Foundations on Rock: Second Edition

Foundations on Rock

Second edition

Foundations on Rock Duncan C.Wyllie Principal, Golder Associates, Consulting Engineers Vancouver, Canada

With a Foreword by Richard E.Goodman Professor of Geological Engineering, University of California, Berkeley, USA Second edition

E & FN SPON An imprint of Routledge London and New York

First edition published 1992 by E & FN Spon, an imprint of Chapman & Hall Second edition published 1999 by E & FN Spon, 11 New Fetter Lane, London EC4P 4EE Simultaneously published in the USA and Canada by Routledge 29 West 35th Street, New York, NY 10001 This edition published in the Taylor & Francis e-Library, 2005. “To purchase your own copy of this or any of Taylor & Francis or Routledge’s collection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.” E & FN Spon is an imprint of the Taylor & Francis Group © 1992, 1999 Duncan C.Wyllie All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. The publisher makes no representation, express or implied, with regard to the accuracy of the information contained in this book and cannot accept any legal responsibility or liability for any errors or omissions that may be made. The right of Duncan C.Wyllie to be identified as the author of this publication has been asserted by him in accordance with the Copyright, Design and Patents Act 1988. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data A catalogue record for this book has been requested ISBN 0-203-47767-7 Master e-book ISBN

ISBN 0-203-78591-6 (Adobe eReader Format) ISBN 0-419-23210-9 (Print Edition)

Contents

1 1.1

Foreword to first edition

xiv

Introduction

xv

Introduction to first edition

xvii

Notation

xix

Note

xxi

Characteristics of rock foundations

1

Types of rock foundation

1

1.1.1

Spread footings

2

1.1.2

Socketed piers

3

1.1.3

Tension foundations

3

1.2

Performance of foundations on rock

4

1.2.1

Settlement and bearing capacity failures

4

1.2.2

Creep

5

1.2.3

Block failure

5

1.2.4

Failure of socketed piers and tension anchors

6

1.2.5

Influence of geological structure

7

1.2.6

Excavation methods

7

1.2.7

Reinforcement

7

1.3

Structural loads

8

1.3.1

Buildings

9

1.3.2

Bridges

10

1.3.3

Dams

11

1.3.4

Tension foundations

11

1.4

Allowable settlement

11

v

1.4.1

Buildings

11

1.4.2

Bridges

12

1.4.3

Dams

13

1.5

Influence of ground water on foundation performance

14

1.5.1

Foundation stability

14

1.5.2

Dams

14

1.5.3

Tension foundations

16

1.6

Factor of safety and reliability analysis

16

1.6.1

Factor of safety analysis

16

1.6.2

Limit states design

17

1.6.3

Sensitivity analysis

18

1.6.4

Coefficient of reliability

18

1.7 2 2.1

References

25

Structural geology

27

Discontinuity characteristics

27

2.1.1

Types of discontinuity

27

2.1.2

Discontinuity orientation and dimensions

29

2.2

Orientation of discontinuities

30

2.3

Stereographic projection

31

2.3.1

Pole plots

34

2.3.2

Pole density

34

2.3.3

Great circles

36

2.3.4

Stochastic modeling of discontinuities

38

2.4

Types of foundation failure

39

2.5

Kinematic analysis

39

2.5.1

Planar failure

41

2.5.2

Wedge failure

41

2.5.3

Toppling failure

41

2.5.4

Friction cone

41

2.6

Probabilistic analysis of structural geology

43

vi

2.6.1

Discontinuity orientation

43

2.6.2

Discontinuity length and spacing

45

2.7

References

48

Rock strength and deformability

50

3.1

Range of rock strength conditions

50

3.2

Deformation modulus

52

3.2.1

Intact rock modulus

53

3.2.2

Stress-strain behavior of fractured rock

55

3.2.3

Size effects on deformation modulus

58

3.2.4

Discontinuity spacing and modulus

60

3.2.5

Modulus of anisotropic rock

61

3.2.6

Modulus-rock mass quality relationships

62

3

3.3

Compressive strength

64

3.3.1

Compressive strength of intact rock

66

3.3.2

Compressive strength of fractured rock

66

3.4

Shear strength

71

3.4.1

Mohr-Coulomb materials

71

3.4.2

Shear strength of discontinuities

71

3.4.3

Shear strength testing

77

3.4.4

Shear strength of fractured rock

80

3.5

Tensile strength

82

3.6

Time-dependent properties

83

3.6.1

Weathering

84

3.6.2

Swelling

86

3.6.3

Creep

87

3.6.4

Fatigue

92

References

92

Investigation and in situ testing methods

97

Site selection

97

3.7 4 4.1 4.1.1

Aerial and terrestrial photography

98

vii

4.1.2 4.2

Geophysics Geological mapping

100 103

4.2.1

Standard geology descriptions

103

4.2.2

Discontinuity mapping

108

4.3

Drilling

110

4.3.1

Diamond drilling

110

4.3.2

Percussion drilling

115

4.3.3

Calyx drilling

116

4.4

Ground water measurements

116

4.4.1

Water pressure measurements

118

4.4.2

Permeability measurements

121

4.5

In situ modulus and shear strength testing

124

4.5.1

Modulus testing

124

4.5.2

Direct shear tests

132

4.6

References

132

Bearing capacity, settlement and stress distribution

138

5.1

Introduction

138

5.2

Bearing capacity

140

5.2.1

Building codes

140

5.2.2

Bearing capacity of fractured rock

141

5.2.3

Recessed footings

145

5.2.4

Bearing capacity factors

146

5.2.5

Foundations on sloping ground

147

5.2.6

Bearing capacity of shallow dipping bedded formations

147

5.2.7

Bearing capacity of layered formations

152

5

5.3

Bearing capacity of karstic formations

153

5.3.1

Characteristics of solution features

154

5.3.2

Detection of solution features

155

5.3.3

Foundation types in karstic terrain

157

5.4

Settlement

163

viii

5.4.1

Settlement on elastic rock

164

5.4.2

Settlement on transversely isotropic rock

169

5.4.3

Settlement on inelastic rock

173

5.4.4

Settlement due to ground subsidence

174

5.5

Stress distributions in foundations

175

5.5.1

Stress distributions in isotropic rock

175

5.5.2

Stress distributions in layered formations

179

5.5.3

Stress distributions in transversely isotropic rock

180

5.5.4

Stress distributions in eccentrically loaded footings

182

References

185

5.6 6

Stability of foundations

189

6.1

Introduction

189

6.2

Stability of sliding blocks

189

6.2.1

Deterministic stability analysis

191

6.2.2

Probabilistic stability analysis

195

6.3

Stability of wedge blocks

196

6.4

Three-dimensional stability analysis

201

6.5

Stability of toppling blocks

202

6.6

Stability of fractured rock masses

206

6.7

External effects on stability

209

6.7.1

Seismic design

209

6.7.2

Scour

210

6.8 7 7.1

References

213

Foundations of gravity and embankment dams

215

Introduction

215

7.1.1

Dam performance statistics

216

7.1.2

Foundation design for gravity and embankment dams

217

7.1.3

Loads on dams

218

7.1.4

Loading combinations

219

7.2

Sliding stability

220

ix

7.2.1

Geological conditions causing sliding

220

7.2.2

Shear strength

221

7.2.3

Water pressure distributions

221

7.2.4

Stability analysis

223

7.2.5

Factor of safety

227

7.2.6

Examples of stabilization

227

7.3

Overturning and stress distributions in foundations

228

7.3.1

Overturning

230

7.3.2

Stress and strain in foundations

230

7.4

Earthquake response of dams

235

7.4.1

Introduction

235

7.4.2

Measured motions of foundation rock

236

7.4.3

Sliding stability and overturning under seismic loads

237

7.4.4

Finite element analysis

238

7.4.5

Earthquake displacement analysis

239

7.5

Preparation of rock surfaces

243

7.5.1

Shaping

244

7.5.2

Cleaning and sealing

245

7.5.3

Rebound

246

7.5.4

Solution cavities

246

Foundation rehabilitation

247

7.6.1

Monitoring

248

7.6.2

Grouting, sealing and drainage

248

7.6.3

Anchoring

249

7.6.4

Scour protection

249

7.6

7.7

Grouting and drainage

250

7.7.1

Grouting functions

252

7.7.2

Grout types

252

7.7.3

Mechanism of grouting

253

7.7.4

Drilling method

254

x

7.7.5

Hole patterns

255

7.7.6

Grout mixes

256

7.7.7

Grout strength

257

7.7.8

Grout pressures

257

7.7.9

Grouting procedures

259

7.7.10

Permeability criteria for grouted rock

259

7.7.11

Monitoring grouting operations

261

7.7.12

Leaching

261

7.7.13

Drainage

263

7.8

References

263

Rock socketed piers

269

Introduction

269

8 8.1 8.1.1

Types of deep foundations

269

8.1.2

Investigations for socketed piers

269

8.2

Load capacity of socketed piers in compression

271

8.2.1

Mechanism of load transfer

272

8.2.2

Shear behavior of rock sockets

272

8.2.3

Factors affecting the load capacity of socketed piers

274

8.2.4

Socketed piers in karstic formation

283

8.3

Design values: side-wall resistance and end bearing

283

8.3.1

Side-wall shear resistance

283

8.3.2

End-bearing capacity

285

8.4

Axial deformation

286

8.4.1

Settlement mechanism of socketed piers

286

8.4.2

Settlement of side-wall resistance sockets

287

8.4.3

Settlement of end loaded piers

288

8.4.4

Settlement of socketed, end bearing piers

289

8.4.5

Socketed piers with pre-load applied at base

294

8.5 8.5.1

Uplift Uplift resistance in side-wall shear

294 295

xi

8.5.2 8.6

Uplift resistance of belled piers Laterally loaded socketed piers

296 297

8.6.1

Computing lateral deflection with p-y curves

297

8.6.2

p-y curves for rock

300

8.6.3

Socket stability under lateral load

303

8.7

References

304

Tension foundations

310

9.1

Introduction

310

9.2

Anchor materials and anchorage methods

311

9

9.2.1

Allowable working loads and safety factors

311

9.2.2

Steel relaxation

314

9.2.3

Strength properties of steel bar and strand

315

9.2.4

Applications of rigid bar anchors

315

9.2.5

Applications of strand anchors

317

9.2.6

Cement grout anchorage

318

9.2.7

Resin grout anchorage

324

9.2.8

Mechanical anchorage

326

9.3

Design procedure for tensioned anchors

326

9.3.1

Mechanics of load transfer mechanism between anchor, grout and rock

326

9.3.2

Allowable bond stresses and anchor design

329

9.3.3

Prestressed and passive anchors

332

9.3.4

Uplift capacity on rock anchors

333

9.3.5

Group action

342

9.3.6

Cyclic loading of anchors

342

9.3.7

Time-dependent behavior and creep

342

9.3.8

Effect of blasting on anchorage

344

9.3.9

Anchors in permafrost

345

9.4

Corrosion protection

345

9.4.1

Mechanism of corrosion

346

9.4.2

Types of corrosion

347

xii

9.4.3

Corrosive conditions

349

9.4.4

Corrosion protection methods

350

9.4.5

Corrosion monitoring

352

9.5

Installation and testing

353

9.5.1

Water testing

353

9.5.2

Load testing

354

9.5.3

Acceptance criteria

356

9.6

References

357

10

Construction methods in rock

360

10.1

Introduction

360

10.2

Drilling

360

10.2.1

Diamond drilling

362

10.2.2

Percussion drilling

363

10.2.3

Rotary drills

365

10.2.4

Overburden drilling

367

10.2.5

Large diameter drilling

368

10.2.6

Directional drilling

370

10.3

Blasting and non-explosive rock excavation

373

10.3.1

Rock fracture by explosives

374

10.3.2

Controlled blasting

376

10.3.3

Blasting horizontal surfaces

378

10.3.4

Ground vibration control

379

10.3.5

Vibrations in uncured concrete

383

10.3.6

Non-explosive excavation

384

10.4

Bearing surface improvement and rock reinforcement

386

10.4.1

Trim blasting

386

10.4.2

Surface preparation

386

10.4.3

Dental concrete

388

10.4.4

Shotcrete

388

10.4.5

Shear keys

390

xiii

10.4.6

Rock bolts

391

10.4.7

Tensioned rock anchors

391

10.4.8

Concrete buttress

391

10.4.9

Drain holes

391

10.5

Contracts and specifications

392

10.5.1

Components of contract documents

392

10.5.2

Types of contract

393

10.5.3

Rock excavation and reinforcement specifications

394

10.6

References

398

Appen dix I

Stereonets for handplotting of structural geology data

401

Appen dix II

Quantitative description of discontinuities in rock masses

405

Appen dix III

Conversion factors

422

Index

425

Foreword to first edition

Duncan Wyllie has given us a complete, useful textbook on rock foundations. It is complete in its coverage of all parts of this important subject and in providing reference material for follow-up study. It is eminently useful in being well organized, clearly presented, and logical. Rock would seem to be the ultimate excellent reaction for engineering loads, and often it is. But the term ‘rock’ includes a variety of types and conditions of material, some of which are surely not ‘excellent’ and some that are potentially dangerous. Examples of frequently hazardous rock masses are those that contain dissolved limestones, undermined coal-bearing sediments, decomposed granites, swelling shales and highly jointed or faulted schists or slates. Moreover, the experience record of construction in rocks includes numerous examples of economic difficulties revolving around mistaken or apparently malevloent behavior of rock foundations. Such cases have involved excavation overbreak, deterioration of prepared surfaces, flooding or icing by ground water seepage, accumulation of boulders from excavation, gullying or piping of erodible banks, and misclassification or misidentification of materials in the weathered zone. Another class of difficult problems involve the forensic side of siting in evaluating potentialities for rock slides, fault movement, or long-term behavior. Problems of investigating and characterizing rock foundations are intellectually challenging; and it may require imagination to tailor the design of a foundation to the particular morphological, structural and material properties of a given rock site. Thus the field of engineering activity encompassed in this book is interesting and demanding. The subject is worthy of a book on this subject and of your time in studying it. Richard E.Goodman Berkeley, California

Introduction

The first edition of Foundations on Rock was written during the period 1988 to 1990. In the decade that has passed since the initial material was collected on this subject, there has been steady development in the field of rock engineering applied to foundations, but no new techniques that have significantly changed design and construction practices. Consequently, the purpose of preparing this second edition, which has been written between 1996 and 1998, has been to update the technical material, and add information on new projects where valuable experience on rock foundations has been documented. The following is a summary of the material that has been added: • Chapter 1: expanded discussion on acceptable reliability levels for different types of structures in relation to the consequences of failure, as well as methods of risk analysis; • Chapter 2: new material has been added on typical probability distributions for discontinuity lengths and spacing, and methods of collecting data on these features; • Chapter 3: information is included on the deformation behavior of very weak rock that has been determined from in situ testing; • Chapter 4: the procedures for mapping geological structure has been extensively revised to conform to the procedures drawn up by the International Society of Rock Mechanics, and has now been consolidated in Appendix II. It is intended that this information will help in the production of standard mapping results that are comparable from project to project; • Chapter 5: a list of projects with substantial foundations bearing on rock has been included describing the rock conditions and the actual bearing pressures that have been successfully used. Also, the section on the detection of karstic features and the design of foundations in this geological environment has been greatly expanded. With respect to prediction of foundation performance, an example of numeric analysis of the stability of jointed rock masses has been included; • Chapter 6: an example has been prepared of probabilistic stability analysis to calculate the coefficient of reliability of a foundation. Also, a technique for assessing scour potential of rock is presented in detail; • Chapter 7: with the increasing need to rehabilitate existing dams either to meet new design standards, or to repair deterioration, a section on foundation improvement, scour potential and tie-down anchors has been added; • Chapter 8: for the design of laterally loaded rock socketed piers, new information is provided on p-y curves for very weak rock; • Chapter 9: the testing procedures and acceptance criteria for tensioned anchors has been updated to conform with 1990’s recommended practice; • Chapter 10: new information has been added on contracting procedures, and in particular Partnering.

xvi

It is believed that this is still one of the few books devoted entirely to the subject of rock foundations. As with the first edition, it is still intended to be a book that can be used by practitioners in a wide range of geological conditions, while still providing a sound theoretical basis for design. The preparation of this edition has drawn extensively on the knowledge of many of the author’s colleges in both the design and construction fields, all or which are gratefully acknowledged. In addition, Glenda Gurtina has provided great assistance in the preparation of the manuscript and Sonia Skermer has prepared all the new artwork to her usual high standard. Finally, I would like to thank my family for supporting me through yet another book project. Duncan Wyllie Vancouver, 1998

Introduction to first edition

Foundations on Rock has been written to fill an apparent gap in the geotechnical engineering literature. Although there is wide experience and expertise in the design and construction of rock foundations, this has not, to date, been collected in one volume. A possible reason for the absence of a book on rock foundations is that the design and construction of soil foundations is usually more challenging than that of rock foundations. Consequentially, there is a vast collection of literature on soil foundations, and a tendency to assume that any structure founded on ‘bedrock’ will be totally safe against settlement and instability. Unfortunately, rock has a habit of containing nasty surprises in the form of geological features such as solution cavities, variable depths of weathering, and clay-filled faults. All of these features, and many others, can result in catastrophic failure of foundations located on what appear to be sound rock surfaces. The main purpose of this book is to assist the reader in the identification of potentially unstable rock foundations, to demonstrate design methods appropriate for a wide range of geological conditions and foundation types, and to describe rock construction methods. The book is divided into three main section. Chapters 1–4 describe the investigation and measurement of the primary factors that influence the performances of rock foundations. Namely, rock strength and modulus, fracture characteristics and orientation, and ground water conditions. Chapters 5–9 provide details of design procedures for spread footings, dam foundations, rock socketed piers, and tension foundations. These chapters contain worked examples illustrating the practical application of the design methods. The third section, Chapter 10, describes a variety of excavation and stabilization methods that are applicable to the construction of rock foundations. The anticipated audience for this book, which has been written by a practising rock mechanics engineer, is the design professional in the field of geotechnical engineering. The practical examples illustrate the design methods, and descriptions are provided of investigation methods that are used widely in the geotechnical engineering community. It is also intended that the book will be used by graduate geotechnical engineers as a supplement to the books currently available on rock slope engineering, geological engineering and rock mechanics. Foundations on Rock describes techniques that are common to a wide selection of projects involving excavations in rock and these techniques have been adapted and modified, where appropriate, to rock foundation engineering. Much of the material contained in this book has been acquired from the author’s experience on projects in a wide range of geological and construction environments. On all these projects there have, of course, been many other persons involved: colleagues, owners, contractors and, equally importantly, the construction workers. The author acknowledges the valuable advice and experience that have been acquired from them all. There are many people who have made specific contributions to this book and their assistance is greatly appreciated. Sections of the book were reviewed by Herb Hawson, Graham Rawlings, Hugh Armitage, Vic

xviii

Milligan, Dennis Moore, Larry Cornish, Norm Norrish and Upul Atukorala. In additon a number of people contributed photographs and computer plots and they are acknowledged in the text. Important contributions were also made by Ron Dick who produced all the drawings, and Glenys Sykes who diligently searched out innumerable references. Finally, I appreciate the support of my family who tolerated, barely, the endless early-morning and late-night sessions that were involved in preparing this book. D.C.Wyllie

Notation

The following symbols are used in this book. A B b Cd Cf CR c D d Em Er Em(b) Em(s) e FS F fr fd Gr, m G1, 2

Cross-sectional area (m2, inch2) Width of footing, diameter of pier, burden (blasting) (m, ft) Radius of footing (m, ft) Dispersion coefficient (structural geology); influence factor for foundation displacement Correction factor for foundation shape Coefficient of reliability Cohesion (MPa, p.s.i.) Diameter, depth of embedment (m, ft) Diameter (m, ft) Mean value of displacing force (MN, lbf) Deformation modulus of rock mass (MPa, p.s.i.) Deformation modulus of intact rock (MPa, p.s.i.) Deformation modulus of rock mass in base of pier (MPa, p.s.i.) Deformation modulus of rock mass in shaft of pier (MPa, p.s.i.) Eccentricity in foundation bearing pressure Factor of safety Foundation factor (seismic design); shape factor (falling head tests) Resisting force (MN, lbf) Displacing force (MN, lbf); factor in limit states design Shear modulus: intact rock (r), rock mass (m) (MPa, p.s.i.) Viscoelastic constants defining creep

characteristics of rock (MPa, p.s.i.) Height (m, ft); horizontal component of force(s) (MN, lbf) h Head measurement in falling head test (m) I Importance factor in seismic design Point load strength (MPa, p.s.i.) Is Pressure gradient ih K Bulk modulus (MPa, p.s.i.) Factor for construction type in seismic Ks design k Permeability (m/s); blast vibration attentuation factor Stiffness, normal and shear (GPa/m, kn, s p.s.i./in) L, l Length of foundation, outcrop, socket (m, ft) l, m, n Unit vectors of direction cosines (structural geology) m Rock mass strength factor (Hoek-Brown strength) N Normal force (MN, lbf); number (of analyses) bearing capacity factor P Probability; rate of energy dissipation (kW/m2) H

p PF Q Qs q qa

Pressure (MPa, p.s.i.) Probability of failure Foundation load (MN, lbf) Seepage rate (l/s, ft3/s) Flow rate (l/s, gal/s); foundation bearing pressure (MPa, p.s.i.) Allowable foundation bearing pressure

xx

R Re r S S SD s T U u V v W Z a

(MPa, p.s.i.) Force modification factor in seismic design Resultant unit vector Reynolds number Radius (m, ft) Spacing (m, ft); shear force (MN, lbf); seismic response factor Siemen (unit of conductivity) Standard deviation Rock mass strength factor (Hoek-Brown strength) Basic time lag (s); rock bolt tension (MN, lbf) Water uplift force (MN, lbf) Water uplift pressure (MPa, p.s.i.) Water force in tension crack (MN, lbf); vertical component of force(s) (MN, lbf); base shear Zonal velocity ratio in seismic design Weight of sliding block; weight factor in seismic design Mean value Factor for seismic intensity Dip direction of plane, or trend of force (degrees); adhesion factor of pier side-

ß ? ?w d ? e ? ? v s su(m) su(r) t ø ? ? ?

walls Settlement angular distortion, dip (degrees); blast vibration attenuation factor Unit weight (kN/m3, lbf/ft3) Unit weight of water (kN/m3, lbf/ft3) Settlement; displacement (mm, in) Settlement relative deflection; displacement (mm, in) Strain (%) Dynamic viscosity—rock creep (MPa min., p.s.i. min., poise (cgs units)) Apex angle of rock cone (degrees) Poisson’s ratio Normal stress (MPa, p.s.i.) Uniaxial compressive strength of rock mass (MPa, p.s.i.) Uniaxial compressive strength of intact rock (MPa, p.s.i.) Shear stress (MPa, p.s.i.) Friction angle (degrees) Dip of plane or force (degrees) Settlement tilt (degrees) Factor in rock anchor bond strength calculation Water table

Note

The recommendations and procedures contained herein are intended as a general guide and prior to their use in connection with any design, report or specification they should be reviewed with regard to the full circumstances of such use. Accordingly, although every care has taken in the preparation of this book, no liability for negligence or otherwise can be accepted by the author or the publisher.

1 Characteristics of rock foundations

1.1 Types of rock foundation There are two distinguishing features of foundations on rock. First, the ability of the rock to withstand much higher loads than soil, and second, the presence of defects in the rock which result in the strength of the rock mass being considerably less than that of the intact rock. The compressive strength of rock may range from less than 5 MPa (725 p.s.i.) to more than 200 MPa (30 000 p.s.i.), and where the rock is strong, substantial loads can be supported on small spread footings. However, a single, low strength discontinuity oriented in a particular direction may cause sliding failure of the entire foundation. The ability of rock to sustain significant shear and tensile loads means that there are many types of structures that can be constructed more readily on rock than they can be on soil. Examples of such structures are dams and arch bridges which produce inclined loads in the foundation, the anchorages for suspension bridges and other tie-down anchors which develop uplift forces, and rock socketed piers which support substantial loads in both compressive and uplift. Some of these loading conditions are illustrated in Fig. 1.1 which shows the abutment of an arch bridge. The load on the footing for the arch is inclined along the tangent to the arch, while the loads on the column and abutment are vertical; the load capacity of these footings depends primarily on the strength and deformability of the rock mass. The wall supporting the cut below the abutment is anchored with tensioned and grouted rock bolts; the load capacity of these bolts depends upon the shear

strength developed at rock-grout interface in the anchorage zone. If the material forming the foundations of the bridge shown in Fig. 1.1 was all strong, massive, homogeneous rock with properties similar to concrete, design and construction of the footings would be a trivial matter because the loads applied by a structure are generally much less than the rock strength. However, rock almost always contains discontinuities that can range from joints with rough surfaces and cohesive infillings that have significant shear strength, to massive faulted zones containing expansive clays with relatively low strength. Figure 1.1 shows how the geological structure can affect the stability of the foundations. First, there is the possibility of overall failure of the abutment along a failure plane (a-a) passing along the fault, and through intact rock at the toe of the slope. Second, local failure (b) of the foundation of the vertical column could occur on joints dipping out of the slope face. Third, settlement of the arch foundation may occur as a result of compression of weak materials in the fault zone (c), and fourth, poor quality rock in the bolt anchor zone could result in failure of the bolts (d) and loss of support of the abutment. Foundations on rock can be classified into three groups—spread footings, socketed piers and tension foundations—depending on the magnitude and direction of loading, and the geotechnical conditions in the bearing area. Figure 1.2 shows examples of the three types of foundations and the following is a brief description of the principal features of each. The basic geotechnical information

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CHARACTERISTICS OF ROCK FOUNDATIONS

Figure 1.1 Stability of bridge abutment founded on rock: (a-a) overall failure of abutment on steeply dipping fault zone; (b) shear failure of foundation on daylighting joints; (c) movement of arch foundation due to compression of lowmodulus rock; and (d) tied-back wall to support weak rock in abutment foundation.

required for the design of all three types of foundation consists of the structural geology, rock strength properties, and the ground water conditions as described in Chapters 2–4. The application of this data to the design of each type of foundation is described in Chapters 5–9. 1.1.1 Spread footings Spread footings are the most common type of foundation and are the least expensive to construct. They can be constructed on any surface which has adequate bearing capacity and settlement characteristics, and is accessible for construction. The bearing surface may be inclined, in which case steel dowels or tensioned anchors may be required to secure the footing to the rock. For footings located at the crest or on the face of steep slopes,

the stability of the overall slopes, taking into account the loads imposed by the structure, must be considered (Fig. 1.2(a)). Dam foundations, which fall into the category of spread footings, are treated as a special case in this book. Loads on dam foundations comprise the weight of the dam together with the horizontal water force which exert a non-vertical resultant load (Fig. 1.2(b)). Furthermore, uplift forces are developed by water pressures in the foundation. These loads can be much larger than the loads imposed by structures such as bridges and build ings. In addition there is the need for a high level of safety because the consequences of failure are often catastrophic. Dams must also be designed to withstand flood conditions, and where appropriate, earthquake loading. The design of dam foundations, excluding foundations for arch dams, is discussed in Chapter 7.

TYPES OF ROCK FOUNDATION

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Figure 1.2 Types of foundations on rock: (a) spread footing located at crest of steep slope; (b) dam foundation with resultant load on foundation acting in downstream direction; (c) socketed pier to transfer structural load to elevation below base of adjacent excavation; and (d) tie-down anchors, with staggered lengths, to prevent uplift of submerged structure.

1.1.2 Socketed piers Where the loads on individual footings are very high and/or the accessible bearing surface has inadequate bearing capacity, it may be necessary to sink or drill a shaft into the underlying rock and construct a socketed pier. For example, in Fig. 1.2(c) a spread footing could not be located on the edge of the excavation made for the existing building, and a socketed pier was constructed to bear in sound rock below the adjacent foundation level. The support provided by socketed piers comprises the shear strength around the periphery of the drill hole, and

the end bearing on the bottom of the hole. Socketed piers can be designed to withstand axial loads, both compressive and tensile, and lateral forces with minimal displacement. Design methods for socketed piers are discussed in Chapter 8. 1.1.3 Tension foundations For structures that produce either permanent or transient uplift loads, support can be provided by the weight of the structure and, if necessary, tiedown anchors grouted into the underlying rock (Fig. 1.2(d)). The uplift capacity of an anchor is

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CHARACTERISTICS OF ROCK FOUNDATIONS

determined by the shear strength of the rock-grout bond and the characteristics of the rock cone that is developed by the anchor. The dimensions of this cone are defined by the developed anchor length, and the apex angle of the cone. The position of the apex is usually assumed to be at mid-point of the anchor length, and the apex angle can vary from about 60° to 120°. An apex angle of about 60° would be used where there are persistent discontinuities aligned parallel to the load direction, while an angle of about 120° would be used in massive rock, or rock with persistent discontinuities at right angles to the load direction. In calculating uplift capacity, a very conservative assumption can be made that the cone is ‘detached’ from the surrounding rock and that only the weight of the cone resists uplift. However, unless the anchor is installed in a rock mass with a cone-shaped discontinuity pattern, significant uplift resistance will be provided by the rock strength on the surface of the cone. The value of the rock strength depends on the strength of the intact rock, and on the orientation of the geological structure with respect to the cone surface. As shown in Fig. 1.2(d), the lengths of the anchors can be staggered so that the stresses in the rock around the bond zones are not concentrated on a single plane. Design methods for tension anchors, including testing procedures and methods of corrosion protection, are described in Chapter 9. 1.2 Performance of foundations on rock Despite the apparently favorable stability conditions for structures founded on strong rock, there are, unfortunately, instances of foundation failures. Failures may include excessive settlement due to the presence of undetected weak seams or cavities, deterioration of the rock with time, or collapse resulting from scour and movement of blocks of rock in the foundation. Factors that may influence stability are the structural geology of the foundation, strength of the intact rock and discontinuities, ground water pressures, and the

methods used during construction to excavate and reinforce the rock. The most complete documentation of foundation failures has been made for dams because the consequences of failure are often catastrophic. Also, the loading conditions on dam foundations are usually more severe than those of other structures so study of these failures gives a good insight on the behavior and failure modes of rock foundations. The importance of foundation design is illustrated by Gruner’s examination of dam failures in which he found that one third could be directly attributed to foundation failure (Gruner, 1964, 1967). The following is a review of the stability conditions of rock foundations. 1.2.1 Settlement and bearing capacity failures Settlement and bearing capacity type failures in rock are rare but may occur where large structures, sensitive to settlement, are constructed on very weak rock (Tatsuoka et al., 1995), and where beds of low strength rock or cavities formed by weathering, scour or solution occur beneath the structure (James and Kirkpatrick, 1980). The most potentially hazardous conditions are in karstic areas where solution cavities may form under, or close to, the structure so that the foundation consists of only a thin shell of competent rock (Kaderabek and Reynolds, 1981). Rock types susceptible to solution are limestone, anhydrite, halite, calcium carbonate and gypsum. The failure mechanism of the foundation under these conditions may be punching and shear failure, or more rarely bending and tensile failure. Lowering of the water table may accelerate the solution process and cause failure long after construction is complete. A related problem is that of a thin bed of competent rock overlying a thick bed of much more compressible rock which may result in settlement as a result of compression of the underlying material (mechanism (c) in Fig. 1.1). Loss of bearing capacity with time may also occur due to weathering of the foundation rock. Rock types which are susceptible to weathering include

TYPES OF ROCK FOUNDATION

poorly cemented sandstones, and shales, especially if they contain swelling clays. Common causes of weathering are freeze-thaw action, and in the case of such rocks as shales, wetting and drying cycles. Foundations which undergo a significant change in environmental conditions as a result of construction, such as dam sites where the previously dry rock in the sides of the valley becomes saturated, should be carefully checked for any materials that may deteriorate with time in their changed environment. 1.2.2 Creep There are two circumstances under which rocks may creep, that is, experience increasing strain with time under the application of a constant stress. First, creep may occur in elastic rock if the applied stress is a significant fraction (greater than about 40%) of the uniaxial compressive strength (σu). However, at the relatively low stress level of 40% of σu the rate of creep will decrease with time. At stress levels greater than about 60% of σu, the rate will increase with time and eventually failure may take place. At the stress levels usually employed in foundations it is unlikely that creep will be significant. A second condition under which creep may occur is in ductile rocks such as halite and some sediments. A ductile material will behave elastically up to its yield stress but is able to sustain no stress greater than this so that it will flow indefinitely at this stress unless restricted by some out-side agency. This is known as elastic-plastic behavior and foundations on such materials should be designed so that the applied stress is well below the yield stress. Where this is not possible, the design and construction methods should accommodate timedependent deformations. Time-dependent behavior of rock is discussed in more detail in Section 3.6.

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1.2.3 Block failure The most common cause of rock foundation failure is the movement and collapse of blocks of rock formed by intersecting discontinuities (mechanism (b) in Fig. 1.1). The orientation, spacing and length of the discontinuities determines the shape and size of the blocks, as well as the direction in which they can slide. Stability of the blocks depends on the shear strength of the discontinuity surfaces, and the external forces which can comprise water, structural, earthquake and reinforcement loads. Analysis of stability conditions involves the determination of the factor of safety or coefficient of reliability, and is described in more detail in Section 1.6.4 and Chapter 6. An example of a block movement failure occurred in the Malpasset Dam in France where a wedge formed by intersecting faults moved when subjected to the water uplift forces as the dam was filled (Londe, 1987). The failure resulted in the loss of 400 lives. Bridge foundations also experience failure or movement as a result of instability of blocks of rock (Wyllie, 1979, 1995). One cause of these failures is the geometry of bridge foundations, with the frequent construction of abutments and piers on steep rock faces from which blocks can slide. Other causes of failure are ground water effects which include weathering, uplift pressures on blocks which have a potential to slide, river scour and wave action which can undermine the foundation, and traffic vibration which can slowly loosen closely fractured rock. It is standard practice on most highways and railways to carry out regular bridge inspections which will often identify deteriorating foundations and allow remedial work to be carried out. It is the author’s experience that rock will usually undergo observable movement sufficient to provide a warning of instability before collapse occurs. An example of the influence of structural geology on stability is shown in Fig. 1.3 where a retaining wall is founded on very strong granite containing sheeting joints dipping at about 40° out of the face. Although the bearing capacity of the rock was

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CHARACTERISTICS OF ROCK FOUNDATIONS

Figure 1.3 Retaining wall foundation stabilized with reinforced concrete buttress and rock bolts.

ample for this loading condition, movement along the joints and failure of a block in the foundation resulted in rotation of the wall. Fortunately, early detection of this condition allowed remedial work to be carried out. Thisconsisted of concrete to fill the cavity formed by the failed rock and the installation of tensioned bolts to prevent further movement on the joints. 1.2.4 Failure of socketed piers and tension anchors The failure of socketed piers is usually limited to unacceptable movement which may occur as a result of loss of bond at the rock-concrete interface on the side walls, or compression of loose material

at the base of the pier. A frequent cause of movement is poor cleaning of the sides and base of the hole, or in the case of karstic terrain, collapse of rock into an undetected solution cavity. In the case of tensioned anchors, loss of bond at the rock-grout interface on the walls of the hole may result in excessive movement of the head, while corrosion failure of the steel may result in sudden failure long after installation. The long term reliability of tensioned anchors depends to a large degree on the details of fabrication and installation procedures as discussed in Chapter 9.

TYPES OF ROCK FOUNDATION

1.2.5 Influence of geological structure The illustrations of foundation conditions shown in Figs 1.1 and 1.3, and the analysis of foundation failures, show that geologic structure is often a significant feature influencing the design and construction of rock foundations. Detailed knowledge of discontinuity characteristics— orientation, spacing, length, surface features and infilling properties—are all essential information required for design. The examination of the structural geology of a site usually requires a threedimensional analysis which can be most conveniently carried out using stereographic projections as described in Chapter 2. This technique can be used to identify the orientation and shape of blocks in the foundation that may fail by sliding or toppling. It is also necessary to determine the shear strength of discontinuities along which failure could take place. This involves direct shear tests, which may be carried out in the laboratory on pieces of core, or in situ on undisturbed samples. Methods of rock testing are described in Chapter 4. 1.2.6 Excavation methods Blasting is often required to excavate rock foundations and it is essential that controlled blasting methods be used that minimize the damage to rock that will support the planned structure. Damage caused by excessively heavy blasting can range from fracturing of the rock with a resultant loss of bearing capacity, to failure of the slopes either above or below the foundation. There are some circumstances, when, for example, existing structures are in close proximity or when excavation limits are precise, in which blasting is not possible. In these situations, non-explosive rock excavation methods, which include hydraulic splitting, hydraulic hammers and expansive cement, may be justified despite their relative expense and slow rate of excavation (see Section 10.3.6). A typical effect of geological conditions on

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foundation excavations is shown in Fig. 1.4 where the design called for a notch to be cut in strong granite to form a shear key to resist horizontal forces generated in the backfill. However, the bearing surface formed along pre-existing joints and it was impractical to cut the required notch; it was necessary to install dowels to anchor the wall. Only in very weak rock is it possible to ‘sculpt’ the rock to fit the structure, and even this may be both expensive and ineffective. Methods of rock excavation are discussed in Chapter 10. 1.2.7 Reinforcement The reinforcement of rock to stabilize slopes above and below foundations, or to improve bearing capacity and deformation modulus, has wide application in rock engineering. Where the intact rock is strong but contains discontinuities which form potentially unstable blocks, the foundation can be reinforced by installing tensioned cables or rigid bolts across the failure plane. The function of such reinforcement is to apply a normal stress across the sliding surface which increases the frictional resistance on the surface; the shear strength of the steel bar provides little support in comparison with the friction component of the rock strength. Another function of the reinforcement is to prevent loosening of the rock mass, because reduction in the interlock between blocks results in a significant reduction in rock mass strength. Where the rock is closely fractured, pumping of cement grout into holes drilled into the foundation can be used to increase the bearing capacity and modulus. The effect of the grout is to limit interblock movement and closure of discontinuities under load, both of which increase the strength of the rock mass and reduce settlement. Where it is required to protect closely fractured or faulted rock faces from weathering and degradation that may undermine a foundation, shotcrete can often be used to support the face. However, shotcrete will have no effect on the stability of the overall

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CHARACTERISTICS OF ROCK FOUNDATIONS

Figure 1.4 Construction of rock foundation: (a) attempted ‘sculpting’ of rock foundation to form shear key; and (b) ‘asbuilt’ condition with footing located on surface formed by joints.

foundation. Methods of construction and rock reinforcement are discussed in Chapter 10. 1.3 Structural loads The following is a summary of typical loading

conditions produced by different types of structures based on United States’ building codes and design practices (Merritt, 1976). The design information required on loading conditions consists of the magnitude of both the dead and live loads, as well as the direction and point of application of these loads. This information is then used to calculate the bearing pressure, and any overturning moments

TYPES OF ROCK FOUNDATION

acting on the foundation. An important aspect in foundation design is communication between the structural and foundation engineers on the factors of safety that are incorporated in each part of the design. If the structural engineer calculates the dead and live loads acting on the foundation and multiplies this by a factor of safety, it is important that the foundation engineers do not apply their own factors of safety. Such multiplication of factors of safety can result in overdesigned and expensive foundations. Conversely, failure to incorporate adequate factors of safety can result in unsafe foundations. A description of methods of calculating loads imposed by structures on their foundations is beyond the scope of this book; this is usually the responsibility of structural engineers. The following four sections provide a summary of the design methods, and the appropriate references should be consulted for detailed procedures. 1.3.1 Buildings Loads on building foundations consist of the dead load of the structural components, and the live load associated with its usage, both of which are closely defined in various building codes. For dead loads, the codes describe a wide range of construction materials such as various types of walls, partitions, floors finishes and roofing materials and the minimum loads which they exert. An option that may be suitable for poor foundation conditions is the use of lightweight aggregate in concrete which reduces the dead load for concrete slabs from 24 Paper millimeter of thickness (12.5 p.s.f. per inch) for standard concrete, to 17 Pa per millimeter of thickness (9 p.s.f. per inch). A special case is the dead load on buried structures in which a considerable load is exerted by the backfill—granular fill has a density of about 19 kN/ m3 (120 lb/ft3), and a 3 m thick backfill will exert a dead load equal to about seven floors of an office building. A very significant reduction in the foundation loads can be achieved by using

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lightweight fills such as styrofoam which has a density of 0.3 kN/m3 (2 lb/ft3) and is used in road fills on low strength soils. The disadvantage of styrofoam is that it is flammable and soluble in oil, so must be carefully protected. The live loads, which are determined by the building usage, are defined in the codes and range from 12 kN/m2 (250 lb/ft2) for warehouses and heavy manufacturing areas, 7.2 kN/m2 (150 lb/ft2) for kitchens and book storage areas, and 1.9 kN/ m2 (40 lb/ft2) for apartments and family housing. Live loads are generally uniformly distributed, but are concentrated for such usage as garages and elevator machine rooms. Additional loads result from snow, wind and seismic events, which vary with the design of the structure and the geographic location. Wind, snow and live loads are assumed to act simultaneously, but wind and snow are generally not combined with seismic forces. Ground motion in an earthquake is multidirectional and can induce forces in the foundation of a structure that can include base shear, torsion, uplift and overturning moments. The magnitude of the forces depends, for a single-degree-of-freedom structure, on the fundamental period and damping characteristics of the structure, and on the frequency content and amplitude of the ground motion. The resistance to the base shear, torsion forces and overturning moments is provided by the weight of the structure, the friction on the base, and if necessary, the installation of tie-down anchors. The total base shear at the foundation, which can be used as measure of the response of the structure to the ground motion, is the sum of the horizontal forces acting in the structure and is given by (Canadian Geotechnical Society, 1992; National Building Code of Canada, 1990): (1.1) where Ve is the equivalent lateral seismic force representing elastic response, R is a force modification factor and Ue is a calibration factor with a value of 0.6. The lateral seismic force Ve is defined by:

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CHARACTERISTICS OF ROCK FOUNDATIONS

(1.2) The following is a discussion on each of these factors. • R, force modification factor, is assigned to different types of structure reflecting design and construction experience, and the evaluation of the performance of structures during earthquakes. It endeavors to account for the energy-absorption capacity of the structural system by damping and inelastic action through several load reversals. A building with a value of R equal to 1.0 corresponds to a structural system exhibiting little or no ductility, while construction types that have performed well in earthquakes are assigned higher values of R. Types of structures assigned high values of R are those capable of absorbing energy within acceptable deformations and without failure, structures with alternate load paths or redundant structural systems, and structures capable of undergoing inelastic cyclic deformations in a ductile manner. • v, zonal velocity ratio, which varies from 0.0 for seismic zone 0 located in areas with low risk of seismic events, to 0.4 for seismic zone 6 where there is active seismic activity resulting from crustal movement. For example, in North America, zone 0 lies in the central part of the continent, while zone 6 lies along the east and west coasts. • S, seismic response factor, which depends on the fundamental period of the structure, and the seismic zone for a particular geographic location. • I, importance factor, has a value of 1.5 for buildings that should be operative after an earthquake. Such buildings include power generation and distribution systems, hospitals, fire and police stations, radio stations and towers, telephone ex changes, water and sewage pumping stations, fuel supplies and civil defense buildings. Schools, which may be needed for shelter after an earthquake, are assigned an I value of 1.3, and most other buildings are assigned a value of 1.0. • F, foundation factor, accounts for the geological conditions in the foundation. As earthquake motions propagate from the bedrock to the ground surface, soil may amplify the motions in selected frequency ranges close to the natural frequencies of the

surficial layer. In addition, a structure founded on the surficial layer and having some of its natural frequencies close to that of the layer, may experience increased shaking due to the development of a state of quasi-resonance between the structure and the soil. For structures founded on rock, the foundation factor F is usually taken as 1.0. However, in steep topography there may be amplification of the ground motions related to the three-dimensional geometry of the site. For example, at the Long Valley Dam in California, the measured acceleration on the abutment at an elevation of 75 m (250 ft) above the base of the dam was a maximum of 0.35g compared with the maximum acceleration at the base of 0.18g (Lai and Seed, 1985). The amplification of ground motion in canyons has been studied extensively for dam design and both three-dimensional and twodimensional models have been developed to predict these conditions (Gazetas and Dakoulas, 1991). • Q, weight factor, is the weight of the structure. 1.3.2 Bridges Loads that bridge foundations support consist of the dead load determined by the size and type of structure, and the live load as defined in the codes for a variety of traffic conditions. For example, an HS20–44 highway load, representing a truck and trailer with three loaded axles, is a uniform load of 9.34 kN per lineal meter of load lane (0.64 kips per lineal foot) together with concentrated loads at the wheel locations for moment and shear. For railway bridges, the live load is specified by the E number of a ‘Cooper’s train’, consisting of two locomotives and an indefinite number of freight cars. Cooper’s train numbers range from E10 to E80, with E80 being for heavy diesel locomotives with bulk freight cars. For both highway and railway bridges, impact loads are calculated as a fraction of the live load, with the magnitude of the impact load diminishing as the span length increases. Methods of calculating impact loads vary with the span length, method of

TYPES OF ROCK FOUNDATION

construction and the traffic type. Other forces that may affect the foundations are centrifugal forces resulting from traffic motion, wind, seismic, stream flow, earth and ice forces, and elastic and thermal deformations. The magnitude of these forces is evaluated for the particular conditions at each site. 1.3.3 Dams Loads on dam foundations are usually of much greater magnitude than those on bridge and building foundations because of the size of the structures themselves, and the forces exerted by the water impounded behind the dam. The water forces are usually taken as the peak maximum flood (PMF), with an allowance for accumulations of silt behind the dam, as appropriate. Any earthquake loading can be simulated most simply as a horizontal pseudostatic force proportional to the weight of the dam. The resultant of these forces acts in a downstream direction, and the dam must be designed to resist both sliding and overturning under this loading condition. There may also be concentrated compressive stresses at the toe of the dam and it is necessary to check that these stresses do not cause excessive deformation. A significant difference between dams and most other structures is the water uplift pressures that are generated within the foundations. In most cases there are high pressure gradients beneath the heel of the dam where drain holes and grout curtains are installed to relieve water pressures and control seepage. The combination of these load conditions, together with the high degree of safety required for any dam, requires that the in vestigation, design and construction of the foundation be both thorough and comprehensive. 1.3.4 Tension foundations Typical tension loads on foundations consist of bouyancy forces generated by submerged tanks, angle transmission line towers and the tension in

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suspension bridge cables. Foundations may also be designed to resist uplift forces generated by overturning moments acting on the structure resulting from horizontal loads such as wind, ice, traffic and earthquake forces. 1.4 Allowable settlement Undoubtedly the most famous case of foundation settlement is that of the Leaning Tower of Pisa which has successfully withstood a differential settlement of 2 m and is now leaning at an angle of at least 5°11' (Mitchell et al., 1977). However, this situation would not be tolerated in most structures, except as a tourist attraction! The following is a review of allowable settlement values for different types of structures. 1.4.1 Buildings Settlement of building foundations that is insufficient to cause structural damage may still be unacceptable if it causes significant cracking of architectural elements. Some of the factors that can affect settlement are the size and type of structure, the properties of the structural materials and the subsurface soil and rock, and the rate and uniformity of settlement. Because of these complexities, the settlement that will cause significant cracking of structural members or architectural elements, or both, cannot readily be calculated. Instead, almost all criteria for tolerable settlement have been established empirically on the basis of observations of settlement and damage in existing buildings (Wahls, 1981). Damage due to settlement is usually the result of differential settlement, i.e. variations in vertical displacement at different locations in the building, rather than the absolute settlement. Means of defining both differential and absolute settlement are illustrated in Fig. 1.5, together with the terms defining the various components of settlement. Study of cracking of walls, floors and structural

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CHARACTERISTICS OF ROCK FOUNDATIONS

Figure 1.5 Definition of settlement terminology for buildings (Wahls, 1981): (a) settlement without tilt; (b) settlement with tilt. di is the vertical displacement at i; dmax is the maximum displacement; dij is the displacement between two points i and j with distance apart lij; ? is the relative deflection which is the maximum displacement from a straight line connecting two reference points; ? is the tilt, or rigid body rotation; is the angular distortion; and ?/L is the deflection ratio, or the approximate curvature of the settlement curve.

members shows that damage was most often the result of distortional deformation, so ‘angular distortion’ ß has been selected as the critical index of settlement. These studies have resulted in the following limiting values of angular distortion being recommended for frame buildings (Terzaghi and Peck, 1967; Skempton and McDonald, 1956; Polshin and Tokar, 1957): – structural damage probable; – cracking of load bearing or panel walls likely; – safe level of distortion at which cracking will not occur. In the case of load bearing walls, it is found that the deflection ratio ?/L is a more reliable indicator of damage because it is related to the direct and

diagonal tension developed in the wall as a result of bending (Burland and Wroth, 1974). The proposed limiting values of ?/L for design purposes are in the range 0.0005–0.0015. 1.4.2 Bridges Extensive surveys of horizontal and vertical movement of highway bridges have been carried out to assess allowable settlement values (Walkinshaw, 1978; Grover, 1978; Bozozuk, 1978). It is concluded that settlement can be divided into three categories depending on its effect on the structure: 1. tolerable movements; 2. intolerable movements resulting only in poor riding characteristics; and 3. intolerable movements resulting in structural damage. It is not feasible to specify limiting settlement values for each of these three categories because of the wide variety of bridge designs and subsurface

TYPES OF ROCK FOUNDATION

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Figure 1.6 Engineering performance of bridge abutments and piers on spread footings (Bozozuk, 1978).

conditions. For example, Walkinshaw reports of tolerable vertical movements that ranged from 13 to 450 mm (0.5 to 17.7 in), although the average value was about 85 mm (3.3 in). Intolerable vertical movements causing only poor riding quality averaged about 200 mm (7.9 in), while vertical movements causing structural damage varied from 13 to 600 mm (0.5 to 23.6 in) with an average value of about 250 mm (10 in). As a comparison with these results, Fig. 1.6 shows the results of the survey carried out by Bozozuk of bridge abutments and piers on spread footings with lines giving the limits of tolerable, harmful but tolerable, and intolerable movements. The conclusions that can be drawn from these studies are that tolerable movements can be as great as 50–100 mm (2–4 in), and that structural damage may not occur until movements are in excess of 200

mm (8 in). Also, differential and horizontal movements are more likely to cause damage that vertical movements alone. One possible reason is that vertical settlement of simply supported spans can readily be corrected by lifting and shimming at the bearing points (Grover, 1978). In comparison, horizontal movements are more difficult to correct, with one of the most important effects being the locking of expansion joints. 1.4.3 Dams Allowable settlement of dams is directly related to the type of dam: concrete dams are much less tolerant of movement and deformation than embankment dams. There are no general guidelines on allowable settlements for dams because the

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CHARACTERISTICS OF ROCK FOUNDATIONS

foundation conditions for each structure should be examined individually. However, in all cases, particular attention should be paid to the presence of rock types with differing moduli, or seams of weathered and faulted rock that are more compressible than the adjacent rock. Either of these conditions may result in differential settlement of the structure. 1.5 Influence of ground water on foundation performance The effect of ground water on the performance of foundations should be considered in design, particularly in the case of dams and bridges. These effects include movement and instability resulting from uplift pressures, weathering, scour of seams of weak rock, and solution (Fig. 1.7). In almost all cases, geological structure influences ground water conditions because most intact rock is effectively impermeable and water flow through rock masses is concentrated in the discontinuities. Flow quantities and pressure distributions are related to the aperture, spacing and continuous length of the discontinuities: tight, impersistent discontinuities will tend to produce low seepage quantities and high pressure gradients. Furthermore, the direction of flow will tend to be parallel to the orientation of the main discontinuity set. 1.5.1 Foundation stability Typical instability caused by water uplift forces acting on potential sliding planes in the foundation is illustrated in Fig. 1.7(a). The uplift force U acting on the sliding plane reduces the effective normal force on this surface, which produces a corresponding reduction the shear strength (see Chapter 3). For the condition shown in Fig. 1.7(a), the greatest potential for instability is when a rapid and draw down in the water level occurs there is insufficient time for the uplift force to dissipate.

The flow of water through and around a foundation can have a number of effects on stability apart from reducing the shear strength. First, rapid flow can scour low strength seams and infillings, and develop openings that undermine the foundation (Fig. 1.7 (a)). Second, percolation of water through soluble rocks such as limestone can cause cavities to develop. Third, rocks such as shale may weather and deteriorate with time resulting in loss of bearing capacity. Such weathering may occur either so rapidly that it is necessary to protect bearing surfaces as soon as they are excavated, or it may occur a considerable time after construction causing long term settlement of the structure. Fourth, flow of water into an excavation can make cleaning and inspection of bearing surfaces difficult (Fig. 1.7(b)) and result in increased construction costs. 1.5.2 Dams In dam foundations it is necessary to control both uplift due to water pressures to ensure stability, and seepage to limit water loss (Fig. 1.7(c)). Control measures consist of grout curtains and drains to limit seepage and reduce water pressure as described in Chapter 7. The rock property that determines seepage quantities and head loss is permeability, which relates the quantity of water flow through the rock to the pressure gradient across it. As discussed at the start of this section, water flow is usually concentrated in the discontinuities, so seepage quantities will be closely related to the geological structure. For example, seepage losses may be high where there are continuous, open discontinuities that form a seepage path under the dam, while a clay filled fault may form a barrier to seepage. The study of seepage paths and quantities, and calculation of water pressure distributions in the foundation is carried out by means of flow nets (Cedergren, 1989). A flow net comprises two sets of lines—equipotential lines (lines joining points along which the total head is the same) and flow lines (paths followed by water flowing through the saturated rock)— that are

TYPES OF ROCK FOUNDATION

15

Figure 1.7 Typical effects of ground water flow on rock foundations: (a) uplift pressures developed along continuous fracture surface; (b) water flow into hole drilled for socketed pier; and (c) typical flow net depicting water flow and uplift pressure distribution in dam foundation (after Cedergren, 1989).

drawn to form a series of curvilinear squares as

16

CHARACTERISTICS OF ROCK FOUNDATIONS

shown in Fig. 1.7(c). The distribution of equipotential lines can also be used to determine the uplift pressure under a foundation which is also shown in Fig. 1.7(c). 1.5.3 Tension foundations Where tension foundations are secured with anchors located below the water table, it is necessary to use the buoyant weight of the rock in calculating uplift resistance provided by the ‘cone’ of rock mobilized by the anchor. Figure 1.2(d) shows an example of such an installation where the rock in which the tiedown anchors is located below the water table and the effective unit weight of the rock is about 16 kN/ m3 (100 lb/ft3). Another important factor in design is provision for protection of the steel against corrosion, with corrosion occurring most rapidly in low-pH and salt-water environments. Protective measures for ‘permanent’ installations consist of plastic sheaths grouted on to the anchors and full grout encapsulation which produces a crack resistant, high-pH environment around the steel (see Chapter 9). 1.6 Factor of safety and reliability analysis Structural design and geotechnical analysis are usually based on the following two main re quirements. First, the structure and its components must, during the intended service life, have an adequate margin of safety against collapse under the maximum loads and forces that might reasonably occur. Second, the structure and its components must serve the designed functions without excessive deformations and deterioration. These two service levels are the ultimate and serviceability limit states respectively and are defined as follows. Collapse of the structure and foundation failure including instability due to sliding, overturning, bearing failure, uplift and excessive seepage, is termed the ultimate limit state of the structure. The onset of excessive deformation and of deterioration

including unacceptable total and differential movements, cracking and vibration is termed the serviceability limit state (Meyerhof, 1984). The following is a discussion on a number of different design methods for geotechnical structures. Factor of safety analysis is by far the most widely used technique and factor of safety values for a variety of structures are generally accepted in the engineering community. This provides for each type of structure to be designed to approximately equivalent levels of safety. Adaptations to the factor of safety analysis include the limit states and sensitivity analysis methods, both of which examine the effect of variability in design parameters on the calculated factor of safety. An additional design method, reliability analysis, expresses the design parameters as probability density functions representing the range and degree of variability of the parameter. The theory of reliability analysis is well developed and its major strength is that it quantifies the variability in all the design parameters and calculates the effect of this variability on the factor of safety (Harr, 1977). However, despite the analytical benefits of reliability analysis, it is not widely used in geotechnical engineering practice (as of 1998). 1.6.1 Factor of safety analysis Design of geotechnical structures involves a certain amount of uncertainty in the value of the input parameters which include the structural ge ology, material strengths and ground water pressures. Additional uncertainties to be considered in design are extreme loading conditions such as floods and seismic events, reliability of the analysis procedure, and construction methods. Allowance for these uncertainties is made by including a factor of safety in design. The factor of safety is the ratio of the total resistance forces—the rock strength and any installed reinforcement, to the total displacing forces —downslope components of the applied loads and the foundation weight. That is,

TYPES OF ROCK FOUNDATION

(1.3) The ranges of minimum total factors of safety as proposed by Terzaghi and Peck (1967) and the Canadian Foundation Engineering Manual (1992) are given in Table 1.1. The upper values of the total factors of safety apply to normal loads and service conditions, while the lower values apply to maximum loads and the worst expected geological conditions. The lower values have been used in conjunction with performance Table 1.1 Values of minimum total safety factors

observations, large field tests, analysis of similar structures at the end of the service life and for temporary works. The factors of safety quoted in Table 1.1 are employed in engineering practice, and can be used as a reliable guideline in the determination of appropriate values for particular structures and conditions. However, the design process still requires a considerable amount of judgment because of the variety of geological and construction factors that must be considered. Examples of conditions that would generally require the use of

Failure type

Category

Safety factor

Shearing

Earthworks Earth retaining structures, excavations Foundations

1.3–1.5 1.5–2.0 2–3

factors of safety at the high end of the ranges quoted in Table 1.1 include: 1. a limited drilling program that does not adequately sample conditions at the site, or drill core in which there is extensive mechanical breakage or core loss; 2. absence of rock outcrops so that detailed mapping of geological structure is not possible; 3. inability to obtain undisturbed samples for strength testing, or difficulty in extrapolating laboratory test results to in situ conditions; 4. absence of information on ground water conditions, and significant seasonal fluctuations in ground water levels; 5. uncertainty in failure mechanisms of the foundation and the reliability of the analysis method. For example, planar type failures can be analyzed with considerable confidence, while the detailed mechanism of toppling failures is less well understood; 6. uncertainty in load values, particularly in the case of environmental factors such as wind, water, ice and earthquakes where existing data is limited; 7. concern regarding the quality of construction, including materials, inspection and weather

17

conditions. Equally important are contractual matters such as the use of open bidding rather than pre-qualified contractors, and lump sum rather than unit price contracts; 8. lack of experience of local foundation performance; and 9. usage of the structures; hospitals, police stations and fire halls and bridges on major transportation routes are all designed to higher factors of safety than, for example, residential buildings and warehouses. 1.6.2 Limit states design In order to produce a more uniform margin of safety for different types and components of earth structures and foundations under different loading conditions, the limit states design method has been proposed (Meyerhof, 1984; Ontario Highway Bridge Design Code, 1983; National Building Code of Canada, 1985). The two Canadian codes are based on unified limit states design principles with common safety and serviceability criteria for all materials and types of construction. Limit states design uses partial factors of safety which are applied to both the loads, and the

18

CHARACTERISTICS OF ROCK FOUNDATIONS

resistance characteristics of the foundation materials. The procedure is to multiply the loads by a load factor fd and the resistances, friction and cohesion, by resistance factors , fc as shown in Table 1.2. The values given in parenthesis apply to beneficial loading conditions such as dead loads that resist overturning or uplift. In limit states design the Mohr-Coulomb equation for the shear resistance of a sliding surface is expressed as (1.4) The cohesion c, friction coefficient, tan , and water pressure U are all multiplied by partial factors with values less than unity, while the normal stress a on

the sliding surface is calculated using a partial load factor greater than unity applied to the foundation load. 1.6.3 Sensitivity analysis Another means of assessing the effects of the variability of design parameters on the factor of safety is to use sensitivity analysis. This procedure consists of calculating the factor of safety for a range of values of parameters, such as the water pressure, which cannot be precisely defined. For example, Hoek and Bray (1981) describe the sta

Table 1.2 Values of minimum partial factors (Meyerhof, 1984) Category

Item

Load factor

Loads

Dead loads Live loads, wind, earthquake Water pressure (U) Cohesion (c)—stability, earth pressure Cohesion (c)—foundations Friction angle

(fDL) 1.25 (0.8) (fLL) 1.5 (fu) 1.25 (0.8)

Shear strength

bility analysis of a quarry slope in which sensitivity analyses were carried out for both the friction angle (range 15°–25°) and the water pressure—fully drained to fully saturated (Fig. 1.8). This plot shows that water pressures have more influence on stability than the friction angle. That is, a fully drained, vertical slope is stable for a friction angle as low as 15°, while a fully saturated slope is unstable at an angle of 60°, even if the friction angle is 25°. 1.6.4 Coefficient of reliability The factor of safety and limit states analyses described in this section involves selection of a single value for each of the parameters that define the loads and resistance of the foundation. In reality, each parameter has a range of values. A method of examining the effect of this variability on the factor of safety is to carry out sensitivity analyses as described in Section 1.6.3 using upper

Resistance factor

(fc) 0.65 (fc) 0.5 f( ) 0.8

and lower bound values for what are considered to be critical parameters. However, to carry out sensitivity analyses for more than three parameters is a cumbersome process and it is difficult to examine the relationship between each of the parameters. Consequently, the usual design procedure involves a combination of analysis and judgment in assessing the influence on stability of variability in the design parameters, and then selecting an appropriate factor of safety. An alternative design method is reliability analysis, which systematically examines the effect of the variability of each parameter on the stability of the foundation. This procedure calculates the coefficient of reliability CR of the foundation which is related to the more commonly used expression probability of failure PF by the following equation: (1.5) The term coefficient of reliability is preferred for psychological reasons: a coefficient of reliability of

TYPES OF ROCK FOUNDATION

19

Figure 1.8 Sensitivity analysis showing the relationship between factor of safety and slope angle for range of water pressures and friction angles (Hoek and Bray, 1981).

