit the previously determined relationship too well. The actual preconsolidation pressure could vary over a five-fold range for any given liquidity index value. It should be noted that sensitivity was not determined for sample data shown in Fig. 3 and, therefore, no evaluation can be made of the effect of sensitivity on the relationship between liquidity index and consolidation pressure. However, experience indicates that sensitivity of these soils generally ranges from 2 to 6 and is most typically near 4. For the Chicago-area soils studied herein, the liquidity index appears to provide only a crude estimate of the preconsolidation pressure. However, the lower curve shown on Fig. 3 apparently does give a reasonable estimate of the minimum value of the preconsolidation pressure for any given liquidity index. Predictions for Soft Chicago Clay Utilizing Peck's data [7], predictions have been made for the preconsolidation pressures for numerous samples of the "soft Chicago clay" deposit. The data used were from 14 borings from the downtown district performed for the Chicago subway system around 1940. In these borings, 2-in.-diameter Shelby tube samples were taken as continuously as possible through this clay stata. Water content, Atterberg limits, and unconfined compressive strength tests

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510

LABORATORY SHEAR STRENGTH OF SOIL

were performed on virtually every sample. Very erratic variations in unconfined compressive strength and water content were noted within and from different borings. Thus the deposit is not uniform. In general^ the unconfined compressive strength of the samples ranged from 19 to 96 kPa (0.2 to 1.0 tons-force/ft^), while the plasticity index varied from 10 to 23 percent. Occasional zones of stiffer materials, with unconfined compressive strengths of % to 172 kPa (1.0 to 1.8 tons-force/ft^), were encountered in the borings. A summary plot of the predicted preconsolidation pressures (by Eq 2) versus elevation (CCD is Chicago City datum) is presented in Fig. 4. The average effective overburden pressure profile for the downtown Chicago area is also shown on this figure. A number of the data points plot below the effective overburden pressure line, indicating the respective samples to be underconsolidated. However, the softer consistency samples were undoubtedly disturbed to some extent. An investigation made in connection with the soil testing program for the Chicago subway indicated that the strength of the 2-in.-diameter Shelby tube samples was about 75 percent of that of hand-cut samples carefully taken from the subway headings [7]. Correction for the disturbance effect would shift these data points over to the profile line for the effective overburden pressure. As can be seen from Fig. 4, the majority of the data points plot between the lines representing overconsolidation ratios of 1.0 to 2.5, which indicates the soft clay deposit is normally consolidated to slightly overconsolidated. This correlates well with the OCR values shown in Table 1 for the "soft Chicago clay" samples (Samples 8 to 30), which are typically in the range of 1.1 to 2.5. The predicted results also compare favorably with the results of carefully conducted consolidation tests on the compressible clays [7,8] along with local experience [9]. The indicated slight degree of overconsolidation for the soft clay deposit is believed to be the result of two low-water stages of Lake Michigan, when the water level dropped as much as 80 ft below that of the present lake [7]. During these low-water stages, partial desiccation of the deposit occurred. Practical Applications Prediction of Preconsolidation Pressure Determination of the preconsolidation pressure is very important, since clays compress very little and settlement occurs very rapidly when the clay is subjected to pressures (applied plus overburden) smaller than the maximum past (preconsolidation) pressure. However, accurate determination of the most probable preconsolidation pressure from one-dimensional consolidation tests is not an easy task. Great care must be exercised during the field sampling, transporting, handling, and laboratory trimming operations to avoid sample disturbance, which would lead to underestimation of the preconsolidation Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

ANDERSON AND LUKAS ON PRECONSOUDATION PRESSURE

511

PRECONSOLIDATION PRESSURE OR EFFECTIVE OVERBURDEN PRESSURE (TSF)

5.0

6.0

(Note: Itsf »95.8KN/m )

Average Effective Overburden Pressure Profile (OCR <• I)

\

-45FIG. 4—Summary of predicted preconsolidation pressure values based on Peck's work [7] for "soft Chicago Clay" deposit.

pressure. In addition, relatively large diameter [7.5 mm (3 in.) or greater] samples are required. Thus good quality consolidation tests are a costly proposition, which is seldom justified on small projects. On the other hand, Atterberg Limits and unconfined compressive strength tests are inexpensive to perform. For clays where Skempton's correlation (Eq 1) is valid, the prediction procedure employed in this paper can be a valuable aid in the evaluation of the preconsolidation pressure. On projects where questionable consolidation tests have been performed, the predicted preconsolidation pressures can be used as a check on the values determined from the tests [6]. On small projects, this procedure can be utilized to estimate the maximum past (preconsolidation) pressure of the deposit under consideration. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

512

UBORATORY SHEAR STRENGTH OF SOIL

Prediction of Undrained Shear Strength Another use of the s^/p ratio is the prediction of the undrained shear strength of a clay deposit for embankment construction projects. The predicted value of the undrained shear strength («„') is Su'=P-i^u^V)

(3)

where p represents Pc o r p , and (5,/p) is determined by Eq 1. Wu et al [10] reported measurements of the shear strength of a slightly overconsolidated glacial lake clay deposit before and after construction of an embankment near Toledo, Ohio. The shear strength was measured by unconfined compression tests and also predicted by consolidated-undrained triaxial and simple shear tests. The results are presented in Table 2 along with the predicted values of s„ by Eq 3. It should be noted that the predicted 5,,-values by Eq 3 are as close to the measured s„-values as any of the values predicted by the laboratory shear tests. The measured i„-values for the varved clay are probably fairly accurate, while the unconfined compression test undoubtedly underestimates the shear strength for the sensitive clay. Similarly, the 5„/p ratio can be utilized to predict the increase in shear strength resulting from a change in effective stress for stage construction of embankments over soft ground. Ladd et al [//, 12] published results for a test embankment and subsequent embankment fills over a deposit of sensitive marine clay (slightly overconsolidated to normally consolidated) in New Hampshire. The plasticity index for the clay deposit was 15 + 3 percent, which leads to a s „ / p ratio of 0.17 ± 0.01 by Eq 1. Field vane shear tests and laboratory consolidation tests indicate a ratio of s„ top^ of 0.17 ± 0.01 for the entire deposit, which correlates perfectly with the calculated 5,/p ratio. Various special laboratory shear tests were performed to evaluate the ratio of s„ to (j^, whereCT„<,is the vertical consolidation stress. The results are given in Table 3. Total stress stability analyses for the test embankment failure with circular failure arcs indicated that the in situ value of syp was probably lower than the value of 0.20 obtained from the direct simple shear tests. The direct simple shear tests did, however, predict very well the increase in s„, measured by the field vane, with consolidation under embankment fills. Therefore the s,/p ratio computed by Eq 1 would have predicted the initial in situ strength ratio and increase in s„ due to embankment loading as well as any of the special laboratory shear tests. Sununaiy and Conclusions The i „ / p ratio developed by Skempton can be utilized to predict the preconsolidation pressure for clay deposits once the Atterberg limits and undrained shear strength have been determined. The validity of this approach has been demonstrated by test results on clays with various geologic origins

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ANDERSON AND LUKAS ON PRECONSOLIDATION PRESSURE

513

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514

LABORATORY SHEAR STRENGTH OF SOIL

TABLE 3—Ratio of undrained shear strength to vertical consolidation stress for various test procedures. Type of Test (1)

*„/V (2)

Consolidated-undrained triaxial compression Plane strain active Plane strain passive Direct simple shear

0.25 ± 0.02 0.295 0.13 0.20

from the Chicago area. In addition, preconsoiidation pressures have also been predicted for the "soft Chicago clay" deposit utilizing Peck's data. The predicted values indicate that the deposit is normally consolidated to slightly overconsolidated, which correlates well with results of consolidation tests and local experience. From the material presented in this paper, it is concluded that: 1. For lightly overconsolidated clays where Skempton's relationship is valid, a reasonable estimate of the preconsoiidation pressure can be obtained utilizing the s,/p ratio. The data presented herein indicate a good correlation between the predicted and measured preconsoiidation pressures up to a pressure of 575 kPa (6 tons-force/ft^), while above this pressure level the predicted values are consistently higher than the measured values. The clays under consideration generally have a plasticity index less than 45 percent. 2. The relationship between liquidity index and measured preconsoiidation pressure is rather poor for the Chicago area soils studied herein. However, the lower curve shown in NAVFAC DM-7 apparently does provide a reasonable estimate of the minimum value of the preconsoiidation pressure for any given liquidity index. 3. The prediction method demonstrated in this paper has several practical applications. On small projects, the predicted preconsoiidation pressure can be utilized as an estimate of the maximum past (preconsoiidation) pressure of a clay deposit. The predicted preconsoiidation pressure can also be used as a check on questionable consolidation test results. In addition, the s,/p ratio from Eq 1 can be employed to estimate the undrained shear strength for projects involving embankment construction over soft ground. Acknowledgments All of the test data shown in Table 1 are from the project files of Soil Testing Services, Inc. As such, some of the data may not be of research quality. The writers are indebted to this firm for allowing the use of these data. Grateful appreciation is also expressed to Dr. S. A. Gill and C. N. Baker, Jr., for their thorough review of this paper. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

ANDERSON AND LUKAS ON PRECONSOLIDATION PRESSURE

515

References \l] Skempton, A. W., Proceedings of the Institution of Civil Engirwers. London, Vol. 7, 1957, pp. 305-307. [2] Peck, R. B., Hanson, W. E., and Thombum, T. H., Foundation Engineering, 2nd ed., Wiley, New York, 1974, pp. 93-94. [3] Umbe, T. W. and Whitman, R. V., Soil Mechanics. Wiley, New York, 1969, Ch. 28, pp. 429-432. |4] "Soil Mechanics, Foundations, and Earth Structures," Design Manual NAVFAC DM-7, Naval Facilities Engineering Command, Department of the Navy, March 1971, pp. 7-3-9 to 7-3-15 and 7-6-1. [5] Duncan, J. M. and Buchignani, A. L., "An Engineering Manual for Settlement Studies," Geotechnical Engineering Research Report, Department of Civil Engineering, University of California, Berkeley, March 1975, pp. 35-36. [6] Peck, R. B., "The Selection of Soil Parameters for the Design of Foundations," Second Nabor Carrillo Lecture, Mexican Society for Soil Mechanics, 1974, pp. 1-47. [7] Peck, R. B. and Reed, W. C , "Engineering Properties of Chicago Subsoils," University of Illinois Engineering Experiment Station Bulletin No. 423, 1954, pp. 1-62. (S) Parsons, J. D. and Peck, R. B., Proceedings of the American Society of Civil Engineers. Vol. 82, No. 1028, 1956. (91 Baker, C. N., Jr., and Wiesinger, F. P. in Performance Monitoring for Geotechnical Construction. ASTM STP 584. American Society for Testing and Materials, 1975, pp. 127-140. [10] Wu, T. H., Chang, N. Y., and Ali, E. M., Journal of the Geotechnical Engineering Division. American Society of Civil Engineers (ASCE), Vol. 104, No. GT7, July 1978, pp. 889-905. [11] Ladd, C. C. in Proceedings. ASCE Specialty Conference on Performance of Earth and Earth-Supported Structures, 1972, Vol. 1, Part 1, pp. 101-128. [12] Ladd, C. C., Rixner, J. J., and Gifford, D. C. in Proceedings. ASCE Specialty Conference on Performance of Earth and Earth-Supported Structures, 1972. Vol. 1, Part 1, pp. 211-242.

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/. R. F. Arthur,' a C. Ladd^

S. Bekenstein, ^ /. T. Germaine, ^ and

Stress Path Tests with Controlled Rotation of Principal Stress Directions

REFERENCE; Arthur, ]. R. F., Bekenstein, S., Germaine, J. T., and Ladd, C. C , "Stress Path Tests with Controlled Rotation of Principal Stress Directions," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 516-540. ABSTRACT; University College London (UCL) has developed a new flexible boundary plane strain shear apparatus for investigating stress-strain-strength anisotropy in sands. Called the Directional Shear Cell (DSC), it has the unique capability of controlling the major principal stress direction by varying the normal stress and shear stress acting on four faces of a cubical sample constrained between two rigid end plattens. The paper describes the device and its use, and presents results from a Massachusetts Institute of Technology (MIT) test program run on dense and loose Leighton Buzzard Sand to independently evaluate the device and for comparison with data obtained at UCL to investigate the effects of induced anisotropy due to prestraining. The DSC has now been used to measure inherent anisotropy in loose sand. These data are presented and MIT's progress in modifying the DSC to enable KQ consolidated-undrained testing of soft clays is described. KEY WORDS: anisotropy, deformation, drained shear tests, equipment, laboratory test measurement, sand, shear strength, soil structure, strain, strain measurements, stress path, stress strain curve. X-ray

Several factors inhibit continued progress in developing improved procedures for predicting the in situ deformation behavior of soils from results of laboratory tests. Perhaps the most important of these, other than sample disturbance, results from an inability to realistically imitate in the laboratory the varied stress path conditions encountered in the field, most especially those involving a rotation of the principal stress directions. Professional practice therefore largely ignores the stress-strain-strength anisotropy exhibited by both granular and cohesive soils since (1) it is difficult to measure ex' Reader in Soil Mechanics, University College London, London, England. ^Research assistant, research assistant, and Professor of Civil Engineering, respectively, Massachusetts Institute of Technology, Cambridge, Mass. 02139. 516 Copyright by Downloaded/printed Copyright 1981 University of

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ARTHUR ET AL ON STRESS PATH TESTS

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perimentally; (2) most theoretical models used for predicting deformations also ignore anisotropic soil behavior; and (J) little information exists for guidance as to its relative importance vis-a-vis other factors known to influence predicted field performance. Realistic simulation of in situ stress paths requires development of new laboratory test devices capable of controlling both the magnitude and direction of the principal stresses. Experimental research can then identify the main factors influencing stress-strain-strength anisotropy and eventually generate a data bank on representative soil types showing the effects of deposition, stress history, drainage conditions, etc. Such information is needed both to evaluate the limitations of existing models of soil behavior and to develop new constitutive relationships which better represent the stress-strain anisotropy of soils under generalized states of stress. This paper describes a test apparatus recently developed at University College London (UCL) for investigating stress-strain-strength anisotropy in sands. Called the Directional Shear Cell (DSC), it has the unique capability of controlling the major principal stress direction during plane strain shear. Experimental data obtained at the Massachusetts Institute of Technology (MIT) using the DSC are presented for the purpose of evaluating its versatility and reliability compared with other test devices and to illustrate the highly anisotropic behavior of sand during drained shear. The paper also describes current efforts to modify the DSC in order to investigate undrained anisotropy in soft clays. Background Underlying Principle The Directional Shear Cell (DSC) is a flexible boundary plane strain shear apparatus wherein the major principal stress (aj) direction can be controlled by varying the normal stress (a) and shear stress (T) acting on four faces of a cubical sample constrained between two rigid end plattens. Figure la illustrates the underlying principle (two sets of normal pressure bags apply a„ and Ob, and a system of "shear sheets" apply T^ and T/,), while Fig. 16 shows Mohr circles representing three states of stress. Hence any a,-direction can be achieved between plane strain compression (Point 1) and extension (Point 3) by changing the relative magnitudes of <Ja> <^fc» ^nd r. Definitions and Measurement of Anisotropy In 1944 Casagrande and Carillo [1]^ distinguished between two forms of anisotropy in soils which they called inherent and induced. Inherent •'The italic numbers in brackets refer to the list of references appended to this paper.

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518

LABORATORY SHEAR STRENGTH OF SOIL

ag a (Tfj applied via "normol pressure bogs"

To ° - T | , applied vio two sets of "sheer sheets"

Origin of plones

T

0

-I--

0

O-o'^, 0-b = l , T = 0

1' n-

•

/ ^

0

O-fl » l , 0-^ = 3, T = 0

I

FIG. 1—Principle underlying DSC (at small strains), (a) Imposed stresses: (b) Mohr circles of stress.

anisotropy was defined as a "physical ciiaracteristic inherent in the material, and entirely independent of the applied strains," whereas induced anisotropy was defined as "due exclusively to the strain associated with the applied stresses". Although these definitions were developed to describe strength anisotropy, Arthur et al [2] considered them equally applicable to stressstrain behavior. We shall now illustrate how the Directional Shear Cell (DSC) Can be used to measure both types of anisotropy in granular soils. Figure 2a defines the axes relative to the direction of sand deposition, and Fig. 2b defines the (redirection (^-angle) for test specimens sheared in the x-y plane. The normal stresses,CT<,and a^, nominally act along the x and y axes and the influence of inherent anisotropy is eliminated since the sand has Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

ARTHUR ET AL ON STRESS PATH TESTS

Direction of deposition

519

Nomlnol
axis

Nominol o" directions

FIG. 2—Measurement of anisotropy with DSC. (a) Sample orientation: (b) Tests in x-y plane (no inherent anisotropy): (c) Tests in x-z plane (with inherent anisotropy).

been deposited in the direction of the intermediate principal stress {02). Thus DSC tests run in this plane at varying ^-angles should all yield identical stress-strain curves if the apparatus performs as intended (the paper presents actual results for comparison). Arthur et al [2] and Rodriguez [3] also used x-y plane tests to investigate the effects of induced anisotropy as follows: 1. Prestrain the test specimen during a first shear at some given ai-direction (say, 1^^). 2. Unload the sample and then perform a second shear at a different CTj-direction (say, yj/g)3. This produces a jump rotation (d = ypg — ^^) in the ff]-direction. This paper presents additional results showing the effects of induced anisotropy on the stress-strain behavior of dense and loose sand. Figure 2c defines the aj-direction (8-angle) for samples sheared in the x-z plane. The test specimen now possesses inherent anisotropy and its effects can be measured by varying the 5-angle. The paper presents data for a loose sand, which is the first time that the DSC has been used to investigate inherent anisotropy, and compares these results with prior studies [4-7] Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

520

LABORATORY SHEAR STRENGTH OF SOIL

wherein the depositional direction had to be varied relative to the fixed CT]-direction of the shear device. Description of Directional Shear Cell Major Components The DSC, a plane strain device, is designed to shear cubical sand samples (100-mm cube) enclosed in a thin rubber membrane (Fig. 3) up to 15 percent strain. One side remains open during sand deposition, with two vacuum lines being attached during final sealing. The sample becomes rigid under vacuum, which permits handling. Figure 4 illustrates the method used to apply normal and shear stresses to the four vertical faces of the cubical test specimen. Two pairs of reinforced rubber pulling sheets surround the sample, their ends being attached to a load frame-hydraulic piston assembly which applies the desired shear forces (area times T^ and r^,), and two sets of pressure bags transmit a„ and a^ through the "shear sheets" and onto the sample. The view in Fig. 5 of the partially assembled DSC shows the sample resting on the bottom end platten with the shear sheets attached to their load frames and two of the four pressure bags in place. Hydraulic lines connect the pressure bags and shear sheet loading system to separate normal and shear stress control panels fitted with pressure regulators, gages, etc. The picture in Fig. 6 of the fully assembled device shows the top platten in place and the plate camera used to photograph the grid drawn on the top plane strain side of the sample membrane. This technique enables strain measurements during shear of loose sand, while radiographs of embedded shot record strains in samples of dense sand. Pressure Bags and Shear Sheets To function properly, the DSC must impose uniform normal and shear stresses to the four boundary surfaces while the shape and dimensions of the sample change during plane strain shear. Rigid plattens can apply reasonably uniform normal stresses when the platten-sample interface is lubricated and no local variations in stiffness occur close to the platten [8]. This latter requirement is difficult to achieve when testing sand, and becomes near impossible with the additional need to apply uniform shear stresses to the faces of the sample. Thus pressurized flexible bags are best suited for applying normal stresses. These bags can be easily manufactured from natural latex with suitably placed reinforcement to prevent local blowouts. Retaining vanes along the sides provide lateral stability (Figs. 4 and 5). These can be adjusted, along with the rigid backing plates, to maintain parallel alignment as the test specimen deforms during shear.

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ARTHUR ET AL ON STRESS PATH TESTS

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FIG. 3—DSC sample enclosed in thin rubber membrane with two vacuum lines and top grid pattern.

The shear sheets used to apply the shear stresses {T^ and T^) represent a unique feature of the DSC. As shown in Fig. 7, they have three basic components: a shear sleeve, stretching strips, and reinforced pulling sheets. The inner rubber shear sleeve transmits shear to the sample by adhesion between the rubber surfaces of the sleeve and the sample membrane which have been cleaned by a solvent and then roughened with acetone. A sand layer, glued to the inside of the sample membrane, provides traction at the sand-membrane interface. The stretching strips serve the key function of distributing the applied tangential force to the shear sleeve. The two ends of these unreinforced rubber strips (6 by 25 mm long) are glued at 5-mm intervals to the outside of the Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

522

LABORATORY SHEAR STRENGTH OF SOIL

t Reinforced rubber pulling sheets.

Rigid backing plate. I Pressure bag Pressure bag ^1 retaining vanes

Unreinforced' N rubber strips ^

^////////////////A SOmnn

0

Irtxarea

SCALE FIG. 4—Method used to apply normal and shear stresses in the DSC.

shear sleeve and the inside of the reinforced pulling sheets. A special lubricant allows the stretch in the strips to reach 300 to 400 percent of their original length even though appreciable normal stress is transmitted across the strips from the pressure bags. An hydraulic piston-load frame assembly (Figs. 5, 6 and 7) applies the tangential shear force to the inextensible reinforced pulling sheets. Lubricated thin rubber sheets are placed between the pulling sheets and the pressure bags to reduce friction. The stresses become nonuniform at the two comers where the sheets intersect, so acrylic prisms are glued to the inside of the sample membrane at these locations (Fig. 4). As the sample deforms, the directions of the pulling sheets must be progressively realigned. This is accomplished by rotating the hydraulic pistons along the circular frame shown at the bottom of Fig. 6. Pressure transducers on the control panel measure directly the applied normal stresses (a„ and a/,), but the shear sheets require calibration due to frictional effects. Figure 8 illustrates the results and method, which involves the following steps: (/) place test specimen under vacuum in DSC and apply

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ARTHUR ET AL ON STRESS PATH TESTS

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FIG. 5—View of partially assembled DSC showing sample with shear sheets and two of the four pressure bags.

equal pressure to all four pressure bags; (2) isolate two adjacent bags from the pressure source to keep them at constant volume; (3) load the two shear sheets between these pressure bags by applying equal pressure to their hydraulic pistons; {4) with proper alignment, the two adjacent pressure bags should record identical pressure increments equal to T^ = T^ ; and (5) repeat the above procedure at higher normal stresses. The resulting linear calibration plotted in Fig. 8 is essentially independent of normal stress and has been found to remain constant unless the shear sheets are damaged or altered in form. Sample Preparation, Assembly, and Shear Sample preparation begins by glueing two acrylic prisms to diagonally opposite corners of the sample membrane (Fig. 4) and glueing a sand layer to the vertical sides of the membrane supported within a preparation box. Sand is then deposited through air along the z-axis (Fig. 2) by either slow pluviation to obtain dense samples or rapid release of a large quantity to obtain loose samples (with dense sand, the process is halted at midheight to embed a horizontal grid of tungsten shot (Fig. 4). After deposition, a small "vacuum cleaner" removes excess sand, followed by glueing a separate rubber sheet to Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

524

LABORATORY SHEAR STRENGTH OF SOIL

FIG. 6—View of assembled DSC and plate camera.

the exposed flaps of the rubber membrane and inserting two vacuum lines (Fig. 3). With vacuum applied, the sample is removed from the preparation box, placed on the well-lubricated bottom glass platten, enclosed by the shear sheets and pressure bags (Fig. 5), the top glass platten (also well-lubricated) lowered into place, and the pressure bag backing plates secured to the end plattens via vertical rods etc. After applying a uniform normal stress, the vacuum is released, the top plate locked into final position, and a radiograph or photograph taken to give the zero strain at start of test condition. The desired major principal stress direction (
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ARTHUR ET AL ON STRESS PATH TESTS

525

FIG. 7—Three basic components of the shear sheets.

shear stresses (T^ and TJ). A typical stress controlled test, usually run at constant ff3' = 14 kPa, proceeds as follows: 1. Use the control panels to adjust the pressure in the pressure bags and the shear sheet hydraulic pistons, with full vacuum'' acting on the sample to prevent straining during stress application. 2. Release vacuum and take radiograph/photograph when a flowmeter on the normal stress control panel indicates no further straining. 3. Reapply vacuum and adjust pressures for the new stress increment. In addition, the positions of the normal pressure bags and shear sheets may also have to be adjusted to maintain proper alignment as the test specimen deforms (Fig. 9). Step 3 is repeated until failure, that is, when gross distortion occurs under a small stress increment. If rupture layers develop during shear, these can be readily detected from radiographs. ''Used for convenience and not necessary with small stress increments.

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526

LABORATORY SHEAR STRENGTH OF SOIL

50

1

r

.•^PRESSURE CONSTANT -VOLUME CONSTANT

40

SAMPLE UNDER VACUUM

30-

^Tg X AREA

e a.

' J T ^ X AREA 20 -

VOLUME CONSTANT PRESSURE CONSTANT

(r(kPa)

To

Tb

IS

0

a

30

« » • •

50

8

12

16

20

To

Tb

4

0

24

PISTON READING {mV/9.998V) FIG. 8—Calibration of the shear sheets.

FIG. 9—DSC for loose sand sample near failure with ^ = 45 deg.

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ARTHUR ET AL ON STRESS PATH TESTS

527

Measurement of Strains Radiographs of embedded shot in dense samples (Fig. 4) and photographs of inked lines on the top membrane of loose samples (Fig. 6) record displacements during shear. An optical comparator measures and digitizes these coordinates, from which a computer program determines strain magnitudes and directions. Several interrelated factors affect the accuracy of this strain measurement technique, but based on past experience at University College London [9] mean linear strains can be measured to 0.03 percent, with a standard deviation of 0.3 percent for measurements over a 10-mm length. Figure 10 shows the magnitude and direction of the major principal strains (€]) measured in a dense sand sample sheared to /? = o\ lo^ = 5.5 in the

Sample Boundary ndary^

Direction and Magnitude of €,

O

Averoge €, ' 1.18% Average f, direction = 37.4° 1

LO

O

O

30= 0.347. SO =3.8°

1 = 1.0% strain

FIG. 10—Distribution of strain magnitudes and directions from dense sand sheared in DSC at^ = 40 deg m = 5.5).

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528

LABORATORY SHEAR STRENGTH OF SOIL

x-y plane at lA = 40 deg. The scatter in both quantities is mainly attributed to errors in the measurement technique. Though costly, the radiograph/photograph technique provides vital information regarding uniformity of strain distributions within test specimens and whether or not the axes of principal stress and strain directions coincide. This information is needed to properly evaluate the performance of newly developed shear devices, especially those with flexible boundaries [10]. It also gives a more complete picture of soil behavior. Comparable information in shear devices with rigid boundaries would require equally comprehensive measurements of stress distribution within the sample. Experimental Program and Results Introduction The research was conducted under a NSF Grant for the purpose of investigating the stress-strain-strength anisotropy of soils under generalized states of stress. After acquiring the Directional Shear Cell from University College London, MIT performed a series of "check" tests on dry sand to independently evaluate the device and for comparison with data obtained at UCL [2,3], The experimental program was then extended to include the effects of inherent anisotropy and to modify the DSC to enable consolidatedundrained testing of soft clays. MIT and UCL both used standard Leighton Buzzard Sand [subrounded and close graded, US sieve 20-30 (0.84 to 0.60 mm), specific gravity = 2.66). The two methods of deposition previously described yielded: Dense samples Loose samples

Void Ratio (e) Relative Density (D,) 0.53 ± 0.01 = 95% 0.74 ± 0.02 = 25%

Test Program on Sand The experimental program involved three basic types of drained shear tests: monotonic loading of "isotropic" samples, tests on "prestrained" samples to study induced anisotropy, and measurement of inherent anisotropy. Monotonic Loading—Samples are sheared in the x-y plane, to eliminate inherent anisotropy, with different directions of the major principal stress (i/'-angle) to the j^-axis (Fig. 2b). If the DSC and experimental techniques work perfectly, such tests should yield unique stress-strain data for identical samples independent of the i/'-angle. Tests in this series were sheared by increasing R ( — Oi'/oi') at constant 03' = 14 kPa, and are designated by D(V') andX(\i') for dense and loose sand, respectively. Induced Anisotropy—These tests measure the effects of induced

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ARTHUR ET AL ON STRESS PATH TESTS

529

anisotropy due to prestraining. Samples are again sheared in the x-y plane to eliminate inherent anisotropy. The test procedure generally followed that used at UCL [2,3,11], namely: 1. First shear loading with a selected (j|-direction (i/-^) o a given shear stress level {R = b for dense sand and R — 4 for loose sand), followed by unloading to R = 1. 2. Second shear loading to failure with a different a,-direction (iZ-g), thus causing a jump rotation {d — \pB ~ ^A) 'n the principal stress direction. 6 was varied from 0 to 90 deg, with 03' = 14 kPa during both shears. These tests are designated by Z)(I/'^,I/'B) and L{^A'^U) for dense and loose sand, respectively. In addition, some tests on dense sand involved "unloading" during the second shear, as will be described under Results. Inherent Anisotropy—In these tests, loose sand was again deposited along the 2-axis, but with the test specimens now oriented for shearing in the x-z plane (Fig. 2c). Thus tests performed at different 6-angles ((j,-direction relative to the z-axis of deposition) measure the effects of inherent anisotropy. They are designated by LI(b) and required development of a new sample preparation technique [12], This program also included two tests on specimens /Co"Consolidated prior to shear. Results of Monotonic Loading Tests Dense Sand—Figure 11 presents representative stress-strain data on dense sand from monotonic loading tests and Xht first shear loading portion of the induced anisotropy test series. The major (ej) and minor (ej) principal strains are average accumulated incremental values based on 36 "points" obtained from radiographs of a 7 by 7 matrix of embedded shot. The results show good agreement in the R versus e\ data from the \l/ — Q deg and the V* = 40 and 50 deg tests, these giving a well-defined best estimate curve with relatively little scatter. However, most of the tests sheared zX\j/ = 20 and 70 deg encountered unexpected problems, to be discussed subsequently, that resulted in much greater strains or premature failure or both. In addition, tests run at ^i* = 0 and 90 deg yielded higher /^-values at failure. This problem, wherein "unstressed" shear sheets apparently inhibit formation of rupture layers, will also be discussed. Otherwise, the DSC functioned as designed. The strain distributions were relatively uniform^ (for example. Fig. 10), with a coefficient of variation largely attributed to scatter in the measurement technique. The axes of major principal stress and strain coincided within ± 5 deg (for example. Fig. 10), this variation being within measurement capabilities. Coincidence of these axes serves as an important *As uniform as those determined by Phillips [9] in the middle third of homogeneous sand samples tested in triaxial compression with lubricated ends.

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530

LABORATORY SHEAR STRENGTH OF SOIL

check that correct combinations of normal and shear stress were applied in order to achieve the desired CT]-direction. The £[ versus €3 data in Fig. 11 can be represented with relatively little error by a linear relationship. This implies a constant dilation angle during shear, defined by . (661+663) V = —arc sm (6e, - §63)

The f-angle averaged 13 deg, with a range of 10 to 14 deg. Loose Sand—The stress-strain data on loose sand, Fig. 12, include results from monotonic loading and the first shear loading portion of induced anisotropy tests. The strains are average values based on 16 "points" obtained from photographs of a 5 by 5 grid of lines linked on the top rubber membrane (Fig. 6). The R versus ei data tend to be more randomly scattered than those observed with dense sand. However, the overall agreement is judged reasonable, with no consistent trend as i/- increases from 0 to 45 deg, and the major principal stress and strain directions coincided within ± 5 deg. The 6) versus €3 relationship from individual tests is approximately linear, but the corresponding dilation angles (average »' = — 5 deg, standard deviation = 3.5 deg) show more scatter than measured in dense sand. Furthermore, these tests had much less uniform strain distributions than for dense sand, and this non-uniformity varied in a fairly consistent manner with the amount of shear applied to the shear sheets (see subsequent discussion under Experimental Problems). Measurement of Induced Anisotropy Loading Tests: Dense Sand—Figure 13 presents stress-strain curves from the second shear of dense samples which had been prestrained to R = 6.0. Compared with isotropic sand (monotonic loading curve from Fig. 11), induced anisotropy produces a much stiffer response at small 0-angles, and then much larger strains as d increases to 75 deg. Pre-straining also causes a pronounced change in the shape of the stress-strain curves, from the typical hyperbolic to an almost linear relationship, as the jump rotation angle increases. Also note the excellent agreement between the two pairs of tests run at 0 = 40 and 70 deg, with interchanged ^ angles during first and second shear. However, in both cases, the tests with r^g = 0 deg produced higher Rfvalues (see discussion under Experimental Problems). Induced anisotropy caused relatively little change in the slope of lines fitted through the €] versus 63 data (average dilation angle j* = 14 deg), but these lines tended to become more offset from the origin as 6 increased. Significant deviations in the axes of major principal stress and strain also occurred at intermediate rotation angles {6 = 40 to 75 deg). In all cases, the

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ARTHUR ET AL ON STRESS PATH TESTS

^

Symbol

0° 0° 0° 0° 0° 0° 0° 20° 20° 40° 40° 40° 50° 70° 70°

0

531

a A t> V <]

O

FIG. 11—Stress-strain data from moiiotonic loading tests on dense sand.

ti-direction rotated beyond the a,-direction, and this deviation decreased to zero as R increased to 6, even though the sand still exhibited highly anisotropic stress-strain behavior (see Ref 12 for details). Figure 14 compares the MIT data to those reported by UCL [2] via a plot of strain ratio versus ^-angle wherein strain ratio (SR) = €, (2"'' shear)/ei (P' shear) obtained at 7? = 6.0 for the two loadings. Both sets of data show the same basic trend, though UCL measured somewhat larger overall strain magnitudes (thought due to slightly different end plate conditions). Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

532

LABORATORY SHEAR STRENGTH OF SOIL

5.0

4.5

'/'

• Best Estimate and Range

0° 0° 0° 0° 0° 0° J 0° 0°" 10° 30°

Symbol D A V

< 0

o o

o • •

A 45° * No shear sheets

0

1

2

3

4

5

6

7

8

e, (%) FIG. 12—Stress-strain data from points).

motiotonic

loading tests on loose sand Ifj-data

from

16

Unloading Tests: Dense Sand—These tests followed a different stress path during second shear. After initial prestraining to R = 6.0, the samples were isotropically consolidated to 120 kPa and then sheared with a jump rotation by decreasing a^' at constant CTJ'. In spite of being "unloaded" during second shear, the values of strain ratio plotted in Fig. 14 from these tests follow the same pattern of change with rotation angle as the loading tests. Thus prestraining has a far greater effect than changes in average confining stress during shear.

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ARTHUR ET AL ON STRESS PATH TESTS

533

Test No. Symbol D0,0

— O — 8.1

D20,0

— D — 8.9 18°

DO,40

b" It

-A—

16"

71 14°

D40,0

8.5

DO, 70

— < — 6.8

D70,0,

8.0

14°

74

13°

8.1

14'

DO, 75 D0,90|

— O—

FIG. 13—Stress-strain curves from loading tests on dense sand with induced anisotropy.

Loading Tests: Loose Sand—Figures 15 and 16 present the same type of information for loose sand as previously shown for dense sand. The effects of induced anisotropy are also very similar, namely: (/) much stiffer response, with characteristic hyperbolic stress-strain curve, at small rotation angles; (2) much softer response, with an almost linear/? versus ei relationship, at large rotation angles; and (3) good agreement between the MIT and UCL results in terms of normalized strains (though UCL again obtained larger strain magnitudes). Deviations in the major principal stress and strain directions also followed the same pattern as described before. All cj versus €3 data essentially fall on the same line, giving an average v = + 1 deg compared with —5 deg for isotropic loose sand. Measurement of Inherent Anisotropy Inherent anisotropy has a vety significant effect on the stress-strain behavior of loose Leighton Buzzard Sand, as demonstrated by the results plotted in Fig. 17. Though a special sample preparation technique had to be developed to perform DSC tests in the x-z plane [12], the data appear both reliable and consistent since (7) the pair of tests run at 6 = 70 and 90 deg show excellent agreement, and (2) the strain distributions were quite uniform, at least in the 6 = 40, 60, and 70 deg tests. The influence of inherent anisotropy is as dramatic as previously shown for induced anisotropy, Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

534

LABORATORY SHEAR STRENGTH OF SOIL

3.0 M I T Loading Tests

0

MIT Unlooding Tests

D

1

1

r

1

2.8 2.6 Artt)ur et al ( 2 )

2.4

/°

R=6

2.2

— .

o

2.0

o

c«

tn

/

O

I.U

0

-

Vt

1.6

~' vu

•V

14

i_

o0) x: tn

1.2

c CM

in

*—' ^

/

0.8

-

D

II

a. (/)

06 0.4

" D

-

^XO

0.2 1

0

1

1

1

10

20

30

1

40 50 60 9 (degrees)

1

1

1

70

80

90

FIG. 14—Strain ratio versus rotation angle for dense sand with induced anisotropy.

O^O

90.0 Test No

/ / / / ' /

[

r

/ /

,X' /

h

':^ Bd'^

^

I Average Monotonic Loading Curve from

, /

^

\

1

1

.

1

1

Rf

V

— 0 — 5.0

0°

L0,20

— D — 4.5

1'

L0,50

—0--

L0,60

—

L0,70|

—

4.9

-1°

A—

-

3°

<] —

-

0°

LOJOj — 1 > — 4.8 -1°

Fig. 12

1

Symbol

L0,0

1

L0,80

—V—

-

2°

L0,90*

—o—

5.5

3°

»No st> ear shee s

10

FIG. 15—Stress-strain curves from loading tests on loose sand with induced anisotropy (ti'datafrom 16 points).

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ARTHUR ET AL ON STRESS PATH TESTS

2.0 5

1.6

-; 1.4

O

• o V

R =4

-

-

a

@

-

\© o -

/o

0.8

o

c

-

(3)

1.2 --

S 10 „

1

-

V>

UJ

O" — I —

1.8 RODRIGUEZ

j"

1—— 1 —

•

MIT

535

~

o/

0.6 0.4

-

O/a

-

0.2 T

0

i

l

l

1

10 20 30 40

50

1

1

1

60 70

1

80 90

6 (degrees) FIG. \b—Stniiii ratio versus rotation angle for loose sand with induceJ anisotropy.