99% is more acceptable to an owner than a probability of failure of 1%. Reliability analysis was first developed in the 1940’s and is used in the structural and aeronautical engineering fields to examine the reliability of complex systems. Among its early uses in geotechnical engineering was in the design of open pit mine slopes where a certain risk of failure is acceptable and this type of analysis can be readily incorporated into the economic planning of the mine (Canada DEMR, 1978; Pentz, 1981; Savely, 1987). Examples of its use in civil engineering are in the planning of slope stabilization programmes for transportation systems (Wyllie et al., 1979; McGuffey et al., 1980), landslide hazards (Cruden and Fell, 1997) and in design of storage facilities for hazardous waste (Roberds, 1984, 1986). There is sometimes reluctance to use probabilistic design when there is a limited amount of design data which may not be representative of the population. In these circumstances it is possible to

use subjective assessment techniques that provide reliable probability values from small samples (Roberds, 1990). The basis of these techniques is the assessment and analysis of available data, by an expert or group of experts in the field, in order to arrive at a consensus on the probability distributions that represent the opinions of these individuals. The degree of defensibility of the results tends to increase with the time and cost that is expended in the analysis. For example, the assessment techniques range from, most simply, informal expert opinion, to more reliable and defensible techniques such as Delphi panels (Rohrbaugh, 1979). A Delphi panel comprises a group of experts who are each provided with the same set of data and are required to produce a written assessment of this data. These documents are then provided anonymously to each of the other assessors who are encouraged to adjust their assessments in light of their peer’s assessments. After several iterations of this process, it should be possible to arrive at a

20

CHARACTERISTICS OF ROCK FOUNDATIONS

Figure 1.9 Risks for selected engineering projects (Whitman, 1984).

consensus that maintains anonymity and independence of thought. The use of reliability analysis in design requires that there be generally accepted ranges of reliability values for different types of structure, as there are for factors of safety. To assist in selecting appropriate reliability values, Athanasiou-Grivas (1979) provides charts relating factor of safety and probability of failure. Also, Fig. 1.9 gives a relationship between required levels of annual probability of failure for a variety of engineering projects, and the consequence of failure in terms of lives lost. For example, for structures such as low

rise buildings and bridges with low traffic density where failure could result in less than about five lives lost, the range of annual probability of failure should not excced about 10-2–10-3 In comparison, for dams where failure could result in the loss of several hundred lives, annual probability of failure should not exceed about 10-4–10-5 Despite the wide range of values shown in Fig. 1.9, this approach provides a useful benchmark for the ongoing development of reliability based design (Salmon and Hartford, 1995). (a) Distribution functions

TYPES OF ROCK FOUNDATION

21

Figure 1.10 Properties of the normal distribution (Kreyszig, 1976): (a) density of the normal distribution with mean and various standard deviations (SD); and (b) distribution function F(z) of the normal distribution with mean 0 and standard deviation 1.

In reliability analysis each parameter for which there is some uncertainty is assigned a range of values which is defined by a probability density function. Some types of distribution functions that are appropriate for geotechnical data include the normal, beta, negative exponential and triangular distributions. The most common type of function is the normal distribution in which the mean value is the most frequently occurring value (Fig. 1.10(a)). The density of the normal distribution is defined by: (1.6) where

is the mean value given by (1.7)

and SD is the standard deviation given by

(1.8) and is the number of samples. As shown in Fig. 1.10(a), the scatter in the data, as represented by the width of the curve, is mea sured by the standard deviation. Important properties of this function are that the total area under the curve is equal to 1.0. That is, there is a probability of unity that all values of the parameter fall within the bounds of the curve. Also, 68% of the values will lie within a range of one standard deviation either side of the mean and 95% will lie within two standard deviations either side of the mean. Conversely it is possible to determine the value of a parameter defined by a normal distribution by stating the probability of its occurrence. This is shown graphically in Fig. 1.10(b) where F(z) is the distribution function with mean 0 and standard

22

CHARACTERISTICS OF ROCK FOUNDATIONS

Figure 1.11 Calculation of coefficient of reliability using normal distributions: (a) probability density functions of the resisting force fr and the displacing force fd in a foundation; and (b) probability density function of difference between resisting and displacing force distributions

deviation 1. For example, a value which has a probability of being greater than 50% of all values is equal to the mean, and a value which has a probability of being greater than 16% of all values is equal to the mean minus one standard deviation. The normal distribution extends to infinity in both directions which is often not a realistic expression of geotechnical data in which the likely upper and lower bounds of a parameter can be defined. For these conditions, it is appropriate to use the beta distribution which has finite maximum and minimum points, and can be uniform, skewed to the left or right, U-shaped or J-shaped (Harr, 1977). For conditions in which there is little information on the distribution of the data, a simple triangular distribution can be used which is defined by three values: the most likely and the minimum and maximum values. Examples of probability distributions are shown in the worked example in Section 6.2. (b) Coefficient of reliability calculation The coefficient of reliability is calculated in a similar manner to that of the factor of safety in that

the relative magnitude of the displacing and resisting forces in the foundation are examined (see Section 1.6.1). Two common methods of calculating the coefficient of reliability are the margin of safety method and the Monte Carlo method as discussed below. The margin of safety is the difference between the resisting and displacing forces, with the foundation being unstable if the margin of safety is negative. If the resisting and displacing forces are mathematically defined probability distributions— fD(r) and fD(d) respectively in Fig. 1.11(a)—then it is possible to calculate a third probability distribution for the margin of safety. As shown in Fig. 1.11, there is a probability of failure if the lower limit of the resisting force distribution fD(r) is less than the upper limit of the displacing force distribution fD(d). This is shown as the shaded area on Fig. 1.11(a), with the probability of failure being proportional to the area of the shaded zone. The method of calculating the area of the shaded zone is to calculate the probability density function of the margin of safety: the area of the negative portion of

TYPES OF ROCK FOUNDATION

this function is the probability of failure, and the area of the positive portion is the coefficient of reliability (Fig. 1.11(b)). If the resisting and displacing forces are defined by normal distributions, the margin of safety is also a normal distribution, the mean and standard deviation of which are calculated as follows (Canada DEMR, 1978): (1.9) (1.10) and are the mean values, and SDr and where SDd are the standard deviations of the distributions of the resisting and displacing forces respectively. Note that the definition of the conventional factor of safety is given by Having determined the mean and standard deviation of the margin of safety, the coefficient of reliability can be calculated from the properties of the normal distribution. For example, if the mean margin of safety is 2000 MN and the standard deviation is 1200 MN, then the margin of safety is zero at 2000/ 1200, or 1.67 standard deviations. From Fig. 1.10 (b), where the margin of safety distribution is represented by F(z), the probability of failure is 5%,

23

and the coefficient of reliability is 95%. Note that the margin of safety concept discussed in this section can only be used where the resisting and displacing forces are independent variables. This condition would apply where the displacing force was the structural load, and the resisting force was the installed reinforcement. However, where the resisting force is the shear strength of the rock, then this force and the displacing force are both functions of the weight of the foundation, and are not independent variables. Under these circumstances, it is necessary to use Monte Carlo analysis as described below. Monte Carlo analysis is an alternative method of calculating the coefficient of reliability which is more versatile than the margin of safety method described above. Monte Carlo analysis avoids the integration operations which can become quite complex, and in the case of the beta distribution cannot be solved explicitly. The particular strength of Monte Carlo analysis is the ability to work with any mixture of distribution types, and any number of variables, which may or may not be independent of each other. The Monte Carlo technique is an iterative procedure comprising the following four steps (Fig. 1.12).

24

CHARACTERISTICS OF ROCK FOUNDATIONS

Figure 1.12 Flow chart for Monte Carlo simulation to calculate coefficient of reliability of a structure (Athanasiou-Grivas, 1980).

1. Estimate probability distributions for each of the variable input parameters. 2. Generate random values for each parameter; Fig. 1.10(b) illustrates the relationship for a normal distribution between a random number between 0 and 1 and the corresponding value of

the parameter. 3. Calculate values for the displacing and resisting forces and determine if the resisting force is greater than the displacing force. 4. Repeat the process at least 100 times and then determine the ratio:

TYPES OF ROCK FOUNDATION

(1.11) where M is the number of times the resisting force exceeded the displacing force (i.e. the factor of safety is greater than 1.0) and N is the number of analyses. An example of the use of Monte Carlo analysis to calculate the coefficient of reliability of a bridge foundation against sliding is given in Section 6.2 in Chapter 6—Stability of Foundations (Figs 6.4 and 6.5). This example shows the relationship between the deterministic and probabilistic analyses. The factor of safety is calculated from the mean or most likely values of the input variables, while the probabilistic analysis calculates the distribution of the factor of safety when selected input variables are expressed as probability density functions. For the unsupported foundation, the deterministic factor of safety has a value of 1.28, while the probabilistic analysis shows that the factor of safety can range from a minimum value of 0.38 to a maximum value of 3.99. The proportion of this distribution with a value greater than 1.0 is 0.78, which represents the coefficient of reliability of the foundation. This example illustrates that, for these particular conditions, the coefficient of reliability is well below the target level for foundations shown in Fig. 1.9. This low value for the coefficient of reliability is a function of both the low factor of safety, and the wide ranges of uncertainty in the input parameters. 1.7 References Athanasiou-Grivas, D. (1979) Probabilistic evaluation of safety of soil structures. ASCE, J. Geotech. Eng., 105 (GT9), 1091–5. Athanasiou-Grivas, D. (1980) A reliability approach to the design of geotechnical systems. Rensselaer Polytechnic Institute Research Paper, Transportation Research Board Conference, Washington, DC. Bozozuk, M. (1978) Bridge abutments move. Research Record 678, Transportation Research Board, Washington, DC. Burland, J.B. and Wroth, C.P. (1974) Allowable and differentiated settlement of structures, including

25

damage and soil-structure interaction. Proc. Conf. on Settlement of Structures, Cambridge, England, pp. 611–54. Canada Department of Energy, Mines and Resources (1978) Pit Slope Manual., DEMR, Ottawa. Canadian Geotechnical Society (1992) Canadian Foundation Engineering Manual. BiTech Publishers Ltd, Vancouver, Canada. Cedergren, H.R. (1989) Seepage, Drainage and Flow Nets, 3rd edn, Wiley, New York. Cruden, D.M. and Fell, R. (eds) (1997) Landslide risk assessment. Proc. International Workshop on Landslide Risk Assessment, Honolulu, HI, Balkema, Rotterdam. Gazetas, G. and Dakoulas, P. (1991) Aspects of seismic analysis and design of rockfill dams. Proc. 2nd Int. Conf. on Recent Advances in Geotechnical Earthquake Engineering and Soil Dynamics, St. Louis, MO, Paper No. SOA12, pp. 1851–88. Grover, R.A. (1978) Movements of bridge abutments and settlements of approach pavements in Ohio. Transportation Research Board, Research Record 678, Washington, DC. Gruner, E. (1964) Dam disasters. Proc. Inst. of Civil Eng., 24, Jan., 47–60. Discussion, 27, Jan., 344. Gruner, E. (1967) The mechanism of dam failure. 9th ICOLD Congress, Istanbul, 11, Q.34, R.12, 197–206. Harr, M.E. (1977) Mechanics of Particulate Media—a Probabilistic Approach. McGraw-Hill, New York. Hoek, E. and Bray, J. (1981) Rock Slope Engineering, 2nd. edn, IMM, London. James, A.N., Kirkpatrick, I.M. (1980) Design of foundations of dams containing soluble rocks and soils. Q. J. Eng. Geol., London, 13, 189–98. Kaderabek, T.J. and Reynolds, R.T. (1981) Miami limestone foundation design and construction. ASCE Geotech. Eng. Div., 7 (GT7), 859–72. Kreyszig, E. (1976) Advanced Engineering Mathematics. Wiley, New York, 770–6. Lai, S.S. and Seed, H.B. (1985) Dynamic response of Long Valley Dam in the Mammoth Lake earthquake series on May 25–27, 1980. University of California, Berkeley, Report No. UCB/EERC-85/12, November. Londe, P. (1987) Malpasset Dam. Proc. International Workshop on Dam Failures, Purdue Uni., Engineering Geology (ed. Leonards), 24, Nos. 1–4, Elsevier, Amsterdam. McGuffey, V., Athanasion-Grivas, D., Iori, J. and Kyfor, Z. (1980) Probabilistic Embankment Design—A Case

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CHARACTERISTICS OF ROCK FOUNDATIONS

Study. Transportation Research Board, Washington, DC. Merritt, F.S. (1976) Standard Handbook for Civil Engineers, McGraw-Hill, New York, Ch. 15. Meyerhof, G.G. (1984) Safety factors and limit states analysis in geotechnical engineering. Can. Geotech. J., 21, 1–7. Mitchell, J.K., Vivatrat, V. and Lambe, T.W. (1977) Foundation performance of the Tower of Pisa. Proc. ASCE, 103(GT3), 227–49. National Building Code of Canada, (1990) Associate Committee on the National Building Code, National Research Council of Canada, Ottawa. Ontario Ministry of Transportation and Communication (1983) Highway Bridge Design Code. Toronto, Canada. Peck, R.B. (1976) Rock foundations for structures. Proc. of Specialty Conference on Rock Engineering for Foundations and Slopes, ASCE, Boulder, Colorado, II, 1–21. Pentz, D.L. (1981) Slope stability analysis techniques incorporating uncertainty in the critical parameters. Third Int. Conf. on Stability in Open Pit Mining, Vancouver, Canada. Polshin, D.E., Tokar, R.A. (1957) Maximum allowable nonuniform settlement of structures. Proc. 4th Int. Conf. on Soil Mechanics and Foundation Engineering, London 1, 402–6. Roberds, W.J. (1984) Risk-based decision making in geotechnical engineering: overview of case studies. Engineering Foundation Conf. on Risk-based Decision Making in Water Resources. Santa Barbara, California. Roberds, W.J. (1986) Applications of decision theory to hazardous waste disposal. ASCE Specialty Conf. GEOTECH IV, Boston, Massachusetts. Roberds, W.J. (1990) Methods of developing defensible subjective probability assessments. Transportation Research Board, Annual Meeting, Washington, DC. Rohrbaugh, J. (1979) Improving the quality of group judgment: social judgment analysis and the Delphi

technique. Organizational Behaviour and Human Performance, 24, 73–92. Salmon, G.M. and Hartford, N.D. (1995) Risk analysis for dam safety. International Water Power and Dam Construction, 21, 38–9. Savely, J.P. (1987) Probabilistic analysis of intensely fractured rock masses. Sixth International Congress on Rock Mechanics, Montreal, 509–14. Skempton, A.W. and MacDonald, D.H. (1956) Allowable settlement of buildings. Proc. Inst. Civil Eng., Part III, 5, 727–68 Tatsuoka, F., Kohata, Y., Ochi, K. and Tsubouchi, T. (1995) Stiffness of soft rocks in Tokyo metropolitan area—from laboratory to full-scale behaviour. Proc. 8th Int. Congress on Rock Mechanics, Workshop on Rock Foundation, Tokyo, Balkema, September, 3–17. Terzaghi, K. and Peck R. (1967) Soil Mechanics in Engineering Practice. Wiley, New York. Wahls, H.E. (1981). Tolerable settlement of buildings. ASCE, 107(GT11), 1489–504. Walkinshaw, J.L. (1978) Survey of bridge movements in the western United States. Research Record 678, Transportation Research Board, Washington, DC. Whitman, R.V. (1984) Evaluating calculated risk in geotechnical engineering. J. Geotechnical Eng., ASCE, 110(2), 145–88. Wyllie, D.C. (1979) Fractured bridge supports stabilized under traffic. Railway Track and Structures, July, 29–32. Wyllie, D.C., McCammon, N.R. and Brumund, W.F. (1979) Use of risk analysis in planning slope stabilization programmes on transportation routes. Research Record 749, Transportation Research Board, Washington, DC. Wyllie, D.C. (1995) Stability of foundations on jointed rock—case studies. Proc. 8th Int. Congress on Rock Mechanics, Workshop on Rock Foundation, Tokyo, A.A.Balkema, Postbus 1675, NL–3000BR, September, 253–8.

2 Structural geology

2.1 Discontinuity characteristics The design of any structure located either in or on rock, must include a thorough examination of the structural geology of the site. Even the strongest rock may contain potentially unstable blocks formed by sets of discontinuities, or possibly even a single discontinuity. These blocks may fail by sliding or toppling. Where such blocks occur in a cut above the foundation, they may impact the structure, whereas unstable blocks in the foundation may move causing settlement, or fail entirely, resulting in collapse of the structure. The photograph in Fig. 2.1 shows a wedge shaped block of rock, formed by two intersecting discontinuities, that has failed forming a steep cliff face. Houses have been constructed along the crest of this cliff and any further excavation at the toe is likely to cause similar wedge failures which would destroy a number of the buildings. The stability of the foundation of these houses is entirely dependent upon the properties of the discontinuities, that is, their orientation, length and shear strength. The strength of the intact rock, which has ample capacity to support the light loads imposed by the houses, is not an issue. This is a typical example of a situation where foundation design must focus on the structural geology of the site, and not on the rock strength. Analysis of the stability of blocks of rock in foundations requires reliable information on the following two categories of discontinuity characteristics:

1. the orientation and dimensions of the discontinuities, which define the shape and size of the blocks, and the direction in which they may slide (this chapter describes methods of analyzing data on the orientation and dimensions of discontinuities); 2. the shear strength properties of the discontinuities which determines the resistance of the block to sliding (this is discussed in Chapter 3). 2.1.1 Types of discontinuity Geological investigations usually categorize discontinuities according to the manner in which they were formed. This is useful for geotechnical engineering because discontinuities within each category have similar properties as regards both dimensions and shear strength properties which can be used in the initial review of stability conditions of a site. The following are standard definitions of the most commonly encountered types of discontinuities. (a) Fault A discontinuity along which there has been an observable amount of displacement. Faults are rarely single planar units; normally they occur as parallel or sub-parallel sets of discontinuities along which movement has taken place to a greater or less extent. (b) Bedding plane This is a surface parallel to the surface of deposition, which may or may not have a physical expression.

28

STRUCTURAL GEOLOGY

Figure 2.1 Intersecting discontinuities in strong rock produced wedge failure in foundation of houses along crest of slope (photograph by Turgut Çanli).

Note that the original attitude of the bedding plane should not be assumed to be horizontal. (c) Foliation Foliation is the parallel orientation of platy minerals, or mineral banding in metamorphic rocks. (d) Joint A joint is a discontinuity in which there has been no observable relative movement. In general, joints intersect primary surfaces such as bedding, cleavage and schistosity. A series of parallel joints is called a joint set; two or more intersecting sets produce a joint system; two sets of joints approximately at right angles to one another are said to be orthogonal. (e) Cleavage Parallel discontinuities formed in incompetent layers in a series of beds of varying degrees of competency are known as cleavages. In general, the term implies that the cleavage planes are not

controlled by mineral particles in parallel orientation. (f) Schistosity This is the foliation in schist or other coarse grained crystalline rock due to the parallel arrangement of mineral grains of the platy or prismatic type, such as mica. These descriptions of discontinuity categories are well established in engineering practice and the likely properties of each can be anticipated from their categories. For example, faults are major structures containing weak infillings such as crushed rock and clay gouge, whereas joints have lengths which are much shorter than faults and joint infillings are often thin and cohesive, or entirely absent. However, standard geological names alone rarely give sufficient detailed information for design purposes on the properties of a dis continuity, especially for foundations where particulars of such

DISCONTINUITY CHARACTERISTICS

29

Figure 2.2 Influence of discontinuity length and orientation on the stability of a foundation: (a) continuous joints dip into slope—stable foundation; and (b) continuous joints dip out of slope—unstable foundation.

characteristics as the infilling thickness can have a significant influence on settlement. For this reason, geological descriptions are useful in understanding the general conditions at a site, but further specific geotechnical studies are almost always required before proceeding to final design. 2.1.2 Discontinuity orientation and dimensions The four important properties of discontinuities that determine the shape and size of blocks are: 1. 2. 3. 4.

Orientation; Position; Length; Spacing.

The two sketches in Fig. 2.2 illustrate how these four properties influence the stability of a foundation. In both cases there are two sets of discontinuities: set A dips out of the face at an angle of about 40°, and set B dips into the face at a steep

angle. In Fig. 2.2(a) set A is discontinuous and more widely spaced than set B. This foundation would be stable because the discontinuities daylighting in the face are not continuous and only one small, unstable block has been formed on the face. In contrast, in Fig. 2.2(b), the discontinuities dipping out of the face are continuous and movement of the entire foundation on these discontinuities is possible, with set B forming tension cracks. A typical example of such a condition would be a bedded sandstone containing a discontinuous conjugate joint set. If the beds dip into the face the foundation would be stable, and if they dip out of the face at an angle of 40°, which is usually greater than the friction angle of sandstone surfaces, it is likely that the foundation would slide on the beds. The conditions shown in Fig. 2.2 also illustrate the influence of discontinuity spacing on settlement. In this example, the spacing of the discon tinuities is such that the footing is predominantly on intact rock. Consequently, closure of the discontinuities is unlikely to be of concern and settlement will be a function of the deformation modulus of the intact rock. However, in the case of highly fractured rock,

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settlement may occur as a result of discontinuity closure, particularly if the joint infilling comprises compressible materials such as clay. In this case settlement would be a function of the rock mass deformation modulus. As regards the overall stability of the foundation, closely fractured rock may be sufficiently interlocked to prevent movement of the entire foundation in a block type failure as shown in Fig. 2.2(b). However, raveling of small fragments may occur as a result of frost action or river scour, and this may eventually undermine the footing (Fig. 2.2(a)). 2.2 Orientation of discontinuities The first step in the investigation of discontinuities in a foundation is to analyze their orientation and identify sets of discontinuities, or single discontinuities, that could form potentially unstable blocks of rock. Information on discontinuity orientation may be obtained from such sources as surface and underground mapping, diamond drill core and geophysics, and it is necessary to combine this data into a system that is readily amenable to analysis. This analysis is facilitated by the use of a simple and unambiguous method of expressing the orientation of a fracture. The recommended terminology for orientation is the dip and dip direction which are defined as follows and shown schematically in Fig. 2.3. 1. Dip is the maximum inclination of a discontinuity to the horizontal (angle ?). 2. Dip direction or dip azimuth is the direction of the horizontal trace of the line of dip, measured clockwise from north (angle a). As will be demonstrated in Section 2.3, the dip/dip direction system facilitates field mapping and the plotting of stereonets, and the analysis of discontinuity orientation data. Strike, which is an alternative means of defining the orientation of a plane, is the trace of the intersection of an inclined plane with a horizontal

reference plane. The strike is at right angles to the dip direction of the inclined plane. The relationship between the strike and the dip direction is illustrated in Fig. 2.3(b) where the plane has a strike of N60E and a dip of 30SE. In terms of dip and dip direction, the orientation of the plane is 30/150 which is considered to be a simpler nomenclature. By always writing the dip as two digits and the dip direction as three digits, e.g. 090 for 90°, there can be no confusion as to which set of figures refers to which measurement. Strike and dip measurements can be readily converted into dip and dip direction measurements if this mapping system is preferred. In defining the orientation of a line, the terms plunge and trend are used. The plunge is the dip of the line, with a positive plunge being below the horizontal and a negative plunge being above the horizontal. The trend is the direction of the horizontal projection of the line measured clockwise from north, and it corresponds to the dip direction of a plane. Discontinuity mapping is carried out with a geological compass, of which there are several different types. The Brunton compass is widely available, but has a disadvantage in that measurement of the dip and dip direction require separate operations. Also, it is designed to measure strike rather than dip direction; this requires that a conversion be made which can be a possible source of error. There are a number of compasses specifically designed for structural mapping which allow dip and dip direction to be measured simultaneously; these compasses are manufactured by the Breihthaupt Company and the Freiberg Company, both in Germany, and the Showa Sokki Company in Japan. A particular feature of these structural compasses is their ability to map a discontinuity accurately when only a small portion of a plane is exposed. In these circumstances it can be difficult to determine the true dip, as opposed to the apparent dip which is always a flatter angle. The true dip can be visualized by rolling a ball down the plane: the ball will roll down the line of maximum inclination which corresponds to the true dip of the

DISCONTINUITY CHARACTERISTICS

31

Figure 2.3 Terminology defining discontinuity orientation (dip and dip direction): (a) isometric view; and (b) plan view.

plane. Figure 2.4 shows the operation of a structural compass; the lid is placed on the discontinuity surface and the body of the compass is leveled using the spirit level before reading the dip direction on the 360° compass scale, and the dip on a scale on the hinge. The orientation of overhanging surfaces can also be measured by placing the partially closed

compass lid on the discontinuity surface and making the readings in the usual way. 2.3 Stereographic projection The analysis of structural geology orientation

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Figure 2.4 Photograph of structural compass measuring dip and dip direction of discontinuity surface.

measurements requires a convenient method of handling three-dimensional data. Fortunately the stereographic projection, which is used extensively in the fields of cartography, navigation and crystallography, is ideally suited to geological applications. The stereographic projection is a procedure for mapping data located on the surface of a sphere on to a horizontal plane, and can be used for the analysis of the orientation of planes, lines and forces (Donn and Shimmer, 1958; Phillips, 1972; Goodman, 1976; Hoek and Bray; 1981). There are several different types of stereographic projections, but the one most suitable for geological applications is the equal area net, or Lambert projection, which is also used by geographers to represent the spherical shape of the Earth on a flat surface. In structural geology, a point or line on the sphere representing the dip and dip direction of a discontinuity can be projected on to a horizontal surface. In this way an analysis of threedimensional data can be carried out in two dimensions. An important property of the equal area projection is that any solid angle on the surface of the reference sphere is projected as an equal area on to a horizontal surface. One of the applications of this property is in the contouring of pole populations to find the orientation of sets of discontinuities as described in Section 2.3.2.

The principle of the projection method is illustrated in Fig. 2.5. The basic element of the pro-jection is a reference sphere which is oriented in space, usually with respect to true north. When a plane (discontinuity) is centered in the reference sphere, the intersection between the plane and the surface of the sphere is a circle which is commonly known as a great circle (Fig. 2.5(a)). The orientation of the great circle is a unique representation of the orientation of the plane. The upper and lower halves of the sphere give identical information and in engineering applications the usual procedure is to use the lower half of the sphere only. The projection is known, therefore, as a lower hemisphere projection. Note that this pro- jection technique only examines the orientation of planes and there is no information on their position in space. That is, it is assumed that all the planes pass through the center of the reference sphere. If the stereographic projection identified a plane on which the foundation could slide, its location on the geological map would have to be examined to determine if it intersected the foundation. An alternative means of representing the orientation of a plane is the pole of the plane. The pole is the point at which the surface of the sphere is pierced by a radial line in a direction normal to the plane. The merit of the pole projection is that the complete

DISCONTINUITY CHARACTERISTICS

33

Figure 2.5 Stereographic representation of the orientation of a plane: (a) plane surface location in lower hemisphere of the reference spehere showing great circle and pole to plane; (b) vertical section through reference sphere showing lower hemisphere, equal-area projections of great circle and pole; and (c) plan view of reference plane showing projections of great circle and pole.

orientation of the plane is represented by a single point which facilitates analysis of a large number of planes compared with the use of great circles. The most convenient means of examining the orientation data provided by the great circles and the poles is to project the lines and points on to a horizontal reference plane which is a twodimensional representation of the surface of the sphere. The equal-area projection for any point on the surface of the reference sphere is accomplished by drawing an arc about the lower end of the vertical axis of the sphere from the point to the horizontal base plane (Fig. 3.5(b)). Figure 3.5(c) shows a plan

view of the horizontal reference plane, and the positions of the pole and great circle of a plane with a dip of 30° and a dip direction of 150°. The great circle and the pole for the same plane lie on opposite sides of the stereonet, so the dip direction is measured from the top of the circle for the great circle, and from the bottom of the circle for the pole. Also, a plane with a shallow dip has a pole close to the center of the reference circle, while the great circle for the same plane is located close to the perimeter of the circle. Stereographic projections of both planes and great circles can be prepared by hand by plotting the data

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on standard sheets with lines representing dip and dip direction values (Appendix I). Alternatively, there are computer programs available that will not only plot poles and great circles, but will also plot selected data. This selection feature will prepare plots, for example, of only faults, or of only joints with lengths greater than a specified length. Selective plots have particular value where there is a great quantity of geological data and it is important to identify features that have a particular significance to stability. The analysis of structural geological data by stereographic methods is usually a three stage process as follows. 1. Plot poles to show the orientation of all the discontinuities. 2. Contour the data to find the prominent discontinuity sets. 3. Use great circles of the discontinuity sets or prominent discontinuities to show the shape of blocks that they form, and the direction in which they may slide or topple. Two different types of stereonet, the polar net and the equatorial net, are used when plotting this data by hand. The polar plot is used to plot poles, while the equatorial net can be used to plot either poles or great circles (see Appendix I). These three stages of the analysis of structural geology data are described in this section. 2.3.1 Pole plots Pole plots, in which each plane is represented by a single point, are the most convenient means of examining the orientation of a large number of discontinuities. The plot provides an immediate visual depiction of concentrations of poles representing the orientations of sets of discontinuities, and the analysis is facilitated by the use of different symbols for different types of discontinuities. A typical pole plot generated by a stereo-graphic computer program is shown in

Fig. 2.6. This is a lower hemisphere, equal angle projection of 1391 original poles at a site where the rock type is a highly metamorphosed phyllite. The rock contains discontinuity sets comprising the foliation and two sets of joints; where more than one pole has the same orientation, a number or letter is plotted indicating the number of poles at that point on the net, as shown by the legend. If the geological mapping data has identified the type of each dis continuity, the data can also be plotted with the symbol F representing the foliation and J representing the joints, for example. The dip direction scale (0°–360°) shown around the periphery of the pole plot has zero degrees at the bottom of the plot because the poles lie at the opposite side of the circle to the great circles (see Fig. 2.5(c)). Therefore the foliation planes lying in the NE quadrant and close to the periphery of the circle, have a dip direction of between about 220° and 280°, and a steep dip between about 60° and 80°. Pole plots can also be prepared by hand on a polar net in which the dip and dip directions are directly located by the radial and circular lines respectively (Appendix I). 2.3.2 Pole density All natural discontinuities have a certain amount of variation in their orientations which results in scatter of the pole plots. If the plot contains poles from a number of discontinuity sets, it can be difficult to distinguish between the poles from the different sets, and to find the most likely orientation of each set. However, by contouring the plot, the most highly concentrated areas of poles can be more readily identified. The usual method of generating contours is to use the contouring package contained with most stereographic projection computer programs. However, contouring can also be readily be carried out by hand using the techniques described by Hoek and Bray (1981). Figure 2.7 shows a contour plot of a the poles plotted in Fig. 2.6. The pole plot in Fig. 2.6 shows

DISCONTINUITY CHARACTERISTICS

35

Figure 2.6 Pole plot of foliation and joints; lower hemisphere, equal-area projection (plot by Mark Goldbach).

that the orientation of the foliation planes has relatively little scatter; the contour plot of these poles has a maximum concentration of 16% at a dip of 65° and a dip direction of 245°. In contrast, the joint orientations show much more scatter, and on the pole plot it is difficult to identify discontinuity sets. However, on the contoured plot, it is possible to distinguish clearly two sets of orthogonal joints. Set A has a shallow dip of about 28°, and a dip direction of about 080° which is in a direction at 180° to the foliation. Set B has a near vertical dip and a dip direction approximately at right angles to set A. The poles for set B lie on opposite sides of the contour plot because some dip steeply to the NW and some steeply to the SE. In Fig. 2.7 the different pole concentrations are shown by symbols for each 4% contour interval. The percentage concentration refers to the number

of poles in each 1% area of the surface of the lower hemisphere. Thus if the computer counts 28 poles out of a total of 1391 poles in a 1% area of the lower hemisphere, then the concentration level in that area is 2%. By successively counting each area, a contour plot showing the pole concentrations of all the data can be developed. A further use of the stereographic projection program in analyzing structural data is to prepare plots of data selected from the total data collected. For example, joints with lengths which are only a small fraction of the foundation dimensions are unlikely to have a significant influence on stability or settlement. Therefore it would facilitate design to prepare a stereographic plot showing only those discontinuities which have lengths greater than a specified length. Figure 2.8 is a pole plot of the same data shown in Fig. 2.6 in which only

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Figure 2.7 Contour plot of the poles shown in Fig. 2.6.

discontinuities with lengths greater than 4m (13 ft) have been plotted. This plot shows that only 163 discontinuities, or 12% of the total number have lengths greater than 4 m, and that virtually all of these discontinuities are either the foliation or joint set A. Similar selections can be made, for example, of discontinuities that have a certain type of infilling, or are slickensided, or show evidence of seepage, provided that the mapping identifies this level of detail of each surface. Appendix II contains field mapping sheets for recording details of discontinuity properties by the use of codes that are input directly into the stereographic analysis program. The assignment of poles into discontinuity sets is usually achieved by a combination of contouring, visual examination of the stereonet, and a knowledge

of geological conditions at the site which will frequently show the trends in orientation of the sets. It is also possible to identify discontinuity sets by rigorous and less subjective analysis of clusters in orientation data. A technique presented by Mahtab and Yegulalp (1982) identifies clusters from random distributions of orientations using the Poisson distribution. 2.3.3 Great circles Once the orientation of the discontinuity sets, as well as important discontinuities such as faults, have been identified on the pole plots, the next step in the analysis is to determine if these discontinuities form potentially unstable blocks in

DISCONTINUITY CHARACTERISTICS

37

Figure 2.8 Selective pole plot of data in Fig. 2.6 for all discontinuities with lengths greater than 4 m (plot by M.Wise).

the foundation. This analysis is carried out by plotting great circles of each of the discontinuity set orientations, as well as the orientation of the face of the cut on which the foundation is located. In this way the orientation of all the surfaces that have an influence on stability are represented on a single diagram. Figure 2.9 shows the great circles of the joint sets identified on the contoured pole plot in Fig. 2.7. It is usually only possible to have a maximum of about six great circles on a plot, because with a greater number, it is difficult to identify all the intersection points of the circles. The procedure for plotting great circles using an equatorial net is shown in Appendix I. The primary purpose of plotting great circles of discontinuity sets in a foundation is to determine the

shape of blocks formed by intersecting discontinuities, and the direction in which they may slide. For example, in Fig. 2.1 the foundation failure only occurred at the location where the discontinuities intersected to form a wedge with a particular shape and orientation with respect to the face. It is, of course, important to identifysuch potential failures before movement and collapse actually occurs. This requires an ability to visualize the three-dimensional shape of the wedge from the traces of the discontinuities on the face of the original slope. The stereographic projection is a convenient means of carrying out the required threedimensional analysis, keeping in mind that this procedure examines only the orientation of the discontinuities and not their position. If the stereonet

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Figure 2.9 Plot of great circles representing the three discontinuity sets identified on the contour plot of Fig. 2.7.

shows the possible occurrence of a potentially unstable block, examination of the location of the discontinuities on the geological map would determine if they intersect the foundation. Two intersecting planes may form a wedge shaped block as shown in Fig. 2.1. The direction in which this block may slide is determined by the trend of the line of intersection, with failure being possible only if the trend is out of the slope face. The plunge of the line of intersection gives an indication of the stability condition of the block: the block is unlikely to slide if the plunge is at a shallow angle. The orientation of the line of intersection between two planes is represented by the point where the two great circles intersect. For the data shown on the pole plot (Fig. 2.6), intersections occur between joint sets A and B (I1), between set B and the foliation (I2), and set A and the foliation (I3). The orientation of intersection line I3 is shown in Fig. 2.9, and the method of determining the trend and plunge of lines is described in Appendix I. For the conditions shown in Fig. 2.9, the wedge formed by intersection I3 will slide towards a direction of

158° and at a shallow dip angle of 8°. 2.3.4 Stochastic modeling of discontinuities The main limitation of the use of stereonets in foundation design is that they provide only the orientation, but no spatial information on the discontinuities. In fact, discontinuities are distributed in space and have variable attitudes, sizes and shapes which lend themselves to their representation as stochastic models (Dershowitz and Einstein, 1988; Kulatilake, 1988; Einstein, 1993). The development of a three-dimensional model of the rock mass incorporating the discontinuity sets and the intersections between discontinuities provides a useful tool for the study of a number of rock mechanics applications, including fluid flow through fractured rock masses which may prove useful in consolidation grouting of foundations. With respect to the stability of rock f oundations, the model of the rock mass will indicate the shape and size of potentially unstable blocks of rock, and

DISCONTINUITY CHARACTERISTICS

the extent of intact rock that lies on the boundaries of the block. The existence of such intact ‘rock bridges’ has a significant influence on stability because the strength of the intact rock is very much greater than that of the discontinuity surfaces, and the three-dimensional model of rock mass helps to define the location and size of the bridges (Einstein, 1993). In turn this information can be used to design rock bolting patterns to reinforce the rock. The stochastic model will show the probability of failure rather than the factor of safety (see Section 1.6). 2.4 Types of foundation failure A great circle stereographic plot of discontinuity sets can be used to identify the shape of blocks in the foundation, and make an assessment of their stability conditions (Fig. 2.10). Four distinct types of slope failure can be distinguished, the characteristics of which depend on the relative orientation between the slope face and the discontinuity (Hoek and Bray, 1981). For each of the failure types there is a distinct method of stability analysis which takes into account the shape and size of the block, the shear strength of the sliding surfaces, water pressures and the foundation loads. These analysis methods are described in Chapter 6. The first three block types—plane, wedge and toppling blocks—have distinct shapes as defined by the geological structure. The differences between these three shapes are that in the case of the planar and wedge blocks (Figs. 2.10(a) and (b)), the structure dips out of the face, and on the stereonet the poles are on the opposite side of the net from the great circle of the face. In the case of toppling blocks (Fig. 2.10(c)), the structure dips into the face and on the stereonet the poles are on the same side of the net as the great circle of the face. The fourth type of failure, circular failure, occurs in soil, rock fill or closely fractured rock containing no persistent discontinuities dipping out of the slope (Fig. 2.10(d)). For cuts in fractured rock, the sliding surface forms partially along discontinuities that are

39

oriented approximately parallel to this surface, and partially through intact rock. Because of the relative high shear strength of rock compared with that of discontinuities, this type of failure will only occur in closely fractured rock where the major portion of the sliding surface comprises discontinuity surfaces. It is found that where a failure occurs under these conditions, the sliding surface can be approximated by a large-radius circular arc forming a shallow failure surface. Stability analysis of this failure mode in rock can be carried out in an identical manner to that of a soil, with the use of appropriate strength parameters. 2.5 Kinematic analysis Once the type of block failure has been identified on the stereonet, the same diagram can also be used to examine the direction in which a block will slide and give an indication of possible stability conditions. This procedure is known as kinematic analysis. An application of kinematic analysis is the rock face shown in Fig. 2.1 where two joint planes form a wedge which has slid out of the face and towards the photographer. If the slope face had been less steep than the line of intersection between the two planes, or had a strike at 90° to the actual strike, then the wedge formed by the two planes would not have been able to slide. This relationship between the direction in which the block of rock will slide and the orientation of the face is readily apparent on the stereonet. However, while analysis of the stereonet gives a good indication of stability conditions, it does not account for external forces such as foundation loads, water pressures or reinforcement comprising tensioned rock bolts, which can have a significant effect on stability. The usual design procedure is to use kinematic analysis on the stereonet to identify potentially unstable blocks, followed by detailed stability analysis of these blocks using the procedures described in Chapter 6. An example of kinematic analysis is shown in Fig. 2.11 where a footing is located at the crest of a

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Figure 2.10 Main types of block failures in foundations, and structural geology conditions likely to cause these failures (after Hoek and Bray, 1981): (a) plane failure in rock containing continuous joints dipping out of slope face, and striking parallel to face; (b) wedge failure on two intersecting discontinuities; (c) toppling failure in strong rock containing discontinuities dipping steeply into face; and (d) circular failure in rock fill, soil, and closely fractured rock with randomly oriented discontinuities.

DISCONTINUITY CHARACTERISTICS

steep slope which contains three sets of discontinuities. The potential for these discontinuities to form unstable blocks in the foundation depends on their dip and dip direction relative to the face; stability conditions can be studied on the stereonet as described below. 2.5.1 Planar failure A potentially unstable planar block is formed by plane AA, which dips at a flatter angle than the face and is said to ‘daylight’ on the face (Fig. 2.11(a)). However, sliding is not possible on plane BB which dips steeper than the face and does not daylight. Similarly, discontinuity set CC dips into the face and sliding cannot occur on these planes, although toppling is possible. The poles of the slope face and the discontinuity sets (symbol p) are plotted on the stereonet in Fig. 2.11 (b), assuming that all the discontinuities strike parallel to the face. The position of these poles in relation to the slope face shows that the poles of all planes that daylight, and are potentially unstable, lie inside the pole of the slope face (pf). This area is termed the daylight envelope and can be used to identify potentially unstable blocks quickly. The dip direction of the discontinuity sets will also influence stability. Sliding is not possible if the dip direction of the discontinuity differs from the dip direction of the face by more than about 20°. That , is, the block will be stable if because under these conditions there will be an increasing thickness of intact rock at one end of the block which will have sufficient strength to resist failure. On the stereonet this restriction on the dip direction of the planes is shown by two lines and defining dip directions of . These two lines designate the lateral limits of the daylight envelope on Fig. 2.11(b). 2.5.2 Wedge failure Kinematic analysis of wedge failures (Fig. 2.10(b)) can be carried out in a similar manner to that of

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plane failures. In this case the pole of the line of intersection of the two discontinuities is plotted on the stereonet and sliding is possible if the pole The direction of daylights on the face, i.e. sliding of kinematically permissible wedges is less restrictive than that of plane failures because there are two planes to form release surfaces. A daylighting envelope for the line of intersection, as shown on Fig. 2.11(b), is wider than the envelope for plane failures. The wedge daylight envelope is the locus of all poles representing lines of intersection whose dip directions lie in the plane of the slope face. 2.5.3 Toppling failure For a toppling failure to occur the dip direction of the discontinuities dipping into the face must be within about 20° of the dip direction of the face so that a series of slabs are formed parallel to the face. Also, the dip of the planes must be steep enough for interlayer slip to occur. If the faces of the layers have a friction angle , then slip will only occur if the direction of the applied com pressive stress is at with the normal to the layers. angle greater than The direction of the major principal stress in the cut is parallel to the face of the cut (dip angle ?f), so interlayer slip and toppling failure will occur on planes with dip ?p when the following conditions are met (Goodman and Bray, 1976): (2.1) These conditions on the dip and dip direction of planes that can develop toppling failures are defined on Fig. 2.11(b). The envelope defining the orientation of these planes lies at the opposite side of the stereonet from the sliding envelopes. 2.5.4 Friction cone Once one has determined from the daylight envelopes whether a block in the foundation is kinematically permissible, it is possible to examine stability conditions on the same stereonet. This

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Figure 2.11 Kinematic analysis of blocks in foundations: (a) discontinuity sets in foundation; and (b) daylight envelopes plotted on equal-area projection stereonet.

analysis is carried out assuming that the shear strength of the sliding surface comprises only the friction component and the cohesion is zero. Consider a block at rest on an inclined plane with a friction angle of between the block and the plane (Fig. 2.12(a)). For an at-rest condition, the force vector normal to the plane must lie within the

friction cone. When the only force acting on the block is gravity, the pole to the plane is in the same direction as the normal force, so the block will be stable when the pole lies within the friction circle. The envelopes on Fig. 2.12(b) show the possible positions of poles that may form unstable blocks. Envelopes have been drawn for slope face angles of

DISCONTINUITY CHARACTERISTICS

60° and 80° which show that the risk of instability increases as the slope becomes steeper as indicated by the larger envelopes for the steeper slope. Also, the envelopes become larger as the friction angle diminishes. The envelopes also indicate that, for the simple gravity loading condition, instability will only occur in a limited range of geometric conditions.

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described below. A measure of the dispersion, and from this the standard deviation, of a discontinuity set can be calculated from the direction cosines as follows (Goodman, 1980). The direction cosines of any plane with dip ? and dip direction a are the unit vectors l, m and n, where: (2.2)

2.6 Probabilistic analysis of structural geology In carrying out probabilistic design of foundations it is necessary to express the orientation and length of discontinuities in terms of probability distributions rather than single values. This information will give the most likely value of each parameter as well as the probability of its occurrence within a range of possible values. The probability distribution of discontinuity orientation can be calculated from the stereonet, while the distributions of length and spacing are calculated from field measurements as described in the following sections. The calculated values of the mean and standard deviation of the design parameters can be input into the Monte Carlo analysis to determine the coefficient of reliability as described in Section 1.6.4. 2.6.1 Discontinuity orientation The natural variation in orientation of discontinuities results in there being scatter of the poles when they are plotted on the stereonet. It is useful to incorporate this scatter into the stability analysis of the foundation because, for example, a wedge analysis using the mean values of pair of discontinuity sets may show that the line of intersection of the wedge does not daylight in the face and that the foundation is stable. However, an analysis using orientations other than the mean values may show that some unstable wedges can be formed. The risk of occurrence of this condition would be quantified by calculating the mean and standard deviation of the dip and dip direction as

For a number of poles, i, in one set the direction cosines (lR, mR and nR) of the mean orientation of the discontinuity set is the sum of the individual direction cosines, as follows: (2.3) where is the magnitude of the resultant vector given by (2.4) The dip ?R and dip direction aR of the mean orientation are: (2.5)

A measure of the scatter of a set of discontinuities comprising N poles can be obtained from the dispersion coefficient Cd which is calculated as follows: (2.6) If there is little scatter in the orientation of the discontinuities, the value of Cd is large, and its value diminishes as the scatter increases. From the dispersion coefficient it is possible to calculate from equation 2.7 the probability P that a pole will make an angle ?° or less than the mean orientation, where (2.7) For example, the angle from the mean defined by one standard deviation occurs at a probability P of 0.

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Figure 2.12 Combined kinematic and simple stability analysis using friction cone concept: (a) friction cone in relation to block at rest on an inclined plane; and (b) stereographic projection of friction cone superimposed on daylighting envelopes.

16 (refer to Fig. 1.10). If the dispersion is 20, one

standard deviation lies at 7.6° from the mean.

DISCONTINUITY CHARACTERISTICS

Equation 2.7 is applicable when the dispersion in the scatter is approximately uniform about the mean orientation, which is the case in joint set A in Fig. 2.6. However, in the case of the foliation in Fig. 2.6, there is much less scatter in the dip than in the dip direction. The standard deviations in the two directions can be calculated approximately as follows from the stereonet. First, two great circles are drawn at right angles corresponding to the directions of dip and dip direction respectively. Then the angles corresponding to the 7% and 93% levels, P7 and P93 respectively, are determined by counting the number of poles in the set and removing the poles outside these percentiles. The equation for the standard deviation along either of the great circles is as follows (Morriss, 1984): (2.8) More precise methods of determining the standard deviation are described by McMahon (1982), but the approximate method given by equation 2.8 may be sufficiently accurate, considering the difficulty in obtaining a representative sample of the discontinuities in the set. An important aspect of accurate geological investigations is to account for bias when mapping a single face or logging a single borehole when few of the discontinuities aligned parallel to the line of mapping are measured. This bias in the data can be corrected by applying the Terzaghi correction as described in Section 4.2. 2.6.2 Discontinuity length and spacing The length and spacing of discontinuities determines the size of blocks that will be formed in the foundation. Designs are usually concerned with persistent discontinuities that could form blocks with dimensions great enough to influence overall stability of the foundation. However, discontinuity dimensions have a range of values and it is useful to have an understanding of the distribution of these values in order to predict how the extreme values may be compared with values obtained from a small sample. This section discusses probability distributions for the length and spacing of

45

discontinuities, and discusses the limitations of making accurate predictions over a wide range of dimensions. (a) Probability distributions Discontinuities are usually mapped along a scanline, such as drill core, slope face or wall of a tunnel, and individual measurements are made of the properties of each fracture, including its visible length and the spacing between discontinuities in each set (Appendix II). The properties of discontinuities typically vary over a wide range and it is possible to describe the distribution of these properties by means of probability distributions. A normal distribution is applicable if a particular property has values in which the mean value is the most commonly occurring. This condition would indicate that the property of each discontinuity, such as its orientation, is related to the property of the adjacent discontinuities reflecting that the discontinuities were formed by stress relief. For properties that are normally distributed, the mean and standard deviation are given by equations 1.7 and 1.8. A negative exponential distribution is applicable for properties of discontinuities, such as their length and spacing, that are randomly distributed indicating that the discontinuities are mutually independent. A negative exponential distribution would show that the most commonly occurring discontinuities are short and closely spaced, while long, widely spaced discontinuities are less common. The general form of a probability density function f(x) of a negative exponential distribution is (Priest and Hudson, 1981): (2.9) and the associated cumulative probability F(x) that a given spacing or length value will be less than dimension x will is given by: (2.10) where x is a measured length or spacing and is the mean value of that parameter. A property of the negative exponential distribution is that the standard deviation is equal to the mean value.

46

STRUCTURAL GEOLOGY

Figure 2.13 Histogram of joint trace lengths, and best fit exponential and log-normal curves (Priest and Hudson, 1981).

From equation 2.10 for a set of discontinuities in which the mean spacing is 2 m, the probabilities that the spacing will be less than 1 m and 5 m respectively are:

Equation 2.10 could be used to estimate the probability of occurrence of discontinuities with a specified length. This result could be used, for example, to determine the likelihood of a plane being continuous through a foundation. Another distribution that can be used to describe the dimensions of discontinuities is the log-normal distribution which is applicable where the variable is normally distributed (Baecher et al., 1977). The log-normal distribution function for the variable y is (2.11) where is the mean value and SDx is the standard deviation of the variable x. Figure 2.13 shows the measured lengths of 122

joints in a Cambrian sandstone for lengths of less is 1.2 m (Priest and than 4 m; the mean length Hudson, 1981). To this data have been fitted both exponential and log-normal curves for which the correlation coefficients r are 0.69 and 0.89 respectively. While the log-normal curve has a higher correlation coefficient, the exponential curve has a better fit at the longer discontinuity lengths. This demonstrates that for each set of data the most appropriate distribution should be determined. (b) Discontinuity length (persistence) Discontinuities are often mapped on a rock face or wall of a tunnel where the lengths of some of the discontinuities are greater than the dimension of the mapped face. In this case it is not possible to measure the actual discontinuity lengths. Techniques have been developed whereby the mean length of the discontinuities in the outcrop can be estimated from observations of the lengths of the discontinuities relative to the dimension of the mapped face, without making any measurements of the actual discontinuity lengths (Kulatilake and Wu, 1984; Pahl, 1981; Priest and Hudson, 1981). Figure 2.14 illustrates a rock face containing a

DISCONTINUITY CHARACTERISTICS

number of discontinuities of a single set, the lengths of which fall into one of the following three categories: 1. contained discontinuities (Nc)—the length is less than the height of the face and both ends of the discontinuity are visible; 2. intersecting discontinuities—one end of the discontinuity is visible in the face; 3. transecting discontinuities (Nt)—the length of the discontinuity is greater than the height of the face and neither end is visible. Based on this categorization of the discontinuity length, the mean length can be estimated from the following equation which is independent of the assumed form of the statistical distribution of the discontinuity lengths (Pahl, 1981): (2.12) where (2.13) and (2.14) and ? is the dip of the discontinuities, L is the length of the mapped face, H is the height of a horizontal scan line above the base of the outcrop and N' is total number of discontinuities within the scanline. Figure 2.14 shows discontinuities for a single set for which the average length and spacing have be calculated. For the joints illustrated in Fig. 2.14 the average length calculated using equations 2.12, 2.13 and 2.14 is 4.3 m (14.1 ft) and this is drawn to scale on the Figure. In reality, the face would contain several sets of discontinuities and the mapping method would depend on the use to which the data would be applied. For example, if the properties of the rock mass were being studied, then it would be appropriate to map every discontinuity within the scanline area to find the average length of all discontinuities. However, if the mapping were being

47

carried to investigate a specific set of discontinuities that would form potential sliding planes in a foundation, then it would be appropriate to distinguish those discontinuities belonging to the set in question. While the calculated average length is an estimate because it is not possible to measure the full length of many of the discontinuities, this value is consistent with the observation that about half the discontinuities have lengths less than the height of the scan line. Furthermore, the lengths are distributed such that there are only four discontinuities with lengths more than about twice the height of the scan line and it is likely that the range of lengths would fit either an exponential or log-normal distribution (Fig. 2.13). (c) Discontinuity spacing The spacing of discontinuities can be measured along a scan line on a slope face or wall of a tunnel (Priest and Hudson, 1976), or in a borehole. Discontinuities in a diamond drill hole can be examined in the core if the recovery is acceptable, and it is possible to distinguish the natural discontinuities from mechanical breaks. It is also possible to examine the spacing and orientation of discontinuities in the wall of the hole using a borehole camera (see Section 4.3). As discussed in (b) above, the design application will determine if all discontinuities are to be considered in measuring spacing, or only those belonging to a single set. One approach that may be taken to study the spacings of different sets of discontinuities is to make measurements along scanlines with different orientations, preferably with a scanline at right angles to each set if this is physically possible (Hudson and Priest, 1979; 1983). The average spacing of discontinuities is found by counting the number, N'', that intersect a scanline of known length L, with an adjustment being made if the discontinuities are not oriented at right angles to the scanline. For the condition shown in Fig. 2.14 where the scanline is horizontal and the dip of the discontinuities is ?, the average spacing is given by:

48

STRUCTURAL GEOLOGY

Figure 2.14 Rock outcrop showing discontinuity length, termination and spacing; terminations categorized as either contained (c) or transecting (t) discontinuities.

(2.15) Figure 2.14 shows that there are a total of 13 discontinuities with an average dip of 65° that intersect the 27 m long scanline. From equation 2. 15, the average spacing is 1.9 m (6.2 ft) which is drawn to scale on the Figure. If the variation in the spacing can be described by an exponential distribution, then the probability that the spacing will be less than a specified value is given by equation 2.10. 2.7 References Baecher, G.B., Lanney, N.A. and Einstein, H. (1977) Statistical description of rock properties and sampling. Proc. 18th U. S. Symp. Rock Mech. Johnson Publishing, Keystone, Colorado. Cruden, D.M. (1977) Describing the size of discontinuities. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 14, 133–7. Dershowitz, W.S. and Einstein, H.H. (1988)

Characterizing rock joint geometry with joint system models. Rock Mech. Rock Eng., 20(1), 21–51. Donn, W.L. and Shimer, J.A. (1958) Graphic Methods in Structural Geology. Appleton Century Crofts, New York. Einstein, H.H. (1993) Modern developments in discontinuity analysis. Comprehensive Rock Engineering, Pergamon Press, pp. 193–213. Einstein, H.H., Veneziano, D., Baecher, G.B. and O’Reilly, K.J. (1983) The effect of discontinuity persistence on slope stability. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 20, 227–36. Goodman, R.E. (1976) Methods of Geological Engineering in Discontinuous Rocks, West, St. Paul, MN. Goodman, R.E. (1980) Introduction to Rock Mechanics, Wiley, New York. Goodman, R.E. and Bray, J. (1976) Toppling of rock slopes. Proc. Speciality Conf. On Rock Engineering for Foundations and Slopes, Boulder Colorado, ASCE, Vol II. Hoek, E. and Bray, J. (1981) Rock Slope Engineering, 3rd edn, IMM, London. Hudson, J.A. and Priest, S.D. (1979) Discontinuities and

DISCONTINUITY CHARACTERISTICS

rock mass geometry. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 16, 336–62. Hudson, J.A. and Priest, S.D. (1983) Discontinuity frequency in rock masses. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 20, 73–89. Kikuchi, K., Kuroda, H. and Mito, Y. (1987) Stochastic estimation and modelling of rock joint distribution based on statistical sampling. Sixth Int. Conf. on Rock Mechanics, Montreal, pp. 425–8. Kulatilake, P.H. S. (1988) State of the art in stochastic joint geometry modeling. Proc. 29th U.S. Symp. Rock Mech. (eds. P.A.Cundall, R.I.Sterling and A.M.Starfield) Balkema, Rotterdam, pp. 215–29. Kulatilake, P.H.S. and Wu, T.H. (1984) Estimation of the mean length of discontinuities. Rock Mech. and Rock Eng., 17(4), 215–32. Mahtab, M.A. and Yegulalp, T.M. (1982) A rejection criterion for definition of clusters in orientation data. Proc. 22nd. Symp. Rock Mechanics, Berkeley, CA, Soc. Min. Eng., American Inst. of Mining, Metallurgical,

49

Petroleum Eng., pp. 116–23. McMahon, B.K. (1982) Probabalistic Design in Geotechnical Engineering, Australian Mineral Foundation, AMF Course 187/82, Sydney. Morriss, P. (1984) Notes on the Probabalistic Design of Rock Slopes, Australian Mineral Foundation, notes for course on Rock Slope Engineering, Adelaide, April. Pahl, P.J. (1981) Estimating the mean length of discontinuity traces. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 18, 221–8. Phillips, F.C. (1972) The Use of Stereographic Projection in Structural Geology, 3rd edn, Arnold, London. Priest, S.D. and Hudson, J.A. (1981) Estimation of discontinuity spacing and trace length using scanline surveys. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 18, 183–97. Priest, S.D. and Hudson, J.A. (1976) Discontinuity spacings in rock. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 13, 135–48.

3 Rock strength and deformability

3.1 Range of rock strength conditions Determination of the appropriate strength parameters to use in the design of foundations depends on the type of foundation, the load conditions, and the characteristics of the rock in the bearing area. The importance of using the appropriate strength parameter is illustrated in Fig. 3.1, which shows a number of different foundation loading conditions and the rock strength parameters that apply to the design of each. The following is a list of basic rock strength parameters and their applications in foundation design: 1. deformation modulus—calculation of settlement (Fig. 3.1(a, b)); 2. compressive strength; of rock mass—bearing capacity of spread footings (Fig. 3.1(b)); 3. compressive strength of intact rock—bond stress of socketed piers and tensioned anchors is correlated with intact rock strength on the basis of empirical tests (Figs 3.1(c, d); 4. shear strength—shear resistance at interface between structure and foundation, and stability of sliding blocks (Fig. 3.1(b, e)) 5. tensile strength—punching or flexural failures where a weak bed underlies a layer of stiffer rock (Fig. 3.1(f)); 6. time dependent properties—settlement may occur with time as a result of rock creep, or degradation of the rock due to weathering. In determining the rock strength for each of these applications, it is most important to account for the

presence of discontinuities, such as joints, faults or bedding planes. For most conditions this requires that the rock mass strength properties, rather than the intact rock properties be used in design. The rock mass is the in situ, fractured rock which will almost always have significantly lower strength than the intact rock because the discontinuities divide the rock mass into blocks. The strength of the rock mass will depend on such factors as the shear strength of the surfaces of the blocks, their spacing and continuous length, and their alignment relative to the load direction. For example, the wedge of rock at the downstream toe of the dam foundation shown in Fig. 3.1(b) could fail in shear along a surface lying partially through intact rock and partially along existing discontinuities. Furthermore, if the loads are great enough to extend discontinuities and break intact rock, or if the rock mass can dilate resulting in loss of interlock between the blocks, then the rock mass strength may be significantly diminished from that of the in situ rock. Foundations located in fractured rock which are designed using the strength values of intact samples tested in the laboratory are likely to be significantly under-designed. Other conditions that may be encountered are foundations containing potentially unstable blocks, formed by single or intersecting discontinuities, that may slide from the foundation (Fig. 3.1(e)). In these circumstances, the shear strength parameters of the discontinuities themselves must be used in design rather than the shear strength of the rock mass. This shows the importance of carrying out careful geological mapping to identify such critical

ROCK STRENGTH AND DEFORMABILITY

51

Figure 3.1 Rock strength parameters related to the design of rock foundations: (a) settlement due to compression of soft seams and intact rock; (b) shear and deformation of fractured rock mass; (c) side-wall bond strength and end bearing of a socketed pier; (d) shear strength of rock-grout interface; (e) shear failure on a continuous fracture dipping out of the face; and (f) punching or flexural failure of a thin bed of rock overlying weaker material.

geological features and ensure that the strength testing program is appropriate for the likely mode of failure and rupture surface position. Chapter 4 describes methods of in situ modulus and strength testing, and Chapters 5–9 describe the application of the test results to the design of different types of foundations. One of the first decisions to be made in drawing up a testing program is whether to rely solely on laboratory tests, or to carry out more expensive in situ tests. Laboratory testing is appropriate where the test sample, which will usually have dimensions no larger than 100 mm (4 in) diameter, is representative of the rock properties. Tests that can

be carried out in the laboratory are uniaxial compressive strength testing, and shear testing to determine the friction angle of rock surfaces. However, it is rarely possible to carry out laboratory tests on a fractured rock mass because of the difficulty in obtaining undisturbed samples which are large enough, i.e. at least 1 m (3 ft) in diameter, to be representative of the in situ rock. If a large sample is available, then correspondingly large testing equipment will be required to load the sample to stress levels that will be acting in the foundation. One of the few laboratories capable of testing fractured rock masses is the University of California at Berkeley which has a 0.9 m (36 in)

52

RANGE OF ROCK STRENGTH CONDITIONS

diameter triaxial cell to which an axial load of 17.6 MN (4×106 lb) and a confining pressure of 5.1 MPa (750 p.s.i.) can be applied. The cell has been used to test rock fills. Laboratory tests on fractured rock have been carried out by Brown (1970), and simulations of fractured rock made up of blocks of materials such as cement and plaster of paris (Reik and Zacas, 1978). In situ testing is sometimes carried out in the design of dams and major bridges. This testing can consist of borehole jacking tests, plate load tests, and radial jacking tests to determine rock mass modulus, and direct shear tests to determine the shear strength of discontinuities critical to stability. These tests are carried out where there is access during the exploration program to a site that is representative of the foundation conditions. As a back up to laboratory or in situ tests, it is useful to check the test results against values calculated from the performance of actual foundations in similar geological conditions. Observations of settlement under known loading conditions will provide information on rock mass modulus values, while shear strength parameters can be back calculated from slope failures. While these observations will provide modulus and shear strength values of much larger samples than is possible with in situ testing, the reliability of the result will depend on the accuracy with which the loads, water pressures and movement mechanisms are known. 3.2 Deformation modulus For many structures founded on rock, loads are well within the elastic limit of the rock mass. Consequently all deformation and settlement occurs as soon as the load is applied, and there is no time dependent effect. Furthermore, settlement that does occur will be minimal and is not considered as a specific item in design. However, circumstances where foundation settlement must be considered are heavily loaded structures, particularly where the rock conditions

vary across the site. Such structures include highrise buildings, with individual footings on different rock types, and long bridges where differential settlement between piers must be controlled. In the case of settlement, concrete structures are, of course, much more susceptible to damage from differential settlement than embankment dams, and conditions are most severe where the foundations comprise materials with different moduli. For the conditions shown in Fig. 3.2, differential settlement can induce stresses in the concrete sufficient to develop cracking. The cracks will develop at the contacts between the foundation materials where the concrete attempts to bridge across the lower modulus rock (E2) and concentrates the load on the higher modulus rock (E1). This effect will be of most concern for arch dams if the width of the low modulus rock is equal to or greater than the width of the foundation, or where one abutment has a moduli different from the reminder of the foundation. Also, the cyclic loading that often occurs in dams due to changing reservoir levels can produce permanent displacement as a result of nonrecoverable strain in the foundation rock. The ratio of the deformation moduli of the concrete in the dam Ec and the foundation rock Er will influence the magnitude of stresses in the concrete. However, even for arch dams if the ratio Ec/Er is constantacross the foundation, its magnitude has little effect on the stress levels. Even if the ratio Ec/ Er varies by a factor of five, the stress levels determined by the Trial Load Method show that the stresses only vary by about 20%, so there is usually no need to determine precise values for the rock modulus (ICOLD, 1993) In most structures, the area of the bearing surface will be greater than the discontinuity spacing so settlement will be the result of both the deformation of the intact rock and the clo sure of discontinuities. That is, settlement will depend on the rock mass modulus and not the intact rock modulus. The difficulty and expense of obtaining large, undisturbed rock mass samples has meant that modulus measurements are made by in situ testing. The test methods include borehole pressuremeter,

ROCK STRENGTH AND DEFORMABILITY

53

Figure 3.2 Shear stresses developed in a concrete dam founded on rock with variable modulus (after Goodman, 1980).

plate load, flat jacks, pressure chamber and geophysical testing as described in Chapter 4. Deformation measurements have also been made of the foundations of structures during and after construction so as to compare the modulus calculated from these displacements with those obtained from testing. Guidici (1979) describes the modulus testing programme at the Gordon Dam in Tasmania where the plate jacking tests gave deformation modulus: back analysis values of between 12 and 40 GPa (1.74×106-5.8×106 p.s.i.) while the modulus calculated from deformation measurements ranged from about 12 to 24 GPa (1. 74×106-3.48×106p.s.i.). The lower modulus exhibited by the larger, in situ sample could be accounted for by the number of discontinuities increasing with increasing sample size. The deformability of rock as discussed in the previous paragraph is characterized by a modulus describing the relationship between the applied load and the resulting deformation. The fact that jointed rock masses do not behave elastically has prompted the usage of the term deformation modulus rather than the elastic modulus or Young’s modulus. Their definitions are as follows (ISRM, 1975):

• deformation modulus—the ratio of stress to corresponding strain during loading of a rock mass including elastic and inelastic behavior; • elastic modulus—the ratio of stress to corresponding strain below the proportional limit of a material. The following sections describe the modulus characteristics of a variety of different rock masses, and the influence of the measurement method on the test results. 3.2.1 Intact rock modulus The usual method of measuring the deformation modulus of intact rock is to test pieces of diamond drill core in uniaxial compression, with the test being a component of a compressive strength test. The most common core size used in geotechnical studies is NQ core with a diameter of 52 mm (2 in), and the test sample is cut so that the length to diameter ratio is 2.0. As there is some influence of specimen size on strength and modulus, it is preferable to standardize sample dimensions if

54

RANGE OF ROCK STRENGTH CONDITIONS

Figure 3.3 Axial and diametral stress-strain curves for intact rock tested in uniaxial compression.

possible. It is also necessary to grind the ends of the sample parallel and to use platens with the same diameter as the core; these procedures will minimize the development of stress concentrations at the ends of the sample. The International Society of Rock Mechanics Committee on Laboratory Tests (1972) gives the following tolerances for cylindrical test specimens. 1. The ends of the specimen shall be flat to 0.02 mm (0.0008 in). 2. The ends of the specimen shall be perpendicular to the axis of the specimen within 0.001 radian. 3. The sides of the specimen shall be smooth and free of abrupt irregularities and straight to within 0.3 mm (0.012 in) over the full length of the specimen.

Strain measurements are usually made with strain gauges glued to the surface of the sample; with a combination of axial and circumferential strain gauges it is possible to measure both the modulus and Poisson’s ratio of the sample. The stress-strain behavior of a rock can be plotted directly on an X–Y plotter during testing as shown in Fig. 3.3. Note that it is preferable to use strain gauges glued to the rock surface to measure strain in the rock directly, rather than such instruments as LVDTs (linear variable differential transformers) mounted on the platens. The reason for this is that slight imperfections at the contact between the steel and the rock may lead to movements of the platens that are not related to strain in the rock. The plots in Fig. 3.3 show two cycles of a compression test on a sample of strong gneissic rock which exhibits approximately linear stressstrain behavior, no hysteresis and no permanent

ROCK STRENGTH AND DEFORMABILITY

deformation. The rock is therefore showing near perfect elastic behavior. A perfectly elastic material is one that follows the same path during both the loading and unloading cycles, that is, hysteresis is zero and all the energy stored in the rock during loading is released during unloading. An elastic material is one that returns to zero strain at the end of the unloading cycle, although the loading and unloading cycles may follow different paths indicating that some energy is dissipated in the rock mass during the loading and unloading

55

cycles. The elastic constants calculated from the plots in Fig. 3.3 over the linear portion of the stress-strain curve are as follows:

Table 3.1 Typical elastic constants for intact rock Rock type

Young’s modulus GPa (p.s.i.×106) Poisson’s ratio Reference

Andesite, Nevada Argillite, Alaska Basalt, Brazil Chalk, USA Chert, Canada Claystone, Canada Coal, USA Diabase, Michigan Dolomite, USA Dolomite, Canada Gneiss, Brazil Granite, California Limestone, USSR Salt, Ohio Sandstone, Germany Shale, Japan Siltstone, Michigan Tuff, Nevada

37.0(5.5) 68.0(9.9) 61.0(8.8) 2.8(0.4) 95.2(13.8) 0.26(0.04) 3.45(0.5) 68.9(10) 51.7(7.5) 64.0(9.3) 79.9(11.6) 58.6(8.5) 53.9(8.5) 28.5(4.1) 29.9(4.3) 21.9(3.2) 53.0(7.7) 3.45(0.5)

Table 3.1 shows the results of uniaxial compression tests carried out to determine the elastic constants of a variety of rock types (Lama and Vutukuri, 1978a, b)). 3.2.2 Stress-strain behavior of fractured rock The typical load-deformation behavior of two rock masses subjected to cyclic loading is shown in Fig. 3.4. Figure 3.4(a) shows the results of a plate

0.23 0.22 0.19 – 0.22 – 0.42 0.25 0.29 0.29 0.24 0.26 0.32 0.22 0.31 0.38 0.09 0.24

Brandon (1974) Brandon (1974) Ruiz (1966) Underwood (1961) Herget (1973) Brandon (1974) Ko and Gerstle (1976) Wuerker (1956) Haimson and Fairhurst (1970) Lo and Hori (1979) Ruiz (1966) Michalopoulos and Triandafilidis (1976) Belikov (1967) Sellers (1970) van der Vlis (1970) Kitahara et al. (1974) Parker and Scott (1964) Cording (1967)

load test carried out on massive gneiss with an average compressive strength of 110 MPa (16 000 p.s.i.) from the Churchill Falls project in Quebec, Canada (Benson, 1970). Figure. 3.4(b) shows the results of Goodman jack tests carried out in sandstone with a compressive strength of about 4 MPa (580 p.s.i.) on the Peace River in Alberta, Canada (Saint Simon et al., 1979). The stress-deformation curves in Fig. 3.4 show typical inelastic behavior as characterized by the modulus of deformation. The pertinent features

56

RANGE OF ROCK STRENGTH CONDITIONS

Figure 3.4 Typical results of in situ modulus testing: (a) plate load test in gneiss (Benson, 1970); and (b) Goodman jack test in sandstone (Saint Simon et al., 1979).

of these tests are first, the increase in gradient of the curve with each load increment, and second, the permanent deformation that occurs on removal of the load. With each load cycle at a progressively higher stress, the modulus increases as indicated by the increase in gradient of the stress-strain curves; this is more noted in the case of the relatively larger volume of rock in the plate load test. This increase in modulus is the result of closure of discontinuities in the rock mass, and the progression of loading into deeper lying, and less disturbed rock. These discontinuities may be both natural surfaces and fractures opened by blasting in preparing the site. The test conditions and results should be carefully evaluated and related to the likely foundation conditions of the structure where the rock may be either more or less stress relieved depending on such factors as the method of preparation of the bearing surface, and whether geological conditions at the test site are representative of the overall foundation. Other features of the stress-strain curves in Fig. 3.4 are the permanent deformation that occurs after the removal of the load, and the envelopes indicating the relationship between stress and deformation with increasing stress. The permanent deformation is the result of both closure of discontinuities, and

crushing of rock in areas of stress concentration. In the case of the gneiss, the permanent deformation has stabilized after two cycles, whereas in the weaker sandstone, there is additional deformation after each cycle, possibly as the result of progressive rock fracture. The changing modulus of the rock mass with incrementally increasing load is shown by the deformability envelope as illustrated in Fig. 3.4. If the envelope is concave downwards (Fig. 3.4(a)), this demonstrates an increasing modulus with load as the discontinuities close (as discussed above) which would be favorable for foundation stability. However, a concave upwards envelope (Fig. 3.4 (b)), may indicate the development of plastic processes in the rock and the possibility of creep in the foundation. The deformation properties of rock masses is usually only of concern for weak rocks where there is a possibility of creep or excessive deformation in the foundation. In contrast, for foundations in strong rock the stresses are usually well below the plastic limit so that settlement will be elastic with no time dependency and there is less need for extensive in situ testing. An example of deformation moduli measurements of weak rocks are a series of plate load tests carried out in Poland as part of the

ROCK STRENGTH AND DEFORMABILITY

foundation investigation and design work for two gravity dams (Thiel and Zabuski, 1993; Thiel, 1974). One site is in the Carpathian Mountains where the predominant rock types are flyschs, and limestones, marls and shales. The beds in these units are generally steeply dipping, but the rocks are highly tectonically disturbed, faulted, and contain irregularly spaced orthogonal jointing; the shale usually occurs as a weak and degradable interbed. The other site is in the Brystrzyckie Mountains where the rock is a distinctly foliated and anisotropic mica schist containing biotite and muscovite aligned parallel to the foliation.

57

The plate load tests were set up in tunnels and comprised a set of four hydraulic jacks, applying a vertical load, that were capable of applying a maximum pressure of 4 MPa (580 p.s.i.) to a sample with an area of 2 m2 (21.5 ft2). Multistage testing was carried out with the load increased in 0.08 to 0. 2 MPa increments to a maximum pressure that was 1.5–2 times the maximum design bearing pressure in the foundation. Creep measurements were also carried out by applying a constant load for up to 30 hours, with the test being terminated when the creep rate was less

Table 3.2 Deformation moduli for very poor quality rock determined by plate load tests (Thiel and Zabuski, 1993) Rock type

Geological characteristics RMR ≈ 45 to 18

Sandstone

Deformation modulus MPa

Sandstone containing shale interbeds comprising 5–10% of rock; layer thickness 500–1500 mm (20–60 in) Shale/sandstone Interbedded sequence with approximately equal proportions of shale and sandstone; layer thickness 300–600 mm (12–25 in.): Slightly folded and fractured Highly folded and fractured Shale Interbedded sequence of clay shale with 5–10% sandstone, very highly folded and fractured; layer thickness less than 300 mm (<12 in) Limestone Interbedded with clayey-shale infilling, infilling thickness 1–5 mm (0. 04–0.2 in); layer thickness 60–200 mm (2–8 in) Marl Layer thickness 15–150 mm (0.6–6 in) Clayey shale Layer thickness less than 1 mm (<0.04 in) Mica schist Biotite/muscovite Muscovite/biotite

than 0.01 mm (0.0004 in) per hour over four hours. Table 3.2 shows the deformation moduli measured in the plate load tests for a variety of very weak rocks. The quality of these rocks has been expressed in terms of the rock mass rating (RMR) and had values of between 18 and 45 which are characterized as poor quality rock. The RMR rating system is described in more detail in Section 3.2.6 and Fig. 3.10 shows the relationship between RMR values and the in situ deformation moduli for a wide range of rock quality. The possibility of permanent deformation of foundation rocks should be considered for dams subjected to significant cyclic loading as a result of fluctuations in reservoir level. As shown in Fig. 3.5,

10

3–5 1.5–2.0 0.3–0.8

2.1 1.6 0.4 4.5 1.3

incremental inelastic deformation may occur with each cycle, with the greatest deformation occurring in the center of the dam where the foundation is the most heavily loaded. Such differential settlement can induce fractures in the structure. The plate load tests, reported in Table 3.2, also measured the permanent deformation resulting from cyclic loading and found, for these particular conditions, that significant permanent deformation occurred for rocks with deformation moduli less than about 2 GPa (Fig. 3.6).

58

RANGE OF ROCK STRENGTH CONDITIONS

Figure 3.5 Permanent deformation of abutments and foundation due to cyclic reservoir levels (Goodman, 1980).

Figure 3.6 Relationship between irreversible displacement dirr and deformation modulus Em for rock masses listed in Table 3.2 (Thiel and Zabuski, 1993).

3.2.3 Size effects on deformation modulus Deformation moduli tests are performed on pieces of rock core, on small volumes of in situ rock, and occasionally by measuring the settlement of structures. Because the objective of these tests is to determine the modulus of large rock masses in foundations, it is necessary to have a means of relating test results from a variety of methods to the modulus of foundation-scale rock volumes. Of

particular importance is the determination of modulus values under earthquake loading. The results of many test methods have been compared to determine if relationships can be established between modulus and test volume. It has been concluded that the following approximate relationship between moduli measured by different methods will generally apply (Raphael and Goodman 1979):

ROCK STRENGTH AND DEFORMABILITY

59

Figure 3.7 Relation between seismic and static moduli as a function of shear wave length in hammer seismic profiles (Raphael and Goodman, 1979).

where Estatic is the modulus for rock loaded by plate bearing, borehole jack or dilatometer/test; Eearthquake is the modulus for rock mass subject to shaking at 1–10 Hz; Eseismic is the modulus for rock mass subject shock waves with frequency of several hundred hertz in seismic geophysical testing; and Eintact rock is the modulus for intact rock specimens. The basis of this relationship is that intact rock samples containing no discontinuities will have the highest modulus, while larger, fractured samples tested in situ will have lower modulus values as a result of closure of the discontinuities. Rock masses subjected to shock waves (seismic or earthquake) will show intermediate modulus values where the stress levels are low and there is less closure of the discontinuities than that induced by the higher stresses in plate load tests. Methods of modulus testing are described in Section 4.5. Values of Estatic have been compared with results determined by seismic testing, Eseismic, and tests in the laboratory on pieces of intact rock core, Eintact rock. Theratio Eseismic/Estatic, which has been determined by Schneider (1967) from tests at 14 different sites, was found to vary between 2 and 13 (Fig. 3.7). This ratio, as well as the wavelength of the shear seismic wave, increases as the fracturing of the rock becomes more intense. The ratio Eseismic/

Estatic increases with closer fracturing because the value of Estatic diminishes significantly when the rock mass is more readily deformed under local loading. Other modulus results have been examined to compare a variety of in situ tests, Estatic, with laboratory tests on pieces of rock core, Eintact, from the same site. These results of 78 such tests have been used to establish values for the ratio Eintact rock/ Estatic as shown in Table 3.3 (Heuze, 1980). Information on the degree of fracturing at these sites is not available. The conclusions that can be drawn from the modulus values determined by different methods of testing are, first, that the modulus of fractured rock diminishes as the discontinuity intensity increases. Second, there is considerable scatter in the results, especially when the volume of rock being tested is large and the properties variable. As a consequence of this scatter, the relationship given in this section between modulus values determined by different methods is only approximate, and for final design purposes, results from a number of test methods are preferred.

60

RANGE OF ROCK STRENGTH CONDITIONS

3.2.4 Discontinuity spacing and modulus

on the rock mass modulus, it is useful

With the very great influence of geological structure

Table 3.3 Ratios Eintact rock/Estatic for various types of field deformability tests Type of test

Number of tests

Mean ratio

Platebearing Full scale deformation Flat jacks Borehole jack or dilatometer Pressure chamber Petit seismique Others

27 14 10 9 8 5 5

3.1 2.4 1.9 3.0 2.2 2.9 2.4

to have a method of relating the properties of the discontinuities to the relationship between laboratory and field modulus values. Goodman and Duncan (1971) describe such a procedure, and Raphael and Goodman (1979) describe the application of the method to the determination of the rock mass modulus of closely fractured rock forming the foundation of a dam in California. Consider an isotropic and linearly elastic rock with elastic constants for the intact rock of Er (Young’s modulus) and vr (Poisson’s ratio). The properties of the discontinuities that determine the relationship between the modulus of the intact rock and that of the rock mass are the fracture spacing S and stiffness k of the discontinuities in each set. The normal stiffness kn of a discontinuity is defined as the normal closure dn that occurs on the application of a normal load a and is given by (Fig. 3.8(a)): (3.1) Normal stiffness of a discontinuity tends to be highly non-linear, with the major portion of the closure taking place at low stress levels. The deformation of discontinuities is defined by their normal and shear stiffnesses kn and ks respectively, where kn is the slope of normal stressnormal displacement curve s/dn, and ks is the slope of the shear stress-shear displacement curve t/ds. Both these parameters can be obtained from the results of direct shear tests to determine the friction angle of discontinuity surfaces. If the spacing of the

discontinuities is S and the modulus of the intact rock is Er, then on application of a normal stress a, the deformations will be as follows (Fig. 3.8(b)):

The total deformation of a rock mass upon application of a stress a is the sum of the rock deformation S(s/Er) and the joint deformation s/kn. Therefore, the deformation modulus of the rock mass Em is related to the properties of the intact rock and the discontinuities by: (3.2) An application of this equation is as follows. The value of Er is determined by laboratory testing and the value of Em by in situ methods such as plate load tests. For a particular set of joints with spacing, S, the stiffness can be calculated. This result can then be used to estimate the influence on rock mass deformation modulus of different discontinuity spacings. Similarly, an equation can be developed for the rock mass shear modulus Gm in the case of shear loading of the model shown in Fig. 3.8: (3.3) where Gr is the shear modulus of the intact rock and ks is the shear stiffness of the discontinuities. Equations 3.2 and 3.3 can be combined to estimate

ROCK STRENGTH AND DEFORMABILITY

61

Figure 3.8 Model of rock mass relating discontinuity stiffness to rock mass modulus: (a) typical normal stress-normal closure behavior of discontinuity in rock; and (b) model of fractured rock mass containing one set of uniformly spaced discontinuities.

the deformation modulus of a rock mass containing several sets of discontinuities inclined at different orientations with respect to the applied load (Chappell and Maurice, 1980). These equations will provide some indication of the influence of the geological structure on the rock mass modulus, and may be of value in interpreting the results of in situ

modulus measurements. 3.2.5 Modulus of anisotropic rock Many rock types exhibit anisotropic strength and modulus, and it is important that the values used in

62

RANGE OF ROCK STRENGTH CONDITIONS

Figure 3.9 Variation in modulus of elasticity with direction of loading in anisotropic (schistose) rock (Pinto, 1970).

design are appropriate for the direction of loading. Typical anisotropic rock types are the sedimentarymetamorphic sequence of shale-slate-phyllite-schist which will usually contain sets of parallel discontinuities and, in the case of schist and phyllite, have low strength mica aligned with these discontinuities. The mass modulus of these rock types is likely to be lower in the direction normal to the orientation of the predominant geological structure as a result of closure of these discontinuities (Fig. 3.9). Laboratory and in situ testing programs have been conducted to determine elastic constants in directions parallel and perpendicular to the orientation of the predominant geological structure in anisotropic rock. The modulus ratio is known as the degree of anisotropy, and is given the term E0/ E90—modulus parallel/perpendicular to planes of weakness (bedding or foliation) in the rock. Surveys

conducted by Lama and Vutukuri (1978a, b) of rock modulus testing programs show that the modulus is usually higher in the direction parallel to the structure and that the degree of anisotropy varies between 1 and 3.2 (Table 3.4). Seismic testing to determine the dynamic modulus shows values of the E0/E90 ratio of between 1.0 and 1.2. These low ratios can be attributed to the low stress levels of seismic testing that produces little closure of discontinuities. Note that the shear strength of anisotropic rock types is usually much lower in the direction parallel to the main structure because displacement will take place more readily along these planes (Section 3.4). Therefore it is important to examine both the direction and type of loading with respect to the orientation of the geological structure in the design of any foundation in these rock types.

Table 3.4 Modulus ratios of anisotropic rock Rock type

E0/E90

Reference

Clay shale Slate Phyllite Schist

1.36–2.86 1.7 1.28–1.33 1.3–3.2

Stepanov and Batugin (1967) Bamford (1969) Lekhnitskii (1966) Pinto (1970)

3.2.6 Modulus-rock mass quality relationships With rock mass modulus being highly dependent on

both the geological structure and the size of the test sample, Bieniawski (1978) has proposed a method of estimating in situ modulus from an index which

ROCK STRENGTH AND DEFORMABILITY

characterizes the overall properties of the rock mass quality. This index is known as the rock mass rating (RMR) and is widely used in the assessment of tunnel support requirements (Bieniawski, 1976). The advantage of this approach is that the index is determined from readily measured parameters: the compressive strength of the intact rock, the characteristics of the discontinuities determined by mapping and drilling, and ground water conditions. Table 3.5 shows the six parameters that describe the rock mass and the rating points that are assigned to each range of values of the parameters. The RMR rating is calculated by adding the points for each

parameter. The influence of discontinuity orientation on foundation performance is taken into account in the settlement and stability analyses, rather than by adjusting the RMR value. An unfavorable joint orientation with respect to settlement would be in a direction at right angles to the load direction resulting in closure of discontinuities and settlement. This contrasts with an unfavorable orientation with respect to sliding, where the discontinuities would be in a direction parallel to the load direction (Chappell and Maurice, 1980).

Table 3.5 RMR classification of jointed rock masses (extract from Bieniawski, 1974) Parameter

Ranges of values

A. Classification parameters and their ratings 1 Strength Point load >8 MPa 4–8 MPa of intact strength rock index material >1.2 ksi 0.6–1.2 0.3–0.6 0.8–0.3 ksi ksi ksi Uniaxial >200 MPa 100–200 compressi MPa ve strength

2

Rating Drill core quality RQD

3

Rating Spacing of joints

4

Rating Condition of joints

15 90%– 100% 20 >3 m (>10 ft) 30 Very rough surfaces Not continuou s No separation Hard joint wall rock

2–4 MPa

1–2 MPa

For this low range

uniaxial compressive test is preferred 50–100 MPa

25–50 MPa

10–25

3–10

1–3

12 75%–90%

7 50%–75%

MPa 4 25%–50%

MPa 2 <25%

MPa 1

0

17 1–3 m (3– 10 ft)

13 8 0.3–1 m 50–300 (1–3 ft) mm (2–12 in) 20 10 Slightly Slicken rough sided surfaces surfaces or Separatio Gouge <5 n <1 mm mm thick or

25 Slightly rough surfaces Separatio n <1 mm

Hard joint wall rock

63

Soft joint Joints wall rock open 1–5 mm Continuou

3 <50 mm (<2 in)

5 Soft gouge >5 mm thick or

Joints open >5 mm Continuous joints

64

RANGE OF ROCK STRENGTH CONDITIONS

Parameter

Ranges of values s joints Rating 25 20 12 6 0 5 Ground Completel Moist Water Severe water problem water y dry only under (interstitia moderate l water) pressure Rating 10 7 4 0 When calculating rock strength using Table 3.7, rating=10; ground water pressures accounted for in stability analysis. B. Rating adjustment for joint orientations Orientation of joints Very Favorable Fair Unfavorab Very unfavorable favorable le 0 −2 −7 −15 −25 Adjustme nt for foundatio ns When calculating rock strength using Table 3.7, adjustment=0; joint orientation accounted for in stability analysis.

The empirical relationship between the RMR rating value and the in situ rock mass modulus is shown in Fig. 3.10. For the seven different projects studied by Bieniawski in developing this relationship, Em is given by the following equation: (3.4) The obvious deficiency of this equation is that it does not give modulus values for RMR values less than 50. Additional studies carried out on rock masses with qualities ranging from poor to very good indicates that the modulus is related to the rock mass rating over the range of about 20–85 by the following equation (Serafim and Periera, 1983): (3.5) 3.3 Compressive strength Compressive strength values of rock are used in the determination of rock mass strength parameters as described below in Section 3.3.2, the bond strengths at the rock-concrete interface in drilled piers and tensioned anchors, for the bearing capacity of spread footings and the calculation of rock mass strengths. In the case of bond strength, empirical relationships have been developed between

compressive strength of intact rock and working bond strengths that have been found to operate satisfactorily in practice. In the case of spread footings where the bearing area is larger than the spacing between discontinuities, the bearing capacity can be calculated from the compressive strength of the rock mass. The following is a discussion on methods of determining the compressive strength of both intact rock, and the rock mass. In many instances it is not necessary to make accurate measurements of compressive strength, particularly during the reconnaissance stage of a project and where the compressive strength is not used directly in foundation design. In these circumstances it is satisfactory to make an estimate of the compressive strength based on observations of the in situ rock condition and simple field tests. Table 3.6 shows the relationship between these descriptions of the rock mass and ranges of uniaxial compressive strength. For comparison purposes, the soil descriptions and strengths are also

ROCK STRENGTH AND DEFORMABILITY

65

Figure 3.10 Relationship between in situ modulus and rock mass rating (Bieniawski, 1978; Serafim and Pereira, 1983). Table 3.6 Classification of rock material strengths (ISRM, 1981) Grade Description R6

Extremely strong rock

R5

Very strong rock

R4

Strong rock

R3

Medium weak rock

R2

Weak rock

R1

Very weak rock

R0 S6 S5 S4

Extremely weak rock Hard clay Very stiff clay Stiff clay

Field identification Specimen can only be chipped with geological hammer Specimen requires many blows of geological hammer to fracture it Specimen requires more than one blow with a geological hammer to fracture it. Cannot be scraped or peeled with a pocket knife; specimen can be fractured with single firm blow of geological hammer Can be peeled with a pocket knife; shallow indentations made by firm blow with point of geological hammer Crumbles under firm blows with point of geological hammer; can be peeled by a pocket knife Indented by thumbnail Indented with difficulty by thumbnail Readily indented by thumbnail Readily indented by thumb but penetrated only with great difficulty

Approximate range of compressive strength MPa

(p.s.i)

>250

(>36 000)

100–250

(15 000–36 000)

50–100

(7 000–15 000)

25–50

(3 500–7 000)

5–25

(725–3 500)

1–5

(150–725)

0.25–1 >0.5 0.25–0.5 0.1–0.25

(35–150) (>70) (35–70) (15–35)

66

RANGE OF ROCK STRENGTH CONDITIONS

Grade Description

Field identification

Approximate range of compressive strength MPa

S3

Firm clay

S2

Soft clay

S1

Very soft clay

Can be penetrated several inches by 0.05–0.1 thumb with moderate effort Easily penetrated several inches by 0.025–0.05 thumb Easily penetrated several inches by fist <0.025

shown in Table 3.6. The letter designations (R0 etc.) can be used on drill logs and field mapping sheets to record the rock strength values (Appendix II). 3.3.1 Compressive strength of intact rock The compressive strength of intact rock can readily be measured using either a compression machine or a point load tester (Fig. 3.11(a)). The compression machine gives the more precise results but it is necessary to prepare the samples in the manner described in Section 3.2.1 on modulus testing. Estimation of compressive strength with the point load testing equipment has the advantage that tests can be conducted on lengths of unprepared core in axial and diametral directions, as well as on irregular lumps of rock (ISRM, 1985). The equipment is portable and can readily be used in the field. The principle of operation is that a compressive load is applied through two conical platens which causes the rock to break in tension between these two points. If the distance between the platens is D and the breaking load is P, then the point load index, Is is given by: (3.6) where De, the equivalent core diameter is given by: or and . A is the minimum cross-sectional area of a lump sample for a plane through the platen contact points, where W is the specimen width. The size-corrected point load strength index Is(50)

(p.s.i) (7–15) (4–7) (<4)

of a rock specimen or sample is defined as the value of Is that would have been measured by a diametral For tests conducted on test with samples with dimensions different from 50 mm, the results can be standardized to a size-corrected point load strength index by applying a correction factor kPLT as follows: (3.7a) The value of the size correction factor kPLT is shown in Fig. 3.11(b) and is given by: (3.7b) It has been found on average that the uniaxial compressive strength is about 20–25 times the point load strength index. However, tests on many different types of rock show that the ratio can vary between 15 and 50, especially for anisotropic rocks. Consequentially, the most reliable results are obtained if a series of uniaxial compression tests are carried out to calibrate the point load tests. Point load test results are not acceptable if the failure plane lies partially along a pre-existing discontinuity in the rock, or is not coincident with the line between the platens. For tests in weak rock where the platens indent the rock, the test results should be adjusted by measuring the amount of indentation and correcting the distance D. 3.3.2 Compressive strength of fractured rock Fractured rock will, of course, have a much lower compressive strength than intact rock. Studies have been conducted on the load capacity of mine pillars which demonstrate the decrease in strength that occurs as the sample size is increased (Bieniawski, 1968; Pratt, 1972). These tests show that once the

ROCK STRENGTH AND DEFORMABILITY

67

Figure 3.11 Point load testing (ISRM, 1985): (a) point load test equipment; and (b) relationship between sample equivalent core diameter De and size correction factor kPLT.

side length is greater than about 1 m (3 ft) there is little decrease in strength with larger samples (Fig. 3.12). The minimum strength is about 20–30% of the maximum strength measured on core samples, provided that the sample contains no through-going plane that would control the rock strength.

It is difficult to determine the compressive strength of fractured rock in the laboratory. First, it is necessary to obtain undisturbed samples of fractured rock, and then second to test a sufficiently large sample that is representative of the discontinuity conditions. To avoid the expense of carrying out

68

RANGE OF ROCK STRENGTH CONDITIONS

Figure 3.12 Effect of specimen size on measured uniaxial strength (Heuze, 1980).

laboratory testing, it is usual to use empirical relationships between the rock mass strength and the discontinuity characteristics as described in this section. For most foundations, the rock is loaded in a triaxial stress field consisting of the foundation load and the confinement produced by the surrounding rock. Therefore, in calculating the bearing capacity of the rock, it is necessary to have a strength criterion that is expressed in terms of the principal stresses acting on the rock, and takes into account the characteristics of the fractured rock mass. Such a criterion will allow the state ofstress at any point in the foundation to be compared with the rock mass strength at that point, which will identify areas where there is excessive compressive stress, or tensile stress, so that the design can be modified accordingly. This approach is useful in the case of dam foundations where the stress distribution is usually non-uniform across the bearing surface, and also for foundations located on the crest of steep slopes. A strength criterion for fractured rock has been developed by Hoek (1995, 1988) and Hoek and Brown (1988) which can be applied readily to the design of foundations. This is an empirical criterion that has been developed by trial and error and is

based on the observed behavior of rock masses, model studies to simulate the failure mechanism of jointed rock, and triaxial compression tests of fractured rock. Hoek’s expression for the maximum at failure is: principal effective stress (3.8) where is the minimum principal stress or confining stress; su(r) is the uniaxial compressive strength of the intact rock; and m and s are dimensionless constants. It is assumed that failure process is defined by the major and minor principal stresses and that the intermediate principal stress has no particular influence on failure (Jaeger and Cook, 1976). The constants m and s depend on both the rock type and the discontinuity characteristics. The values of m and s given in Table 3.7 are those of disturbed rock because of the loosening that occurs in surface excavations made for foundations. In using Table 3.7 it is necessary to define the condition of the rock mass in terms of one of five categories of rock type, one of six categories of rock quality, and the intact rock strength. The rock quality categories vary from intact rock, to weathered, heavily fractured rock, or rock fill, with each category defined either by a description of the rock mass or

ROCK STRENGTH AND DEFORMABILITY

by the RMR quality rating (see Table 3.5). Where possible, the strength values determined from equation 3.8 are compared with other sources of

69

rock strength such as those obtained from the back analysis of failures of slopes

Table 3.7 Approximate relationship between rock mass quality and material constants (Hoek and Brown, 1988)

70

RANGE OF ROCK STRENGTH CONDITIONS

Figure 3.13 Strength of fractured rock (Hoek, 1983).

in similar geological conditions (see Fig. 3.21 and

Table 3.8).

ROCK STRENGTH AND DEFORMABILITY

The typical shape of the strength envelope defined by equation 3.8 is shown in Fig. 3.13. The steep gradient of this curve clearly demonstrates that has a significant increasing confining pressure effect on improving the strength and bearing capacity of the rock. Foundations on steep slopes where there is little confining pressure and loosening of the rock mass can occur, will have a lower bearing capacity than foundations on a continuous horizontal surface where the bearing rock is confined. The curve in Fig. 3.13 also shows that the uniaxial compressive strength of the rock mass su(m) is defined by the following equation: (3.9) or (3.10) Equation 3.10 shows that the ratio su(m)/su(r) diminishes rapidly as the rock becomes more fractured, and that the rock mass has essentially zero compressive strength when the discontinuity spacing is less than about 0.3 m (parameter . This relationship between the compressive strengths of the rock mass and intact rock can be compared with the rapid decrease in rock mass strength with specimen size shown in Fig. 3.12. 3.4 Shear strength Where a structure is located on a steep slope, or where lateral loads are substantial such as in a dam foundation, shear failure of the entire foundation can take place even though the bearing stress is well below the allowable bearing capacity of the rock. The shear failure surface may, in strong, jointed rock, lie on a single discontinuity oriented subparallel to the direction of the applied load (see Fig. 3.1(e)), or in weak, closely fractured rock follow a path comprising both discontinuities and intact rock (see Fig. 3.1(b)). Shear type failures may also occur where a cavity or bed of very weak material underlies the rock in the bearing area and a

71

disk of competent rock punches through into the cavity (see Fig. 3.1(f)). 3.4.1 Mohr-Coulomb materials For all shear type failures, the rock can be assumed to be a Mohr-Coulomb material in which the shear strength of the sliding surface is expressed in terms of the cohesion c and the friction angle . The shear strength t developed when an effective normal stress a’ is acting on a sliding surface is (Fig. 3.14 (a)): (3.11) Equation 3.11 is expressed as a straight line on Fig. 3.14(b) which also shows the relationship between the available shear strength t and the actual shear stress acting in the foundation tf. The foundation will be stable when the ratio t/tf, or the factor of safety FS, is greater than 1.0. Figure 3.14 (b) also illustrates how the factor of safety will diminish if the normal stress is reduced by water pressures acting on the shear plane, or the cohesion is lost as a result of heavy blasting during construction. The following sections describe typical values for friction angle and cohesion and methods of measuring these rock properties. 3.4.2 Shear strength of discontinuities If structural mapping identifies discontinuities in a foundation on which shear type failures may take place, it will be necessary to determine the friction angle and cohesion of the discontinuity surface in order to carry out stability analyses, and design remedial work if required. Data collected in the mapping program will include the roughness of the discontinuity surface, the strength of the rock on the sliding surface, and the thickness and characteristics of any infilling material (Appendix II). All these parameters modify the shear strength of the discontinuity surfaces. (a) Friction angle

72

RANGE OF ROCK STRENGTH CONDITIONS

Figure 3.14 Shear strength of a Mohr-Coulomb material: (a) normal (sf) and shear (tf) forces acting on sliding surface in foundation; and (b) Mohr diagram of linear strength envelope.

For a planar, clean discontinuity in rock, the cohesion will be zero and the shear strength will be defined solely by the friction angle. The following are typical ranges of basic friction angles for a variety of rock types (Barton, 1973; Stimpson, 1975). Generally, fine grained rock and rock with a high mica content will tend to have a low friction angle, while course grained, strong rock will have a high friction angle. The friction angles listed below should be used as a guideline only because actual values will vary widely with site conditions. 1. Low friction rocks—friction angle about 20– 27°: schist, high mica content; shale; marl; 2. Medium friction rocks—friction angle about 27–34°: sandstone; siltstone; chalk; gneiss; slate; 3. High friction rocks—friction angle about 34– 40°: basalt; granite; limestone; conglomerate.

(b) Surface roughness All natural rock surfaces are rough and irregular to varying degrees. These surface irregularities, which are given the general term asperities, produce interlock between discontinuity surfaces which can contribute significantly to their shear strength (Patton, 1966). Asperities can be considered in their simplest form as a series of saw teeth in which the inclination of the face of each tooth is at an angle i. When normal and shear forces are applied to a block of rock containing a saw-tooth discontinuity with no infilling, the shear strength of the discontinuity is: (3.12) This relationship shows that effective friction angle of a rough surface is equal to the sum of the basic friction angle of the rock and the inclination of the asperities (Fig. 3.15). Methods of measuring the inclination angle i of natural discontinuities which consider both the direction of sliding and the scale of irregularities are described in Section 4.2. Another factor to consider in determining the friction angle of a rough surface is that the asperities may be sheared off as displacement occurs with a consequent reduction in the friction angle. With increasing stress levels, there is a transition from dilation to shearing, and the degree to which the asperities are sheared off will depend on both the magnitude of the normal force in relation to the compressive strength of the rock on the discontinuity surface, and the displacement

ROCK STRENGTH AND DEFORMABILITY

distance. A rough discontinuity that is initially undisturbed and interlocked will have a friction known as the peak shear strength. angle of With increasing normal stress and displacement the asperities will be sheared off and the friction angle will progressively diminish to a minimum value of the basic, or residual friction angle of the rock, (Fig. 3.15). Barton (1973) studied the shear strength behavior of artificially produced rough, clean joints and developed the following empirical equation: (3.13) where JRC is the joint roughness coefficient, JCS is the compressive strength of the rock on the discontinuity surface, and a’ is the applied normal stress on this surface. The value of the coefficient JRC can be estimated by comparing the condition of the discontinuity surface with the description of the surface and standard profiles with JRC values ranging from 20 to 5 as shown in Fig. 3.16. The variation in the degree of roughness shown on the

73

profiles is a function of both the wavelength and amplitude of the asperities. Rough surfaces have high amplitude, short wavelength asperities compared with smoother surfaces, and the degree of roughness can be expressed approximately as the ratio between the amplitude and the wavelength. The amplitude/wavelength ratio varies from a high value of about 30% for a JRC of 20 (surface (a)), to a low value of about 3% for a JRC of 5 (surface (c)). The term (JRC log10 JCS/s') is equivalent to the roughness angle i, and is equal to 0 at high stress , and the asperities are levels when sheared off. At low stress levels the ratio JCS/s' tends to infinity and the roughness component of the strength becomes very large. For realistic design values of the roughness component, the term should not exceed about 50°, and the useful range for the ratio JCS/s' is between about 3 and 100. (c) Cohesion The preceding section discussed rough, clean discontinuity surfaces with rock to rock contact and no infilling, in which the cohesion is zero and the shear strength is composed solely of the friction

Figure 3.16 Definition of joint roughness coefficient, JRC (Barton, 1973): (a) rough undulating—tension joints, rough sheeting, rough bedding, ; (b) smooth undulating—smooth sheeting, non-planar foliation, undulating bedding, ; and (c) smooth nearly planar—planar shear joints, planar foliation, planar bedding, .

angle of the rock material. However, cohesion is developed on discontinuity surfaces in many conditions and because even a small cohesive strength can have a significant effect on the shear strength of rock, it is important that this rock

strength parameter be properly accounted for in design. In the worked example discussed in Section 6.2 there is a cohesion of just 25 kPa (3.6 p.s.i.) on a sliding surface with an area of 190 m2 (2045 ft2), and the shear strength due to cohesion is 4.8 MN (1.

74

RANGE OF ROCK STRENGTH CONDITIONS

Figure 3.15 Effect of surface roughness and normal stress on the friction angle of a discontinuty surface.

07E6 lbf). The frictional component of the shear strength due only to the weight of the block is 13.3 MN (3E6 lbf) so the cohesive strength is about one quarter of the total shear strength. This illustrates the importance of both measuring cohesion and using careful blasting during construction that does not disturb the surface and diminish the cohesion. The following are some of the conditions in which cohesion is developed on sliding surfaces. For intact rock and jointed, strong rock masses with no through-going discontinuities parallel to the sliding surface, the cohesion will usually have values of several hundred kilopascals and at these high strengths there is very little risk of shear failure. For rough rock surfaces, an apparent cohesion is developed as the asperities are sheared off when movement occurs. The magnitude of the apparent

cohesion is the intercept on the shear stress axis of a tangent to the curved shear strength envelope on a Mohr diagram (Fig. 3.22); the apparent cohesion will increase with increasing normal stress until the residual strength of the surface is reached. For discontinuities containing infillings, the cohesion will depend on both the characteristics and thickness of the infilling as described in the next section. An indirect method of determining the cohesion of intact rock is to measure the uniaxial compressive strength in a compression machine or point load tester, and tensile strength by means of the Brazilian test on disks of core. This data can be used to generate a Mohr’s envelope, the intercept of which with the shear stress axis gives the cohesion. An application of this method was in the design of footings located on weak limestone beds overlying compressible materials where punching failure of

ROCK STRENGTH AND DEFORMABILITY

the limestone was likely (Kaderabek and Reynolds 1981). To account for the reduced strength of the inplace, fractured rock, the design shear strength was taken as 20% of the strength determined from the laboratory results. This indirect method was used because of the difficulty of performing direct shear tests on intact rock. (d) Infillings If the discontinuity contains an infilling then the shear strength properties of the discontinuity are often modified, with both the cohesion and friction angle of the surface being influenced by the thickness and properties of the infilling. For example, for a clay-filled fault zone in granite, it would be assumed that the shear strength of the discontinuity would be that of the clay and not the granite. In the case of a healed, calcite-filled discontinuity, a high cohesion would only be used in design if it were certain that the discontinuity would still be healed after any disturbance caused by blasting in preparing the foundation. The presence of infillings in a foundation can have a significant effect on performance and it is important that infillings be identified in the investigation program, and appropriate strength parameters used in design. If the infilling thickness is more than about 25–50% of the amplitude of the asperities, then there will be little or no rock to rock contact, and the shear strength properties of the discontinuity will be the properties of the infilling. Figure 3.17 shows the results of direct shear tests carried out to determine the peak friction angle and cohesion of filled discontinuities (Barton, 1974). Examination of these tests shows that the results can be divided into two groups as follows: 1. Clays—montmorillonite and bentonitic clays, and clays associated with coal measures have friction angles ranging from about 8° to 20° and cohesion ranging from 0 to about 200 kPa (4000 p.s.f.). Some cohesion were measured as high as 380 kPa (8000 p.s.f.). 2. Faults, shears and breccias—the material formed in f ault zones and shears in rocks such as granite, diorite, basalt, and limestone will

75

contain clay as well as granular fragments. These materials have friction angles ranging from about 25° to 45°, and cohesion ranging from 0 to about 100 kPa (2000 p.s.f.). The coarser grained rocks such as granites tend to have higher friction angles than finer grained limestones. Some of the tests also determined residual shear strength values. It was found that the residual friction angle was only about 2–4° less than the peak friction angle, while the residual cohesion was essentially zero. An additional factor to consider regarding shear strength is the shear strength-displacement behavior of the discontinuity infilling. In analyzing the stability of foundations, this behavior will indicate whether there is likely to be a reduction in shear strength with displacement, possibly resulting in failure following a small amount of movement. Filled discontinuities can be divided into two general categories, depending on whether there has been previous displacement (Nicholson, 1983; Barton, 1974). These categories are further subdivided into either normally-consolidated (N-C) or over-consolidated (O-C) materials (Transportation Research Board, 1996) as follows. 1. Recently displaced discontinuities—these types include faults, shear zones, clay mylonites, and bedding-surface shears. In faults and shear zones, the infilling is formed by the shearing process, which may have occurred many times and produced considerable displacement. The gouge formed in this process may include both clay-size particles, and breccia with the particle orientation and striations of the breccia aligned parallel to the direction of shearing. In contrast, mylonites and bedding-surface slips are discontinuities that were originally clay bearing and along which slip occurred during folding or sliding (Fig. 3.18). For these types of discontinuities their shear strength will be at or close to the residual

76

RANGE OF ROCK STRENGTH CONDITIONS

Figure 3.17 Peak shear strength of filled discontinuities (Barton, 1974). Note that pairs of numbers indicate ranges of strength.

strength and there will be little reduction in strength with further shearing (Fig. 3.18, graph I). Any cohesive bonds that existed in the clay due to previous over-consolidation will have been destroyed by shearing, and the infilling will be equivalent to the normally consolidated state. However, with increased water content, strain softening may occur resulting in a further reduction in strength. For infillings of displaced discontinuities, peak shear strengths may be used in design. 2. Undisplaced discontinuities—infilled discontinuities that have undergone no previous displacement include igneous and metamorphic rocks that have weathered along discontinuity surfaces to form clay layers. For example, diabase weathers to amphibolite and eventu ally to clay. Other undisplaced discontinuities

include thin beds of clay and weak shales that are sometimes found with sandstone in interbedded sedimentary formations. Hydrothermal alteration is another process that forms infillings that can include low-strength materials such as montmorillonite, and highstrength materials such as quartz and calcite. The infillings of undisplaced discontinuities can be divided into normally-consolidated (NC) and over-consolidated (O-C) materials that have significant differences in peak strength values, but similar residual strengths (Fig. 3.18, graphs II and III). While the peak shear strength of over-consolidated clay infillings may be high, there can be a significant loss of strength due to softening, swelling and pore-pressure changes on unloading. Unloading occurs when rock is excavated for a foundation or slope, for

ROCK STRENGTH AND DEFORMABILITY

77

Figure 3.18 Simplified division of filled discontinuities into displaced and undisplaced, and normally-consolidated (N-C) and over-consolidated (O-C) categories.

example. Strength loss also occurs on displacement of brittle materials such as calcite, but there is little strength loss with sand and gravel infillings. For infillings of undisplaced discontinuities, residual shear strengths should be used in design.