5

1

1

1

„.

1

1

1

• ^

4

*

Test No

S/mbol

V

LI 0

^>-

7°

L I 40

—D—

3°

LtSO

--0--

-5°

L I 70,

-A--

•7°

L I 702 .-V—•

-6°

L I 90, . . - 0 - .

•2°

3

L I 902

2<

LK„0 M^

1

1

1

1 8

1

1

1 14

LK„90

- 0 -

0°

• •

5°

-

FIG. 17—Stress-strain curves from loading tests on hose sand with inherent anisotropy Itl-datujrom 16 points).

both regarding alterations in the basic shape of the stress-strain curves and changes in strain level with increasing rotation angle. But fundamental differences also exist between the two types of anisotropy. Whereas inherent anisotropy causes a continuous increase in strain as & rotates from 0 to 90 deg, the strains in the tests with induced anisotropy rise to a maximum at

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536

LABORATORY SHEAR STRENGTH OF SOIL

0 = 70 ± 10 deg and then decrease at ^ = 90 deg (Figs. 14 and 16). No deviation occurred between the major principal stress and strain directions in the inherent tests, in spite of the marked R versus ej anisotropy, but these samples did show a fairly consistent change in the dilation angle (v) from positive to negative to zero as d increased. Figure 17 also presents results from two test specimens anisotropically consolidated to a„ = 80 kPa and a/, — 40 kPa (thus assuming A^o = 0-5). They were then sheared by varying the stress ratio at constant mean principal stress, one in plane strain compression (6 = 0 deg) and the other in plane strain extension (6 = 90 deg). Though not directly comparable to the other test data, because of the different stress paths, their behavior is dominated by the effects of inherent anisotropy. Although only one of the inherent tests was actually carried to failure (R^ = 4.6 for LI7O2), the results in Fig. 17 suggest little strength anisotropy, that is, changes in Rf with 6-angle. Most other investigations of inherent anisotropy have shown moderate to significant strength anisotropy [4-6,13], especially with plane strain testing of dense Toyoura sand [7]. These studies do indicate larger strains at failure with increasing 6-angle, but none show such dramatic changes in the basic shape of the stress-strain curves as observed in the DSC. This is the only device which measured inherent anisotropy by varying aj relative to the depositional axis, rather than vice versa. Further research is certainly needed regarding the effects of sand type, mode of deposition, and the precise testing techniques. Experimental Problems and Present Limitations of the Directional Shear Cell Experimental Problems Figure 11 presented results from first loading tests run on isotropic dense sand sheared at different (/--angles. Two of the tests sheared at i/- = 20 and 70 deg (which are identical regarding operation of the DSC since the a^, and Of, normal stresses are simply interchanged) plotted beyond the range of the other tests. Several other 20 and 70 deg tests, not shown, also developed excessive strains or premature failure or both. This experimental problem is thought to be caused by the reduced thickness of the shear sheets where they fold around diagonal comers (the upper and lower comers in Fig. 7), which produces a shear stress component from the pressure bags and local overstressing. Arthur et al [14] predict the formation of rupture layers across these same diagonals whenCTJis oriented at 20 or 70 deg, and hence local overstressing at these comers leads to progressive straining and premature failure. This problem can be corrected by using uniformly thick shear sheets. Dense sand sheared at t/- = 0 or 90 deg, that is, with unstressed shear sheets, gave larger values of Rj (8.4 ± 0.4) than measured at intermediate

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ARTHUR ET AL ON STRESS PATH TESTS

537

CT]-directions or in samples without shear sheets {Rf = 6.9 ± 0.4). Thus unstressed shear sheets apparently inhibit the formation of rupture layers. However, the results in Figs. 11 and 13 suggest little influence on measured stress-strain data prior to failure. DSC tests run on loose sand, with and without induced anisotropy, had much less uniform strain distributions than with dense sand, and these distributions varied in a fairly consistent manner with the amount of shear applied to the shear sheets. Comparison of the average ei-values (see Refs 3 and 12) based on 16 points (the full grid) versus only the 4 interior points generally showed the following at /? = 4.0: e, (16)/e, (4) = 0.85 + 0.07 at i/- = 0 and 10 deg €,(16)/e,(4) = 1.04 ± 0 . 0 3 at !/< = 30 and 45 deg Larger interior strains occurred with unstressed shear sheets and more uniform strains with highly stressed shear sheets. It is believed that this results from insufficient compression/extension of unstressed shear sheets, an arching action. The problem occurs in loose samples because the sand is more compressible and the stress levels lower compared with the stiffness of the shear sheets. It can be avoided by using thinner shear sheets for these soils. However, in spite of this problem, it should be noted that: 1. Average strains based on the entire grid, which are thought to be more representative of the behavior of loose sand, indicate that the DSC yields essentially identical R versus ej curves at different i/'-angles (Fig. 12), though with more scatter than observed for dense sand. 2. Loose sand samples with inherent anisotropy generally had a more uniform strain distribution. The MIT tests recorded smaller strains in both dense and loose sand samples than observed at UCL. This difference is tentatively attributed to variations in the magnitude of the intermediate principal stress during shear caused by differences in the thickness of lubricating grease applied to the top and bottom plane strain sides. Closer control over this variable should reduce scatter in test results. Means for measuring the intermediate principal stress should also be developed. Present Limitations The maximum boundary shear stress that the present DSC can apply is 50 kPa. It will be difficult to increase this limit by more than a factor of five, or to convert the device for strain controlled testing. The DSC is therefore restricted to stress controlled testing at relatively low shear stress levels. MIT is developing procedures to enable KQ consolidated-undrained testing of soft clays in the DSC with pore pressure measurements. Radiographs of Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

538

UBORATORY SHEAR STRENGTH OF SOIL

shot embedded in a modelling clay indicate that the existing shear sheet design can transfer shear stress from the sample membrane to the clay and produce uniform strain distributions. Since clay samples can not be easily backpressured in the DSC, special procedures have been developed to obtain fully saturated samples of resedimented Boston Blue Clay, along with compatible trimming equipment. A miniature piezometer probe [15] has been developed for measuring pore pressure in the center of the sample. The total stress path will be controlled to maintain the excess pore pressure near zero, hence minimizing water migration to or from the sample boundaries which are flexible and contain entrapped air. The dimensional and deformation restraints imposed by the present DSC limit allowable strains during ATfl-consolidation prior to shear. Initial testing will therefore use overconsolidated samples trimmed such that final consolidation produces a 100-mm cubic sample (the current size of sand specimens). Drainage will be provided via porous comer prisms (Fig. 4) and filter strips placed on the top and bottom surfaces. Problems have occurred in using the DSC with sands and more will undoubtedly develop while extending its capabilities to clays. But the authors believe that the effort is justified in view of the limitations of other sophisticated shear devices, namely [//]: (7) true triaxial cells are restricted to a 90 deg rotation of the principal stress direction; (2) the Cambridge simple shear apparatus is restricted to shear in the no-extension directions; and (3) hollow cylinder tests may also involve shear in no-extention directions, nonuniform stresses when unequal inner and outer cell pressures are used, and variations in b = (ff2 ~
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ARTHUR ET AL ON STRESS PATH TESTS

539

rect combinations of normal and shear stress were applied in order to achieve the desired CT)-direction. 3. Tests sheared withCT|oriented at 20 and 70 deg to the reference axes are identical in terms of cell and sample geometry, yet produce very different stress-strain data with anisotropic test specimens (Figs. 13, 15 and 17). The DSC is ideally suited to investigate stress-strain anisotropy in sands. Data presented herein (Figs. 13 to 16) show the same effects of induced anisotropy due to prestraining as previously reported by UCL [2,3,11]; namely, 1. A very stiff response, with characteristic hyperbolic stress-strain curve, at small rotation angles (0 = ^B ~ ^A)2. A much softer response, with an almost linear/? versus ej relationship, at large rotation angles. 3. Very significant deviations in the axes of major principal stress and strain at intermediate rotation angles {6 — 40 to 75 deg), but only at low /?-values. Development of new sample preparation techniques [12] also enables measurement of inherent anisotropy with the DSC. Results on loose LBS (Fig. 17) show very dramatic effects, with much larger changes in the shape of the stress-strain curves with rotation angle (6) than previously reported in the literature [4-7], Furthermore, inherent anisotropy produced the softest response at S = 90 deg compared with 0 = 70 ± 10 deg for samples having induced anisotropy. Experimental problems with the DSC were encountered in the MIT test program (for example, premature failure of dense sand sheared at ^^ = 20 and 70 deg, and nonuniform strain distributions in many of the loose sand samples). These problems can be resolved by the simple means discussed previously. The DSC is also currently restricted to drained stress controlled tests on sand at relatively low shear stress levels (T <50 kPa), although it has been used to study the cyclic behavior of sand with continuously rotating principal stress directions [//]. MIT is now developing procedures to enable Kg consolidated-undrained testing of soft clays with pore pressure measurements in the DSC. While not an easy task, the authors believe the effort justified in view of the potential ability of the DSC to more fully investigate stress-strain-strength anisotropy in plane strain shear than now possible with other test devices. Acknowledgments The MIT test program was partially funded by a NSF Research Grant (ENG78-10732) entitled "Stress-Strain Anisotropy of Soils Under Generalized States of Stress" and used radiography facilities made possible by a

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540

LABORATORY SHEAR STRENGTH OF SOIL

NSF Equipment Grant (ENG78-10435). University College London constructed the DSC under the supervision of J. R. F. Arthur, who spent his sabbatical leave at MIT during the 1978-79 academic year, and also processed the radiographs-photographs for the strain measurements. References |/1 Casagrande, A. and Carillo, N.. Boston Societv of Civil Engineers, Vol. 31, 1944. pp. 74-87. [21 Arthur, J. R. F., Chua, K. S., and Dunstan, T., Geotechnique, Vol. 27, No. 1, 1977, pp. 13-36. [3] Rodriguez del C , J. L, "Induced Anisotropy in a Loose Sand," Ph.D. thesis, University of London, 1977. \4] Oda. U.. Soils und Foundations. Vol. 12, No. 1, 1972, pp. 17-36. 15) Arthur, J. R. F. and Menzies, B. K., Geotechnique, Vol. 22, No. 1, 1972, pp. 115-128. |6| Arthur, J. R. F. and Phillips, A. B., Geotechnique, Vol. 25, No. 4, 1975, pp. 799-815. |7] Oda, M.. Koishikawa, I., and Higuchi, T., Soils and Foundations. Vol. 18, No. 1, 1978, pp. 25-38. \H] Kirkpatrick, W. M. and Belshaw, D. J., Geotechnique. Vol. 18, No. 3. 1968. pp. 336-350. [9] Phillips, A. B., "Strength and Deformation of Layered Sand," Ph.D. thesis, University of London, 1972. \10\ Arthur, J. R. F., British Journal of Non-Destructive Testing. Jan. 1977, pp. 9-13. [//] Arthur, J. R. F., Chua, K. S., Dunstan, T., and Rodriguez del C , J. I., Journal of the Geotechnicul Engineering Division. American Society of Civil Engineers, Vol. 106, GT4. April 1980, pp. 419-433. \12] Bekenstein, S., "Directional Shear Tests on Leighton Buzzard Sand", S. M. thesis. Department of Civil Engineering, Massachusetts Institute of Technology, 1980. [13] Mahmood, A., Mitchell, J. K., and Lindblom, U. in Soil Specimen Preparation for Laboratory Testing, ASTM STP 599, American Society for Testing and Materials, 1976, pp. 169-192. [14] Arthur, J. R. F, Dunstan, T., Al-ani, 0- A. J. L., and Assadi, A., Geotechnique, Vol. 27, No. 1, 1977, pp. 53-74. [15] Wissa, A. E. Z., Martin, R. T., and Garlanger, J. E. in Proceedings, American Society of Civil Engineers Special Conference on In Situ Measurement of Soil Properties, Raleigh, N.C., Vol. 1, 1975, pp. 536-545.

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Gilbert Y. Baladi,'R. W. Lentz,^ T. Goitom,'and T. D. Boker'

Shear Strength of Cohesionless Soils from Incremental Creep Test Data

REFERENCE: Baladi, Gilbert Y., Lentz, R. W., Goitom, T., and Boker, T. D., "Shear Strength of Cohesionless Soils from Incremental Creep Test Data," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 541-550. ABSTRACT: Results of incremental creep tests performed on cohesionless subgrade materials and stamp sand are presented with the results of conventional triaxial tests performed on the same soil at comparable density and water content. The Mohr-failure envelope and the shear strength data from the incremental creep tests are presented. The shear strength values of the specimens of the incremental creep tests are compared with the shear strength values obtained from conventional triaxial and cyclic triaxial tests. This comparison showed that the incremental creep test data could be and were used to model and predict the behavior of granular materials subjected to cyclic loading. KEY WORDS; shear strength, cohesionless soils, incremental creep tests, cyclic loading, triaxial loading, plastic strains

Permanent deformation of a composite pavement system is the result of two different mechanisms: densification (volume change) and shear deformation (plastic flow with no volume change) [/.2].^ The portion of the deformation due to densification can be minimized by proper compaction control during construction \2-5\. The limitation of plastic flow on the other hand is a basic requirement in any structural design of a pavement system. Consequently, the success of such a design method will depend upon the availability of reliable procedures for the determination of constitutive strength and stress-deformation relationships for pavement and subgrade materials \l,3.4,6-12\. Further, researchers have indicated the need for the develop'Assistant Professor of Civil Engineering, Michigan State University, E. Lansing, Mich. 48824. ^Assistant Professor of Civil Engineering, University of Missouri, Rolla, Mo. •'Research assistant, Michigan State University, E. Lansing, Mich. 48824. •"Ministry of Public Works, Monrovia, Liberia. ^The italic numbers in brackets refer to the list of references appended to this paper.

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reserved); pursuant

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02:25:09

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No

542

LABORATORY SHEAR STRENGTH OF SOIL

ment of short and simplified test methods such that the time and man power requirements for each test are kept at a minimum [4,8,9,11,13]. This paper introduces a simplified testing procedure (incremental creep test) whereby the parameters of the test could be and were used to calculate the shear strength and to predict the accumulated plastic deformation of cohesionless materials subjected to cyclic loading. This incremental creep test may be described as a typical conventional triaxial test except that the axial loading is increased incrementally. Each increment is left on the sample until the axial strain rate reaches a certain value. Test Materiak The primary material used in this investigation was a clean uniform sand which is a typical subgrade soil encountered in the northern part of Michigan's lower peninsula. The material was obtained from test site 2-N at a depth of 0.6 to 0.9 m (2 to 3 ft) beneath the roadway of U.S. 27 near Grayling, Michigan, as part of a previous research project [14]. The soil is of the Grayling soil series as defined by the Michigan Department of Transportation (MDOT) Soil Manual [15]. The grain size distribution of this material is shown in Fig. 1; also shown are the specific gravity, absorption capacity, and coefficient of uniformity. Moisture-density relationships at three different compaction efforts are shown in Fig. 2. The top two curves were obtained using AASHTO Standard Methods T-99 and T-180 [16] [ASTM Methods for Moisture-Density Relations of Soils and Soil-Aggregate Mixtures Using 5.5-lb (2.49-kg) Rammer and 12-in. (305-mm) Drop (D 698-78) and ASTM

100

80

C^ = 1.80 Gs = 2.62

S

Absorption Capacity = 0.44%

60

a w 20 _

00

'•

•

•

•

I

•

ko-O.

•

'

•

•

'

•

•

•

1. 0.1 0.01 Equivalent Grain Size Diameter (mm)

'

0.001

FIG. I—Grain size distribution curve of highway subgrade sand.

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BAUDI ET AL ON SHEAR STRENGTH OF COHESIONLESS SOILS

543

S = 100%

Degree of Saturation = S = 60%

1.7

O ^

ASTM Method D 1557-78 ASTM Method D 698-78

Q

ASTM Method D 698-78 r e d u c e d to 10 b l o w s / l a y e r 3 1 gm/cm = 62.4 pcf I

1 10

I 15

1 20

I 25

Water Content, (%) FIG. 2—Moisture-density

relationship for highway subgrade

sand.

Methods for Moisture-Density Relations of Soils and Soil-Aggregate Mixtures Using a 10-lb (4.54-kg) Rammer and 18-in. (457-mm) Drop (D 1557-78), respectively]. These methods require that samples be compacted in layers (three for T-99 and five for T-180) into a 943.9-cm3 (1/30-ft^) cylindrical mold by applying 25 hammer blows per layer. The hammer for Method T-99 weighs 2.49 kg (5.5 lb) and is dropped 30.48 cm (12 in.). Method T-180 requires a hammer that weighs 4.52 kg (10 lb) and drops 45.72 cm (18 in.). The resulting compactive effort applied is 18 062 cm-kg/cm^ (12 375 ft-lb/ft^) for Method T-99 and 82 100 cm-kg/cm^ (56 250 ft-lb/ft^) for Method T-180. The bottom curve in Fig. 2 was obtained using a compaction effort of 7224 cm*kg/cm^ (4950 ft*lb/ft^). The procedure used was the same as for Method T-99 except that only 10 blows were applied to each layer. The second material used in this study was a stamp sand obtained from Michigan Department of Transportation, Testing and Research Division. Stamp sand is a material that is the product of stamp-mill crushing of rock, uniformly graded in size from coarse to fine, approximately all of which will pass No. 4 U.S. Standard sieve and be retained on No. 100 [75]. The grain size distribution of the samples obtained is shown in Fig. 3; also shown are specific gravity, absorption capacity, and coefficient of uniformity. Moisturedensity relationships for stamp sand at three different compactive efforts are Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

544

LABORATORY SHEAR STRENGTH OF SOIL

100 ^*^No

C =3.25 \

60

-

40

-

20

-

0

II

G = 2.71

\

80 -

^

Abscrption Capacity = 1.8%

\

1

1 1 1 1 1 J..! — 11

10

It 1 l.,L.l„,t, 1

1

1 " •• ' • •

•

^ , 1 1 0.001

1 t1 1J . ±

1 0.1 0.01 Equivalent Grain Size Diameter,(mm)

FIG. 3—Grain size distribution curve of stamp sand.

shown in Fig. 4. The procedures used to obtain these relationships were identical to those used for the highway subgrade sand. Experimental Procedure The test samples were compacted at specified densities and water contents using a specially designed compaction mold that can be attached to the base pedestal of the MTS hydraulic system [17]. After compaction, the samples were trimmed at the top, the triaxial cell was assembled, and the desired lateral pressure was applied. At this point all readings were recorded (two axial and two radial linear variable differential transformers (LVDTs), pore pressure transducer, and load cell). The axial loading was applied gradually in increments of approximately 10 percent of the estimated sample strength [18]. The size of the load increments was reduced as the failure stress was approached to allow for a reliable determination of strength. Each increment of load was maintained until the rate of strain decreased to less than 3.3 microstrain per second at which time the deformation reading was recorded. Both load and deformation readings were read from a digital voltmeter. It should be noted that the load control mode of the MTS electro-hydraulic system does not allow the load to decrease to the ultimate strength level as the sample deforms [17]. Khosla and Wu used similar procedures to study stress-strain behavior of sand [19]. Figure 5 shows the general stress path of the incremental creep test. The horizontal axis represents the value of the first stress tensor invariant (Jj),

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BALADI ET AL ON SHEAR STRENGTH OF GOHESIONLESS SOILS

545

S = 100%

Degree of Saturation = S - 60%

10 15 Water Content, (%) O ^

ASTM Method D 1S57-78 ASTM Method D 698-78

Q

ASTM Method D 698-78 reduced to 10 b l o w s / l a y e r 1 gm/cm

3

~ 62.4pcf

FIG. 4—Moisture-density relationship for stamp sand.

while the vertical axis is the square root of the second invariant of the stress deviator tensor {\U{) [20], where / , = '/3(a, + 2a,) 4j7

=

N/'/3 (ff|

+

2CT3)2 -

(1) 2CT,ff3 -

(7^3

(2)

Results and Discussion The ratio of the principal stress difference to the hydrostatic pressure and the value of the total sample strain resulting from the incremental creep tests for the highway subgrade materials and the stamp sand are plotted in Figs. 6 and 7, respectively. The hydrostatic pressure of each test is also shown in the

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546

LABORATORY SHEAR STRENGTH OF SOIL

./^

f

y——

I Stress path in thejj' time plane

Stress path in thejjj, Jj^/3 plane

time

Stress path in the Ji/3, time plane

:: i-^ =

U

(trj^ + 2
FIG. 5—Time dependent stress path in terms of the stress tensor and stress deviator tensor invariants.

.8 1.0 Total axial s t r a i n (%)

1.2

1.4

FIG. 6—Stress ratio versus total axial strain for highway subgrade sand (1 kPa = 145.038 X I0~^ psi).

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BAUDI ET AL ON SHEAR STRENGTH OF COHESIONLESS SOILS

547

25 psi

.6 .8 Total axial strain

1.0 (%)

FIG. 7—Stress ratio versus total axial strain for stamp sand (I kPa = 145.038 X 10 ' psi).

figures. The stress conditions at failure^ for each of the samples are plotted as Mohr circles in Figs. 8 and 9, respectively. The failure envelopes constructed tangent to the circles in each figure are slightly curved. This indicates that the angle of internal friction, <^, decreases somewhat as the confining pressure is increased. This is consistent with results expected for uniformly graded sand [21]. As indicated in Fig. 8, the angle of internal friction for the highway subgrade sand was found to vary from 43 deg at confining pressure of 34.47 kPa (5 psi) to 38 deg at confining pressure of 344.74 kPa (50 psi). A conventional triaxial test on duplicate samples showed the angle of internal friction to vary from 36 to 45 deg for the same range of confining pressure. Table 1 provides a list of the total vertical strain at failure and the angle of shearing resistance for both the incremental creep (IC) test and the conventional triaxial (CT) test data. Examination of the values listed in Table 1 indicates that the failure envelope is different for the IC test and CT test. This difference, however, is small in the value of the angle of internal friction and very significant in the ''Failure stress (strength) is defined in this paper as the stress at which the sample undergoes large rapid deformation.

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548

LABORATORY SHEAR STRENGTH OF SOIL

Mohr-failure envelope

Compacted at 99% ASTM Method D 1557-7 f

. 38" - 43"

1 kPa = 145.038 x 10^'psl

FIG. 8—Mohr circles for the incremental

creep tests of highway subgrade

materials.

600

450

w = 7.15% Compacted at 94% Of ASTM Method D 6 9 8 - 7 8 ^ = 41° - 51° 1 kPa = 145.038 x 10 ' p s i Mohr-failure envelope

-300

iSl50

150

300

450 600 Normal S t r e s s , (kPa)

FIG. 9—Mohr circles for the incremental

750

creep tests of stamp

sand.

total vertical strains. Khosla and Wu [19] reported that the angle of internal friction obtained from the CT test is higher than those from cyclic triaxial tests. Also, cyclic triaxial test data of the highway subgrade materials and the stamp sand tend to confirm Khosla and Wu's findings. These data showed that the failure envelope, obtained from incremental creep test, more accurately represents the failure envelope obtained from cyclic triaxial tests. Further, it was shown [22,23] that the accumulated plastic strain under any

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BALADI ET AL ON SHEAR STRENGTH OF COHESIONLESS SOILS

549

TABLE 1—Total vertical strain and the angle of shearing resistance from incremental creep (IC) test and conventional triaxial fCT) test data." IC Test

CT Test

03, kPa

t. %

0, deg

6, %

34.47 193.05 344.47

0.6 L6 L2

43 40 38

6.0 6.5 6.3

, deg 45 40 36

"1 kPa = 145.038 X 10 ^ psi.

number of load repetitions could be accurately predicted using the stressstrain curves from the incremental creep tests. Conclusions The use of the incremental creep test data (stress-strain curve and failure envelope) offers a promising approach to modeling and predicting the behavior of granular materials subjected to cyclic loading. Compared with the conventional triaxial test, the incremental creep test is simpler and requires less time, simpler equipment, and much less man power to execute. Parameters obtained from the IC test were successfully used to predict the elastic and plastic behavior of granular materials subjected to cyclic loadings. References [/] Barksdale, R. D. in Proceedings, 3rd International Conference on the Structural Design of Asphalt Pavements, London, 1972, pp. 161-174. [2] Yoder, E. J. and Witczak, M. W., Principles of Pavement Design. 2nd ed., Wiley, New York, 1975. [3] AASHO Committee on Design, AASHO Interim Guide for Design of Pavement Structures. American Association of State Highway Officials, 1972, Washington, D.C. [-^l Monismith, C. L., Ogawa, N., and Freeme, C. R., Transportation Research Record. No. 537, 1975, pp. 1-17. [5] Roston, J. P., Roberts, F. L., and Baron, W., "Density Standards for Field Compaction of Granular Bases and Subbases," National Cooperative Highway Research Program 172, 1976, Washington, D.C. |6] Brown, S. F., Journal of the Geotechnical Engineering Division. American Society of Civil Engineers, Vol. 100, No. GT7, July 1974, pp. 825-841. [7\ Finn, F. N., Nair, K., and Monismith, C. L. in Proceedings. 3rd International Conference on the Structural Design of Asphalt Pavements, London, 1972, pp. 392-409. [8] Hufferd, W. L. and Lai, J. S., "Analysis of N-Layered Viscoelastic Pavement Systems, "Final Report to Federal Highway Administration, Report No. FHWA-RD-78-22, 1978. |9) Kenis, W. J. in Proceedings. 4th International Conference on the Structural Design of Asphalt Pavements, Ann Arbor, Mich., 1977, Vol. I, pp. 101-130. [10] Nair, K. and Chang. C. Y., "Flexible Pavement Design and Management-Materials

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550

LABORATORY SHEAR STRENGTH OF SOIL

Characterization," National Cooperative Highway Research Program 140, Washington, D.C., 1973. [//] Pell, P. S. and Brown. S. F. in Proceedings, 3rd International Conference on the Structural Design of Asphalt Pavements, London, 1972, pp. 326-342. [12] Young, M. A. and Baladi, Gilbert Y., "Repeated Load Triaxial Testing — State of the Art," Division of Engineering Research, Michigan State University, E. Lansing, Mich., March 1977. [13] Brown, S. F., Transportation Research Record. No. 616, 1976, pp. 22-27. [14] Baladi, Gilbert Y. and Boker, T. D., "Resilient Characteristics of Michigan Cohesionless Roadbed Soils in Correlation to the Soil Support Values," Final Report, Grant 75-1679, Division of Engineering Research, Michigan State University, E. Lansing, Mich., 1978. [15] Field Manual of Soil Engineering. 5th ed., Michigan Department of State Highways, Lansing, Mich., Jan. 1970. [16] Standard Specifications for Highway Materials and Methods of Sampling and Testing. 11th ed., American Association of State Highway and Transportation Officials, Washington, D.C., 1974. [17] Lentz, R. W., "Permanent Deformation of Cohesionless Subgrade Material under Cyclic Loading," Ph. D. thesis, Michigan State University, E. Lansing, Mich., 1979. [18] Bishop, A. W. and Henlcel, D. J., The Measurement of Soil Properties in the Triaxial Test. 2nd ed., Edward Arnold, London, 1%2. [19] Khosia, V. K. and Wu, T. H., Journal of the Geotechnical Engineering Division. American Society of Civil Engineers, Vol. 102, No. GT4, April 1976, pp. 303-321. [20] Baladi, G. Y., "Lecture Series on Constitutive Equations," given at Purdue University, West Lafayette, Ind.; conducted by the Waterways Experiment Station, Structure Laboratory, Vicksburg, Miss., 1980. [21] Lambe, T. W. and Whitman, R. V., Soil Mechanics. Wiley, New York, 1%9. [22] Lentz, R. W. and Baladi, Gilbert Y., "Simplified Procedure to Characterize Permanent Strain in Sand Subjected to Cyclic Loading." Proceedings. International Symposium on Soils under Cyclic and Transient Loading, Swansea, U.K., Jan. 1980., published by A. A. Balkema, Rotterdam, 1980. [22] Lentz, R. W. and Baladi, Gilbert Y., "I^diction of Permanent Strain of Sand Subjected to Cyclic Loading," Transportation Research Board, No. 749, National Academy of Science, Washington, D.C. 1980.

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J. R. Lambrechts^ and J. J. Rixner^

Comparison of Shear Strength Values Derived from Laboratory Triaxial, Borehole Shear, and Cone Penetration Tests

REFERENCE: Lambrechts, J. R. and Rixner, J. J., "Comparison of Shear Strength Values Derived from Laboratory Triaxial, Borehole Shear, and Cone Penetration Tests," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 551-565. ABSTRACT; To determine the shear strength of two different soils, in situ and laboratory tests were performed and the results compared. The soil shear strength parameters were required to evaluate the cause of movements of a steel sheet pile cofferdam in which piles were being driven for a bridge pier. Two in situ techniques, the Quasi-Static Cone Penetration Test and the Borehole Shear Test, and laboratory ClU triaxial compression tests were used to determine the drained shear strength parameters (c and 0) of silt and varved silt soils. Shear strength parameters derived from all three procedures were in close agreement. The angle of internal friction of the varved silt ranged from 28 to 33 deg, and the range for the silt was 32 to 36 deg. Soil densification during sampling and sample transportation is thought to have slightly increased ^-values from the CIU tests. Based on field observations, slope inclinometer measurements, and tension crack occurrence around the land-side of the cofferdam, it was concluded that a "classical" active earth pressure wedge acted against the land-side of the cofferdam. An overall equivalent 0, ranging from 26 to 34 deg, was derived from the location of this wedge.

KEY WORDS: varved silt, silt, shear strength, angle of internal friction, borehole shear test, cone penetrometer test, triaxial test, sample disturbance, active earth pressure

Two in situ test procedures, the Borehole Shear Test, which has had relatively limited use in geotechnical engineering practice, and the Cone Penetration Test, were used in conjunction with a laboratory triaxial testing program to evaluate shear strength of silt and varved silt soils. Shear strengths of these soils were required for an evaluation of cofferdam in' Staff engineer and vice president, respectively, Haley & Aldrich, Inc., Cambridge, Mass. 02142. 551 Copyright by Downloaded/printed Copyright 1981 University of

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552

LABORATORY SHEAR STRENGTH OF SOIL

stability. Results of each type of test are presented and remarks made regarding the relative agreement of shear strengths derived by each procedure. Observed soil movements resulting from cofferdam instability are also discussed as they relate to the evaluation of soil shear strength for these two strata. The causes of cofferdam instability are not addressed. Background During pile driving inside a cofferdam for a bridge pier in the Ashuelot River in Keene, New Hampshire, deflections of up to 30 cm occurred in the long sides of the 21 by 4.5 m steel sheet pile cofferdam. Slope inclinometers installed 3.4 m from the land-side of the cofferdam showed lateral soil movements of 18 to 23 cm toward the river, and cracks in the soil around the land-side of the cofferdam were observed. Pile driving was halted and an assessment was made of the overall stability of the cofferdam. Specific soil stratification and shear strength properties required to evaluate the movements could not be determined from available subsurface information and soil properties. Ten additional Standard Penetration Test (SPT) borings were drilled to better define subsurface stratigraphy; three of these borings were near the distressed cofferdam, the other seven were at other bridge pier and abutment locations. A cross section of the cofferdam presented in Fig. 1 shows soil stratigraphy interpreted from all subsurface information, slope inclinometer displacements, and locations of ground surface cracks adjacent to the slope inclinometers. The soil strata shown in Fig. 1 were generally defined as follows: • Embankment fill—loose to very compact, medium to fine sand with traces of silt, coarse sand, and gravel. • Flood plain alluvium—loose to medium compact layers of silty medium to fine sand and silt with little fine sand. • Varved silt—predominantly a very soft to soft silt in layers 6 to 13 mm thick (occasionally up to 80 mm thick) separated by thin clay laminae 1 to 3 mm thick. • Silt—loose to medium compact silt with traces of fine sand. • Deltaic sand—loose to medium compact, medium to fine sand. • Glacial till—very compact, sandy silt to silty or gravelly coarse to fine sand. Ranges of classification and identification properties for the silt and varved silt soils, including total unit weight, natural water content, Atterberg Limits, and grain size distribution data, are presented in Table 1. Shear strength of each soil stratum was required to assess cofferdam stability. Reasonable shear strength values for the fill, alluvium, deltaic sand, and glacial till, all of which were predominantly sands, could be

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LAMBRECHTS AND RIXNER ON SHEAR STRENGTH VALUES

LOCATIONS OF CRACKS IN S O I L BEHIND:

SLOPE INDICATOR HORIZONTAL D E F L E C T I O N S (m)

COFFERDAM BRACING

553

SI-14

SI-15

i ,J_

EMBANKMENT FILL ,/

1,

—

FLOOD PLAIN ALLUVIUM

^iO°?oo^

- °°°-e --""-• 0

1 2

"

' SCALE

DELTAIC

SAND

GLACIAL

TILL

LOCATION

3

4

5

°^

d.

o

t

D

INCLINOMETER CASING

^'-°''^

IN

METRES

FIG. 1—Section and subsurface profile.

TABLE 1—Classification and identification properties. Soil Stratum Property

Varved Silt

Silt

Total unit weight, (kg/m-')" Specific gravity Natural water content, % Liquid limit, % Plastic limit, % Percent finer than: 0.074 mm (No. 200 sieve) 0.03 mm 0.01 mm 0.003 mm 0.001 mm

1722 to 1849 2.80 39.5 to 50.2 37.6 to 58.5 22.2 to 27.7

1921 to 2047 2.74 25.5 to 29.3

96 to 99 93 to 97 75 to 83 33 to 48 20 to 35

85 to 98 40 to 58 6 to 15

non-plastic

"lOOkg/m^ = 6.24 1b/ft^.

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554

LABORATORY SHEAR STRENGTH OF SOIL

derived from SPT A^-values. However, determination of shear strength values for the silt and the varved silt soils was more difficult. Further borings and in situ testing were carried out near the distressed cofferdam to assess the shear strengths of the silt and varved silt strata. Additional work included three cased 15.2-cm-diameter borings, in which 7.6- and 12.7-cm-diameter thin-walled tube samples of soil were taken and Borehole Shear Tests performed. Also, Quasi-Static Cone Penetration probes were performed at three locations. A plan of the cofferdam, showing locations of the nearby additional borings, cone penetration probe tests, the adjacent slope inclinometers, and the crack in the soil around the cofferdam, is presented in Fig. 2. Shear Strength Test Procedures and Results To determine the shear strength parameters of the silt and varved silt strata, detailed field and laboratory test programs were conducted. In situ testing included Borehole Shear Tests and Quasi-Static Cone Penetration Tests. Laboratory consolidated isotropically undrained triaxial compression tests with pore pressure measurements were performed on specimens trimmed from 7.6- and 12.7-cm-diameter thin-walled tube samples of both soils. Borehole Shear Tests Eight (8) Borehole Shear Tests (BST) were performed: one in the varved sih and two in the silt in Borehole B-201, two BSTs in the varved silt and two in the silt in Borehole B-203, and one additional BST in the underlying sand in Borehole B-203. The Borehole Shear Test is a test in which the shear resistance of the soil is determined in the borehole by pressing two ridged plates horizontally against the borehole sides under a controlled pressure (normal stress) and then pulling upwards on the shearing device at a constant rate until the maximum force is reached (which can be converted to a maximum shear stress). A schematic representation of the Borehole Shear Device is shown in Fig. 3. The test is repeated at the same location by increasing the pressure on the plates and again pulling on the shearing device. Sufficient time must be allowed for the borehole sides to consolidate at each level of normal stress before shear force is applied. The rate of shearing should be slow enough to allow drained conditions in the shear zone. Shear strength parameters c and 4) are determined by plotting shear stress versus normal stress and drawing the Mohr-Coulomb failure line. Equipment used and test procedures were as recommended by Wineland [2].2 The BSTs were performed in holes left after taking 7.6-mm-diameter 2 The italic numbers in brackets refer to the list of references appended to this paper.

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LAMBRECHTS AND RIXNER ON SHEAR STRENGTH VALUES

555

APPROXIMATE LOCATION OF CRACK IN SOIL WALE AND STRUT BRACING SYSTEM

8-7

B-6

o

STANDARD PENETRATION TEST BORINGS

DC-2 0

1 2

SCALE

3 IN

4

5

METRES

THIN-WALLED TUBE SAMPLE BORINGS CONE PENETRATION TEST

SI-14 -z4- " ' S L O P E

INCLINOMETER

FIG. 2—Site and subsurface investigation plan.

thin-walled tube samples of soil. Ten minutes were allowed for consolidation of the borehole sides under the first level of normal pressure at each test location; five minutes were allowed for consolidation at each subsequent pressure level. The rate of shear head displacement was generally 0.05 mm/s, as recommended by Wineland. Plots of shear stress versus normal stress for the Borehole Shear Tests

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556

LABORATORY SHEAR STRENGTH OF SOIL

UPWARD PULL CREATES SHEAR FORCE ON SHEAR HEAD PLATES

HYDRAULIC PRESSURE EXPANDS SHEAR PLATES AGAINST BOREHOLE SIDES, CREATING NORMAL FORCE

FIG. 3—Schematic of Borehole Shear Device (after Mitchell el al [l]).

performed in the varved silt and the silt strata are presented in Fig. 4. Generally, a friction angle and cohesion intercept were easily derived; however, straight-forward interpretation of the results of Test 3 in Borehole B-201 and Test 4 in Borehole B-203 was difficult. Quasi-Static Cone Penetration Tests The three Quasi-Static Cone Penetration Tests (CPT) were performed in accordance with ASTM Method for Deep, Quasi-Static, Cone and FrictionCone Penetration Tests of Soil (D 3441-79). A Fugro mechanical-frictiontype cone which measured sleeve friction 20 cm behind the cone was used. Plots of cone resistance, q^, and friction ratio, FR, for each test are presented in Fig. 5. Stratigraphies shown are from the adjacent borings as noted and may vary from conditions actually encountered in each CPT.

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LAMBRECHTS AND RIXNER ON SHEAR STRENGTH VALUES

16

BOREHOLE B-201 VARVED SILT

557

BOREHOLE B-201 SILT TEST 2 -

o

8

TEST 3

TEST I

BOREHOLE B-203 VARVED SILT

BOREHOLE B-203 SILT

m 12 TEST I-

TEST 4 -

TEST 3

D ° J

\

D D I

0 i

[

16 0 NORMAL STRESS, a,,

I

\

I

16

L.