3.4.3 Shear strength testing The friction angle of a rock surface can be determined in the laboratory using the direct shear test equipment shown in Fig. 3.19. This is portable equipment that can be used in the field if required, and is ideally suited to testing samples with dimensions up to about 75 mm (3 in), such as NQ and HQ drill core. The most reliable values are obtained if a sample with a smooth, planar surface

78

RANGE OF ROCK STRENGTH CONDITIONS

Figure 3.19 Equipment for performing direct shear tests on rock fractures with diameters up to about 75 mm. True vertical displacement= gauge reading×(a/b).

is used because it is found that with an irregular surface, the test results can be difficult to interpret. The test procedure consists first of using plaster of Paris or sulphur to set the two halves of the sample in a pair of steel boxes. Particular care is taken that the two pieces of core are in their original, matched position and the discontinuity surface is exactly parallel to the direction of the shear force. A normal load is then applied using the cantilevers and the shear load is gradually increased until a sliding failure occurs. Dial gauges or LVDT’s (linear variable differential transformers) are used to measure both the shear and horizontal displacements from which a pair of plots of shear displacement against shear stress, and shear displacement against normal displacement is produced (Fig. 3.20(a)). Examination of the shear stress-shear displacement plot will usually show an approximate peak shear stress. The normal stress at this shear stress value is calculated from the applied normal load and the contact area, with a correction made for the decrease in contact area that takes place with shear displacement. The sample is then

reset to its original position, the normal load increased and another shear test conducted. Each test will produce a pair of peak shear stress-normal stress points which are plotted to determine the friction angle of the surface (Fig. 3.20(b)). The plots of shear and normal displacement (ds and dn respectively) are used to estimate the surface roughness angle (i) of the sample as follows: (3.14) This value of i is then subtracted from the friction angle calculated from the plot of shear and normal stresses at failure to obtain the basic friction angle of the rock. In some cases, the shear test can be conducted on a sawn sample so that there is no roughness component of the friction angle. The first test on any sample will often give a higher than the (peak) shear strength (symbol subsequent tests (residual shear strength, symbol because the interlock between the surface asperities will be progressively sheared off with each test at increasing normal loads as shown by the curved shear strength envelope shown in Fig. 3.20(b). The

ROCK STRENGTH AND DEFORMABILITY

79

Figure 3.20 Typical results of a direct shear test to determine the friction angle of a fracture surface: (a) plots of shear displacement against shear stress and normal displacement; and (b) plot of normal stress against shear stress.

degree to which the asperities are sheared off will, of course, depend on the ratio JCS/s' (refer to equation 3.13), with the asperities being sheared off readily when the value of the ratio is low. Note that the

shear strength envelope for a clean discontinuity with no cohesion passes through the origin of the Mohr diagram. It is rarely possible to measure the cohesion of a

80

RANGE OF ROCK STRENGTH CONDITIONS

surface with the direct shear test because if the cohesion is very low, it is difficult to obtain an undisturbed sample, and with higher cohesion, the plaster of Paris holding the sample is likely to fail before the sample shears. 3.4.4 Shear strength of fractured rock Structures founded on fractured rock containing no distinct discontinuity surface on which sliding can take place may still fail in shear if the shear strength of the rock mass is exceeded. The rupture surface will be composed of both natural discontinuities and shearing through intact rock. Because of the difficulty and expense of sampling and testing large samples of fractured rock, two em-pirical methods of determining the friction angle and cohesion of rock masses are described in this section. In both methods it is necessary to categorize the rock mass in terms of the intact rock strength and the characteristics of the discontinuities. This requires considerable experience and it is advisable to compare the strength values obtained by both methods to check that consistent values are used in design. (a) Back analysis of failures The strength of a rock mass can be found by carrying out a back analysis of a failed slope or foundation. This involves performing a stability analysis with the factor of safety set at 1.0 and using

available information on the position of the failure surface, the ground water conditions at the time of failure, and the foundation load if applicable. There are, of course, two unknowns in this analysis: the friction angle and the cohesion. By carrying out a number of stability analyses with a range of cohesion values it is possible to calculate a corresponding value for the friction angle (at and prepare a plot of cohesion against friction values can be angle. From this plot a pair of selected for design purposes. Hoek and Bray (1981) describe the back analysis of three different slope failures from which rock mass strengths were determined (Section 1.6.3). If it is not feasible to carry out a back analysis in similar geological conditions to that in which the foundation is to be constructed, it is possible to use published results of strength values as shown in Fig. 3.21. Figure 3.21 shows the results of back analyses of slope failures in a variety of geological conditions, and the shear strength parameters (c and values) calculated at failure at the sites listed in Table 3.8. The properties of the rock mass are categorized according to the strength of the intact rock, and the discontinuity characteristics— spacing, orientation and surface properties. By adding additional points to Fig. 3.21 for local geological conditions, it is possible to draw up a readily applicable rock mass strength design chart for shear type failures.

Table 3.8 Source of shear strength data plotted in Fig. 3.21 Point number Material 1 2 3 4 5 6

Disturbed quartzites Soil

slates

and

Location

Slope height m (ft)

Reference

Knob Lake, Canada

–

Coates et al. (1965)

Jointed porphyry Rio Tinto, Spain Ore body hanging wall in Grangesberg, Sweden granitic rocks Rock slopes with slope angles of 50° to 60° Bedding planes in Somerset, England limestone

–

Whitman and (1967) 50–110 (150–360) Hoek (1974) 60–240 (200–800) Hoek (1974)

Bailey

300 (1000)

Ross-Brown (1973)

60 (200)

Roberts and Hoek (1972)

ROCK STRENGTH AND DEFORMABILITY

Point number Material

Location

Slope height m (ft)

Reference

7

London clay

England

–

8 9 10 11 12 13 14 15 16

Gravelly alluvium Faulted rhyolite Sedimentary series Koalinized granite Clay shale Clay shale Chalk Bentonite/clay Clay

– – – 75 (250) – – 15 (50) – –

17

Weathered granites

Pima, Arizona Ruth, Nevada Pittsburgh, Pennsylvania Cornwall, England Fort Peck Dam, Montana Gradiner Dam, Canada Chalk cliffs, England Oahe Dam, South Dakota Garrison Dam, North Dakota Hong Kong

Skempton and Hutchinson (1969) Hamel (1970) Hamel (1971a) Hamel (1971b) Ley (1972) Middlebrooks (1942) Fleming et al. (1970) Hutchinson (1970) Fleming et al. (1970) Fleming et al. (1970)

13–30 (40–100)

18

Weathered volcanics

Hong Kong

30–100 (100–300)

19 20

Sandstone, siltstone Argillite

Alberta, Canada Yukon, Canada

240 (800) 100 (300)

(b) Curved shear strength envelopes (HoekBrown strength criterion) In conditions where the characteristics of a fractured rock mass can be defined in terms of an RMR rating (Table 3.5), the shear strength can be defined by a curved envelope given by the following equation (Hoek, 1998, 1983): (3.15) is the where t is the shear stress at failure, and instantaneous friction angle at given values of t and s'. The value of is the inclination of the tangent to the Mohr failure envelope at the point (s, t) as shown in Fig. 3.22 and is given by: (3.16) where (3.17) (3.18)

81

Hoek and Richards (1974) Hoek and Richards (1974) Wyllie and Munn (1979) Wyllie (1977)

The dimensionless constants m and s depend on the rock type and the degree of fracturing of the rock mass and are defined in Table 3.7 in Section 3.3. The instantaneous cohesion ci is the intercept of the line defining the instantaneous friction angle on the shear stress axis, and is given by: (3.19) The features of the curved shear strength envelope are that at low normal stress levels, the blocks of rock are interlocked and the friction angle is high, whereas at higher normal stress levels, shearing of the rock is initiated with the result that the friction angle diminishes. The cohesion progressively increases with the normal stress as a result of the greater confinement of the rock mass. The procedure for using the curved strength envelopes in stability analysis is to determine the normal stress levels acting on a potential failure surface in the foundation and calculate the instantaneous cohesions and friction angles in this stress range. The stability analysis is carried out in the normal manner, except that a range of ci and values are used corresponding to the variation in

82

RANGE OF ROCK STRENGTH CONDITIONS

Figure 3.21 Relationship between friction angles and cohesive strength mobilized at failure for the analyzed slopes listed in Table 3.8 (Hoek and Bray, 1981).

normal stress distribution along the sliding surface (see Chapter 6).

3.5 Tensile strength Tensile stresses are very rarely permitted in the design of structures in rock because the tensile

ROCK STRENGTH AND DEFORMABILITY

83

Figure 3.22 Non-linear Mohr envelope for shear strength of fractured rock mass (Hoek, 1983).

strength of a fractured rock mass is effectively zero. Some loading conditions that will result in the development of tensile stresses are tie-down anchors for structures subject to uplift loads such as towers and submerged tanks, and overturning moments as a result of high wind/seismic/water loading on tall structures. While tensile testing of rock is not commonly carried out, the following is a summary of possible methods. Direct testing in pure tension gives the most reliable results, and can be performed by gluing steel platens to the ends of a core sample. The platens are attached to the testing machine with chains or cables so that there are no bending moments developed as the load is applied. Indirect testing methods include bending tests on lengths of core, and the Brazilian test which involves applying a diametral compressive stress to a disk of rock. The indirect test methods are relatively simple to perform but the test results can be difficult to interpret. In general, it is recommended that the test method simulate the actual loading condition in the foundation as closely as possible. Lama and Vutukuri (1978a, b) have carried out a survey of tensile strength tests carried out on laboratory samples of intact rock. Comparison of these results with compressive strengths of intact rock shows that the ratio between the tensile and compressive strengths st(r)/su(r) lies within a narrow

range. The majority of these rocks have tensile strengths which are about 4–7% of the compressive strength, while some sedimentary rocks show st(r)/su (r) ratios of 14–16%. One test carried out on schist showed st(r)/su(r) ratios of 6% and 1% in directions perpendicular and parallel respectively to the foliation. The non-linear Mohr strength envelope developed by Hoek (Hoek and Brown, 1988; Hoek, 1983) also approximates the tensile strength of a fractured rock mass as: (3.20) Evaluation of this equation shows that for a good quality rock mass—slightly weathered rock, , discontinuity spacing 1–0.3 m —and a compressive strength of intact rock of 80 MPa, the tensile strength is . This approximately 0.4 MPa result illustrates that the tensile strength of the fractured rock mass is significantly less (1/200) than the compressive strength of the intact rock. 3.6 Time-dependent properties The design of a foundation must consider its long term performance because, unfortunately, rock properties change with time (Deere and Patton,

84

RANGE OF ROCK STRENGTH CONDITIONS

1971). These property changes include weathering that results in loss of bearing capacity, swelling resulting in uplift of the structure, creep resulting in long term settlement and fatigue resulting in fracture of the rock (Fig. 3.23). The following is a discussion on the geological, environmental and mechanical conditions that can cause foundation conditions to change with time (see Section 5.3). 3.6.1 Weathering Weathering can be either a surface phenomenon in which case it may be visible and therefore controllable, or it may occur beneath the exposed surface and can be difficult to detect (Fig. 3.23(a)). In either case, the depth and extent of weathering can be highly variable and in conditions where the rock is susceptible to weathering, thorough exploration programs are required to detect any zones of weakness such as solution cavities, scour channels, compressible seams or low strength formations. Table 3.9 lists weathering grades and descriptions based on visual examination of field samples that can be used in investigation programs. The processes of weathering are divided into those which cause disintegration and those which cause decomposition as described in this section (Krynine

Table 3.9 Weathering and alteration grades (ISRM, 1981)

Grade Term I II

III

IV

V VI

Fresh

and Judd, 1957). (a) Disintegration weathering Disintegration of rock is the result of cyclical changes in environmental conditions such as wetting and drying, and freezing and thawing. In addition, weathering will be accelerated where the foundation is exposed to wind or flowing water resulting in fragments of weathered rock being continuously removed to expose a new surface and start another weathering cycle. Rock types which are susceptible to disintegration weathering are sedimentary rocks such as weak sandstones and shales, particularly if they contain swelling clay, and metamorphic rocks with a high mica content. (b) Decomposition weathering Decomposition refers to the changes in rock produced by chemical agents such as oxidation, hydration, carbonation and the chemical effects of vegetation. Oxidation is the process whereby oxygen is added to the minerals composing the rock as seen, for example, as yellow discoloration in rocks containing iron. An example of hydration, which is the chemical addition of water to minerals, is the decomposition of the feldspar in granite to form clay of the kaolinite type. Carbonation is the solution of the rock material by water containing a considerable amount of carbon dioxide, which is the case in most surface waters.

Description

No visible sign of rock material weathering; perhaps slight discoloration on major discontinuity surfaces. Slightly weathered Discoloration indicates weathering of rock material and discontinuity surfaces. All the rock material may be discolored by weathering and may be somewhat weaker externally than in its fresh condition. Moderately weathered Less than half of the rock material is decomposed and/or disintegrated to a soil. Fresh or discolored rock is present either as a discontinuous framework or as corestones. Highly weathered More than half of the rock material is decomposed and/or disintegrated to a soil. Fresh or discolored rock is present either as a discontinuous framework or as corestones. Completely weathered All rock material is decomposed and/or disintegrated to soil. The original mass structure is still largely intact. Residual soil All rock material is converted to soil. The mass structure and material fabric are destroyed. There is a large change in volume, but the soil has not been significantly transported.

ROCK STRENGTH AND DEFORMABILITY

85

Figure 3.23 Time-dependent effects on rock foundations: (a) weathering: surface disintegration and solution; (b) uplift due to swelling of clay seams; (c) settlement due to rock creep; and (d) fatigue failure due to cyclic loading.

Rock types which have a low solubility are dolomite, calcite and strong limestone, while some high-solubility rocks are halite, gypsum and sylvite. Vegetation also contributes to weathering because organic acids formed when vegetation decays tend to increase the solution power of natural water. Another type of decomposition weathering is that of rocks containing sulfides such as pyrrhotite which

release sulphuric acid that attacks concrete and steel, and has harmful environmental effects if the acidic water reaches the ground water. Where weathering occurs at depth in the foundation, it will preferentially be initiated along discontinuities which are the flow paths for ground water seepage. Where the rock is soluble, ground water seepage may develop cavities in the

86

RANGE OF ROCK STRENGTH CONDITIONS

foundation, while in other cases there may be reduction in shear strength as low strength materials form on the discontinuity surfaces. Particular attention should be paid to weathering where construction, such as filling of a reservoir, will change the ground water conditions resulting in saturation and increased seepage that may accelerate weathering and rock degradation. Common methods of controlling weathering of foundation rock are protection of exposed bearing surfaces with shotcrete, grouting to minimize seepage, and burying the foundation below the frost level. Shotcrete is discussed in Section 10.4 in construction procedures, while grouting is discussed in Chapter 7, related to the construction of dam foundations. 3.6.2 Swelling The causes of swelling in rock can be divided into two broad categories related either to changes in stress conditions, or to chemical reactions (Lindner, 1976). The effect of swell on structures may be overall or differential heave (Fig. 3.23(b)), as well as the development of external pressures in rigid, buried structures. For example, measurement of swelling pressures in Jurassic claystone have recorded values as high as 1400 kPa (200 p.s.i.) after a period of one day (Madsen, 1979) and heaves of more than 100 mm (4 in) have been measured. The usual method of foundation construction on swelling rock is the use of piles that extend to below the depth of potential swelling. As described in Section 8.5, the piles must be capable of withstanding any tensile forces developed by swelling of the ground through which they pass. Also of importance in design is the attachment of all ground supported appurtenances such as services, tunnels and driveways that will undergo relative movement with respect to the pile supported structure. (a) Stress relief There are two common causes of stress relief in rock foundations. First, changes in ground water

conditions, as may be caused by filling a reservoir in the case of dams, or fluctuations in river levels in the case of bridges, can result in internal nonequilibrium swell. Second, reduction in external forces as a result of making a deep excavation, for example, may cause viscoelastic heave. Swelling due to reduction of internal forces in intact rock can occur in rock types such as mudstones, shales and weakly-cemented sandstones. These rocks may undergo large volumetric increases upon the addition of water in a process which is unrelated to chemical reaction; such swelling is also time dependent. The primary reasons for swelling are cation hydration of the particle structure, the attraction of water to the surface of particles, and the interaction of particle force fields. All these phenomenon are influenced by the presence or absence of water. Another factor influencing swell is the cementation of the rock and its ability to resist the tendency for the particles to separate upon contact with water. Heave may also occur as the result of swelling of clay contained in faults or weathered seams. Types of clay that exhibit swelling behavior are montmorillonite, saponite and vermicullite, while non-swelling clays are kaolinite, illite and chlorite (Mitchell, 1976). The potential for swelling can be related approximately to the Atterburg limits and the clay fraction of the sample. When the plasticity index and the clay content are both greater than about 20– 30%, the potential for swelling may be high (Holtz and Gibbs, 1956; van der Merwe, 1964). Identification of swelling clays can also be carried out using X-ray diffraction analysis which will show the proportions of the different types of clay present in a sample. Rocks may also swell as a result of stress relief which takes the form of viscoelastic deformation of the rock on removal of the confining stress. For example, in eastern Canada where the ratio of the horizontal to vertical stress field can be as high as one order of magnitude (Lo, 1978; Sbar and Sykes, 1973), excavation of a few meters of overburden can induce the floor of excavations to buckle or

ROCK STRENGTH AND DEFORMABILITY

‘pop-up’, and the sides of excavations to move horizontally. The heave can take the form of some instantaneous movement, followed by creep. Creep can be partially suppressed by applying an external pressure with tensioned rock anchors, for example (Trow and Lo, 1988). Creep is discussed further in Section 3.6.3. (b) Swelling related to chemical reactions Swelling can result from chemical reactions such as hydration, oxidation or carbonation which create byproducts that occupy a larger volume than the original materials. For example, the addition of water to some types of sulfides can cause very large deformations and pressures (Dougherty and Barsotti, 1972). Hydration causes the conversion of anhydrite (CaSO4) to gypsum (CaSO4.2H2O) which occurs with an expansion in volume which can take place violently (Brune, 1967). Einfalt et al. (1979) discuss tests to measure swelling pressure and the use of sodium chloride solution as a drilling fluid to obtain undisturbed samples of these sensitive materials. Another chemical reaction resulting in swelling is the decomposition of ultrabasic, mainly olivine bearing rock, into serpentine (Widerhofer, 1972). 3.6.3 Creep Creep is the term given to the slow and continuous distortion of rock in response to shearing stresses. Under these conditions rock behaves partly as a viscous liquid in which the relationship between the shear stress t and the shear strain rate e is (3.21)

87

where ? is the dynamic viscosity which has the dimensions force-time/length2. Most rocks exhibit both instantaneous (elastic) deformation and delayed deformation when loaded, and are known therefore as viscoelastic. The general form of a complete strain curve for rock has up to four components (Fig. 3.23(c)). For stress level s1, there is first, the instantaneous strain due to the elastic deformation of the rock, and this is followed by three time dependent strain components. During primary creep (I) the strain rate diminishes with time (transient creep), which is followed by secondary creep (II) during which the strain rate is constant (steady state creep). If the applied stress is near the peak strength, the rock can exhibit tertiary creep (III) in which the strain rate increases with time (accelerating creep) and eventually rupture occurs. At lower stress levels (s2 in Fig. 3.23(c)), deformation will comprise an elastic component, followed by short period of primary creep after which the strain is constant. Of great importance in the design of foundations is the stress level that will initiate creep. It is normal practice to design footings such that the bearing pressure is well below that which would develop the onset of creep. As a guideline on allowable pressures, Table 3.10 shows transition pressures from brittle to ductile behavior at room temperature. Rock types that are susceptible to creep under low pressures are weak clay shales and tar sands, while salt will creep at all stress levels. A series of creep tests were conducted by Hardy et al. (1970) on samples of intact limestone

Table 3.10 Brittle to ductile transition for rocks (Goodman, 1980) Rock type

Gauge pressure, MPa (p.s.i.)

Rock salt Chalk Compaction shale Limestone Sandstone Granite

0 <10 0–20 20–100 >100

(0) (<1500) (0–3000) (3000–15 000) (>15 000)

88

RANGE OF ROCK STRENGTH CONDITIONS

with a uniaxial compressive strength (su(r)) of 62– 76 MPa (9000–11 000 p.s.i.). These tests showed that no creep occurred at stress levels less than about 40% of su(r) and that secondary creep was not initiated at stress levels below about 60% of su(r). If creep were to occur in a foundation, it would be preferable that it be primary or transient creep such that the creep rate rapidly diminished to zero. The rate of primary creep at time t is approximated by the following equation: (3.22) where and a are determined by curve fitting to transient laboratory or in situ creep data. This equation does not express any physical mechanism of creep, but assumes that the decay rate is a linear function of the currently remaining transient creep concentration. (a) Creep mechanisms The mechanism of creep, which is related to both the mineralogy and crystal structure of rock, is somewhat different for different rock types (Dusseault and Fordham, 1993). • Strong rock In rock containing low porosity silicates the dominant creep mechanism is microcrack generation and propagation along grain boundaries, a cumulative and irreversible damaging process that either stabilizes with no further strain (e?0), or accelerates to exhibit tertiary creep and failure (e?8). Under conditions usually found in foundations, these rock cannot display steady-state creep. Dilation accompanies creep in low porosity rocks as polycrystal debonding and microcrack propagation results in volume increases. The presence of water reduces surface energy requirements for microcrack propagation, and apparently ‘dry’ in situ rocks have sufficient moisture to aid hydration of covalent silica bonds with consequent cumulative and irreversible damage. • Carbonates Carbonates are highly soluble in mildly acidic waters and have excellent cleavage compared with most silicates. Thus they can more easily display dislocation behavior, microcracking, crushing, dissolution and fabric deterioration. Under high stresses and with water

flow in joints, carbonates creep through dissolution and plastic yield of reduced area contacts. Marls and argillaceous limestones of intermediate porosity may show rapid creep rates, depending on clay content and whether it exists in discrete bands rather than as a disseminated constituent. • Sandstones Strong, quartzose sandstones usually behave similarly to low porosity silicates and exhibit, at most, some transient creep before stabilizing. However, high porosity, poorly cemented sandstones may undergo an increase in grain packing density on loading which is only time dependent if accompanied by grain-scale creep processes such as solution, microcracking or dislocation glide, or transient pore pressures. For high porosity (>30%) sandstones and chalk under an applied constant stress, the creep rate may suddenly increase due to structural collapse and densification, followed by stabilization (e?0). The creep rate is also related to the grain size, with finer grained rock creeping more than course grained. Creep rates decrease in the following sequence: gypsum sands? chalk?calcarenites? lithic arenites?feldspathic arenites?quartz arenites. • Shales Highly overconsolidated and metamorphic shales and slates tend not to creep except along discontinuities and fissility planes, particularly if they are filled with low friction materials such as graphite, phyllosilicates or gypsum. However, high porosity or chemically susceptible shales will display discontinuity creep as well as bulk creep deformation due to consolidation and deterioration upon exposure to different chemical conditions. Chemical changes can include pyrite alteration, gypsum dissolution or hydration, or stress relief swelling triggered by pore pressure chemistry changes, particularly if the shale contains swelling clays such as smectite. • Salt Saltrocks such as halite and sylvite creep when subject to any appreciable shear stress. Upon stress change they exhibit instantaneous strain followed by creep that is initially rapid but then decelerates (primary creep) to steady state creep constant) if conditions remain constant. However, if microcracking occurs will change and the fabric

ROCK STRENGTH AND DEFORMABILITY

89

Figure 3.24 Simulation of rock creep behavior: (a) spring and dashpot model (Burger substance) simulating creep behavior for rock loaded in uniaxial compression; and (b) typical creep curve for Burger substance.

will adjust to a new equilibrium structure. In general, creep in saltrocks is dependent on both the and the moisture content. stress level (b) Creep simulation The creep behavior of rock can be simulated by models comprising springs and dashpots, with the spring representing elastic strain and the dashpot representing viscous strain. The best simulation of rock creep is provided by a combination of a spring and a dashpot in series and another spring and dashpot in parallel known as a Burger substance (Fig. 3.24(a)). The axial strain with time, e1(t), in a Burger substance subjected to a constant axial stress s1 is (Goodman, 1980):

of viscous flow, G1 determines the amount of delayed elasticity, and G2 is the elastic shear modulus. Values for the viscoelastic constants can be obtained by conducting creep tests either in the laboratory, or in situ by means of radial jacking tests or plate jacking tests. The general procedure is to measure both the elastic strain, and the strain with time from which the strain rate and the intercepts e0 and eB (Fig. 3.24(b)) are determined. The viscoelastic constants are calculated from these measured results using equations 3.24 and 3.25 (Goodman, 1980). (3.24) (3.25)

where is the bulk modulus (assumed to be independent of time), ?1 determines the rate of delayed viscosity, ?2 determines the rate

The constants G1 and ?1 are determined from equation 3.26 where q is the positive distance between the creep curve and the line asymptotic to

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the secondary creep curve at any time t.

(3.27b) (3.26)

A semilog plot of log10 q versus t has intercept (s1/ 3G1) and slope (-G1/2.3?1). (c) In situ creep measurement Estimation of possible creep rates for foundations will require information on the long term deformation characteristics of the in situ rock mass, rather than laboratory testing of intact samples. An important requirement for in situ testing, that may have a duration of days or weeks, is that temperature and humidity be as uniform as possible and similar to conditions that are likely to exist in the actual foundation. This is most easily achieved in a borehole or exploration adit, but is likely to be more difficult at the ground surface. Two common methods of conducting in situ creep tests are the dilatometer test and the plate load test (Goodman, 1980). • Dilatometer: the dilatometer applies a uniform radial stress a to the circumference of a drill hole (radius r) to produce an outward radial displacement ur(t) at the wall of the hole that is measured over time t. The procedure is to conduct a series of tests at sustained pressure increments, for each of which the radial displacement with time is given by: (3.27) For this loading condition there is no change in the mean stress with time, compared with a cylindrical core loaded in uniaxial compression, so there is no term in K (bulk modulus) influencing the time history of radial displacement. The radial displacement with time follows a curve similar to that shown in Fig. 3.24(b) and the viscoelastic constants are calculated as follows. At time the radial displacement is: (3.27a) The asymptote to the displacement-time curve has intercept on the displacement axis:

and slope (sr/?2). The constants G1 and ?1 are again determined from a semilog plot of log10 q versus t (see Fig. 3.24(b)) in which sr/2G1 is the intercept on the time axis and -G1/2.3?1 is the slope. • Plate load test: the plate load test is carried out on a larger volume of rock than is possible with a dilatometer in a drill hole, and will provide information on the creep behavior of the rock mass. Figures 4.17 and 4.18 show typical arrangements for plate load tests. For the test at the surface the reaction is provided by a steel beam secured to the rock with rock anchors, while the test arrangement in the tunnel allows deformation measurements to be made in any direction normal to the tunnel axis. The application of a constant pressure a that is applied suddenly to a flexible bearing plate of circular shape with radius r produces an average displacement at the rock surface. If it is assumed that the rock is incompressible (bulk modulus, and the Poisson’s ratio v equals 0.5, the average settlement varies with time according to: (3.28) The initial displacement d0 is given by (3.28a) and after the delayed elasticity has occurred, the average settlement of the plate tends to the line (3.28b) (d) Viscoelastic constants for in situ rock Creep tests carried out in the laboratory on core samples of intact rock provide information on the viscoelastic properties of the rock under carefully controlled conditions. However, if the possibility of creep in a foundation is of concern, it may be necessary to carry out in situ tests to determine the influence on the creep characteristics of the jointed rock mass, as well as the influence of environmental conditions such as temperature and humidity that will occur in the actual foundation.

ROCK STRENGTH AND DEFORMABILITY

The difference in creep characteristics of intact rock and the rock mass is illustrated by comparing viscoelastic constants obtained from laboratory and in situ tests. Hardy et al. (1970) conducted creep tests on samples of intact Indiana limestone with a unconfined compressive strength of 62–76 MPa (9000–11 000 p.s.i.), a mean grain size of 14 mm and a porosity of 17.2%. The test procedure was to load cylindrical samples with diameter 28.5 mm (1. 12 in) in uniaxial compression by the use of dead weights, and to increase the load in increments. It was found that steady state creep was initiated at a stress level of about 39.5 MPa (5723 p.s.i.), which is about 60% of the uniaxial compressive strength of the rock. The viscoelastic constants obtained in this test are listed in Table 3.11.

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In situ methods for creep testing include the application of radial compression in boreholes (dilatometer), and plate load tests in tunnels and at the ground surface. For example, Pusch (1993) conducted a series of plate load tests at the surface on slightly weathered gneiss with subhorizontal layering to investigate creep behavior of foundation rock. Also, Chin and Rogers (1987) conducted in situ creep tests using a water-filled rubber membrane in 137 mm (5.4 in) diameter, 230 mm (9 in) deep drill holes lined with a segmental cast concrete lining that allowed radial expansion. Application of a water pressure produced a uniform radial pressure to the walls of the drill hole and the radial displacement was mea

Table 3.11 Viscoelastic constants for intact and in situ rock obtained from creep tests Rock type, test method

Applied pressure, MPa (p.s.i.)

Bulk modulus, GPa (106p.s.i)

G1 GPa (106p.s.i)

G2 GPa (106p.s.i)

η1 GPa (106p.s.i)

η2 GPa (106p.s.i)

Limestone, 40 26.2 159 17.2 495 14 617 fresh1 (5723) (3.8) (23.0) (2.5) (71.8) (2.120) Limestone, 0.25 – 0.195 0.22 653 973 502 (35.6) (0.028) (0.032) (94.7) (141.1950) weathered2 Carbonic 0.29 – 0.818 0.186 349 1535 (42.7) (0.118) (0.027) (50.7) (223) shale3 Tuff, 0.15 – 0.339 0.049 355 1010 (21.3) (0.049) (0.007) (51.4) (147) Weathered4 Notes: 1Indiana Limestone, strong, fresh rock—core samples loaded in uniaxial compression (Hardy et al., 1970). 2Limestone, thin bedded, weathered—radial compression loading in borehole (Chin and Rogers, 1987). 3Carbonic shale with clayey shale—radial compression loading in borehole (Chin and Rogers, 1987). 4Tuff, weathered—radial compression loading in borehole (Chin and Rogers, 1987).

sured in four directions with dial gauges mounted horizontally at the mid-height of the cylinder. Tests were carried out in shale, on thin-bedded, weathered limestone and tuff; the calculated values of the viscoelastic constants are shown in Table 3.11. (e) Creep in shear loading An extensive series of tests to determine the creep characteristics of a bedded sandstone-siltstonemudstone sequence under shear load has been carried out for the foundation design of the Ghe Zhou Ba gravity dam in China (refer to Section 7.2.6 and Fig. 7.8(b)). The bedding dips downstream at an angle of about 4°-6° and there are

extensive clay infillings in the bedding planes which are potential sliding surfaces within the foundation. Tests were carried out in the laboratory and in situ with blocks as large as 1700 mm by 11 700 mm with combinations of normal and shear stress ratios, and test durations as long as 70 000 minutes (Tan, 1993). One result of this investigation was to show the shear strength determined in the long term creep test, which simulates the loading condition in the foundation, is significantly less than that shown by the conventional rapid test. The 29 000 minute duration creep test gave cohesion and friction angle values of 4.9 kPa (0.7 p.s.i.) and 11.3° respectively,

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while the rapid test gave cohesion and friction angle values of 29.4 kPa (4.3 p.s.i.) and 16.7°. The tests also showed that creep occurred at shear stress levels as low as 3.9 kPa (0.6 p.s.i.) at a normal stress level of 49 kPa (7.1 p.s.i.) but was linear on a semilogarithmic time plot indicating that secondary creep was taking place. An incremental increase in the shear stress to 11.8 kPa (1.7 p.s.i.) was sufficient to cause increasing strain and rupture of the sample. However, an increase in the normal stress resulted in a corresponding increase in the shear stress required to cause rupture. This testing showed the potential for sliding failures in the foundation and it was decided to strengthen the rock against buckling and dilatancy. These measures included the construction of a concrete apron downstream of the dam and installation of 168 vertical piles, 20 m deep with diameters of 850 mm and 210 mm; the piles were securely attached to the apron and extended to the depth of a more competent sandstone layer. This arrangement provided confinement of the rock between the relatively stiff apron and the sand stone beds. Furthermore, uplift pressures were reduced by constructing an upstream apron and installing a grout curtain and system of drain holes. 3.6.4 Fatigue Foundations of vibrating or rotating machinery may be subjected to stresses which vary with time and result in fatigue failure of the bearing rock (Fig. 2.23 (d)). Such failure could take the form of fracture of intact rock and loosening of fractured rock due to crushing of points of contact between blocks of rock. The results of cyclic loading tests on pieces of intact rock in the laboratory indicate that the fatigue limit of rock may be in the range 10 000– 100 000 cycles. The stress at failure under this loading condition is about 80% of the static strength for compressive loading only, and about 60% of the static strength for tensile loading only. In comparison, for compression-tension loading the

fatigue strength drops to about 30% of the static strength (Brighenti, 1979). The fatigue strength of rock has been studied only to a limited extent and the results obtained have been somewhat contradictory because of the wide range of loading and geological conditions that need to be studied. The loading conditions include vibration frequency, duration, magnitude and sign (compression only, tension only or compression-tension combined). Testing has generally been carried out in the laboratory on samples of intact rock for comminution studies, and the fatigue behavior of fractured rock is less well known. These results are only indicative of the reduction in strength that may occur due to fatigue loading, and a prudent design procedure would be to use a bearing pressure of perhaps 25–50% of the normal static bearing pressure to allow for the loss of strength with time. Another important design consideration is the loss of bearing capacity in cyclic loading due to the progressive loosening of closely fractured rock. 3.7 References Bamford, W.E. (1969) Anisotropy, and the natural variability of rock properties. Proc. Symp. Rock Mech., Sydney, 1–10. Barton, N.R. (1973) Review of a new shear strength criteria for rock joints. Engineering Geology, 7, 189–236. Barton, N.R. (1974) Review of the Shear Strength of Filled Discontinuities. Norwegian Geotechnical Institute, Publication No. 105. Barton, N.R., Lien, B. and Lunde, J. (1974) Engineering classification of rock masses for the design of tunnel support. Rock Mechanics, 6(4), 189–236. Belikov, B.P. (1967) Plastic constants of rock forming minerals and their effect on the elasticity of rock. In Physical and Mechanical Properties of Rock (ed.B. V.Zalesskii) Israel Programme for Scientific Translations, Jerusalem, pp. 124–40. Benson, R.P. (1970) Rock mechanics aspects in the design of the Churchill Falls underground power-house, Labrador. PhD Thesis Univ. of Illinois at UrbanaChampaign.

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Bieniawski, Z.T. (1968) The effect of specimen size on compressive strength of coal. J. Rock Mech. Mining Sci., 5, 325–53. Bieniawski, Z.T. (1974) Geomechanics classification of rock masses and its application in tunnelling. Proc. 3rd Int. Cong. Rock Mech., Denver 2(2), 27–32. Bieniawski, Z.T. (1976) Rock mass classifications in rock engineering. Proc. Symp. Exploration for Rock Engineering (ed. Z.T.Bieniawski), Vol. 1, A.A. Balkema, Rotterdam, pp. 97–106. Bieniawski, Z.T. (1978) Determining rock mass deformability: experience from case histories. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 15, 237–47. Brandon, T.R. (1974) Rock Mechanics Properties of Typical Foundation Rocks. US Bureau of Reclamation, Denver, Rep. REC-ERC-74–10, pp. 61. Brighenti, G. (1979) Reactions of rock to fatigue loading. Proc. 4th Int. Con. on Rock Mechanics, Montreux, Vol. 1, pp. 65–70. Brown, E.T. (1970) Strength of models of rocks with intermittent joints. J. Soil Mech. Fdn. Eng., ASCE, 96, 1935–9. Brune, J.D. (1967) Anhydrite and gypsum problems in engineering geology. Eng. Geol. Bull. A. E. G., 52, 191. Chappell, B.A. and Maurice, R. (1980) Classification of rock mass related to foundations. Int. Conf. on Structural Foundations on Rock, Sydney, pp. 29–35. Coates, D.F., Gyenge, M. and Stubbins, J.B. (1965) Slope stability studies at Knob Lake. Proc. Rock Mech. Symp., Toronto, pp. 35–46. Cording, E.J. (1967) The stability during construction of three large underground openings in rock. Ph. D. Thesis, Univ. 111., Urbana, 111. D’Andrea, D.V., Fischer, R.L. and Fogelson, D.E. (1965) Prediction of Compressive Strength from Other Rock Properties. US Bureau of Mines Report of Investigations, RI 6702, 23. Deere, D.U. and Patton, F.D. (1971) Slope stability in residual soils. Proc. 4th Pan American Conf. on Soil Mechanics and Foundation Engineering, San Juan, p. 87. Dougherty, M.T. and Barsotti, N.J. (1972) Structural damage and potentially expansive sulphide materials. Bull Eng. Geol., Vol. IX(2), 105–25. Dusseault, M.B. and Fordham, C.J. (1993) Timedependent behavior of rocks. Comprehensive Rock Engineering, Pergamon Press, UK, Vol. 3, pp. 119–49. Einfalt, H.-C., Fecker, E. and Gotz, H.-P. (1979) The

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three-phase-system clay-anhydrite-gypsum and its timedependent behavior on saturation with water-base solutions. Proc. 4th Int. Con. on Rock Mechanics, Montreux, Vol. 1, pp. 123–9. Fleming, R.W., Spencer, G.S. and Banks, D.C. (1970) Empirical study of the Behavior of Clay Shale Slopes. US Army Nuclear Cratering Group Technical Report, No. 15. Gerrard, C.M., Davis, E.H. and Wardle, L.J. (1975). Estimation of the settlement of cross-anisotropic deposits using isotropic theory. Univ. Sydney, School Civil Eng., Res. Rep. No. R-191. Goodman, R.E. (1980) Introduction to Rock Mechanics, Wiley, New York, pp. 193–204. Goodman, R.E. and Duncan, J.M. (1971) The role of structure and solid mechanics in the design of surface and underground excavations in rock. Proc. Conf. on Structure, Solid Mechanics and Engineering Design, Part 2, Paper 105, Wiley, New York, p. 1379. Guidici, S. (1979) Measurements of rock deformation in the abutment of an arch dam. Int. Conf. on Rock Mechanics, Montreux, Vol. 2, pp. 167–73. Gysel, M. (1987) Design methods for structures in swelling rock. Int. Conf. on Rock Mechanics, Montreal, pp. 377–81. Haimson, B.C. and Fairhurst, C. (1970) Some bit penetrations characteristics in pink Tennessee marble. Proc. 12th Symp. Rock Mech, Rolla, Missouri, pp. 547–559. Hamel, J.V. (1970) The Pima Mine slide, Pima County, Arizona. Geol. Soc. of America, Abstracts with Programs, 2(5), 335. Hamel, J.V. (1971a) Kimberley Pit slope failure. Proc. 4th Pan-American Conf. on Soil Mechanics and Foundation Engineering, Puerto Rico, Vol. 2, pp. 117–27. Hamel, J.V. (1971b) The slide at Brilliant cut. Proc. 13th Symp. on Rock Mechanics, Urbana, Illinois, pp. 487–510. Hardy, H.R., Jr., Kim, R.Y., Stefanko, R. and Wang. Y.J. (1970) Creep and microseismic activity in geologic materials. Proc. 11th Symp. on Rock Mechanics, AIME, pp. 377–414. Herget, G. (1973) Variation in rock stresses with depth at a Canadian iron mine. Int. J. Rock Mech. Min. Sci., 10, 37–51. Heuze, F.E. (1980) Scale effects in the determination of rock mass strength and deformability. Rock Mechanics 12, 167–92.

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Hoek, E. (1970) Estimating the stability of excavated slopes in opencast mines. Trans. Inst. of Mining and Metall, 79, A109–32. Hoek, E. (1974) Progressive caving caused by mining an inclined ore body. Trans. Inst. of Mining and Metall, 83, A133–9. Hoek, E. (1983) Strength of jointed rock masses. Geotechnique 33,3, 187–223. Hoek, E. (1998) Practical estimates of rock mass strength. Int. J. Rock. Mech. Mining Sci. (in publication) Hoek, E. and Bray, J. (1981) Rock Slope Engineering, 3rd edn. IMM, London. Hoek, E. and Brown, E.T. (1988) The Hoek-Brown failure criterion—a 1988 update. 15th Canadian Rock Mechanics Symposium, Toronto, Canada. Hoek, E. and Richards, L.R. (1974) Rock Slope Design Review. Golder Associates Report to the Principal Govt Highway Engineer, Hong Kong. Holtz, W.G. and Gibbs, H.T. (1956) Engineering problems in expansive soils. ASCE Trans., 121, 641– 8. Hutchinson, J.N. (1970) Field and laboratory studies of a fall in upper chalk cliffs at Joss Bay, Isle of Thanet. Proc. Roscoe Memorial Symp., Cambridge. ICOLD (1993) Rock Foundations for Dams. ICOLD, Bulletin 88, Paris. International Society for Rock Mechanics (ISRM), Committee on Laboratory Testing (1979) Suggested methods for determining the uniaxial compressive strength and deformability of rock materials. Int.J. of Rock Mech., 16(2), 137–40. International Society for Rock Mechanics (1981) Suggested Methods for the Quantitative Description of Discontinuities in Rock Masses. Pergamon Press, UK. International Society for Rock Mechanics (ISRM) (1985) Suggested method for determining point load strength. Int. J. of Rock Mech., 22(2), 53–60. Jaeger, J.C. and Cook, N.G. W. (1976) Fundamentals of Rock Mechanics. Chapman &; Hall, London, p. 99. Kaderabek, T.J. and Reynolds, R.T. (1981) Miami limestone foundation design and construction. ASCE, 107(GT7), pp. 859–72. Kitahara, Y., Fujiwara, Y., Kawamura, M. (1974) The stability of slope during excavation—the method of observation and analysis. Rock Mech. in Japan, II, 187–9. Ko, H.Y. and Gerstle, K.H. (1976) Elastic properties of two coals. Int. J. Rock Mech. and Min. Sci. & Geomech. Abstr., 13, 81–90.

Krynine, D.P. and Judd, W.R. (1957) Principles of Engineering Geology and Geotechnics. McGraw-Hill, New York, p. 84. Kutter, H.K. and Rautenberg, A. (1979) The residual shear strength of filled joints in rock. Int. Conf. on Rock Mechanics, Montreux, Vol. 1, 221–7. Lama, R.D. and Vutukuri, V.S. (1978a) Handbook on the Mechanical Properties of Rocks. Vol. I, Trans Tech Publications, Claustal, Germany, pp. 87–138. Lama, R.D. and Vutukuri, V.S. (1978b) Handbook on the Mechanical Properties of Rocks. Vol. II, Trans Tech Publications, Claustal, Germany, pp 105–48. Lee, C.F. and Lo, K.Y. (1976) Rock squeeze study of two deep excavations at Niagara Falls. Proc. Specialty Conf. on Rock Engineering for Foundations and Slopes, Vol. 1, ASCE Boulder, Co, Boulder CO, pp. 116–31. Lekhnitskii, S.G. (1966) Stress distribution close to a horizontal working of elliptical shape in a transversely isotropic mass with inclined planes of isotropy. Mech. Solids, 1(2), 35–41. Ley, G.M.M. (1972) The properties of hydrothermally altered granite and their application to slope stability in open cast mining. MSc Thesis, London University. Lindner, E. (1976) Swelling rock: a review. Proc. Specialty Conf. on Rock Engineering for Foundations and Slopes, ASCE, Boulder, CO, pp. 141–81. Lo, K.Y. (1978) Regional distribution of in situ horizontal stresses in rocks of southern Ontario. Can. Geotech. J., 15, 371–81. Lo, K.Y. and Hori, M. (1979) Deformation and strength properties of some rocks in southern Ontario. Can. Geotech. J. 16, 108–20. Madsen, F.T. (1979) Determination of the swelling pressure of claystones and marlstones using mineralogical data. Int. Conf. on Rock Mechanics, Montreux, Vol. 1, pp. 237–41. Michalopoulos, A.P. and Triandafilidis, G.E. (1976) Influence of water on the hardness, strength and compressibility of rock. Bull. Assoc. Eng. Geol., XIII (1), 1–22. Middlebrook, T.A. (1942) Fort Peck slide. Proc. ASCE, 107 (Paper 2144), 723. Mitchell, J.K. (1976) Fundamentals of Soil Behaviour. Wiley, New York, pp. 24–46. Nicholson, G.A. (1983) Design of Gravity Dams on Rock Foundations: Sliding Stability Assessment by Limit Equilibrium and Selection of Shear Strength Parameters. Technical Report GL-83–13,

ROCK STRENGTH AND DEFORMABILITY

Geotechnical Laboratory, US Army Engineer Waterways Experiment Station, Vicksburg, MS. Nose, M. (1964) Rock tests in situ, conventional tests on rock properties and design of Kurobegwa No. 4 Dam Trans. ICOLD, Edinburgh, Vol. 1, pp. 219–52. Parker, J. and Scott, J.J. (1964) Instrumentation for room and pillar workings in a copper mine of the Copper Range Company, White Pine, Michigan. Proc. 6th Symp. Rock Mech., Rolla, Missouri, pp. 669–720. Patton, F.D. (1966) Multiple modes of shear failure in rock. Proc. 1st Int. Cong. on Rock Mechanics., Lisbon, Vol. 1, pp. 509–13. Peterson, R. and Peters, N. (1963) Heave of spillway structures on clay shales. Can. Geotech. J., 1(1), 5–15. Pinnaduwa, H.S.W. and Kulatilake, A.M. (1985) Estimating elastic constants and strength of discontinuous rock. ASCE, J. Geotech. Eng., V.111(7), 847–64. Pinto, J.L. (1970) Deformability of schistose rock. Proc. 2nd Cong. Int. Rock Mech., Belgrade, Vol. 1, pp. 491–6. Pratt, H.R. (1972) The effect of specimen size on the mechanical strength of unjointed diorite. Int. J. Rock Mech. & Min. Sci., 9, 513–29. Pusch, R. (1993) Mechanisms and consequences of creep in crystalline rock. Comprehensive Rock Engineering, Pergamon Press, UK, Vol. 1, pp. 227–41 Raphael, J.M. and Goodman, R.E. (1979) Strength and deformability of highly fractured rock. ASCE, 105 (GT11), 1285–300. Reik, G. and Zacas, M. (1978) Strength and deformation characteristics of jointed media in true triaxial compression. Int. J. Rock Mech. Min. Sci. and Geomech. Abstr., 15, 295–303. Roberts, D. and Hoek, E. (1972) A study of the stability of a disused limestone quarry face in the Mendip Hills, England. 1st Int. Conf. on Stability in Open Pit Mining, Vancouver, AIME, New York, pp. 239–56. Ross-Brown, D.R. (1973) Slope design in open cast mines. Ph. D. Thesis, London University. Rowe, R.K. (1982) The determination of rock mass modulus variation with depth for weathered or jointed rock. Can. Geotech. J., 19, 29–43. Ruiz, M.O. (1966) Some technological characteristics of 26 Brazilian rocks. Proc. 1st. Cong. Int. Soc. Rock Mech., Libon, Vol. 1, pp. 115–19. Saint Simon, P.G. R., Solymar, Z.V. and Thompson, W.J. (1979). Dam site investigations in soft rocks of Peace River Valley, Alberta. 4th Int. Conf. on Rock

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Mechanics, Montreux, pp. 553–60. Sbar, M.L. and Sykes, L.R. (1973) Contemporary compressive stress and seismicity in North America, an example of intra-plate tectonics. Geological Survey of America, 84(6), 1861–82. Schneider, B. (1967) Moyens Nouveaux de Reconnaissance des Massifs Rocheux. Supplement to Annales de L’Institut Technique de Batiment et des Travaux Publics, 20(235–6), 1055–93. Sellers, J.B. (1970) The measurement of rock stress changes using hydraulic borehole gauges. Int. J. Rock Mech. Min. Sci., 7, 423–35. Serafim, J.L. and Pereira, J.P. (1983) Considerations of the geomechanics classification of Bieniawski. Proc. Intl. Symp. Eng. Geol. and Underground Construction., Lisbon, pp. 1133–44. Skempton, A.W. and Hutchinson, J.N. (1969) Stability of natural slopes and embankment foundations. State of the art report. Proc. 7th Intl. Conf. on Soil Mechanics, Mexico, Vol. 1, pp. 291–340. Stepanov, V. and Batugin, S. (1967) Assessing the effect of the anisotropy of rocks on the accuracy of stress determinations by the relief method. Sov. Min. Sci., 3, 312–5. Stimpson, B. (1975) Personal communication. Tan, T.K. (1993) The importance of creep and timedependent dilatancy, as revealed from case records in China. Comprehensive Rock Engineering, Pergamon Press, UK, Vol. 3, pp. 709–44. Thiel, K. (1974) Influence of the system of static load on the deformability of rocks in field tests. Proc. Third Cong. of Int. Society of Rock Mechanics, Denver, Vol. 2, pp. 209–15. Thiel, K. and Zabuski, L. (1993) Rock mass investigations in hydroengineering. Comprehensive Rock Engineering, Pergamon Press, UK, Vol. 3, pp. 839–61. Transportation Research Board, (1996) Landslides— Investigation and Mitigation. National Research Council, Special Report 247, Washington, DC. Trow, W.A. and Lo, K.Y. (1988) Horizontal displacements induced by rock excavation: Scotia Plaza, Toronto, Ontario. Can. Geotech. J., 26, 114–21. Tschebotarioff, K. (1973) Foundations, Retaining and Earth Structures. McGraw-Hill, New York pp. 173–83. Underwood, L.B. (1961) Chalk foundations at four major dams in the Missouri River basin. Trans. 8th Cong. on Large Dams, Vol. 1, 23–47.

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van der Merwe, D.H. (1964) The prediction of heave from plasticity index and percentage clay fraction of soils. The Civil Engineer in South Africa, 103–7. van der Vlis, A.C. (1970) Rock classification by the simple hardness test. Proc. 2nd Cong. Int. Soc. Rock Mech., Belgrade, Vol. 2, pp. 23–30. Wuerker, R.G. (1956) Annotated tables of strength of rock. Trans. AIME, Pet. Paper N-663-G. Whitman, R.V. and Bailey, W.A. (1967) Use of computers in slope stability analysis. ASCE, J. of Soil Mech. and Foundation Division, 93, 475–98. Widerhofer, R. (1972) Method of recent Japanese tunnel

construction through ground of expansive character. Int. Sym. for Underground Construction, Lucerne, pp. 146–57. Working Group on Bridge Foundations, Committee on Soft Rock Mechanics, JSCE (1981) Proc. Int. Sym. on Weak Rock, Tokyo, pp. 1303–14. Wyllie, D.C. (1977) Project files. Wyllie, D.C. and Munn, F.J. (1979) Use of movement monitoring to minimize production losses due to pit slope failure. 1st Symp. on Stability in Coal Mining, Miller Freeman Publications, pp. 75–95.

4 Investigation and in-situ testing methods

4.1 Site selection Investigations for foundations follow the usual procedure for geotechnical projects comprising a staged program with the objective of progressively refining the information required for final design. Typically, the four stages of a complete investigation are as follows: 1. Reconnaissance—examination of published geological maps and reports, study of air photographs, gathering of local experience on foundation performance, field visits; 2. site selection—test pits, outcrop mapping, geophysics, index tests of rock properties, limited diamond drilling at alternative sites; 3. preliminary site investigation—diamond drilling of selected site, detailed mapping of out-crops and exploration adits, laboratory testing; 4. detailed investigations—drilling of selected geological features critical to foundation performance, in situ testing, laboratory testing. A distinguishing feature of investigations for rock foundations is that it is particularly important to focus on the details of the structural geology. For example, the.orientation of one clay-filled discontinuity can make the difference between stability and instability, or a compressible seam may cause settlement of the structure. This condition means that it is usually necessary to carry out a drilling program to investigate sub-surface conditions, and in some cases drive exploration

adits to examine in situ conditions. Figure 4.1 shows a diamond drill on a platform on a steep cliff investigating the foundations for a bridge abutment. However, drilling may not be required in circumstances where the applied loads are significantly less than the bearing capacity of the rock, where there is no possibility of a sliding type failure, or where there are extensive outcrops and the sub-surface conditions can be confidently established by interpretation. This chapter describes investigation methods for rock foundations, with emphasis on in situ testing methods and detailed structural geology studies. In situ testing is one of the particular features of investigation programs for major structures founded on rock because of the difficulty in sampling and testing large samples representative of the rock mass. Samples that are representative of both the intact rock and the discontinuities may be as large as 1 m (3 ft) in diameter. Samples this large are very difficult to recover undisturbed, and the required testing equipment would have to exert extremely high forces even to deform the rock mass. At the early stages of most projects there may be some choice available in the site of the structure. Under these circumstances, one of the first tasks in the geotechnical program is to evaluate alternative sites and to recommend which site is the most favorable. In this reconnaissance stage of the project the objective of the investigation would be to concentrate on large scale geological features that would influence the overall stability of the structure. These features include landslides, contacts between rock types with significantly

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Figure 4.1 Photograph of diamond drill investigating rock conditions for bridge abutment (photograph by Tony Rice).

different engineering properties, fault zones and persistent sets of discontinuities sets that dip out of any face in which a steep cut is to be made. Geological information of this nature would form part of the input for the overall site selection study that would include alignment studies in the case of bridges on transportation routes. In the case of dam projects, the site selection should take into consideration the foundations of the dam itself, the spillway and the powerhouse. Geological conditions that could justify moving a structure would be a very significant hazard such as a major landslide, movement of which could destroy the structure, or karstic terrain which contains substantial cavities. For other geological features such as faults or continuous bedding planes that would only cause local instability, remedial measures such as rock reinforcement could be carried out during construction (see Chapter 10). The following is a discussion on some of the

reconnaissance techniques that may be used early in a project, mainly for the purpose of site selection. It is very rare that the information gathered at this stage of a project would be adequate for use in final design, so these studies would have to be followed by more detailed investigations such as surface mapping and drilling. 4.1.1 Aerial and terrestrial photography The study of stereo pairs of vertical aerial photographs and oblique terrestrial photographs provides much useful information on the larger scale geological conditions at a site (Peterson et al., 1982). Often these large features will be difficult to identify in surface mapping because they are obscured by vegetation, rock falls or more closely spaced discontinuities. Photographs most commonly used in geotechnical engineering are

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black and white, vertical photographs taken at heights of between 500 and 3000 m (1500 and 10 000 ft) with scales ranging from 1:10 000 to 1:30 000. On some projects it is necessary to have both high and low level photographs, with the high level photographs being used to identify landslides, for example, while the low level photographs provide more detailed information on geological structure. One of the most important uses in foundation engineering of aerial photographs is the identification of landslides which have the potential for causing movement, or even destruction of facilities on which they are constructed. Landslides features that are often readily apparent on vertical aerial photographs are tension cracks and scarps along the crest of the slide, hummocky terrain in the body of the slide and areas of fresh disturbance in the toe, including sudden changes in river directions. Figure 4.2 shows a landslide area in the side of a steep glacial valley in the Coastal Range of western Canada. Area a, which is a talus slope, is an ancient slide, while in area b, which is a potential slide of similar proportions, there are a number of tension cracks with widths up to 15 m (50 ft). The cause of these slides are sets of orthogonal joints, one of which dips out of the valley wall at an angle of about 50°, and a second vertical set striking at right angles to the valley that forms side release surfaces. By comparing photographs taken over a number of years it may be possible to determine the rate of movement of a slide, and whether it is growing in size. Related to landslides are debris flows which occur in mountainous terrain with high precipitation levels such as occurs on the north west coast of North America, in Japan, the Alps and Himalayas. Potential sites of debris flows are evident on aerial photographs as areas of erosion in steep banks in the upper reaches of the creeks, as well as fans of accumulated debris at the toe of the slope. Debris flows are highly fluid mixtures of water, solid particles and organic matter. This mixture has a consistency of wet concrete and consists of about 70–80% water, and solid material ranging from clay and silt sizes up to boulders several meters in

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diameter. The organic matter can include bark mulch as well as large trees and logs swept from the sides of the channel. Debris flows usually occur during periods of intense rainfall or rapid snow melt and a possible triggering event can be the failure of a temporary dam, formed by slope failure or a logjam, that releases a surge of water and solid material. Where such flows originate in streams with gradients steeper than about 20°– 30°, they move at velocities of approximately 3–5 m/s (10–16 ft/s), with pulses as great as 30 m/s (100 ft/s). At this speed, material is scoured from the base and sides of the channel so the volume of the flow increases as it descends. This combination of high density and high velocity can cause devastation to any structure built in their path. Bridges constructed over creeks which are susceptible to debris flows must be adequately sized to accommodate the likely flow volume, and footings should not be located in the creek bed unless they are designed to withstand the considerable impact loads (Skermer, 1984; VanDine and Lister, 1983). Other features that may be evident on aerial photographs are major geological structures such as faults, bedding planes and continuous joint sets. The photographs will give some information on the position, length and continuity of these features. However, to establish the orientation (dip and dip direction) of a discontinuity, it is necessary to fix the positions of a minimum of three, and preferably four, points on the same surface. This technique has been used predominately with terrestrial photographs where individual discontinuities with large exposures can be clearly identified; even on low level aerial photographs it is rare to be able to see exposures of a single discontinuity surface, except perhaps in the case of a fault scarp. Structural mapping from aerial photographs is normally only carried out when there is no access to the face; direct surface mapping which allows the characteristics of each discontinuity to be examined in detail is preferable. Other information that can be obtained from aerial photographs is the location of gravel deposits, rock outcrops and the study of river hydraulics for siting

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Figure 4.2 Vertical aerial photograph stereo pair showing typical features of a major rock slide in a glaciated valley: (a) slide scarp; (b) slide debris; (c) tension cracks; (d) valley floor; and (e) talus slope.

dams and bridges. 4.1.2 Geophysics Geophysical methods are often used in the preliminary stages of a site investigation to provide such information as the depth of weathering, the bedrock profile, contacts between rock types of significantly different density, the location of major

faults and solution cavities, and the degree of fracturing of the rock (Griffiths and King, 1988). The results obtained from geophysical measurements are usually not sufficiently accurate to be used in final design and they should always be calibrated by putting down a number of test pits or drill holes to spot check actual properties and contact elevations. However, geophysical surveys provide a continuous profile of subsurface condi tions and this information can be used as a

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fill-in between drill holes. Most geophysical investigations for engineering purposes consist of seismic, resistivity or ground penetrating radar surveys carried out on the ground surface as described in this section. Downhole techniques are also available to measure the properties of materials in the walls of the drill hole, or alternatively between adjacent holes. Downhole geophysics may be used in percussion drill holes, which are less expensive and faster to drill than diamond drill holes, as part of the preliminary investigation of a site. (a) Seismic surveys The primary purposes of seismic surveys are to determine the approximate location and density of layers of soil and rock, a well defined water table, or the degree of fracturing, porosity and saturation of the rock. Seismic velocity can also be related to the rippability of the rock mass (see Section 10.5.3). The seismic method is effective to depths in the range of tens of meters to a maximum of a few hundred meters. Discontinuities within the rock such as joints and shears will not be detected by seismic methods unless there is shear displacement and a distinct elevation change of a layer with a particular density as a result of fault movement. However, continuous overwater seismic profiling using a repeating shock source called a ‘sparker’ may recognize discontinuity zones. Seismic surveys measure the relative arrival times, and thus the velocity of propagation of elastic waves traveling between a shallow energy source and a number of transducers set out in a straight line along the required profile. The energy source may be a hammer blow, an explosion of a propaneoxygen mixture in a heavy chamber (gasgun), or a light explosive charge. In elastically homogeneous ground subject to a sudden stress near its surface, three elastic pulses travel outward at different speeds. Two are body waves that are propagated as spherical fronts affected to only a minor extent by the free surface of the ground, and the third is a surface wave which is confined to the region near the surface, its amplitude falling off rapidly with depth. The two body waves, namely the primary or

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‘P’ wave and the secondary or ‘S’ wave, differ in both their direction of motion and speed. The P wave is a longitudinal compressive wave in the direction of propagation, while the S wave induces shear stresses in the medium. The velocities of the primary (Vp) and secondary (Vs) waves are related to the elastic constants and density of the medium by the equations (4.1) (4.2) where K is the bulk modulus, G is the shear modulus and ? is the density. The velocity of the S wave in most rocks is about one half that of the velocity of the P wave. The S wave is not propagated at all in fluids. The value of the ratio Vp/ Vs depends only on the Poisson’s ratio of the medium. Figure 4.3 shows typical P wave velocities for a range of different materials. The surface wave, which travels about 10% slower than the S waves, causes a surface disturbance in homogeneous ground called the Raleigh wave. The Raleigh wave has both vertical and horizontal components, with the horizontal motion being of rather smaller amplitude than the vertical, and 90° out of phase with it. The resultant path of an element of the medium during passage of a Raleigh wave cycle follows an ellipse lying on the plane of propagation. The magnitude of the ground motion becomes negligibly small within a distance below the free surface of the same order of magnitude as the wavelength of the disturbance. The amplitude of the waves decreases with distance from their source as a result of spreading of the wave energy over the increasing wave front area. Earth materials are imperfectly elastic leading to energy loss and attenuation of the seismic waves that is greater than would be expected from geometric spreading alone. This reduction in amplitude is more pronounced for less consolidated rocks. Also, the reduction in amplitude is greater for higher frequencies resulting in selective loss of the higher

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Figure 4.3 Approximate ranges of P wave velocities Vp for some common geological materials (Griffiths and King, 1988).

frequencies as the pulse propagates. The sonic velocity of the elastic wave will be greater in higher density material, and in more massive rock compared with closely fractured rock. Where a layer of denser material underlies a less dense layer, such as soil overlying bedrock, then the elastic wave velocity will be greater in the bedrock and the contact between the layers will act as a refracting surface. In a specific range of distances from the shot point, the times of first arrival at different distances from the shot point will represent waves traveling along this surface. This information can be used to plot the profile of the contact between the two layers. (b) Resistivity surveys At locations where the rock types have similar densities and seismic surveys would be ineffective,

resistivity surveys can provide information on variations in the geological structure and material type. Since most rocks are themselves nonconductive, the electrical resistivity of a rock derives mainly from the salinity of the ground water occupying pores and discontinuities. Accordingly, rock formations will differ in resistivity because of porosity and jointing differences, with the resistivity decreasing with greater discontinuity frequency. For example, in faults and shears the water content may be higher than the country rock and anomalously low resistivity will be measured. Conversely, in porous country rock, a discontinuity may act as a drain and appear as an anomaly of high resistivity (Stahl, 1973). Resistivity surveys may also be used to detect such structures as clay-filled sinkholes in limestone

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because the clay will tend to have a relatively low resistivity compared with the surrounding rock and will show up as an anomaly. The conductivity of clay takes place by way of weakly bonded surface ions whereas rocks are themselves nonconducting. In general, the resistivities of formations vary widely not only from formation to formation but also within a particular deposit, this being particularly true for near surface unconsolidated materials (Griffiths and King, 1988). Consequently there is no precise correlation of lithology with resistivity and it is preferable that the results of resistivity surveys be calibrated with boreholes or test pits. (c) Ground penetrating radar Ground penetrating radar (GPR) is a technique for mapping bedrock depth, changes in rock type, discontinuities in bedrock, soil strata and the water table in course grained soils, as well as voids, pipes and solution cavities (Inkster et al., 1989). The technique has been used to detect features with thickness of a few tens of millimeters at a range of several meters, and to map geological structures at depths of up to 50 m. GPR systems for geological investigations usually comprise a sled equipped with transmitting, receiving and recording equipment that is towed along the survey line at a fixed distance above the ground surface to produce a continuous subsurface profile. The transmitter introduces a short pulse of high frequency (10–1000 MHz) electromagnetic energy into the ground that is reflected by layers with differing electrical properties and detected at the receiver. The propagation characteristics of the GPR signal depend largely on the electrical properties of the materials being probed, with the two parameters of concern being the conductivity which controls the attenuation of the signal through the ground, and the dielectric constant which controls the signal velocity. The most important factor is the conductivity: higher conductivity materials attenuate the radar signal more quickly, giving rise to radar reflections. The electrical properties of geological materials are primarily controlled by the

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water content with the conductivity of soils being related to the volumetric water content. In rocks, the radar is sensitive to changes in rock type and waterfilled or dry discontinuities. GPR is of limited use when the conductivity is greater than about 10–15 mS/m. Clays, for example, are relatively conductive and opaque so the depth of penetration in these materials may be limited to about 1 m (3 ft), while in sands and gravels it is possible to achieve penetrations of as much as 10 m (30 ft). GPR is also used to map discontinuities in rock, with reflections being generated as a result of the dielectric constant of the infilling material being different from that of the host rock, or where the discontinuities are filled with water. Discontinuities in granite have been detected at depths up to 50 m (Davis and Annan, 1989). 4.2 Geological mapping Geological mapping of surface outcrops or exploration adits usually furnishes the fundamental information on site conditions, and is often the basis for many subsequent engineering decisions such as relocation of the structure, type of structure that will be built, or the need for rock reinforcement. While mapping is a vital part of the investigation program, it is also an inexact process because a certain amount of judgment is usually required to extrapolate the small amount of information available from surface outcrops and drill core to the overall foundation. This section describes mapping techniques that have been developed to assist in producing both consistent results, and information that can be used directly in design. 4.2.1 Standard geology descriptions In order to produce geological maps and descriptions of the engineering properties of the rock mass that can be used with confidence in design, is it important to have a well defined process that produces comparable results obtained by different

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personnel working at several sites. To meet these requirements, standard mapping procedures have been drawn up which have the following objectives: • They should provide a language enabling observers to transmit their general impression of a rock mass, particularly with regard to its anticipated mechanical behavior. The language of the geological description must be unambiguous; different observers of a given rock mass should describe the rock mass in the same way. • They should contain, as far as possible, quantitative data of interest to the solution of definite practical problems. • Whenever possible, they should use simple measurements rather than visual observations alone. • They should provide a complete specification of the rock mass for engineering purposes. The process of drawing up the descriptions of the rock material and the rock mass is a progressive process that starts with general information collected during reconnaissance surveys, and progressively provides more detailed information required for design. The types of information collected and the detail to which they are investigated will depend on site conditions, the requirements of the project and the importance of each rock property to the long term performance of the structure. As all these factors will vary from project to project, it is important that investigations programs remain flexible and are drawn up to suit the particular requirements of each site. The following is a summary of information that may be collected to provide a complete description of the rock mass, and some brief comments on how these properties influence the performance of the rock mass. This information is based primarily on the procedures developed by the International Society of Rock Mechanics (1981b), with some additional information from the Geological Society Engineering Group Working Party (1977). More details of the mapping data are provided in Appendix II which includes mapping field sheets,

and tables relating descriptions of rock mass properties to quantitative measurements. An important first step in any reconnaissance stage of a project is to define zones, in each of which the geological properties are uniform with regards to the requirements of the project (International Society of Rock Mechanics, 1981 a or b). The zoning of the rock mass should provide information on the location, orientation and type of boundary between each zone, as well as some information on the engineering properties of the rock mass in each zone. By defining the boundaries of each zone it is possible to determine the extent to which the foundation characteristics will vary across the site, as well as the possible need to move the structure to avoid materials with insufficient bearing capacity, or locations with a potential for instability. The following is a list, and a brief description of the parameters that define the characteristics of the rock mass. Sets of discontinuities usually occur in orthogonal sets (mutually at right angles) in response to the stress field that has deformed the rock. This is shown in the photograph in Fig. 4.4(a), where the bedding dips into the face and the joints form wedges. Orthogonal structure is also illustrated in the stereonet in Fig. 2.7. Figure 4.4(b) shows the rock mass characteristics in diagrammatic form. This section describes each of these 12 parameters, and discusses their influence on foundation performance. Many of the rock mass parameters are discussed in more detail in Chapters 2 and 3 on structural geology and rock strength respectively and the appropriate references are quoted. Complete mapping and measurement procedures are described in the ISRM publication Suggested Methods for the Quantitative Description of Discontinuities in Rock Masses (ISRM, 1981b). I Rock material description (A) Rock type The rock type is defined by the origin of the rock (i.e. sedimentary, metamorphic or igneous), the mineralogy, the colour and grain size as shown in Tables II.1 and II.2 (Deere and Miller, 1966). The importance of defining the rock type is that there is wide experience in the performance of different rock types and this

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Figure 4.4 Characteristics of discontinuities in rock masses: (a) photograph of rock mass containing three orthogonal

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behavior of the rock. (B) Wall strength The strength of the rock forming the walls of discontinuities will influence the shear strength of rough discontinuities because high stresses are generated at local contact points during shearing. If the rock strength is low relative to the magnitude of these stresses the asperities will be sheared off resulting in a loss of the roughness component of the friction angle. The rock strength is quantified by the Joint Compressive Strength (JCS) term discussed in Section 3.4.2(b). It is often adequate to estimate the compressive strength from the simple field tests as shown in Table II.3, or if core or lump samples are available, by carrying out point load tests. The Schmidt hammer test is also a method of estimating the compressive strength of rock at discontinuity surfaces. (C) Weathering Loss of rock strength due to weathering will influence both bearing capacity of structures founded at shallow depth, and the shear strength of discontinuities due to the reduction in the roughness component during shearing. Weathering of rock takes the form of both disintegration and decomposition as discussed in more detail in Section 3.6.1. Table II.4 lists terms used to describe weathering grades with respect to the proportion of decomposed rock. These categories can be used to estimate the rock strength (see (B) above). II Discontinuity description (D) Discontinuity type Discontinuity types range from clean tension joints of limited length to faults containing several centimeters of clay gouge and lengths of several kilometers; obviously the shear strength of such discontinuities will be very different. Section 2.1.1 lists the most common types of discontinuities. (E) Discontinuity orientation The orientation of discontinuities is expressed as the dip and dip direction (or strike) of the surface (Section 2.2). The definition of the dip and dip direction, and the procedures for analyzing orientation measurements using the stereonet are discussed in detail in Chapter 2. (F) Roughness The roughness of a discontinuity

surface is often an important component of the shear strength, especially where the discontinuity is undisplaced and interlocked. Roughness becomes less important where the discontinuity is infilled or displaced and interlock is lost. Roughness should be measured in the field on exposed surfaces with lengths of at least 2 m if possible, and in the anticipated direction of sliding. A quantitative measure of roughness based on observations of the combination of surface irregularities (at a scale of several centimeters) and waviness (at a scale of a several meters) of discontinuity surfaces is shown in Fig. II.3 and Table II.5. These observations of roughness can be related to a roughness angle (i) by direct measurement using the procedures described in Section 4.2.2(c), or by the use of the joint roughness factor (JRC) as described in Section 3.4.2(b). Usual practice would be to use the roughness scale shown in Fig. II.3 when mapping the discontinuity surfaces, and then to calibrate these observations with a limited number of detailed measurements of actual roughness angles of critical features using the technique shown in Fig. 4.6. (G) Aperture Aperture is the perpendicular distance separating the adjacent rock walls of an open discontinuity, in which the intervening space is air or water filled; Table II.6 lists terms describing aperture dimensions. Aperture is thereby distinguished from the width of a filled discontinuity. It is important in predicting the likely behavior of the rock mass, such as deformation under stress changes and permeability, to understand the reason that open discontinuities develop. Possible causes include washing out of infillings, solution of the rock forming the walls of a discontinuity, shear displacement of rough discontinuities, tension features at the head of landslides and relaxation of steep valley walls following glacial retreat or erosion. Aperture may be measured in outcrops or tunnels provided that care is taken to discount blast induced open fractures, in drill core if recovery is excellent, and in boreholes using a borehole camera if the walls of the hole are clean. III Infilling

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Figure 4.5 Bias in the occurrence of discontinuities in rock faces and tunnel walls.

(H) Infilling type and width Infilling is the term for material separating the adjacent walls of discontinuities, such as calcite or fault gouge; the perpendicular distance between the adjacent rock walls is termed the width of the filled discontinuity. A complete description of filling material required to predict the behavior of the discontinuity include the following: mineralogy, particle size, overconsolidation ratio, water content/permeability, wall roughness, width and fracturing/crushing of the wall rock. If the infilling is likely to influence the performance of the foundation, samples of the material (undisturbed if possible) should be collected, or an in situ test may be carried out. Details of the influence of fillings on shear strength are discussed in Section 3.4.2(d), and on settlement of footings in Section 5.3.1. IV Rock mass description (I) Spacing Discontinuity spacing can be mapped in rock faces and in drill core, with the true spacing being calculated from the apparent spacing for discontinuities inclined to the face as shown in Fig. 4.5. Tables II.7 and II.9 provides terms that can be used to express spacing and block size respectively. Measurement of discontinuity spacing of each set of discontinuities will define the size and shape of blocks and give an indication of stability modes such as toppling failure. The spacing is also related to the rock mass strength because in closely fractured rock the individual discontinuities will more readily join together to form a continuous zone of weakness. A qualitative relationship

between discontinuity spacing and the strength of discontinuity rock masses is discussed in Sections 3.3.2 and 3.4.4. (J) Persistence Persistence is a measure of continuous length or area of the discontinuity. Table II. 8 provides terms that can be used to express persistence values. This parameter defines the size of blocks and the length of potential sliding surfaces, so the mapping should concentrate on measuring the persistence of the set of discontinuities that will have the greatest influence on stability. Persistence of discontinuities is one of the most important rock mass parameters, and also one of the most difficult to measure. This is because usually only a small part of the discontinuity is visible in the face, and in the case of drill core no information on persistence is available. Procedures for estimating the probability distributions of persistence from field measurements in an outcrop or tunnel, where the dimensions of the face are less than the persistence of some of the discontinuities, are discussed in Section 2.6.2. (K) Number of sets The number of sets of discontinuities that intersect one another will influence the extent to which the rock mass can deform without failure of the intact rock. As the number of discontinuity sets increases and the block size diminishes, the greater the opportunity for blocks to rotate, translate and crush under applied loads. The mapping should distinguish between systematic discontinuities that are members of a set and random discontinuities the orientation of which

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are less predictable. Appendix II provides terms describing the number of discontinuity sets. (L) Block size/shape The block size and shape are determined by the discontinuity spacing and persistence, and the number of sets. The block size can be estimated by selecting several typical blocks and measuring their average dimensions which are then recorded using the terms in Table II.9. Block shapes include massive, blocky, tabular, columnar, irregular and crushed. V Groundwater (M) Seepage Observations of the location of seepage provides information on aperture and persistence because ground water flow is confined almost entirely in the discontinuity (secondary permeability). Table II.10 describes seepage in filled discontinuities, while Table II.11 provides terms which describe seepage conditions in unfilled discontinuities. These observations will also indicate the position of the water table, or water tables in the case of rock masses containing alternating layers of low and high permeability rock such as shale and sandstone. In dry climates the evaporation rate may exceed the seepage rate and it may not be possible readily to observe seepage locations, while in cold weather icicles provide a good indication of even very low seepage rates. The flow quantities will also help anticipate conditions during construction such as flooding and pumping requirements of excavations, and the likely performance of the foundation with respect to seepage. Using these terms outlined in this section, a typical description for a rock material would be as follows: Grey, fine grained, crystalline, slightly weathered, moderately strong basalt. Note that the rock name comes last because this is less important then the engineering properties of the rock. An example of a rock mass description is as follows:

Columnar jointed with vertical columns and one set of horizontal joints, spacing of vertical joints is very wide, spacing of horizontal joints wide, joints lengths are 3 to 5 m (10 to 16 ft) vertically and 0.5 to 1 m (1.5 to 3 ft) horizontally; joint aperture is extremely narrow and the discontinuity infilling is very soft clay. The vertical columnar joints are smooth, while the horizontal joints are very rough. No seepage. 4.2.2 Discontinuity mapping One of the most important components of any surface mapping program is the definition of the structural geology according to the parameters shown in Fig. 4.4. It is recommended, wherever possible, that the mapping be carried out by the same person or engineering group that will carry out the design. This will help to ensure that the objectives of the mapping program are clearly identified and the data collected are relevant to the design. For example, a large number of short, impersistent joints that have little influence on the rock mass strength should be given much less attention during mapping than one clay filled fault on which the whole foundation could fail. A design engineer analyzing the data who is not familiar with the site, may not be able to distinguish on a contoured stereo net the relative importance of the many impersistent joints and the single fault. As discussed in Chapter 2, the most convenient means of expressing the orientation of discontinuities for engineering purposes is in terms of the dip and dip direction. Special geological compasses are available with which dip and dip direction can be measured simultaneously and directly, with no need to make any conversions of the readings before plotting them on the stereo net. A compass made by the Showa Sokki company in Japan is specifically designed for discontinuity mapping and also has a built-in inclinometer (Fig. 2.4). (a) Mapping methods

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The most common methods of structural mapping are line and window mapping, both of which can be used either on surface outcrops or in exploratory adits. Line mapping comprises stretching a tape along the face and mapping every discontinuity that intersects the line; line lengths are normally between 50 and 100 m (150–300 ft). If the end points of the line are surveyed, then the location of all the discontinuities can be determined. Window mapping comprises mapping all discontinuities within a representative segment or ‘win dow’ of fixed size, spaced at regular intervals along the exposure. The intervening areas are examined for similarity of structure. The length of a window would normally be about 10 m (30 ft). Either of these mapping techniques may be used in the site selection phase of a project, depending on the extent of the face available for mapping. Once the final site has been selected, it may be appropriate to conduct detailed mapping at the foundation location. For example, in one spillway foundation project, every discontinuity was numbered and its extent and location marked on a plan of the site. The properties of each discontinuity were then mapped and recorded in a table which enabled the designers to study any individual feature that could have an influence on stability. (b) Corrections for discontinuity orientation An important factor to consider in the interpretation of mapping results is the relative orientation between the face and the discontinuities. This relative orientation introduces a bias to both the discontinuity spacing and the number of discontinuities that are mapped. The bias arises because all discontinuities oriented at right angles to the face will be visible on the face, while few discontinuities oriented sub-parallel to the face will be visible (Fig. 4.5). The bias in spacing can be corrected as follows (Terzaghi, 1965): (4.3) where S is the true spacing between discontinuities of the same set, Sapp is the measured (apparent) spacing and ? is the angle between face and strike of discontinuities. The number of discontinuities in a set can be

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adjusted to account for the relative orientation between the face and the strike of the discontinuity as follows: (4.4) where N is the adjusted number of discontinuities and Napp is the measured number of discontinuities. For example, a vertical drill hole will inter sect few steeply dipping discontinuities and the Terzaghi correction will calculate an appropriate increase in the number of these surfaces. Furthermore, some stereonet programs will use the Terzaghi correction to increase the number of discontinuities and allow for the bias in sampling orientation; this more accurately represents the population of discontinuities. (c) Roughness measurements A component of the friction angle of most discontinuities is the surface roughness, and an important part of any mapping program is measurement of this parameter. During the preliminary stages of an investigation program it is usually satisfactory to make a visual assessment of the roughness angle using the method described by Barton (1973) to determine joint roughness coefficient (JRC) values of typical discontinuities (see Section 3.4.2). If in the final design stage of a project a few discontinuities having a significant effect on stability have been identified, there are a number of methods of accurately measuring the surface roughness of these critical surfaces. For example, a mechanical profilometer can be used to measure the variation in height of a rock surface relative to a planar reference surface, with care being taken to measure the roughness in the direction of sliding. Tse and Cruden (1979) demonstrate that it is possible to correlate these measurements with the standard profiles proposed by Barton to define JRC values, and Yu and Vayassade (1991) describe the sensitivity of these measurements to the sampling frequency. An alternative method of measuring roughness developed by Fecker and Rengers (1971) consists of measuring the orientation of the discontinuity

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with a geological compass to which a series of plates of different diameters are attached to the lid (Fig. 4.6(a)). If the diameter of the larger plates is about the same dimensions as the wavelength of the roughness, then the measured orientation will be approximately equal to the average orientation of the surface. However, the smaller diameter plates will show a scatter in the orientation measurements as the plates lie on irregularities with shorter wavelengths. If the orientation measurements are plotted on a stereo net, the degree of scatter in the poles about the mean orientation is a measure of the roughness. Alternatively, a plot of plate diameter against roughness angle i will show that short wavelength asperities ?1 have higher roughness angles than those with longer wavelengths ?2 (Fig. 4.6(b)). An important factor to consider in the measurement of roughness is the minimum wave-length of the asperities that should be used in design. As a guideline for design, it is suggested the selection of a value for i depends on the dimensions of the bearing area relative to maximum wavelength. For example, in the case of a spread footing with a bearing surface area not more than the wavelength ? 2, a roughness angle corresponding to plate diameters of 2d–3d for which the i value is about 15° would be appropriate (Fig. 4.6(b)). However, in the case of a structure with a bearing surface equal to several multiples of ?2, a roughness angle corresponding to plate diameters of 6d–8d for which the i value is about 5° may be suitable. The scale effect results in some reduction in roughness angle with larger samples such that the shorter wavelength asperities seem to have less influence on overall friction angle for in situ conditions where the sliding surface has a length of at least several meters (Patton and Deere, 1970; Barton and Choubey, 1977). In general, the total friction angle used in design would normally not exceed about 50°. The other factor to consider in the selection of i is the magnitude of the normal stress on the surface compared with the compressive strength of the rock (see Section 3.4.2).

4.3 Drilling Detailed foundation design will usually require more information on the sub-surface characteristics of the bearing material than can be extrapolated from surface mapping. Methods of drilling that can be used for subsurface investigations include diamond drilling, and occasionally percussion or large diameter drilling: calyx drilling. If exposures for bedrock mapping are limited, test pits may be excavated to expose the underlying rock. However, test pits will not be able to penetrate to a significant depth into the rock, unless it is very weak, so test pits will rarely provide information on subsurface rock properties. 4.3.1 Diamond drilling Diamond drilling is the most common method of sub-surface exploration for rock; it is used to obtain intact and undisturbed core samples that provide information on geological conditions, as well as samples for laboratory testing (see Section 10.2.1). Similarly to surface mapping, it is important to use standard core logging procedures so that conditions between sites can be compared (ISRM, 1981a). (a) Core logging A typical core log in Fig. 4.7(a) shows common data which are recorded on drill logs. Note that on the logs that qualitative data—RQD and discontinuity frequency (number of discontinuities/ unit length)—are plotted in the form of histograms such that zones of closely fractured or weak rock appear as wide bars that can be readily identified when scanning the log. Discontinuity frequency and RQD are defined as follows, with care being taken to distinguish between natural discontinuities and drill induced (mechanical) breaks in the core:

An RQD value of 100% means that every piece of

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Figure 4.6 Measurement of surface roughness values with plates of different diameters attached to the lid of a geological compass: (a) dip measurements with plates of differing diameters; and (b) relationship between roughness measurements and plate diameters.

core has a length greater than 100 mm (4 in.) and is indicative of good quality rock. It is also important to take a color photograph, complete with a legend, scale and color chart, of each core box (Fig. 4.7 (b)). (b) Core recovery An important requirement for diamond drilling conducted for foundation engineering purposes is

complete recovery of the core. All zones and seams of weak and fractured rock must be recovered which requires the use of techniques that minimize breakage and loss of core. This can be achieved with minimum N size core (45 mm, 1.775 in. diameter) because core breakage increases with decreasing core size. Core quality is also enhanced with the use of a triple tube core barrel in which the

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inner tube is mounted on bearings that do not rotate during drilling so there is little spinning or vibration of the core. When the core barrel is recovered at the end of the drill run, the inner tube is pumped out of the core barrel rather than hammered out, as is the case with a double tube barrel. The usual procedure for logging the core is to lay the inner barrel, which is split longitudinally, on a cradle, such as a length of L-section steel, so that the upper half of the barrel can be removed without disturbing the core. This allows the core to be logged while it is still in the barrel. A further refinement for drilling in very poor rock is to use a transparent perspex inner tube in which the core can be logged once it is removed from the split triple tube. Careful drilling for foundation investigations will usually require that the drillers work on an hourly rate; drillers working on a footage basis with a production bonus will tend to sacrifice quality for quantity. In very closely broken rock standard drilling techniques may not be adequate to obtain good quality core and in these circumstances it may be necessary to use a procedure developed by Rocha (1967). This involves grouting a steel rod into a pilot hole and then overcoring this to remove an integral sample comprising both the rod and the surrounding core. If the rod is oriented before it is grouted in place, then it is also possible to orient the core (see below). Core recovery values are usually used in conjunction with RQD measurements to assess the rock mass quality. For example, a rock mass comprising a strong, slightly weathered rock containing wide, clay-filled seams may give the appearance of having a high RQD value if the clay is lost in the drilling. However, the core recovery values would show the amount of missing core and allow a true value of the RQD to be calculated. (c) Core orientation A possible requirement of diamond drilling for foundation engineering is orientation of the core so that the dip and dip direction of the discontinuities can be determined. For example, it may be necessary to orient a drill core where there is a possibility of shear failure taking place on persistent

discontinuities, or settlement due to compression of clay filled seams. In a vertical drill hole the dip of all the discontinuities intersected by the hole can be determined, but there is no information on their dip direction; in an inclined drill hole it is not possible to determine either dip or dip direction of discontinuities from examination of the core. Methods of orienting discontinuities during drilling include marking a line of known orientation on the core and measuring the position of the discontinuity relative to this line, and the use of the borehole camera as described below. A simple and effective core orienting device is the clay impression core barrel (Fig. 4.8(a)) which utilizes a modified inner core barrel with conventional wire-line diamond drilling equipment (Call et al., 1982). The barrel is eccentrically weighted with lead and lowered into an inclined borehole so that its orientation with respect to the vertical is known, i.e. the weight rotates to the bottom of the hole. Modeling clay protrudes from the downhole end of the inner barrel such that it also extends through the drill bit when the inner and outer tubes are engaged. The barrel assembly is pressed against the hole bottom which causes the clay to take an impression of the core stub left from the previous core run. The inner barrel is then retrieved with the wire-line and a conventional barrel is lowered to continue coring. At the completion of the run, the recovered core is fitted together and the core is oriented by matching the piece of core from the upper end of the core run with the oriented clay imprint. A reference line, which represents the top of the core, is run from the oriented core stub along the length of the core. All the discontinuities in the core can then be oriented relative to this line and their dip and dip direction calculated if the dip and plunge of the hole are known (Fig. 4.8(b)). Computer programs are available to convert core discontinuity angles directly to dips/dip directions and plot them on a stereo net. The clay impression barrel can only be used in inclined holes within the dip range 45°–70° where the weighted barrel will orient itself as it is lowered

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Figure 4.7 Diamond drill core logging procedures: typical diamond drill core log and photograph of diamond drill core with length scale and color reference scale.

down the hole. In shallow vertical holes, the core barrel may be oriented by scribing an oriented

reference line down the side of the drill rods as they are lowered down the hole. A disadvantage of the

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Figure 4.8 Clay impression core barrel orientation procedures: (a) core barrel used to orient diamond core in inclined drill holes (Call et al., 1982); and (b) dip/dip direction measurements of discontinuity in oriented core.

clay impression barrel method is that only the top piece of each core run is oriented, and if there is a zone of fractured rock in which it is not possible to fit all the core fragments together then the orientation line will be lost below this point. Another method of orientating core is the Christienson-Hugel technique that scribes three continuous, oriented longitudinal grooves down the side of the core as it enters the barrel during drilling

(Boart Longyear Co., 1996). The grooves are cut by three tungsten carbide scribes located just behind the bit, and the scribes are spacedaround the circumference of the core such that it is possible to determine the top of each piece of core. The reference groove is fixed relative to the orienting lug, and the orientation of the lug is measured with a multi-shot directional survey instrument located in the upper part of the non-magnetic core barrel. The

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multi-shot instrument takes photographs of the lug and a compass at any interval depending on the required frequency of orientation measurements. Once the orientation of the reference groove has been measured on the film, the orientation of each discontinuity is determined using a goniometer, or the technique illustrated in Fig. 4.8 (b). A disadvantage of these two core orientation techniques is that they interrupt and slow down the drilling, and the orientation measurements are made on disturbed core. Alternative procedures to measure the orientation of discontinuities in situ are the side scanning borehole video camera, or the impression packer. The impression packer makes an imprint of the discontinuities in the wall of the hole, while the video camera provides a continuous, colored, 360° record of features in the wall of the drill hole, including water and gas discharges. The camera housing also contains a compass to determine the orientation of the camera in the hole, and the depth down the hole is precisely measured with a sensor on the cable on which the camera is suspended. Software that processes the recorded video image can rotate the ‘core’ so that it can be viewed from any direction, or can display an unwrapped view of the wall of the hole. The unwrapped view shows each discontinuity in the form of a sine wave from which the orientation of the discontinuity, as well as its width, can be determined. The procedure is to use a mouse to digitize points along the trace of the discontinuity which are then fitted to a true sine wave from which the orientation is calculated (Fig. 4.9). An essential part of any oriented core measurements is borehole surveying to determine the dip and plunge of the hole at selected intervals. With this information, measured discontinuity orientations can be corrected for the true inclination of the hole. Hole survey instruments include the Sperry Sun and Eastman multi-shot tools that take photographs of a compass and dip circle at pre-set time intervals. The tool is lowered down the hole on the wireline and the depth recorded at the times that the photographs are taken. In this way the orientation of the hole at a number of depths can be obtained. The Tro-Pari

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instrument is a single shot tool that has the compass and dip circle mounted on gimbals that are locked in position after a time interval that is sufficient to lower the instrument to the bottom of the hole. 4.3.2 Percussion drilling Percussion drilling using a pneumatic or hydraulic drill is less expensive and has a faster penetration rate than diamond drilling (see Section 10.2.2). However, because no core is obtained it will not provide much more information than the depth to bedrock, and the approximate variation in rock strength by observing changes in the penetration rate and the color of the cuttings. This information would only suffice in the case of the design of foundations for structures with low bearing pressures. However, instrumentation is available that can be attached to percussion drill rigs to record and produce plots of a number of different geological parameters continuously during drilling (Lutz and Morey, 1988). Typical parameters that can be recorded with this instrumentation include: 1. instantaneous feed rate which is related to the mechanical properties of the rock such as modulus and hardness; 2. tool thrust which supplements the feed rate data when cavities are encountered; 3. tool torque which can be used to identify gravel and boulder zones; 4. drilling fluid pressure which is related to the permeability of the formation being drilled; pressures are high in plastic deposits such as clay, and low in sands and gravel; and 5. drill string vibration which is related to the rock hardness. Percussion drilling with automatic recording instruments could be used to back up a diamond drilling program with the core being a reference to calibrate the percussion results.

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Figure 4.9 Orientation of discontinuity in borehole using image from 360° scanning video camera: (a) core-like image of drill hole showing elliptical intersection between hole and discontinuity; and (b) expanded (‘unwrapped’) view of borehole wall with discontinuity displayed as sine wave (Colog Inc., 1995).

4.3.3 Calyx drilling At locations where it is necessary to observe in situ rock conditions and also obtain large diameter core for testing purposes, core holes with diameters of 1– 3 m (3–10 ft) can be drilled with a Calyx drill. This comprises a steel barrel, equipped with tungsten carbide teeth, to which both a thrust and torque can be applied. After the drill has advanced by about 1 m (3 ft), the core is broken off either by driving wedges into the annulus, or by an explosive method using a detonating cord placed at the bottom of the annulus. The core is removed by grouting a lifting eye into the top of the core and pulling it out with a crane. 4.4 Ground water measurements The main effects of ground water on foundation

performance are uplift pressures that reduce the shear strength resistance of discontinuity surfaces, and seepage that results in loss of storage water, and in extreme cases, scour of weak seams within the rock mass. The relationship between the distribution of water pressures within the rock mass and the rate of seepage through it is given by Darcy’s Law which states that (Fig. 4.10): (4.5) where Qs is the seepage volume per unit time, k is the coefficient of permeability, A is the cross-sec tional area of the sample, and ih is the pressure gradient. The pressure gradient is given by (4.6) is the head loss between the ends of where the sample with length l. The head h is equal to the pressure P, at depth h, divided by the water density, ? w (Fig. 4.10). The relationships in equations 4.5 and 4.6 show that

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Figure 4.10 Definition of permeability in terms of Darcy’s law.

the definition of ground water conditions within a foundation requires information on at least two of the three parameters, namely the seepage rate per unit area Qs/A, the pressure gradient ih and the permeability k, the usual units of which are m/s. This section describes methods of measuring ground water pressure and rock mass permeability. (a) Permeability The permeability of most intact rock (primary permeability) is essentially zero and the flow of water in a rock mass (secondary permeability) is concentrated in the discontinuities. Consequently, ground water conditions are highly dependent upon the orientation, length, width and infilling characteristics of the discontinuities. In the design of investigation programs, as well as drainage and grouting systems, drill holes should be oriented to intersect discontinuities that are expected to carry water. In rock types such as sedimentary and metamorphic rocks, in which there is a predominant discontinuity orientation, ground water flow will be concentrated in a direction parallel to the predominant discontinuities, i.e. the bedding or foliation. Such rock types will exhibit anisotropic permeability. That is, the permeability will be significantly greater parallel to the bedding than perpendicular to it. A modified form of Darcy’s law can be used for anisotropic rock as follows: (4.7) where k1 and k2 are the permeabilities parallel and

perpendicular to the predominant discontinuity set, respectively. The permeability of a rock mass is highly dependent upon the width of the discontinuities, and it has been shown that the permeability of an array of smooth, parallel discontinuities is proportional to the cube of the opening width of the discontinuity (Louis, 1967). Therefore blasting and stress relief that result in opening of discontinuities can produce a significant increase in seepage quantities. Another factor to consider is that Darcy’s law is only applicable for low velocity, laminar flow conditions. These conditions will usually apply in the case of jointed rock and in fact no lower limit is known to exist for Darcy’s law (Todd, 1959). However, Darcy’s law cannot be used for materials with large diameter solution openings and very steep gradients. A guideline on applicable conditions for Darcy’s law is when the Reynolds number is less than 1. Reynolds number (Re) is given by (4.8) where ?w is the fluid density, v is the flow velocity, d is the diameter (of a pipe), and ? is the viscosity of the fluid. Because of the very great influence of the discontinuities on the permeability of the rock mass, ground water studies should consist of in situ measurements with as little disturbance of the rock mass as possible. Common investigation methods described below consist of the installation of

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piezometers in drill holes to measure water pressure, and conducting falling head and pump tests to measure permeability. 4.4.1 Water pressure measurements A piezometer is a system installed in a drill hole to measure the water pressure existing at a point, or over a nominated interval, in a saturated material. Piezometers can also be used for ground water sampling, permeability testing, and as observation wells during pump tests. With careful installation, they will also allow long term monitoring of ground water conditions. The measured pressure values can be used directly in stability and seepage analyses. In planning a piezometer installation, two important decisions that have to be made are the location of the point of measurement, and the method of measuring the piezometric level. First, the location of the point of measurement is determined by the geometry of the foundation, with the pressure being measured in the vicinity of potential failure surface where uplift pressures could cause instability. Also, the measurement zone must intersect discontinuities that communicate hydraulically with the general discontinuity pattern in the area; the appropriate location of the measurement zone is determined, where possible, from examination of drill core. The second factor to consider in piezometer installations is the method of measuring the changes in pressure in the piezometer. If the volume of water that is required to register a head fluctuation in a piezometer is large relative to the rate of entry at the intake, there will be a time lag introduced into the piezometer readings. This factor is especially pertinent to head measurements in low permeability formations (Freeze and Cherry, 1979). For this reason, piezometers in rock usually consist of a pressure-measuring device installed in a sealed section of the drill hole. The volume change within this sealed section, caused by the operation of the piezometer, should be very small in order that the response of the complete installation to pressure changes in the surrounding rock is rapid. If a device

is used that requires a large volume change for its operation, the change in pressure induced by this change in volume may give rise to significant errors in measurement (Terzaghi and Peck, 1967). Ground water pressures may be monitored in open holes if the permeability of the rock mass is greater than about 10−6 m/s. Rock types such as coarse grained sandstones and highly fractured rock may have permeabilities as high as 10−6 m/s, but most competent rocks that would be suitable for the foundations of large structures have permeabilities of less than 10−7 m/s. Therefore, open standpipes are rarely utilized in monitoring of ground water pressures in rock and one of the types of piezometer installations discussed below are usually used. (a) Standpipe piezometers A standpipe piezometer consists of a length of plastic pipe, with a perforated or porous section at the lower end which is encased in clean gravel or sand to provide a good hydraulic connection with the rock (Fig. 4.11). This section of the piezometer, which is the point where the water pressure is measured, is isolated from the rest of the hole with a seal(s) comprising filter layers to prevent contamination of the clean sand, and a layer of bentonite. The bentonite is usually placed in the form of compacted balls that will fall a considerable depth down a water-filled hole before they expand. In very deep holes the balls can be first soaked in oil to form a protective layer that delays their expansion. However, cement is preferred as a seal for holes with depths greater than about 300 m (1000 ft). The water level in a standpipe piezometer can be measured with a well sounder consisting of a graduated electrical cable, with two bared ends, connected to an electrical circuit consisting of a battery and an ammeter. When the bared ends come into contact with the water the circuit is closed and a current is registered on the ammeter. The advantages of this type of piezometer are that it is simple and reliable, but has the disadvantages that there must be access to the top of the hole, and there can be significant time lag in low permeability rock. (b) Pneumatic piezometers

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Figure 4.11 Typical standpipe piezometer installation.

A rapid response time can be achieved using pneumatic piezometers which comprise a valve assembly and a pair of air lines that connect the valve to the surface. The valve is placed in the sealed section of the piezometer to measure the water pressure at that point. The operating principle is to pump air down the supply line until the air pressure equals the water pressure in the sealed section and the valve opens to start air flowing in the return tube. The pressure required to open the valve is recorded on a pressure gauge at the surface. Pneumatic piezometers are suitable for low permeability rock installations and are particularly useful for foundation installations where pressures are being measured under the structure and access to the collar of vertical drill holes is not possible. The disadvantages of this type of piezometer are the risk

of damage to the lines either during construction or operation, and the need to maintain a calibrated readout unit. (c) Electronic transducers Water pressure measurements with electrical transducers allow very rapid response time and the opportunity to record and process the results at a considerable distance from the structure. Common types of electrical transducers include strain gauges and vibrating wire gauges that measure pressure with a high degree of accuracy. It is recommended that all transducers be thoroughly tested and calibrated before installation (Patton, 1987). It should also be kept in mind that the long term reliability of these sensitive electrical instruments may not equal that of the structure and provision should be made for their maintenance and possible

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Figure 4.12 Multiple completion piezometer installation (MP System, Westbay Instruments) with probe positioned to make pressure measurement (Black et al., 1986): (a) probe located at measurement port coupling; and (b) probe measuring fluid pressure outside coupling.

replacement. (d) Multi-completion piezometers At locations where there are rock types with differing permeabilities, it is possible that zones of high ground water pressure may exist within a generally depressurized area. In such circumstances, it may be desirable to measure the ground water pressure at a number of points in a drill hole. This can be achieved by installing multiple standpipe piezometers in a single drill hole with bentonite or cement seals between each section of perforated pipe. The maximum number of such standpipes that can be installed in an NX borehole is three; with more pipes, placement of filter and effective seals becomes very difficult. An alternative method of measuring water pressures

at a number of different points in a drill hole is to use a multi-port (MP) system which also allows measurement of permeabilities and retrieval of water samples (Black et al., 1986). The MP system is a modular multiple-level ground water . monitoring device employing a single, closed access tube with valved ports (Fig. 4.12). The valved ports are used to provide access to several different levels of a drill hole in a single well casing. The modular design permits as many monitoring zones as desired to be established in a drill hole. The system consists of casing components which are permanently installed in the drill hole, and pressure transducers, sampling probes and specialized tools that are lowered down the hole. The casing components include casing sections of various lengths, two

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types of valved port couplings with capabilities either to measure pressure or take samples. The port assemblies can be isolated in the drill hole by sealing the annulus between the monitoring zones using either pairs of packers, or by filling the annulus with a cement grout or bentonite seal. The MP system has been used in drill holes up to 1200 m (4300 ft) deep. 4.4.2 Permeability measurements Permeability is the fundamental parameter governing the flow and pressure distribution of ground water in the rock mass (Cedergren, 1989). Permeability values are required for a number of foundation design procedures, including seepage in dam foundations, and the effect of drainage and grouting on ground water pressure distributions. Because ground water flow in fractured rock takes place predominately in the discontinuities, it is necessary that permeability measurements be made in situ; it is not possible to simulate a fractured rock mass in the laboratory. The following is a brief description of the two most common methods of in situ permeability testing, namely variable head tests, and pumping tests. Detailed procedures for permeability tests are described in the literature and the tests themselves are usually conducted by specialists in the field of hydrology. (a) Variable head tests The principle of the variable head tests is to hydraulically isolate a section of a drill hole, either in a standpipe piezometer or in an open hole with inflatable packers. Water is then removed from the standpipe or drill rods so that the water pressure in the test section differs from the equilibrium ground water pressure. This results in water flowing from the rock surrounding the test section until equilibrium is re-established (rising head test). Permeability is determined by measuring the rate at which a known volume of water flows from the rock under a known head. In the falling head test the rate at which the water falls in the rods or pipe is measured, while in the constant head test the

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volume of water required to keep the water in the rods at a constant level is measured. Permeability tests carried out in piezometers are limited to the section defined by the position and length of the perforated portion of the piezometer. However, in an open hole the use of inflatable packers allows tests to be carried out in any position in the hole and over any length of hole so the permeability of selected discontinuity zones can be investigated. Permeability measurements can be made during diamond drilling using a triple packer system that is lowered through the rods so that the test is conducted in a portion of the hole below the bit (Fig. 4.13). The packer system consists of three inflatable rubber packers, each 1 m (3 ft) long which is sufficient to minimize the risk of leakage past the packer. The lower two packers are joined by a perforated steel pipe, the length of which depends on the required test length, while the top and middle packers are joined by a solid pipe. The whole packer assembly is lowered down the drill hole on the wire line through the drill rods and the lower two packers extend through the bit into the open hole, while the upper packer is located in the lower end of the core barrel. The three packers are then inflated with nitrogen through a small diameter plastic tube that runs down the hole to seal the packer assembly into the rods and isolate a length of drill hole below the bit. If water is introduced into the drill rods it will flow through the perforated pipe into the rock isolated by the two lower packers. This flow of water is measured by monitoring the change of water level in the drill rods. The procedure for the variable head test is first to establish the rest water level which is the static equilibrium level of the water table at the drill hole location (Fig. 4.14). The pumping of circulation water during drilling will disturb this equilibrium and the permeability results will be in error if insufficient time is allowed for equilibrium conditions to be re-established. Once equilibrium has been established, water is removed from the standpipe (piezometer test) to lower the water level by about 1–2 m (3–6 ft) and the rate at which the

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Figure 4.13 Triple packer arrangement for making falling-head permeability tests in conjunction with diamond drilling.

water level rises in the pipe is measured. For a test

set up such as shown in Fig. 4.14, the permeability k

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Figure 4.14 Method of calculating permeability for variable head test in cased observation well. (a) test arrangement showing variable heads h and times t; and (b) plot of head increase against time.

is calculated from the following relationship: (4.9) where A is the cross-sectional area of the standpipe is the internal radius of the standpipe; L is the length of the uncased test section; t1 and t2 are the times at which the water level has risen distances of h1 and h2 respectively above the new equilibrium level established by removing water from the hole. The differential heads h1 and h2 as well as the initial equilibrium head h0 are defined in Fig. 4.14(a), while a typical semilog plot of the rise in water level in the casing with time is shown in Fig. 4.14(b). The different diameters of the drill hole and standpipe are accounted for by the shape factor, F which for this test arrangement is given by: (4.10) where R is the radius of the drill hole.

(b) Pumped wells The main limitations of permeability tests carried out in drill holes are that only a small volume of rock in the vicinity of the hole is tested, and it is not possible to determine the directional anisotropy of the rock mass. Both these limitations are overcome by conducting pump tests, as described briefly below. A pump test arrangement consists of a vertical well equipped with a pump, and an array of piezometers in which the water table elevation can be measured in the rock mass surrounding the well. The piezometers can be arranged so that the influence of various geologic features on ground water conditions can be determined. For instance, piezometers could be installed on either side of a fault, or in directions parallel and perpendicular to sets of persistent discontinuities such as bedding planes. Selection of the best location for both the pumped well and the observation wells requires considerable experience and judgment and should

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only be carried out after thorough geological investigations have been carried out. The test procedure consists of pumping water at a steady rate from the well and measuring the drop in water level in both the pumped well and the observation wells. The duration of the test can range from as short as eight hours to as long as several weeks depending the permeability of the rock mass. When the pumping is stopped, the water levels in all the wells are measured until a static water level is determined—this is known as the recovery stage of the test. Plots of draw down (or recovery) against time can be used to calculate permeability values using methods described by Cedergren (1989), Todd (1959), Jacob (1950) and Theis (1935). Because of the cost and time required for pump tests, they are usually only conducted for the design of major structures such dams where both seepage and uplift are of concern. For other structures, installation of piezometers to measure the ground water table and conduct falling head tests usually provides sufficient information on ground water conditions for design purposes. 4.5 In situ modulus and shear strength testing In situ testing of deformation modulus and shear strength is sometimes required for the design of foundations for major structures such as dams and bridges. Circumstances where this might be car ried out include foundations comprising closely fractured and weak rock that could compress, resulting in settlement of the structure, or continuous, low strength discontinuities on which sliding could take place. The need for in situ testing would arise when it is not possible to obtain undisturbed samples, or sufficiently large samples, for laboratory testing. 4.5.1 Modulus testing While the modulus of intact rock can be determined by laboratory tests on pieces of core, the modulus of

fractured rock masses, which depends upon both strain of intact rock, and closure and movement of the discontinuities, must be determined by in situ methods. With all in situ tests there will be some disturbance of the rock, particularly where blasting must be used to prepare the site, and the test must be designed to evaluate the extent of this disturbance. Furthermore, excavation of the foundation may also involve some disturbance to the rock and it is important to make an assessment of the degree of disturbance at the test site compared with the likely condition in the foundation. Three methods of in situ modulus testing are described in this section, starting with tests on small volumes of rock at the periphery of a drill hole and progressing to large scale tests conducted in tunnels. The choice of the appropriate testing method will depend on such factors as the spacing of the discontinuities in comparison with the test volume, the magnitude of the test load in comparison with the structural load, and, of course, time and budget constraints. (a) Borehole tests The deformation modulus can be measured in boreholes using either a borehole dilatometer or a borehole jack. The advantages of borehole testing are that modulus measurements can be made remote from the surface as part of the exploration program, and different geological conditions at the site can be examined. Also, the tests can be carried out relatively quickly and at a lower cost compared with plate load and radial jacking tests. The disadvantages of borehole tests are that the volume of rock tested is small and the measurements are only in the direction at right angles to the borehole axis which may not coincide with the loading direction of the structure. The dilatometer The dilatometer exerts a uniform radial pressure on the walls of the drill hole by means of a flexible rubber sleeve. The expansion of the borehole is measured by the oil or gas flow into the sleeve as the pressure is raised (Goodman et al., 1968), or by potentiometers or linear variable differential

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transformers (LVDT) built inside the sleeve (Rocha et al., 1966). This latter type, in which the measurement devices are arranged at right angles, has the advantage that the anisotropy of the rock can be measured. Figure 4.15 shows the components of a Colorado School of Mines (CSM) type flexible dilatometer. The expansion volume of the borehole is measured with a hand-operated screw pump in which the number of turns or part turns are precisely measured; this requires that the hydraulic system be of rigid construction to minimize errors in measuring dilation. Alternatively, the volumetric expansion can be measured directly in the probe (Bourbonnais, 1985). Figure 4.16 shows typical pressure-dilation graphs for a calibration test carried out in a material of known modulus, and a test carried out in rock. A complete test usually consists of three loading and unloading cycles, with dilation and pressure readings being taken on both the loading and unloading cycles. The shear modulus Gd and the modulus of elasticity Ed of the rock in the drill hole test section are given by (ISRM 1987): (4.11) and (4.12) where L is the length of test section (cell membrane); d is the diameter of drill hole test section; VR is Poisson’s ratio of the rock; ? is the pump con stant (the fluid volume displaced per turn of pump wheel). The stiffness of rock in test section kR is (4.13) where ks is the stiffness of hydraulic system (equation 4.16) and kT is the stiffness of overall system plus rock (ratio D/C in Fig. 4.16). The rock stiffness kR is calculated from calibration of the hydraulic system and the results of a pressuredilation test carried out in a calibration cyl inder of known modulus. The steps for calculating the rock stiffness are as follows. If the elastic modulus and

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Poisson’s ratio of the calibration cylinder are Ec and vc respectively, then the shear modulus Gc of the calibration cylinder is given by (4.14) and the stiffness of the calibration cylinder kc is (4.15) where , and ri, ro are the inside and outside radii of the calibration cylinder respectively. The stiffness of the hydraulic system, ks, is calculated from the stiffness of the calibration cylinder and the slope of the calibration pressuredilation curve, km (ratio B/A in Fig. 4.16) as follows: (4.16) It is also necessary to make a correction for pressure losses due to the rigidity of the membrane. This is determined by inflating the dilatometer in the air without confinement to show the pressure required to inflate the membrane and the hydraulic system. (4.17) where pi,corr is the corrected pressure; pi is the indicated pressure; n is the number of turns to attain pi, and mp is the slope of pressure-dilation curve for dilation in air (MPa/turn). Another correction is required to account for loss of volume in the hydraulic system that takes place in inflating and seating the membrane. For the test measurements shown in Fig. 4.16, the net corrected number of turns ?ncorr is calculated from (4.18) (b) Borehole jack As an alternative to the flexible dilatometer, the borehole jack can be used to measure rock deformability in a drill hole. The jack exerts a directional pressure by means of semi-cylindrical steel loading platens, with the deformation being measured with linear variable differential transformers (LVDTs) built into the cell. Calculation of the modulus is carried out in a

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Figure 4.15 Dilatometer for making modulus measurements in boreholes (ISRM, 1987): (a) components of a dilatometer system; and (b) cross section showing fabrication details of CSM-type dilatometer. 1. Piston actuator. 2. Vernier. 3. Valve. 4. Pressure transducer. 5. Pressure readout. 6. High-pressure stainless-steel tubing. 7. Polyurethane rubber membrane. 8. Removable end cap. 9. High-pressure connection. 10. Pipe thread for insertion tool. 11. Fluid passage.

similar manner to that of the dilatometer, except that allowance must be made for the more difficult boundary conditions. It has been shown by finite element analysis that calculated values of rock modulus should be corrected to account for the variation in the ratio between the steel and the rock moduli (Heuze and Salem, 1977). When the

modulus of the steel is much greater than that of the intact rock (Esteel/Erock>75), the correction factor is negligible because there is little deformation of the steel platens as the pressure is applied. However, when the rock modulus is high compared with the steel modulus, the modulus value calculated from the jack test is less than the true rock modulus

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Figure 4.16 Typical pressure-dilation graphs for a CSM dilatometer test (ISRM, 1987).

and the correction factors shown in Table 4.1 should be applied. (c) Plate load test The plate load test comprises application of a compressive stress normal to the rock surface and measuring the deformation of the rock as the load is applied. The test can be carried out in an exploration adit where the opposite wall of the adit provides the reaction to the applied load, and with the load oriented to coincide with the direction of the structural load, such as the thrust of the abutment of an arch dam. In low modulus rock where substantial deformation is expected, the load can be applied by means of an hydraulic jack. However, the test can be time consuming and expensive because of great weight of the jack and an alternative means of applying the load is to use flatjacks placed between

the two reaction surfaces (Fig. 4.17). Although flatjacks are lighter and easier to handle than hydraulic jacks, they have limited expansion capacity (about 5 mm or 0.2 in.), and a series of flatjacks are required if substantial deformation is expected. Where it is necessary to conduct a test at the ground surface, the reaction can be applied by means of a cables anchored at some depth below the surface using an arrangement such as that shown in Fig. 4.18 (Pusch, 1993). Site preparation consists of removing all rock that may have been loosened by blasting during excavation of the adit and then using grout to create a uniform bearing surface normal to the load direction. The theoretical basis for the plate load test is that the load is applied to an infinite half space, a condition that is not met in a tunnel

Table 4.1 Correction factors for borehole jack modulus measurements Erock/Ecalc

Esteel/Erock

1.09

30.0

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Erock/Ecalc

Esteel/Erock

1.75 2.38 2.86 3.7

7.5 4.8 3.9 3.2

which consists of a small hole in an essentially infinite volume of rock. In order to minimize the restraining effect of the surrounding rock on the deformation induced by the plate loading test, it has been shown that the width of the tunnel should be not less than twice the diameter of the loaded plate as shown in Fig. 4.19 (Misterek et al., 1974). Deformation measurements are made with a tunnel diameter gauge that registers the increase in width of the tunnel, and with multi-position extensometers (MPBX) installed in holes drilled into the rock along the load axis. The depth of the extensometer holes must be such that the deepest anchor is beyond the zone of deformation, a distance of about six times the flatjack diameter. With the use of LVDTs to measure the relative displacement between the anchors and the heads at the rock surface, a continuous reading of deformation can be obtained at some distance from the test location. The extensometer readings provide information on the variation of modulus with depth, the location of open discontinuities and the extent of the blast damage zone. The modulus is calculated from the displacement measurements using equations developed by Timoshenko and Goodier (1951), assuming that the rock is a homogeneous infinite half space of elastic isotropic material. For a test condition in which the bearing plate is circular and has a circular hole in the centre through which the deformation measurements are made, the deformation modulus Ez at any depth z is given by the following expression (ISRM, 1981a and b) (4. 19) where ?z is the measured deflection at depth z below the lower surface of the bearing plate; p is the

applied pressure on the bearing plate; v is the Poisson’s ratio; r1 is the radius of hole in the centre of the bearing plate; r2 is the outer radius of bearing plate; and C is a constant (see below). For a circular bearing plate with radius r and no centre hole and deflection measurements made at depths z below the rock surface, the deformation modulus is given by (4.20) For measurements at the surface of the rock where this expression reduces to (4.21) The theoretical solution for a perfectly rigid plate gives the constant C as p/2, or 1.57. However, allowance must be made for the slight flexibility of the plate through which the load is applied which results in the deformation being somewhat greater than the theoretical deformation. This results in the calculated modulus being less than the true modulus and for this reason the constant C is usually given the value of 2. Heuze and Salem (1977) examined a number of different test conditions and give values for correction factors that should be applied to tests results. These conditions include the ratio Esteel/ Erock, the plate geometry, the anisotropic characteristics of the rock, and the effect of rock breakage under the plate. These calculations show that use of a value of 2 for the constant C is generally satisfactory. However, for anisotropic rock, the plate load test will tend to over-estimate the modulus where the load is applied at an oblique angle to the direction of greatest compression, or lowest modulus. Under these conditions the constant C

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Figure 4.17 Typical set up for a uniaxial jacking test in which the load is applied through hydraulic flatjacks (Misterek et al., 1974, © ASTM, reprinted with permission). 1. Concrete pad. 2. 1 m diameter flatjack. 3. Particle board pad. 4. Top plate. 5. MPBX anchors-5 or more/hole. 6. MPBX sensor head. 7. Rubber sleeve over lead wires. 8. Transducer lead wire. 9. Hydraulic hoses. 10. Hydraulic pump, 70 MPa. 11. Data-acquisition system MPa. 12. NX drill hole, depth=6 flatjack diameters. 13. Prepared diameter, 1.5 to 2×flat jack diameter. 14. Base plate. 15. Screws for set up and removal. 16. Tunnel diameter gauge. 17. 254 mm diameter aluminum columns. 18. Tunnel surface.

may have a value as low as 1.0–0.8. (d) Radial jacking test The plate load test has a number of limitations, namely that the load is applied along a single axis and, in the case of widely jointed rock, the loaded area may encompass few if any discontinuities in which case the rock mass is not being tested. These limitations are overcome to some degree by the radial jacking test in which a uniform radial pressure is applied to a length of the periphery of a tunnel, and radial deformations are measured along a number of axes. The results of this test will provide the deformation modulus of a larger volume of the rock mass than is possible with the plate load test and, in the case of anisotropic rock, will show the variation of the modulus with respect to the bedding or foliation orientation. Although more information on rock conditions is

provided by the radial jacking test than the plate load test, the high cost and time required for conducting the test means that very few will be carried out and thus the results may not be representative of the overall site. Details of the set up, testing and analysis procedures are described by Wallace et al. (1969), Misterek (1969), Golze (1977), ISRM (1981a). The test set up consists of first carefully preparing a length of tunnel by removing all blast damaged rock and irregularities so that the rocksurface is as close to a circular shape as possible. The tunnel diameter should be about 2.5 m (8 ft). The test length should at least equal to the diameter, and the length of the tunnel with a circular section should be about 1.5 times the length of the test length to eliminate possible end effects. A shotcrete or concrete lining is then placed to produce a smooth bearing surface

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INVESTIGATION AND IN-SITU TESTING METHODS

Figure 4.18 Typical arrangement of plate load test at ground surface (Pusch, 1992). 1. Hydraulic jacks. 2. Steel beam reaction head. 3. Steel lid. 4. Tie rods. 5. Concrete foundation. 6. Schistose gneiss. 7. 100 mm dia. anchor holes.

for the jacks. If the purpose of the test is to measure the rock modulus, then the lining should be segmented so that it produces no restraining effect on the radial strain of the rock. If the purpose of the test is to examine the lining together with the rock, then the lining should not be segemented and its properties should be modeled according to those of the prototype. A series of radial holes are then drilled and multiposition extensometers installed with the longest anchor at a depth where no rock deformation will take place. This depth is about two diameters from the loaded surface, which can be checked by carrying out trial calculations of deformation versus depth for typical test parameters. The number of extensometers installed in the central plane of the test section can vary from 4 to 16 equally spaced

around the circumference. Additional reference extensometers arrays can be placed at distances of 0. 5 and 1.0 times the test length along the tunnel to measure deformation remote from the pressure zone. Where the rock is anisotropic or contains a predominant discontinuity set, some extensometers can be oriented parallel and perpendicular to the structure. The pressure can be applied either using water pressure (Fig. 4.20, Oberti et al., 1986), or a series of hydraulic flatjacks (Fig. 4.21; ISRM, 1981a or b). The advantage of using water pressure is that uniform pressure can be applied over a considerable length of the tunnel, but it is necessary that the rock surface be completely sealed, which may be difficult in low modulus rock. Details of the setup of a radial jacking test using flatjacks shown in

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Figure 4.19 Required dimensions of adit for conducting uniaxial jacking tests (Misterek et al., 1974, © ASTM reprinted with permission): (a) analysis condition—loading at boundary of semi-infinite elastic solid; and (b) site conditions showing required dimensions of tunnel. Note: R is the radius of the loaded area and the diagrams are not to scale.