20

(Pax 10*), { l o " Pa = 208.9 Ib/ft^)

FIG. 4—Borehole Shear Test results.

Laboratory Triaxial Tests Consolidated isotropically undrained triaxial compression tests with pore pressure measurements, CIU, were performed on samples of the varved silt and the silt soils. Test specimens were trimmed from thin-walled tube samples of soil and were 36 mm in diameter and approximately 74 mm long. Test procedures were generally as outlined by the U.S. Army Corps of Engineers [3]. Sufficient back pressure was applied to achieve pore pressure response, B-value, greater than 0.95 prior to shear for each test. The rate of axial strain during shear was 2.2 percent per hour. Plots of axial stress difference, CTJ — a^, and change in pore pressure, AM, versus axial strain, ta, for the varved silt and the silt soils are presented in Figs. 6A and 6B, respectively. Four specimens of each soil type were tested. Interpretation and Discussion of Strength Test Data The friction angle, (j), and cohesion, c. from Borehole Shear Tests were determined from data plotted in Fig. 4 and are summarized in Table 2.

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558

UBORATORY SHEAR STRENGTH OF SOIL

I ^

O O

(SSJtaui)

33WdHns ONnOHO mOT39

Hld30

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LAMBRECHTS AND RIXNER ON SHEAR STRENGTH VALUES

c

Si.T

A

.

1 .

VARVED SIL^

A

o

-

V

0 69

1 38

2 76

559

T

X 2C INITIAL E ' f CONFINING PRESSURE IPo X 10^)

0

35

FIG. 6—Triaxial Test stress-slrain data.

Several data points in Test 3 from Borehole B-201 in the silt soil (two points not shown, shear stress greater than 16 Pa) were not considered in determining and c because the observed shear stress values were judged to be inordinately high. The two points used to determine 4> and c were achieved

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560

LABORATORY SHEAR STRENGTH OF SOIL

TABLE 2—Summary of Borehole Shear Test results.

Boring No.

Test No.

Soil Stratum Tested

Apparent Angle of Internal Friction, deg

B-201 B-201 B-201 B-203 B-203 B-203 B-203

1 2 3 1 2 3 4

varved silt silt silt varved silt varved silt silt silt

19 36 32 29 31 33 34

Apparent Cohesion, Pa" 6.0 11.5 12.9 9.6 3.4

X X X X X 0 0

10^ 103 103 103 103

"103 Pa = 20.88 lb/ft2.

after the shear plates had been retracted and reseated in the hole. In Tests 2, 3 and 4 in Borehole B-203, it is believed that the decrease in shear stress at increasing normal stress was due to a decrease in soil strength in the sides of the borehole to a residual value due to shearing by the plates. Full expansion of the shear head may also explain the low shear stress values. The
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LAMBRECHTS AND RIXNER ON SHEAR STRENGTH VALUES

561

TABLE 3—Summary of Cone Penetration Test results. Soil Stratum Varved Silt

Silt

Cone Penetration Test No.

9c*, Pa''

FR*, %

9 / , Pa''

FR*, %

DC-l" DC-2 DC-3

0 0 3.9 X 105

undefined undefined 7

5.4 X 105 29.4 X 105 27.5 X 105

5.0 2.5 2.6

" Results possibly adversely affected by prior boring B-8, 0.6 m away. * Average values used in determining shear strength parameters. ' P a = Pascals; 5 X 105 pg = 5 1 kg/cm^.

used to estimate values of ^ from q^ values; (j> ranged from 26 to 30 deg for the varved silt and from 28 to 34 deg for the silt. Trofimenkov's method gave a $ value several degrees below the other methods and appears to be too conservative, a conclusion also reached by Mitchell and Lunne. The cone penetration test would therefore predict $ values of 28 to 30 deg for the varved sih soil and 32 to 34 deg for the silt soil. From the CIU test stress-strain plots in Fig. 6, it may be observed that the varved silt and clay contracted when sheared, behavior indicative of a loose soil. However, the silt dilated and behaved as a dense soil. Shear strength parameters were determined from stress path plots for each laboratory CIU test as shown in Fig. 7. The stress path for test specimen CIU-4 was slightly above the trend of the other three silt samples probably because its density was 11.5 kg/m^ greater than the other silt specimens. The effective angle of friction of the varved silt was determined to be 33 deg and that of the silt soil 36 deg. Comparison of Results Summarized in Table 4 are the shear strength parameters determined by the Borehole Shear Tests, Cone Penetration Test, and CIU triaxial test for both the varved silt and the silt soils. In general, the CIU tests predicted higher values of 4> than did either in situ test. This may have resulted from minor amounts of densification thought to have occurred to varying degrees to all samples during sampling and transport to the laboratory (one 61-cmlong sample was observed to have decreased nearly 5 cm in length; it was not tested). The Borehole Shear Test procedure appeared to yield reasonable values of 0 and c, although several of the BST data points were disregarded in determination of shear strength parameters. These shear strength values were close to those from the triaxial tests. Except for Test 1 in Borehole B-201,

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562

LABORATORY SHEAR STRENGTH OF SOIL

X

X

CT; (N

in

^H ^ O — II II g II

^^

ao oc u u •o -o O *N m n

•o

O ttO a> T3 vO

• ^

,

m o ii m m

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OS oil •a -a

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II II II II -s--s--s--e-

^ c s

£ B

I ca

<

*. 3

li|

c S

c

O Cu

rt

2 .i> iO e " I S S P = -5 JQ

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LAMBRECHTS AND RIXNER ON SHEAR STRENGTH VALUES

563

1^

•

0 to

•

n

•

o

<

<

U3

CO

o

O

01

o

1_i

a) Q Ui

-1 in

> < >

— U. 1/5 X

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564

LABORATORY SHEAR STRENGTH OF SOIL

the BST (t> and c values were indicative of drained test conditions. The close agreement of <^ and c values of one BST in silt with those from the CIU tests on silt may be due to normal scatter in the BST data, BST test at an initially denser location in the silt, or soil densification under the BST consolidation pressures of the shear plates. Analysis of the cone penetration test data in the varved silt was difficult because q^. from each test in the upper half of the stratum was less than 5 X 10^ Pa (5 kg/cm^) and was often zero. Published correlations between q^ and <}> at such low values of ^^ are rather imprecise. The correlations used, however, indicated a very loose condition (0 = 26 to 30 deg). Borehole Shear Test results confirmed rather low ^-values. The higher ^^-values in the silt soil (generally ^^ ~ 20 to 40 X 10^ Pa) allowed easier determination of (j) from q^ using correlations developed for fine sands; the / ranged from 26 to 34 deg. Summai^ and Conclusions In situ and laboratory tests were used to determine shear strengths of two soils required to evaluate the cause of large movements of a steel sheet pile cofferdam. Both the Borehole Shear Device and the Quasi-Static Cone Penetrometer were successfully used in silt and varved silt soils to define drained shear strength parameters. Correlations developed for fine sands were used to relate q^ to in the cone penetration tests. Laboratory CIU triaxial tests on thin-walled tube samples of these soils yielded values somewhat higher than the field tests. It is thought sample densification during sampling and transport may have caused 0 to increase. Standard Penetration Test iV-values were also used to develop 0 values. Friction angles determined by the laboratory and field tests were generally within 3 deg of each other. The inclination of active earth pressure failure wedge against the cofferdam corroborated the ranges of (j).

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LAMBRECHTS AND RIXNER ON SHEAR STRENGTH VALUES

565

Acknowledgments This investigation was carried out for the Materials and Research Division of the New Hampshire Department of Public Works and Highways whose permission to report the findings of this study is appreciated. The Borehole Shear Device and Quasi-Static Cone Penetrometer were supplied by the D.O.T./Federal Highway Administration. C. L. Guild Drilling Company performed the detailed subsurface investigation and performed the in situ testing under the direct supervision of Haley & Aldrich, Inc. personnel. Haig Merguerian of Haley & Aldrich, Inc. supervised the laboratory tests. References [1] Mitchell, J. K., Guzikowski, F., and Villet, W. C. B., "The Measurement of Soil Properties In Situ," Report from Department of Civil Engineering, University of California, Berkeley, 1978, pp. 22, 23. [2] Wineland, J. D., "Borehole Shear Device," in Proceedings, American Society of Civil Engineers, Specialty Conference on In Situ Measurement of Soil Properties, Vol. 1, 1975, pp. 511-522. [3] United States Army Corps of Engineers, Engineering and Design—Laboratory Soils Testing, Manual No. EM 1110-2-1906, U.S. Department of the Army, Washington, D.C., Nov. 1970. I-^J Mitchell, J. K. and Lunne, T. A., "Cone Resistance as Measure of Sand Strength,"iourna/ of the Geotechnicat Engineering Division, American Society of Civil Engineers, Vol. 104, No. GT7, July 1978, pp. 995-1012. (5] Peck, R. B., Hanson, W. E., and Thornburn, T. H., Foundation Engineering, John Wiley & Sons, New York, 1974, p. 310.

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A. J. Lutenegger^ and G. R. Hallberg^

Borehole Shear Test in Geotechnical Investigations

REFERENCE: Lutenegger, A. J. and Hallberg, G. R., "Borehole Shear Test in Geotechnical Investigations," Laboratory Shear Strength of Soil. ASTM STP 740. R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 566-578. ABSTRACT: The concept of Borehole Shear presents a unique alternative in shear strength testing of soil and rock in that tests may be conducted rapidly on the sides of the hole on relatively undisturbed material; therefore the inherent problems associated with obtaining equivalent information from laboratory tests are eliminated. In contrast to other methods of measuring in situ shear strength (that is, vane shear, cone penetrometer and pressuremeter) the Borehole Shear Test (BST) and Rock Borehole Shear Test (RBST) give discrete values of friction angle and cohesion; therefore more complete analyses may be made for such fundamental problems as bearing capacity and slope stability. In the past the BST has been considered a drained test and the effective parameters 0 ' and c' have been reported. This may not always be the case. The general use, operation, assumptions, and problems of the test are examined and examples of the interpretation of resuhs are given. Because of the time, economics, and accuracy of this method, the technique of Borehole Shear should see increased use in future in situ geotechnical testing. KEY WORDS: Borehole Shear, in situ shear strength, shear tests, soil mechanics, shear stress

The concept of Borehole Shear, determining shear strength parameters on the sides of a test borehole, presents a rather unique solution to the problem of in situ evaluation of shear strength of soil and rock. The resultant separate determination of internal friction (0) and cohesion (c) are essential quantities required for solving the stability problems of soil mechanics, that is, earth pressure, bearing capacity, and slope stability. Since its introduction into the literature, the concept of Borehole Shear has remained essentially the same; only the equipment has undergone an evolu' Research Fellow, Geotechnical Research Laboratory, Iowa State University, Ames, Iowa 50010. ^ Chief, Geological Studies, Iowa Geological Survey, Iowa City, Iowa 52240. Copyright by Downloaded/printed University of Copyright

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LUTENEGGER AND HALLBERG ON BOREHOLE SHEAR TEST

567

tionaty process. The current Borehole Shear Test (BST) equipment is lightweight and portable, requires no external power to operate, and a complete test can usually be accomplished in about an hour. Problems have arisen, however, and the most commonly asked question is "What does the Borehole Shear Test really measure?" The purpose of this paper is to address this question by reviewing previous work, presenting new data relative to interpretation of the results, and discussing various problems associated with the use of the test. Borehole Shear Testing The fundamental idea involved in Borehole Shear entails performing a series of direct shear tests on the inside of a borehole [1].^ This is accomplished by forcing serrated plates against the periphery of a hole and pulling the plates axially, along the hole, to induce shear (Fig. 1). As in conventional direct shear testing, a series of tests with increasing applied normal stress (CT„) is performed, while the corresponding shear stress (T) is measured. The results are then plotted to describe the Mohr-Coulomb failure envelope, with internal friction angle i) and cohesion intercept (c). The technique is the same in both soil and rock; however, because of differences in behavior, the test procedure varies. The device currently in use is similar in design and concept to the in situ device of Cambell and Hudson [2] and the interface friction device of Thorley et al [3], both of which have seen limited use. During testing, the shear head is lowered to the desired test depth and the plates are expanded against the hole by CO2 to a known normal stress. The use of a pressure regulator maintains a constant value of a« during testing. Testing is commonly made in a cavity produced by pushing a Shelby tube; however, undersized auger holes may be used, provided the holes are then reamed smooth to the proper size. In soft-to-medium soils, shear plates with a contact area of 32.3 cm^ (5 in.2) are employed. Teeth are composed of twenty-five 60 deg wedges, spaced at 2.5 mm (0.1 in.), as shown in Fig. 2a. This gives a tooth spacing to tooth depth ratio of 1.15. Since a fundamental requirement of the test is to have soil-to-soil shearing, rather than soil-to-plate, it is essential that the shear plates fully penetrate the test material. In softer soils, this presents no problem, and is accomplished by the conventional plates described above. In stiff soils conventional plates may give extremely low or even negative values of cohesion. This is thought to be a result of inadequate seating. Adjacent failure wedges from tooth penetration probably prevent seating of conventional teeth except at extremely high values of normal stress; hence smaller plates and fewer teeth are utilized (Fig. 2b). The tooth spacing to tooth depth ratio of these plates is 5.74. These modified teeth simply replace The italic numbers in brackets refer to the list of references appended to this paper.

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568

UBORATORY SHEAR STRENGTH OF SOIL

f

J

i.

NOMINAL 76 mm ( 3 i n . ] DIA. BOREHOLE FIG. I—Borehole Shear.

0.1

[a]

yvV\A/WWWWVV\AAAAAAAVVV

0.Q87

60" 2.5

0.54

[b]

K_ 60"

Q,Q94

FIG. 2—Shear plate design, (a) BST soft-medium soil; (b) BST stiff soil. (Note: 1 in. = 25.4 mm.)

the conventional teeth on the shear head and, since the area is only 6.5 cm^ (1 in.^), the available nomial and shearing stress ranges are five times that available using conventional plates with the same expansion and pulling apparatus. After allowing time for consolidation foUowmg application of normal stress, usually 5 to 10 min, shearing is induced by pulling the shear head

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LUTENEGGER AND HALLBERG ON BOREHOLE SHEAR TEST

569

along the hole by means of a screw mechanism and closed hydraulic system. Normally the required movement for shearing is only about 5 mm (0.2 in.). The peak value of shear stress is recorded and used in date reduction. Following shear, the shear stress is removed by returning the shear head to the original position, and the normal stress is increased to a higher value. With conventional plates this ensures testing at the same location for all data points. Schmertmann [4] has pointed out that this technique is analogous to state testing in the laboratory, that is, shearing is induced repeatedly in the same soil, at successively higher stresses. The technique of repeatedly shearing the same zone with the BST has been compared with shearing in a fresh zone [5], with both methods giving essentially the same results for . Occasionally the first data point will fall below the linear envelope developed from subsequent points. These data are not usually used in the linear regression for and c, and are generally attributed to inadequate seating of shear plates, which will be discussed further. In using the BST with the smaller, modified shear plates, shearing occurs directly on the face of the borehole and the shearing surface is destroyed. Thus the shear head must be removed from the hole, and the teeth cleaned prior to the next application of normal stress. For successive data points, up to four tests may be conducted at the same depth by simply rotating the shear head. Since the soil may not be identical at all locations, one would expect that the excellent linearity generated by stage testing with conventional plates would be lost. In fact, this is not the case. An alternative testing technique which reduces testing time when using modified plates is to stage test following initial shearing. Since stage testing generally gives lower values of cohesion, the friction angle obtained from this portion of the test is plotted and translocated through the initial data point obtained from fresh shearing. This technique is illustrated in Fig. 3. Interpretation of Test Results As originally introduced [6] the first BST were analyzed on a total stress basis. However, since the tests were performed on a dry silt, the results were reported as effective parameters 4>' and c ' . Comparison with laboratory direct shear and triaxial tests showed that BST results fell in between. Results of comparative studies with conventional laboratory results have been reported by various investigators [1,7-10], A summary of available data for friction angle is shown in Fig. 4. The soil materials tested ranged from cohesionless sands (SW) to cohesive clays (CH). Although a considerable amount of scatter is indicated and BST results fall between drained and undrained, it is of interest to note that, with the exception of one point, all undrained laboratory tests give values lower than BST. In many cases, BST results tend to compare better with drained laboratory results, particularly at higher values of 0. It should be emphasized, however, Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

570

LABORATORY SHEAR STRENGTH OF SOIL

NORMM, STRESS

FIG. 3—Stage testing BST modified shear plates.

that no clear-cut relation exists for all materials. Wineland [10] has suggested that plasticity might be used as a qualitative indication of the drainage conditions; that is, high-plasticity clays may behave more as undrained and lowplasticity soils as drained. This appears to have some merit. The problem of positive pore pressures generated during shear appears to remain a difficult point. In saturated clays, if the soil is sheared at a faster rate than it drains, or if drainage is prohibited, positive pore pressure develops. In sands, or dry cohesive soils, this does not appear to present a problem, and results compare better with drained tests. Positive pore pressures are generally detected by a flattening of the failure envelope. This flattening can also be caused if the shear head is fully expanded, in that the normal stress on the control console can be increased without a further increase in applied normal stress on the shear plates. One method to detect if the flattening is caused by pore pressure is to repeat the test point with increased consolidation time. At present, no provision is made for detecting negative pore pressure. The problem of test drainage must be viewed from an individual test standpoint; saturated clays which have very low permeability should probably be treated as undrained, which would be on the safe side for design. As an example, consider the data shown in Fig. 5 for a very clay-rich shale. With initial void ratio e^ = 0.36 and saturation 5 = 100 percent, these results would no doubt be considered undrained, since the pore water has no means of escape. In some cases, the initial portion of a test may give data which could be considered drained, with the latter portion indicating undrained conditions, as in Fig. 6. For this test data, up to about 193 kPa (28 psi) normal stress, = 31.7 deg, c = 27 kPa (3.9 psi); after 193 kPa (28 psi), <^ = Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

LUTENEGGER AND HALLBERG ON BOREHOLE SHEAR TEST

ACD OCU •CD ACU

triaxial triaxial d i r e c t shear d i r e c t shear

o 40 -

o

A

o

• A.

0 0

o oo

Ay

6A

o EST

/

0

0

20

A A

o

30 -

571

0°

./{.

-

o

A A

10 -_

o/

A

0

o

1 10

A 1 20

1 30

1 40

9 , degrees LABORATORY TESTING FIG. 4—Comparison between reported laboratory <j> and BST <

T, Y = 121.7 pcf (1.95 g/cm £20

w = 16.9% S =1

(() = 4.6 c = 11.5 psi (79.3 kPa)

J_ 10

20

30

40

J_ 50

NORMAL STRESS, psi FIG. S—Undrained BST results—Juniper Hillmember, clay shale.

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572

LABORATORY SHEAR STRENGTH OF SOIL

Y = 115.4 pcf (1.85 g/cm'^) w = 15.3% S = 100%

c^ = 3.9 psi (26.9 kPa) = 20.5* C2 = 10.9 psi (75 kPa)

J

L TO

20

30

40

50

NORMAL STRESS, psi FIG. 6—Drained-undrained BST results—glacial till.

20.5 deg, c = 75 kPa (10.9 psi). A subsequent test at this location, after the water table had risen above the test zone, gave 0 = 20.5 deg, c = 42 kPa (6.1 psi) using the modified shear plates. This illustrates that prior to being fully saturated, results should be interpreted as effective stress; after saturation, and where drainage may not occur, results should be considered on a total stress basis. An interpretation problem previously mentioned often occurs in very stiff or overconsolidated soils using conventional shear plates. In these soils, penetration of the plates may be prevented, particularly at low normal stresses, and results may be misleading. This is illustrated in Fig. 7 which presents data from a test on firm glacial till using conventional plates. Note that the first few data pomts fall well below the envelope derived from the latter points. One might think that the latter points may indicate developement positive pore pressure; however, the saturation is low enough to consider these results on a drained basis. In addition, the initial data points give a negative value of cohesion, again indicative of improper seating. Continuing the test to higher normal stresses produces a realistic failure envelope as shown. The shearing area is taken as the gross contact area of the shear plates. For stiff materials tested with the modified plates and fresh shearing surfaces, this is probably valid since shearing most likely occurs only within that area. For stage testing, where the shear surface is slightly outward from the surface of the hole, end effects may produce an increased shearing area. If this is the case, one would expect only a reduction in cohesion, a result of increased shearing area under zero normal stress. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

LUTENEGGER AND HALLBERG ON BOREHOLE SHEAR TEST

573

Y = 108.6 pcf (1.74 g/cm^) w = 15.9% S =

(|) = 27.0 c = 4.3 psi {29.7 kPa)

10

15

20

25

NORMAL STRESS, psi FIG. 7—Effect

of inadequate shear plate seating.

Two problems related to interpretation which have not been addressed concern the use of drilling mud and borehole disturbance. In cohesionless sands or soft materials below the water table, maintenance of borehole stability often requires the use of drilling mud. The effect of mud on BST results is not known. Since the shear plates probably become filled with the slurry upon insertion, the initial data point may not be a true indication of soil shear strength. However, subsequent points at higher normal stress should provide extension of the shear zone into the proper strata. Borehole disturbance created by drilling operations is a difficult factor to assess and has not been evaluated. In relation to other forms of in situ testing, however, where insertion of various probes is now a common practice, the development of a self-boring device does not appear practical. Limitations In a recent review of in situ techniques for measuring shear strength, Mitchell [//] concluded that the BST is best suited for use in stiff-to-hard clays where an open borehole can be maintained, and for undrained and possibly drained shear strength of residual soils. This is certainly true and tests performed by the authors in glacial till, where borehole stability is not a problem, give excellent results. However, use of the BST in softer materials has not particularly presented any major difficulties. The authors have performed many tests in metastable silts where instability in the form of isolated zones of borehole squeeze is sometimes a problem. The shear head may be encased in a protective shield, lowered into a borehole, and then withdrawn Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

574

LABORATORY SHEAR STRENGTH OF SOIL

prior to testing. This keeps the shear plates clean upon insertion, and allows the shear head to be placed at an otherwise unstable location. In such material drained friction angles as low as 3.4 deg have been measured. Tests have been conducted on a variety of materials, including glacial till, loess, sand, alluvial silts, weathered shale, gumbotill and even lake sediments [7]. As available commercially, the test equipment is supplied with sufficient materials to test at depths up to 7.6 m (25 ft), with additional equipment available to extend the limit of testing to greater depths. One of the most obvious limitations is that a borehole is required; however, as discussed previously, this may be made with any number of sampling devices, preferably a thin-walled tube. Application Since the shear strength of soil is in part dependent on the type of test used in measurement, which test resuhs should be used in analysis? From a realistic standpoint, those tests which accurately describe field behavior appear to be most useful for design. Depending on the field situation, then, the applicability of certain tests is always questionable. Realistically, the BST may be used on any soil mechanics problem which requires knowledge of shear strength parameters 4> and c. Perhaps one of the most versatile applications for the BST has been in the determination of strength parameters for analysis of landslides. A recent criticism of this application [12] contends that the use is limited because shearing in the test occurs in a different direction than that involved in the landslide process, and if the soil is anisotropic, then shear strength determined in the test is probably a measure of the stronger direction. If this is the case, then analysis of slopes with the BST is on the unsafe side. The BST was initially successful in predicting the stability of natural slopes in thick loess [13]. In active landslides where the factor of safety is presumably 1.0 the BST can be conducted directly in the shear zone. Handy and Williams [14] used the BST to analyze an active landslide of compacted fill overlying shale, obtaining a factor of safety equal to 0.9 assuming saturated unit weight and full pore pressure. Two years following successful stabilization, subsequent BST gave a new minimum (saturated) factor of safety of 2.6. Nickel [9] has presented results for active slide investigations in Kansas, where the factor of safety ranged from 0.95 to 1.10. The inability to obtain a reasonable number of undisturbed samples for laboratory testing has also led some investigators to rely on BST results for slope stability analysis [15]. For long-term stability of slopes in soft clays, the measurement of soil creep or time-dependent strain, using the BST has been successfully demonstrated [16] for both primary and tertiary creep behavior. This is achieved by holding both the normal and shear stresses constant and measur-

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LUTENEGGER AND HALLBERG ON BOREHOLE SHEAR TEST

575

ing the shear deformation at various times. The result is a time-deformation curve (Fig.8). The deformation rate may then be calculated from the slope of the linear portion of the creep curve. The yield stress is interpreted by extrapolating to zero deformation rate on a rate versus shear stress diagram (Fig. 9). Laboratory correlation with simple shear tests produced primary creep curves similar to BST curves within the same range of shear stress [76]. By performing tests at different values of normal stress and obtaining a series of creep curves for various values of shear stress, a creep failure envelope may also be developed. It appears that the BST has some definite advantages over other forms of testing for slope stability analysis in that: {!) again, if both 0 and c can be determined, a more precise calculation of factor of safety (F.S.) could be made instead of simply assuming 4> = 0 and using undrained shear strength Su', (2) for active slides, shear strength may be determined directly in the zone of shear to give the most realistic values for calculations; (3) if the area will not allow a drill rig to take samples, the use of a lightweight field test becomes necessary; and (4) measurement of soil creep. Rock Borehole Shear Test (RBST) The concept of Borehole Shear has been extended into in situ rock testing by the developers of the soil device [17] and while perhaps beyond the scope of this discussion it is worthy of mention. The RBST is nearly identical in operation to the BST, with the exception that the equipment has greater

.SANDY CLAY LOAM

600

_a^ " 6 psi (41.4 kPa)

(39 kPa)

J

l__L

J I I_J L I .L I 1 2 1 8 2 4 3 0 3 6 TIME (minutes)

VTfe-

FIG. 8—BST creep curves (modified from Ref 16).

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576

LABORATORY SHEAR STRENGTH OF SOIL

12

SANDY CLAY LOAM w = 20.41 10 t-a^ = 5 p s i

2 O H

A 20 min

<; s Pi o w o 0

_L 2

4

A 50 m i n J L_ 6 8

SHEAR STRESS ( p s i ) FIG. 9—Determination of yield stress {from Ref 16).

capacity to generate higher normal and shearing stresses. Developed primarily for use in mines on soft rock such as coal and shale, comparisons between RBST and triaxial shear show close agreement of friction angle but some loss of cohesion, probably from the seating of the shear plates [17\. Some comparative triaxial data give higher values of friction angle, probably a result of core recovery of the strongest material. Again, the unique advantage of the RBST, apart from the obvious economic factors, is that tests can be run directly in a mine or quarry, on the walls, floor, or ceiling as necessary. A more complete discussion of this test and comparative triaxial analyses is presented by Panek [18]. Conclusions The use of the BST does not eliminate the need for other tests, and it is not meant to be cost comparative with vane shear or the standard penetration test. Where soil conditions are highly variable, the number of tests required to characterize a site might not be cost-effective. Rather, where soil conditions at a site are less complex, BST would be much more economical than laboratory direct shear or triaxial to obtain equivalent information. Test interpretation for effective friction angle and cohesion should be based on judgement of the drainage characteristics of the soil and test conditions.

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LUTENEGGER AND HALLBERG ON BOREHOLE SHEAR TEST

577

As an alternative to other forms of measuring the in situ shear strength of soil and rock, Borehole Shear offers some distinct advantages: 1. Separate determination of both 0 and c. 2. Any borehole which stays open, or presumably can be maintained open with drilling water or mud, may be tested. 3. Time required to obtain a failure envelope is about one hour, depending on consolidation time and test conditions. This is considerably less than for equivalent laboratory tests. 4. In unstable conditions, such as landslides, where the use of drilling equipment is not possible, hand-augered holes may be tested. 5. Tests may be conducted in any direction that the borehole can be made. The BST has been used horizontally in roadcuts, and the REST has been used horizontally to measure the strength of mine pillars, and even upside down, for testing mine roofs. 6. Tests results may be analyzed in the field. This enables the operator to determine if any of the data points need repeating or if more points are required. 7. Tests are conducted in a very small zone, thus decreasing the variability of laboratory testing samples either from more than one hole or sampling tube. 8. The problems of undisturbed sample recovery are eliminated, since one is testing the hole, not the core. 9. Operation of both BST and RBST is simple, and can be carried out easily by technicians or competent drill crews. 10. Test equipment is completely portable and requires no external power sources or specialized drilling attachments. 11. Measurement of soil creep behavior. Problems still associated with this technique of testing include: 1. Interpretation from unknown drainage conditions may be difficult. 2. Effect of borehole disturbance is not known. 3. Effects of drilling mud on results are not known. 4. The proper rate of shear strain has not been investigated.

Acknowledgments This work is a part of ongoing cooperative research by the Geotechnical Research Laboratory, Iowa State University, and the Iowa Geological Survey. Funding in part was provided by the Engineering Research Institute, Iowa State University. The authors wish to thank R. L. Handy for his cooperation and assistance in preparing this manuscript.

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578

UBORATORY SHEAR STRENGTH OF SOIL

References [1] Handy, R. L. and Fox, N. S., Highway Research News, No. 27, 1967, pp. 42-52. [2] Cambell, D. B. and Hudson, W. R., "The Determination of Soil Properties In Situ, "Research Report 89-7, Center for Highway Research, Univ. of Texas-Austin, 1969. [3] Thorley, A., Broise, Y., Calhoon, M. L., Zeman, Z. P., and Watt, W. G. in Proceedings. Conference on In Situ Investigations in Soil and Rocks, Institute of Civil Engineers, London, 1970, pp. 155-165. [4] Schmertmann, J. H. in Proceedings, Conference on In Situ Measurement of Soil Properties, American Society of Civil Engineers, Vol. 2, 1975, pp. 57-138. [5] Yang, K. H., "Shear Strength of Chemically Modified Fine-Grained Soils," unpublished M.S. thesis, Iowa State University, Ames, Iowa, 1975. [6] Fox, N. S., Lohnes, R. A., and Handy, R. L., Proceedings of the Iowa Academy of Science. Vol. 73, 1966, pp. 193-204. [7] Easton, C. N., Lohnes, R. A., and Handy, R. L. in Proceedings. International Symposium on the Engineering Properties of Sea-Floor Soils and Their Geophysical Identification, UNESCO, 1971, pp. 26-36. [8] Lutenegger, A. } . , Remmes, B. D., and Handy, R. L., Journal of the Geotechnical Engineering Division. American Society of Civil Engineers, Vol. 104, 1978, pp. 1403-1407. [9] Nickel, S. H. in Proceedings. Conference on In Situ Measurement of Soil Properties, American Society of Civil Engineers, Vol. 2, 1975, pp. 172-174. [10] Wineland, J. D. in Proceedings, Conference on In Situ Measurement of Soil Properties, American Society of Civil Engineers, Vol. 1, 1975, pp. 511-522. [11] Mitchell, J. K., "In Situ Techniques for Site Characterization," Site Characterization and Exploration, American Society of Civil Engineers, New York, 1979, pp. 107-129. [12] Sowers, G. F. and Royster, D. L., "Field Investigation," Landslides: Analysis and Control, Special Report 176, National Academy of Sciences, Washington, D.C., 1978, p. 107. [13] Lohnes, R. A. and Handy, R. L., Journal of Geology, Vol. 76, 1968, pp. 247-258. [14] Handy, R. L. and Williams, W. W., Civil Engineering, Vol. 37, 1967, pp. 62-65. [15] Tice, J. A. and Sams, C. E., "Experiences with Landslide Instrumentation in the Southeast," Transportation Research Record, No. 482, 1974, pp. 18-29. [16] Lohnes, R. A., Millan, A., and Handy, R. L., Journal of the Soil Mechanics and Foundations Division, ASCE, Vol. 98, 1972, pp. 143-147. [17] Handy, R. L., Pitt, J. M., Engle, L. E., and Klockow, D. E. in Proceedings, 17th Symposium on Rock Mechanics, 1976, pp. 4B6-1-4B6-11. [18] Panek, L. A. in Proceedings, 4th Congress, International Society for Rock Mechanics, Vol. 2, 1979, pp. 509-515.

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R. L. McNeill' and S. L. Green'

Concepts for a Shear-Normal Gage to Estimate In Situ Soil Strengtii and Strength Angle

REFERENCE: McNeill, R. L. and Green, S. L., "Concepts for a Shear-Normal Gage to Estimate In Situ Soil Strengtii and Strength Angle," Laboratory Shear Strength of Soil. ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 579-593. ABSTRACT; Concepts are developed whereby the in situ shear strength (S) and the effective soil strength angle (0') at large strains can be calculated from the readings of a combined shear/normal-stress gage mounted on the face of a rough penetrator. It is possible to calculate S and (t>' even if interface friction is the mechanism of failure, unless that friction is local to the gage face. For the case of local friction, the method yields only the interface friction angle 6. Experimental results are encouraging, and the method is being studied for application to a deepwater wire-line device for in situ determinations of S and (j)'. KEY WORDS: angle of internal friction, clays, deepwater, friction angle, geotechnical engineering, in situ testing, interface friction, marine soils, penetrator, radial stress, shear strength, shear stress, soils, static strength, strength angle, stress gage, wire line

Experience is showing, as offshore work moves into deeper water, that conventional methods of determining in situ soil strengths are in some cases inadequate. The situation is expected to worsen as even deeper waters are explored over the next decade. Soil strengths are presently measured by boring/sampling/laboratoty testing or by in situ testing. The first procedure is often unsatisfactory, especially if the water is deep or the soils contain gas or clathrates, because of pressure release, temperature change, and sample disturbance. The in situ methods consist mainly of Standard Penetration Tests (SPT), cone-penetration tests, and vane-shear tests. The SPT is an impact-dynamic test which relies solely on empirical correlations to yield an estimate of soil strength, 'Technical staff member. Sandia National Laboratories, Albuquerque, N.M. 87185. 579 Copyright by Downloaded/printed Copyright 1981 University of

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02:2

580

LABORATORY SHEAR STRENGTH OF SOIL

and its results can be substantially in error, especially in cohesive soils. There are many types of cone-penetration tests, all of which rely either on empirical correlations or on modifications to or adaptations of bearing-capacity theory to yield estimates of soil strength. Cones are simple to use because they require only a pushing motion. They are widely used in marine exploration. The vane-shear test requires a twisting motion in addition to the pushing motion, but it measures soil strength directly by mobilizing that strength on an assumed cylindrical surface of shear. Existing cone and vane devices are designed for a few hundred feet of water; it is expected that considerable modification, and even redevelopment, will be required to operate in a few thousand feet of water, which is where much of the activity will be in the next decade. In most practical engineering problems, it is necessary to know not only a soil's present strength, but also how that strength and other properties will change in response to the future stresses which will be imposed on the soil. The SPT and the cone-penetrometer and vane-shear tests offer no direct information on how a soil's strength will change. Estimates of such information are presently obtained by laboratory testing, which consists of applying the anticipated stresses and measuring the soil's response to them in order to determine the soil's strength angle (t>'. This procedure, however, has the serious flaws of pressure release and sample disturbance, and confidence in the results is often quite low. It is therefore generally agreed among practitioners and researchers that there is a clear need to develop new and improved in situ methods for determining soil strength and effective strength angle, especially for deepwater situations. In an attempt to solve these problems, Texas A&M University has developed and used for about one year, a pressurized core barrel [1],^ which acquires samples preserved at their in situ pressure. The samples are sealed at their in situ pressures, raised to the surface, transported to a special pressurized laboratory chamber, and tested while the in situ pressure is maintained. The core barrel has been proved to depths of about 300 ft of water, the limit at which laboratory technicians can work in the special pressurized laboratory chamber. Work is underway to develop a core barrel for deeper water with an associated high-pressure testing facility. It is presently expected that the testing capability will initially be limited to vaneshear or unconfined tests, performed remotely within the high-pressure testing facility. Sandia National Laboratories is working to develop deepwater in situ testing instruments to be made available to government and industry. The first version of these, a pilot project to evaluate concepts and identify opportunities, is the Geotechnically Instrumented Seafloor Penetrator [2]. The present version, an instrument test platform, is a static penetrator which ^The italic numbers in brackets refer to the list of references appended to this paper.

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MCNEILL AND GREEN ON A SHEAR-NORMAL GAGE

581

penetrates to a given depth, measures pore pressures continuously as a function of time, and transmits its data, on command, acoustically to a small boat on the surface. It is clear from the work to date that one promising way to estimate soil strength and its changes with time is by using penetrators [3], both static and dynamic. This paper has as a background the general notion of a small cylindrical static penetrator that is to be handled by wire line and pushed by the drill bit. This work is intended to provide insight into soilstrength phenomenology for purposes of guiding further theoretical and instrumentation developments, and for purposes of designing field and laboratory experiments. Valuable insight into the expected performance of penetrators can be gained by studying the results of pile-load tests, which are the reverse of a penetrator strength test. The soil's strengths are determined by conventional means, and then are integrated along the pile's skin area to calculate the load the pile can carry. The calculated load is then compared with the actual load as measured in the pile-load test. Experience shows that in most cases this procedure results in a calculated load which is higher than the actual load [4]. These experiences seem to indicate that (/) the true mechanism of stress transfer and strength mobilization is not accurately accounted for in the calculational procedure; or (2) sliding friction, at a value less than the soil strength, is playing some role in the mechanism; or (J) both. Studies have been presented that seek to account for both factors in a rigorous way using the theory of an expanding cavity [5,6]. Those studies are not yet complete. The work presented in this paper bypasses the fundamental mechanisms of the insertion of a penetrator. Instead, the effect of the insertion upon the soil is postulated, and the opportunities for novel instrumentation to measure soil properties are investigated. Finally, the derived principles are tested against data from the literature. Concepts The developments presented here assume that the cavity made by a static penetrator develops under the near-simultaneous applications of the surfacetraction shear of the downward-moving penetrator, and of the increased radial stresses required to expand a cavity in the soil. After the penetrator nose has passed, the conditions at the face of the penetrator are postulated to be as shown on the upper left-hand side of Fig. 1: (/) the shear stress at the face of the penetrator in the r-v plane is Sp-, and (2) the largest stress in the planes normal to or tangential to the face of the penetrator is the radial stress, a / (in this paper, all normal stresses are effective stresses, assuming that any static penetrator would have a pore-pressure measuring capability). The radial stress a/ is not, however, the largest possible normal stress, as shown by the limit equilibrium circle on the right-hand side of Fig. 1: the largest normal stress is the major principal stress, a / , which is inclined

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582

LABORATORY SHEAR STRENGTH OF SOIL

b

S 'SS3J(S JDSMS

I I

O

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MCNEILL AND GREEN ON A SHEAR-NORMAL GAGE

583

radially off the vertical into the penetrator axis, as shown on the lower left of Fig. 1. Both of the a^'-a^' planes are probably actively failing, as shown, and, for a rough penetrator, the actual soil-shear failure surface is probably in the soil and some distance out from the penetrator. Thus, if a thin skin of soil is postulated to be adhering to the face of the penetrator, the shear stress at the face of the penetrator, Sp, is larger than the shear strength of the soil, Ss, and that shear stress could be approximately equal to the maximum shear, S,„; see Fig. 1. This point is studied with experimental data at the end of the section on Experimental Study. Inspection of the limit-equilibrium Mohr's circle in Fig. 1 indicates that, if it were possible to measure Sp and a/ while the penetrator is loaded andCTI' when the penetrator is unloaded, it should in principle be possible to calculate the effective strength angle, ' = arcsin / — - — 2ffiAff

\ .