Fig. 4.21 illustrates the use of circular steel sets and shaped wooden lagging, located at a uniform distance from the flatjacks, to provide reaction to the applied pressure. The deformation is measured with short, single position extensometers referenced to a central, independently supported beam. The rock mass deformation modulus is calculated along any radius from the pressure-deformation measurements assuming that the test consists of a circular hole in an infinite elastic medium with a uniform radial pressure applied to a finite length of the surface of the hole. An exact solution to this condition has been presented by Tranter and Craggs (1945) which assumes that the rock is continuous, homogeneous, isotropic and elastic. It is considered that these conditions are adequately satisfied for the radial jacking test because the discontinuities do not open or fail by shear. The following calculation procedure provides a reasonably accurate analysis of the test results; a more detailed analysis can be carried out by numerical methods. If flatjacks are used (Fig. 4.21), the applied load

values are first corrected to give an equivalent distributed pressure p1 on the test chamber lining: (4.22) where p1 is the distributed pressure on the lining at radius r1; b is the width of the flat jack; r1 is the radius at flatjacks; pm is the manometric pressure in the flatjacks. The equivalent pressure p2 at a measuring radius r2 just beneath the lining and outside the zone of irregular stresses beneath the lining and any loose rock is calculated as follows: (4.23) Superposition of displacements for two ‘fictitious’ loaded lengths is used to give the equivalent displacements A for an infinitely long test chamber (Fig. 4.22): (4.24) where ?A1 is the measured deformation at the center of the test chamber; and ?B is the measured

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Figure 4.20 Radial jacking test: pressure applied with water pressure and extensometers aligned parallel and perpendicular to geological structure (Oberti et al., 1986). 1. Extensometer lead wires. 2. MPBX—total of four. 3. Steel tube. 4. Waterproof lining. 5. Reinforced concrete ring. 6. Inflatable rubber ring. 7. Roller to position tube.

de formation at a distance L from the center of the test chamber (where L is the length of the test chamber). The result of the long duration test ?d under maximum pressure (max. p2) is plotted on the displacement graph (Fig. 4.23). Test data for each cycle are proportionally corrected to give the complete long-term pressure-displacement curve. The elastic component ?e and the plastic component ? p of the total deformation ?t are obtained from the deformation at the final unloading: (4.25) The elastic modulus E and the deformation modulus of the rock mass, Em at radial distance r2 (Fig. 4.21) are obtained from the pressure-displacement curves (Fig. 4.23) using the following formulae based on the theory of elasticity: (4.26) (4.27) where p2 is the maximum test pressure; and v is the estimated value for Poisson’s ratio. As an alternative to equations 4.26 and 4.27, the

moduli of undisturbed rock may be calculated taking into account the effect of a fissured and loosened region by using the following formulae: (4.28) (4.29) where r3 is the radius to the limit of the assumed fissured and fractured zone. 4.5.2 Direct shear tests Direct shear tests may be conducted in situ where there is a discontinuity that has a critical influence on sliding stability, and which contains an infilling such as a sensitive clay that would be disturbed by removing the sample for laboratory testing. Probably the most important purpose of an in situ shear test is to determine the cohesion of the dis continuity infilling because this strength parameter can have a very significant effect on the stability. It is difficult to obtain an intact, undisturbed sample of a discontinuity containing a soft clay and

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Figure 4.21 Details of the arrangement of flat jacks in a radial jacking test (ISRM, 1981). 1. Circular steel set. 2. Wedge to expand steel set. 3. Central reference beam. 4. Expansion measuring surface, radius r2 . 5. Flatjack radius r1. 6. Steel rod. 7. Dial gauge extensometer. 8. Hardwood lagging. 9. Flatjack. 10. Shotcrete lining. 11. Rock surface. 12. Extensometer drill hole.

determine the peak shear strength in the laboratory. However, if the infilling is thick enough, samples can be dug out of the discontinuity and recompacted into a laboratory shear box and the approximate cohesion determined in this manner. An effective test program would consist of a limited number of in situ tests, backed up by extensive laboratory testing. A typical in situ direct shear test set up is shown in Fig. 4.24 (Saint Simon et al., 1979). In the case of tests conducted in adits, the reaction for the normal load is obtained from the opposite wall of the adit. Tests can be conducted on a rock surface using cables anchored into the rock adjacent to the test site to supply the normal reaction. The first task in the test is to isolate a block of rock above the discontinuity surface without disturbing the infilling; in weak rock such as shales it may be possible to use hand excavation methods, but in

stronger rocks, diamond saws would have to be employed. Wherever possible, the direction of the shear load should be set up so that it is coincident with the likely direction of sliding. For example, on the Nukui arch dam project in Japan, the shear strength of a vertical fault in one abutment was tested in direct shear by setting up both the normal and shear load acting horizontally. The test procedure would be similar to that of the laboratory direct shear test in that a constant normal load is applied and the shear load is gradually increased until sliding takes place. The normal and shear displacements are measured with dial gauges. If there are two shear load jacks operating in opposite directions, the sample can be reset after each test, in order to conduct tests at a number of different normal loads and obtain values of both the peak and residual strengths. 4.6 References

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Figure 4.22 Method of superposition to give displacements for equivalent uniformally distributed loading—elimination of end effects (ISRM, 1981). Barton, N.R. (1973) Review of a new shear strength criteria for rock joints. Engineering Geology, 7, 189– 236. Barton, N.R. and Choubey, V. (1977) The shear strength of rock joints in theory and practice. Rock Mechanics, 10(1–2), 1–54. Black, W.H., Smith, H.R. and Patton, F.D. (1986) Multilevel ground water monitoring with the MP System. Proc. NWWA-AGU Conf. on Surface and Borehole Geophysical Methods and Groundwater Instrumentation, Denver, CO, pp. 41–61. Boart Longyear Co. (1996) Oriented core drilling service technical literature. Bourbonnais, J. (1985) New developments in rock testing and monitoring equipment for tunneling projects. Proc. 5th Annual Canadian Tunneling Conference, Montreal, pp. 106–125. Call, R.D., Savely, J.P. and Pakalnis, R. (1982) A simple core orientation device. In Stability in Surface Mining (ed. C.O.Brawner), SME, AIME, New York, pp. 465–81. Cedergren, H.R. (1989) Seepage, Drainage and Flownets, 3rd edn, Wiley, New York. Colog Inc. (1995) Borehole Image Processing System

(BIP), Golden, Colorado and RaaX Co. Ltd, Australia. Davis, J.L. and Annan, A.P. (1989) Ground penetrating radar for high resolution mapping of soil and rock stratigraphy. Geophysical Prospecting, 37, 531–51. Deere, D.U. and Miller, R.P. (1966) Engineering Classification and Index Properties of Intact Rock. Technical Report No. AFWL-TR-65–116. Air Force Weapons Laboratory, Kirkland Air Force Base, New Mexico. Fecker, E. and Rengers, N. (1971) Measurement of large scale roughness of rock planes by means of profilometer and geological compass. Proc. Symp. on Rock Fracture, Nancy, Paper 1–18. Freeze, R.A. and Cherry J.A. (1979) Groundwater, Prentice-Hall, New Jersey, p. 234. Geological Society Engineering Group Working Party (1970) The logging of rock cores for engineering purposes. Q. J. Eng. Gel., 3, 1–24. Geological Society Engineering Group Working Party (1977) The description of rock masses for engineering purposes. Q. J. Eng. Gel., 10, 355–88. Golze, A.R. (ed.) (1977) Handbook of Dam Engineering. Van Nostrand Reinhold, New York, pp. 235–40. Goodman, R.E. (1976) Methods of Geological

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Figure 4.23 Typical pressure-displacement curves for radial jacking test (ISRM, 1981). Engineering. West, St. Paul, pp. 102–22. Goodman, R.E., Van, T.K. and Heuze, F.E. (1968) The measurement of rock deformability in boreholes. Proc. 10th Symp. on Rock Mechanics, AIME, Austin, Texas, pp. 523–55. Griffiths, D.H. and King, R.F. (1988) Applied Geophysics for Geologists and Engineers, (2nd edn), Pergamon Press, Oxford. Heuze, F.E. and Salem, A. (1977) Rock deformability measured in situ—problems and solutions. Int. Symp. on Field Measurements in Rock Mechanics, Zurich, pp. 375–87. Hiltscher, R., Carlsson, A. and Olsson, T. (1984) Determination of the deformation properties of bedrock under turbine foundations. Rock Mech., 17, 37–49. Horslev, M.S. (1951) Time lag and Soil Permeability in Ground Water Measurements. US Corps of Engineers Waterways Experiment Station, Bulletin No. 36. International Society for Rock Mechanics (ISRM) (1981a) Rock Characterization, Testing and Monitoring; ISRM Suggested Methods. (ed. E.T.Brown). Pergamon Press, Oxford. International Society for Rock Mechanics (ISRM) (1981b) Basic geological description of rock masses. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 18, 85–110 International Society for Rock Mechanics (ISRM)

(1981c) Suggested Methods for the Quantitative Description of Discontinuities in Rock Masses (ed. E. T.Brown), Pergamon Press, Oxford. International Society for Rock Mechanics (ISRM) (1987) Suggested methods for deformability determination using a flexible dilatometer. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 24(2), 123–34. Inkster, D.R., Rossiter, J.R., Goodman, R., Galbraith, M. and Davis, J.L. (1989) Ground penetrating radar for subsurface environmental applications. 7th Thematic Conference on Remote Sensing for Exploration Geology, Calgary, Alberta, Canada, pp. 127–40. Jacob, C.E. (1950) Flow of ground water, in Engineering Hydraulics (ed. H.Rouse), Wiley, New York, pp. 321–86. Lo, K.Y. and Yung, T.C. B. (1987) A field method for the determination of rock mass modulus. Can. Geotech. J., 24, 406–413. Louis, C. (1967) A study of Groundwater Flow in Jointed Rock and its Influence on the Stability of Rock Masses. Doctorate Thesis, University of Karlsrue (in German). English translation Imperial College (London) Rock Mechanics Research Report No. 10, Sept. 1969. Lutz, J. and Morey, J. (1988) Utilization and Computerization Processing of Exploratory Drilling Parameter Recordings. JEAN LUTZ S.A. Technical

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Figure 4.24 Typical set up for an in situ direct-shear test in an adit (Saint Simon et al., 1979). 1. Rock anchor. 2. Hand-placed concrete. 3. WF beam. 4. Hardwood. 5. Steel plates. 6. 30 ton jack. 7. Dial gauge. 8. Steel rollers. 9. Reinforced concrete. 10. Bearing plate. 11. Styrofoam. 12. 50 ton jack. 13. Steel ball. Literature No. 88–136. Misterek, D.L. (1969) Analysis of data from radial jacking tests. Determination of the in situ modulus of deformation of rock, ASTM STP 477, Am. Soc. for Testing and Materials. pp. 27–38. Misterek, D.L., Slebir, E.J. and Montgomery, J.S. (1974) Bureau of Reclamation procedures for conducting uniaxial jacking tests. Field testing and instrumentation of rock, ASTM, STP 554, Am. Soc. Testing and Materials, pp. 35–51. Oberti, G., Bavestrello, F. and Rossi, R.P. (1986) Rock mechanics investigations, design and construction of the Ridracoli Dam. Rock Mech. and Rock Eng., 19, 113–42. Patton, F.D. (1987) Personal communication. Patton, F.D. and Deere, D.U. (1970) Significant geological factors in rock slope stability. Proc. Symp. on Planning Open Pit Mines, Johannesburg, South Africa. Balkema, Amsterdam, pp. 143–51. Peterson, J.E., Sullivan, J.T. and Tater, G.A. (1982) The use of computer enhanced satellite imagery for geologic reconnaissance of damsites. ICOLD, 14th Cong. on Large Dams, Rio de Janiero, Q53, R26, Vol. II, pp. 449–71. Rocha, M. (1967) A method of integral sampling of rock

masses. Rock Mech. 3(1), 1–12. Rocha, M., DaSilveira, A., Grossman, N. and DeOliveira, E. (1966) Determination of the deformability of rock along boreholes. Proc. 1st ISRM Cong., Lisbon, Vol. 1, pp. 697–704. Saint Simon, P.G. R., Solymar, Z.V. and Thompson, W.J. (1979) Damsite investigation in soft rocks of Peace River Valley, Alberta, Canada. Proc. 4th Int. Conf. on Rock Mechanics, Montreux, Vol. 2, Int. Soc. Rock Mechanics, pp. 553–60. Skermer, N.A. (1984) M Creek debris flow disaster. Canadian Geotechnical Conference: Canadian Case Histories, Landslides, Toronto, pp. 187–94. Stahl, R.L. (1973) Detection and Delineation of Faults by Surface Resistivity Measurements—Gas Hills Region, Wyoming. US Bureau of Mines, RI 7824. Terzaghi, R. (1965) Sources of errors in joint surveys. Geotechnique, 15, 287. Terzaghi, K. and Peck, R.P. (1967) Soil Mechanics in Engineering Practice (2nd edn), Wiley, New York, pp. 660–73. Theis, C.V. (1935) The relation of the lowering of the piezometric surface, and the rate and duration of discharge of a well using ground water storage. Trans. Amer. Geophysical Union, 16, 519–24.

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Timoshenko, S. and Goodier, J.N. (1951) Theory of Elasticity, (2nd edn), McGraw-Hill, New York. Todd, D.K. (1959) Ground Water Hydrology. Wiley, New York, pp. 47–9 and pp. 78–114. Tranter, C.J. and Craggs, J.W. (1945) The stress distribution in a long circular cylinder when a discontinuous pressure is applied to the curved surface. Phil. Mag., 36, 241–50. Tse, R. and Cruden, D.M. (1979) Estimating joint roughness coefficients. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 16, 303–7. VanDine. D.F. and Lister, D.R. (1983) Debris torrents -a

137

new natural hazard? The British Columbia Professional Engineer, 34(12), 9–12. Wallace, G.B., Slebir, E.J. and Anderson, F.A. (1969) In situ methods for determining deformation modulus used by the Bureau of Reclamation. Determination of the in situ modulus of deformation of rock, ASTM STP 477, Am. Soc. for Testing and Materials, pp. 3–26. Yu, X. and Vayassade, B. (1991) Joint profiles and their roughness parameters. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 28(4), 333–6.

5 Bearing capacity, settlement and stress distribution

5.1 Introduction Two types of rock foundations, each requiring different design procedures, are illustrated in Fig. 5.1. The upper photograph shows spread footings for a cut and cover structure founded on an interbedded sequence of very weak sandstone and shale. With each footing surrounded by a considerable extent of intact rock, the primary design task for these foundations is determination of the allowable bearing pressure and the magnitude of the settlement. The lower photograph shows a bridge foundation located near the crest of a vertical slope in very strong granite. The rock has adequate bearing capacity for the applied loads and settlement will be elastic and negligible. Therefore, the primary design task is to ensure that blocks of rock in the foundation formed by continuous joints are stable against toppling and sliding. This chapter describes methods for determining the bearing capacity and settlement of footings on fractured rock, while Chapter 6 discusses foundation stability. Most foundations consist of square or rectangular reinforced concrete structures that are sized to ensure that the rock can support the structural loads without excessive settlement. A particular feature of spread footings on rock is that the bearing surface need not be normal to the direction of the applied load because rock has significant shear strength, and it is possible to install anchors to provide additional shear resistance if required. Thus, vertical loads can be supported on sloping rock faces, or inclined loads on horizontal surfaces. Where external loads such as wind, water

and seismic forces act on a structure, overturning moments and uplift forces may be developed and the foundation design must accommodate these conditions. When uplift forces are developed it may be necessary to install tie-down anchors (see Chapter 9). The majority of foundations on rock are spread footings at the ground surface, but there are conditions for which this type of footing may not be suitable. These conditions include locations where the available bearing area is insufficient resulting in excessive contact pressure, or where suitable bearing surfaces occur at a considerable depth and it is uneconomical to excavate the overlying weak material. In these cases socketed piers would be required (see Chapter 8). The design of surface footings on rock encompasses the following three tasks that examine different aspects of foundation performance: 1. the bearing capacity of the rock to ensure that there will be no crushing or creep of the material within the loaded zone; 2. settlement of the foundation which will result from both elastic and inelastic strain of the rock, and possibly compression of weak seams within the volume of rock compressed by the applied load; 3. sliding and shear failure of blocks of rock formed by intersecting discontinuities within the foundation. This condition usually occurs where the foundation is located on a steep slope and the orientation of the discontinuities is such that the blocks can slide out of the open face.

BEARING CAPACITY OF FRACTURED ROCK

Figure 5.1 Photographs of foundations on rock showing different geometrical and geological conditions: (a) spread footings for a cut and cover structure founded on very weak, horizontally bedded rock; and (b) bridge footing on very strong rock containing continuous vertical discontinuities (photograph by Mark Goldbach).

139

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The performance of a foundation must be checked with respect to all three of these conditions because they are independent of each other. For example, a footing on very strong rock with ample bearing capacity and minimal settlement may still fail if blocks formed by persistent discontinuities can slide from the foundation. Also, a footing on a thin slab of strong rock may exhibit excessive settlement as a result of compression of an underlying soft seam despite the upper layer having adequate bearing capacity and there being no open face on which a sliding failure could take place. 5.2 Bearing capacity The usual method of determining allowable bearing pressures is to use published tables or building codes relating allowable values to rock type. However, in circumstances where the rock conditions do not match descriptions in the codes, it is more appropriate to use limit equilibrium or numerical methods incorporating appropriate rock mass strength parameters. The method used will depend on such factors as movement tolerances and the complexity of geological conditions at the site. Thus, for a low rise building located on a uniform rock type it is common to use the codes to determine the allowable bearing pressure, while for a dam or large bridge on fractured rock containing seams of compressible rock, more detailed analysis may be required (Rawlings and Wyllie, 1986). For rock foundations where the rock is stronger than the concrete from which the footing is constructed, the bearing capacity of the rock will be of no consequence. It is found that bearing capacity problems usually relate to details of the structural geology. This section describes methods of determining the bearing capacity of foundations in the following geological conditions: 1. fractured and weathered rock; 2. shallow dipping bedding planes; 3. layered formations; 4. karstic formations.

5.2.1 Building codes For many structures, the required dimensions of the footing bearing area can be determined from published tables or building codes which list allowable bearing pressure for various rock types. Table 5.1, from the building code for the city of Rochester, New York, gives allowable bearing pressures for three classes of rock defined by their strength, and describes the influence of discontinuities on bearing capacity (Goodman, 1980). Table 5.2 lists allowable bearing pressures for a variety of geological conditions defined by rock type and age. The bearing pressures listed in Table 5.2 have been developed from observations of existing stable structures and incorporate a substantial factor of safety, so settlement should be minimal. However, the values given are related mainly to the rock strength, and must be reduced where the rock is weathered, fractured, or is non-homogeneous and contains seams of weak and decomposed rock. Usually allowable bearing pressures are determined from the allowable settlement, which in rock is mainly related to the discontinuity characteristics. Settlement results from closure of open discontinuities, and compression of seams containing low strength infillings. Where the rock is sound but fractured, the bearing pressures given in Table 5.2 can be modified to ensure that settlement is minimal. The effect of fracture intensity on bearing capacity can be estimated from the RQD of drill core as follows (Peck et al., 1974): • RQD>90%–no reduction; • RQD>50%, <90%–reduce bearing pressure by factor of about 0.25–0.7; • RQD<50%–reduce bearing pressure by a factor of about 0.25–0.1; reduce bearing pressure further if extensive clay seams present. The application of the allowable bearing values in Table 5.2 and these reduction factors requires information on sub-surface conditions and the application of some judgment. If it is considered that

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Table 5.1 Provisions of the Building Code for Rochester, New York (dates given in parenthesis)

*The 1.5 m (5 ft) depth limit for weak seams is a guideline that may not be applicable under all conditions. An estimate on the volume of rock influenced by a foundation load can be obtained by assuming that the stress in the rock is insignificant once the stress level is less than 10% of the applied stress. For isotropic, elastic rock, the stress distribution in the foundation takes the form of a cone, with a side slope angle of 1H:2V, defining the rate at which the foundation stress diminishes with depth. Under these conditions, the 10% stress level occurs at a depth equal to about twice the width of the footing.

the actual rock properties do not meet the general conditions applicable to Table 5.2, or for the design of structures such as dams or nuclear power plants where a particularly high degree of reliability is required, there are a number of methods of calculating the allowable bearing capacity as described below. Shown on Table 5.3 are actual bearing pressures used on a number of projects reported in the literature, as well as the type of structure and the geology. The bearing pressures quoted are not necessarily the limiting value for the site because it is likely that the design bearing pressures are dependent on such factors as the type of structure and its tolerance for settlement, and the required size of the bearing surface to accommodate the structure. The bearing pressures in Table 5.3 range from a high of 7.2 MPa for very strong granitic rock on the Canadian shield for a comparatively lightly

loaded structure, to a low of 0.2 MPa for a bridge constructed on shale in Spain. These values can be compared with those prescribed by Building Codes in Table 5.2. 5.2.2 Bearing capacity of fractured rock Figure 5.2(a) shows a foundation bearing on a horizontal rock surface. At bearing pressures well below the ultimate bearing capacity the rock will behave elastically and the settlement of the footing can be calculated from equation 5.18 in Section 5.4.1. However, at increased loads where the pressure approaches the ultimate bearing capacity of the rock, fractures will be initiated which will grow and coalesce forming wedges and areas of crushed rock (Fig. 5.2(a)). These conditions will result in dilatancy of the rock and the formation

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Table 5.2 Allowable bearing pressures for fresh rocks according to typical building codes. Reduce values to account for weathering, unrepresentative fracturing or non-homogeneous rock*. Values from Thorburn (1966), Woodward et al. (1972) and Ontario Ministry of Transport and communications (1983)

Table 5.3 Allowable bearing pressures (qa) for completed projects Number Project

Location

1

Museum

Sudbury, Canada

2

Steel arch bridge– 220 m span Apartment building

New Jersey, USA

3 4 5

Rock type

Igneous-quartzite conglomerate Grand Canyon, USA Dolomitic limestone

Steel truss bridge– West Virginia, USA 760 m long Humber suspension UK bridge

qa MPa (ksf) 7.2 (150)

Reference

Franklin and Pearson (1985) 2.4 (50) Cannon and Turton (1994) Diabase, fractured; 2 (40); 0.6 (12) Kaufman and Brand till (30 blows/ft) (1991) Sandstone; shale 1.5 (30); 1(20) Kaufman and Brand (1991) Chalk 1.25 (26) Simm (1984)

BEARING CAPACITY OF FRACTURED ROCK

143

Number Project

Location

Rock type

qa MPa (ksf)

Reference

6

Bridge

Galacia, Spain

Shale and schist

1.0 (20)

7

Suspension bridge– 1990 m span

Kobe, Japan

8

10

Concrete box girder Brisbane, Australia bridge– 260 m span Nuclear power Lancashire, UK station Viaduct bridge Galacia, Spain

Sedimentary—soft 0.88 (18) claystone and sandstone Sedimentary—coal, 0.8 (17) shale, siltstone Sandstone, 0.63 (13) mudstone Granite—weathered 0.72(15)

Serrano and Olalla (1995) Yamagata et al. (1995)

11

Cable stayed bridge

Badajoz, Spain

12

Bridge

River Lagos Spain

9

Gneiss—highly weathered Shale and quartzshale

of radial fractures that expand outwards and can eventually reach the surface to create a wedge of rock. Displacement of such a wedge can result in sudden failure of the footing. The diminished strength of the rock under the footing (zone A) compared with the unfractured surrounding rock (zone B) is illustrated in the Mohr diagram (Fig. 5.2(b)). This diagram demonstrates that the rock under the footing is in a state of triaxial compression with the major principal stress equal to the bearing pressure (q) and the minor principal stress equal to the confinement applied by the surrounding rock. The maximum stress that the surrounding rock can sustain is the uniaxial compressive strength of the rock mass σu(m) in zone B, assuming that the footing is at the ground surface. These conditions apply where there are no predominant discontinuities that can form preferred failure surfaces, or where the rock is porous, such as chalk, that can compress under the foundation loading. Calculation of the bearing capacity of closely fractured, or very weak rock based on the failure mechanism illustrated in Fig. 5.2, can be carried out in a manner similar to soil mechanics. This procedure, as developed by Bell and extended by Terzaghi (1943), is a simplified and conservative analysis which approximates the curved shear failure surfaces that develop in the foundation

0.43 (9) 0.3 (6)

Williams (1989) Thompson and Leach (1991) Serrano and Olalla (1995) Serrano and Olalla (1995) Serrano and Olalla (1995)

because no exact mathematical solution has been derived for analyzing such a failure. The simplified analysis assumes straight lines for the failure surfaces, and ignores the weight of the rock in the foundation as well as the shear stresses that develop along the vertical interface between the two wedges. The analysis is based on the assumption that active and passive wedges, defined by straight lines, are developed in the rock under the footing, and the shear strength parameters of these sur faces are those of the rock mass (Fig. 5.3(a)). For a footing of infinite length bearing on a horizontal rock surface, the rock under the foundation is assumed to be in compression similar to a specimen in a triaxial compression test. The major principal stress in zone A, s1A, is equal to the footing pressure q, if the weight of the rock beneath the footing is neglected. Zone B is like a triaxial compression test with the major principal stress s1B acting horizontally, and the minor principal stress s3B acting vertically. If the footing is at the ground surface s3B is zero, while if the footing is below the rock surface, the surcharge qs is equal to the average vertical stress produced by the rock weight above the footing level. At the moment of foundation failure both zones shear simultaneously and the minor principal stress in zone A, s3A, equals the major principal stress in zone B, s1B. The minor principal stress in zone A is

144

BEARING CAPACITY, SETTLEMENT AND STRESS DISTRIBUTION

Figure 5.2 Bearing capacity of foundation bearing on rock surface: (a) formation of fractured rock (A) beneath footing contained by wedges of intact rock surrounding footing (B); and (b) Mohr diagram of stresses in bearing rock.

produced by the resistance of zone B to being compressed, which is the uniaxial compressive strength of the rock mass (Fig. 5.3(b)). The strength of rock in triaxial compression (s1, s3) can defined as a curved envelope (Hoek-Brown strength criterion) as described in Section 3.3.3. Using this criterion, the strength of a fractured rock mass is (5.1) where m and s are constants which depend upon the type of rock and the degree to which the rock is fractured (see Table 3.7); su(r) is the unconfined compressive strength of intact rock, and s1, s3 are the major and minor principal stresses respectively. Equation 5.1 gives the major principal stress acting on zone A, s1A. The minor principal stress on zone A, s3A, is the strength of the rock in zone B, and is equal to the uniaxial strength of the rock mass when the surcharge is zero. The uniaxial compressive strength of a fractured rock mass is (5.2)

and the bearing capacity is equal to the major principal stress in zone A which is given by ( 5 . 3 ) The plot in Fig. 5.3(b) shows the relationship between the strength s1A and the confining stresses provided by the surrounding rock s3A. This illustrates that a very significant increase in the bearing capacity is produced by a small increase in the confining pressure. The allowable bearing pressure qa is related to the rock mass strength by the factor of safety FS and the correction factor Cf1: (5.4) The factor Cf1 is applied to the calculated allowable bearing pressure to account for the shape of the foundation and has the values given in Table 5.4

BEARING CAPACITY OF FRACTURED ROCK

145

Figure 5.3 Analysis of bearing capacity of fractured rock: (a) active A and passive B wedges in foundation; and (b) curved rock mass strength envelope. Allowable bearing pressure=qa, strength of bearing rock=s1A, factor of safety

(Sowers, 1970). A more comprehensive procedure for calculating the ultimate bearing capacity of fractured rock is described by Serrano and Olalla (1994) in which the rock mass strength is defined by the Hoek and Brown strength criteria as above. The method of analysis can accommodate recessed footings, inclined loads and foundations located on sloping ground surfaces. For most loading conditions on sound rock the factor of safety will be in the range 2–3 for which there is little risk of settlement. A factor of safety of 3 is used for the dead load plus the maximum live load. If part of the live load is temporary such as wind and earthquake, then a factor of safety of 2 can be used (US Department of the Navy, 1982). In the equations to calculate the allowable bearing capacity for a fractured rock mass with the strength

defined by curved strength envelopes, it is important to distinguish between the compressive strength of the intact rock and that of the rock mass. The intact rock strength su(r) is determined from laboratory tests on rock cores, while for fractured rock the strength is defined by equation 5.1 with the degree of fracturing of the rock mass being accounted for by the constants m and s. 5.2.3 Recessed footings In the case of a footing which is recessed into the rock surface, it is necessary to modify equation 5.4 to account for the increase in the stress s1s as a result of the confining stress qs applied at the ground surface. That is, the minor principal stress

146

BEARING CAPACITY, SETTLEMENT AND STRESS DISTRIBUTION

Table 5.4 Correction factors for foundation shapes Foundation shape

Cf1

Cf2

Strip Rectangular

1.0

1.0

1.12 1.05 1.25 1.2

0.9 0.95 0.85 0.7

Square Circular

s3B is equal to qs and the modified value of the allowable bearing pressure is as follows. Curved strength envelope: (5.5) where (5.6) 5.2.4 Bearing capacity factors For weak rock with little fracturing, an expression for the allowable bearing capacity is the Bell solution , which is developed using the same principles as described in Section 5.2.2. This bearing capacity analysis takes into account the weight of the rock in the active wedge, as well as the confinement provided by the surrounding rock where the footing is recessed below the surface. The Bell solution for the allowable bearing capacity for a strip, square or circular footing is (5.7) where B is the footing width (for strip or square footing) or diameter (for circular footing); ?r is the rock density; D is the depth of embedment; and c is the rock mass cohesion. The correction factors Cf1 and Cf2 which account for the footing shape are given in Table 5.4. The terms Nc, N? and Nq are bearing capacity factors defined as follows (Lambe and Whitman, 1969):

(5.8) The factor Nc shows where the influence of the cohesion, the factor N? shows the influence of the soil weight and foundation width, and the factor Nq shows the influence of the surcharge. As discussed in Section 5.2.2 above, the activepassive wedge analysis is a simplified and conser vative method of analysis. Furthermore, values for the bearing capacity factors determined from laboratory experiments show that the actual values are higher than the theoretical values, particularly for rough bearing surfaces and high friction angles. Figure 5.4 shows values for the three bearing capacity factors in relation to the friction angle based on the trial wedge method developed by Terzaghi (1943). These experimental values are known to underestimate actual values in foundations and can differ from values calculated in the Bell solution (equation 5.8). The conditions for which equation 5.7 and the bearing capacity factors given by Fig. 5.4 can be used are as follows: 1. loading is vertical and concentric; 2. depth of embedment D is less than or equal to B; 3. foundation rock is uniform to depth below the maximum expected shear surface; 4. water level is lower than depth of the shear surface; 5. foundation rock has strength parameters

BEARING CAPACITY OF FRACTURED ROCK

defined by friction angle and cohesion; 6. friction and adhesion on the vertical sides of the footing are neglected. Note that equation 5.7 can be simplified if the weight of the wedge of rock in the foundation is It ignored, and the footing is at the surface is justified to ignore the weight of the rock where it is a small proportion of the foundation load. Under these conditions, equation 5.7 reduces to (5.9)

5.2.5 Foundations on sloping ground For conditions where the foundation is located on a sloping ground surface, it is necessary to modify the bearing capacity factors to account for the reduced lateral resistance provided by the smaller mass of rock on the downslope side of the footing. On shallow slopes where the slope angle is less than , bearing capacity or settlement will usually control the allowable working load on the footing. For , it is seldom slopes angles greater than necessary to check bearing capacity because the stability of the slope will be the controlling factor (Hong Kong Geotechnical Engineering Office, 1981). For foundations on sloping ground surfaces, the allowable bearing pressure is calculated as follows: (5.10) where Ncq and Nc? are bearing capacity factors given in Fig. 5.5, and Cf1 and Cf2 are correction factors which account for the footing shape and are given in Table 5.4. The value of the factor Ncq depends on the stability number No which is defined as (5.11) where ?r is the rock density, c is the rock mass cohesion and H is the slope height as shown in Fig. 5.5. The calculation of allowable bearing capacity using

147

the bearing capacity factors given in Fig. 5.5 and equations 5.10 and 5.11 assumes that the water table is at a depth at least equal to the width of the footing below the base of the footing. Where the water table is higher than this level, stability analyses should be carried out including the effect of water pressures in the foundation. For foundations located on level ground at the crest of a slope, the allowable bearing pressure will be reduced if the foundation is at a distance less than about six footing widths behind the crest. The stability of slopes with foundations located close to the crest can be checked by the methods of stability analysis described in Chapter 6 using a factor of safety of 2–3 so that deformation will be minimal. 5.2.6 Bearing capacity of shallow dipping bedded formations In the methods of calculating bearing capacity described in Section 5.2.2, the failure mechanism involved development of a passive wedge of rock that induced a confining stress on the active wedge of rock beneath the footing. The magnitude of this confining stress depends on the strength of the rock mass composed of either intact rock, or interlocking fragments of intact rock. However, if the rock contains sets of discontinuities that form one or more of the surfaces of this wedge, the bearing capacity of the foundation may be reduced for two reasons. First, the shape of the wedge will be defined by the orientation of the discontinuities and the dimensions and surface area of the wedge may be limited and second, the strength of the discontinuities is usually significantly less than that of the rock mass. These conditions could result in failure of the foundation due to displacement of the passive wedge. Figure 5.6 shows a foundation containing two sets of conjugate joints dipping at angles ?1 and ?2 which form the base surfaces of an active wedge (A) and a passive wedge (B) respectively. The minimum principal stress s3A acting horizontally on the active wedge A can be calculated from equation 5.12 as

148

BEARING CAPACITY, SETTLEMENT AND STRESS DISTRIBUTION

Figure 5.4 Bearing capacity factors for footings located on horizontal ground surface (US Dept of the Navy, 1982).

follows (Ladanyi and Roy, 1971):

(5.12)

BEARING CAPACITY OF FRACTURED ROCK

149

Figure 5.5 Values for bearing capacity factors for footings located on sloping ground surface (US Dept of the Navy, 1982).

from which the allowable bearing pressure is (5.13)

where B is the width of foundation; ?1 is the dip of discontinuity set 1; c1, c2 are the cohesions of discontinuity sets 1 and 2 respectively;

150

BEARING CAPACITY, SETTLEMENT AND STRESS DISTRIBUTION

Figure 5.6 Bearing capacity of foundation on rock containing inclined bedding planes and orthogonal joint sets.

follows and and are the friction angles of discontinuity sets 1 and 2 respectively. If the rock surface around the footing is subjected to a surcharge pressure qs, as might be the case if the footing were recessed into the ground surface, then the bearing capacity is significantly increased due to the confinement provided to the passive wedge. The surcharge qs is incorporated into the analysis of the bearing capacity by modifying equation 5.12 as

(5. 14) One method of improving the bearing capacity of a foundation on a layered formation is to install rock bolts that are anchored below the level of the passive wedge and then tensioned against the rock surface. This has the effect of applying an artificial surcharge at the ground surface; equation 5.14 can be used to calculate the magnitude of the bolting force required to achieve the required bearing capacity.

EXAMPLE 5.1 BEARING CAPACITY

The following is an example comparing the allowable bearing capacities calculated by the alternative methods described in this section. Consider a 2 m wide strip footing bearing on the surface of a fair quality limestone in which the average discontinuity spacing is 400 mm and the discontinuities contain some clay. The strength properties of the rock are as follows:

1. unconfined compressive strength of intact rock, , 2. curved strength envelope parameters: . 3. rock density,

MPa or 11 000 p.s.i. (Table 3.6); (Table 3.7);

BEARING CAPACITY OF FRACTURED ROCK

Note that for a strip footing, the correction factors Cf1 and Cf2 are equal to 1. BUILDING CODES From Tables 5.1 and 5.2, a bearing capacity of about 1– 2 MPa (21–42 kips ft-2) can be interpreted for rock which is moderately strong and has a moderate discontinuity spacing. HOEK-BROWN STRENGTH CRITERION The allowable bearing pressure for a rock mass with the strength properties defined by a curved strength envelope is calculated using equation 5.4. For a factor of safety of 3, and the values of m, s and su(r) given above, the allowable bearing pressure is calculated to be 1.14 MPa (23.8 ksf). BELL SOLUTION Application of equation 5.7 to calculate allowable bearing capacities from the bearing capacity factors requires values for the rock mass friction angle and cohesion. These two parameters are obtained from equations 3.16–3.19. For an average pressure on the foundation of 2 MPa, the instantaneous values for the friction angle cohesion are 25° and 0.54 MPa respectively and the value of the factor is 2.47. From equations 5.8 the bearing capacity factors are:

From equation 5.7, the allowable bearing pressure, assuming a strip footing of width 2 m, is:

This calculation shows that the weight of the rock wedge (the second term in equation 5.7) in the foundation has little influence on the allowable bearing pressure. If the foundation were recessed a depth of 1 m below the ground surface, the third term in equation 5. 7 becomes 0.14. Therefore, recessing the footing to a depth of only 1 m has little influence on the bearing capacity. Values for the bearing capacity values can also be obtained from Fig. 5.4 from which the allowable bearing capacity calculated from equation 5.7 is 3.7 MPa (77 ksf).

As discussed in Section 5.2.4, the Bell solution (equation 5.7) is a conservative method of calculating bearing capacity, and the use of bearing capacity factors given in Fig. 5.4 will give higher bearing capacities. Furthermore, the low bearing capacities given by the building codes are an indication of the conservatism that is built into the building codes to account for the range of geological conditions that the codes can accommodate. SHALLOW DIPPING BEDDED FORMATIONS If the rock contains two sets of orthogonal joints which dip at and the allowable bearing capacity is calculated from equation 5.13. Assume that the friction angle of both these joint surfaces is 25° so that the factors If the cohesion of both joint sets is zero, the allowable bearing capacity is 0.03 MPa (0.54 ksf), and if the cohesion is 0.5 MPa (72.5 p.s.i.), the allowable bearing capacity increases to 1.8 MPa (38 ksf). This result shows that persistent

151

152

BEARING CAPACITY, SETTLEMENT AND STRESS DISTRIBUTION

Figure 5.7 Spread footings on layered rock formations with rigid upper layer and weaker lower layer and weaker lower layer (Sowers, 1976): (a) punching failure; (b) buckling failure; and (c) bending failure.

discontinuities oriented approximately parallel to the surfaces of the active and passive wedge in the foundation will significantly reduce the allowable bearing capacity.

5.2.7 Bearing capacity of layered formations Where a footing is located on a thin slab of strong rock overlying a considerable thickness of much weaker rock, there are three possible failure mechanisms. The footing may punch through the stronger, upper layer, or the upper layer could fail in either buckling or bending (Fig. 5.7). In all these cases, failure of the upper layer of rock is likely to result in a sudden and substantial settlement of the foundation if the material in the lower layer has little load bearing capacity. Hoek and Londe (1974) quote a case of a footing for a high-rise building with a load of 2000 MN (225 000 ton) that punched through a 10 m (33 ft) thick sound limestone bed.

Another possible failure mode is that of settlement of the combined two layer system; calculation of settlement is described in Section 5.3. With the upper layer of rock having a significantly higher modulus than the lower layer, the upper layer will carry most of the load and foundation stability will depend primarily on the capacity of this layer. The usual procedure in the initial stages of design would be to assume that the upper layer carries all the load since this will produce a conservative design. If the deformation moduli of the two materials can be accurately defined, then finite element analysis, for example, may be carried out to determine the stress distribution between the layers more precisely and the foundation design could be modified accordingly.

BEARING CAPACITY OF FRACTURED ROCK

The mode of failure of the upper layer will depend on the rock mass properties of each layer, and the ratio of the thickness of the upper layer H to the width B of the footing. If the ratio H/B is low and the lower layer is compressible such as weathered or porous rock, then a punching type failure may take place. However, if the lower layer is plastic and incompressible such as clay or soft shale, then the upper layer may buckle (Sowers, 1976). For higher values of the ratio H/B and if the lower layer is compressible, then the upper layer may fail in bending. For a punching type failure, the bearing capacity of the foundation is found by multiplying the shear strength of the rock in the upper layer by the surface area of the failure surface. This surface can be assumed to be cylindrical in shape with an area equal to the product of the perimeter of the footing and the thickness of the bed. Sowers (1977) describes punching failures of a spread footing located on porous Miami oolite overlying a thick bed of considerably weaker porous oolite and sand. One failure occurred under a 1.5 m (5 ft) thick fill, and another under a spread footing which had been recessed into the upper bed thus diminishing the surface area available to resist punching failure. The calculated perimeter shear in the upper oolite crust was about 90 kPa (1.87 ksf). Remedial measures for these punching failures comprised grouting the lower bed to improve its bearing capacity, and in other locations cavities in the oolite were cleaned of sand and then filled with concrete. The shear strength of the rock in the upper layer may be determined by direct shear testing, if a machine with sufficient capacity to fail intact rock is available. An alternative means of determining shear strength is to construct a Mohr’s envelope from the tensile and compressive strengths of the intact rock (Kaderabek and Reynolds, 1981). Where the mode of failure comprises bending and tension, the stability of the foundation is assessed by comparing the tensile strength of the rock with the tensile stress level in the lower side of the slab. The theoretical tensile stresses in the lower side of the upper layer can be calculated using the methods of

153

Roark and Young (1970), assuming the bearing slab is circular in shape, is simply supported around the edges and no support is provided by the underlying, compressible material. The tensile stress st in the center of the lower surface of a circular slab loaded with uniform load Q acting over an area with radius B/2 is (Fig. 5.7(c)): (5.15) where M is the maximum moment at the center of the slab under the applied load given by (5.16) where r is the radius of circular slab supporting the load, H is the thickness of the slab and v is the Poisson’s ratio of the rock. The value of the parameter r0 depends on the relative dimensions of the diameter of the loaded area B and the thickness of the slab: (5.17) In applying this equation, a decision has to be made on the appropriate value for the radius of the slab r if this is not defined by the geology or topography of the site. A sensitivity analysis will show that the stress level reaches an approximate maximum value as the radius increases and this will give an indication of the likely stress level that should be used in design. Kaderabek and Reynolds (1981) report that full scale load tests were carried out to try and induce a beam tension failure, but none occurred despite the theoretical maximum tensile stress exceeding the laboratory tensile strength by a factor of 2. There has been no reported failure of this type in the south Florida area (Kaderabek and Reynolds, 1981). 5.3 Bearing capacity of karstic formations The design of foundations in karstic formations is one of the most challenging tasks in rock foundation

154

BEARING CAPACITY, SETTLEMENT AND STRESS DISTRIBUTION

engineering and there are unfortunately instances of failures related to solution of lime-stones and the formation of sink holes (Sowers, 1975; Costopolous, 1987). These failures are the result of both the location of structures on undetected solution features, and the development of sink holes after construction because of pumping to dewater nearby excavations. Successful foundation design in these conditions requires first the location of solution cavities so that the structure is suitably sited, and second, the determination of appropriate bearing values and construction procedures (Knott et al., 1993). 5.3.1 Characteristics of solution features The formation of solution features is the result of chemical solution of limestone by percolating ground water containing dissolved carbon dioxide which makes the water slightly acidic. During the early stages of solution, cavities will tend to form on joints and bedding along which the water flow is concentrated and the cavities may follow a reasonably regular pattern. As the solution process develops and the cavities enlarge, their size, location and shape become impossible to predict with any certainty, and careful and detailed investigation programs are required when designing foundation in these formations. The following is a brief description of common karst features. • Slots and pinnacles Slots are narrow, linear features dissolved along a guiding structural feature such as a joint or bedding plane, with pinnacles of rock remaining between the slots (Fig. 5.8(a)). These features are formed by dissolution along vertical fractures or by downcutting due to lateral ground water flow along the bottom of slots. The slots usually have maximum widths of about 1–2 m (3–6 ft) but their depths can be as great as 10 m (30 ft) and their lengths can be traced for hundreds of meters. The peaks of the pinnacles are often rounded and streamlined. Slots and pinnacles have also been observed in tilted and folded rock with dips as great as 45°, in which the upper parts of the

slots are vertical, while in the lower part of the slots the control of inclined features becomes more noticeable. Where the limestone contains a more chemically resistant bed, overhangs or even bridges may form in the slots as the less resistant rock is dissolved more rapidly on each side of this bed. Slots appear to have poorly developed internal drainage systems with infiltrating ground water being collected and moved laterally from minor slots to master slots under the residual soil blanket. Therefore, piping and sediment transport are less effective than in solution cavities and there is often a thick layer of soil overlying and masking the slots that may eventually collapse into the slot. Voids in the soil zone occur due to migration of soil particles into the underlying drainage cavities, and usually occur near the top of rock and enlarge until they collapse and form sink holes. • Karst valleys In karst regions the surface drainage is typically diverted into underground routes resulting in the disruption of the surface drainage. For example, tributary streams end abruptly in swallow holes and high-order streams emerge from karst springs. Most large scale drain-age basins have both fluvial (surface) and karst (underground) drainage components, and when all the flow is underground a dry valley is created. • Negative relief landforms Karst regions typically have low areas, or sinkholes, which slope down into closed depressions in which the only ground water exit is underground; sinkholes may develop suddenly with collapse of the soil layer, or may settle slowly over time (Fig. 5.8(b)). Solution cavities form where high permeability pathways accelerate dissolution of the rock and enlarge drainage paths into which soil and insoluble residue, and eventually boulders and rock fragments, are transported by piping, washing and gravitational collapse. These flow pathways form chimneys which may have vertical, sloping and horizontal sections and are controlled by resistant beds that concentrate the water flow. Sinkholes are usually bowl shaped depressions that may be barely perceptible or have diameters as large as 1000 m (3000 ft). Where a resistant caprock bed limits the

BEARING CAPACITY OF FRACTURED ROCK

horizontal development of the solution cavity it may have steep sides and greater depth than a cavity in more uniform rock. • Positive relief landforms Some positive karstic landforms include pinnacles in the form of isolated spires above the surrounding terrain, and residual hills shaped as cones (near vertical sides) and towers (vertical sides) where resistant caprock protects the limestone from dissolution while the surrounding rock is dissolved. • Caves Caves can be either single conduits or interconnected mazes which can be categorized by their shape as follows. A linear passage is a straight segment that follows a well defined discontinuity, an angulate passage has straight sections connected by sharp bends formed as the water flow follows the regional joint pattern, and a sinuous passage consists of broad sweeping curves and typically occurs in flat lying rocks. Interconnected mazes can comprise a network of passages formed on the regional joint pattern. • Residual soil Residual soil is the material that remains after the carbonate rock has been dissolved and carried away, and typically occupies only a tiny fraction of the original volume of rock. It comprises the insoluble materials of the rock such as silica in the form of chert or quartz, clay minerals and other clastics, and often iron oxide which remain after the limestone is dissolved (Sowers, 1976a). The residual soil forms a blanket over the rock surface and partially or entirely fills cavities and seams that are eroded into these openings by seeping water. Eventually, channels may become clogged by the eroding residual soil which will halt further solution and result in increased dissolution at other points. The strength of residual soils often decreases with depth because of the migration of soil particles and the higher moisture content, with the soil close to the contact with the rock being much softer and often pasty. Generally, the soil is structureless due to the great reduction in volume during its formation and subsequent transportation. The rocksoil interface is well defined and sharp, usually with some limestone or chert boulders floating in the soil mass above the boundary. However, in highly sandy

155

or shaley limestones with high proportions of impurities, some relic structure may be seen and the rock interface may comprise a zone of highly weathered limestone. In many areas, sedimentary, colluvial or glacial deposits may overlie the residual soil. 5.3.2 Detection of solution features The detection and location of solution features usually involves application of a number of integrated techniques starting with collection of past experience and historical records, as well as aerial photography for site reconnaissance, followed by geophysics for site specific studies, and finally drilling for detailed design. In locations where solution cavities are suspected, it is usual to locate drill holes at each footing or pier position. Aerial photographs can be used to detect karstic terrain which is shown by such topographic features as basin-studded plains, narrow U-shaped valleys with vertical sides, rolling topography, and scalloped effect around river systems, with streams entrenched in bedrock on rectangular patterns. It is often useful to examine photographs over an extended time period which may show, for example, the progressive development of solutioning, or that sinkholes have been obscured by human activities. Geophysical methods suitable for the detection of solution cavities are ground penetrating radar (GPR), microgravity surveys and electrical resistivity (see Section 4.1.2). The selection of the most appropriate technique(s) for each site will depend on the particular site conditions, with the decision being made by personnel with experience in the area. For example, GPR has been used successfully in Florida where the cavities are overlain by sand (Benson, 1984), but is less successful in Pennsylvania where the overburden is a clayey soil with a high moisture content. The reliability of geophysics to detect solution cavities and predict their shape is limited because these features often occur at variable depths, have

156

BEARING CAPACITY, SETTLEMENT AND STRESS DISTRIBUTION

Figure 5.8 Diagram of sink hole development: (a) section showing stages of ravelling into enlarged joints by roof spalling and soil erosion; and (b) plan showing development of sink holes along alignment of joint sets (adapted from Knott et al., 1993).

irregular shapes and can be filled with materials which can include air, water, clay and boulders. For

this reason drilling is often carried out for final design.

BEARING CAPACITY OF FRACTURED ROCK

Diamond drilling is the most reliable method of investigating karstic terrain because it is possible to distinguish between bedrock, boulders and soil infilling, and to obtain samples for laboratory strength testing. Percussion drilling, which is faster and less expensive than diamond drilling, may also be used as a supplementary investigation method where, for example, there is a need to examine a large number of lightly loaded footings. Percussion drilling needs full-time inspection (or recording devices) to note changes in penetration rates and the nature of the cuttings. As a guideline on the number of drill holes that may be needed to investigate a foundation, it can be shown that if a solution cavity occupies 10% of the surface of the bearing area, then 16 uniformly spaced drill holes are required to be certain of detecting this feature, and if only five holes are drilled, the probability of detection drops to 50% (Benson et al., 1982). 5.3.3 Foundation types in karstic terrain The types of foundations suitable for karstic terrain may be grouped under the three headings: shallow foundations, foundation treatment and deep foundations. These are discussed briefly below and their advantages and limitations are described in Table 5.5. (a) Shallow foundations Shallow foundations are used where the rock is at a shallow depth of less than about 3 m (10 ft), or suitable bearing soils are available at the surface. They can also be used in conjunction with foundation treatments such as pressure grouting, compaction grouting, jet grouting or overexcavation and backfill of soft areas with concrete or granular material. For small cavities where there is sound rock around the periphery, it is often possible to enlarge and reinforce the foundation to bridge over the solution feature, using a conservative bearing capacity, or to construct pedestals bearing on prepared surfaces. If the arrangement of the holes or footings results in some eccentricity of the foundation it may be necessary to combine one or

157

more footings to form a strap or mat foundation. Figure 5.9 shows a number of different designs for a series of foundations where the load is carried on the peripheral rock (Katzenbach and Romberg, 1987). With shallow foundations there may be a risk of settlement, particularly where the footing is bearing on the overburden soil. Settlement, which can arise as the result of compression and consolidation of the soil, may be irregular and depend more on the thickness of the soil overlying pinnacles and slots rather than on the magnitude of the foundations loads. In the more highly stressed areas of the soil above the pinnacles, compression may result in the soil punching into the areas of deeper, softer soil. Furthermore, the soil may also consolidate under the increased loads and this may occur at a slower rate than the compression and continue for a year or more. These processes may be accelerated by lowering of the water table, by construction dewatering for example. Probably the most frequent cause of settlement is raveling and erosion of the soil into underlying solution cavities where the particles are carried away by the ground water system. These processes may occur slowly and progressively if the cavities are of limited size, or rapidly if an arch or bridge were to collapse. Where footings are located on rock, there may be a risk that the bearing material is a pinnacle that could move under the increased loading, or an underlying cavity could collapse. (b) Foundation treatment Foundation treatment for shallow foundations consists of filling cavities and placing the footing on the fill. Shallow, cone shaped cavities are cleaned as deep as possible and plugged with lean concrete forming a plug that is at least 1.5 times thicker than its width. If drilling with a jack hammer shows that the rock around the pit is sound, then the bearing capacity of the foundation will not be impaired. Fill methods that have been used include graded gravel for low capacity loads (Couch, 1984), mixtures of 70% cement, 25% sand and 5% bentonite pumped into voids (Klopp, 1969), grouting of sand filled seams (Sowers, 1977), lean ‘dental’ concrete

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BEARING CAPACITY, SETTLEMENT AND STRESS DISTRIBUTION

(Antes, 1981) and mass concrete fill in cleaned out voids to support a mine hoist (Wagener, 1984). Grouting is usually carried out where the footing bears on rock containing voids, to both strengthen the rock and prevent migration of soils into the open cavities. The procedure is to drill a pattern of holes

into the bearing rock and inject grout at low pressure; successive series of holes are then drilled at progressively closer split spacing (primary, secondary and tertiary holes) until the grout take diminishes. The grout may be either neat cement, or contain fillers such as sand (e.g. mix ratio 2 parts

Table 5.5 Foundation types in karstic terrain (Knott et al., 1993) Foundation type I Shallow foundations Spread footings: on soil; on granular pad on soil

Advantages

Limitations

Low cost foundations; granular pads Susceptible to settlement damage due improves shallow soil bearing to consolidation, desiccation or capacity. migration of soil particles, or if low strength soil present. Collapse of underlying cavities could also damage footing. Use with extreme caution. Spread footings bearing on rock Low cost foundation; potential Potential for differential settlement if eliminated for settlement due to soft seams are not removed from consolidation, desiccation or joints in underlying rock. Footing migration of soil particles. could also be damaged by settlement of weathered rock or collapse of cavities below bearing surface. Grouting may be required to fill voids in rock. Footing supported by pedestals Less costly than deep foundations; Depth to bedrock must be reasonably bearing on rock allows flexibility during construction well known before construction. Same limitations apply as to spread footings on rock. Spread footings bearing on lean Reduced risk of settlement due to Higher cost than spread footings on concrete pad over rock consolidation, desiccation or rock. Footings can be damaged by migration of soil particles. Can settlement of underlying weathered eliminate visible soil filled slots. zones or collapse of cavities. May require grouting to fill voids. II Foundation treatment Spread footings on rock or soil with Low cost foundations; grouted pad Susceptible to settlement damage due grout cap to fill voids in soil and rock improves shallow soil bearing to consolidation, desiccation or capacity, and modulus of rock. migration of soil particles, or if low strength soil present. Collapse of underlying cavities could also damage footing. Use with extreme caution. Spread footings with vibra- Potentially cheaper than some other Provides pathway for water to seep replacement (stone columns) deep foundation treatments into underground karst drainage network, resulting in potential for particle migration and increased solution activity. Generally not a good approach for karst areas. Deep dynamic compaction Voids in soil can be collapsed. Does not work well in clayey soil. Potentially less costly than some Does not eliminate potential for

BEARING CAPACITY OF FRACTURED ROCK

Foundation type

Advantages other deep treatment techniques.