(1)

I

Aa2 + Sp^ where ACT = O)' —CT^',as shown in Fig. 1. The derivation of Eq 1 is given in Fig. 2. The values of Sp and a/ could be measured by a gage that simultaneously measures shear and normal stresses [7,8]. The value a,' would be the normal-stress measurement on that gage when the penetrator is not loaded, if one assumes that the large cavity-expansion radial stress maintains the soil in the critical state [9]. Thus, referring to Fig. 1, it is in principle possible to calculate the strength angle, 0 ' , from a load-unload cycle on a rough penetrator, which forces the shear failure to occur in the soil. Then, using <j>' and the measuredCTJ', the shear strength of the soil {S^) and the maximum shear (S„,) can be calculated. It is in principle possible to do the same thing even if the penetrator is smooth so that the failure occurs in interface friction. Figure 3 has been prepared to aid in this discussion of possible friction failure. In this case, failure will occur at the face of the penetrator. If the friction strength (S/) is close to the value of the soil shear strength, (S^), then the soil will be at or near its limit-equilibrium state (Fig. 3). For overall failure in friction along the entire penetrator, or at least an appreciable length of it, the maximum value of the interface friction Sf is S^= a/ tan 6

(2)

Thus, if the shear Sf and radial a/ stresses are measured, it is in principle possible to calculate the value of 5 for that soil and that penetrator surface. If the value of oi' is also available, the value of <^' can also be calculated using Eq 1, assuming the soil is at or near the critical state.

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584

LABORATORY SHEAR STRENGTH OF SOIL

C = Center,

8™= Rodius

9=orcsin

= orcsin (

= arcsin

W:I -am/ -s

c Sin a

!ii-

,

\ %_ Sm

AT

2S„

a^=2ACrs„=AT^.Sp^S„=^|i|^ 4> =arcsin /•

2Ti'^^T

VA
I

Eqn.(l)

FIG. 2—Derivation of Eq I.

Failure will occur in friction only if the friction Sy is less than the soil strength S,. For overall failure in friction along the entire length of the penetrator, or at least along an appreciable length of it, the two are conveniently related from the geometries of Figs. 1 and 3 as follows: ^/

sin d

Sg

cos (j)'

(3)

where 6 is the angle shown in Fig. 3 and is given by d = d + arcsin

sin 5 s i n '

(4)

Equation 3 is interesting because it shows that there is a unique relationship between the friction strength and the soil shear strength, even if failure occurs in friction. Equation 3 is plotted in Fig. 4, which shows that for all practical values of ' between 25 and 40 deg, the curves are almost identical and

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MCNEILL AND GREEN ON A SHEAR-NORMAL GAGE

585

Normal Stress, (T

'6' = i 8 » arcsin

rsm 8 V

FIG. 3—Stale of stress for failure by interface

friction.

are indistinguishable as a practical matter. This result suggests that if the ratio Sf/S^ is known (for example, from a pile-load test or a properly instrumented penetrator) and is less than unity, then that result can be used to estimate the friction angle 8. Figure 4 and Eq 3 also show that failure will not occur in friction, but rather in soil shear, for values of the friction angle 5 greater than about 15 deg for weak soils or about 19 deg for strong soils. Presumably friction failure can occur for higher values of 5 if the soil has a shear-stress (cohesion) intercept. The foregoing conclusions regarding the friction/shear-strength relationship will not necessarily be true if the friction failure is localized as is shown in Fig. 5. The left-hand side of Fig. 5 gives an example of a shear/normalstress gage embedded in the wall of a penetrator, but the gage surface is smooth with respect to the penetrator surface. It is assumed that the gage face is small compared with the circumference of the penetrator. In this case, the friction Sf on the gage face will be smaller than the adjacent soil shear S^, but the radial stress on the gage would likely be about the same as the adjacent value a/. The friction angle 8 could be calculated from Eq 2, but the measurement would yield nothing about the limit-equilibrium circle or the strength angle '. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

586

LABORATORY SHEAR STRENGTH OF SOIL

1

~ <7> b

00 6

r6

i

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£ =

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~-~—1

^''~~^ «0 •ec c S)
I

i«> .o c o u in

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1 \

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c 5 o

g *•

M

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( \ \

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CVJ

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^

^ "viBSS^ 1

k

' s / *s ouoy

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MCNEILL AND GREEN ON A SHEAR-NORMAL GAGE

b

587

I?
I •*i.

S 'ssaj(S JD»MS

i

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588

LABORATORY SHEAR STRENGTH OF SOIL

These theoretical developments have shown that it is in principle possible to calculate the effective strength angle <j}' from the measurements of the shear and normal stresses and their changes as load is varied. These provide a strong motivation to develop a small shear/normal-stress gage. The results of some closely related experiments will now be presented and analyzed to assess whether the theoretical developments show promise for use in practice. Experimental Study The experiments to be reported here were performed independently of these theoretical developments and about two years earlier at the Civil Engineering Research Facility, operated by the University of New Mexico (UNM) for the Air Force Weapons Laboratory [8]. The stress conditions are probably not precisely the same as in situ, but the results provide a good opportunity to test the gage hypothesis. The experiments were performed to evaluate the performance of a unique combined shear-stress and normal-stress dynamic gage, designed to measure the response of buried concrete walls to dynamic loads imposed on the ground surface. The gage is essentially a cylindrical dual cantilever beam, instrumented with strain gages circuited to read simultaneously the normal and shear stresses on the end of the cantilever, and designed to be cast with its rigid case into a concrete wall so that the end of the sensing cantilever is flush with the face of the wall. The cantilever is about 2.54 cm (1 in.) in end diameter, about 3.2 cm (IV4 in.) in cantilever length on each end, and is mounted in a case about 7.6 cm (3 in.) in diameter and 12 cm (4^/4 in.) long. Thus it is somewhat large and heavy. For the experiments to be analyzed, the gage was prepared for testing by casting it in a 15.2-cm (6-in.)-diameter concrete cylinder so that the end of the cantilever was flush with the circumference of the cylinder. The concrete cylinder with the gage was then placed in a specially designed test cell shown schematically in Fig. 6. The 5.08-cm (2-in.) annulus between the gage cylinder and the rubber membrane was filled with dry Ottawa sand, and the annulus between the steel jacket and the rubber membrane was pressurized to generate confining radial pressure on the sand surrounding the concrete cylinder. Then load was applied axially to the steel follower, which was free to pass through the bottom of the test cell when the load was raised to the point at which the shearing strength of the sand at that confining pressure was exceeded. Load cells were placed above and below the concrete clyinder containing the gage, so that the average shear stress could be calculated for comparison with the gage value. Thus the results of a typical test (Fig. 7) show the value Sg for the shear stress measured by the gage and the average value S^ calculated from the differences in the load-cell readings. The tests proceeded as follows and as shown in Fig. 7: the cell was

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MCNEILL A N D GREEN O N A SHEAR-NORMAL GAGE

589

Load from Testing Mochine

Steel Follower

Steel Jacket

Upper Load Cell °^ _"

^

ConereJe •• . » Cylinder *. ' . Cose

J

L

^Sensing face

Gauge

ifliifiiP-^ steel Follower

\ \ Bottom NNPIatenW,

FIG. b—UNM test setup.

pressurized to develop the initial radial stress, <7|', measured by the gage; during this phase, small shear stresses were recorded on the gage and the load cells, due presumably to inhomogeneities in the sand; when the radial stress a,' had become constant (Time A in Fig. 7) load would be applied to develop the shear stresses S^ and 5^; this would continue until the cylinder was moving under constant load (Time C); at which time the load would be removed. There were often some residual measured shear stress (Time D) after load removal. In all cases, the radial stress, a/, responded immediately to the application of shear stress (Time A) by reducing, as predicted by the theoretical considerations in Fig. 1 and Eq 1. The reduction continued throughout the period of increasing shear stress, even reflecting perturbations in the rate of

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590

LABORATORY SHEAR STRENGTH OF SOIL

5000

1,500

0J

E 2 4000

eg

E

1,000 i

*» 3000

in

500

I

1000

8 £1 in

— 0 240

Time Seconds FIG. 1—Results of UNM Test No. 5.

shear-Stress application. For example, the increase in the rate of shear-stress application at Time B in Fig. 7 is reflected as an increase in the rate of radialstress reduction at the same Time B. The data for all of the reported tests are given in Table 1. The results of an analysis of a typical test are given in Fig. 8. The measured values, shown by heavy dots, are the major principal stress a j ' , the radial stress a/ at maximum load, the shear stress Sg measured by the gage, and the average shear stress 5c calculated from the load cells. Motivated by the observation in Table 1 that the calculated average shear stress S^ usually exceeds the gage shear stress Sg, it was preliminarily assumed that the rough concrete cylinder was moving by forcing the soil to fail, as in Fig. 1, but that the soil on the more smooth gage face might be failing locally in interface friction, as in Fig. 5. On this basis, the strength angle (j>' was calculated using S^ and Eq 1, and the friction angle 6 was calculated using Sg and Eq 2; the results are shown for a typical test in Fig. 8. Then, using the measured major principal stress CTi' and the calculated strength angle 4>', the shear strength S^ and the maximum shear S„, were calculated, as shown for a typical test in Fig. 8. The calculated strength and friction angles for all of the reported tests are given in Table 2. The obvious trends in Table 2 are (/) the calculated strength angles for the first four tests are extremely low for this sand; (2) the calculated friction angles for the first four tests are in the range of values, less than 15 to 19 deg (Fig. 4), for which interface-friction failure is expected to occur; (3) the calculated strength angles for the last five tests appear reasonable for this sand; and (4) the calculated friction angles for the last five tests are well above values for which interface-friction failure is expected to occur. It is also noted in Table 2 that Test 8 is the first test in which the radial stress was taken to a very high value (7650 kPa). Based on these observations, it is hypothesized that failure by mixed general and local friction oc-

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MCNEILL AND GREEN ON A SHEAR-NORMAL GAGE

591

TABLE 1—Basic data from UNM experiments |8]. Test

No.

a,', kPa

o/. kPa

4310 4270 4520 4760 7650 4140 7650 8140 4070

3100 3410 3620 3960 3000 3060 4830 6550 2830

3 4 5" 6 8 II 16 17 18

S^, kPa

855 910 950 1080 2400 1190 2430 2710 1280

5,, kPa 1200 1215 1250 1280 2510 1325 2425 2345 1470

"Presented in total in Figs. 7 and 8.

-•-

Measured in test

-O-

Calculated from test date.

2 4 , 3 " ' (Eqn I)

2000 Normal

3000

Stress, CT, K N / m

2

FIG. 8—Analysis of UNM Test No. 5.

curred during the first four tests; but that the high stresses of Test 8 must have dimpled and therefore roughened the concrete cylinjier and the gage face, so that subsequent tests represent failure by soil shear. On these bases the data were re-analyzed with the results shown in Table 3, which deals only with the last five tests, where soil-shear failure was indicated. The strength angles (0^ and (f)^) were calculated using Eq 1, using the gage and the average calculated shear stresses, respectively. As shown in Table 3, the values vary from test to test, but the average values, 29.1 and 29.8 deg, agree well, and agree with the value of about 30 deg expected for this sand in this condition. The values of both the gage and the average calculated shear stresses exceeded the shear strength S^ (Fig. 8) in all cases, and on the average by about 12 percent. Thus the shear stress at the face of the rough cylinder, and therefore presumably at the face of a rough penetrator, is larger than the

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592

LABORATORY SHEAR STRENGTH OF SOIL

TABLE 2—Preliminary analysis of UNM data. Test

No.

3 4 5* 6 8 11 16 17 18

a, ', kPa

*', deg"

6, deg

4310 4270 4520 4760

22.7 25.5 24.3 25.5

15.4 14.9 14.7 15.3

7650 4140 7650 8140 4070

30.3 28.6 28.2 26.8 35.3

23.1 21.6 26.7 18.4 24.4

"Calculated from Eq 1 using average calculated shear stress, S^. from Table 1. ^Presented in total in Figs. 7 and 8.

TABLE 3—Analysis of UNM data. Test

No.

a,', kPa

g', d e g

c': d e g

s,/s,„

s/s,„

8 11 16 17 18

7650 4140 7650 8140 4070

27.8 23.7 28.2 38.2 27.4

30.3 28.6 28.2 26.8 25.3

0.99 1.00 0.99 0.87 1.00

0.98 0.99 0.99 0.93 0.99

29.1

29.8

0.97

0.98

Average

shear strength on the failure plane which is in the soil at some distance away from that face. In contrast, for the first four tests (Tables 1 and 2), before the face was dimpled and roughened, the gage shear stress was less than the shear strength in all cases, and their average ratio was about 0.8. In that case, the failure was occurring by interface friction at an average friction angle of about 15 deg. Reference to Fig. 4 shows that, for a ratio of friction shear stress to shear strength, Sf/S, = 0.8, and for all values of strength angle 0 ' between 30 and 40 deg, the friction angle would have to be about 15 deg. That value seems to be in reasonable agreement with the calculated and expected values reported for the first four tests in Table 2. The information in the data from the last five tests can be used to evaluate the relative magnitude of the shear stress at the penetrator face. The final two columns of Table 3 present the gage and the average calculated shearstress values, normalized to the value of the maximum shear. The average values, 0.97 and 0.98, seem to furnish experimental evidence that the shear Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

MCNEILL AND GREEN ON A SHEAR-NORMAL GAGE

593

stress at the penetrator face builds up to essentially the maximum shear for the limit-equilibrium state of stress for a rough penetrator. Conclusions The derived equations, simple in form and easy to apply, require only that the soil be in a state of failure. When the shear and normal stresses are measured with axial load on the penetrator, and normal stress is measured with no load on the penetrator, the strength angle or the friction angle, or both, can be calculated for these conditions of large strains. Existing gages which simultaneously measure shear and normal stresses are large and heavy. There is a need to develop a small shear/normal stress gage, capable of being housed in a wire-line tool geometry. Acknowledgments This work was prepared by Sandia National Laboratories, Albuquerque, N.M and Livermore, Calif, for the U.S. Department of Energy under contract BE-AC04-76DPOO789. E. Reece and D. Kestly of Sandia National Laboratories beneficially reviewed the theoretical concepts and have contributed substantially to defining the principles of a shear/normal gage. The following researchers from the University of New Mexico were very helpful by freely furnishing their data and by critiquing the fundamental concepts: D. Calhoun, J. Nielsen, and S. Picket. The figures were drawn by I. McNeill. The test was prepared by N. Gatchell. References [/] Dunlap, W., personal communication (developments expected to be published in 1981), Feb. 1980. [2] Reece, E. W., Ryerson, D. E., Kestly, J. D., and McNeill, R. L. "The Development of In Situ Marine Seismic and Geotechnical Instrumentation Systems," Proceedings, Fifth POAC Conference, Trondheim^ Norway, 1979. |J| McNeill, R. L., "Enhancement of Geophysical Soil Profiles Using Instrumented Marine Sediment Penetrators," OTC3526, Proceedings. Offshore Technology Conference, 1979. [4] Tomlinson, M. J., Foundation Design and Construction, Wiley, N.Y., 1969. [5] Esrig, M. I., Kirby, R. C , and Bea, R. G., "Initial Development of a General Effective Stress Method in the Prediction of Axial Capacity for Driven Piles in Clay," OTC2943, Proceedings, Offshore Technology Conference, 1977. [<5] Esrig, M. I. and Kirby, R. C , "Advances in the General Effective Stress Method for the Prediction of Axial Capacity for Driven Piles in Clay," OTC3406, Proceedings, Offshore Technology Conference, 1979. [7] Hanna, T. H., Foundation Instrumentation, Trans Tech, Clausthal, Germany, 1979, pp. 138-141. [8] Pickett, S. P., "Development and Evaluation of a Triaxial Interface Stress Transducer," AFWL-TR-77-90, Air Force Weapons Laboratory, Kirtland AFB, N.M. Aug. 1977. [9] Woodward-Clyde Consultants, Predictions of Axial Capacity for Offshore Piles, Report on Phase II Study, Clifton, N.J., 1976.

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David Miedema,' Jack Byers, ^ and Richard McNearny^

Residual Shear Strength Determination of Overconsolidated Nespelem Clay

REFERENCE: Miedema, David, Byers, Jack, and McNeamy. Richard, "Residual Shear Strength Determhiation of Overconsolidated Nespelem Clay," Laboratory Shear Strength of Soil. ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 594-609. ABSTRACT: Peaking operations at Grand Coulee Powerplant, Washington, could result in future downstream river fluctuations of up to 12 m (38 ft) within a 24-h period and trigger dangerous landslides. Much of the riverbank consists of old landslide deposits in varved, overconsolidated clays and silts. The residual shear strength of the clay was determined from drained, repeated (reversing) direct shear tests on slickensided or precut sliding surfaces under three normal loads. Two displacement rates were initially used. The residual strength, measured after large cumulative displacements, was used in slope stability analyses. This paper describes problems encountered during testing, the test procedure adopted, the fully automated direct shear apparatus and data recording system, results to date, and planned future research. In one of the downstream riverbank areas, a residual shear strength range of 10 to 13 deg was confirmed by a back analysis of a recent slide. KEY WORDS: shear strength, residual shear strength, direct shear test, overconsolidated clay, slope stability, repeated direct shear test

Numerous landslides have occurred along the banks of the Columbia River in the vicinity of Grand Coulee Dam, Washington. The most recent slide occurred along the right bank of a populated area known as Coulee Dam East on June 4, 1978, after an unusual 4-m (14-ft) river water level fluctuation in 8 h. Figure 1 is an aerial view of the area showing Coulee Dam East, part of the Coulee Third Powerplant, and the recent slide. The slide was found to be a localized reactivation of an old slide and limitations were placed on river fluc'Civil engineer. Soil Mechanics Section, Geotechnical Branch, Water and Power Resources Service, Denver, Colo. 80225. ^Supervisory civil engineer. Soil Testing Section, Geotechnical Branch, Water and Power Resources Service, Denver, Colo. 80225. 594 Copyright by Downloaded/printed Copyright 1981 University of

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MIEDEMA ET AL ON SHEAR STRENGTH OF NESPELEM CLAY

595

tuations. However, future peaking operations of the present powerplant could result in 7-m (22-ft) river fluctuations, and with the proposed extension of the powerplant the total daily river fluctuation would be about 12 m (38 ft) at this location. A full investigation and analysis of the 6-mile stretch of river downstream of the dam is now underway by the Water and Power Resources Service (formerly the Bureau of Reclamation). As part of this investigation, the residual shear strength of the riverbank clay soil was required for use in slope stability studies. This paper describes experiences in determining the residual shear strength parameters using the repeated (reversing) direct shear test. Geology The geology of the area is complex. During the Ice Age (Pleistocene Age) one lobe of the continental glacier originating in present-day British Columbia crossed the Columbia River forming an ice dam a few miles northwest of Coulee Dam. In time, a huge lake was formed with a depth of at least 300 m (1000 ft). On a yearly cycle, melting water carried silts and clays into the lake; the silts settled before the clays, forming distinct layers of each. When the glacier advanced, it compressed the layers. As the ice retreated, glacial

FIG. 1—Coulee Dam East area.

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596

LABORATORY SHEAR STRENGTH OF SOIL

tills were deposited and eventually buried as deposition continued. These deposits of varved clays, containing some sand interbeds, are known as the Nespelem formation. Breaching of the ice dam during major glacial retreats resulted in nearly complete removal of the Nespelem formation along the west bank of the river and its partial removal along the east bank. River undercutting triggered numerous prehistoric slides in the area [/].•' An interpretive geologic section (Fig. 2) shows, in general, the various materials forming the riverbank. On the east bank, porous alluvial terrace deposits overlie the Nespelem formation through which an old slide is traced. Basal gravels overlie the granite rock in places. The west bank consists of old channel fill. The critical material is found in the old shear zones of the Nespelem formation, which are described in the geologic logs as consisting of "highly brecciated and partly to completely remolded bedding and laminae; slickensided clay; wet to very wet soft seams of clay". Residua] Shear Strength After a slide has taken place in an overconsolidated clay, the strength along the slip surface is equal to the residual value [2]. Many welldocumented slope stability studies have confirmed this concept [3-6]. This lower bound strength may be determined in the laboratory using repeated direct shear tests, triaxial compression, or ring (rotational) shear tests. The repeated direct shear test was the first choice of the methods in our laboratory because an existing shear apparatus required only minor modifications and the specimens could be readily oriented along the preexisting slip planes. Currently, companion remolded samples are also being tested in a rotational shear apparatus, but there are insufficient data to compare the results at this time. Considerable research and study has been done by others on the repeated direct shear test [7-9]. The emphasis of this study is toward obtaining reliable values of residual shear strength within a short time span for use in slope stability studies. Test Procedures More than one-hundred, 150-mm (6-in.)-diameter Denison samples of the Nespelem formation were obtained from the eight areas under study. The samples were shipped to the Water and Power Resources Service Geotechnical Laboratory in Denver, Colorado, where the sample liners were removed and the samples inspected and photographed. Fifty-one-mm (2-in.)-square specimens were cut from the samples for testing. Specimens having natural slickensides were selected for testing when possible, but most specimens were tested on a precut plane. The soft, wet clay seams were easily wire cut. The italic numbers in brackets refer to the list of references appended to this paper.

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MIEDEMA ET AL ON SHEAR STRENGTH OF NESPELEM CLAY

jooo

597

(rssrj

FIG. 2—Interpretive geologic section.

but problems with squeezing and erosion of the material developed during testing. A few of the hard, dry clay specimens were precut and tested. All the precut and slickensided specimens were wetted with distilled water. Peak strength values for two specimens were obtained by shearing the intact clay, but the uneven shear surface that formed resulted in erratic values and this procedure was discontinued in favor of the precut specimens. The procedure and equipment were based on studies by Townsend and Gilbert on the residual shear strength of clay shales [9]. Initially, an existing direct shear apparatus was modified to allow the shearbox to reverse directions (Fig. 3). Two additional standard reversing shear devices from Wykeham Farrance Ltd. of England were later modified and used for testing. The modification allows the shearbox to reverse its direction of travel once a predetermined displacement is reached. A minicomputer controls the reversals and records the test results. Once the test is completed, the data stored in the minicomputer are transferred electronically to the mainframe computer for plotting. The repeated direct shear test apparatus is a strain-controlled testing system consisting of a 25-mm (l-in.)-thick aluminum or stainless steel shearbox, a pneumatic normal loading system, displacement measuring equipment, a motor and gearbox assembly, and a load cell, all of which are placed in a rigid frame to prevent excessive deflections of the system once the test is in progress. The top half of the shearbox remains stationary while the bottom Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

598

LABORATORY SHEAR STRENGTH OF SOIL

FIG. 3—Repeated direct shear device.

half slides on roller bearings. Porous stones are placed on the top and bottom of the specimen in the shearbox to facilitate drainage. A normal stress is applied through the pneumatic loading system. The vertical and horizontal displacements are measured by linear variable displacement transducers (LVDTs). The force required to shear the soil is measured by a load cell. The test is automatically controlled and monitored with a minicomputer. The 0.318-mm (0.0125-in.) gap betv^een the shearbox halves is set with gap

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MIEDEMA ET AL ON SHEAR STRENGTH OF NESPELEM CLAY

599

screws and is checked daily with a feeler gage. The specimen is submerged in water for the duration of the test. A typical test consists of determining the residual strength of each specimen under three normal stresses of 276, 483, and 690 kPa (40, 70, and 100 psi). The 51-mm (2-in.) square by 25-mm (1-in.) thick specimen is allowed to consolidate for at least 8 h (usually overnight) prior to horizontal displacement. Slow displacement rates are used to ensure no excess pore pressure development. Two displacement rates of 0.127 mm/min (0.(X)5 in./min) and 0.013 mm/min (0.0005 in./min) were used to see if the rate affected the measured strength. After a forward displacement of 4.3 mm (0.17 in.), the shearbox is automatically reversed. It passes through the zero displacement position and moves 4.3 mm (0.17 in.) in the reverse direction. This cycle is repeated as many times as required to reach residual strength. Usually 3 to 5 cycles and cumulative displacements of 51 to 89 mm (2 to 3.5 in.) per normal load are required. Once the residual strength has been attained under a given normal load, the horizontal displacement is stopped, the normal stress is increased, and the steps are repeated for the next normal stress. The total cumulative displacement for the test varies from 152 to 254 mm (6 to 10 in.). Once the test is concluded, the shear surface is examined and photographed. Index properties are obtained from the shear zone and specimen trimmings. The following sources of error must be closely monitored: 1. A test apparatus that is improperly aligned or has loose connections. 2. Closing of the shearbox gap due to squeezing or erosion of material under high normal stresses. 3. A shear surface may form which is not planar, or consists of heterogeneous material, or dries out. 4. Deformation rates that are too fast to allow for dissipation of excess pore pressure.

Test Results Minor variation was found in the properties of the 17 specimens tested to date. Classified as fat clay (CH), the liquid limit (LL) ranged from 55 to 87 percent and the plasticity index (PI) from 33 to 54 percent. The gradation analysis indicated a high percentage (50 to 85 percent) of particles smaller than 0.002 mm (2/i) in size. These results are summarized in Table 1. The clay minerals generally consisted of 20 to 25 percent montmorillonites (smectites), 10 to 15 percent illite-micas, and 5 to 10 percent kaolinite. The remaining major minerals were feldspars (20 to 25 percent) and quartz (10 to 15 percent). The overconsolidation ratio based on one-dimensional consolidation tests ranged from about 3 to 5.

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600

LABORATORY SHEAR STRENGTH OF SOIL

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MIEDEMA ET AL ON SHEAR STRENGTH OF NESPELEM CLAY

601

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602

LABORATORY SHEAR STRENGTH OF SOIL

Five plots are used to evaluate the test data. Figure 4, shear force versus horizontal displacement, shows the cycles required to reach residual strength under one normal load. Figure 5 is an enlargement of the central portion of Fig. 4. Reduction of shear force with cumulative horizontal displacement is shown in Fig. 6 and is used to monitor the progress of the test. Minor specimen erosion can be observed in Fig. 7, vertical displacment versus cumulative horizontal displacement. Figure 8 shows the residual strength envelope and a summary of the soil properties. The shear stress value selected is obtained at the central position (zero-displacement location) so that area corrections are not required. Shearing force values are not exactly the same in the forward and reverse stroke; the average value for the two strokes is used to determine the strength envelope. A straight line fit of the data points was made using a least squares linear regression analysis. For most tests, cohesion values of less than 14 kPa (2 psi) were obtained. These cohesion values were considered to be apparent rather than true values and were not recommended for use in the slope stability analyses. The residual effective angle of internal friction (<^ \) for the six areas under study ranged from 7 to 14 deg with most tests between 11 and 13 deg (Table 1). There were variations, however, between areas. For example, 'r for samples tested from Coulee Dam East varied from 11 to 14 deg whereas (t> \ for Coulee Dam Northeast varied from 7 to 10 deg. There was no apparent trend relating <> / \ to the displacement rate. Residual strength increased with a decrease in displacement rate for ten tests, it remained the same for five tests, and it decreased in one test. It is believed that other factors, such as material erosion, had more effect than displacement rate. Residual shear strength decreases with increasing PI and LL, as shown in Fig. 9 [10]. Results of our testing to date are plotted on these curves with nearly all points falling between the dashed average line and the lower bound of the curve. This is reassuring and provides confirmation that the tests results are reliable. In addition, the shape of the curve is such that a 2-deg variation in <> / \ would normally be expected for a soil having this range in PI and LL. Slope Stability Analysis The 4 June 1978 slide at Coulee Dam East was analyzed [//] to obtain the friction angle required in the clay to provide a factor of safety of 1.0. The reliability of a back analysis of this type depends primarily on accurate pore water pressure measurements and a well-defined surface of sliding. Fortunately, the piezometric data had been monitored in three nearby observation holes at the time of the slide. Surface geometry was known and the geologic profile was interpreted from drill hole log information (Fig. 10). Four failure surfaces were assumed, originating from the head of the main scarp and exiting at different locations beneath the river, because the exact

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MIEDEMA ET AL ON SHEAR STRENGTH OF NESPELEM CLAY

603

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604

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MIEDEMA ET AL ON SHEAR STRENGTH OF NESPELEM CLAY

605

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location of the toe was not known. Using the Spencer slope stability method [12], the back calculated friction angle ranged from 10 to 13 deg. Considering the assumptions inherent in this type of analysis, the agreement between the laboratory tests and the back calculated friction angle is good. Discussion Residual shear strength is a lower bound value which is required when dealing with material which has been subjected to previous shear movements. The question of how to fit a failure envelope to the test data was the subject of considerable discussion. Four ways to interpret the data are: 1. A straight line fit of the data with a real cohesion value. 2. A straight line fit of the data with the cohesion intercept considered as an apparent cohesion. 3. A straight line envelope which is forced to pass through the origin. 4. A curved envelope which passes through the origin. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

606

LABORATORY SHEAR STRENGTH OF SOIL

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MIEDEMA ET AL ON SHEAR STRENGTH OF NESPELEM CLAY

0;,

20

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-

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20

30

40

50

60

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80

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Plasticity Index {%)

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FIG. 9—Relation between residual friction angle and plasticity (compiled by Deere. 1974) (after Mitchell [\0]).

A curved failure envelope appeared to fit the data in some cases better than a straight line; but because of scatter in the data definite trends were not found. It is believed that the nonhomogeneity of the Nespelem formation accounts for much of the scatter in the test data. When data become available, we plan to compare results from the repeated direct shear test with those from the rotational shear test using companion specimens of the Nespelem and homogeneous clays. We also plan to investigate: 1. The effect of specimen thickness on the displacement rate for drained conditions. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

608

LABORATORY SHEAR STRENGTH OF SOIL

\

t

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Soo •

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FIG. 10—Coulee Dam East cross section (1 ft = 0.30 m).

2. The effects of varying the gap thickness. 3. Residual shear strength differences for intact, precut, and remolded specimens of the same soil.

Conclusions The repeated direct shear test is a convenient and reliable method to measure the residual shear strength of a soil. The automated reversal modification, computerized data collection, and plotting of results helped to expedite the tests. Residual shear strength values obtained showed good agreement with previously published results relating residual shear strength to a soil's liquid limit and plasticity index. The measured values for one area also agreed well with those obtained from a back analysis of a recent slide.

Acknowledgments Abel Benavidez and Les Shehorn, Civil Engineering Technicians, were instrumental in specimen preparation and testing, and contributed to the development of the testing apparatus and data acquisition systems.

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MIEDEMA ET AL ON SHEAR STRENGTH OF NESPELEM CLAY

609

References [/] Salter, Norris, "The Geologic Story of the Columbia Basin," unpublished. 12] Skempton, A. W., Geotechnique Vol. 14, No. 2, 1964, pp. 77-101. [J] Skempton, A. W. and Petley, D. J. in Proceedings, Geotechnical Conference, Oslo, Vol. 2, 1967, pp. 29-46. \4] Bjerrum, h.. Journal of the Soil Mechanics and Foundations Division. American Society of Civil Engineers, Vol. 93, No. SMS, 1967, pp. 3-49. [5] Palladino, D. M., and Peck, R. B., Geotechnique. Vol. 22, No. 4, 1972, pp. 563-595. [6] Insley, A. E. et al, Canadian GeotechnicalJournal. Vol. 14, No. 3. 1977, pp. 408-428. [7] Kenney, T. C . in Proceedings, Geotechnical Conference, Oslo, Vol. 1, 1967, pp. 123-129. \S] Cullen, R. M., and Donald, I. B. in Proceedings. First Australia-New Zealand Conference on Geomechanics, Melbourne, Vol. 1, 1967, pp. 1-10. [9] Townsend, F. C. and Gilbert, P. A., "Residual Shear Strength and Classification Indexes of Clay Shales," Technical Report S-71-6, U.S. Army Waterways Experiment Station, Vicksburg, Miss. 1974 [10] Mitchell, J. K., Fundamentals of Soil Behavior. Wiley, New York, 1976, p. 285. [//] Munger, D. F., "Stability Back Analysis to Determine Residual Shear Strengths of the Nespelem Clays—Coulee Dam East Boat Ramp Slide Area," Technical Memorandum VI-224-3, Water and Power Resources Service, Denver, Colo. 1980. [12] Wright, S. G., "SSTABl—A General Computer Program for Slope Stability Analyses," Research Report No. GE-74-1, Department of Civil Engineering, University of Texas at Austin, August 1974.

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D. H. Shields^ and N. A. Skermer^

The Need for Pore Pressure Information from Shear Tests

REFERENCE: Shields, D. H. and Skermer, N. A., "The Need for Pore Pressure Information from Shear Tests," Laboratory Shear Strength of Soil. ASTM STP 740. R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 610-618. ABSTRACT: Geotechnical engineers are familiar with the role that time plays in the stability of the sides of an excavation. The sides of trenches dug through silts and fine sands are often observed to stand vertically for perhaps 10 or 15 min, then start to fail; railroad cuts through London clay started to fail after 60 years. The time to failure is a function of both the permeability and the volume change characteristics of the soil or rock which is involved. In open pit mining, the time to failure is of utmost importance, yet it is only now that theoretical tools are available which enable the engineer to design slopes for both economy and safety. This recent theoretical work points out the need for the pore pressure response of the soil or rock to be measured during strength testing. The need and the test requirements are the subject of this article. KEY WORDS: mining, pit slopes, shear strength, pore pressure, dilatancy, consolidation

The way in which a material generates its shearing resistance is of considerable importance in the design of side slopes for open excavations. This statement is particularly true for high slopes such as those encountered in open pit mining. It is not sufficient to measure only the physical MohrCoulomb strength properties of the material; the volume change/pore pressure response during shearing must also be measured and taken into consideration during design. Classical limit analysis is used to compute the stability of a slope. Figure 1 illustrates the method of slices as applied to an open pit coal mine. Here, typically, the required shearing resistance of the soil or rock is only some fraction of the ultimate resistance of the material, depending upon the slope 'Professor and Head, Department of Civil Engineering, University of Manitoba, Winnipeg, Manitoba. ^Geotechnical engineer. West Vancouver, British Columbia, Canada. 610 Copyright by Downloaded/printed Copyright 1981 University of

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SHIELDS AND SKERMER ON PORE PRESSURE INFORMATION

611

geometry and the pore pressure conditions. This fact can be illustrated by referring to a typical element of soil at the bottom of a slice; for example, A in Fig. 1. The element carries a share of the load created by the gravitational forces on the material inside the segment of the circle; this share can be represented by the shear stress r which is, for all intents and purposes, constant. According to the Coulomb concept of shear strength, sufficient cohesion and friction must be generated in the soil to resist the stress T; that is, c'„ + ff'(tan0% = r

(1)

where c '„, = mobilized cohesion in terms of effective stresses, (tan (/) ')„ = mobilized friction in terms of effective stresses, and ff' = effective stress acting normal to the shear plane. The ratio between the strength of the material and the mobilized resistance the material has to generate is denoted the factor of safety, F. Usually, then, Eq 1 is written c'

, tan.^'

where c ' = Mohr-Coulomb effective stress cohesive strength, and tan 0 ' = Mohr-Coulomb effective stress frictional resistance. Equation 2 can also be written ^ \ ( , tan 0 ' j + (a-u)-y-

... (3)

where a = total stress acting normal to the plane of sliding, and « = pore pressure. Since a, as well as r, is practically constant for a given slope geometry, and c ' and (j)' are constants for a particular soil or rock, it follows that

FaJ_ u that is, the factor of safety is a function of the pore water pressure. (There is evidence to show that the function is linear; see, for example. Bishop and Morgenstem [1]?) It is extremely important, therefore, that the pore pressure response of the soil in the slope during excavation be predicted ac•'The italic numbers in brackets refer to the list of references appended to this paper.

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612

LABORATORY SHEAR STRENGTH OF SOIL

- ORIGINAL GRADE ORIGINAL GROUNDWATER LEVEL S.

FIG. 1—Creation of a slope by excavation.

curately to avoid failure of the slope, on the one hand, or a too conservative and costly design, on the other hand. During excavation, the soil is subjected to (/) total stress unloading due to the removal of material, and (2) shear strains, as the soil resists the unbalanced gravitational forces created as the slope is formed. Both unloading and shear straining cause pore pressure changes; changes which must be predicted if the pore pressure assumed in a stability analysis is to be meaningful. Strength tests on the soil must be run in such a way that pore pressure response information becomes available for design. Evaluation of Pore Pressures within a Slope During Excavation Consider the case of a new mine in an open, flat-lying area, underlain by cohesive soil of low permeability such as clay or shale. The groundwater table lies close to the ground surface. A typical configuration might be that shown in Fig. 1. Assuming instantaneous removal of load B due to excavation, there will be a relief of stress at ^4. If .4 is originally at a depth of, say, 30 m, the original pore pressure would be about 300 kPa. If fi is 20 m high, and the pore pressure coefficient of the soil (BY is 1.0 (during unloading), then the change in pore pressure (Aw) at A due to excavation might be 400 kPa. So far, then, excavation has caused the pore pressure to drop from + 300 kPa to —100 kPa (Fig. 2). Analysis of the slip circle shown in Fig. I would show that the shear stress acting through A would be on the order of 70 kPa and the total stress acting normal to the slip surface approximately 200 kPa. The soil can be assumed to have shear strength parameters of c ' (effective stress cohesion) = 20 kPa and '^B = Au/Aff„ where u is pore pressure and <j„ is vertical total stress.