Pressure injected footings (PIF) on rock.

Adaptable to variable rock surfaces and ground water conditions. Ability to break through voids in soil due to impacts. Impacts also load tests PIF as it is being driven.

III Deep foundations Drilled shafts in rock

Adaptable to variable depths, can assess the presence of cavities by drilling probe holes, can drill through weathered zones and voids.

H-piles to rock

Low cost for deep foundations if actual lengths are known. Easy to drive. Additional piles can be added to provide redundancy. Hardened tips can help to reduce tip damage.

Mini-piles or pin piles into rock

Successful in areas where other methods failed. Can verify capacity by drilling probe hole or test loading, or by providing long bond zone below top of rock. Suitable for highly variable rock surfaces, voids in soil or rock, high ground water tables.

sand to 1 part water) or fly ash, depending on cost, required strength and the widths of the voids (see also Section 7.6). Possible limitations of grouting are that the grout could preferentially flow into, but not necessarily fill, a single open cavity and penetrate minimally into tighter cavities. Diamond drilling would often be required to confirm the quality and extent of the grouting. Another means of increasing the bearing capacity where the vertical depth of the solution cavities is limited, is to use dynamic compaction to break up and consolidate the upper layer. Couch (1984)

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Limitations particle migration. Generally not a good approach for karst areas. Ability to break through voids needs to be verified. Cannot evaluate conditions below pile tip. Similar limitations to spread footings on untreated rock. Foundation type not commonly used. Experienced personnel needed on site to determine shaft depth. Relatively high cost. Ground water can be a problem. Hard rock drilling can be a problem overcome by correct equipment. Capacity uncertain due to potential for pile damage from driving, voids may be present under pile and poor tip contact on sloping rock. Variable lengths may result in differential settlement due to elastic shortening. Difficult to estimate pile length requirements. May have to telescope holes several times to penetrate boulders, fractured rock. Pregrouting of overburden may by necessary to penetrate soft or collapsed zones and stabilize voids. Lateral stability should be evaluated, particularly for voids in soil. Must assure capacity of rock using long bond zone in rock if voids or soil filled slots may exist. Load tests may be required where rock quality is questionable based on drilling. Costly pile type.

reports the use of a 15 tonne weight dropped from a height of 18 m (60 ft) to consolidate the upper 8–10 m (25–30 ft) of the foundation by collapsing the cavities. The limitations of dynamic compaction are that it does not reduce the potential for soil migration into underlying cavities, and the results can be difficult to quantify. (c) Deep foundations Deep foundations are those with their depth at least twice their width, and include drilled shafts, H-piles and pin piles; they are used where the depth to sound rock exceeds the depth of normal excavating

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BEARING CAPACITY, SETTLEMENT AND STRESS DISTRIBUTION

equipment. The following is a brief description of each foundation type (Knott et al., 1993). • Drilled shafts, or caissons These are formed by drilling a large diameter hole (up to about 1 m or 40 in) to a depth where there is a rock stratum capable of supporting the load on the shaft; the hole is then filled with concrete. Drilled shafts are typically used where the rock surface is very irregular and consequently their lengths are often variable across a site which requires suitable contractual terms to accommodate this condition (Brown, 1991). The capacity of the shaft is usually based on end bearing on rock and very high bearing capacities can be achieved in sound rock, but the rock below the shaft should be probed for cavities, clay seams and weathered rock by drilling exploratory holes. Additional capacity can be obtained by drilling a socket into rock and accounting for the rockconcrete shear strength (see also Chapter 8). The hole is usually drilled with an auger through the soil and weathered rock to form a uniform bearing surface on sound rock. The augering may need to be supplemented with DTH percussion drilling, coring, or drilling and blasting to remove protruding soil and rock. During these operations care must be being taken that the air used to lift the cuttings does not blow out soil seams and that the blasting does not open new seepage paths. Where clay filled seams are encountered in the base, they could be cleaned out and filled with concrete, or rock bolts could be installed from the base of the caisson into sound rock to tie the caisson to the shaft. Alternatively, a pipe pile or H-pile could be driven through the bottom of the shaft into the seam, provided that the seam is not so deep that an excessive length of pile is required to achieve satisfactory bearing. Where the caisson hangs up above a cavity, it may be possible to install pin piles from within the shaft to pass through the cavity into sound rock (Sowers, 1984). Inflow of ground water into the drill hole can be a significant problem and pumping should only be carried out if there is no risk that this will produce settlement in nearby structures due to the removal of the underlying soils. Furthermore, the pumping

volume may be significant; Wagener (1982) reports that a pump with a capacity of 27 000 liters per hour (7100 gal/h) was not able to dewater an 18 m (60 ft) deep shaft. If dewatering is not possible, then the tremie method (pipe extending to lower end of shaft) or bottom dump buckets can be used to place the concrete through the water. Some of the concerns with this situation are that segregation of the concrete may occur, and that flowing ground water may wash fines from the concrete as it sets. The quality of the concrete should be checked by coring, with grouting carried out if necessary, to fill voids. The drainage of limestone foundations can have a number of detrimental effects on stability. First, the increased seepage gradients can result in faster rates of solution with consequent enlargement of solution cavities which increases the stress on the adjacent rock. Second, the increase in the effective unit weight of the rock has the effect of increasing the loading on the rock. Third, the flow of water may dislodge loosely consolidated infilling material. • End bearing piles Piles are the most common type of deep foundation because they are cheaper to install than drilled shafts and additional piles can readily be driven to account for piles that do not have the full bearing capacity. The piles are driven to top of rock or into the rock to penetrate the weathered rock and cavities. The piles are usually equipped with hardened tips and stiffened ends to minimize tip damage and provide capacity to penetrate the rock. Where tip damage is particularly severe, damage can be minimized by pre-drilling a large diameter hole through any obstructions into sound rock and then concreteing the pile into the hole. H-piles are used more frequently than pipe piles, and compact sections, such as HP 12×57 instead of HP 12×53, are used to help resist buckling. The bearing capacity of piles will depend on the rock conditions at the tip; piles may enter pits or open joints with the result that they will bend and twist and have a lower bearing capacity, for a specified deflection, than shorter piles (Fig. 5.10). Piles will also have reduced bearing capacity where

BEARING CAPACITY OF FRACTURED ROCK

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Figure 5.9 Examples of construction procedures for spread footings on karstic terrain (after Katzenbach and Romberg, 1987): (a) concrete-plug; (b) partial replacement of collapse material with concrete; (c) footing supported by underground bridge; (d) shallow foundation with screw jacks for adjustment; (e) driven pile in collapse material, with socketed pier in rock.

they are end bearing on a hard seam above a

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BEARING CAPACITY, SETTLEMENT AND STRESS DISTRIBUTION

Figure 5.10 Influence of karstic structure on pile support (after Sowers, 1976). 1. Long, supported pile. 2. Pile bent and wedged in crack. 3. Pile tip damaged on sloping rock surface. 4. Pile bearing on pinnacle. 5. Pile bent and not supported. 6. Short, supported pile.

compressible seam, where they strike a sharp projection and the end is split, or where they punch into porous rock. Furthermore, piles may stop on a weak pinnacle that resists impact from driving, but may gradually move under applied load. If the solution cavity is very deep and end bearing piles cannot be used effectively, then batter piles may be required to locate areas of sound rock. In assessing the bearing capacity of piles driven in cavernous limestone, some precautions that may be taken are as follows. Where the irregular rock bearing surface results in the pile lengths differing by more than about 10%, an elastic analysis is required to estimate each pile’s share of the total load and assess the need for additional piles (Sowers, 1975). Furthermore, the load capacity may be reduced, compared with end bearing on sound rock, by as much as 25% to account for the uncertain bearing conditions (Daly, 1990). Finally, where the quality of the bearing rock is uncertain, the bearing capacity can be checked by pre- or postdrilling holes with an airtrack to check that

approximately 3m (10ft) of sound rock exists below the bearing level (Wagener, 1982). Methods of assessing the capacity of piles include specifying a refusal limit, and dynamic pile monitoring (RojasGonzalez et al., 1993). • Pin piles (micro or mini piles) These consist of small diameter, typically about 180 mm (17 in) diameter, grouted pipe sections inserted into an oversized hole that has been drilled to a specified distance into rock (Fig. 5.11). Conventional drilling equipment is used but telescoping holes may be required in poor ground in order to install several stages of casing. This allows piles to be installed through soil into a wide variety of rock conditions, inclined at a variety of angles, and located where there is restricted access for larger drills or pile driving equipment, and where piling vibrations are not permitted (Bruce and Nicholson, 1989). The grout may be neat cement grout or a sandcement mix which is placed with a tremie tube extending to the bottom of the pipe. When the pipe is full, a pressure fitting is attached to the top of the

BEARING CAPACITY OF FRACTURED ROCK

pile and further grout is injected until it returns at the annulus. Pin piles in rock can be designed for load transfer by end bearing, skin friction, or a combination of both. Skin friction in the soil portion of the pile is not considered in the capacity calculations, but it is developed in the rock portion and can be an important component of the capacity where there are voids below the tip and end bearing is uncertain. The overall load capacity of the pile is limited by the small cross-sectional area of the steel and grout and their resistance to bursting, buckling and cracking, as well as shear failure along the periphery, particularly where the drill hole has intersected cavities in the rock. Pin piles have been used in the renovation and expansion of the Orchestra Hall in Chicago, where limited head room precluded the use of driven piles and hand excavated caissons would have been too expensive. The construction procedure was to use an hydraulic rotary drill to advance holes to a depth of 30 m (100 ft) through clay and hard pan and penetrate to a depth of about 0.5 m into the limestone bedrock. The drill rod was a 180mm (7 in) diameter, 13mm (0.5in) wall thickness steel pipe, fitted with a sacrificial carbide cutting shoe, that remained in the hole as the pin pile. After drilling, a rebar cage was placed at the tip of the pile and a tremie tube was used to fill the pile with neat cement grout (28 day unconfined compressive strength of 41MPa or 6000p.s.i.). Finally, additional grout was pumped down the pile under pressure to fill the tip area and the drill hole annulus. Load tests on selected pin piles showed load capacities of between 1.87 and 2.45 MN (420 and 550 kips) with a permanent deformation of 24 and 2.5 mm (0.95 and 0.1 in) respectively, with 100% of the load being carried at the pile tip and none in skin friction (Scherer et al., 1996). 5.4 Settlement For many foundations on rock, the bearing material can be considered to be elastic and isotropic so

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settlement occurs as the load is applied, and there is no time dependent effect. Under these conditions, settlement can be calculated using elastic theory with appropriate values for the modulus and Poisson’s ratio of the rock mass. The mechanism of settlement of foundations on rock depends on the combined properties of the intact rock and the discontinuities, and depending on these properties, four different types of settlement can be identified: 1. settlement resulting from a combination of strain of the intact rock, slight closure and movement of discontinuities, and compression of any minor clay seams. If the rock is strong and elastic, and any clay seams present are thin (less than a few millimeters thick), it can be assumed that the settlement will also be elastic, and elastic theory can be used to calculate settlement. Elastic theory can be applied to the calculation of settlement of foundations on isotropic, homogeneous formations, layered formations and transversely isotropic materials. 2. settlement resulting from the movement of blocks of rock due to shearing of discontinuity surfaces. This will most often occur where foundations are located at the crest of a steep slope and potentially unstable blocks of rock are formed in the face. In hard rock where there is little difference between the peak and residual strength of the discontinuities, a small amount of displacement may be followed by sudden collapse. 3. time dependent settlement which includes foundations on ductile rocks such as salt which strain continuously at any stress level, and brittle rocks if the applied stress exceeds the yield stress (see Table 3.10). Time dependent settlement may also occur if the rock contains substantial seams of clay or other plastic rock. 4. settlement due to subsidence of the underlying strata which can occur in coal mining areas where collapse of the openings occurs following extraction of the coal resulting in the formation of a trough shaped depression at the

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BEARING CAPACITY, SETTLEMENT AND STRESS DISTRIBUTION

Figure 5.11 Typical pinpile installed in hole drilled into karstic bedrock (adapted from Knott et al., 1993).

ground surface (see Section 5.4.4). The following is a summary of methods of calculating settlement; for complex geological conditions where none of these methods apply, numerical analysis may be required.

5.4.1 Settlement on elastic rock Elastic theory can be used to calculate settlement for a range of geological conditions which include homogeneous, isotropic rock, layered formations and transversely isotropic rock (Fig. 5.12). The data required for these analyses comprise the rock properties expressed in terms of the modulus and

BEARING CAPACITY OF FRACTURED ROCK

Poisson’s ratio of each formation, the position and thickness of each layer, where applicable, and the foundation shape and bearing pressure. When calculating settlement using the procedures described in the following sections, it is advisable to carry out sensitivity analyses to determine the influence of the layer dimensions and elastic properties of the rock mass on settlement. Rock mass moduli can rarely be determined with precision, so it is important to calculate the settlement for the range of moduli and dimensions that may exist at the site. (a) Homogeneous, isotropic rock Where the rock mass is homogeneous and isotropic (Fig. 5.12(a)), the vertical settlement dv is given by equation 5.18 for a foundation approximated as one or more uniformly distributed loads acting on circular or rectangular areas near the surface of a relatively deep stratum (Schleicher, 1926): (5.18)

165

where q is the uniformly distributed bearing pressure; B is the characteristic dimension of the loaded area, which for a circular area is the diameter, and for a rectangular area is the smaller dimension; Cd is a parameter which accounts for the shape of the of the loaded area and the position of the point for which settlement is being calculated; v is Poisson’s ratio and E is Young’s modulus. Table 5.6 gives values for parameter Cd for circular, square and rectangular footings bearing on uniform, elastic rock. The use of equation 5.18, together with the appropriate shape and rigidity factor Cd, allows calculation of settlement for a wide range of foundation shapes. (b) Layered formations The settlement of footings on layered formations, where the upper layer is relatively thin compared with the footing dimensions, can be calculated using elastic theory in a similar manner to that of isotropic rock. This section demonstrates the application of this method to the following three geological conditions (Fig. 5.12(b, c, d)):

Table 5.6 Shape and rigidity factors Cd for calculating settlements of points on loaded areas at the surface of an elastic half space (after Winterkorn and Fang, 1975) Shape

Center

Corner

Middle of short side

Middle of long side

Average

Circle Circle (rigid) Square Square (rigid) Rectangle: Length/width 1.5 2 3 5 10 100 1000 10000

1.00 0.79 1.12 0.99

0.64 0.79 0.56 0.99

0.64 0.79 0.76 0.99

0.64 0.79 0.76 0.99

0.85 0.79 0.95 0.99

1.36 1.52 1.78 2.10 2.53 4.00 5.47 6.90

0.67 0.76 0.88 1.05 1.26 2.00 2.75 3.50

0.89 0.98 1.11 1.27 1.49 2.20 2.94 3.70

0.97 1.12 1.35 1.68 2.12 3.60 5.03 6.50

1.15 1.30 1.52 1.83 2.25 3.70 5.15 6.60

1. a compressible layer overlying a rigid base, such as a surface layer of weathered rock overlying fresh rock; 2. a relatively thin bed of compressible rock within a formation of stiffer rock;

3. a bed of stiff rock beneath which there is a much thicker bed of more compressible rock. These conditions are most likely to be encountered in sedimentary formations where, for example, there

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is a bed of low modulus clay shale within a stiffer sandstone. Where the actual conditions at a site do not exactly match any of the models shown in Fig. 5.12(b, c, d), or the moduli are not known accurately, a sensitivity analysis would be carried out to examine the influence of modulus ratios and bed thickness on the settlement magnitude. In most cases the calculated settlement will be sufficiently accurate when compared with the estimates made of the modulus values and the allowable settlement tolerance of the structure. Where the models are not sufficiently accurate, as may be the case for inclined beds of varying thickness (Fig. 5.12(e)), numerical analysis will be required. (c) Compressible layer on rigid base The model shown in Fig. 5.12(b) of a compressible layer overlying a rigid base can be used, for example, where there is a zone of weathering over fresh rock extending to a considerable depth. The effect of the rigid base is to diminish the settlement as compared with that produced where the weathered rock extends to a considerable depth. Settlement is calculated using equation 5.18, with replacing Cd. Table 5.7 gives values shape factor for a variety of foundation shapes for the factor bearing on an elastic layer of thickness H underlain by a rigid base; the values given in the Table are applicable to the center of the footing (Fig. 5.12(b)). The assumptions made in the calculation of the are that, at the interface between the factor compressible upper layer and the rigid base, there are no horizontal shear stresses acting and no horizontal displacement. (d) Compressible bed within stiff formation Settlement of a formation consisting of a relatively

thin bed of compressible rock underlying a bed of stiffer rock (Fig. 5.12(c)) can be calculated in a similar manner to that of a compressible layer overlying a rigid base. The calculation procedure assumes that the lower bed is infinite and acts as a rigid base, and that the middle and upper beds act as a single, compressible bed. Using these can be obtained assumptions, the shape factor from Table 5.7, and the settlement is calculated using the modulus of the weighted average of the two beds. Thus the effective modulus of the two layers is (E1H1+E2H2)/(H1+H2), and the value of H applied in Table 5.7 is (H1+H2). Equation 5.18 is then used to calculate the settlement. This calculation method tends to over-estimate the settlement amount because it does not account for the load distributing effect of the upper stiff layer. The upper layer supports a significant portion of the load and there is less load distributed into the lower, compressible bed (see Fig. 5.23). (e) Stiff layer overlying compressible formation Another geological condition that may be encountered is that of layer of stiff rock overlying a less stiff material of infinite depth. For this condition, the surface settlement dv of a uniformly loaded circular footing with diameter B is calculated as follows: (5.19) where a is a correction factors given in Table 5.8 determined by the relative moduli of the two materials (E1/E2) and the ratio H/B, where H is the thickness of the upper layer (Fig. 5.12(d)). The term d8 is the settlement calculated assuming that the foundation material is entirely composed of

Table 5.7 Values of the shape factor for settlement of the center of a uniformly loaded area on an elastic layer underlain by a rigid base (Winterkorn and Fang, 1975) H/B

Circle

Rectangle shape infinite strip

0.1 0.25 0.5 1.0

0.09 0.24 0.48 0.70

0.09 0.24 0.48 0.75

0.09 0.23 0.47 0.81

0.09 0.23 0.47 0.83

0.09 0.23 0.47 0.83

0.09 0.23 0.47 0.83

0.09 0.23 0.47 0.83

0.09 0.23 0.47 0.83

BEARING CAPACITY OF FRACTURED ROCK

Figure 5.12 Methods of settlement calculation for foundations on isotropic, layered and transversely isotropicrock.

H/B

Circle

Rectangle shape infinite strip

1.5

0.80

0.86

0.97

1.03

1.07

1.08

1.08

1.08

167

168

H/B

BEARING CAPACITY, SETTLEMENT AND STRESS DISTRIBUTION

Circle

Rectangle shape infinite strip

2.5 3.5 5.0 8

0.88 0.91 0.94 1.00

0.97 1.01 1.05 1.12

1.12 1.19 1.24 1.36

1.22 1.31 1.38 1.52

the lower material (elastic properties E2, v2) with

1.33 1.45 1.55 1.78

1.39 1.56 1.72 2.10

1.40 1.59 1.82 2.53

1.40 1.60 1.83 8

the factor Cd determined from Table 5.6.

EXAMPLE 5.2 SETTLEMENT-ELASTIC ROCK

This example demonstrates the use of the settlement calculations described in this section and illustrates the effect of the different geological formations on settlement magnitudes. Consider a 2m by 3 m (6 by 10 ft) rectangular footing supporting a applied load of 40 MN (9000 kips) so that the uniform applied bearing pressure is 6.7 MPa (150 ksf). Settlement is calculated as follows: (a) If the foundation is composed of a uniform bed of isotropic rock, the shape factor is determined from Table 5.6. The length to width ratio of the footing is 1.5 and the value of Cd at the center of the footing is 1.36. If the modulus is 2 GPa (0.29×106p.s.i.) and the Poisson’s ratio is 0.25, the settlement calculated from equation 5.18 is

(b) If the relatively compressible material occurs in a bed that is 3 m (10 ft) thick and the underlying material is relatively stiff and extends to a considerable depth, settlement is From Table 5.7 has a value of 0.97 for and calculated using shape factor Substituting this value in equation 5.18 gives a settlement of 6 mm (0.24 in), a reduction of about 40% as compared with the isotropic case. (c) Where the foundation material is predominantly a moderately stiff rock, but contains a 3 m (10 ft) thick bed of compressible rock at a depth of 2 m (6 ft), settlement is calculated as follows. If the moduli of the two materials are 10 GPa and 2 GPa respectively, the Poisson’s ratios are both 0.25, the weighted average modulus of the two upper beds is 5.2 GPa (0.75×106 p.s.i.). The combined thickness of the two upper beds is 5 m so the ratio H/B is 2.5 and the value of from Table 5.7 is 1.12. Equation 5.18 gives a settlement of 2.7 mm (0.11 in). (d) Where the foundation comprises a layer of relatively stiff rock with modulus 10 GPa (1.45×106 p.s.i.) overlying a considerable thickness of more compressible rock settlement is calculated using the correction factors on Table 5.8 and equation 5.19. If the upper bed is 3 m thick, the ratio H/B is 1.5 and the correction factor a is 0.357 (by interpolation) for a modulus ratio of 5.0. The value of 600 is 8.5 mm from (a) above, so the settlement of the layered system is

BEARING CAPACITY OF FRACTURED ROCK

(f) Inclined, variable thickness beds The settlement calculation methods described in this

169

section only apply to horizontal beds of uniform thickness. For conditions such as that shown

Table 5.8 Elastic distortion settlement correction factor a, at the center of a circular uniformly loaded area on an elastic layer E1 underlain by a less stiff elastic material E2, of infinite depth; (Winterkorn and Fang, 1975) H/B 0 0.1 0.25 0.5 1.0 2.5 5.0 8

E1/E2 1

2

5

10

100

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

1.00 0.972 0.885 0.747 0.627 0.55 0.525 0.500

1.00 0.943 0.779 0.566 0.399 0.274 0.238 0.200

1.00 0.923 0.699 0.463 0.287 0.175 0.136 0.100

1.00 0.76 0.431 0.228 0.121 0.058 0.036 0.010

in Fig. 5.12(e) where the foundation contains an inclined, variable thickness bed, it is necessary to use numerical methods, such as finite element analysis or finite difference analysis, to calculate settlement. These methods allow the inclination, thickness, position and properties of one or more beds to be accurately modeled, as well as the incorporation of non-vertical loads. An example of numerical analysis is the calculation of settlement for a series of bridge piers founded, at different levels, on a massive but very weak rock (Fig. 5.13). Both the horizontal and vertical movements are calculated, as well as the stresses at any point in the foundation. Calculation of the stresses, and comparing them with the rock strength, allows areas of potential rock failure to be identified. The analysis shown in Fig. 5.13 was performed using the program FLAC—Fast Lagrangian Analysis of Continua (Itasca Corp., 1995) which is a finite difference analysis that simulates the behavior of materials such as rock and soil that behave according to linear or non-linear stress/strain laws in response to the applied forces or boundary conditions. Some of the other features of the program include interface elements to simulate planes along which slip can occur, ground water pressures, structural elements to simulate rock bolts and dynamic analysis. A method of modeling a jointed rock mass in which displacement and opening of the

discontinuities occurs is to use the program UDEC — Universal Distinct Element Code (Itasca Corp., 1986). Figure 7.11 in Chapter 7 shows an example of the use of the three-dimensional version of UDEC (3DEC) to model the foundation of an arch dam. Chapter 7 describes the functions of UDEC; however, detailed description of numerical analysis is beyond the scope of this book. 5.4.2 Settlement on transversely isotropic rock The calculation of settlement of foundations on transversely isotropic uniform rock, such as sandstones, shales and schists, free of beds of compressible rock, can be carried out using equations developed by Kulhawy and Goodman (1980), Kulhawy (1978) and Gerrard and Harrison (1970). These equations give the value of the vertical settlement of a rigid circular load placed on the horizontal surface of a transversely isotropic rock mass in which the load axis is coincident with the vertical modulus axis z. The properties of the rock are defined by the vertical and horizontal deformation modulus (Ez and Eh respectively), the shear modulus between the horizontal and vertical planes (Ghv) and the following values of Poisson’s ratio. Vhh Poisson’s ratio for horizontal stress on the

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Figure 5.13 Example of numerical analysis using FLAC to calculate displacement vectors in a series of stepped foundations on homogeneous, isotropic, very weak rock (model by U.Atukorala and M.Kelly).

Figure 5.14 Model of a fractured rock mass with three orthogonal joint sets for calculation of settlement of circular footing with vertical applied load.

Vhz vzh

complimentary horizontal strain Poisson’s ratio for horizontal stress on vertical strain Poisson’s ratio for vertical stress on the horizontal strain

The settlement dv is given by one of three equations

depending on the value of the factor ß2 which is governed by the properties of the rock mass. The equations for settlement are as follows: ß2 positive: (5.20a)

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ß2 negative:

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(5.25) (5.20b)

(5.20c) The appropriate equation to use is defined by: (5.21) The factors a, c', d, and e2 are defined by the following equations: (5.22a)

(5.22b) (5.22c) (5.22d) where Q is the load applied to the footing; and b is the radius of the loaded area. In the case of square or rectangular footings, an equivalent radius can be calculated from the area of the footing, i.e. for square footing of side length B. Note that Gerrard and Harrison give solutions for settlement of strip footings on orthorhombic rock, and for other loading cases on transversely isotropic rock. The deformation and shear moduli, and the Poisson’s ratio of the rock mass model illustrated in Fig. 5.14 can be calculated from the elastic properties of the intact rock, the spacing of the discontinuities, and their normal and shear stiffnesses. The equations for the rock mass elastic parameters are as follows: (5.23) (5.24)

for subscripts

with

and

The elastic properties of the intact rock and the discontinuities are defined by the following parameters: Er is the intact rock deformation modulus; vr is the intact rock Poisson’s ratio; Gr is the intact rock shear modulus, and (5.26) S x, y, z

is the spacing of each of the three sets of discontinuities; kni is the normal stiffness of the discontinuities of discontinuity set i; and ksi is the shear stiffness of discontinuity set i. A survey of joint stiffnesses determined by both laboratory and in situ testing shows the following typical range of normal stiffness kn and shear stiffness ks (Kulhawy, 1978). 1. For

sandstone,

dry

sawed

joint:

2. For marly, sand filled joint, 1–2 mm thickness: 3. For shale interbed, wet, 2–5 mm thickness: The horizontal deformation modulus Eh, and the shear modulus Ghz, used in the calculation of settlement are found from equations 5.23 and 5.24 as: (5.27) (5.28) From equation 5.25, the values for the Poisson’s ratios used in the settlement calculation are: (5.29) and the ratio of the vertical to horizontal deformation moduli is given by

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(5.30)

EXAMPLE 5.3 SETTLEMENT OF FRACTURED ROCK

The following example illustrates the method of calculating settlement of foundations bearing on fractured rock. Consider a vertical bridge pier with a load Q of 40 MN and a footing area of 2 m by 2 m bearing on a moderately weak sandstone. Laboratory tests conducted on pieces of core show that the elastic properties of the intact rock are as follows:

From equation 5.26 the shear modulus Gr of the intact rock is found to be 4 GPa.

If the rock contains horizontal bedding planes with a clay infilling, and two sets of vertical joints which are clean and tight, the effect of these discontinuities on settlement is as follows. The spacings of these discontinuity sets, and their normal and shear stiffnesses determined from in situ direct shear tests, are: Bedding planes:

Joints:

From equations 5.23, 5.24 and 5.25, the deformation and shear moduli, and the Poisson’s ratio of the rock mass are calculated to be:

and

From equation 5.21, the factor ß2 is found to be 1.48 and the settlement from equation 5.20b is 34.1

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Figure 5.15 Influence of modulus ratio on settlement of a uniformly loaded circular area bearing on transversely isotropic rock.

mm. The influence of the ratio of the horizontal Eh to vertical Ez moduli on the settlement of the foundation is shown in Fig. 5.15. With increasing thickness of the clay infilling in the bedding planes, there is a corresponding decrease in the normal and shear stiffnesses (i.e. more compression under applied load). If the properties of the vertical joints and the value of Eh are unchanged, the ratio Eh/Ez will increase. Figure 5.15 shows that the settlement varies between 10.5 mm when the rock is isotropic to about 62.5 mm when Equations 5.20–5.22 can also be used to determine the effect of differing properties of the vertical discontinuities on settlement. For example, consider a rock mass comprising a series of horizontal slabs each 0.25 m thick, and the horizontal bedding planes forming these slabs have normal and shear stiffnesses of 2 and 1 GPa respectively. The vertical modulus is 0.48 GPa. The horizontal slabs can be simulated by setting and with the vertical joints having the same stiffness values as in the previous example. The horizontal modulus is 9.1 GPa, and the ratio the shear modulus GPa. The settlement is calculated to be 27.7 mm, which compares to a settlement of 34.1 mm when the spacing of all the discontinuities is 0.25m. This shows that the relatively stiff, horizontal slabs have some effect in limiting settlement. The settlement of an isotropic rock foundation can be calculated using equations 5.20 or equation 5. 18. For example, Fig. 5.15 shows that when the ratio the settlement is 10.5 mm. In comparison, using equation 5.18 with a shape factor Cd of 0.79 for a rigid, circular footing, a modulus of 2 GPa and a Poisson’s ratio of 0.05, the calculated value of the settlement is 9 mm.

5.4.3 Settlement on inelastic rock For footings on elastic rock, the total settlement will occur as the load is applied. However, time dependent settlement is likely where the foundation

contains seams of compressible material such as clay, or ductile materials such as salt or tar sand. Other conditions where time dependent effects may take place include weathering resulting in decreased bearing capacity, swelling due to stress relief, changes in internal stress conditions, or chemical

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reactions in the rock. Time dependent properties of rock are discussed in more detail in Section 3.6. Where the foundation contains compressible seams of soil, settlement due to compression of the soil can be determined using conventional soil mechanics principles. Compression is a three stage process comprising distortion, consolidation and secondary compression. Distortion occurs as the load is applied and is assumed to be elastic. Consolidation settlement determines the time rate of settlement and depends on the rate at which water is expelled from the void spaces in the soil. Thus, water flows readily through clean sands so consolidation settlement will be essentially instantaneous, while the consolidation of clays may take place over a period of months. Secondary compression occurs as the result of yielding and compression of the soil skeleton and is also time dependent. In computing the rate of compression, the stress level in the soil seam(s) can be determined using the methods described in Section 5.5 which give the stress distributions in both homogeneous and layered formations. Where the foundation conditions cannot be modeled by one of the methods given in Section 5.5 it will be necessary to use numerical analysis to determine the stress distributions (see Fig. 5.13). Foundations on ductile rocks, or rocks stressed above the brittle to ductile transition stress (see Section 3.6.3) will settle (creep), with the rate of creep dependent upon the level of the applied stresses, and the time for which the load is applied. As shown in Fig. 3.23(c), during primary creep the strain rate diminishes with time so that after a certain period settlement will cease. However, if the bearing stress is greater than that which induces the onset of secondary creep, settlement will continue indefinitely. The finite difference analysis program FLAC (Itasca, 1995), which can analyze stress and strain conditions in foundations, as shown in Fig. 5.13, can incorporate plastic materials and calculate timedependent settlement. For example, the rock could be modeled as a visco-elastic material defined by

equation 3.23 which gives the axial strain with time of a Burger substance subjected to a constant axial stress. 5.4.4 Settlement due to ground subsidence In coal mining areas where structures are located above active or abandoned mines there is a risk that collapse of the underground openings can induce subsidence or sink holes at the ground surface. It is usual practice in coal mines that the collapse is part of the extraction sequence. For example, in longwall mining where as much as 90% of the coal is mined, the roof caves as the continuous miner and the shield supports advance and no attempt is made to maintain stable openings. This can result in trough subsidence at the surface which takes the form of a shallow, dishshaped depression formed by sagging and downwarping of the overlying rock formations into the mined out area (Karfakis, 1993). The dimensions of a subsidence trough are related to the thickness of the seam and the width of extraction, and the depth of the seam below the surface, with an approximate horizontal limit for the trough width defined by lines inclined at angles of 35° from the vertical at the edges of the extraction area (Fig. 5.16). Charts have been developed which relate the shape of the subsidence trough to the dimensions D, W and M, and which show, for example, that the maximum subsidence at the center of the trough is about 80–90% of the seam thickness when the extraction width exceeds the mining depth , and drops to 10% of the seam thickness (National Coal Board, 1975). when Much of the early work on subsidence above coal mines was undertaken in Britain, although it has subsequently been found that the same principles apply in most other coal mining areas. Factors that may influence the magnitude and characteristics of the subsidence are the type of rock above the mined seam, faulting and seam inclination, surface topography and the extent of ground water infiltration into the disturbed rock mass (Whittaker and Reddish, 1989).

BEARING CAPACITY OF FRACTURED ROCK

Structures located on the surface within the subsidence trough will experience horizontal and vertical displacement, tilt and bending, as well as tensile (+e) or compressive (-e) strain depending on their position within the trough. Typical strain and displacement profiles are shown in Fig. 5.16. Another factor to consider is the change in subsidence with time. For example, a highway bridge constructed in a sink hole area above a flooded salt mine was designed to accommodate future settlements of as much as 600 mm vertically and 150 mm horizontally over 50 years (Matthews et al., 1998). In room and pillar operations, the pillars are sized so that they can support the weight of the entire overlying rock above both the pillars and the rooms. However as the workings are abandoned and the coal in the pillars and the rock in the roof of the rooms deteriorates, due to flooding or changes in moisture content, the openings eventually collapse. This can result in the formation of a ‘chimney’ of broken rock that can eventually reach the surface to form a sink hole. The formation of such sinkholes depends on such factors as the width of the room, the depth below the surface, the nature of the overlying strata and the drainage of water into the caved ground. Remedial action that may be taken to limit the damage caused by sinkholes include control of surface water infiltration, and backfilling through a hole drilled from the surface. 5.5 Stress distributions in foundations Most rock foundations will behave as linear elastic materials so it is possible to use elastic theory to calculate stress distributions that are induced in the rock. The reasons for using elastic theory are first, the availability of solutions for linear elastic media with boundary conditions that approximate those of actual engineering situations. Second, studies have shown that elastic theory will predict reasonably well actual stresses measured in the field (Morgan and Scala, 1968; Bozozuk, 1972). For the design of rock foundations it is necessary to

175

have a means of determining stress distributions for both isotropic and transversely isotropic rock. Typical uses of stress distributions are in the calculation of settlement of layered formations where it is necessary to determine the stresses in each layer and the resulting consolidation that will take place. Another use of stress distribution calculations is in the examination of the interaction between the stress fields induced, for example, by two nearby foundations, or a foundation and a nearby tunnel. Using superposition, it is possible to add the stresses induced by each structure and determine whether there is any portion of the rock that is overstressed. The method of determining whether the rock is overstressed is shown in Fig. 5.3 where the strength of an isotropic fractured rock mass is plotted as a curved envelope in terms of the major and minor principal stresses (reference Section 3.3.2). The actual principal stresses acting at any point in the foundation s1 and s3 are plotted on this diagram and the factor of safety FS is then the ratio between the strength s1A at the applied minor principal stress s3, and the applied major principal stress s1, that is (5.31) where m and s are constants defined in Table 3.7; and su(r) is the unconfined compressive strength of intact rock. Contours of the factor of safety can be plotted to show areas that may be overstressed. 5.5.1 Stress distributions in isotropic rock The distribution of stresses within an elastic halfspace resulting from a point load applied normal to the surface and for small strains, as illustrated in Fig. 5.17, is given by Boussinesq (1885). The equations are as follows:

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Figure 5.16 Subsidence of ground surface across longwall extraction based on European coal mining observations and predictions. (a) subsidence profile; (b) strain profile; and (c) displacement profile (Whittaker and Reddish, 1989).

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177

Figure 5.17 Stresses in an elastic half space due to a point load at the surface (Winterkorn and Fang, 1975).

where v is Poisson’s ratio and, r, z and R are dimensions defined in Fig. 5.17. These stresses are those that would occur in a weightless linear elastic medium; they must be superimposed upon the pre-existing stresses due to the weight of the material. It should be noted from these equations that the stresses are independent of the elastic constants. (a) Distributed loads The Boussinesq equations can be applied to the stress analysis of foundations if they are modified to obtain the stresses under a distributed load. This can be achieved by superposition, in which the force acting on a differential area is integrated over the entire loaded area. Thus the vertical stress at depth z at any point beneath a distributed load applying a pressure q is given by (5.33) where Iz is an influence factor, the value of which depends upon the shape of the applied load and the location of the point at which the stress is measured

(Winterkorn and Fang, 1975). Figures 5.18 and 5.19 give the values for influence factors for the vertical normal stress for any combination of depth z and radial distance r under circular and rectangular uniformly loaded areas. The stress distribution for a square footing can be approximated by a circular distributed load of the same area. For example, the vertical stresses at a number of points in the foundation rock are calculated as follows. A 2 m by 2 m square footing (equivalent circular is loaded dimension, to 40 MN, the applied pressure At a depth below the influence factor the edge of the footing and the vertical stress For a rectangular footing with the Therefore, at a depth of 3 m value of the influence factor is 0.095. Under the corner of the footing, the vertical stress Plotting the stress distributions calculated from the

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Figure 5.18 Influence diagram for vertical normal stress sz at various points within an elastic half space under a uniformly loaded circular area (Winterkorn and Fang, 1975).

influence factors as stress contours provides a useful visual representation of both the stresses at any point in the foundation, and the shape of the stress ‘bulb’. Figure 5.20 shows two vertical stress profiles, one under the center of the loaded area and the other at a distance of the width of the footing from the center of the footing. Figure 5.21(a) shows the contours of the vertical normal stress beneath a uniformly loaded circular area, and illustrates how the stresses are distributed in the rock beneath the foundation. (b) Line loads In the case of a line load on an isotropic, linear elastic foundation (Fig. 5.21(b), the principal stresses at any point consist only of a radial stress sr given by equation 5.34, with the tangential and shear stresses s? and tr? both being zero (Goodman, 1980): (5.34)

where Q is the line load (MN/m), ? is the angle from

the vertical, and r is the radial distance from the point of application of Q. The stresses consist of a series of vectors radiating from Q, with the length of the vectors being proportional to the magnitude of the stress, and being constant along any stress contour. The contours of radial stress for a line load consist of a series of circles tangent to the point of application of the load and centered at a depth Q/(pr) (Fig. 5.21 (b)). Stress contours produced by distributed and line loads are compared in Figs. 5.21 (a) and (b). Equation 5.34 can also be used to determine the stress distributions beneath a line load inclined at an angle to the ground surface (Fig. 5.22). Under these conditions, two sets of circular stress contours are developed, one set for tensile stresses and the other for compressive stresses. In intact rock this stress condition will be of little concern because the rock will be able to withstand a small tensile stress without extensive fracturing of the rock. However, if the rock contains sets of discontinuities that form wedges in the foundation oriented approximately

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179

Figure 5.19 Influence diagram for vertical normal stress at a point within an elastic half space beneath the corner of a uniformly loaded rectangular area (Winterkorn and Fang, 1975).

normal to the stress directions, then this condition may result in movement of these wedges and failure of the foundation. A stability analysis of the wedge could be carried out using the XSTABL method of analysis in which the failure surface can be modeled as a series of straight lines, anisotropic strengths can be defined, andthe external load applied in any direction (see Section 6.5).

5.5.2 Stress distributions in layered formations In layered formations where a stronger rock overlies a much weaker rock, the upper formation will carry the majority of the load and the stress levels in this layer will be considerably higher than those in the lower layer. Stress distributions in layered systems for elastic materials have been developed primarily

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Figure 5.20 Distribution of vertical stress due to a loaded circular area on linear elastic half-space: (a) along vertical lines; (b) along horizontal lines (after Winterkorn and Fang, 1975).

for pavement structures (Peattie, 1962; Burminster, 1965) and the results can be applied to geological formations. Figure 5.23 shows how the vertical stress distribution in a two layer system varies with the relative moduli of the two layers; at a modulus ratio of 100 virtually all the load is carried in the upper layer (Winterkorn and Fang, 1975). The limitations of stress distribution calculation methods developed for pavements are that the layers must be both horizontal and of uniform thickness. In the many geological situations where these conditions are not applicable, numerical analysis must be used to calculate stresses in the layers. 5.5.3 Stress distributions in transversely isotropic rock The stress distributions determined by elastic theory for isotropic rock are modified, in transversely isotropic rock, by the presence of sets of discontinuities such as bedding planes, joints and foliation. The orientation of the discontinuities and the friction angle of these surfaces , limit the

range of directions that the stresses can take. According to the definition of interlayer friction, the absolute value of the angle between the direction of the radial stress and the normal to the planes must be equal to or less than (Fig. 5.24). Therefore, the bulb of pressure cannot extend beyond the lines with the normal to the layers. drawn at an angle Because the bulb of pressure in anisotropic rock is confined more narrowly than in isotropic rock, it must continue more deeply, meaning that the stresses are higher at a given depth below the load than would be the case for isotropic rock (Goodman, 1980). The model used to calculate the stress distribution consists of a half space containing a set of discontinuities inclined at an angle ? to the load direction, loaded by a line load Q which can be inclined at any angle (Fig. 5.25). The stress in the rock for these load conditions is entirely radial sr with the tangential and shear stresses being zero. If the line load is decomposed into components Qx and QY parallel and perpendicular to the discontinuities (5.35) The radial stress at any point defined by the radial

BEARING CAPACITY OF FRACTURED ROCK

181

Figure 5.21 Stress contours for footings located on isotropic linear elastic half-space: (a) vertical normal stresses beneath uniformly loaded circular area, radius b; and (b) radial stresses beneath line load.

Figure 5.22 Stress contours beneath inclined line load showing zones of compressive and tensile stress.

distance r, and angle ß with respect to the discontinuity orientation, is given by

describing the properties of a transversely isotropic rock mass and are given by:

(5.36)

(5.37)

where h and g are dimensionless quantities

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Figure 5.23 Vertical normal stress beneath center of uniformly loaded circular area at the surface of two-layer elastic system (after Winterkorn and Fang, 1975).

(5.38)

where E and v are the modulus and Poisson’s ratio of the intact rock respectively; S is the discontinuity spacing; kn, ks are the normal and shear stiffness of the discontinuities respectively which define the anisotropy of the rock mass; and ß is the angle between discontinuity orientation and radial stress direction. These equations can be used to calculate contours of equal radial stress within the foundation.Two plots of the radial stresses are shown in Fig. 5.25 which demonstrates the influence on the stress concentrations of both discontinuity orientation and stiffness ratio. For the particular conditions shown, the contours are elongated when the stiffness ratio

(kn/ks) is as great as about 100, and are nearly circular at a stiffness ratio of 10. These equations were first developed by Bray (1977) and were checked against model tests previously carried out by Gaziev and Erlikhman (1971). Applications of these equations would be in the study of interacting stress fields from adjacent footings, or for example, stress fields produced by a footing and a tunnel below the structure. 5.5.4 Stress distributions in eccentrically loaded footings On tall structures, horizontal forces produced by such conditions as earthquakes, wind and centrifugal traffic loads, induce moments at the foundation level which modify the pressure distribution beneath the footing. For a strip footing of width B with loads comprising a vertical load Q and an overturning

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183

Figure 5.24 Narrowing and deepening of the bulb of pressure due to limited shear stress along discontinuities (Goodman, 1980).

moment M, the resultant force will lie a distance e from the axis of the footing. The term e is the eccentricity of the loading condition and is given by (Merritt, 1976): (5.39) If the distance e is less than B/6, that is, the resultant force is within the middle third of the base of the footing, then the maximum and minimum pressures (q1 and q2) at the edges of the footings are (Fig. 5.26(a)): (5.40) (5.41) while for a rectangular footing with length L and and the moment applied about the width B long axis of the footing, the maximum and minimum pressures will be

(5.42) (5.43) where Q is the applied vertical load, M is the applied moment and e is the loading eccentricity. Under these conditions, the pressure under the footing is entirely compressive and it is necessary to check that the allowable bearing capacity is not exceeded in the high stress area at the edge of the footing. However, this calculation assumes that the footing is rigid, and the flexibility of standard reinforced concrete footings means that actual pressures will be less than those given in equations 5.40–5.43. If the resultant lies outside the middle third, that is the bearing is only on a portion of the footing and tensile forces develop along one side (Fig. 5.26(b)). For this condition on a strip footing

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Figure 5.25 Contours of radial stress under line loads on transversely isotropic rock calculated by equations 5.36 to 5. 38: (a) geological structure aligned horizontally (90° to vertical load); and (b) geological structure aligned at -30° to vertical load.

the pressure distribution is triangular and extends over a width of 3(B/2–e), with the maximum pressure being: (5.44)

While for a rectangular footing of width B and length L, the maximum pressure is (5.45) For footings on rock where the loading condition

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185

Figure 5.26 Stress conditions produced by footings subjected to overturning: (a)

results in stability can be improved by installing tie-down anchors around the edge of the footing. The anchors, which introduce a stabilizing moment to counteract the overturning moment M, are designed with sufficient length to develop a cone of rock in the foundation. The overturning resistance provided by this cone comprises both the weight of the cone and the strength of the rock on the surface of the cone. Methods of rock anchor design are discussed in Section 9.3.4. 5.6 References Antes, D.R. (1981) Footings and piles: a practical foundation solution in cavernous Leithsville carbonate formation. Proc. Design and Construction of Foundations on the Carbonate Formations of New Jersey and Pennsylvania, New Jersey Institute of Technology, Newark, NJ, pp. 79–97. Benson, R.C. (1984) Evaluation of differential settlement or collapse potential. Presentation to Transportation Research Board, Annual Conference, Washington, DC. Benson, R. C, Glaccum, R.A. and Noel, M.R. (1982) Geophysical Techniques for Sensing Buried Wastes and Waste Migration. Environmental Protection

Agency, National Water Well Association, Dublin, OH. Boussinesq, M.J. (1885) Applications des potentials, a l’etude de l’equilibre et du movement des solides elastique. Gauthier-Villars, Paris. Bozozuk, M. (1972) The Gloucester Test Fill, PhD thesis, Purdue University. Bray, J. (1977) Unpublished notes, Imperial College, London. Brown, A.D. (1991) Construction and design of drilled shafts. Hard Pinnacle Limestones, Recognizing Solutions to Today’s Problems and Defining Tomorrow’s Challenges. Deep Foundation Institute, Chicago, IL, pp. 123–40. Bruce, D.A. and Nicholson, P.J. (1989) The practice and application of pin piling. ASCE Foundation Engineering Conference, Northwestern University, Evanston, IL, pp. 1–19. Burmister, D.M. (1965) Influence Diagrams for Stresses and Displacements in a Two Layer Pavement System for Airfields. Contract NBY 13009, Dept of the Navy, Washington, DC. Cannon, J.A. and Turton, R.D. (1994) Spanning the Grand Canyon. Civil Engineering, New York, November, pp. 38–41. Canadian Geotechnical Society (1978) Canadian Foundation Engineering Manual. Montreal, Section 2, pp. 6–9.

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Costopolous, S.D. (1987). Geotechnical engineering work for the restoration of the Temple of Apollo Epicurius, Bassae. Sixth Int. Con. on Rock Mechanics, Montreal, ISRM, 327–30. Couch, F.B. (1984) Solutions to special problems in karstic limestone bedrock. Presentation to Transportation Research Board Symposium, Washington, DC. Daly, P. (1990) Review of pile driving records at three sites in Yuen Long. Karst Geology in Hong Kong, (eds R.L.Langford, A.Hansen and R.Shaw), Geological Society of Hong Kong, Bulletin No. 4, Hong Kong, pp. 123–34. Fang, H-Y., ed. (1991) Foundation Engineering Handbook, (2nd edn), Chapman & Hall, New York. 923 pp. Franklin, J.A. and Pearson, D (1985) Rock engineering for construction of Science North, Sudbury, Ontario. Canadian Geotechnical J., 22, 443–55. Gaziev, E. and Erlikhman, S. (1971) Stresses and strains in anisotropic foundations. Proc. Symp. on Rock Fracture, ISRM, Nacy, Paper II–1. Gerrard, C.M. and Harrison, W.J. (1970) Circular loads applied to a cross-anisotropic half-space, and Stresses and displacements in a loaded orthorhombic halfspace. Technical papers 8 and 9, Division of Applied Geomechanics, Commonwealth Scientific and Industrial Research Organization, Australia, 1970. (Reproduced as Appendices A and B in Poulos and Davis, 1974.) Goodman, R.E. (1980) Introduction to Rock Mechanics, Wiley, New York, pp. 305–8. Hoek, E. and Londe, P. (1974) The design of rock slopes and foundations. Third Int. Cong. on Rock Mechanics, ISRM, Denver, pp. 2–40. Hong Kong Geotechnical Engineering Office (1981) Geotechnical Manual for Slopes, Hong Kong, pp. 129–34. Itasca Consulting Group (1987) Fast Lagranian Analysis of Continua (FLAC), Version 2.00. Minneapolis. Itasca Consulting Group (1996) Universal Distinct Element Code (UDEC), Version 3.0. Minneapolis, Minnesota. Jaeger, J.C. and Cook, N.G. W. (1976) Fundamentals of Rock Mechanics. Chapman & Hall, London. Kaderabek, T.J. and Reynolds, R.T. (1981) Miami limestone foundation design and construction. ASCE, 107(GT7) 859–72. Karfakis, M.G. (1993) Residual subsidence over

abandoned coal mines. Comprehensive Rock Engineering, Pergamon Press, Oxford, Vol. 5, pp. 451–76. Katzenbach, R. and Romberg, W. (1987) Foundation of high valley bridges in triassic sediments., Sixth Int. Con. on Rock Mechanics, Montreal, ISRM, pp. 419–23. Kaufman, J.L. and Brand, A.H. (1991) Foundation studies in a fault zone and a steep valley slope. Proc. Symp. on Detection of, and Construction at, the Soil/ Rock Interface, Orlando, Florida. Geotechnical Special Publication, No. 28, ASCE, New York, pp. 73–90. Klopp, R. (1969) Engineering geological problems during the foundation of the Biggetal power plant on karstified Devonian reef limestones in the Sauerland, and their solution (in German). Rock Mechanics, 1, 145–156. Knott, D.L., Rojas-Gonzalez, L.F. and Newman, F.B. (1993) Current Foundation Engineering Practice for Structures in Karst Areas. Federal Highway Administration, Washington DC and Pennsylvania Department of Transportation, Harrisburg, PA, Report number FHWA-PA-91–007+90–12. Kulhawy, F.H. (1978) Geomechanical model for rock foundation settlement. ASCE, 104(GT2), 211–27. Kulhawy, F.H. and Goodman, R.E. (1980) Design of foundations on discontinuous rock. Proc. Int. Conf. on Structural Foundations on Rock, Sydney, pp. 209–20. Ladanyi, B. and Roy, A. (1971). Some aspects of the bearing capacity of rock mass. Proc. 7th Canadian Symp. Rock Mechanics, Edmonton. Lemos, J.V. (1995) Experimental study of an arch dam on a jointed rock foundation. Proc. 8th Int. Cong. on Rock Mechanics, Tokyo, Vol. 3, Balkema, Rotterdam, pp. 1263–66 Lambe, T.W. and Whitman, R.V. (1969) Soil Mechanics. John Wiley, New York. Matthews, S.L., Matzat, J.W. and Walker, S.E. (1998) Losing ground. Civil Engineering, ASCE, Washington, DC, April, 59–60. Merritt, F.S. (1976) Standard Handbook for Civil Engineers. McGraw-Hill, New York, pp. 7–24. Morgan, J.R. and Scala, A.J. (1968) Flexible pavement behavior and application of elastic theory—a review. Proc. 4th Conf. of the Australian Road Research Board, Melbourne 4, Part 2, p. 1201. National Coal Board (1975). Subsidence Engineer’s Handbook. London, UK. Ontario Ministry of Transport and Communications (1983) Ontario Highway Bridge Design Code,

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Highways Engineering Division, Toronto, p. 147. Peattie, K.R. (1962) Stress and Strain Factors for Threelayer Elastic Systems. Highway Research Board Bulletin, No. 342. Peck, R.B., Hanson, W.E. and Thornburn, T.H. (1974) Foundation Engineering, Wiley, New York, pp. 361–3. Poulos, H.G. and Davis, E.H. (1974) Elastic Solutions for Rock and Soil Mechanics, Wiley, New York, pp. 138–64. Rawlings, G.E. and Wyllie, D.C. (1986) Bridge abutments on rock. Transportation Geotechnique, Vancouver Geotechnical Society, Vancouver. Roark, R.J. and Young, W.C. (1970) Formulas for Stress and Strain, McGraw-Hill, New York, pp. 325–67. Rojas-Gonzalez, L.F., Knott, D.L. and Newman, F.B. (1993) Current Practice for Dynamic Pile Monitoring in the United States. Research Project 90–12, Commonwealth of Pennsylvania Department of Transportation, Office of Research and Special Studies. Scherer, S.D., Walter, W.H. and Johnson, R. (1996) Chicago’s micropile debut. Civil Engineering, ASCE, 66(8), 51–3. Schleicher, F. (1926) Zur theorie des Baugrundes. Der Bauingenieur, 48, 49. Serrano, A. and Olalla, C. (1994) Ultimate bearing capacity of rock masses. Int. J. Rock Mech. Mining Sciences & Geomech. Abstr., 31(2), 93–106. Serrano, A. and Olalla, C. (1995) Allowable bearing capacity of typical rock masses depending on RMR and compression strength of intact rock. Proc. Int. Workshop on Rock Foundation, Tokyo, Japan, Balkema, Rotterdam, pp. 321–5. Simm, K.F. (1984) Engineering solutions to geological problems in the design and construction of the Humber Bridge. Q. J. Eng. Geol., 17, 301–6. Sowers, G.F. (1970) Introductory Soil Mechanics and Foundations, Macmillan New York, pp. 395–6. Sowers, G.F. (1975) Failures in limestone in humid subtropics. ASCE, 101(GT8), 771–87. Sowers, G.F. (1976) Foundation bearing in weathered rock. Proc. of Specialty Conf. on Rock Eng. for Foundations and Slopes, ASCE, Geotech. Eng. Div., Boulder CO., Vol. II, pp. 32–41. Sowers, G.F. (1977) Closure to failures in limestone in humid subtropics. ASCE, 103(FT7), Proc. Paper 11521, 807–13. Sowers, G.F. (1976a) Settlement in terrains of well-

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indurated limestone. Analysis and Design of Building Foundations (ed. H.Y.Fang) Envo Publishing Co., pp. 701–25. Sowers, G.F. (1984) Correction and protection in limestone terrain. Sinkholes: their Geology, Engineering and Environmental Impact, Proc. First Multi-disciplinary Conf. on Sinkholes (ed. B.Peck), Balkema, Rotterdam, pp. 373–8. Terzaghi, K. (1943) Theoretical Soil Mechanics. John Wiley, New York. Thompson, R.P. and Leach, B.A. (1991) Settlement prediction and measured performance of Heysam II Power Station. Proc. 10th European Conf. Soil Mechanics and Foundation Engineering, Florence, Italy, Balkema, Rotterdam, pp. 609–14. Thorburn, S.H. (1966) Large diameter piles founded in bedrock. Proc. of Symposium on Large Bored Piles, Inst. of Civil Eng., London, pp. 95–103. US Department of the Navy (1982) Foundations and Earth Structures, Design Manual 7.2, Alexandria, VA, pp. 72–130. Wagener, F.M. (1982) Engineering construction in dolomite. Ph. D. thesis, University of Natal, published by Geotechnical Div., SAICE, Johannesburg, South Africa. Wagener, F.M. and Day, P.W. (1984) Construction on dolomite in South Africa. Sinkholes: their Geology, Engineering and Environmental Impact, Proc. First Multi-disciplinary Conf. on Sinkholes (ed. B.Beck), Balkema, Rotterdam, pp. 403–11. Whittaker, B.N. and Reddish, D.J. (1989) Subsidence Occurrence, Prediction and Control. Elsevier, Amsterdam. Williams, D.J. (1994) Geotechnical input to major bridge project. J. Geotechnical Eng., 115(3), 322–39. Winterkorn, H.F. and Fang, H-F. (1975) Foundation Engineering Handbook. Van Nostrand Reinhold, New York, pp. 148–66. Woodward, R.J., Gardner, W.S. and Greer, D.M. (1972) Drilled Pier Foundations, McGraw-Hill, New York. Yamagata, M., Nitta, A. and Yamamoto, S. (1995) Design and its evaluation through displacement measurement for the Akashi Kaikyo Bridge foundation. Proc. Int. Workshop on Rock Foundation, Tokyo, Japan, Balkema, Rotterdam, pp. 35–46.