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SHIELDS AND SKERMER ON PORE PRESSURE INFORMATION

613

FS = 1 . 3

+100

lt,^________

FS

= 1,3

TtT

t i.

J

f s^^/y 5 -100

1 :

-200-

TiriE

- EXCAVATION

FIG. 2—Pore pressure dissipation with and without consideration of stress-dilatancy effects.

0 ' (effective stress friction angle) = 30 deg. Given this information, it is possible to calculate what the strain induced pore pressure changes might be in the slope, provided relevant pore pressure response information is available for the soil. The first step in calculating the strain induced pore pressure changes is to calculate the degree to which the strength of the soil is mobilized. Referring to Eq 3 and assuming, for the moment, w = —100 kPa (as a result of the removal of B, as explained previously), then 70 kPa = ^

r

+ [200 - (-100)]

'^^^ F

kPa

(4)

F = 2.71 An Fof 2.71 means that some 37 percent of the strength of the soil has had to be mobilized to hold up the slope. In order to mobilize this strength, the soil in A had to undergo a certain amount of deformation (strain). Since the soil has low permeability, it is reasonable to assume that the required deformation will take place without drainage of pore water (no volume change) and there will be a pore pressure change. The second step is to measure the pore pressure response of the soil to shear straining. A laboratory test result could be presented in the form shown in Fig. 3 which relates pore pressure to the mobilization of shear strength. (A somewhat idealized test result is illustrated in Fig. 3 to facilitate this demonstration.) According to the test, there is a linear decrease in pore

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614

LABORATORY SHEAR STRENGTH OF SOIL

T SHEAR STRESS

FAILURE STRESS (F = 1,0)

PORE PRESSURE, U, WITH RELATION TO ORIGINAL BACK PRESSURE

FIG. 3—Pore pressure response during an undrained compression test.

pressure with increase in shear stress until the failure strength of the soil is reached. At failure, the pore pressure continues to decrease, but after a certain amount of strain (and strength decrease), the material ceases to want to dilate and the pore pressure starts to increase. The residual strength of the soil is reached at X, and there is no further increase or decrease in pore pressure. Note that, for this particular test, at failure {F = 1.0) the pore pressure was —240 kPa. The third step is to determine the pore pressure generated when 70 kPa of shear stress is induced into element A of soil. As a first approximation, the strain-induced pore pressure at 37 percent of the ultimate strength can be taken off the test curve. This pore pressure is —240/2.71 = — 89 kPa; when added to the —100 kPa pore pressure caused by the removal of B (Fig. 1), the pore pressure in element A would be —189 kPa. It is now necessary to repeat Steps 1 and 3 until the factor of safety and the pore pressure are in agreement. In this particular example, agreement occurs with F = 3.35 and M = - 1 7 1 kPa; that is, 70s

20 3.35

+ [200-(-100-71)]

tan 30 deg 3.35

(5)

In conclusion, stress relief, due to unloading during excavation, caused a 400 kPa reduction in pore pressure, while shear straining caused a further 71 kPa reduction (Fig. 2). At this point, then, a slope stability analysis could be carried out using pore pressures calculated throughout the mass in the same

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SHIELDS AND SKERMER ON PORE PRESSURE INFORMATION

615

way as shown previously. The mine engineer would use the results of such analyses to determine the stability of various slope configurations immediately after excavation has taken place. This would be particularly useful in the design of a box cut, for example. With Time The pore pressures created by unloading and shear straining are not in equilibrium with the new drainage conditions. If the slope were to be left standing long enough (and not excavated away during the next mining operation), then a groundwater flow pattern, such as that illustrated in Fig. 4, could eventually evolve. In Fig. 4, groundwater is assumed to flow parallel with the slope so that at A, the pore water pressure will, with time, attain, say, +85 kPa. The rate at which the pore pressure adjusts from —171 kPa to +85 kPa is controlled by two factors: (1) the consolidation characteristics of the soil during stress relief; and (2) the strain/pore pressure response of the soil. Ignoring, for the moment, the effects of the strain inducing changes in pore pressure, the consolidation characteristics for the soil can be used to obtain the dissipation curve (Curve I) of Fig. 2. Hydraulic conductivity {K) and specific storage (S^) define the coefficient of consolidation (c,,).^ These parameters, together with the excavated slope geometry, can be input to a simple two-dimensional finite-element seepage computer program [2]. Different boundary conditions can be examined (Fig. 5). The upper nodes representing the ground surface are fixed at atmospheric pressure (zero), and the vertical line of nodes of the toe of the slope is made a no-flow boundary. The lower boundary can be assumed to be either impermeable, or the contact with a prolific aquifer of constant head. Hydraulic anisotropy can be introduced by varying the ratio of A'-major to /ir-minor. The direction and degree of anisotropy is a matter of geological field investigation. Judgement

FIG. 4—Long-term flow configuration in a slope. K/S,.

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616

LABORATORY SHEAR STRENGTH OF SOIL

GROUND SURFACE BEFORE MINING

GROUND SURFACE AT ZERO PRESSURE AFTER EXCAVATION

BOUNDARY IMPERMEABLE TO FLOW

DIRECTION OF K MINOR

BOUNDARY EITHER CONSTANT HEADy OR IMPERMEABLE TO FLOW

DIP OF BEDDING AND DIRECTION OF K MAJOR

FIG. 5—Finite-element seepage idealization.

is required in picking an appropriate value for c„, since laboratory tests on small samples tend to give values that are too low. Supplementary data from field pumping tests are often useful. The unloading effect on excavation is simulated by applying instantaneous pore pressures at each node in the mesh equal to the original groundwater pressure minus the total weight of excavated soil above that node. Material inhomogeneity, such as more permeable layers, can also be built into such an analysis. Curve I is obtained from the pore pressure distributions computed along the assumed failure surface at various intervals of time after excavation. According to Curve I, a factor of safety of 1.3 would be reached in element A after a time of tj-years. This time estimate is based on the calculation of pore pressure which would correspond to F = 1.3; that is, 20 , _„„ , tan 30 deg 70 = — + ( 2 0 0 - u ) - ^ ; ^ M = 77 kPa

However, taking into consideration the fact that as the pore pressure dissipates there is a reduction in effective stress and more strain will be required to maintain equilibrium, the real pore pressure dissipation curve will be Curve II of Fig. 2. For example, a 40 kPa increase in pore pressure due to drainage would decrease F from 3.35 (Eq 5) to 3.01. At the same time, as the value of F decreases, according to Fig. 3, there will be a corresponding decrease in u. Equilibrium would again be established with F = 3.07 and u = —138 (instead of « = —131 as a simple addition of +40 kPa to u = —171 would imply). Curve II is generated using a finite-element model which considers both Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

SHIELDS AND SKERMER ON PORE PRESSURE INFORMATION

617

dissipation of pore pressure due to consolidation and pore pressure generation caused by shear strains. The real time to reach a factor of safety of 1.3 for this slope (u = 77 kPa) would be ^2 in Fig. 2. For this example, tj will be at least twice tu and the use of consolidation theoiy alone (Curve I) would seriously underestimate the safe life of the slope. If a mine engineer had to design a slope to last a definite length of time, say, one year, he could save considerable money by taking the effects of dilatancy into account. He might, for example, be able to get away with a 45-deg slope instead of a 30-deg slope. Clearly, however, the flatter the excavated pit slope angles, the less will be the induced shear stresses and the more nearly the actual pore pressure distribution will approach the condition represented by Curve I, as computed previously. There is now ample evidence that construction pore pressures in slopes take an inordinately long time to "decay" [3,4], For example, there were still depressed pore pressures in the banks of the Panama Canal some 60 years after construction. The slow rate of decay can be attributed, probably, to the combined effects of dilatancy and stress relief, as outlined previously. Of course, if the soil or rock were to have a tendency to consolidate or compact, that is, reduce in volume, during shear, the effect of shear strains would be just the opposite; a slope would fail much sooner than simple consolidation theory would imply. Test Requirements Consolidation (rebound) tests must, of course, be run on the material to determine the rate at which the induced pore pressures will want to dissipate. The effects of bedding, fissures, boundary conditions, etc., must be taken into consideration during such tests [5]. Equally importantly, the pore pressure response of the soil during shear must be measured. This can be done directly in carefully run triaxial tests on good quality, undisturbed samples. It is important that the relevant stress level be used during testing, the correct stress path be followed, the test be undrained, and the back pressures in the sample be sufficiently high to prevent the pore pressures becoming less than atmospheric (assuming the soil to be saturated or nearly so). Lateral reduction tests are probably best to simulate the stress path which slope material will undergo in the field. Given the test requirements outlined in the previous paragraph, it is unfortunate, indeed, that drained tests have almost become the standard test for slope stability work. The problem is that it is very difficult for the mine engineer to use the results of drained tests, since he rarely designs for drained conditions. Volume change data from drained tests can be used to give a qualitative "feel" for the problem of strain-induced pore pressure changes; namely, is the material dilatant or not? It is impossible, at the present state of the art, to obtain quantitative pore pressure predictions from such tests. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

618

LABORATORY SHEAR STRENGTH OF SOIL

Conclusions Mathematical tools are now available to enable more sophisticated analyses to be undertaken of excavated slopes. The immediate requirement is for pore pressure data from carefully conducted laboratory tests. Such tests are well within current capabilities, at least in clay, yet they are very seldom carried out in practice. It is realized that accurate pore pressure response measurements in shale during tests are very difficult; it is hoped that this paper will stimulate research into this problem. Acknowledgments The authors are grateful to their colleagues, Douglas Yee and Bruce Kjartanson, for their comments. References [;] Bishop, A. W. and Morgenstem, N., Geotechnique. VoL 10, 1960, pp. 129-150. [2] Eigenbrod, K. D., Canadian Geotechnical Journal, VoL 12, 1975, pp. 429-440. [3] Lutton, R. L. and Banks, D. S., "Study of Clay Shale Slopes along the Panama Canal; Report 1—East Culebra and West Culebra Slides and the Model Slope," Technical Report 5-70-9, U.S. Army Engineers, Waterways Experiment Station, Vicksburg, Miss., 1970. [4] Skempton, A. W. in Proceedings, 9th International Conference of Soil Mechanics and Foundations Engineering, Tokyo, 1977, pp. 25-34. [5] Rowe, P. W., Geotechnique. Vol. 22, 1972, pp. 193-300.

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Vincenzo Silvestri^

Behavior of an Overconsolidated Sensitive Clay in Drained K„-Triaxial Tests

REFERENCE: Silvestri, Vincenzo, "Behavior of an OTerconsoUdated Sensitive Clay in Drained /To-Triaxial Tests," Laboratory Shear Strength of Soil, ASTM STP 740. R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 619-630. ABSTRACT: In order to understand the mechanisms that govern the development of lateral stresses in overconsolidated clay deposits, specimens of an undisturbed sensitive clay from Lachute (P.Q.) were tested in a triaxial chamber under A^o-conditions. The resuhs of these tests show that the response of the clay can be divided into three distinct phases of deformation. At low stress levels, the clay behaves as an elastic material. At intermediate stress levels, the clay behaves as a plastic material. At high stress levels, the clay becomes normally consolidated. The experimental data are used to establish a model describing the mobilization of lateral stresses, and it is shown that the in situ coefficient of earth pressure at rest cannot be determined by laboratory testing. The theory of anisotropic elasticity is used to predict the development of lateral stresses and pore water pressures at low stress levels. Predicted values are compared with those measured underneath the St. Alban (P.Q.) test fills. KEY WORDS: overconsolidated sensitive clays, coefficient of earth pressure, clay model, theory of anisotropic elasticity, critical shear stress, pore pressure coefficient B.

Nomenclatiue A_ B Of,' Oy,' Oy, KQ KQ

Pore water pressure coefficient Pore water pressure coefficient Horizontal effective stress Vertical effective stress Vertical total stress Coefficient of earth pressure at rest Incremental coefficient of earth pressure

'Assistant Professor, Department of Civil Engineering, Ecole Polytechnique, Montreal, P. Q., Canada.

Copyright by ASTM Downloaded/printed by Copyright 1981 b y A S T M University of British

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No

620 AM <j)' Oyg' Oho' e ay,„' Oyp' liyi, /Xftv lihh Eh Ey

LABORATORY SHEAR STRENGTH OF SOIL Excess pore water pressure Angle of shearing resistance Present or initial vertical effective stress Present or initial horizontal effective stress Void ratio Maximum past vertical effective pressure Vertical preconsolidation pressure Poisson's ratio for the strain in the horizontal direction due to a vertical stress Poisson's ratio for the strain in the vertical direction due to a horizontal stress Poisson's ratio for the strain in the horizontal direction due to a horizontal stress Young's modulus in the horizontal plane Young's modulus in the vertical direction

Most of the data on the behavior of overconsolidated clays during consolidation under conditions of no lateral strains have been obtained with the aim of determining the in situ coefficient of earth pressure at rest, KQ, defined as the ratio of a/,', the horizontal effective stress, to a^', the vertical effective stress [1-3].^ These studies have shown that KQ is a complex function of soil type, loading history, and stress level. For unloading cases of known overconsolidation ratio and soil type, the in situ value of KQ can be estimated with reasonable accuracy [4,5]. However, during recompression or reloading from the in situ stresses, there exists no procedure to evaluate the stress path followed by the overconsolidated clay. A limited number of studies have shown that during recompression the coefficient of incremental pressure at rest, KQ, defined as the ratio of ACT/,', the horizontal effective stress increment, to Aa\, the vertical effective stress increment, is much smaller than the original value of KQ acting in situ [6,7]. In addition, some recent studies have also shown that during recompression, overconsolidated Scandinavian clays reach a critical shear stress which governs the preconsolidation pressure [8.9]. A long-term study is in progress at Ecole Polytechnique aimed at better understanding the influences of the many variables operating during recompression of sensitive overconsolidated clays under conditions of no lateral yield and at further delineating the mechanisms responsible for the observed behavior. In this paper, the framework within which this investigation is being conducted is outlined, the equipment and testing techniques being used are briefly described, and some typical experimental results are presented. A model is presented describing the mechanisms by which lateral stresses are ^The italic numbers in brackets refer to the list of references appended to this paper.

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SILVESTRI ON CLAY BEHAVIOR IN KQ-TRIAXIAL TESTS

621

mobilized in overconsolidated sensitive clays. It is shown that the preconsolidation pressure is related to a critical shear stress. The theory of anisotropic elasticity is used to predict both the coefficient of_incremental pressure at rest, A'o, and the pore water pressure coefficient, B, defined as the ratio of the excess pore water pressure, AM, to the major total principal stress increment, Aa^. Limitations on space preclude a complete discussion of the theory used and the observed results. Clay Material and Test Procedures The soil used in this study is a stiff undisturbed sensitive clay from Lachute (P.Q.). The most relevant geotechnical properties of the clay are given in Table 1. Test specimens 6.3 cm in diameter and 15.0 cm in length were used in all tests. Both isotropic and /^o^consolidation tests were performed. Only the results of the /To-consolidation tests are reported in this paper. The procedure for A'o-consolidation follows that described by Bishop and Henkel [10]. The tests were carried out as drained triaxial tests in which the vertical load was increased in steps, and simultaneously the cell pressure was increased so that the cross section of the samples remained constant. Test Results Stress-Strain Curves The results of a typical /Co'triaxial test are shown in the upper diagram of Fig. 1. Examination of the curve shows that deviation from linearity or yielding occurs at a vertical stress equal to 280 kPa, corresponding to a vertical strain of 2.2 percent. The point of intersection of the tangents to the two initial segments of the experimental stress-strain curve corresponds to a vertical stress of about 360 kPa. Such a value is quite close to the preconsolida-

TABLE 1—Geotechnical properties of the Lachute clay. Water content, % Liquid limit, % Plastic limit, % Plasticity index, % Liquidity index Clay content, % Activity Field vane strength, kPa Sensitivity (by field vane) Vertical preconsolidation pressure, kPa

43 51 23 28 0.71 70 0.40 110 10 370

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622

LABORATORY SHEAR STRENGTH OF SOIL

1 1 1 , 1 1000

0

2

4

6

I I I I I I 8 10 12 14 16 18 20

Axial strain, % FIG. 1—Stress-strain curves.

tion pressure of the clay determined in an oedometer test and reported in Table 1. As the lateral stresses required to maintain the condition of no lateral yield were measured, it is possible to draw a shear stress-axial strain relationship, as shown in the lower diagram of Fig. 1. Examination of the curve indicates that a critical shear stress equal to 100 kPa is reached at an axial strain of 2.2 percent. This critical shear stress corresponds to the vertical stress of 280 kPa mentioned previously. In addition, it is evident that below an axial strain of 2.2 percent, the clay behaves as a pseudo-elastic material, showing a linear relationship between stress and strain. In the range of axial strain from 2.2 to 9.2 percent, the clay appears to behave approximately as an ideal plastic material, showing only a minor increase in shear stress with increasing strain. For axial strains above 9.2 percent, the relationship is typical of that obtained in an oedometer test.

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SILVESTRI ON CLAY BEHAVIOR IN Ko-TRIAXIAL TESTS

623

Stress Paths The stress path followed by the clay during ATo-consolidation is shown in Fig. 2, from which it appears that the soil response may be divided into three distinct phases of behavior. Examination of the curve shown in Fig. 2 provides the following observations: 1. During Phase I, that is, in the stress interval bounded by a / < 280 kPa, the relation between a^' and a^' is linear, and Kg, which represents the slope of the straight line, is equal to 0.23. The vertical stress, ff/ = 280 kPa, may be considered to represent a critical or threshold stress below which the clay behaves as an elastic material, but above which a major structural collapse occurs. 2. During Phase II, that is, in the region bounded by 280 kPa < a / < 490 kPa, the stress path deviates from its original direction and assumes a new direction defined by A'o = 1.0. 3. During Phase III, that is, in the region bounded by CT/ > 490 kPa, the relationship between Oh' and a^' reverts back to that of a normally consolidated clay, and KQ is equal to 0.55. By applying Jaky's approximate expression KQ — I — sin (j)', where (^' is the friction angle of the normally consolidated clay, a value of ' = 26.7 deg is obtained. Such a value is typical of many Champlain Sea clays in their normally consolidated state. The behavior of the Lachute clay may also be examined on a MohrCoulomb diagram, as shown in Fig. 3. Examination of the curve shown in this figure provides the following observations: 1. At the end of Phase I the clay reaches a maximum or critical shear stress equal to 100 kPa. 2. During Phase II, the soil deforms as an ideal plastic material and the critical shear stress remains approximately constant. 3. During Phase III, the soil behaves as a normally consolidated clay and Ko = Ko = 0.55. Clay Model and Prediction ol KQ and B Model Describing the Mobilization of Lateral Stresses On the basis of the response behavior of the Lachute clay shown in Figs. 2 and 3, as well as previous studies reported on London clay [//], Scandinavian clays [9,72], and Champlain Sea clays [13], a model is proposed to describe the mechanisms by which lateral stresses are mobilized in overconsolidated clay deposits. This model is shown in Fig. 4. In Fig. 4a, the void ratio of the clay, originally deposited under certain environmental conditions, follows the

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624

UBORATORY SHEAR STRENGTH OF SOIL

600

\

1

LACHUTE

CLAY

~i

500

r

400 Pho« I

a.

PhoteH

300

200-

Phottlir 100-

0

100

200

300

400 500 ffj, kPO

600

700

800

900

FIG. I—Stress path.

500

400

300

L ACHUT E CLA

r

Phoseu

Pho l e l

Phaselu

^ ^ .^200

100

200

300

400

500

600

700

SOO

(oi+oAVZ, kpa FIG. 3—Mohr-Coulomb diagram.

virgin consolidation line aa up to point A. Because of thixotropic hardening or cementation bonds or both, the clay fabric becomes stiffer and stronger and, as the sediments accumulate, the void ratio decreases along the segment AB. Point B represents the maximum past effective overburden pressure. Due to delayed consolidation, the void ratio decreases along the vertical line EC, as indicated by Bjerrum [9]. Following unloading due to erosion, the effective overburden pressure is reduced to the present overburden pressure, Oyo'• The clay is thus an overconsolidated clay having an overconsolidation ratio equal to Oy^'/a^'. Due to delayed swelling following erosion, the void ratio increases somewhat and reaches the present value of e^.

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SILVESTRI ON CLAY BEHAVIOR IN KQ-TRIAXIAL TESTS

625

a) e - l o g a « relationship \o \

Sedimentotion \A b

void

Thixotropic liordening or etrtitntotlon bonding

ratio

Delayed contolldatlon

e 1 \

Unloading \ ^ \ by eroiionVo \

CHF Y\

Delayed swelling \

\

1

\o

1

.

.

._ „..,

Log ov b) ov-ov relationship (Jim 7le

__ic

Olt* YD

ai

/

/ A E

/ /

A ^

a ^ ^ ^

^A FIG. 4—Clay model.

When a clay of this type is subjected to additional loading in situ, it will, as indicated in Fig. 4a, show a sharp bend at a pressure a^^ which is greater than the maximum past effective vertical pressure,ff^,„,',if the clay fabric has been strengthened by cementation bonds or thixotropic hardening or both. The preconsolidation pressure effect of the clay is thus the result of three contributions: (/) the overconsolidation effect due to erosion, which is constant with depth; the consequence of which is that the clay can carry an additional load equal to (ff„„' — a^g') without any significant volume change; (2) the overconsolidation effect due to delayed consolidation which the clay underwent in the period it carried the load a^„,'; and (J) the overconsolidation effect due to thixotropic hardening or cementation bonds or both. At a vertical stress equal to a^^', the initial clay structure will be destroyed. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

626

UBORATORY SHEAR STRENGTH OF SOIL

If the clay were in the same environment as during deposition, the e-log o,' relation would be to revert back to the virgin compression line a a . However, because of environmental changes that have probably occurred since deposition, a new virgin compression line |3j3 has been created. Examination of the curves shown in Fig. 46 provides the following observations on the mechanisms responsible for the mobilization of lateral stresses in overconsolidated clay deposits during one-dimensional consolidation. During deposition and virgin consolidation, the stress path follows the straight line a ' a ' up to point A. The slope of the line a.'a' is given with sufficient accuracy by /Co = 1 ~ sin (^', where <^' is the angle of shearing resistance for the normally consolidated clay. Due to thixotropic hardening or cementation bonding or both, the clay fabric becomes stiffer; the consequence of which is that the horizontal stress may increase at a rate lower than that during virgin compression, and the clay follows the path AB. Due to delayed consolidation, the clay compresses and, as shown by Bjerrum and Andersen [/2], the lateral stress a;,' increases at a constant value of a^', and the clay follows the path BC. As a result of unloading due to erosion, bothCT;,'and a,' decrease along CT>, and /^o may reach the value of the coefficient of passive pressure [/.2]. Due to delayed swelling following erosion, it is possible for ay,' to decrease somewhat while a,' remains constant, and the clay follows the path T>E. It should be noted that the in situ value of KQ is represented by the ratio of a/,„' to a„', that is, the slope of the straight line from the origin to point E. Upon reloading from the in situ stresses, the clay follows the path EFGH. In the overconsolidated stress region, the slope of the line EF is much smaller than that of the line OE, and as a consequence, during recompression, KQ < KQ in situ. The segment EF corresponds to the behavior of clay during Phase I, as shown in Fig. 2. Once the preconsolidation pressure is reached corresponding to point F, the clay fabric collapses and the soil follows the path FG. At point G, the soil becomes normally consolidated again, and it will follow the path GH along the line jS'iS'. If the clay were in the same environment as during deposition, the a/,'-a,,' relation would be such to revert back to the virgin line a ' a ' . If, however, leaching or other environmental changes have occurred since deposition, a new a/,'-a/ line, /3'/3', has been created. Along jS'jS', /Co is given with sufficient accuracy by Jaky's approximate expression ATQ = 1 — sin <^', where 4>' is the friction angle of the normally consolidated clay. Should a sample of the overconsolidated clay be removed from the ground, the stress path will be along EO in Fig. 4b. Upon reloading in a onedimensional consolidation test, the stresses a/,' and o^' will vary along OIGH. The segment 01 corresponds to the clay response during Phase I and its slope is given by KQ. For the Lachute clay, KQ = 0.23 in this region. It should be noted at once that KQ measured during Phase I is not equal to the in situ value of KQ, since, as discussed previously, the in situ value of ATo is given by the slope of the line OE, which is not equal to that of 01. As a consequence,. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

SILVESTRI ON GUY BEHAVIOR IN KQ-TRIAXIAL TESTS

627

it is not possible to measure in the laboratory the_in situ value of KQ since, as shown previously, one measures the value of KQ during recompression. In order to measure the in situ value of KQ, one must use field tests, as pointed out also by Wroth [5]. At point /, the preconsolidation pressure of the clay is reached and the clay structure collapses. At point G, once again, the clay becomes normally consolidated, and the stresses Of,' and a^' will vary along the Iinei3'i8'. Prediction of Ky and B During Phase I For the sensitive clays of Eastern Canada, a considerable number of studies have shown that deformations are essentially of an elastic nature so long as the shearing stresses are less than the shearing strengths [7.14]. In addition, it has been shown that these clays behave as anisotropic elastic materials having different elastic properties in the vertical and horizontal direction [75.76]. By applying the theory of anisotropic elasticity [77] it can be easily shown that 7^0 is given by

where Hyi, = Poisson's ratio for the strain in the horizontal direction due to a vertical stress, ^AA = Poisson's ratio for the strain in the horizontal direction due to a horizontal stress, £/,=Young's modulus in the horizontal plane, and £",,=Young's modulus in the vertical direction. Even though the parameters n^^, /i/,/,, Ef,, and E^ were not evaluated for the Lachute clay used in this study, it is possible to extrapolate to this soil the results obtained for other sensitive clay of Eastern Canada. Thus, for a sensitive clay from Ottawa, Wong and Mitchell [18] report an average value of Poisson's ratio equal to 0.25 which, when introduced into Eq 1, yields KQ = 0.33, by assuming £"/, = E^. Such a value of KQ is very close to the value of 0.30 measured in a TiCo-triaxial test for the same clay [7]. In addition, by applying the experimental data obtained by Lo et^al [76] on another sensitive clay of Eastern Canada, an average value of KQ equal to 0.23 is obtained. Finally, for the St. Louis (P. Q.) clay studied by Yong and Silvestri [75], n^f, = 0.35, MA/, = 0.20, EH -_A.3\ MPa, andf^ = 6.90 MPa, which, when introduced into Eq 1, yield KQ = 0.27. As the measured value of KQ for the Lachute clay which is equal to 0.23 falls in the range of values predicted earlier for a number of sensitive clays of Eastern Canada, it appears reasonable to assume that the theory of Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

628

LABORATORY SHEAR STRENGTH OF SOIL

anisotropic elasticity may be applied also to the Lachute clay used in this investigation. By using this theory, it is possible to arrive at a mathematical expression for the pore water pressure parameter^. This parameter is given by [19]:

where ni,y = Poisson's ratio for the strain in the vertical direction due to a horizontal stress. As the pore water pressure coefficient B is related to A by the following expression [20]: 5-Zo + (l-^oM

(3)

substitution of Eq 2 into Eq 3 yields

B = Ko + {l-Ko)-

^Ji^:'^""Eh'Ey + 2-

.

(4)

Hhh- 4iu„

For the St. Louis (P. Q.) clay [15], fi^y = 0.24 which, when introduced with the other parameters given above into Eqs 3 and 4, yields/4 = 0.12 and B — 0.36. For the Ottawa clay studied by Lo et al^/6], an average value for B equal to 0.32 is obtained. These values of B are consistent with those reported by Leroueil et al [2/] for a considerable number of case histories related to embankment loadings on sensitive^lay deposits. For the St. Alban (P. Q.) test fills [21], the observed values of B vary for the most part between 0.23 and 0.53, with an average of about 0.35. On the basis of the results presented in this section it may be stated that while the predictive ability of this approach cannot be fully assessed in view of the limited data reported, a preliminary evaluation appears to indicate general consistency in the prediction of both the coefficient of incremental pressure at rest, ATQ, and the pore water pressure parameter B. Conclusions For the specific materials discussed in this paper, the following conclusions have been reached: 1. A clay model has been proposed and found satisfactory to describe the mechanisms by which lateral stresses are mobilized in overconsolidated clay deposits. On the basis of this model it is shown that the in situ values of ATQ cannot be measured in the laboratory; instead one measures the value of KQ during recompression. 2. The response of the Lachute clay analyzed in this paper is characterized

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SILVESTRI ON CLAY BEHAVIOR IN KQ-TRIAXIAL TESTS

629

by three distinct phases of behavior: Phase I linked to a pseudo-elastic response; Phase II related to a critical shear strength; and Phase III related to the normally consolidated clay response. 3. The value of Kg during recompression in Phase I is remarkably constant and has an average value of 0.23 for the Lachute clay. 4. The value of ^o during Phase III is constant and equal to 0.55, from which a friction angle of 26.7 deg is obtained by application of Jaky's expression KQ = I — sin (j)'. 5. Application of the theory of anisotropic elasticity permits one to predict the values of both KQ and B during Phase I. The calculated values of KQ are consistent with that measured for the Lachute clay. It is also shown that the pore water pressure coefficients B calculated by means of the theory of anisotropic elasticity are consistent with experimental data obtained from in situ measurements. Acknowledgments The author wishes to express his appreciation to the National Research Council of Canada for Grant A-6110, under which this study is being carried out. References |/] Bishop, A. W., "Test Requirements for Measuring the Coefficient of Earth-Pressure at Rest," Brussels Conference on Earth Pressure Problems, Brussels, 1958, Vol. 1, pp. 2-14. \2] Brooker, E. W. and Ireland. H. C , Canadian GeotechnicalJoumal. Vol. 2, No. I, 1965, pp. 1-15. \3\ Campanella, R. G. and Vaid, Y. P.. Canadian GeotechnicalJoumal. Vol. 9, No. 3, 1972, pp. 249-260. \4\ Schmidt, B., Canadian GeotechnicalJoumal. Vol. 3, No. 4, pp. 239-242. (5| Wroth, C. P. in Proceedings. American Society of Civil Engineers (hereafter cited as ASCE] Specialty Conference on /« Situ Measurement of Soil Properties, Raleigh, N.C., 1975, Vol. II, pp. 181-230. (6] Simons, N. E. and Som, N. N. in Proceedings. 7th International Conference on Soil Mechanics and Foundations Engineering, Mexico, 1%9, Vol. 1, pp. 369-377. [7] Mitchell, R. J., Sangrey, D. A., and Webb, G. S. in Proceedings. ASCE "Foundations in the Crust of Sensitive Clay Deposits", Specialty Conference on Performance of Earth and Earth-Supported Structures, Lafayette, Ind., 1972, Vol. 1, Part 2, pp. 1051-1072. [8] Berre, T. and Bjerrum, L. in Proceedings, 8th International Conference on Soil Mechanics and Foundations Engineering, Moscow, 1973, Vol. 1.1, pp. 39-49. (9] Bjerrum, L. in Proceedings. 8th International Conference on Soil Mechanics and Foundations Engineering, Moscow, 1973, Vol. 3, pp. 111-159. [10] Bishop, A. W. and Henkel, D. J., The Measurement of Soil Properties in the Triaxial Test. Arnold, London, 1957, p. 190. [//] Chandler, R. J. in Proceedings. Geotechnical Conference, Oslo, 1967, Vol. 2, pp. 177-178. [12] Bjerrum, L. and Andersen, K. H. in Proceedings. 5th European Conference on Soil Mechanics and Foundations Engineering, Madrid, 1972, Vol. 1, pp. 11-20. |/J] Leroueil, S., Tavenas, F. A., and Brucy, ¥., Journal of the Geotechnical Engineering Division. ASCE, Vol. 105, No. GT6, 1979, pp. 759-778. [14] Tavenas, F. A., Chapeau, C , LaRochelle, P., and Roy, M., Canadian Geotechnical Journal. Vol. 11, No. 1, 1974, pp. 109-141.

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630

LABORATORY SHEAR STRENGTH OF SOIL

[IS] Yong, R. N. and Silvestri, V., Canadian GeotechnicalJournal. Vol. 16, No. 2, 1979, pp. 335-350. [/61 Lo, K. Y., Leonards, G. A., and Yuen, C , Norwegian Geotechnical Institute, Publication No. 117, Oslo, 1977, pp. 1-16. [17] Hearmon, R. F. S., An Introduction to Applied Anisotropic Elasticity, Oxford University Press, Oxford, 1%1. [18] Wong, P. K. K. and Mitchell. R. J., Geotechnique. Vol. 25, No. 4, 1975, pp. 763-782. [791 Pickering, D. J., Geotechnique. Vol. 20, No. 3, 1970. pp. 271-276. 120] Wu, T. H., Soil Mechanics, Allyn and Bacon, Boston, 1966, p. 431. [21] Leroueil, S., Tavenas, F., Mieussens, C , and Peignaud, M., Canadian GeotechnicalJournal, Vol. 15, No. 1, 1978, pp. 66-82.

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Discussions

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Suzanne Lacasse^ and Mladen Vucetic^

Discussion of "State of tine Art: Laboratory Strength Testing of Soils"

REFERENCE: Lacasse, Suzanne and Vucetic, Mladen, "Discussion of 'State of the Art: Lalioratoiy Strengtii Testing of Soils'," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 633-637. ABSTRACT: Saada and Townsend, in their state-of-tlie-art paper on laboratory strength testing of soil, present very severe criticisms of the simple shear testing method and the apparatuses presently in use. The discussers do not share this point of view. A fair assessment of a piece of equipment and of the testing procedure calls not only for an enumeration of its shortcomings, but also for a careful evaluation of the significance of these deficiencies on the measured parameters. Saada and Townsend questioned the overall usefulness of the testing method in geotechnical engineering problems. KEY WORDS: direct simple shear test, size effect, test procedures, undrained shear strength, clay

Saada and Townsend, in their state-of-the-art paper on laboratory strength testing of soils,^ present very severe criticisms of the simple shear testing method and the apparatuses presently in use. The discussers do not share this point of view. A fair assessment of a piece of equipment and of the testing procedure calls not only for an enumeration of its shortcomings, but also for a careful evaluation of the significance of these deficiencies on the measured parameters. Saada and Townsend questioned the overall usefulness of the testing method in geotechnical engineering problems. Nonunifonn Stress Distribution The configuration of the simple shear specimen expectedly leads to nonuniformity of stresses. The SGI/NGI apparatus does not provide complementary shear stresses on the vertical sides of the specimen. During shear 'Research Fellow, Norwegian Geotechnical Institute, Oslo, Norway. This publication, pp. 7-77.

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LABORATORY SHEAR STRENGTH OF SOIL

distortion, the soil specimen experiences a nonuniform shear stress distribution over the top and bottom faces and normal stresses develop on all faces Prevost and Heeg [/] investigated theoretically the effects of slippage on the normal and shear stress distribution on the upper and lower faces and edges of the test specimen. Figure 1 illustrates the stresses on the upper and lower faces for conditions of "no slippage" (X = 0) between the top and bottom plates and the soil. The figure also shows the stress distribution for the unlikely condition of X = 0.5, that is, where slippage is such that the center point on the top and bottom faces of the specimen moves by only one half of the horizontal displacement at the edges of the specimen. The analyses, for a height-to-diameter ratio (h/D) of 0.25, show zones of large stress variations at the edges of the specimen. But the data represent the extreme case of stress concentration, as Prevost and Heeg, to produce that figure, used an isotropic elastic soil model. For an elastic-plastic soil, the end effect will be greatly reduced as yield occurs. One can minimize slippage with the insertion of short pins or fins on the faces of the specimen or with a coating of the soilcap interfaces with an epoxy-sand mixture (for testing sands). In most cases, one can detect slippage by studying the experimental stress-strain curve. If in doubt, one can carry out the simple shear test to large strains and observe any differential displacement between top and bottom caps and specimen. In a thorough investigation of the Cambridge and NGI simple shear apparatuses, Budhu and Wood [3] showed that the (average) ratio of shear stress to normal stress on the top and bottom horizontal boundaries underestimated the stress ratio in the center of the sample by about 12 percent in static loading. This average stress ratio is that measured by the NGI apparatus.

New Experimental Results Concerning Specimen Size Effect One means to investigate the boundary effects consists in testing specimens of different diameters while keeping the specimen height constant. In the presence of significant nonuniform stresses on the faces and within the cross section of the specimen, changing of the height-to-diameter ratio of the specimen should lead to different measured values of stiffness and average horizontal shear stress at failure. Figure 2 summarizes the results of simple shear tests recently conducted at NGI on undisturbed specimens of Haga clay Up = 15 percent, S, = 6), sampled in 200-mm-diameter tubes. The investigation looked into the effects of sample size at two overconsolidation ratios (OCR). The overconsolidation ratio of 10 was achieved by rebound of the specimens consolidated under a The italic numbers in brackets refer to the list of references appended to this paper.

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LACASSE AND VUCETIC ON STATE-OF-THE-ART PAPER

635

T - average horizon-tal shear stress applied on the specimen.

FIG. 1—Distribution of shear and normal stresses on top face of specimen [1].

maximum vertical stress of 400 kPa. The test program included tests on specimens with cross-sectional areas of 20, 50, and 104 cm^. Thin specimens of large diameter presumably have a more uniform stress distribution than short thick specimens. The experimental results show very little, if any, size effect on either the measured maximum horizontal shear stress or the stress-strain curve and hence modulus of Haga clay. The differences in measured horizontal shear stress amount to less than the expected scatter in results due to nonhomogeneity of undisturbed soil specimens. Further tests with the 104-cm2 specimens are underway [4]. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

636

LABORATORY SHEAR STRENGTH OF SOIL

g

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of height-to-diameter ratio on direct simple shear test results.

Kovacs [5], whom Saada and Townsend cite to support their arguments, presented very puzzling results with respect to the effects of specimen size on the simple shear cyclic shear modulus of resedimented kaolinite. Saada and Townsend's conclusions differ from those of Kovacs. We also believe that their comments based on Kovacs's results from "unconfined" cyclic shear tests do not constitute a basis for severe criticism of simple shear testing as usually performed. Woods [6], in a careful evaluation of the available apparatuses for measuring dynamic soil properties, recognized the usefulness of the simple shear test despite its shortcomings. He arrived at this conclusion mainly on the basis of good correlations with other reliable data, with has accrued significance in terms of cyclic results.

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LACASSE AND VUCETIC ON STATE-OF-THE-ART PAPER

637

Sununaiy

The design of any experimental device will always be a compromise between the theoretically possible and the practically feasible. Both soil characteristics and equipment features condition the selection of an appropriate testing method for a given problem. It is believed that the advantages of the simple shear test, including the simplicity in setting up the specimen and in carrying out the test, are significant. Soil specimens may be prepared in their undisturbed state, a feature not available for more complex and research oriented tools, which are limited to the testing of redeposited or sedimented specimens. The back pressuring capability in the newer versions of the simple shear apparatus provides added flexibility to the testing method. The possibility of relating stress ratio on the horizontal plane and the inclination of the principal axes of stress exists [3], and the quantity of available evaluated experience for a variety of soils, encourages further use of the equipment. Even in consideration of its shortcomings, some of which appear to have relatively minor effects on the measured parameters, the direct simple shear test is believed to yield very useful results. It represents one of the valuable tools available to define the complex stress-strain-strength behavior of soils in engineering practice. References [/] Prevost, J. H. and Heeg, K., Canadian Geotechnical Journal, Vol. 13, No. 4, 1976, pp. 418-429. [21 Shen, C. K., Sadigh, K., and Herrmann, L. R. in Dynamic Geotechnical Testing. ASTM STP 654. American Society for Testing and Materials, 1978, pp. 148-162. [3\ Budhu, M. and Wood, D. M., "A Study of the Simple Shear Test," Engineering Department, Cambridge University, England, April 1979. [4\ Vucetic, M., "The Influence of Height versus Diameter Ratio on the Behaviour of Haga Clay in the NGI Simple Shear Device," Internal Report 56204-9, 1981, Norwegian Geotechnical Institute, Oslo, Norway. [5] Kovacs, W. D., "Effect of Sample Configuration in Simple Shear Testing," Symposium on Earth and Earth Structures under Earthquake and Dynamic Loads, Roorkee, India, 1973, pp. 82-86. [6] Woods, R. D., "Measurement of Dynamic Soil Properties," Specialty Conference on Earthquake Engineering and Soil Dynamics, American Society of Civil Engineers, Pasadena, Calif., 1978, Vol. I, pp. 91-178.

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J. T. Christian^

Discussion of "State of tiie Art: Laboratory Strength Testing of Soils"

REFERENCE: Christian, J. T., "Discussion of 'State of tlie Art: Laboratory Strengtii Testing of Soils'," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 638-640. ABSTRACT: Finite element analyses of the direct simple shear sample do account for the three-dimensional state of displacement, strain, and stress. Three independent analyses indicate substantial uniformity of stress in the central region of a linearly elastic sample, but stress concentrations at the edges may make the device unsuitable for very sensitive soils or for investigation of progressive failure. The results of photoelastic investigations described in the report include unsymmetric distributions of stress that are mathematically anomalous and are probably caused by inadequate restraints at the boundaries. KEY WORDS: direct shear tests, simple shear tests, finite elements, photo-elasticity

This author must take exception to the comments in the state-of-the-art (SOA) paper by Saada and Townsend^ regarding the analysis of the Norwegian Direct Simple Shear device performed by Lucks et al (SOA Ref 37), and the expanded version of these remarks presented in an earlier paper partially authored by one of the reporters (SOA Ref 40). The photoelastic experiments described in the report may also be in error. Lucks et al described two independent analyses whose results were combined into one technical note. One analysis, performed by H6eg and Brandow, used three-dimensional finite elements. The lateral boundaries were stress free, the bottom was fixed and rigid, and the rough, rigid top boundary was constrained to move uniformly in the X-direction. The horizontal shear stresses on the midplane from this analysis appear to be the ones identified in SOA Fig. 26 as "finite element" results. Clearly, this analysis does not prescribe plane strain deformations. ' Senior consulting engineer. Stone & Webster Engineering Corporation, Boston, Mass. 02107. ^This publication, pp. 7-77.

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CHRISTIAN ON STATE-OF-THE-ART PAPER

639

The second analysis, performed by Lucks and Christian, used a finite element model of an axially symmetric body loaded unsymmetrically. The technique involves expansion of the loads and displacements in a Fourier series in terms of the cylindrical coordinate angle theta. It can express any arbitrary three-dimensional state of stress and strain, provided the material is linearly elastic and has at least two axes of symmetry, the geometry is axially symmetric, and the boundary conditions are expressed in a Fourier series. It happens that for the case of a uniform horizontal displacement of the top platen, the Fourier series degenerates to one term for each component of displacement. Details of this approach were described by Wilson^ and are to be found in standard texts on the finite element method (for example, by Zienkiewicz''). The boundary conditions used by Lucks and Christian were the same as those used by Hoeg and Brandow. The analyses reported by Lucks et al showed substantial uniformity of stress throughout the sample. They also showed significant concentrations of normal stress at the comers of the vertical section of the sample. Some six years later, Shen et al (SOA Ref 39), using the same type of Fourier expansion technique, with a mesh of essentially the same fineness, performed a more comprehensive parametric analysis, incorporating the membrane in the finite element model and including the nonuniform stress distributions due to initial vertical loading. They showed distributions of horizontal shear strain that were in some instances quite nonuniform and in others reasonably close to the pattern of shear stress reported by Lucks et al. Shen et al made the point that much of the nonuniformity is due to the initially imposed vertical displacement and that "a large horizontal displacement... seems to have overriding effect in minimizing the nonuniform shear distribution due to vertical displacement". It should be noted that the extreme instance of nonuniform distribution of shear stress occurred when Poisson's ratio was 0.49 for both the vertical compression and the shear loading. This is, in effect, a case in which the initial vertical load is applied under undrained conditions, which is a very unlikely situation for most testing programs. Both of these analyses are limited to isotropic, elastic materials with rough, rigid end platens. They show that there are concentrations of stress and strain near the comers of the sample, but for most cases the distribution of stress and strain is substantially uniform over the central portion of the sample. These facts indicate that the device is suitable for testing the behavior of most clays under monotonic loading, as described by Ladd.^ They also indicate that the device is not suitable for finding the peak strength of very sensitive clays, as is confirmed by La Rochelle's experience with Leda clays. Wilson, E. L., American Institute of Aeronautics and Astronautics Journal, Vol. 3, No. 12, 1965, pp. 2259-2274. ''zienkiewicz, O. C , The Finite Element Method. 3rd ed., McGraw-Hill, London, 1977, especially Ch. 15. This publication, pp. 643-652.

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640

LABORATORY SHEAR STRENGTH OF SOIL

Cyclic loading on sands is another type of test in which progressive failure is important, and Shen et al pointed out that this may be a serious problem when the Norwegian device is used for dynamic testing. Saada and Townsend describe the results of photoelastic experiments. The results, plotted in SOA Figs. 25 and 26, show at least one anomaly. Figure 26 shows the horizontal shear stresses unsymmetrically distributed about the center of the sample. This is found in none of the finite element analyses and is impossible for an isotropic, elastic, axially symmetric body loaded by displacing a rigid top platen uniformly vertically or horizontally in the X-direction. The photoelastic model replaces the rigid platens with blocks of photoelastic material of about the same thickness as the sample. Despite all efforts to restrain these ends, they cannot guarantee a uniform displacement of the top surface of the cylindrical sample. The resulting vertical strains in the sample are probably the cause of the anomaly obtained by the photoelastic method.

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Panelists' Reports

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C. C. Ladd'

Discussion on Laboratory Shear Devices

REFERENCE: Ladd, C. C , "Discassion on Laboratmy Shear Devices," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 643-652. ABSTRACT: This discussion starts with a general assessment of the capabilities of several types of laboratory shear devices and their corresponding suitability for use in specialized design practice and for basic research into the constitutive stress-strainstrength relationships of soils. It then focuses in greater depth on two specific topics: use of the Geonor Direct Simple Shear (DSS) device for design practice involving soft clays, and experimental requirements needed to reliably measure stress-strain-strength behavior in cross anisotropic soils. KEY WORDS; anisotropy, clay, deformation, laboratory test equipment, sand, shear modulus, shear strength, shear tests

General Assessment of Laboratory Shear Devices Devices and Criteria Table 1 lists the devices considered, using a slightly different terminology than employed in the SOA paper. (SOA denotes the state-of-the-art paper by Saada and Townsend.2) The devices are further described as follows: 1. Triaxial—a conventional triaxial cell having a solid circular specimen and subdivided as either "standard" triaxial compression cells or "special" cells with frictionless end platens, ability to readily achieve /fo-consolidation and/or perform both triaxial compression and extension tests, etc. 2. Direct Simple Shear—the Geonor Direct Simple Shear (DSS) device as described in SOA Ref 11. 3. Plane Strain—devices primarily designed for plane strain compression ' Professor of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Mass. 02139. ^This publication, pp. 7-77.

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644

LABORATORY SHEAR STRENGTH OF SOIL

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LADD ON LABORATORY SHEAR DEVICES

645

and extension testing of solid prismatic specimens (such as some of those listed in Table 2 of the SO A paper). 4. True Triaxial—devices with all rigid, all flexible, or mixed boundary conditions capable of independently controlling the three principal stresses acting on a solid prismatic specimen (but these stresses must coincide with the x-y-z axes). 5. Hollow Cylinder—devices that apply differing combinations of axial and torsional stress to a hollow circular specimen having identical inner and outer fluid pressures (P, = PJ. 6. Directional Shear Cell (DSC)—a flexible boundary plane strain device having the unique capability of controlling the major principal stress direction by varying the normal stress and shear stress acting on four faces of a cubical sample contained between two rigid end plattens (described by Arthur et al [7]).^ The capabilities of these devices are judged (for static loading conditions) according to four criteria: can they reliably measure stress-strain characteristics (relatively uniform and well-defined states of stress and strain) and the Mohr-Coulomb effective stress strength parameters, c ' and 0 ' ; can the devices systematically vary the intermediate principal stress condition as reflected by the value of b = (CT2 ~ '^3)/(<^i ~ 0^3); and can they be used to measure stress-strain-strength anisotropy. As will be discussed in more detail, measurements of anisotropy require the ability to fully control the direction of the major principal stress axis relative to the vertical depositional direction, termed the 6-angle. Finally, the devices are assessed according to certain application areas. Will the data be used for relatively specialized design practice (for example, soft-ground construction involving staged loading, offshore structures, underground construction, etc.) or for basic research to develop further insight regarding constitutive relationships? The former requires that suitable equipment be generally available to the profession and that associated test procedures be relatively straightforward and economical. Assessment The assessments in Table 1 are given in terms of "yes", "no", and "?". A "yes" means that the device has that capability and/or is suited for that application area, a "no" means that it does not, and a " ? " denotes uncertainty. The evaluation obviously involves subjective judgement, and no doubt reflects some bias based on the author's experience (or lack thereof). Nevertheless, everyone should agree that each apparatus has some limitations and none ideally meets all design and research needs. Thus the profession should continue to employ various devices depending on the specific objectives. The italic numbers in brackets refer to the list of references appended to this paper.

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646

LABORATORY SHEAR STRENGTH OF SOIL

The SOA paper discussed the measurement capabilities of the devices in considerable detail. Concerning application areas involving soft sedimentary clays: 1. Specimens must generally be /fo-consolidated in order to simulate in situ stress-strain behavior. This procedure is difficult and/or time consuming, however, unless the device has special features, such as developed by Campanella and Vaid [2] or Bishop and Wesley [J]. 2. Plane strain devices offer little advantage over specialized triaxial cells for most practical design problems. 3. True triaxial devices have been mainly used for research into the effects oib = (CT2 ~ Oi)/{a\ —CT3)with sands, and more recently with clays. They are generally costly and difficult to operate. 4. The hollow cylinder apparatus will also probably remain most useful in research rather than design practice. 5. The DSS and DSC devices are discussed in subsequent sections. Undrained Direct Simple Shear Testing of Soft Sedimentary Clays /lo-consolidated-undrained (CK<^) tests are performed in the Geonor Direct Simple Shear (DSS) apparatus by increasing the horizontal shear stress (,Th) while varying the vertical effective stress {Oy) to maintain constant volume. The state of stress can not be defined solely from knowing the values of T), and CT^', and the basic configuration of the DSS device causes nonuniform stresses within the test specimen. These facts preclude rigorous interpretation of DSS stress-strain data, and "measured" values of c ' and <^' are subject to considerable error [4], In fact, the SOA paper concludes that the DSS device represents little improvement over the direct (box) shear test, and presents extensive results from theoretical elastic analyses and photoelastic studies to support that conclusion. On the other hand, the discussion by Lacasse and Vucetic [5] maintains that nonuniformities predicted from elastic analyses will be greatly reduced as the clay yields during shear. They also present data from C/LQUDSS tests run with varying height-to-diameter ratios (h/D = 0.14, 0.20, and 0.32) on normally and highly overconsolidated samples of a moderately sensitive clay which support their viewpoint. The author feels that C/CQUDSS testing is inappropriate for basic research into constitutive relationships and for measurements of c ' and (^'. However, experience obtained from over 10 years of DSS testing performed in conjunction with design problems involving construction of embankments, tanks, etc., on soft sedimentary clay deposits suggests that CATQUDSS testing offers the following practical advantages: 1. During consolidation prior to shear, one easily obtains the same compression curve and coefficient of consolidation data as gained from con-

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LADD ON LABORATORY SHEAR DEVICES

647

ventional incremental oedometer tests (not true for other devices listed in Table 1). 2. The measured values of maximum horizontal shear stress (T^max.) give a fairly reliable estimate of the undrained shear strength (c„) appropriate for stability analyses involving most soft sedimentary clay deposits, for example, Ladd and Foott [6] and Ladd et al [7]. 3. The measured values of undrained Young's modulus (E„) give a good indication of potential displacements due to in situ undrained shear deformations [7]. tests are also easier to run and less liable to experimental problems than the alternative of performing CKQV triaxial compression and extension tests. This approach is therefore very cost effective for obtaining consolidation-c„ — E„ data, although information regarding pore pressure and effective stress strength parameters, if needed, must be obtained by other means. Figure 1 compares field and laboratory DSS undrained shear strength data. The open squares denote average values of the in situ c„ backcalculated from case histories of loading failures divided by the estimated in situ preconsolidation pressure, P^ [8]. Most of the cases involved embankment failures, including many of those used to develop Bjerrum's [9] field vane correction factor. The solid circles are values of c„ = T), max. divided by the vertical consolidation stress Oy^' from C/CQUDSS tests run at Massachusetts Institute of Technology (MIT) on normally consolidated samples of ten different clays from the U.S. and abroad. The DSS data generally fall within the band from the field cases and follow the same general trend. No other laboratory test. C/IL^OUDSS

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FELD Cu/Ffc DERIVED FROM CASE HISTORES OF "UOADING" FAILURES (AFTER LARSSON, 1980)

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648

LABORATORY SHEAR STRENGTH OF SOIL

and certainly not CIU or CKQV triaxial compression tests, has been shown to produce comparable results. C/CoUDSS-tests also yield very consistent data concerning the effects of stress history on strength, as illustrated by the c,/ayc' versus overconsolidation ratio (OCR) curves plotted in Fig. 2 for six soils ranging from an organic mud flat deposit (Curve 1) to a varved clay (Curve 6). These results serve as a valuable check on data obtained from new deposits and are often used by the author in preliminary designs. Figure 3 presents secant values of E,/c^ plotted versus the applied shear stress ratio from CA^oUDSS tests run on seven normally consolidated soils. Although these soils have quite similar trends regarding variations in modulus ratio during undrained shear, E^c^ is seen to decrease by almost two orders of magnitude with increasing plasticity and organic content of the soil. Moreover, undrained shear deformations observed during construction of embankments on five of these deposits were in general accord with those expected based on the relative magnitudes of Ei/c^ shown in Fig. 3. In conclusion, in spite of theoretical and practical limitations of the Geonor direct simple shear apparatus, C/^^UDSS testing offers important practical advantages compared with other shear devices for design problems involving soft sedimentary clays. Measiuement of Stress-Strain-Strength Anisotropy Background Of the several factors that inhibit continued progress in developing improved procedures for predicting the in situ strength deformation behavior of soils from laboratory test data, one of the most important results from an inability to realistically imitate in the laboratory the varied stress path conditions encountered in the field, most especially those involving a rotation of principal stress directions. Professional practice therefore largely ignores the stress-strain-strength anisotropy exhibited by most granular and cohesive soils since (/) it is difficult to measure experimentally; (2) most constitutive relationships used for predicting deformations also ignore anisotropic soil behavior (the Prevost-Hoeg [10] model representing a notable exception); and (J) relatively little information exists for guidance as to its relative importance vis-a-vis other factors known to influence predicted field performance. Ladd et al [7] distinguish between three forms of anisotropy in /Co-consolidated natural clays: 1. Inherent—that which exists prior to application of shear due to initial deposition of the clay particles and subsequent /Lg-consolidation. 2. Stress-System Induced—that which results solely from the fact that different increments of shear stress are required to produce failure (for KQ ^

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LADD O N LABORATORY SHEAR DEVICES

1.8

I

SOIL NO

© ® ® ®"' 1.4 ® ®'^' 1.6

(%)

(%)

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unity) as the axis of major principal stress at failure (a/y) varies between the vertical (6 = 0) and the horizontal {8 — 90 deg) directions. 3. Combined—the net effect of the inherent and stress-system induced components. Present Measurement Techniques The anisotropy of cohesive soils has frequently been inferred from results of UU, CIU, and/or CID triaxial compression tests performed on specimens cut at different orientations (6-angles) to the vertical. But data from such tests are misleading and/or unreliable since (/) they ignore the stress-system

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650

LABORATORY SHEAR STRENGTH OF SOIL

2000 NO

DESCRIPTION

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0.2

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APPLIED SHEAR STRESS RATIO Tf,/Cu FIG. 3—Normalized Young's modulus versus stress level from CK/iUDSS tests on seven normally consolidated soils |4].

induced component of anisotropy, especially important in sensitive clays (for example, see Ref 7); (2) sample disturbance tends to destroy and hence mask anisotropic behavior, at least with UU tests; and (J) cross anisotropy generates bendings and shears at the ends of inclined test specimens, as demonstrated by Refs 97 and 98 in the SOA paper. Experimental evidence of the importance of combined anisotropy during undrained shear of clays has also been inferred from the following types of CKQU tests: (/) triaxial or plane strain compression (TC or PSC) to measure behavior at 6 = 0 deg; (2) triaxial or plane strain extension (TE or PSE) to measure behavior at 6 = 90 deg; and (J) Geonor direct simple shear to measure behavior at an intermediate (but ill-defined) 6-angle. Results from CA'oUC and E tests should be "corrected" for changes in the CT2-condition (Ref 7, p. 438), while problems associated with interpreting DSS data have already been discussed. In any case, this approach hardly provides detailed data regarding anisotropy for practical problems involving a wide range of principal stress axis rotations, such as occur in most field loading situations. The SOA paper makes frequent reference to the use of the hollow cylinder Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

LADD ON UBORATORY SHEAR DEVICES

651

device (Apparatus No. 5 in Table 1) by Saada et a! in their extensive investigations of the effects of inherent anisotropy on the undrained behavior of soft clays. Their studies employed CIU tests run on samples that had been /Co-consolidated, rebounded to obtain isotropic stresses, and then sheared with differing ratios of axial and torsional stress to vary theff/y^-directionbetween 6 = 0 deg (vertical) and 3 = 90 deg (horizontal). However, these results reflect the combined effects of stress axis rotation and changes in the intermediate principal stress condition since b = (oi —ff3)/(ffi— 03) increases from zero at 6 = 0 deg to 0.5 at 6 = 45 deg and to unity at 6 = 90 deg. Measurements of combined anisotropy in the hollow cylinder device via C/ifoU tests would also be subject to the same problem, that is, separation of anisotropy and changes in b. A New Measurement Technique The Directional Shear Cell (DSC) was recently developed [11] at University College London (UCL) for the specific objective of investigating stress-strainstrength anisotropy in sands. Figure 37 of the SOA paper shows a diagram of the method used to apply normal and shear stresses to the four faces of a cubical sample, constrained between two rigid end platens, in order to fully control the major principal stress direction during plane strain shear. Arthur et al [1] fully describe the flexible boundary DSC and present data obtained at MIT for the purpose of evaluating its versatility and reliability compared with other test devices and to illustrate the highly anisotropic behavior of sand during drained shear. Although fairly complex to operate and employing rather costly radiographic-photographic techniques to measure the distribution of strain magnitudes and directions, the DSC represents a unique research tool for studying anisotropy. It has already been used for extensive measurements of the effects of induced anisotropy due to prestraining [/, / / ] , to study the cyclic behavior of sand with continuously rotating principal stress directions [12], and most recently to measure the inherent anisotropy of a loose sand [/]. MIT is now developing procedures to enable CKQU testing of soft clays in the DSC with pore pressure measurements. Arthur et al [1] discuss some of the problems that have occurred and need to be resolved in order to achieve this capability. While not an easy task, the author believes the effort justified in view of the potential ability of the DSC to more fully investigate the combined stress-strain-strength anisotropy of clays than now possible with other shear devices. Acknowledgments The author thanks the symposium organizers for their highly successful endeavor and congratulates the authors of the SOA paper for their comprehensive and stimulating treatment of laboratory shear devices. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

652

LABORATORY SHEAR STRENGTH OF SOIL

References [1] Arthur, J. R. F., Bekenstein, S., Germaine, J. T., and Ladd, C. C , this publication, pp. 516-540. 121 Campanella, R. G. and Vaid, Y. P., Canadian Geotechnical Journal. Vol. 9, No. 3, 1972, pp. 249-260. [3\ Bishop, A. W. and Wesley, L. D., Geotechnique. Vol. 25, No. 4, 1975, pp. 657-670. 141 Ladd, C. C. and Edgars, L., "Consolidated-Undrained Direct Simple Shear Tests on Saturated Clays," Research Report R72-82, Department of Civil Engineering, Massachusetts Institute of Technology, Cambridge, Mass., 1972. 15] Lacasse, Suzanne and Vucetic, Mladen, this publication, pp. 633-637. 161 Ladd, C. C. and Foott, R., Journal of the Geotechnical Engineering Division, American Society of Civil Engineen, VoL 100, No. GT7, 1974, pp. 763-786. 171 Ladd, C. C , Foott, R., Ishihara, K., Schlosser, F., and Poulos, H. G., in Proceedings. 9th Intemattonal Conference on Soil Mechanics and Foundation Engineering, Tokyo, 1977, Vol. 2, pp. 421-494. [8] Larsson, R., Canadian Geotechnical Journal. Vol. 17, No. 4, 1980, pp. 591-602. 19] Bjerrum, L. in Proceedings. American Society of Civil Engineers Specialty Conference on Performance of Earth and Earth-Supported Structures, Lafayette, Ind., 1972, Vol. II, pp. 1-54. [10] Prevost, J. H. and Hoeg, K. in Proceedings. 9th International Conference on Soil Mechanics and Foundation Engineering, Tokyo, 1977, Vol. 1, pp. 255-261. |//1 Arthur, J. R. F., Chua, K. S., and Dunstan, T., Geotechnique. Vol. 27, No. 1, 1977, pp. 13-36. 1/2] Arthur, J. R. F., Chua, K. S., Dunstan, T., and Rodriguez del C , J. T., Journal of the Geotechnical Engineering Division. American Society of Civil Engineers, Vol. 106, No. GT4, 1980, pp. 419-433.

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Pierre La Rochelle^

Limitations of Direct Simple Siiear Test Devices

REFERENCE: La Rochelle, Pierre, "Limitations of Direct Simple Shear Test Devices," Laboratory Shear Strength of Soil. ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 653-658. ABSTRACT; Tiie Direct Simple Shear (DSS) test devices tiave a major fundamental defect which has been recognized for over 40 years. In this paper, the limitations of the DSS test are emphasized by test results obtained on a highly sensitive and brittle clay of Eastern Canada. The DSS devices are no real improvement over the direct shear devices and the value of the triaxial test is far superior. KEY WORDS: shear strength, shear tests, quick clays, direct shear test

Saada and Townsend, in their state-of-the-art (SOA) paper on laboratory strength testing of soils,^ presented a welcome critical review of the most common shear strength laboratory tests for soils. Some of these tests, such as the direct shear and the triaxial tests, are common tools in commercial laboratories; others, like the true triaxial test or the triaxial test on hollow cylindrical specimens, belong mainly to the research or university laboratories because of their theoretical and technical complexity and, to some extent, because of the importance of the investment which they require. These latter tests provide a better understanding of the fundamental behavior of soils and of the limitations of the strength characteristics measured by the more common tests. One other type of test, the Direct Simple Shear (DSS) test, which seems to be gaining in popularity, has been very severely criticized by Saada and Townsend who rightly "wonder about the forces that made these devices so popular". Their limitations were recognized very early by Hvorslev and Kaufman (SOA Ref 28) who emphasized "the non-uniformity of both normal and shearing stresses due to the couple of the resultant vertical forces which is 'Professor, Department of Civil Engineering, Laval University, Quebec, Canada. ^This publication, pp. 7-77. 653 Copyright by Downloaded/printed Copyright"^ 1981 University of

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654

LABORATORY SHEAR STRENGTH OF SOIL

required to balance the movement produced by the shearing or tangential forces". As a result of that couple, the head platen has a tendency to rotate, which is a significant defect. The author would like to further emphasize the limitations of the DSS test devices by discussing some tests and observations made in the course of an investigation of a flowslide in sensitive clay. That flowslide occurred in 1971 and destroyed part of the village of Saint-Jean-Vianney, Quebec, taking 31 lives; an eyewitness account of that slide has been given by Tavenas et al.^ Different types of shear tests were made on block samples dug out from a trench excavated in the floor of the flowslide crater, and their results were compared. The testing program at the Laboratoire de Geotechnique, Universite Laval, included among other tests some consolidated-undrained (CIU) triaxial tests with pore pressure measurement, and some drained direct shear and direct simple shear tests. The DSS tests were made in an NGI apparatus by A. Landva, who is the engineer who perfected that device at the Norwegian Geotechnical Institute [SOA Ref / / ] . The Saint-Jean-Vianney clay that was tested has a low plasticity, is very brittle, highly sensitive, and has an undrained strength of 250 kPa. The stressstrain and pore pressure curves obtained in a consolidated-undrained triaxial (CIU) test illustrate the typical behavior of this soil (Fig. 1). The strength reaches a peak value at low strain, usually below I percent, and then decreases rapidly to a value approximately constant at large strains. As discussed by previous authors (see, for example. La Rochelle and Lefebvre'*), a series of CIU tests made at different cell pressures on these sensitive soils yields shear strength envelopes which can be drawn both for peak and for large strain values; such envelopes are given in Fig. 2 for the Saint-Jean-Vianney clay. Some drained direct shear tests have also been made on this clay with the shear planes oriented either parallel or perpendicular to the bedding planes; the results are plotted in Fig. 2. It is seen that the corresponding peak strength envelope obtained by the direct shear tests and represented by the dotted line (Fig. 2) is identical to the large strain strength envelope obtained by CIU triaxial tests. Some drained DSS tests were also performed on that clay; the results are plotted in Fig. 3. It is significant that the strength values obtained are identical to those given by the direct shear tests, and correspond to the large strain strength envelope determined in the triaxial tests. During the testing program, it was further observed by Landva that the top platen of the DSS device had a tendency to rotate to the point where a sheet of paper could be introduced between that top platen and the head of the apparatus; this confirms the existence of the couple in the vertical forces which ^Tavenas, F., Chagnon, J. Y., and La Rochelle, P., Canadian GeotechiiicalJournal. Vol. 8, No. 3, 1971, pp. 463-478. •'La Rochelle, P. and Lefebvre, G. in Sampling of Soil and Rock. ASTM STP 483. American Society for Testing and Materials, 1971, pp. 143-163.

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LA ROCHELLE ON DIRECT SIMPLE SHEAR TEST DEVICES

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656

LABORATORY SHEAR STRENGTH OF SOIL

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has been suggested by Hvorslev and explains part of the nonuniformity of the stresses within the sample. Conclusion Following his own observations and experience, the author cannot find any real advantage to the use of the DSS device: it is not appreciably simpler to use than the triaxial apparatus; it does not yield a strength value comparable to the peak strength obtained in the triaxial test; it gives no reliable information on the shear or deformation moduli; even the volumetric moduli obtained in the NGI apparatus on samples of overconsolidated sensitive clays may be adversely influenced by the poor confinement of the reinforced membrane; and for the same reason, the value of the preconsolidation pressure obtained during the consolidation stage in that device can be seriously questioned. For sensitive clays, the maximum values of shear strength determined with the DSS devices seem to correspond to the strength measured with the direct shear test or obtained at large strain in the triaxial test; moreover, the strain developed in the DSS devices is not large enough to allow the determination of the residual strength parameters. It is thus apparent that the DSS devices present no real improvement over

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LA ROCHELLE ON DIRECT SIMPLE SHEAR TEST DEVICES

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658

LABORATORY SHEAR STRENGTH OF SOIL

the direct shear devices and that in all respects, the triaxial test, with all its limitations, is far superior. Saada and Townsend rightly state that the proper place of the DSS devices is perhaps "in the hands of designers who have already conducted a large number of such tests and built structures which behaved satisfactorily". However, it is unfortunate that these devices have been popularized to such an extent, because the experience gained with these devices by one designer on one type of soil is hardly transferable without elaborate checking with another designer or even to a different type of soil, since the test itself has some fundamental defects.

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S. J. Poulos^

Discussion of Soil Testing Practices

REFERENCE: Poulos, S. J., "Discussion of Soil Testing Practices," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 659-666. ABSTRACT: Six questions concerning the advantages and limitations of equipment for measuring shear strength of soils, and related test errors, were posed to the author. The responses are given in this paper. Emphasis is placed on the need to understand the shape of the stress-strain curve when selecting the apparatus. This need arises in soil testing because the soil type, soil structure, state, and stress path all have a strong influence on the stress-strain curves. Details of testing that are discussed are: (/) use of undisturbed or compacted specimens, (2) when to test partially saturated soils, (3) backpressure saturation, and (4) membrane penetration effects. Some suggestions for needed research are given. KEY WORDS: strength, stress-strain, apparatus (equipment), soil testing, back pressure, partial saturation, membrane penetration, research

This paper consists of responses to charge questions proposed at the ASTM Symposium on Laboratory Shear Strength of Soil, held in Chicago, Illinois, June 1980. Each question has been quoted for easy reference. The response follows each question. Of the five types of equipment, how do you view the advantages and limitations of each one? Which ones are most appropriate for design, research, and development of constitutive relationships? The choice of equipment to determine the stress-strain curve of a soil specimen is dependent on the shape of the stress-strain curve and on the portion of the stress-strain curve that is needed for a particular application, be it 'Principal, Geotechnical Engineers, Inc., Winchester, Mass. 01890.

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660

LABORATORY SHEAR STRENGTH OF SOIL

practice or research, or, more specifically, for constitutive relationships. For this reason it is important to understand the major factors that affect stressstrain curves:^ Soil

Structure State Method of Loading The principal features of the soil material that govern the stress-strain curves are the mineralogy, particle shape distribution, particle size distribution, and pore fluid content. The structure is the arrangement of the particles. The particles of a given specimen can be arranged in many different packings. Just as the strength and the deformations of a building are governed by the arrangement of its structural elements, so also is the shape of the stress-strain curve of a specimen, including the peak strength, affected by its structure. The same soil at the same void ratio can have quite different stress-strain curves as a result of structural differences. The state is defined as the combination of void ratio and effective stresses on the specimen at the start of loading. Higher void ratios usually mean lower moduli, lower peak strength, and higher strain at peak. Higher effective stresses usually mean higher moduli, higher peak strengths, and higher strain at peak. The method of loading is the manner in which the total shear and normal stresses are applied, the rate of loading, and the degree of drainage allowed during loading. Each of these components of the method of loading usually has a significant influence on the stress-strain curve of a soil specimen for research and practical purposes. Included in method of loading are effects of time of loading or strain rate, which become significant in some cases. The various features of a stress-strain curve, for example, the initial tangent modulus, peak strength, strain at peak, steady state strength, and the strain required to reach steady state, are of greater or lesser importance, depending on the application. The equipment to be used to measure each of these features of the stressstrain curve must be selected judiciously. One attempt at judging the applicability of various apparatuses is shown in Tables 1 and 2.^ The reader is invited to assign his own numerical values in these tables. A general conclusion that can be reached from Tables 1 and 2 is that no one apparatus can be used for all purposes, which is not surprising in view of the variety of apparatus that have been devised during the past 60 years. ^Poulos, S. J., "The Stress-Strain Curves of Soils," Geotechnical Engineers. Inc., Winchester, Mass., 1971.

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POULOS ON SOIL TESTING PRACTICES

663

The major limitations and advantages of various apparatuses, as viewed by the author, are listed below: Limitations Triaxial

Limited stress paths Limited strain Direct shear Extreme progressive failure Difficult drainage control Unknown stress state Simple shear Substantial progressive failure Very limited stress paths Plane strain Limited strain Somewhat more complicated than triaxial test Limited stress paths True triaxial Very limited strain Complicated Hollow cylinder Limited strain Very difficult to use on undisturbed specimens

Advantages Triaxial

Good control of stresses Good control of drainage Reasonable range of stress paths Good for measuring steady-state strength (that is, residual Direct shear strength) Useful for measuring peak drained strength of undisturbed specimens along horizontal planes when other devices cannot be used Useful for measuring peak undrained strength of undisSimple shear turbed specimens along horizontal planes Stress path theoretically models in situ conditions along failure surfaces Stress path models in situ stress path better than triaxial, Plane strain although rotation of principal planes is not modeled Most stress paths can be modeled, in principle True triaxial Hollow cylinder Most stress paths can be modeled Effects of stress nonuniformities on test results can be evaluated

Is it practical to consider membrane penetration and should corrections be made? Membrane penetration corrections should be considered when the void sizes are large enough and the membrane thin enough to cause pore pressure or

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664

LABORATORY SHEAR STRENGTH OF SOIL

volume changes that are significant to the case in hand. Membrane penetration has the same effect as leakage into the specimen.^ For sands or coarser soils in drained and undrained tests on specimens 71.1 mm (2.8 in.) in diameter and smaller, a correction should be considered. For silts or coarser soils, in undrained tests on fully-saturated specimens, a pore pressure correction should be considered. In all other cases, membrane penetration is usually not important.

Considering the effects of specimen preparation on test results, when are laboratory-compacted specimens appropriate, and when are undisturbed specimens required? Laboratory-compacted specimens are appropriate when compaction is going to be used in the field, that is, to model a compacted embankment or compacted fill. In this case consideration should be given to modeling the compaction method, layer thickness, and the age of the specimen in situ, as well as density and water content. Laboratory-compacted specimens are useful if only the steady-state strength is needed for the application. At large strains the initial structure is obliterated; therefore the method of sample preparation has no practical effect on the resistance at large strains. However, the strains needed to reach the steady state will be affected by the compaction technique. Only the density and stress level have appreciable influence on the steady-state strength. To measure moduli, peak strengths, and strains at peak, compacted specimens are nearly useless as a means for modeling undisturbed specimens. Such an approach should be used only when special tests are carried out to prove the magnitude of the differences involved, in which case one might find that the differences are small enough for practical purposes. For example, if the strain at peak is very large and the soil structure is controlled by sand-sized particles, then the initial structure may have a small influence on the peak strength. In such cases the peak strength of undisturbed specimens could be modeled reasonably by specimens compacted at the same density and water content. What precautions are required in back-pressure saturation of soils? (a) Should swelling clays be allowed to swell during saturation? {b) Considering that dilative soils tend to develop negative pressures and thus extraordinarily high deviator stresses, what point should be considered as failure? (a) Swelling clays should be allowed to swell or not to swell during saturation, as required to model conditions in situ during and after construction. No •'Poulos, S. J., "Control of Leakage in the Triaxial Test," Ph.D. thesis, Harvard University, Cambridge, Mass., 1964 (Harvard Soil Mechanics Series No. 71). Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

POULOS ON SOIL TESTING PRACTICES

665

rule need be established. A judgment should be made, based on tests, as to the effects of differences between the degree of swelling in the laboratory and in situ conditions. (b) In practice, shear strengths based on negative pore pressures in excess of those that can be developed in situ, for the in situ loading condition being considered, should not be used. If a stability analysis is being made in terms of effective stresses, and some means other than the test is being used to predict in situ pore pressures, then the high negative pore pressures in the test do not influence the analysis. In this case, as in all cases when determining the shear strength of soils, it may be desirable to choose a limiting strain as the definition of failure. This selection is dependent upon the geometry of the problem being studied. In research on the steady-state deformation of soils, it is important to use a high enough back pressure so that cavitation will not occur before the steady state is reached. Additional note on back pressure saturation: It is advisable not to allow the effective stress in the specimen to rise to higher values than 50 percent of the effective stress being used during shear. The back pressure should be applied in small increments to ensure that the effective stress of the middle of the specimen does not rise above the desired value. Precautions should be taken to raise the chamber pressure for each increment before raising the pore pressure. Preferably, the valving should be set up so that the effective stress can be set and one knob turned to raise both chamber pressure and pore pressure simultaneously in small increments. Concerning partially saturated soils, are special considerations required for laboratory tests for parameter determination? Should these considerations be included in test standards? The objective of stability analyses is to obtain a reasonably conservative estimate of the factor of safety against ultimate failure for any given loading condition. Therefore a conservative value of strength should be selected. The strength of a partially saturated specimen usually lies between the drained and undrained strength of the same specimen when fully saturated. Thus the drained and undrained strengths on fully saturated specimens represent extremes. If the partially saturated undrained strength is higher than the fully saturated undrained strength, the specimen is contractive. In that case the fully saturated undrained strength should be used unless it can be shown with good certainty that the soil will never become fully saturated in situ. If the partially saturated undrained strength is lower, the specimen is dilative. In this case the partially saturated condition should be used because it yields a lower strength. However, the drained strength may be more critical, in which case the partially saturated condition need not be considered. Thus, in general, the partially saturated condition seldom would be utilized for strength determinations. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

666

LABORATORY SHEAR STRENGTH OF SOIL

When testing partially saturated specimens, the pore pressure measured at the ends may be the pore water pressure or the pore air pressure. The difference between the two, the needed apparatus, and the effect on computed values of 0 should be understood when carrying out such tests/ The special considerations for testing partially saturated specimens should not yet be included in ASTM standards. Their practical application is limited and further development is required before standards may reasonably be set. What areas of shear strength testing need the most additional research and improvement? {a) Equipment (b) Test method (c) Specimen preparation (d) Stress path followed (e) Other (a) An urgent requirement is that different apparatuses be used to test the identical soil to determine how the apparatus affects the data. Several laboratories should carry out the same set of tests to determine the effect of operator differences. An evaluation should then be made of the practical and the theoretical importance of the observed differences. (6) No comment. (c) The specimen should represent the in situ condition. Tests should be made to gain insight into the effects of specimen preparation techniques for nearly all research projects and for many practical applications. {d) Tests on a wide variety of soils with a wide variety of stress paths should be performed and published, (c) (i) In publications that deal with strength, stress-strain, stability, and earth pressure the stress-strain curves should be published. It is alarming to note the paucity of published stress-strain curves even in papers whose major contribution revolves around stress-strain data, (ii) Measure effect of disturbance on modulus for deformation, (iii) Make direct comparisons between data measured in situ and data from laboratory tests.

''Bishop, A. W. and Henkel, D. J., The Measurement of Soil Properties in the Triaxial Test. Edward Arnold, London, 1957.

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Frangois Tavenas^

Some Aspects of Clay Behavior and Their Consequences on IVIodeling Techniques

REFERENCE: Tavenas, Franpois, "Some Aspects of Clay Behavior and Their Consequences on Modeling Techniques," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 667-677. ABSTRACT: Numerical models, as neering, present serious weaknesses. sented, and the differences with the pointed out. Some guidelines for the given.

they are applied presently in geotechnical engiBasic features of natural soils behavior are precommon assumptions in constitutive models are proper use of models and numerical analyses are

KEY WORDS: soils, cohesive soils, stress-strain behavior, numerical models

The complex nature of the mechanical behavior of natural clays has been sufficiently recognized to justify the use of simplifying assumptions in developing constitutive models. Unfortunately, a growing acceptance of the strongly approximate nature of the available models seems to be developing. Since oversimplifications are considered normal, models are often selected for use in an analysis according to their tractability in computer programs rather than their representativity of soil behavior. One of the most disturbing facts in the present stage of vigorous development and use of constitutive models is that some of the most fundamental aspects of natural soil behavior remain essentially ignored. This is often due to the necessity to develop mathematical formulation of too great complexity; it could also be related to the insufficient experimental knowledge of soil behavior. This situation is a potential source of problems, particularly with the increasing use of analytical models in the development of geotechnical designs. It is the purpose of this discussion, first to point out some of the most fundamental aspects ' Professor, Department of Civil Engineering, Laval University, Quebec, Canada. 667 Copyright by Downloaded/printed Copyright 1981 University of

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668

LABORATORY SHEAR STRENGTH OF SOIL

of the mechanical behavior of natural clays, which should necessarily be taken into consideration in a good constitutive model, and then to draw some consequences on the use of modeling techniques in present-day practice. Fundamental Aspects of Natural Clay Behavior Natural clays, as they occur in situ, have been deposited by sedimentation in lakes or seas, and they have been consolidated under one-dimensional strain condition. Even if there are some questions as to the exact nature of the corresponding KQ effective stress condition, there is no doubt that the resulting clay fabric is strongly anisotropic in all natural clay deposits. Consequently, the response of an element in such deposits to stress variations will, by necessity, be anisotropic and reflect the geometrical arrangement of the clay particles and their contacts. In this context, the frequent distinction between "inherent" and "stress induced" anisotropy of soils is neither fundamentally justified nor practically relevant. What is required is simply the experimental knowledge of the anisotropic response of an element in a natural clay deposit to stress and strain variations. But for a few recent off-shore deposits, truly normally consolidated clays do not occur in situ. Overconsolidation may be limited in magnitude, but it is the unavoidable result of such geological processes as erosion, aging, thixotropic hardening and possibly cementation, leaching or groundwater table fluctuations. Consequently, any natural clay deposit submitted to stress variations will, at least initially, present the high stiffness, the brittleness, and the high rates of consolidation typical of overconsolidated soils. Any model intended for use in geotechnical engineering problems involving clayey soils should provide for the proper simulation of these two basic features of natural clay behavior. Experimental work by Tavenas and Leroueil [1,2]^ has shown that the limit state concept is best suited for representing both the anisotropy and the preconsolidation history of natural clays. This concept, initially developed by Roscoe and his co-workers at Cambridge to form the basis of the Cam Clay models [3], has been implicitly used in a variety of constitutive models, referred to as "Cap Models" [4], Unfortunately, the shape assigned to the yield cap in most models does not properly account for the aforementioned effects of anisotropy and geological history. For example, the well-known Modified Cam Clay Model implies a yield cap as in Fig. la, while repeated testing on a variety of natural clays has shown that the actual limit state surface is such as in Fig. lb [5]. Stress-Strain Behavior of Overconsolidated Natural Clays Following the observation that strains are relatively small and more or less reversible in overconsolidated clays, most analytical models presently in use 2 The italic numbers in brackets refer to the list of references appended to this paper.

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TAVENAS ON SOME ASPECTS OF CLAY BEHAVIOR

669

assume an elastic behavior when the applied effective stresses remain within the yield cap. For the sake of simplicity, isotropy is generally assumed, so that the soil's behavior is characterized by a Young's modulus (E) and a Poisson's ratio (v). Unfortunately, the observed stress-strain behavior of natural clays is quite at variance with this simplistic characterization. Recent work at Laval University on the stress-strain-time behavior of intact overconsolidated clays has been summarized by Tavenas and Leroueil [2]. It shows that this behavior is strongly effective stress path dependent and nonelastic. For example, volumetric strains, developed by following a variety of effective stress paths from a given origin stress condition (Fig. 2), are not related to the mean octahedral effective stress but rather to the distance to the limit state surface along the considered stress path. The determining role of this "distance to the limit state surface" as a stress parameter has been confirmed by investigations on the development of strain energy [6] and on the creep behavior of intact overconsolidated clays [7]. The undrained stress-strain response of clays can be approximated by an hyperbolic function. Most recently, Bonal [8] has observed that the parameters of the hyperbolic representation in undrained compression and extension tests (Fig. 3a) are directly related to the length of the effective stress path between the origin stress condition and the limit state (Fig. 3b). The existence of such a relationship has been confirmed for a large series of tests (Fig. 4). The same investigation has shown that the "tangent modulus" in undrained tests is strongly influenced by the previous effective stress history of the specimen. As indicated in Fig. 5a, the tangent modulus, £"„, measured at the effective stress condition, A, varies by a factor of about 6, depending on the stress and strain path followed up t o ^ ; important variations of £•„ are obtained at other stress conditions and for extension as well as compression

o-p (0)

p'

O-p p (b)

FIG. 1—Limit state curves assumed in Cam Clay models and actually observed on natural clays (from Ref S). Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

670

LABORATORY SHEAR STRENGTH OF SOIL

A\\

^ 1

\ii'

/

^

\ \ \ 1^

'#

-^

/

^

1 / ' ^Oy^

y ^

^^—^ 10

15

20

25

30

35

10

45

50

FIG. 2—Stress conditions producing equal volumetric strains in an overconsolidated natural clay.

tests (Fig. 56). Such a stress path dependence of the "modulus" has also been reported by Lambrechts and Leonards [9] for tests on sands. It may well be a common feature to most soils. The behavior described herein is quite different from that implied in the elastic models presently in use, and major developments are required before constitutive models may be considered reasonably representative of the soil's response. Plastic Flow in Normally Consolidated Clays Because of their relative mathematical simplicity, associated flow rules are used in Cap Models to describe the stress-strain behavior of normally consolidated clays. While such flow rules may be acceptable for ideal isotropic soils, they do not properly represent the response of anisotropic natural clays. Experimental studies by Wong and Mitchell [10] and Brucy [11] have shown that normality is satisfied on the limit state surface of an intact clay only near the KQ effective stress condition. At all other locations the plastic strain vectors are not normal to the yield surface but rather inclined towards the A'o stress condition. The use of an associated flow rule is thus an oversimplification. Some sort of kinematic hardening would be more representative, as shown by studies by Lewin [12] and Brucy [11], but the experimental evidence is not yet sufficient to develop a reliable mathematical model.

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TAVENAS ON SOME ASPECTS OF CLAY BEHAVIOR

20

1

671

y ^

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15

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25

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30

35

40

45

2

FIG. 3fl—Relation between effective stress path and hyperbolic stress-strain function for an overconsolidated natural clay (from Ref 8A

Rupture in Overconsolidated Clays In overconsolidated clays, rupture is represented mathematically by using a Mohr-Coulomb type of failure criterion, sometimes combined with a plastic flow rule. Such representation does not account for two important phenomena. As pointed out by Tavenas and Leroueil [1], the failure envelope of natural, overconsolidated clays is a part of their anisotropic limit state surface. It is represented in the a', T space by a curve that bears no relationship to any form of Mohr-Coulomb criterion. This fact was confirmed in controlled stress tests by Wong and Mitchell [10]. In addition, failure is generally associated with the formation of a surface of discontinuity within overconsolidated clays samples and with the development of an important strain softening. Post-failure stress-strain relationships represent in general a structural instability of the clay, which cannot be described in terms of homogeneous plastic flow. Constitutive models capable of handling the development of both discontinuities and instability are thus required to analyze rupture in overconsolidated clays.

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672

LABORATORY SHEAR STRENGTH OF SOIL

C25 4.0 C33 3.6

E62

3.2

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f / y

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FIG. 36—Relation between effective stress path and hyperbolic stress-strain function for an overconsolidated natural clay (from Ref 8).

Effect of Stress Axes Rotations The rotation of the principal stress axes during a stress variation should have a very marked effect on the strain response of anisotropic natural soils. Unfortunately, we essentially ignore this effect due to the absence of proper laboratory investigations on intact soil specimens. Indications provided by studies on artificial anisotropic soils [13] confirm the dramatic changes to the stress-strain response as a result of stress axes rotation. Since such rotations are the rule rather than the exception in all geotechnical engineering problems, it should be the very first priority of research on modeling to carry out the laboratory investigations necessary to define the effects of stress axes

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TAVENAS ON SOME ASPECTS OF CLAY BEHAVIOR

673

a.02

FIG. 4—Relation between the parameter b oj the hyperbolic stress-strain function and the deviator difference between limit state and origin conditions.

1

1 — — 1

1

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32

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FIG. 5a—Stress history dependence of the tangent shear modulus of an overconsolidated natural clay.

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674

LABORATORY SHEAR STRENGTH OF SOIL

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FIG. 5fc—Stress history dependence of the tangent shear modulus of an overconsolidated natural clay.

rotation on the behavior of natural soils and eventually to incorporate these effects into models. Interrelationship of Clay Parameters The investigations by Tavenas and Leroueil [1,2] have shown that all aspects of the behavior of a natural clay can be expressed by reference to its limit state. They are therefore interrelated and dependent on the geological history of the material, resulting in its present structural condition. Important practical consequences follow: 1. All mechanical parameters may be normalized against the preconsolidation pressure which best represents the geological history of the material. The NSP concept proposed by Ladd and Foott [14] is fully applicable. 2. The quality of different laboratory test results on a given material can be checked by considering the necessary interrelationships. 3. Since all mechanical parameters are related to the structure of the intact clay, disturbance of this structure should be avoided. This rules out the experimental procedure proposed by Ladd and Foott [14] for applying the NSP concept in SHANSEP.

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TAVENAS ON SOME ASPECTS OF CLAY BEHAVIOR

675

4. As already pointed out, all mechanical parameters of natural, overconsolidated clays, are strongly effective stress path dependent. Therefore there is no reason to assume that the parameters measured in a given test along a specific stress path could be directly applicable to a field problem implying a different effective stress path. On the other hand, the existence of interrelationships between parameters provides the basis for the development of logical and reliable empirical design relations between laboratory or field test results and overall field behavior. 5. Interrelationships between parameters and normalized properties could be used with benefit in developing relatively simple constitutive models. Rules for the Development and Use of Models At present, models are frequently developed on theoretical considerations, supported by limited experimental evidence, before serious attention is paid to their relevance to field problems. While this may be proper for researchers dealing solely with modeling techniques, it is not the best approach to the development of geotechnical engineering. In view of our very limited knowledge of soil's rheology and field behavior, the successful development and use of analytical models requires an approach of the observational rather than the analytical type. A first step in the analysis of any geotechnical problem should be to identify that problem correctly. This requires the gathering and the qualitative interpretation of all possible field observations. It is an absolute necessity to determine the nature of the processes involved in a problem before carrying out a numerical analysis. In the past, this necessity has often been ignored in favor of the use of "reasonable assumptions" which are usually nothing else than wishful thinking. In using assumptions in place of solid evidence, the risk is great to model the wrong problem, such as carrying out an undrained analysis for a partially drained problem. Once the nature of the problem is established, a model must be selected which represents the right soil's behavior as much as possible. We have seen before that this is not an easy task at present, given our limited knowledge of soils and the many questionable aspects of present constitutive models. In view of this situation, a good model is one in which the physical meaning of the various parameters is sufficiently clear for the analyst to be able to check the validity of the numbers he is using. When comparing the results of the analysis to the field evidence, equal attention should be paid to all output parameters of the problem. In particular, it should go without saying, the predictions should be consistent with soil mechanics principles; for example, a logical relationship should exist between the strains and pore pressures computed from the model. All too often this is not the case and a statement such as "my model is good only for predicting settlements" serves as the only explanation for the fact that the Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

676

LABORATORY SHEAR STRENGTH OF SOIL

most fundamental principle of soil mechanics, e = f{o'), is violated by the results of a numerical analysis. The dangers of using "unbalanced evidence: evidence obtained by eliminating all those facts which do not sustain the claim," pointed out by Terzaghi [15] in 1936, have been magnified in the proliferation of numerical analyses. If some of the key parameters in a geotechnical problem are not properly simulated in a numerical analysis, the entire analysis is questionable. Given the present level of our geotechnical knowledge, there are only very few problems for which these principles can be applied rigorously. Therefore emphasis should probably be on the development of relatively simple conceptual models which can be used, not necessarily in the computer, but rather in our heads or on the back of an envelope to develop a qualitative evaluation of the soil's response in field situations. The Cam Clay models or the YLIGHT variant of that model [1,2] are good examples of useful conceptual tools which can provide a framework for the application of the engineer's judgement. To conclude on the relative necessity and merits of theory and experience in geotechnical engineering, the following statement by Terzaghi [16] may be quoted: "In (von Mises's) field, theory reigns supreme. In my field it can be disastrous unless it is kept on a shelf in a bottle with the label: add no more than five drops to each gallon of experience." Are we not, at present, pouring gallons of theory on drops of good field experience? References [/] Tavenas, F. and Leroueil, S. in Proceedings, 9th International Conference on Soil Mechanics and Foundation Engineering, Tokyo, Vol. 1, 1977, pp. 319-326. [2] Tavenas, F. and Leroueil, S. in Proceedings, 7th International Conference on Soil Mechanics and Foundation Engineering, Brighton, England, Vol. 1, 1979, pp. 281-291. [J] Roscoe, K. N. and Burland, J. B. in Engineering Plasticity. Heyman and Leckie, Ed., Cambridge University Press, 1968, pp. 535-609. [4] Ko, Hon-Yim and Sture, Stein, this publication, pp. 329-386. [5] Leroueil, S. and Tavenas, F., discussion on "Yielding in Soft Clay at Bakebol, Sweden" by D. M. Wood, Geotechnique, in press. [6] Tavenas, F., Des Rosiers, J. P., Leroueil, S., La Rochelle, P., and Roy, M., Geotechnique. Vol. 29, No. 3, 1979, pp. 285-303. [7] Tavenas, F., Leroueil, S., La Rochelle, P., and Roy, M., Canadian Geotechnical Journal. Vol. 15, No. 3, 1978, pp. 402-423. [8] Bonal, E., "Contribution a I'etude de la relation contrainte-deformation des argiles surconsolidees," M.Sc. thesis. Department of Civil Engineering, Laval University, Quebec, Canada, 1980. [9] Lambrechts, J. R. and Leonards, G. A., Journal of the Geotechnical Engineering Division, American Society of Civil Engineers, Vol. 104, No. G T l l , 1978, pp. 1371-1387. \10\ Wong, P. K. K. and Mitchell, R. J., Geotechnique, Vol. 25, No. 4, 1975, pp. 763-782. [//] Brucy, F., "Effet du passage en I'etat normalement consolide sur I'etat limite d'une argile naturelle," M.Sc. thesis. Department of Civil Engineering, Laval University, Quebec, Canada, 1977. [12] Lewin, P. I. in Proceedings, Symposium on the Role of Plasticity in Soil Mechanics, Cambridge, England, 1973, pp. 96-106.

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TAVENAS ON SOME ASPECTS OF CLAY BEHAVIOR

677

[13] Arthur, J. R. F., Chua, K. S., and Dunstan, T., Geotechnique. Vol. 27, No. 1, 1977, pp. 13-30. [14] Ladd, C. C. and Foott, R., Journal of the Geotechnical Engineering Division. American Society of Civil Engineers, Vol. 100, No. GT7, 1974, pp. 763-786. [15] Terzaghi, K. in Proceedings, 1st International Conference on Soil Mechanics and Foundation Engineering, Cambridge, Mass., Vol. 3, 1936, pp. 13-18. [16] Voight, B., Rockslides and Avalanches, Vol. 2, Elsevier, Amsterdam, 1979.

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George Y. BaladV

Development, Testing Requirements, and Fitting Procedure of Elastic-Plastic Models

REFERENCE: Baladi, George Y., "Development, Testing Requirements, and Fitting Procedure of Elastic-Plastic Models," Laboratory Shear Strength of Soil. ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 678-684. ABSTRACT: During the past few decades the dramatic growth of computer technology has been paralleled by an increasing degree of complexity in material constitutive modeling. This paper discusses the development, testing requirements, and fitting procedure of elastic-plastic models. A brief overview of the general characteristics of soil behavior which should be displayed by an elastic-plastic model is presented. The basic requirements and conditions of constitutive models are stated. To construct an elastic-plastic type model the following (minimum) tests are required: (/) loading and unloading in isotropic consolidation and (2) loading and unloading in triaxial shear. Additional tests, such as uniaxial strain tests, proportional loading tests, direct shear tests, etc., are useful for verification of the model fits. KEY WORDS: constitutive models, elastic-plastic models, soil characteristics

The mechanical behavior of soils subjected to externally applied loads is quite complicated. Unlike the properties of most engineering materials, soil stress-strain properties are greatly affected by such factors as soil structure, degree of voids saturation, drainage conditions during loading, loading rate, loading history, and current stress state. Here the term "soil structure" is loosely used to recognize that "microvariables" such as grain size; grain size distribution; grain shape, surface texture, and mineralogy; and grain orientation, packing, and cementation, or bonding, all play an interrelated role in the complex mechanical response of soils. For practical purposes these microvariables are generally not individually characterized; rather "engineering" 'Research civil engineer, Geomechanics Division, Structures Laboratory, Waterways Experiment Station, Vicksburg, Miss. 39180.

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BALADI ON ELASTIC-PLASTIC MODELS

679

variables such as void ratio and relative density, which are more amenable to measurement and certainly more useful to analysts, and which account in a lumped sense for the interplay of many of the microvariables, are used to help characterize, understand, and predict the soils' response. Figure 1 shows a typical behavior of soil subjected to a hydrostatic state of stress (isotropic consolidation test). It is clear from this figure that soils, in general, exhibit a nonlinear compacting hydrostat. Figure 2 shows a typical variety of stress-strain-pore pressure response curves manifested by saturated soils tested in undrained shear in a triaxial compression device. The three specimens were first isotropically consolidated to the same effective mean normal stress level (Point 2), then sheared undrained. The shear curves marked "2 ->• 3" show the typical response of a normally consolidated clay or a very loose sand. The curves marked "2 -• 5" show behavior typical of an overconsolidated clay or a very dense sand. Within the extreme limits of these loose and dense soil responses, there is a graduated response, typified herein by the curves marked "2 -> 4." The latter response depends on the state of compaction (consolidation) of the material. It is clear from this figure that the effective stress is the only part of the total stress that affects soil shear strength.

!•- PLASTIC STRAIN I[AMOUNT OF COMPACTION]

VOLUMETRIC STRAIN

'kk ' V

FIG 1.—Typical behavior of soil under isotropic consolidation test.

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680

LABORATORY SHEAR STRENGTH OF SOIL

EFFECTIVE STRESS PATH —

O

TOTAL STRESS PATH

0

EFFECTIVE MEAN NORMAL STRESS, P

EFFECTIVE MEAN NORMAL STRESS, P'

PRinCIPAL STRAIN DIFFERENCE,e^ - £3

PRJIICIPAL STRAIN

DIFFERENCE, e

FIG. 2—Typical behavior of saturated soil tested under undrained triaxial test conditions.

Figure 3 shows typical (qualitative) stress-strain response curves for soils sheared under drained triaxial compression conditions; that is, the curves marked " 1 " represent dense sand or overconsolidated clay, while the curves marked "2" depict response typical of loose sand or normally consolidated clay. To model the behavior shown in Figs. 1 to 3, one must resort to the theory of continuum mechanics and develop an appropriate constitutive relation. The solution of earth structure problems then becomes a mathematical formalism that can be achieved numerically or by other means. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

BALADI ON ELASTIC-PLASTIC MODELS

(T)

DENSE SAND OR OVERCONSOLIDATED CLAY

(2)

LOOSE SAND OR NORMALLY CONSOLIDATED CLAY

681

PRINCIPAL STRAIN DIFFERENCE, c^ - E3

FIG. 3—Typical behavior of soil tested under drained triaxial (est conditions.

The development of a constitutive model for earth media should be based on physical observations of actual material behavior under both laboratory and field conditions. Therefore an appropriate experimental program has to be conducted. The results of such a program should be plotted in appropriate formats so that the model parameters can be readily determined. The constitutive model should be flexible so that it can account for all or most of the following observed factors: 1. Three-phase (at least two-phase) system. 2. Shear-induced volume changes. 3. Recoverable as well as permanent deformations (that is, elastic and plastic behavior). 4. Isotropic and anisotropic behavior. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

682

LABORATORY SHEAR STRENGTH OF SOIL

Development of a constitutive model that can simulate all of these factors is, of course, a formidable task. In order to keep the model simple and understandable, only the physical factors relevant to the particular problem at hand should be incorporated into the model. The model should (/) be expressed in terms of a three-dimensional coordinate system, (2) apply for any state of stress and deformation, (J) satisfy all of the mathematical restrictions of the theory of continuous mass media, and (4) be easily incorporated into contemporary finite-element and/or finitedifference computer codes. The benefits of such a constitutive relationship that satisfies these requirements are obvious: (/) it would provide a basis for the interpretation and organization of drained and undrained laboratory test data for various states of stress and deformation; and (2) it would provide the means (in conjunction with appropriate computer codes) to perform effective- and /or total-stress analyses for a wide variety of earth structure problems for either transient- or static-type loading conditions. The fundamental procedure for obtaining the functional forms and quantitative parameters used in elastic-plastic constitutive models constructed for use in boundary-value problem solutions should be based on material behavior obtained from various laboratory tests performed on representative material samples. As a minimum, the representative material behavior should consist of loading-unloading isotropic consolidation test data (Fig. 1) and loading-unloading (drained and undrained) triaxial stress test data (Figs. 2 to 4) with lateral strain measurements. Sometimes the results of uniaxial strain, proportional loading, direct shear, and/or other tests are available, but they are not essential tests. The first step in the fitting procedure is to employ the unloading portion of these essential tests to determine the appropriate elastic prescription of the

Pj. = CONFINING PRESSURE ^0)2 ^ (Pc)l

PRINCIPAL STRAIN DIFFERENCE,

FIG. 4—Principal stress difference drained triaxial shear tests.

versus principal

strain difference from

consolidated-

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BALADI ON ELASTIC-PLASTIC MODELS

683

model, since the model behaves elastically during initial unloading in these tests; for example, initial unloading behavior in isotropic consolidation tests is indicative of the bulk modulus K (Fig. 1), and in triaxial stress tests is indicative of the shear modulus G (Fig. 4). Other material property tests or stress paths, if available, may be used to check or adjust the overall fit of the elastic portion of the model. The next step in the fitting procedure is to establish the failure envelope, that is, that portion of the yield surface which absolutely limits the shearing stresses that the material can withstand. While the failure envelope could be chosen as a work- or strain-hardening yield surface, it is generally adequate and much simpler to assume it to be ideally plastic. The failure envelope is generally obtained using failure data from triaxial stress and/or proportional loading shear tests. This envelope is fit as a function of the stresses, which is usually assumed to involve only the first stress invariant and the second invariant of the stress deviator tensor (Fig. 5). The remaining step in the fitting procedure is the most difficult, involving the hardening portion of the model which is obtained by a trial-and-error procedure in which a hardening surface and hardening rule are assumed, and the behavior of this assumed model computed and compared with the representative data. If the fit requires improvement, a new set of parameters is tried and the procedure is repeated. The computation of the model behavior can be based on the equations describing the relations between the stress and strain increments during the common laboratory loading paths. Obviously, the success of such trial-and-error fitting procedures and the rapidity with which they converge are strongly dependent on the experience of the modeller. Knowledge of the effect on the model behavior of changes in the model parameters is important for rapidly obtaining a satisfactory fit. For example, the fitting procedure is greatly simplified by the knowledge (ob-

EFFECTIVE MEAN NORMAL STRESS, P '

FIG. 5—Failure envelope from drained triaxial shear tests.

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684

LABORATORY SHEAR STRENGTH OF SOIL

tained through experience in fitting several models by trial and error) that the hardening rule strongly affects the stress-strain curves for uniaxial strain and hydrostatic stress paths, while the shape of the hardening surface plays an important role in determining the stress-strain behavior for triaxial stress situations and the stress path for uniaxial strain. In fact, the hardening rule has been obtained for the most recent elastic-plastic models by using a separate program to compute the plastic volumetric strain during isotropic consolidation tests. In summary, to construct elastic-plastic type models the following (minimum) tests are required: (/) loading and unloading in isotropic consolidation, and (2) loading and unloading in triaxial shear. Additional tests, such as uniaxial strain tests, proportional loading tests, direct shear tests, etc., are useful for verification of the model fits.

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J.H.A. Crooks^

A Qualitative Stress-Strain (Time) Model for Soft Clays

REFERENCE: Crooks, J. H. A., A Qualitative Stress-Strain (Time) Model for Soft Clays," Laboratory Shear Strength of Soil, ASTM STP 740, R. N. Yong and F. C. Townsend, Eds., American Society for Testing and Materials, 1981, pp. 685-699. ABSTRACT: Successful analytical modeling of tlie behavior of soils requires that these models incorporate the significant factors which control real soil behavior. To illustrate this point, a qualitative stress-strain (time) model for understanding the behavior of soft clays is described. The major feature of the model is the yield envelope—the locus of effective stress states in q-p stress space which result in a change from small strain response to loading to a large strain response. The model is used to provide a qualitative understanding of the behavior of soft clays subjected to embankment loading at two sites. Various features of the soil model, such as normalization of the yield envelope with respect to preconsolidation pressure together with use of strain energy as a parameter to define yield, are also discussed in relation to analytical formulation of the model. KEY WORDS; soft clay, stress-strain (time) model, yield envelope/effective stress paths, embankments, strain energy, SHANSEP

Ko and Sture, in their state-of-the-art paper on data reduction and application for analytical modeling,^ clearly indicate the rapid evolution of constitutive models for the prediction of soil behavior. Notwithstanding the mathematical sophistication of these models and the computational capability which can be utilized in analysis, it is clear that none of the currently available constitutive models can incorporate many important aspects of the behavior of naturally occurring soils (that is, anisotropy, whether inherent or stress-induced, stress-history, and the like). Therefore it is Ukely that for some time to come practicing engineers will rely on the use of soil models and methods of analysis based on observed soil behavior and correlation with field performance. Although it is clear that simultaneous development is required in both approaches, it appears to the author that the more successful constitutive models will be those based on a proper appreciation of real soil 'Principal, Colder Associates, Toronto, Ontario, Canada. ^This publication, pp. 329-386. 685 Copyright by Downloaded/printed Copyright 1981 University of

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LABORATORY SHEAR STRENGTH OF SOIL

behavior. To illustrate this viewpoint, the following discussion describes a qualitative stress-strain (time) model which incorporates many of the significant features of the observed behavior of natural lightly overconsolidated cohesive soils. (Despite recent research efforts, these remain very much a problem material type.) The qualitative application of this model to two case records is presented together with a discussion of some features^ of the model which make its analytical formulation attractive.

Yield Behavior of Liglitly Overconsoiidated Cohesive Soils If "undisturbed" samples of natural, lightly overconsolidated cohesive soils are reconsolidated in laboratory triaxial equipment to their in situ stresses and then subjected to drained loading along different stress paths, there is a stress level associated with each stress path at which the strain response to load changes from small strain to large strain (Fig. 1). Along the KQ stress path this stress level is the preconsolidation pressure. Other examples are the yield points observed in drained compression and extension tests. Further, the maximum shear stress observed in undrained triaxial and extension tests also lie close to the yield envelope determined from drained tests if strain rate effects are taken into account. The locus of the stress states mp-q stress space at which yield occurs along various stress paths is termed the yield envelope. Descriptions of the various features of yield envelopes for natural materials are given by Crooks and Graham [L2]^ and Tavenas and Leroueil [3\ and are not presented in detail in this discussion. Figure 2 shows the yield envelopes determined from two quite different types of Belfast estuarine deposits. Other natural soils have been observed to possess similar yield envelopes [3,4]. Experimentally derived yield envelopes for natural soils such as those shown in Fig. 2 are similar to the limit state surface of the Cambridge Cam Clay model. However, it should be appreciated that there are significant differences between the "models," and certainly at this stage it should not be assumed that the observed yield behavior of natural soils is a manifestation of the Cambridge theory. Instead, it is suggested that the observed yield behavior of natural soils, as described briefly earlier, be considered as a qualitative stress-strain (time) model which incorporates traditional soil parameters, such as preconsolidation pressure and undrained shears strength, within a unified concept. As such, it provides a useful concept for understanding the field behavior of certain soil types under conditions where the rotation of the major principal stresses has not occurred (that is, below the centerline of fills, tanks, and the like). ^The italic numbers in brackets refer to the list of references appended to this paper.

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CROOKS ON QUALITATIVE STRESS-STRAIN (TIME) MODEL

• - I"'

687

^1 * ^3

EXTENSION

FIG. 1—Illustration of yield envelope for natural soil.

Application of the Yield Envelope Concept to Field Loading Cases The yield envelope concept has recently been used to obtain a better understanding of the behavior of soft clays subjected to embankment loading [5]. In summary, the changes in total stresses below the centerline of several embankments were computed using elastic methods [6] modified to allow for perfect plastic and strain-softening behavior. The effective stresses were determined from the computed total stress paths and porewater pressure changes measured in piezometers below the center of the embankments. It was considered that although the methods of analysis were relatively simple, more rigorous approaches were not warranted because of the qualitative nature of the study and also because the results obtained using these meth-

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688

LABORATORY SHEAR STRENGTH OF SOIL

KINNEGAR "CLAY" 3m DEPTH 6i-dz

f=„; KoPo'

~

Mif-—/.

(kg/cm2)

1 \

^^, /^-YIELU 'N^ ^ / ^ ENVELOPE

—"t"—' I

1

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1

0.15

1

1

5 0 % CLAY, 5 0 % SILT W L - 80% Wp~ 3 0 % W - 80% St - 7 ORGANIC CONTENT - 3 - 4 %

02

(kg/cm^)

HOLYWOOD "SILT"

6^-6^

VIELD E N V E L O P E V.

-

ESP FOR CADTEST-^/

4 m DEPTH

1

20% 70% 10% WL ~ Wp W St -

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(kg/cm2) H I ' : KOPO' ~

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1 0,2

1 0,3

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1 ^ 1 0,1

1 0,5

(kg/cm2)

06

SAND SILT CLAY 40% 20% 38% 8

ORGANIC I
FIG. 2—Yield envelopes for Belfast estuarine deposits [17].

ods compare reasonably well with those obtained using more rigorous methods [7]. Kais Bridge The Kars Bridge project involved the two-stage construction of a highway embankment on about 12 to 15 m (40 to 50 ft) of soft-to-fum Leda clay near Ottawa [8]. The undrained shear strength of the clay below the upper 3 m (10 ft) of crustal soils was about 30 kPa (600 Ibf/ft^). KQ was assumed to be 0.7, the value determined at the nearby Gloucester test fill site [9]. The first loading stage involved placement of about 6 m (20 ft) of fill, and the measured porewater pressures indicated essentially "pseudo-elastic" response of the soil, resulting in the effective stress path between Points 0 and 4

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CROOKS ON QUALITATIVE STRESS-STRAIN (TIME) MODEL

689

in Fig. 3. After completion of the Stage I fill, rapid dissipation of the excess porewater pressure increased the effective stresses to Point 5 at which time there was a dramatic decrease in the rate of dissipation. This change in porewater pressure dissipation rate occurred despite the fact that there was no change in boundary drainage or loading conditions. At this stage, the effective stress state at point 5 had reached the yield envelope, which was inferred from the in situ vane strength and preconsolidation pressure at the piezometer tip elevation. Over the following 16 to 17 month period, the excess pore-

30

FILL HEIGHT (ft.)

®

J

20

© _1

1

1

1

1

]

(a)

LOADING

(b)

POREWATER PRESSURE RESPONSE

L_

HISTORY

EXCESS ^u(tt.)

I960

I200|

1961

1962

/[/

&\-&i (lb/8q.ft)400

(lb/jq(t) (c)

STRESS

PATHS BELOW

%_ OF EMBANKMENT

FIG. 3—Kars Bridge embankment [5].

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690

LABORATORY SHEAR STRENGTH OF SOIL

water pressure continued to dissipate slowly to the effective stress state indicated by Point 6 in Fig. 3. When the second stage fill was added, the porewater pressure again increased in pseudo-elastic (and possibly partially drained manner), resulting in the effective stress state at Point 7. Following completion of Stage II loading, the porewater pressure again dissipated rapidly to the effective stress state indicated by Point 8. However, at that point, the rate of porewater pressure dissipation again decreased dramatically and remained slow during the remainder of the monitored period. The behavior observed during the second stage loading is attributed to the development of a "new" yield envelope as a result of secondary consolidation during the period between Points 5 and 6. This behavior was observed at three different depths throughout the soft clay foundation. Mission Bay Dylces This project involved the staged construction of a dyke in Lake Superior in Thunder Bay, Ontario. The instrumented section of the dyke was constructed using granular material end-dumped through 5 m (16 ft) of water. The first stage level was about 1 m (3 ft) above lake water level. The second and third loading stages involved placement of additional 0.9 and 1.2 m (3 and 4 ft) lifts, respectively (Fig. 4). Below the lake bottom is 2 m (6 ft) of loose silts/sands and about 2 m (6 ft) of stiff (crustal) clays. Underlying these materials is 3.7 m (12 ft) of lightly overconsolidated clay with an undrained shear strength of about 20 kPa (400 Ibf/ft^). This stratum in turn overlies a layered clay and silt deposit extending to a glacial till deposit at a depth of about 21 m (70 ft) below lake bottom. Based on the computed total stresses and porewater pressures measured using pneumatic piezometers installed in the center of the soft clay stratum, it appears that the effective stress state following Stage I loading was at Point 1 (that is, on the yield envelope inferred from the measured undrained shear strength and preconsolidation pressure). The addition of berms adjacent to the main dyke to about lake level caused a modest pore pressure increase followed by dissipation which resulted in the effective stress states indicated by Points 2 to 4 (Fig. 4). On application of the second load increment, the porewater pressure in the soft clay increased dramatically and continued to rise even after completion of this stage of the loading. It is evident that at this stage the soft clay at the monitored location had yielded, and the continued increase in excess porewater pressure is attributed to strain-softening within the yielding material. The computed total stress state associated with the completed Stage II loading is at the point marked A. When the measured porewater pressure is used to compute the effective stress state at this time (Point A'), it was found to lie well beyond the Mohr-Coulomb (large strain) failure line and the yield

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CROOKS ON QUALITATIVE STRESS-STRAIN (TIME) MODEL

J

APPLJED LOAD

691

7

®

_BERMS ADDED

JUNE

JULY

AUG,

(o)

SEPT, 1978

AUG, 1979

OCT,

LOADING HISTORY

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EXCESS AuOt,)

©

JUNE

(2) '•}: ©,

JULY

AUG,

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SEPT 1978

OCT.

AUG, 1979

POREWATER PRESSURE RESPONSE

(lb/»q ft) S u VANE

^<"

IN SITU YIELD ENVELOPE

KX-OED«( b 1200

(TSP-U.) ?

L

(lb,/»q.fl.) (c)

STRESS

PATHS BELOW

t

OF EMBANKMENT

FIG. 4—Mission Bay embankment [5].

envelope. Because the clay is a strain softening material, it was assumed that the effective stress state was actually on or close to the Coulomb-Mohr line. Using this line as a restriction on the left side of the q-p plot and the known total vertical stress as a restriction on the right-hand side of the q-p plot, the total stress state at Point 5 was computed by fitting the measured porewater pressure between these two lines. During the period of continued porewater pressure increase following comCopyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

692

LABORATORY SHEAR STRENGTH OF SOIL

pletion of the Stage II loading, it was assumed that the effective stress state continued to lie on the Coulomb-Mohr failure line, and the total stress state at Point 6 was computed in the manner described previously. The application of the final stage of loading was accompanied by only a modest increase in porewater pressure, and resulted in effective and total stress states at Point 7. In the year following completion of the dyke, the excess porewater pressure dissipated relatively slowly to Point 8. At that time the effective stress state in the soft clay had only returned to about the stress state which had existed prior to any fill being placed. While the two analyses described herein are qualitative in nature, it is considered that the effective stress path/yield envelope approach was useful in the understanding of the response of the foundation soils. Folkes [5] successfully used this approach in the analysis of a total of seven embankments on soft clays. Yield Envelope Concept in Analytical Modeling Despite similarities with some of the theoretical models described in the state-of-the-art paper by Ko and Sture, the yield envelope "model" has not yet been formulated analytically although it seems reasonably suited for this purpose. In this respect, two comments are offered: the first is in relation to the yield envelope as an analytical yield criterion, the second is with respect to the formulation of constitutive relationships. The incorporation of constitutive relationships and yield criteria in analytical models can be considerably simplified if these input data for an entire deposit can be normalized with respect to a significant parameter. Research carried out in the past decade has sought to provide such a procedure (for example, the SHANSEP method [10]). However, this approach has been viewed critically by some because the procedure involves the prediction of in situ properties based on the results of laboratory tests on samples which have been normally consolidated (that is, consolidated under axial stresses in excess of the preconsolidation pressure). It has been stated that this procedure involves breaking down the in situ soil structure (that is, particle arrangement) and, since the in situ behavior of many materials is strongly dependent on structure, the application of the SHANSEP approach is limited to a few soils which are essentially unstructured [11,12]. The following data obtained from tests on Belfast clays which are moderately "structured" show that this criticism may not be valid. Ladd et al [13] presented the data shown in Fig. 5 which indicates that the following expression applies to lightly overconsolidated soils (OCR < 2 to 3): (5„/a,c) N.C.

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or

693

Po''{Su/a,,) O.C. = p, {Su/aic) N.C.

In ff/c = po' tests with KQ consolidation, the in situ structure would be preserved, and the measured 5„ is the in situ undrained strength. Therefore it should be possible to predict the in situ undrained strength from the product of the (5„/a/c) ratio from tests on normally consolidated samples and the preconsolidation pressure. Figure 6 shows the application of this procedure to the results of laboratory triaxial compression and extension tests on samples of Belfast clay. In the lower half of Fig. 6 are plotted the undrained shear strengths obtained from compression and extension tests on normally consolidated samples (that is, oic > Pc)- The ratio {Su/oic) for compression tests is 0.33, while the ratio for extension tests is 0.2. In the upper portion of Fig. 6, these ratios have been used together with the measured preconsolidation pressures with depth to predict the variation in compression and extension strengths with depth. The predictions are shown as the dashed lines in the upper right-hand figures in Fig. 6. The predicted variation in undrained strength with depth for compression and extension tests correspond closely with the undrained strengths measured in samples which were anisotropically {KQ) consolidated to their in situ stresses and which therefore retained to a large degree their in situ structure. It is therefore concluded that the aforementioned (modified) SHANSEP approach is applicable to moderately sensitive "structured" Belfast clay. It may be also applicable to other similar materials. To take this conclusion one stage further, it can be argued that the un-

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{-.— n.c. RELATIONSHIP FOR SCLAVS- L A D D ( I 9 7 7 )

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2

3

4 5 6 7 8 9 1 0

OVER CONSOLIDATION RATIO, O.C.R.

FIG. 5—Effect

of stress history on undrained shear strength.

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694

LABORATORY SHEAR STRENGTH OF SOIL

Su (kg/cm2)

STRESS (kg/cm^) O.a

0.4

0.6

COMPRESSION

0.8 0 0

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DEPTH (m)

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EXTENSION

0.2

41.0 1.2 iic(kg/cm2)

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approach in prediction

of undrained strength of Belfast clay.

drained compression and extension strengths are only two points on the more general yield envelope. Therefore normalization with respect to preconsolidation pressure should be applicable to the entire yield envelope. In the upper half of Fig. 7 are plotted the yield envelopes determined from samples at various depths throughout the Belfast clay deposits [14], If the stress states at yield along the individual stress paths used to determine these yield envelopes are normalized with respect to Pc, a general yield envelope range for the entire deposit can be determined as shown in the lower portion of Fig. 7. It is of interest to compare the shape of this general range of normalized yield envelope for Belfast clay with published data for other material types. In the upper portion of Fig. 8 are plotted triaxial compression and extension strengths normalized with respect to preconsolidation pressure for a number of different soil types. While there is clearly scatter in the data, the general Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

CROOKS ON QUALITATIVE STRESS-STRAIN (TIME) MODEL

695

2 (kg/cm2)

005

01

015 02 6i' + 263 ^

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025

03

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(kg/cm^)

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GENERAL RANGE j»\ \ \ , FOR ALL DEPTHS—^ " • l -

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3 fc FIG. 7—Normalizing yield envelopes at various depth W.R.T. p^-Belfast clay deposits [14].

ranges in Su/pc for compression and extension tests, together with the location of Pc as shown in the lower half of Fig. 8, would indicate a yield envelope shape which corresponds well with the normalized yield envelope range obtained for the Belfast clays. Further, it is also noted that for this general yield envelope shape, the ratio of p^ and/>„o (that is, the p '-value at which the yield envelope crosses the q = o axis) is about 1.6 which is the average value for 23 natural clays as reported by Tavenas and Leroueil [15]. In the initial interpretation of yield from laboratory tests on the Belfast Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

696

LABORATORY SHEAR STRENGTH OF SOIL

COMPRESSION DATA FOR : - SCANDANAVIAN CLAYS - EASTERN CANADIAN CLAYS -BANGKOK CLAY -BELFAST CLAY

0.3

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L

0.4

J

0.5

L

06

J 0.7

I 0.8

1 0.9

I 1.0

FIG. 8—Generalized yield envelope.

deposits, the definition of yield was varied depending on stress path direction [2], Thus, along a constantffoctstress path, little volumetric strain occurred and yield was defined using a\ versus ei plots. However, along a constant shear stress path, a clear definition of yield could only be obtained from the <^oct versus Cv plot. This was clearly not desirable since yield should be defined in the same manner regardless of stress path direction. Thus the concept of strain energy (which is equivalent to the work done/unit volume of soil) was used, and yield was defined by plotting this quantity against the magnitude of the stress vector in p-q stress space for each stress path.

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CROOKS ON QUALITATIVE STRESS-STRAIN (TIME) MODEL

697

Figures 9 and 10 show the results of this approach for two types of the Belfast deposits. It is noted that the contours of strain energy in p-q stress space have the same general shape as the yield envelope. The lower portion of these figures shows the relationships between strain energy and stress vector for various stress paths. There is a predictable variation in the gradient of the post-yield portion of the strain energy-stress vector relationships depending on the stress path direction. Further, there appears to be a threshold energy level which causes yield and from these data, this threshold level occurs within a relatively narrow range for a wide variety of stress paths. Tavenas et al [16] used this approach to define yield in similar tests sensitive Leda clays from eastern Canada. They generally confirmed its usefulness, but also indicated that the threshold energy levels for stress paths such as Type A in Fig. 9 are lower than for other stress paths. They also suggested that the threshold energy levels for a number of clays loaded along /(Co-type stress paths, such as Type C stress paths in Fig. 9, were directly proportional to preconsolidation pressure.

STRAIN ENERGY, ^C0NT0UR(kg/cm2) 20

I

THRESHOLD STRAIN ENERGY I 10

\ 12.5

I 15

I 12.5

STRESS VECTOR (SV.) ( kg/cmZ)

FIG. 9—Strain energy plots for Belfast deposits—Hofywood "silt.

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STRESS VECTOR ( S V. ) (Kg/cm2)

FIG. 10—Strain energy plots for Belfast deposits—Kinnegar "clay. " TOTAL STRAIN ENERGY (DURING CONSOLIDATION)

•^ ^

< DC CO

L^_

-DEVIATORIC STRAIN ENERGY (DURING CONSOLIDATION)

/ I

I

\

I

O

STRAIN ENERGY DISSIPATED DURING UNDRAINED SHEARING (kq/cm^ )

FIG. 11—Relationship between strain energy absorbed during consolidation and dissipated during subsequent undrained shearing—Kinnegar "clay. "

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CROOKS ON QUALITATIVE STRESS-STRAIN (TIME) MODEL

699

A final point is illustrated in Fig. 11 where the strain energy absorbed during consolidation and secondary compression of normally consolidated samples (that is, during a 2 to 3 day period following application of the final consolidation stresses) is compared with the energy dissipated during subsequent undrained shearing. For the Belfast deposits, the deviatory component of the strain energy absorbed during consolidation is approximately equal to the strain energy dissipated during subsequent undrained shearing when no volume change is permitted. References [1] Crooks, J. H. A. and Graham, J., Engineering Geology, Vol. 6, 1972, pp. 275-288. [2] Crwks, J. H. A. and Graham, J., Geotechnique, Vol. 26, No. 2, 1976, pp. 293-315. [3] Tavenas, F. and Leroueil, S., "Effects of Stresses and Time on Yielding of Clays," in Proceedings, 9th International Conference on Soil Mechanics and Foundation Engineering, Tokyo, Vol. 1, 1977. [4] Bene, T. and Bjerrum, L., "Shear Strength of Normally Consolidated Clays," in Proceedings, 8th International Conference on Soil Mechanics and Foundation Engineering, Vol. 1, Part 1, 1973. [5] Folkes, D. J., "Stress Path Behaviour below Embankments on Soft Clay," M.Sc. thesis. University of Toronto, Canada, 1980. [6] Poulos, H. G., Geotechnique, Vol. 17, 1967, pp. 378-410. [7] Law, K. T. and Bozozuk, M., Canadian Geotechnical Journal, Vol. 16, 1979, pp. 691-702. [8] Eden, W. J. and Poorooshasb, H. B., Canadian GeotechnicalJoumal, Vol. 5, 1968, p. 28. [9] Bozozuk, M., "The Gloucester Test Fill," Ph.D. thesis, Purdue University, Lafayette, Ind., 1972. [10] Ladd, C. C. and Foott, R., Journal of the Geotechnical Engineering Division, American Society of Civil Engineers, Vol. 100, No. GT7, 1974. [//] Mesri, Journal of the Geotechnical Engineering Division, American Society of Civil Engineers, Vol. 101, No. GT4, 1975, pp. 409-411. [12] Tavenas, F., "The Behaviour of Embankments on Clay Foundations," State-of-the-Art Report, 32nd Canadian Geotechnical Conference, Quebec City, 1979. [13] Ladd, C. C , Foott, R., Ishihara, K., Schlosser, F., and Poulos, H. G., "StressDeformation and Strength Characteristics," in Proceedings, 9th International Conference on Soil Mechanics and Foundation Engineering, Tokyo, State-of-the-Art volume, 1977. [14] Bell, A., "A Geotechnical Investigation of Post Glacial Estuarine Deposits at Kinnegar, Belfast Lough," Ph.D. thesis. Queens University, Belfast, 1977. [15] Tavenas, F. and Leroueil, S. in Proceedings, 5th European Conference on Soil Mechanics and Foundation Engineering, Brighton, Vol. 1, 1979, pp. 281-292. [16] Tavenas, F., Des Rosiers, J-P., Leroueil, S., La Rochelle, P., and Roy, M., Geotechnique, Vol. 29, No. 3, 1979, pp. 285-303. [17] Crooks, J. H. A,, "Laboratory Studies of the Belfast Estuarine Deposits," Ph.D. thesis. Queens University, Belfast, 1973.

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Summaiy

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STP740-EB/Sep.1981

Summary

Summaiy of Ps^rs New Equipment Al-Hussaini and Arthur et al describe new testing devices. Al-Hussaini utilized a thick-wall hollow cylinder for measuring the elastic properties and tensile strength of compacted clays. In this device, tensile stresses are introduced by increasing the pressure inside the hollow cylindrical soil specimen over the outside pressure, thus causing the specimen to crack and fail. Miniature LVDTs were used to monitor the inside and outside diameter deformations, from which the elastic constants were calculated. Arthur et al utilized the Directional Shear Cell (DSC) for measuring the stress-strain-strength anisotropy in sands. The DSC is a flexible boundary plane strain shear device in which the major principal stress direction is controlled by varing both the normal and shear stresses acting on four faces of a cubical specimen constrained between two rigid end platens. The normal stresses are applied through flexible pressure bags, while the shear stresses are applied through rubber shear sheets that are pulled and stretched. The normal stresses are measured directly by monitoring the pressure in the flexible bags; the shearing stresses are determined from careful calibration of the shear sheets. Radiographs of embedded shot were used to determine displacements during shear. Test Equipment Improvements Alva-Hurtado et al, Cheng, Edil et al. Fang and Fernandez, Lade, and Dyvik et al describe improvements to test equipment. Alva-Hurtado et al and Edil et al adapted triaxial equipment to satisfy specialized requirements. Alva-Hurtado et al used a 15.2-cm-diameter triaxial cell with internal tie rods and a low friction piston seal to perform tests on crushed stone. The use of internal tie rods greatly facilitates specimen setup and assures alignment of the loading piston and top platen. Edil et al modified a triaxial base to accept a thermocouple psycrometer, which was used to measure the matrix suction of partially saturated soils. Cheng and Lade both describe hollow cylinder equipment. In order to measure strain rate effects, Cheng performed torsion tests using a rotating flywheel. Lade describes a torsional shear apparatus to which clockwise and Copyright by ASTM Downloaded/printed by Copyright 1981 b y A S T M University of British

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704

LABORATORY SHEAR STRENGTH OF SOIL

counterclockwise shear stresses can be applied. In this apparatus, normal stresses are determined from pressure measurements of the internal and external pressures, and vertical load. Shear stresses are determined from measurements of the applied torque. The vertical and shear deformations are measured by LVDTs, while horizontal deformations are measured by clip gages. Fang and Fernandez used an unconfined penetration test to measure the tensile strength of soils. Direct Simple Shear tests using a calibrated wire-reinforced membrane were reported by Dyvik et al. By calibrating the change in the electrical resistance of the reinforcing wire due to its small elongation, the lateral stress and KQ during specimen consolidation prior to shear could be determined. Control systems for applying loads and pressures to test specimens are described by Law and Mitchell. A servo system for imposing a prescribed stress path to either triaxial or plane strain specimens is described by Xaw. The system uses a minicomputer as a controller and electro-pneumatic transducers to regulate pressures. By programming the minicomputer, linear or curved effective stress paths can be followed; the minicomputer also collects and processes data while the experiment is in progress. The control system described by Mitchell is a neat, simple, economical system using rolling diaphragms and microflow valves to apply loads and pressures to triaxial specimens. The system offers an alternative to conventional gear-driven presses and dead-load hangers. Test Methods Al-Hussaini and Dyvik et al examined methods of determining KQ. Both papers used direct measuring techniques, whereby sensors are in direct contact with the specimen. Al-Hussaini found that direct contact sensors were more reliable than monitoring volume change of pour fluid, which can be influenced by membrane penetration. Koutsoftas provides valuable data for evaluating the shear strength of clay via triaxial compression and extension and direct simple shear tests. Triaxial compression strengths were 1.7 to 1.8 times greater than extension tests, with direct simple shear strengths falling in between. Their difference could be a function of stress-induced anisotropy of the soil or the difference in the tests themselves. Norris examined the critical problem of end restraint and adequacy of "frictionless" end platens using greased end membranes. The thickness of the end membrane affects the measured specimen strength, with thicker end membrane layers producing lower strengths. His results show, unfortunately, that the optional end membrane thickness is a function of specimen height, soil, and confining pressure, and thus is impossible to quantify at this time for various soils.

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SUMMARY

705

Models Prevost describes a general nonlinear, anisotropic, elasto-plastic constitutive model and presents applications thereof to several boundary value problems. The model parameters to characterize the behavior of a soil can be obtained from conventional strength tests. Typically monotonic triaxial compression and extension and cyclic simple shear tests are used. Data reduction is quite complex and a computer program for determining model parameters is presented. Schmertmann presents the results of laboratory tests showing that the increase in the shear strength component of clays which had undergone various chemical, stress, and time treatments was due to an increase in the frictional component of shear resistance with no contribution from the bond component. The increase in the frictional component is attributed to modification in the clay fabric, with a more disposed structure resulting. As a consequence of this data analysis, a quantitative method for estimating the quasi-preconsolidation effect is presented. Yong and Tabba caution that strength and stress-strain parameters used in constitutive models are subject to bias and uncertainties from the sampling and testing technique used to obtain the parameters. In addition, selection of a model or yield criterion implicitly requires certain expectations concerning soil behavior, which may not be applicable. In view of these difficulties, an analytical model of mapping and predicting random soil properties is offered.

Data Reduction Baladi et al present the results of incremental creep test on cohesionless soils and compare these data to model and predicted behavior due to cyclic loading (resilient modulus). Data from the simpler incremental creep tests were used to predict elastic and plastic behavior of granular materials subjected to cyclic loadings. Dmevich normalizes stress-strain curves by use of the maximum shearing stress to normalize shear stress and reference strain to normalize shear strain. The reference strain is defined by the initial tangent shear modulus and maximum shearing stress, which are functions of the effective stress state. Consequently, the normalizing parameters vary with stress points along the stress path, and an incremental procedure is used to normalize curves. Mayne and Swanson provide a large collection of data from the literature, which are subsequently applied to determine critical state parameters. These data show that the critical state pore pressure parameter, AQ, unlike Skempton'sy4, is independent of OCR, initial stress state (KQ), and level of shear to failure. Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

706

LABORATORY SHEAR STRENGTH OF SOIL

Thus only AQ and 4>' are required to predict the undrained strength of clays. The additional parameter, C,,, is required to estimate stress-strain relationships and pore pressure responses during undrained shear. Silvestri analyzed the results of isotropic and KQ consolidation tests on a sensitive clay performed in a triaxial device. It was observed that at low stress levels, the clay behaved as an elastic material, and the lateral stresses and pore water pressure could be predicted at these levels using anisotropic elastic theory and parameters. In Situ Measurements Lambrechts and Rixner, Lutenegger and Hallberg, and McNeill and Green discuss in situ measurements. Lambrechts and Rixner observed close agreement of 0 '-values determined from cone penetration, borehole shear, and triaxial compression tests. Lutenegger and Hallberg describe the borehole shear apparatus and testing experiences with this device. McNeill and Green report on research leading to the development of a combined normal stress/shear stress gage to be mounted on the nose of a penetrometer to be used in offshore investigations. Applications Anderson and Lukas, Miedema et al, and Shields and Skermer address the application of laboratory testing and data reduction to prediction of field response. Anderson and Lukas applied Skempton's Su/3 ratio correlation to estimate preconsolidation pressures of lightly overconsolidated clays. Miedema et al performed repeated direct shear tests to obtain the residual strength parameter to analyze riverbank stability in an area of old landslides. Shields and Skermer consider the importance of pore pressure measurements during laboratory tests to obtain necessary data for analyzing open-pit mining operations. Evaluation of Symposium and Main Ideas Developed The state-of-the-art (SOA) paper by Saada and Townsend, concerned with testing methods, equipment, techniques, and the systematic development and evaluation of available test instruments used for measuring the various kinds of soil response under direct prescribed or indirectly obtained unprescribed loading conditions, showed that there are many very severe constraints and limitations which must be considered in the evaluation of test measurements. For example, the consolidation stress path, membrane penetration, the strain or loading rate selected and end restraint all affect measured values. There are several significant points that need to be noted in regard to the ability of each test instrument to provide the tester with the

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SUMMARY

707

kinds of information desired while satisfying the various conditions of physics and mechanics. It is evident from a review of the various kinds of test instruments and techniques that in soil testing and analysis of test results the actual physical test boundary conditions and the requirements for a proper specification of the boundary values in a mixed boundary value problem analysis are not always reconciled. In addition, homogeneity or uniformity of stress and strain fields developed within the soil do not appear to be properly satisfied from experimental and validation/verification points of view. Of all the test systems examined, it is apparent that the use of direct and simple shear devices should be limited to those situations which allow for a comparative evaluation of test properties with other materials using the same test devices. Lacasse and Vucetic, in their discussion of Saada and Townsend's SOA paper, note that nonuniformities of stresses can be developed in test specimens in the present direct simple shear devices. The supporting information concerning developed maximum horizontal shear stress relative to height/diameter ratios of specimens tested (Lacasse and Vucetic, Fig. 2) shows indeed that there is no apparent difference in shear stress values for all the varying-size specimens tested. It is not clear if the results indicate that extension of the assumption, of a more uniform stress field for these specimens, to thicker specimens can be totally sustained, since the counter proposition can be mounted that all the specimens developed nonuniform stress fields consistent with the test boundary conditions. It is useful to observe that efforts are continuing in the development of newer simple shear devices which would seek to eliminate or considerably minimize the problems giving rise to development of nonuniform stress fields in the test specimens. Until such time when these newer devices become available and proven, the simple shear device can best be used for comparison testing within the same test boundary conditions. Absolute, or near absolute, usage for interpretation of stress-strain and shear strength measurements or shear strength properties with this device cannot be realistically achieved or used as a direct comparison with stressstrain or shear strengths obtained with other kinds of test devices. In fact, it is proper to note that the results of shear resistance tests obtained with a particular test apparatus cannot really be directly compared with test results obtained with other, dissimilar test system. This difference in test results creates the dilemma as to which laboratory test should be selected to obtain parameters desired for a specific boundary value problem. It is noted that photoelastic experiments can indeed serve a useful purpose in the visual "demonstration" of stresses developed in a test specimen subject to simple or complex loading conditions. In using such an experimental technique, the tester can gain valuable insight into modes of response performance of the test material which can be used as a means of calibration of the test system—for example, effectiveness of load transfer from the loading platens, side wall effects, etc.—as also indicated in the discussion by ChrisCopyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

708

LABORATORY SHEAR STRENGTH OF SOIL

tian. In transferring such knowledge to the testing of soil specimens, a common assumption is that similar test boundary effects (control) will prevail. When the soil material behaves in an inelastic fashion, the tester is faced with the problem of deciding how closely the boundary effects shown in the photoelastic experiments can be matched. A similar problem faces the analyst in the analysis or prediction of stress distribution in test specimens. It is incumbent on the analyst to not only use the proper (actual) test material properties in his analysis (models) but also to accurately reflect the test boundary controls. Unless this is achieved, problems such as inaccurate modeling of load and displacement boundary conditions, or improper specification of material properties, or both, can produce inaccurate predictions of stress/strain distributions within test specimens and total material performance. The standard triaxial and true triaxial test systems provide a good means of implementation of the load and displacement boundary conditions. With proper care and diligence it is possible to derive a good control system which will allow one to implement the kinds of boundary conditions necessary to simulate field situations. With the more sophisticated peripheral measuring devices, the true triaxial test systems or variations thereof can begin to permit one to examine stress or displacement boundary conditions or both. Because of the uncertainties in the measurement and control of shearing stresses established at each end of the test platens in the triaxial test systems, more research and development is required to address this problem. To meet the need for a better control and knowledge of the test boundary conditions, the hollow cylinder test technique which allows for a rotation of the principal stress axes has been developed. One of the principal difficulties associated with this kind of test system is the procurement of test samples for evaluation of soil properties. Because of the need for obtaining thin-walled hollow cylinder samples for the test system, there is considerable worry about boundary disturbance effects. One could argue that sample disturbances which are created in preparation of laboratory-prepared or actual natural samples are minor problems in view of the benefits obtained with the use of the more sophisticated hollow cylinder test system. It is clear that while there are several kinds of test systems being devised and developed to permit controlled variation of test boundary conditions and development of more homogeneous stresses and strains within the test samples, present analytical modeling techniques available today, by and large, require only the standard triaxial test. It is noted that from the simple hyperbolic models to the more sophisticated and complex bounding surface models, the kinds of physical test information sought as input demand test information obtainable from standard triaxial tests. Most of these analytical models require shear strength parameters such as friction angle and cohesion, and perhaps elastic and shear or bulk moduli as specific input representing the material properties.

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SUMMARY

709

The notable and interesting point arising from these observations is that one is generally required to apply the Mohr-Coulomb failure criterion for analysis of test data obtained from the conventional triaxial test in order to extract the "mathematical" shear strength parameters <> / (friction angle) and c (cohesion). It is observed that the shear strength parameters obtained with the application of a two-parameter failure theory (based on a rigid-plastic model) are in turn used in analytical yield theory models such as the various cap models. The question one might ask is why one needs the shear strength parameters from a failure theory (which may or may not be admissible) to apply or factor into a yield model? The associated question arising from the above is whether or not the rigid plastic two-parameter failure theory can be logically applied to the kinds of soils being examined. One should ask what kinds of shear strength tests need to be applied to allow one to determine whether the two-parameter failure theory is indeed an applicable or admissible failure theory for application as a data reduction procedure to the test results obtained. Note that the application of the Mohr-Coulomb two-parameter theory requires that the model behave as a rigid-plastic model, and that volume change considerations, intermediate principal stress influence, and boundary energy corrections should be properly factored, understood, and determined. In the case of analytical modeling theories which utilize the elastic, shear, and secant moduli, questions should be asked that relate to the value of these moduli. If the data points are not chosen carefully, that is, indiscriminately, it is possible to obtain values of the various moduli which may not properly represent the material behavior. The more data points obtained and used in the analysis, the better is the accuracy of the initial tangent modulus. Variations in initial tangent modulus can be easily obtained if data points are not chosen to allow for a good discrimination of the initial part of the stressstrain curve. The definition of yield and the identification of the yield point perhaps should also be examined. If one does not unload in a shear strength test to obtain the unloading curve, it is difficult to identify or define where yielding occurs (or occurred) in the stress-strain response performance of the soil. It should be noted that the stress level at which unloading occurs will determine the ratio of the "recovered" to the "nonrecoverable" strains. A very significant concern in the problem of testing techniques and application of modeling procedures is the problem of material and stress-induced anisotropy. Previous testing experience shows that almost all soils are anisotropic. Unfortunately, the strength test systems available today do not permit us to discriminate between the various degrees of soil anisotropy except for stress-induced anisotropic response behavior. It might be noted that there is no consensus, available data, or information that would allow one to quantify soil anisotropy. The present measurements of anisotropy per se relate primarily to differences in shear strength parameters and moduli Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

710

LABORATORY SHEAR STRENGTH OF SOIL

based upon testing of samples with principal stress axis rotated, primarily through hollow cylinder and directional shear test systems. From the true triaxial or conventional triaxial tests, one can rotate the stress axes from vertical to horizontal to obtain differences between horizontally tested and vertically tested samples. Arguments have been mounted regarding the testing of samples mclined at any angle in between vertical and horizontal. The argument is based on the fact that if the specimens are inclined, the manner or mode of deformation with the bedding plane inclined under a vertical stress system does not permit a proper application of the test boundary conditions. Counter arguments raised suggest that since the evidence in support of arguments against testing of inclined bedding of samples with stress directions not normal to the bedding plane has been obtained from polymer tests, there is some doubt as to whether this can be fully sustained since little systematic proper test information on a real clay system has been reported. The above notwithstanding, it is clear that a proper test system for anisotropic soils must be obtained. Care must be exercised in distinguishing between stress-induced anisotropy and inherent or intrinsic anisotropy. The former is obtained through an application of the stress system, while the latter is an inherent property of the test material itself. It is also clear that inherent anisotropy will to a very large degree control the amount of stressinduced anisotropy obtained. However, at the present time there has been no effort made to distinguish between the two, and the test results obtained do not permit one to scrutinize or to separate between the two. While arguments have been raised concerning the fact that there are no test measurements, characterization procedures, or evaluation techniques that will allow one to describe inherent anisotropy, it is clear that anisotropy is a material property and is a part of the composition of the material, and that one must begin to develop test systems or methods of scrutiny that will allow one to quantify inherent (material) anisotropy. The problems concerned with co-axiality, plastic potential and yield surfaces, loading surfaces, irreversibility, and stress-strain formulations can well be summed up by taking note of several simple points. Present plastic yielding theories refer primarily to isotropic stress conditions and in particular to isotropic materials. The reconciliation between the plastic potential and yield surfaces for normality and associated flow rule requirements refer to isotropic materials. If the material is anisotropic, there is no particular requirement why the two surfaces need coincide and why an associated flow rule should hold. It should be noted that the adoption of co-axiality between stress and strain-rate axes as such is an attempt to reconcile mathematics (of the problem) with actual soil performance. The physical aspects of the problem require that one plots the "yield" or failure stress points obtained from actual physical testing of the material in principal stress space. If a yield function i^CTy) can be written and if this is identified as a potential function, differenCopyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

SUMMARY

711

tiation of the potential function provides one with an outward-bound normal unit vector. If this vector is the strain increment (that is dF/doij), then if the principal axes of stress and strain-rate are superposed, reconciliation between the mathematics of the problem (that is, dF/doij) and the physical performance of the material is achieved through coaxiality, since normality will be readily identified from the superposed plot. The imposition of the framework of mathematics under such circumstances is an attempt to properly model the physical testing world. Unless proper care is taken to identify the model constraints and performance, researchers can be easily misled into providing a mathematical facade to a fictitious situation. In the present state of modeling, there is indeed a very serious attempt by the mathematical modelers to try and understand the specifics of actual soil performance under load. Unfortunately, this attempt is sometimes not particularly fruitful, since appreciation of the physics of performance has fallen far short of that necessary to provide the basic elements of a proper modeling procedure. The results from the NSF/NSERC Workshop held at McGill University in May 1980 indicate that unless one provides a vast background of information or understanding of actual soil behavior, mathematical modeling of actual soil performance can indeed be difficult. The need to understand soil behavior is paramount before any physical modeling for mathematical implementation can be obtained. This fact cannot be overstressed. From all the validation tests, verifications, and examples showing application of all the modeling exercises both at the McGill University Workshop and at the ASTM Symposium, it is clear that one must differentiate between the University soils and real soils. Almost all kinds of tests performed to show application of the modeling procedures have been performed on University soils. These are well-controlled and well-behaved, but in actual fact sometimes bear no relation to actual soil material encountered in the field. Modeling procedures must therefore address actual field soils. Unless this is done and until this is performed, it is difficult to determine the real applicability of these modeling procedures. Another point of interest is one which relates to the imposition of test procedures and constraints. Up until now, we have addressed the problem of testing through the imposition of stress or strain control loading. The simulation we seek is one which says that we should try and impose on the test material the kinds of stress situations envisaged in the field. Firstly, there is no real drained or undrained case identified in the field-loading situation. In field performance, one encounters a partly drained situation. Secondly, replication or duplication of the field-loading situation requires that we actually model substrate deformations, as opposed to stress. Since there is no real identifiable unique relation between stress and strain, the imposition of a stress modeling situation does not necessarily bring with it the kind of strains encountered in the field. There has been much mention of stress path history and stress path control Copyright by ASTM Int'l (all rights reserved); Sun Dec 19 02:25:09 EST 2010 Downloaded/printed by University of British Columbia Library pursuant to License Agreement. No further reproductions authorized.

712

LABORATORY SHEAR STRENGTH OF SOIL

on the performance of soils. There is a general tendency to overlook the fact that response performance of soil is more dependent upon the strain path imposed than upon the stress path. Modeling and test procedures etc. should actually be performed with full recognition of current strain path and strain path history. The immediate structure and fabric of the soil is a direct reflection of the strain path history and not the stress path. The stress path is only a means whereby the strain path is obtained. Until there is a unique relation established between stress and strain, the imposition of a stress path does not bring with it the actual realization of the strain path which is encountered in real soil situations. Thus it is necessary, if we are to proceed further in the field of soil testing and in the problem of modeling, to obtain a proper and realistic representation of current strain path and strain path history. In addition, the testing procedures that must be implemented should deal with a strain path control system. While it is true that stress and strain paths are coupled, the absence of a stress-strain path coupling term does not permit one to say directly that stress path control is indeed the only means whereby actual performance of soil can be determined. It is necessary to carefully note that there is a direct relation between an immediate and past structure—and obviously future soil structure—in view of the kinds of events and situations which are imposed or occur in a field soil. To fully appreciate real soils performance, the partly drained case must be understood. Under such circumstances it is necessary to be fully aware of the volumetric strains and strain path history encountered in the field. Conciading Remarks The progress in the last two decades since the previous ASTM shear strength symposium has been considerable, both in the area of experimental testing and in mathematical modeling. The use of true triaxial equipment and hollow cylinders is the major equipment innovation. However, the axisymmetric triaxial test continues to be the mainstay of laboratory shear apparatus. The development of electronic instrumentation and measuring sensors has changed testing standards and knowledge of boundary stresses and displacements. Modeling has progressed from the simple two-parameter Mohr-Coulomb rigid plastic model to post-Terzaghi soil mechanics models with elaborate ellipsodial cap and bounding surfaces. Nevertheless, from the results of this symposium, the following needs are suggested for additional development standards: 1. Standardization of triaxial compression/extension test for CU and CD conditions. 2. The use of stress and strain path prescriptions in test loading of specimens. 3. Evaluation of soil properties of partially saturated soils.

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SUMMARY

713

4. Consideration in laboratory testing and constitutive modeling that partially drained conditions usually occur in field situations. 5. Identification of testing procedures and data reduction methods for obtaining constitutive model parameters. 6. Development of laboratory data which could serve as a hallmark for verifying and improving constitutive models. 7. Development of equipment and testing techniques for determining the tensile properties of cohesive soils. 8. Equipment, procedures, and analytical models for addressing the anisotropic characteristics of soils. 9. The parameter "time" has been essentially omitted from analytical models and laboratory data characterizing soil behavior. In this context, development of both analytical modeling and laboratory characterization using this parameter is warranted. 10. Consideration of end restraint in laboratory tests.

R. N. Yong Geotechnical Research Center, McGill University, Montreal, Canada H3A 2K6; symposium co-chairman and co-editor

F. C. Townsend Department of Civil Engineering, University of Florida, Gainesville, Fla. 32611; symposium co-chairman and co-editor

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STP740-EB/Sep.1981

Index

Anisotropic soil Anisotropic elasto-plastic model, 369 Components, 256, 517 Consolidation, 390 Constitutive equations, 435 Field equations, 433 Measurement, 518, 530, 648 Model parameters, 437 Nonlinear stress-strain, 431 Triaxial testing, 48 B Borehole shear test Comparison with cone, 561 Comparison with triaxial, 561 In situ rock testing, 575 Limitations, 573 Test procedure, 554, 567

Cam-Clay Limitations, 350 Material constants, 349 Model, 345, 419 Modified, 420 Compacted clay Shear behavior, 277 Volume change, 283 Cone penetration Comparison with borehole shear, 561 Comparison with triaxial, 561

Constitutive models Anisotropic elasto-plastic, 358, 678 Cam-Clay, 345 Classification, 330 Deformation, 332 Drucker-Prager, 343 Elasto-plastic stress-strain, 335 Endochronic, 335, 377 Hyperbolic stress-strain, 335 Incremental, 333 Modeling, 330, 668 Perfect and incremental plasticity, 333, 341 Qualitative stress-strain, 685 Weidlinger cap, 350 Critical state Effective stress, 418 Model, 345 Pore pressure parameter, 412, 423 D Directional shear cell, test equipment, 520, 650 Direct shear Apparatus, 11 Residual shear test, 597 Test, 15 Torsional, 19, 23

Finite element analysis Elastic consolidation, 453 Elasto-plastic consolidation, 447 Simple shear, 638 Stress distribution, 30 715

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716

LABORATORY SHEAR STRENGTH OF SOIL

H Hollow cylinder Soil parameters, 213 State of stress, 57, 243 Stress deformation analysis, 211 Test equipment, 208

O Organic soil Consolidation, 229 Shear strength, 226, 233, 238 Stress-strain, 231

K Ko Burette mashed, 83 Direct determination, 200 Lateral strain sensor, 80 Indirect measurement, 203 Prediction, 623 Test equipment, 79 Test procedures, 84, 258, 621, 646 Theoretical evaluation, 87

Photoelastic, studies, 35, 638 Plane strain Comparison with triaxial test, 296 Directional shear cell, 516 Test equipment, 295 Pore pressure, time effect, 615 Preconsolidation pressure Predicted and measured, 505 Prediction, 509 s^/p ratio, 505

M Marine clay Anisotropy, 256 A'o-testing, 258 Strength properties, 263 Stress-strain, 260 Membrane, thickness effect, 303 Mohr-Coulomb Condition, 342 Criterion, 340 Penetrometer application, 579 Strength coefficients, 338 Strength envelope, 459 Strength parameters for "••8^"''= soil, 238

N Normalization Incremental, 389 Stress-strain, 398, 405

R Residual shear strength Analysis, 605 Test procedure, 596 Rockfill, shear strength, 318

St. Venant Analysis, 32 Solution, 30 Sand Incremental creep, 541 Plane strain test, 51, 295 Shear strength, 541 Servo system, stress path control, 164 Shear strength Modeling, 494 Plasticity, 489

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INDEX

Prediction, 497 Random analysis, 485 Residual, 596 Rockfill material, 318 Testing, 11 Uncertainty, 486 Undrained strength ratio, 263 Shear test Anisotropic consolidation, 391 Assessment, 645, 661, 707 Lateral stress measurement, 191 Limitations, 653 NGL 29 Ring shear test, 22 Roscoe, 29 Simple shear test, 28, 37, 391 Stress distribution, 633 Torsional simple shear, 399 Strains Normalization, 388 Plane, 9 Simple shear, 10 Stress Deviator, 8 Effective stress, marine clay, 266 Normalization, 388 Pure shear, 8 Stress path, 164 Theories, 418 Stress-strain Compacted ballast, 104 Hyperbolic parameters, 110 Marine clay, 260 Nonlinear, 432 Normalized, 398 Organic soil, 231 Suction Matrix, 115 Measurement, 123 Osmatic, 115

717

Psychrometer, 116, 123 Soil suction, 115

Tensile Cohesion, 140 Indirect tension test apparatus, 219 Strength, 130 Testing, needs, 712 Torsion test Apparatus, 145, 244 Procedure, 248 Triaxial test Anisotropic consolidation, 46 Anisotropic materials, 48 Backpressure saturation, 45 Comparison with plane strain, 296 Control system, 180 Corrections, 47 End platens, 43 Hollow cylinder, 57 Lateral strain sensor, 80 Multiaxial, 53 Plane strain, 51, 295 Pressure control, 97 Rates of loading, 47 Stress distribution, 41 Test apparatus, 12, 40 Triaxial cell, 95 True triaxial devices, 52 Volume change device, 98

U Unconfined penetration, 130 Unsaturated soil Mechanical behavior, 117 Soil suction, 115

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