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6 Stability of foundations

6.1 Introduction The significant affect of structural geology on the stability of rock foundations has been illustrated in the examples of foundation failures discussed in Section 1.1. For foundations on strong but jointed rock, bearing capacity failures and excessive settlement rarely occur, and a more frequent cause of instability is the movement of blocks of rock. The design information required on structural geology consists of the orientation, length and spacing of discontinuities, and their surface and infilling characteristics (see Chapter 2). The first three parameters define the shape and size of blocks in the foundation and the direction in which they can slide, while the last two parameters determine the shear strength and settlement properties. Blocks formed by geological structure can be divided into three distinct categories—planar, wedge and toppling blocks (Fig. 6.1(a-c)). In contrast, in rock which is either closely or randomly fractured so there is no dominant direction of the structure, a large radius, shallow curved slip surface is usually formed (Fig. 6.1(d)). Typical stereonets depicting each of these four geological conditions are shown in Fig. 2.10, while Figs 2.11 and 2.12 illustrate methods of determining whether the blocks are potentially unstable. It is important to distinguish between the different failure types because each requires a different method of stability analysis. This chapter describes the main features of each of these failures and the corresponding method of stability analysis. Also shown in Fig. 6.1 are two geological conditions which generally form stable

foundations. Where the main geological structure is either parallel to the face (Fig. 6.1(e)) or dipping into the face (Fig. 6.1(f)), sliding is not possible. However, for the conditions shown in Fig. 6.1(e), there is a slight risk of buckling failures if the slope is high and the beds have an outward convex shape (Cavers, 1981). Where the beds dip into the face, the foundation will be stable, but settlement may occur if the beds contain a compressible infilling. The methods of stability analysis presented in this chapter are primarily the limit equilibrium technique that are introduced in Section 1.6. This technique was developed by Hoek and Bray (1981) and has now been adapted to a wide range of geotechnical conditions. 6.2 Stability of sliding blocks A planar failure is formed where a discontinuity is aligned approximately parallel to the face, and dips out of the face, i.e. the discontinuity ‘daylights’ in the face. If the dip of the discontinuity is steeper than the face so that the discontinuity does not daylight, or if the dip is somewhat flatter than the friction angle of the surface, then the foundation is likely to be stable (Fig. 6.2). However, failure may occur on planes dipping out of the face at a flatter angle than the friction angle when destabilizing forces such as ground water pressures, non-vertical foundation loads and seismic forces act on the foundation. Release surfaces are required at either side of the block before move ment will take place and these may be formed by a conjugate joint set

190

STABILITY OF FOUNDATIONS

Figure 6.1 Effect of geological structure on foundation stability and settlement: (a) planar sliding failure on single discontinuity; (b) wedge sliding failure on two intersecting discontinuities; (c) toppling failure of steeply dipping slabs; (d) circular failure in closely fractured rock; (e) stable condition with no daylighting discontinuities; and (f) stable condition, but compressible seam may result in settlement.

striking at right angles to the face, or by the

STABILITY OF SLIDING BLOCKS

191

Figure 6.2 Stability of sliding block related to dip of sliding surface.

geometry of the face itself if it forms an isolated ridge. This section discusses both the commonly used deterministic analysis to calculate the factor of safety (Section 6.2.1), and the probabilistic analysis (Section 6.2.2). 6.2.1 Deterministic stability analysis Consider a strip footing with an applied load Q inclined at an angle ?Q, bearing on a steep rock face (Fig. 6.3). If the rock contains a continuous joint dipping out of the face, a planar block is formed that may fail by shear failure on this surface. The stability of this block is defined by the relative magnitude of two forces acting parallel to the sliding surface: the resisting force fr acting up the surface that resists failure, and an opposite displacing force fd acting down the surface. The ratio of these two forces is termed the factor of safety FS: (6.1) The forces fr and fd are calculated by resolving all

forces acting on the sliding plane into components acting parallel and perpendicular to this surface, assuming that the forces act through the center of gravity of the block so that no moments are developed. To facilitate resolution of the forces into their two components, a convention is adopted for the direction in which they act such that positive normal forces act to increase the compressive force on the sliding plane, and positive shear forces act down the plane to increase the driving force (Fig. 6.3 inset). A method of resolving the forces into their normal and shear components which automatically determines the correct sign of the component is described in the following paragraphs. The first step in calculating the components is to draw up the foundation and its load such that the following two conditions are met. 1. The face is drawn sloping down from left to right; 2. The direction in which a force acts is defined by an angle measured in a clockwise direction (0° to 360°) from a horizontal axis to the right of the force.

192

STABILITY OF FOUNDATIONS

Figure 6.3 Resolution of forces in foundation to determine normal N and shear S components on potential failure surface.

Using these conventions, the normal and shear components, on a plane dipping at angle ?p, of any force Q at an angle ?Q from the horizontal axis are given by: (6.2) where

?p

is

the

dip

of

sliding

(6.3) surface

This procedurecan be applied to the condition shown in Fig. 6.3 to calculate the resisting force fr which is the shear strength of the sliding surface. For a Mohr-Coulomb material, the shear stress on the sliding plane is given by: (6.4) or (6.5) where t is the shear stress on sliding surface, c is the cohesion, is the friction angle, A is the surface area of sliding surface and ?N is the sum of normal forces. For the foundation shown in Fig. 6.3, ?N is the sum of the normal components of the weight of the foundation rock and the footing load, both of which are positive. The weight W of the block of rock is determined from the cross-sectional area of the

block and the unit weight of the rock. W can be expressed in terms of force per unit length of foundation or as a total weight. The total normal force acting on this plane is (6.6) The displacing force fd is the sum of the components of all forces acting parallel to the failure plane. In the case shown in Fig. 6.3, the shear component of Q acts up the plane and is negative, while the shear component of W acts down the plane and is positive. The total displacing force is given by (6. 7) and the factor of safety is given by equation 6.1. Note that for a vertical foundation load no other external loads and a cohesion of zero, as would be the case for a clean, open fracture, the factor of safety is given by: (6.8) That is, the limiting stability condition occurs when the dip of the sliding plane equals the friction angle of this surface, and is independent of the weight of the foundation and the footing load. If the calculation is carried out on a unit length of

STABILITY OF SLIDING BLOCKS

193

Figure 6.4 Forces acting on foundation containing planar discontinuity dipping out of slope face.

foundation, all the forces are expressed in units of N/ m (kips/ft) and the calculation method is appropriate for strip footings with uniform geological conditions along their length. In the case of spread footings, it is necessary to select a length of the foundation, which may be longer than the footing length, on which to carry out the stability analysis. The appropriate analysis length of the foundation will depend on the spacing of discontinuities that form the side faces of the sliding block, and the weight would be calculated from the cross-sectional area of the block, its length and the rock unit weight. The principle of calculating the factor of safety of a block of rock in a foundation by resolving forces to determine the resisting and displacing forces can be extended to more complex conditions as shown in Fig. 6.4. The range of forces that can be accommodated in this analysis is as follows:

1. Foundation loads (Q1, Q2) Each force is the vector sum of the dead and live loads, plus external horizontal forces acting on the structure such as wind, ice, water and earthquake loads. 2. Water forces (U, V) The uplift force U acts on the potential sliding plane, while the thrust force V acts in the tension crack; both these forces act in directions normal to the discontinuities: (6.9) (6.10) where hw is the head of ground water at the base of tension crack; L is the length of tension crack along strike; ?w is the unit weight of water; ?v is the dip angle of water force V; and

194

STABILITY OF FOUNDATIONS

A is the area of sliding plane. 3. Earthquake force (aW) The effect of earthquakes is simulated by a ‘pseudo-static’ hori zontal force aW equal to a fraction of the weight of the block. The earthquake acceleration a is expressed as a portion of the gravity acceleration appropriate to the seismic zone for the project location. 4. Artificial support force (T) These forces are commonly applied by installing rock bolts or cables anchored in sound rock below the potential sliding plane and then tensioning them against the rock face to apply compressive and shear forces on the sliding plane. Figure 6.4 shows a typical foundation which contains a planar discontinuity on which sliding could take place, and is subjected to the load conditions described above. Resolution of these loads into their shear and normal components and examination of the directions in which they act,

shows the influence that each has on stability. The forces U, V, Q1H and aW all have negative (upward) normal components, that diminish the frictional component of the shear strength, and positive (downslope) shear components. Therefore all these forces reduce the factor of safety. However, the foundation weight W, the reinforcing force T and the foundation load Q2 have positive (donwnward) normal components and negative (upslope) shear components that improve the factor of safety. These equations also show that the support provided by the tensioned bolts varies significantly with the angle at which they are installed, and savings in bolting quantities of up to 50% can be achieved by installing bolts at the optimum angle. Bolts installed normal to the sliding plane will increase the normal force only, but at a flatter angle than the normal they will both increase normal force and diminish the displacing force. The approximate optimum plunge ?Topt for the support force is (6.11)

EXAMPLE 6.1 STABILITY ANALYSIS FOR PLANAR FAILURE

The stability of the foundation shown in Fig. 6.4 with respect to sliding failure can be calculated using equations 6.1–6.10. The sliding surface comprises a planar fault with gouge infilling (refer to Fig. 3.17). The following values for the forces and force directions are assumed: Forces:

Angles:

Slope dimensions: Shear strength parameters: The water forces U and V are calculated as follows:

STABILITY OF SLIDING BLOCKS

195

The resisting force is calculated from equations 6.4 and 6.6 as follows:

The displacing force is calculated from equation 6.7 as follows:

The factor of safety is found from The effect of the bolting force T on the factor of safety can be determined by setting which the new factor of safety is

There are a number of limitations to the method of analysis described in Section 6.2, namely, the sliding surface must be planar and the strength properties uniform throughout the foundation, and all forces must act through the center of gravity of the block. If these conditions do not apply, then a more versatile analysis method can be used as described in Section 6.6. It is important to note that in calculating the factor of safety of either a unit length or a specified length of foundation using the method described in this section, it is assumed that no support is provided by the two surfaces at the ends of the block. This is usually a conservative assumption except where the rock contains sets of discontinuities at right angles to the face and oriented such that they act as release

, from

surfaces at either end of the block. Because of this geometric limitation, the planar method of stability analysis is best suited to strip foundations where the structural geology is consistent over the full length of the foundation. Stability analysis of a block of rock supporting a single footing can also be carried out using the three-dimensional wedge analysis (Section 6.3). 6.2.2 Probabilistic stability analysis The coefficient of reliability against sliding of the bridge foundation shown in Fig. 6.4 can be calculated using the Monte Carlo analysis method described in Section 1.6.4 (Chapter 1). Figure 6.5 shows the results of a probabilistic analysis using

*W is calculated from the cross-sectional area of the sliding block, multiplied by the rock unit weight, 0.025 MN/m3. If the total length of the foundations is 5 m, then the minimum length of the foundation block to be used in stability analysis is 5 m, and the values of W and A are:

196

STABILITY OF FOUNDATIONS

the same design parameters as those in Example 6.1, but they are now expressed as probability density functions, rather than discrete values. The end-product of the probabilistic analysis is a distribution of the factor of safety which quantifies the degree of uncertainty in the input values. The example also shows the probability density function of each of the input parameters, and a sensitivity chart identifying which of the parameters has most influence on the coefficient of reliability. This example shows the relationship between the deterministic and probabilistic analyses. In the deterministic analysis the factor of safety is calculated from the mean or most likely values of the input variables, and for the unsupported foundation, the factor of safety has a value of 1.28. However, the probabilistic analysis shows that the factor of safety can range from a minimum value of 0.38 to a maximum value of 3.99 (Fig. 6.5). The proportion of this distribution with a value greater than 1 is 0.78, which represents the coefficient of reliability of the foundation. Also shown in Fig. 6.5 is the distribution of the margin of safety for which the coefficient of reliability is 0.78. This example illustrates that, for these particular conditions, the coefficient of reliability is well below the target level for foundations shown in Fig. 1.9. This low value for the coefficient of reliability is a function of both the low factor of safety, and the wide ranges of uncertainty in the input parameters. The Monte Carlo analysis was performed using the computer program Crystal Ball (Decisioneering, 1994). 6.3 Stability of wedge blocks For a footing of limited areal extent on the crest of a steep face, it is often more appropriate to calculate the stability of a three-dimensional wedgeshaped block rather than the two-dimensional planar block as described in the Section 6.2. A wedge failure is formed by two intersecting discontinuities which both dip out of the face, but are aligned at an oblique angle to the face (Fig. 6.6(a)). Sliding takes

place on both planes simultaneously in the direction of the line of intersection between the planes. The foundation is likely to be stable if the line of intersection is either steeper than the face so that it does not daylight, or if it is flatter than the friction angle in a similar manner to the stability conditions of planar failures. The method of stability analysis of a wedge-shaped block follows the same principles of that of the planar block, except that it is necessary to resolve forces on both the sliding planes. The analysis procedure is to calculate the weight of the wedge, and the area of each face. The weight, as well as all external forces such as the foundation load, water and support forces, are then resolved into their normal and shear components acting oneach of the two sliding surfaces of the wedge. The basic equation for the factor of safety of a wedge is (6.1) where (6.12) and The function f' denotes the shear component of these four forces; N1, N2 are the effective normal forces on planes 1, 2; A1, A2 are the area of planes are the friction angles of planes 1, 2; c1, 1, 2; , c2 are the cohesions of planes 1, 2; W is the weight of wedge; T is the tension in support force; E is the external load; V is the water force in the tension crack. A detailed procedure for calculating the factor of safety of a three-dimensional foundation block is given in Hoek and Bray (1981). The data required for this analysis is as follows. 1. The shape of the wedge is defined by five surfaces: the face of the slope, the upper slope, the tension crack and the two intersecting planes forming the sides of the wedge. The orientation of these surfaces is defined by their dip and dip direction.

STABILITY OF SLIDING BLOCKS

197

Figure 6.5 Results of probabilistic analysis of stability using Monte Carlo analysis to calculate coefficient of reliability CR for foundation shown in Fig. 6.4: (a) probability distributions of design parameters; (b) probability distribution of margin of safety; and (c) sensitivity of input parameters to calculated margin of safety distribution.

2. The dimensions of the wedge are defined by

two lengths: the vertical height H from the apex

198

STABILITY OF FOUNDATIONS

Figure 6.6 Stability of three-dimensional foundation block: (a) isometric view of wedge; and (b) cross section of wedge through line of intersection of planes 1 and 2.

of the wedge to the intersection of plane 1 with the crest of the cut, and the distance L of the tension crack (if any) behind the face as measured along the trace of plane 1.

3. The shear strength of the rock is defined by the cohesion and friction angle of the two sliding planes. The shear strengths of the two planes can have different values as would be the case

STABILITY OF SLIDING BLOCKS

where one discontinuity is a fault with a clay infilling, and the other a clean joint. 4. The weight of the wedge is calculated from the unit weight of the rock and the calculated volume. 5. Water pressures acting on the wedge are determined by assuming that the slope is fully saturated and that the forces U and V are developed by a full head of ground water in the tension crack (Fig. 6.6 (b)). The effective nor mal force N' is the sum of the normal components of W, E, V and T minus the uplift force U. By varying the unit weight of the water, it is possible to simulate varying levels of the water table. 6. External loads on the block consist of the foundation load and a support force; the orientations of both these forces are defined by their trend and plunge. An important component of this analysis is the calculation of the normal forces acting on each plane. This may show that there is no contact on one of the planes with the result that all the shear resistance will be generated on the other plane. This information is required in the calculation of both the factor of safety, and the support force necessary to produce a specified factor of safety. For a wedge which slides on both planes simultaneously, the support force is minimized if it is installed at the optimum orientation. The support force optimum

199

trend is parallel to the trend of the line of intersection between the two planes, and the , where is the optimum plunge is equal to average friction angle of the two planes and ?i is the plunge of the line on intersection. The stability analysis of the three-dimensional wedge block is very versatile and can be applied to a wide range of foundation conditions such as bridge piers located on steep slopes, and the holddown capacity of uplift anchors. If there are a number of external loads such as seismic forces and both vertical and horizontal foundation loads, these can all be combined into a single vector. Situations where this analysis may not produce an accurate solution are where the forces do not act through the center of gravity of the wedge and moments are produced. A limitation of the Hoek and Bray algorithms is that the calculation method requires that the line of intersection of the wedge intercepts the upper slope surface. However, where the line of intersection is flatter than the upper slope, a wedge can still be formed if there is a tension crack that defines the back surface of the wedge. An analysis method that does not have this geometric restriction has been developed using vector algebra (Kielhorn, 1996). A feature of this program is that a rotatable wire frame drawing of the wedge is produced as well as a threedimensional paper cut out model, these are useful aids in checking wedge geometry and the direction of forces.

EXAMPLE 6.2 WEDGE FAILURE STABILITY ANALYSIS

The following is an example of a stability analysis of a wedge block forming the foundation of a bridge pier which applies a vertical external load of 4 MN (900 kips) to the wedge. It is assumed that the geological conditions are those shown on the stereo net in Fig. 2.9 and that the wedge is formed by the foliation and joint set B, and that the intersection of these two planes is along line I2 (dip 61.8° and dip direction 208°). The orientation and shear strength properties of the planes forming the wedge are shown in Table 6.1. The vertical height of the wedge is 25 m (82 ft), the distance to the tension crack along the line of the

200

STABILITY OF FOUNDATIONS

foliation on the upper surface is 6 m (20 ft), and the rock density is 25 kN/m3 (160 lb/ft3). It is assumed that the foundation is dry. With no foundation load acting on the wedge, the factor of safety is 1.73, and with the vertical foundation load applied the factor of safety drops to 1.2. Tensioned rock bolts can be installed to increase the factor of safety to 1.75. The optimal orientation for the bolts is at a trend of 28° and a dip angle of 34° above the horizontal. For bolts installed at this orientation the required bolt force is 2.4 MN (540 kips). However, if the bolts are installed at an angle of 10° below the horizontal, the required bolt force increases to 3.2 MN (720 kips), showing the value of installing bolts at the Table 6.1 Properties of wedge block Pla ne

Di p

Di p dir ect ion

Fri cti on an gle de gre es

Co hes ion kP a (p. s.i)

Fo liat ion

65

24 5

35

Joi nt

85

13 5

20

10 0 (1 4. 5) 50 (7 )

Up per slo pe Sl op e fac e Te nsi on cra ck Li ne of int ers ect

0

20 0

75

20 0

80

18 0

61

20

STABILITY OF SLIDING BLOCKS

201

Figure 6.7 Identification of removable key block in the foundation of a dam (Goodman and Shi, 1985. Adapted by permission of Richard E.Goodman).

Pla ne

Di p

Di p dir ect ion

ion

.8

8

Fri cti on an gle de gre es

Co hes ion kP a (p. s.i)

optimum orientation. In practice, bolts are usually installed at a plunge angle slightly below the horizontal to facilitate grouting.

6.4 Three-dimensional stability analysis In conditions where the shape of a block of rock in a foundation cannot be defined by the five surfaces as shown in Fig. 6.6, there are two other methods of examining the stability of three-dimensional blocks. Details of the analysis procedure of both these methods is beyond the scope of this book, but their basic principles are discussed below. Goodman and Shi (1985) have developed the ‘key block theory’ that is a generalized threedimensional analysis of blocks defined by discontinuity surfaces. The basis of this theory is the definition of blocks, on the basis of their shape, that can slide from the surface of an excavation, or

are ‘removable’. For example, in Fig. 6.7 blocks 2, 3 and 4 in a dam foundation cannot slide because they are constrained by block 1—the key block. If block 1 were to move, then blocks 2, 3 and 4 could also move resulting in failure of the foundation. A stereographic projection method showing the dip and dip direction of the discontinuities and the excavation faces can be used to determine the shape of the blocks and to identify the key block. A generalized three-dimensional slope stability analysis has been developed by Hungr (1987) which is based on Bishop’s method of two-dimensional stability analysis. Instead of dividing the slope into slices as used by Bishop, the three- dimensional analysis divides the slope into columns. The analysis procedure consists of calculating the

202

STABILITY OF FOUNDATIONS

Figure 6.8 Three-dimensional analysis of a slope with a foundation load at the crest (Hungr, 1987).

vertical force equilibrium equation for each column and summing the moment equilibrium for the entire assemblage of columns. These two equilibrium equations, which neglect the vertical shear forces acting on the vertical faces of the columns, are sufficient conditions to determine all the unknown forces and calculate the factor of safety of the slope. Figure 6.8 shows a slope with a surcharge at the crest. A conventional two-dimensional analysis of this slope gives a factor of safety of 1.09, while a three-dimensional analysis gives a factor of safety of 1.25. 6.5 Stability of toppling blocks Toppling failures of foundations may be formed where discontinuities dip into the face and form either a single block, or a series of slabs, such that the center of gravity of the block falls outside the base (Fig. 6.9). These conditions for toppling are only met where the dip angles of both the face and the discontinuities are steep, and the discontinuities are aligned parallel to the face (Goodman and Bray, 1976). Experience has shown that considerable movement may take place as the slabs move

horizontally, but that overall failure of the slope will not occur until there is shear failure of blocks at the toe that act as keystones to constrain the slope. It is likely that the amount of movement prior to overall slope failure will exceed the displacement tolerance of most structures so it is important to identify geological structure that is susceptible to toppling. The analysis of foundations containing blocks which could undergo toppling movement consists of examining the stability conditions of each block in turn starting at the top of the slope. A block will have one of three stability modes: stable, sliding or toppling (Fig. 6.9). The stability mode depends on the dimensions of the block, the shear strength parameters of its faces and the external forces acting on it. For example, short blocks at the crest (blocks 7, 8, 9) for which the center of gravity falls inside the base will be stable, provided that the friction angle of the base is greater than the dip of the base. However, taller blocks in which the center of gravity lies outside the base may topple (blocks 4, 5, 6), depending on the restraint provided by the shear forces on the two sides of the block. If the block does topple, it produces a thrust force against the block below it on the slope. If this next block is

STABILITY OF SLIDING BLOCKS

203

Figure 6.9 Stability of foundation containing toppling blocks (adapted from Goodman and Bray, 1976).

also tall it may topple as a result of this thrust force, even though its center of gravity lies inside the base. At the toe of the slope where the blocks are short and will not topple (blocks 1, 2, 3), the thrust force produced by the upper toppling blocks may be great enough to cause these blocks to slide with the result that the overall slope will be unstable. However, if the toe blocks do not slide or topple, the upper blocks may undergo considerable displacement, but there will be no overall failure. If a footing is located on the slope, this load has the effect of increasing the height of the block. This may cause a stable block to topple, or exacerbate an existing toppling condition by increasing the thrust forces on the lower blocks. The first step in the stability analysis is to determine the dimensions of all the blocks as defined by their width ?x and their height yn (Fig. 6.10). Then, starting at the top of the slope, the forces acting on each block are calculated. These forces comprise all or some of the following:

1. block weight Wn of block n; 2. foundation load Q on the top surface; 3. force Pn produced as a result of toppling of the next higher block (n+1) in the foundation; 4. restraint Pn-1 provided by the next lower block (n-1) in the foundation; 5. shear forces developed on the sides of the blocks; 6. normal and shear forces Nn and Sn respectively acting on the base of the block; 7. water pressures acting on the sides and base of the blocks, the magnitudes of which are denoted by the dimensions yw and zw. The method of calculating whether a block will topple or slide, or be stable, is as follows. First, by resolving all forces acting on a block into components perpendicular and parallel to the base, the normal and shear forces acting on the base are:

204

STABILITY OF FOUNDATIONS

Figure 6.10 Forces acting on a toppling block.

(6.15)

(6.16) where Wn is the weight of block is the dip angle of the base of the blocks; ?Q is the inclination of the load measured in a clock-wise direction from a horizontal axis to the right of the force (the slope is drawn sloping down from left to is the friction angle on the sides of the right); blocks; yw and zw are the heights of the ground water on the upper and lower sides of the block respectively; Q is the foundation load in units of force per unit length of slope; ?r is the rock unit weight; and ?w is the water unit weight. Considering rotational equilibrium, it is found that the force Pn-1,t which is just sufficient to prevent toppling of block n has the value

where Mn and Ln define the points of application of the forces Pn and Pn-1 respectively. The water forces V1 and V3 acting on the sides of the blocks are (6.18) (6.19) Assuming that the blocks are in a state of limiting equilibrium so that equations 6.15 and 6.16 apply, the force just sufficient to prevent sliding of block n has the value

(6.20)

STABILITY OF SLIDING BLOCKS

where is the friction angle on the base of the blocks, and the water pressure acting on the base of the block is (6.21) The stability analysis procedure is to examine the stability condition of each block in turn, starting at the top of the slope. The stability condition of each block is established according to the following criteria. sliding will not occur on the base 1. For of the blocks, provided that no external forces act, i.e. 2. For short blocks near the crest of the slope the blocks will be where stable. this defines the upper 3. Where toppling block, and the forces Pn-1,t and Pn-1,s are calculated. 4. Calculate the forces Pn-1,t and Pn-1,s and determine stability conditions by the following tests: the block is on the point If of toppling and Pn-1 is set equal to Pn-1,t; the blocks If will not slide. 5. In the lower part of the slope where the blocks are short and toppling does not occur, the thrust produced by the upper toppling blocks may be sufficient to cause the toe blocks to slide, i.e. the block is on the point of (a) If sliding and Pn-1 is set equal to Pn-1,s; the block will be stable, or (b) If , the block will slide. (c) If If the bottom block slides, then the overall foundation slope will be unstable. However, even if the bottom block(s) are stable and there is no overall slope failure, considerable displacement of the toppling blocks higher in the slope may still take place. Having calculated the forces acting on each block, it is possible to determine the factor of safety of the foundation by an iterative process as follows. The

205

friction angles are progressively changed until limiting equilibrium conditions are reached and the lowest block is just on the point of sliding. The friction angle required for limiting equilibrium is , and if the friction angle of the base of the blocks is , then the factor of safety is given by (6.22) Methods of stabilizing foundations that can undergo toppling movements can be divided into two categories, namely modifying the shape of the blocks, or installing support (Wyllie, 1980). If potential instability is recognized before construction, the blocks can be shortened by excavating the upper part of the slope so that center of gravity of the blocks falls inside the base. Alternatively, it may be possible to install rock bolts through a number of blocks to increase their effective width, or the toe of the slope can be supported with tensioned rock bolts anchored in stable rock below the zone of movement. The calculation of the required bolt force can be carried out using equations 6.15–6.22 in which the support is an external force, acting into the slope, on any number of toe blocks. The data required for the evaluation of stability conditions of a foundation with a potential for toppling type movement are as follows. 1. The geology of the foundation is defined by the dip ?p and spacing ?x of the set of disconti nuities that dips into the face of the slope. It is also assumed that there is a set of orthogonal discontinuities that dip out of the face to form the base of each block. 2. The dimensions of slope are defined by the dip angles of the face and the upper slope, and the vertical distance between the crest of the slope and the lowest sliding block. An important parameter in defining the height of each block is the angle ß (Fig. 6.9) which must be selected from an inspection of the geological conditions and slope dimensions. It cannot be determined analytically, and its value is critical to stability.

206

STABILITY OF FOUNDATIONS

If ß is large, the blocks will be short and no toppling will occur, while if ß is small, the blocks will be tall and most blocks will topple. 3. From the geology and the slope dimensions, the height of each block yn can be calculated. 4. The shear strength of the rock is defined by the friction angles of the base and sides of the and respectively). This condition blocks may arise where one set of discontinuities is, for example, a set of clay filled bedding planes and the other is a set of joints with rough surfaces. 5. The weight of each block is the product of its cross-sectional area and the rock unit weight. 6. Water pressures act on the sides and base of each block with values defined by the elevation of the water table. 7. The foundation load Q can act on any block(s) and can be inclined at any angle; it should be noted that all forces are expressed as a force per unit length of the foundation. 6.6 Stability of fractured rock masses Where the rock mass contains no dominant geological structure, but is randomly or closely fractured, a rupture surface with an approximately circular shape may develop in a similar manner to failures in soil. This surface will pass partially through intact rock and partially along existing discontinuities to form a shallow, large radius surface. This is in contrast to more deep seated, small radius failures that occur in exca vations made in low friction, cohesive soils. The stability analysis of cut slopes in both soil and rock using limit equilibrium methods is well developed (Bishop, 1955; Janbu, 1954; Nonveiller 1965; Morgenstern and Price, 1965; Sarma, 1979) and these methods can be applied to wide range of geological and geometric conditions. The method of stability analysis for curved rupture surfaces is similar to that for sliding blocks described in Section 6.2 in that a unit thickness of slope is studied and the factor of safety is given by the ratio between the moments of the resisting and

driving forces on the rupture surface. The analysis procedure is to divide the slope into a series of slices, with vertical or non-vertical sides, and then find the effective normal force on the base of each slice, from which the resisting force is given by equations 6.4 and 6.5. The total resisting moment is calculated as the product of the radius of the rupture surface and the sum of the resisting forces on the base of the slices. The moment of the driving force is the sum of the downslope components of the weight of each slice, together with any external and water forces, multiplied by the moment arms. The simplified methods of analysis neglect the effect of normal and shear forces on the sides of the slices without any significant loss of accuracy. The stability analysis program XSTABL (Sharma, 1991), which uses the modified Bishop or Janbu methods of analysis for circular rupture surfaces, can be readily used in the examination of stability of rock foundations. An important feature of this program is the ability to calculate the factor of safety for a variety of surface shapes, and find the surface with the minimum factor of safety. The rupture surfaces, within specified ranges for the shape and position of the surface, are defined by a random number generator. This search routine for the minimum f actor of safety surface is not required if the position of the rupture surface is determined by a pre-existing geological feature. Figure 6.11 shows a foundation on a steep cut face supporting two vertical loads (Q1 and Q2) and an inclined tie-back force T. The slope is made up of three geologic materials—overburden, schistose rock with the foliation dipping at 70° into the face, and a fault zone at the toe, and contains a single water table. The stability analysis of this foundation using the program XSTABL involves the following steps. 1. The ground surface is defined by a series of straight line segments given by x and y coordinates. 2. The subsurface boundaries between material types are also defined by straight line segments.

STABILITY OF SLIDING BLOCKS

207

Figure 6.11 Stability analysis of foundation using XSTABL program.

3. The strength properties of the materials can be defined by Mohr-Coulomb isotropic or anisotropic parameters, or curved (HoekBrown) envelopes. For anisotropic materials, different strengths can be defined for ranges of dip angles as indicated by the inset on Fig. 6.11. Curved strength envelopes, as defined by the parameters m, s (Table 3.7) and su, are used in the analysis in the following manner: the effective normal stress acting on the base of each slice is determined, and the corresponding instantaneous friction angle and cohesion is calculated from equations 3.16–3. 19. This approach results in the shear strength varying along the rupture surface. 4. Water pressures can be defined by a phreatic or piezometric surface comprising a series of straight line segments, or as a pore water pressure grid, or as an ru factor which defines the pore water pressure as a fraction ru of the . total vertical earth pressure 5. External forces are defined in terms of their magnitude, position on the slope and inclination

EXAMPLE 6.3

in the plane of the section. 6. Earthquake forces are simulated as pseudostatic horizontal and vertical seismic coefficients. For example, if a horizontal seismic coefficient of 0.09 is specified, then a horizontal force equal to 0.09 times the weight of the slice is applied to each slice. 7. The rupture surface can be defined as a circular arc, or a series of straight line segments, and a search routine finds the surface with the minimum factor of safety. For a circular surface, limits to the shape and position of the surface are specified by ranges for the initiation and termination points of the surface, and for angular limits for the lower end of the surface. For surfaces comprising straight line segments, a search rectangle can be defined for each junction point between segments. The following example illustrates the use of XSTABL in the stability analysis of the foundation shown in Fig. 6.11.

208

STABILITY OF FOUNDATIONS

STABILITY ANALYSIS USING XSTABL

For the foundation shown in Fig. 6.11 the geological conditions consist of overburden with a thickness of about 15 m overlying a moderately fractured schist in which the schistosity dips into the face at a dip of about 70°. At the toe of the slope there is a fault which has the same orientation as the schistosity and contains a weak, low permeability, crushed rock gouge. The properties of these three materials are defined by their cohesion, friction angle and unit weight. The anisotropic strength of the schist is expressed by assigning a lower strength value in a direction aligned parallel to the schistosity (see inset). The table on Fig. 6.11 lists these input parameters. The input parameters comprise x and y co-ordinate pairs defining the ground surface, material boundaries and ground water surface elements, as well as material strength properties and magnitudes and positions of the external loads. The external loads consists of two foundations simulated by pressures acting vertically and positioned on the two cut benches: A tied-back anchor support force T is simulated as a third external pressure acting at an angle of 20° below the horizontal and positioned on the face below the lower foundation load Q2. Earthquake forces are simulated by pseudo-static horizontal and vertical accelerations of 0.12g and 0. 04g respectively. XSTABL allows the general shape of the rupture surface to be defined, as well as the range over which the initiation and termination points intersect the excavation surface. In this case a Bishop analysis has been carried out for a rupture surface comprising a circular arc with the lower end of the surface at the toe of the slope and the upper end existing at any point at or above the level of load q2. In Fig. 6.11 the rupture surface with the minimum factor of safety is indicated showing that the critical condition is the lower bench containing the low strength fault zone, and supporting the major foundation load. The results of the analysis for a variety of conditions are: (A) Excavated slope with no foundation loads or support, static loading:

(B) Excavated slope with foundation loads: loading (C)

Excavated

slope

with

foundation loads , static loading:

(D) Excavated slope with foundation loads: earthquake accelerations,

, no tie-backs, static

and

support

force:

,

These analyses show the effect of both external loads and material properties on the stability of the foundation slope. An analysis could also be carried out to simulate the effect of heavy blasting in the excavation of the benches for the footings. If the blasting is heavy enough to loosen and shatter the rock, the cohesion may be reduced from 200 to 50 kPa. This reduction in strength results in the factor of safety of the foundation being diminished from 1.48 to 1.07 showing the importance of controlling blasting operations.

STABILITY OF SLIDING BLOCKS

6.7 External effects on stability The following is a discussion of two types of external forces, ground motion due to earthquakes and turbulent water flow, that can have a significant effect on stability, depending on the site conditions. 6.7.1 Seismic design Ground motion due to earthquakes induces forces that act on both the structure and the foundation, and it is necessary to examine the combined effect of these forces to determine the overall stability conditions of the foundation. Earthquake forces can be assumed to act horizontally, or have both horizontal and vertical components. The forces acting on the structure induce a base shear and an overturning moment at the foundation level. Added to these loads are the seismic forces acting on the foundation itself. These forces are significant if there is a steep slope below the structure because it is possible that the whole foundation could slide on a shear plane inclined out of the slope. Examples of slope failures induced by earthquakes are described by Youd (1978), Horner et al. (1987) and Harp and Jibson (1995), while the 1989 Loma Prieta earthquake in California is estimated to have caused between 2000 and 4000 rock, soil and debris falls that blocked many roads (Transportation Research Board, 1996). Design of foundations subjected to seismic forces consists first of anchoring the structure to the foundation, and second ensuring that the foundation itself is stable. Anchoring the structure is required to prevent both shear displacement and uplift resulting from overturning moments acting on the structure. The calculation of these forces is usually part of the structural design and are considered to be additional external loads acting on the foundation. The second stage of the design involves examination of the stability conditions of the foundation under the combined loads imposed by the structure and the seismic forces acting on the foundation itself. The method of analysis consists of

209

calculating the factor of safety assuming that the earthquake is equivalent to a static force acting out of the slope. This technique is termed pseudo-static analysis. For example, if the design earthquake acceleration is 15% of gravity, then a horizontal force equal to 0.15 times the weight of the foundation block is incorporated into the stability analysis as an additional external force acting on the block. In circumstances where the vertical and horizontal earthquake motions may be in phase, a vertical pseudo-static force could also be applied to the foundation. The resultant of the two pseudostatic forces is resolved into components perpendicular and parallel to the sliding surface. The direction of these forces usually has the effect of decreasing the normal force and increasing the displacing force, which reduces the factor of safety. Earthquake accelerations used in design are specified in building codes which divide the country into a number of zones of probable seismic intensity. These zones are based on both historical earthquake records, and the theory of plate tectonics which relates the occurrence of earthquakes to relative movement of crustal plates. Most earthquakes occur along the margins of these plates, with few earthquakes being recorded in the central areas. Therefore, the higher risk seismic zones are situated along the edges of the plates such as the periphery of the Pacific Ocean— the west coasts of North and South America, Japan, the Philippines, New Guinea and New Zealand. The magnitude of the earthquake for design purposes is expressed in terms of an acceleration as a percentage of gravity. The pseudo-static method of stability analysis is widely used in design because it is a simple technique and tends to produce a conservative result. However, in special cases the earthquake is more accurately modeled as a dynamic transient force which is used to determine displacement of the foundation. Methods of calculating displacement of foundations under earthquake loading are described in Section 7.4.

210

STABILITY OF FOUNDATIONS

6.7.2 Scour The analyses presented in this chapter assume that both the geometry of the foundation and the condition of the rock remain constant over the life of the project. However, where foundations are submerged in flowing water or are subject to wave action, scour may result in steepening or undermining of the rock face below the footing. Another effect of both flowing and still water is weathering or dissolution of the rock (see Section 3.6). The following is a discussion on methods of predicting scour related to both the rock characteristics and the water flow conditions. This topic is also discussed in Section 7.6, Rehabilitation of dam foundations, while Section 10.4 discusses methods of stabilizing foundations. The susceptibility of a foundation to scour can be estimated from the following relationship between the erosive power of the water P and the resistance of the rock to scour Kr (Annandale et al., 1996): (6.23) Scour will occur when the power exceeds a threshold value that depends on the characteristics of the rock mass as defined by Kr. As discussed below, P is a function of water flow characteristics around the foundation, while Kr is a function of four quantifiable properties of the rock mass. (a) Scouring action of water Scour can result where water flow over irregular surfaces is accompanied by eddies and turbulence resulting in fluctuating pressures at the surface over which it is flowing. The action of these forces, together with the hydrostatic forces in the cracks, causes a tugging and pulling of the rock which can loosen and remove blocks from the foundation. The erosive power of water P can be related to the magnitude of fluctuating pressures and the resulting rate of energy dissipation, or stream power, by the following equation: (6.24) where ?w is the unit weight of water; q is the unit discharge and ?E is the energy loss (Smith and Annandale, 1996).

A pier is an obstruction to flow which causes secondary currents and vortices to be developed as the flow is deflected downwards in front of the pier, and then contracts and accelerates around the pier. This turbulence produces fluctuating pressures around the pier which is characteristic of energy dissipation and erosive power. The erosive power is greatest around a pier for flat bed flow condition when the turbulence is most intense. If a scour hole develops, the turbulence intensity, and erosive power, diminishes as the scour hole increases in depth. Thus, scour will continue until an equilibrium condition is reached where the energy dissipation due to turbulence results in the erosive power equaling the resistance of the rock. Furthermore, sorting of the scoured material will cause the larger rock fragments to remain in the scour hole providing a protective layer in the base of the hole. Another factor that may limit scour is the increasing erosive resistance of the rock as scour develops where, for example, the degree of weathering and the fracture intensity decreases with depth. The complex flow patterns and related shear stresses at bridge piers are affected by the pier width, shape and alignment to the flow, as well as the depth and velocity of the approach flow and the depth and shape of the scour hole. Of these factors, the pier width is the most influential parameter. Measurements have shown that the shear stress around the pier may be six to eight times that in the flat bed approach flow (Parola, 1993). However, the complexity of the actual flow conditions precludes, at present (1998), the development of an analytical expression for shear stress levels in turbulent flow. The stream power per unit area P, which is the product of the shear stress t and the approach velocity V, for fully developed, turbulent flow can be calculated from: (6.25) where ?w is the water unit weight; y is the flow depth and d is the medium particle diameter on the stream bed. Equation 6.25 can be used to calculate the stream power upstream of the pier which can then be multiplied by a factor in the range 5–15 to give the approximate stream power or energy

STABILITY OF SLIDING BLOCKS

dissipation in the more turbulent flow at the pier. This value of the stream power can then be used in equation 6.23 to assess the susceptibility of the rock to scour. (b) Scour resistance of rock In order to quantify the susceptibility of rock masses to scour, an erodibility index Kr has been developed in which the relevant character of the rock mass is calculated as the product of four parameters (Annandale, 1995): (6.26) This method of calculating the erodibility index is a modification of the Q-system for assessing support requirements for tunnels (Barton et al., 1974), that uses properties of the rock mass that are readily measured in the field. The following is a discussion of each of the four parameters. 1. Ms, the rock mass strength number represents the material strength of an intact representative sample without regard to its geologic heterogeneity within

211

the rock mass. The value of Ms is the product of the uniaxial compressive strength of the rock (units MPa) and its unit weight relative to a standard of 27 kN/m3. For example, a rock with a uniaxial compressive strength of 60 MPa and a unit weight of 25 kN/m3 will have an Ms value of 56 [60×(25/27)]. 2. Kb, the particle-block size number is the mean size of block of rock as determined by joint spacing. Values for Kb can be calculated from the following relationship: (6.27) where RQD is the rock quality designation (see Section 4.3.1) and Jn is the joint set number. The relationship between Jn and the number of discontinuity sets in the rock mass is shown in Table 6.2. The possible range of values for Kb is 1– 100. 3. Kd, the discontinuity or interparticle bond shear strength number is calculated from the ratio (6.28)

Table 6.2 Relationship between number of discontinuity sets and joint set number Jn Number of discontinuity sets

Joint set number Jn

Intact, no or few joints, fissures One discontinuity set One discontinuity set plus random Two discontinuity sets Two discontinuity sets plus random Three discontinuity sets Three discontinuity sets plus random Four discontinuity sets Multiple discontinuity sets

1.0 1.2 1.5 1.8 2.2 2.7 3.3 4.1 5

where Jr is the joint roughness number related to the condition of the discontinuity surfaces, and Ja is the joint alteration number related to the strength of the

material forming the surfaces of the discontinuities. Values for these two parameters are given in Tables 6.3 and 6.4 respectively.

Table 6.3 Relationship between discontinuity surface shape and joint roughness number Jr Discontinuity separation Conditions of rock surface

Joint roughness number Jr

Tight discontinuities

4.0 3.0 2.0 1.5 1.5 1.0

Impersistent discontinuities Rough or irregular, undulating Smooth, undulating Slickensided, undulating Rough or irregular, planar Smooth, planar

212

STABILITY OF FOUNDATIONS

Discontinuity separation Conditions of rock surface Open discontinuities

Joint roughness number Jr

Slickensided, planar 0.5 Open discontinuities, or contain weak infilling that prevents 1.0 rock wall contact Shattered or micro-shattered clays 1.0

Table 6.4 Relationship between discontinuity surface condition and joint alteration number Ja Description of infilling

Joint alteration number Ja for joint width (mm) 1.0*

Tightly healed, hard, nonsoftening impermeable infilling 0.75 Unaltered discontinuity walls, surface staining only 1 Slightly altered, non-softening, non-cohesive rock or crushed rock 2 infilling Non-softening, slightly clayey non-cohesive infilling 3 Non-softening, strongly overconsolidated clay infilling, with or 3* without crushed rock. Softening or low friction clay coatings and small quantities of 4 swelling clays Softening moderately overconsolidated clay infilling, with or without 4* crushed rock Shattered or micro-shattered (swelling) clay gouge, with or without 5* crushed rock. * Discontinuity walls effectively in contact. † Discontinuity walls come in contact after about 100 mm shear. ‡ Discontinuity walls do not come into contact on shearing. § Values added to Barton et al. (1974) data. ** Also applies when crushed rock occurs in clay gouge without rock wall contact.

4. Js, the relative ground structure number represents the effective dip of the least favorable discontinuity set with respect to the flow, and accounts for the shape of the blocks of rock and the ease with which the stream can penetrate the rock surface and dislodge blocks. In general, rock masses

1.0–5.0†

5.0‡

– – 2

– – 2

6§ 6**

10§ 10

8§

13§

8**

13

10**

18

are more resistant to scour if they are slabby rather than blocky, and if the slabs dip upstream rather than downstream. These conditions are quantified in Table 6.5 which relates values for Js to the orientation and spacing of the discontinuity sets.

Table 6.5 Relationship between discontinuity orientation and spacing and relative ground structure number Js Orientation of closer spaced discontinuity Dip of closer spaced discontinuity set Ratio of discontinuity spacing set (degrees) Vertical Discontinuities dip in direction of stream flow 80 70 60 50

1:1

1:2

1:4

1:8

90

1.1

1.2

1.2

1.3

0.7 0.6 0.5 0.5

0.6 0.5 0.5 0.5

0.6 0.5 0.4 0.4

0.5 0.4 0.4 0.4

STABILITY OF SLIDING BLOCKS

213

Figure 6.12 Relationship between erodibility index of rock and soil materials and rate of energy dissipation, showing erosion threshold (Annandale, 1995).

Orientation of closer spaced discontinuity Dip of closer spaced discontinuity set Ratio of discontinuity spacing set (degrees) 40 30 20 10 0 Horizontal Discontinuities dip upstream 20 30 40 50 60 70 80

1:1

1:2

1:4

1:8

0.5 0.6 0.8 1.3 1.1 10

0.5 0.6 0.8 1.1 1.1 0.7

0.5 0.6 0.7 1.0 1.1 0.7

0.5 0.5 0.7 0.9 1 0.8

0.8

0.6 0.5 0.5 0.5 0.6 0.8 1.3

0.6 0.6 0.5 0.6 0.7 0.9 1.4

0.7 0.6 0.6 0.6 0.7 1 1.5

0.7 0.6 0.6 0.6 0.7 1 1.6

(c) Stream power-scour resistance relationship The relationship between the scour resistance of rock and soil materials and the energy dissipation of water flowing over a variety of hydraulic structures has been determined empirically by studying field conditions. The results of 137 such observations distinguished between sites where scour did and did

not occur (Fig. 6.12). The dashed line is the approximate threshold of scour for this data, and the approximate relationship between the erodibility index Kr and the rate of energy dissipation per unit width of flow P(kW/m) is: (6.29) Equation 6.29 and the information presented in

214

STABILITY OF FOUNDATIONS

Fig. 6.12 can be used as a guideline in assessing the susceptibility of a facility to scour. Where there is a risk of scour, preventative measures include modifying the designs to reduce turbulent flows to acceptable levels, or protecting the rock with reinforced concrete aprons or rip rap. 6.8 References Annandale, G.W., Smith, S.P., Nairns, R. and Jones,J. S. (1996) Scour power. ASCE, Civil Engineering, New York, July, pp. 58–60. Annandale, G.W. (1995) Erodibility. J. Hydraulic Research, 33(4), 471–93. Barton, N.R., Lien, R. and Lunde, J. (1974) Engineering classification of rock masses for the design of tunnel support. Rock Mechanics, 6(4), 189–236. Bishop, A.W. (1955) The use of the slip circle in the stability analysis of earth slopes. Geotechnique, 5, 7– 17. Cavers, D.S. (1981) Simple method to analyze buckling of rock slopes. Rock Mech., 14, 87–104. Decisioneering Inc. (1994) Crystal Ball, Release 3.0.1. Boulder, CO. Goodman, R.E. and Bray, J.W. (1976) Toppling of rock slopes. Proc. Specialty Conf. on Rock Engineering for Foundations and Slopes, Boulder, Colorado, ASCE, Vol. 2, 201–34. Goodman, R.E. and Shi, G. (1985) Block Theory and its Application to Rock Engineering. Prentice-Hall, Englewood Cliffs, New Jersey. Harp, E.L. and Jibson, R.W. (1995) Inventory of Landslides Triggered by the 1994 Northridge, California Earthquake. US Geological Survey, Denver, Open-File Report 95–213, pp. 17. Hoek, E. and Bray, J. (1981) Rock Slope Engineering, 2nd edn, IMM, London. Horner, R.B., Lamontagne, M. and Wetmiller, R.J. (1987) Rock and roll in the North West Territoriesthe 1985

Nahanni earthquakes. Geos, Dept. Energy Mines and Resources, Ottawa, pp. 1–4. Hungr, O. (1987) An extension of Bishop’s simplified method of slope stability analysis to three dimensions. Geotechnique, 37, 113–17. Janbu, N. (1954) Application of composite slip circles for stability analysis. Proc. European Conf. on Stability of Earth Slopes, Stockholm, Vol. 3, pp. 43–9. Kielhorn, W. (1996) The Physics of Yet Another Wedge Calculator (YAWC). Coyote Software, Vancouver, Canada. Morgenstern, N.R. and Price, V.E. (1965) The analysis of the stability of general slip surfaces. Geotechnique, 15, 79–93. Nonveiller, E. (1965) The stability analysis of slopes with a slip circle of general shape. Proc. 6th Int. Conf. Soil Mech. Foundation Engineering, Montreal, Vol. 2, pp. 552. Parola, A.C. (1993) Stability of rip rap at bridge piers. J. Hydraulic Eng., 119(10), 1080–93. Sarma, S.K. (1979) Stability analysis of embankments and slopes. J. Geotech. Eng. Div., ASCE, 105, GT12, pp. 1511–1524. Sharma, S. (1991) XSTABL, An Integrated Slope Stability Analysis Method for Personal Computers, Version 4.00. Interactive Software Designs, Inc. Moscow, ID, USA. Smith, S.P. and Annandale, G.W. (1996) Scour in erodible rock II: erosive power at bridge piers. North American Water and Environmental Congress, ASCE. Transportation Research Board (1996) Landslides— Investigation and Mitigation, Chapter 4, Landslide Triggering Mechanisms, National Research Council, Washington, DC, pp. 673. Wyllie, D.C. (1980) Toppling of rock slopes: examples of analysis and stabilization. Rock Mech. 13, 89–98. Youd, T.L. (1978) Major cause of earthquake damage is ground failure. Civil Engineering-ASCE, April, pp. 47–51.

7 Foundations of gravity and embankment dams

7.1 Introduction Dam foundations typically require significantly more extensive investigation and design programs than do buildings, and most bridges. These programs will often comprise driving exploration adits in the foundations and abutments, comprehensive laboratory and in situ soil and rock strength testing, and a detailed analysis of gravity and seepage forces induced in the foundation. Such detailed programs are conducted for one or more of the following reasons. 1. The consequences of failure of a dam are usually very severe and can result in loss of life and property damage. Furthermore, most dams are a vital part of the infrastructure of a community. 2. The loads on dams can be high compared with most other structures, and are also non-vertical. For concrete dams, the shear component of this load acting parallel to the dam foundation in a downstream direction can cause the dam to slide, and the vertical component can result in excessive deformation. 3. The loads are cyclic due to fluctuations in reservoir level and the foundations must be able to withstand these changing stress conditions with no deterioration in their strength. 4. With the large size of most dams it is possible that they will be founded on materials of differing strengths and deformation moduli, causing differential movement to occur; this is most critical for concrete dams.

5. High hydraulic gradients and water pressures are developed in dam foundations and measures must be taken to ensure that the foundation can withstand these pressures, while maintaining seepage quantities at acceptable levels. The photograph in Fig. 7.1 shows the Revelstoke Dam on the Columbia River in British Columbia, Canada. The dam comprises a concrete gravity dam in the river channel with an earthfill embankment section on the right bank. The maximum height of the gravity section is 175 m (575 ft) made up of 23 separate blocks ranging in width from 13 to 26 m (43 to 87 ft). The earthfill dam is 1160 m (3800 ft) long and has a maximum height of about 126 m (413 ft); it is located on a terrace comprising sand, gravel and cobbles at an elevation about 50 m (164 ft) above the foundation of the gravity dam. Preparation of the foundation for the gravity dam required extensive excavation, partly to locate the downstream end of the highest dam blocks below a major shear. The earthfill dam is founded on the granular materials but a core trench was excavated through this material to found the dam core directly on bedrock (Forster, 1986). The discussion of dam foundations in this chapter is restricted to gravity and embankment dams; the design of foundations for arch dams is beyond the scope of this book. Gravity and embankment dams are the two most common types of dams and the general design procedures are well established. However, each project has its unique set of site characteristics that must be considered in

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Figure 7.1 Revelstoke Dam on the Columbia River in Canada, a combined concrete gravity and earthfill dam (photograph courtesy of B.C.Hydro).

investigation, design and construction. The chapter discusses design and construction of rock foundations, as well as improvement techniques for existing foundations where deterioration has occurred (Section 7.6). Deterioration of dams and their foundations is becoming increasingly important in most developed countries with few new dams being constructed, and existing dams increasing in age. 7.1.1 Dam performance statistics An analysis of dam performance provides a useful insight into the reliability of dams, and the causes and types of foundation deteriorations and failures that occur. A detailed study of a total of 178 failures of concrete, masonry and earth dams in 31 countries showed that 25, or 14%, of these failures occurred as the result of deterioration of rock foundations (ICOLD, 1995). An earlier study (Kaloustian, 1984) of a total of 4489 concrete dams on rock foundations as reported between 1900 and 1978 by ICOLD (1979), and supplemented by additional

cases, shows similar results regarding failures, and deteriorations that required significant repair to prevent failure. The primary conclusions of these analyses are as follows. 1. The percentage of failures of large dams has been falling over the four decades since 1950, with 2.2% of dams built before 1950 failing and less than 0.5% failing since that time. 2. The ratio (height H of failed dams/built height) varies little with height showing that large dams fail as often as small dams. However, (100 ft)) failures of small dams are the most common because there is the largest number of these dams. 3. Approximately 80% of the failures were of earthfill and rockfill dams. 4. Most failures involve newly built dams: 59 (33%) of the failures occurred either during construction or within the first year of operation, while 108 (61%) of the failures occurred in the first ten years. 5. Foundation problems are the most common

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS

cause of failure of concrete dams: of the 178 failures, 35 were due to foundations, of which 25 were rock foundations. Internal erosion and insufficient shear strength accounted for 15 of these failures. These figures can be expressed in terms of probabilities which show that the probability of failure of rock foundations has dropped from about 10-4 per dam year in the early 1900’s to about 10-5 per dam year in the 1980’s (see also Fig. 1.9). As there has been a huge increase in the number of dams during

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this period, these figures demonstrate a significant improvement in safety. 6. The types of concrete dams that failed, together with the average age of each type at failure, are as follows: Gravity—six dams with average age of 3. 7 years Arch—three dams with average age of 1.3 years Buttress—one dam with age of 1 year.

Table 7.1 Failures and deteriorations of concrete dams on rock foundations (Kaloustian, 1984)

Permeability: seepage uplift 28 Heterogeneous deformation Shear failure of foundation or abutments Erosion of downstream pool due to surface flow Totals

Of the 110 failures and deteriorations recorded by ICOLD (1979), the causes can be divided into four main categories of external effects: reservoir filling, floods, seismic events, and other assorted causes. Table 7.1 shows the distribution of these incidents according to both the external effects and the type of failure or deterioration. These figures show that ground water effects in the foundation, i.e. seepage and uplift (totaling 61% of the incidents) are the most common. Of the cases shown in Table 7.1, 81% occurred during filling of the reservoir which demonstrates that this is a critical time in the life of a dam when both the structure and its foundation are undergoing rapidly changing gravity and seepage stresses. The dam performance statistics (ICOLD, 1974) have also been analyzed to show the time of failure or deterioration after completion of the dam (Fig. 7.2). Deterioration due to loss of foundation strength usually occurred within the first two years of operation (curve 1), while dam failures generally occurred within four years (curve 2). Deterioration due to seepage and uplift occurred later in the life of the dam but still took place within approximately

Reservoir filling

External effects

Total

Floods

Seismic events

Others

30 2 20 10 1 89

4 – – 2 6 14

2 – 1 – – 3

1 30 – 3 – 4

37 21 15 7 110

the first five years. Two significant rock foundation failures are the Malpasset Dam in France and the Teton Dam in the USA. The Malpasset Dam, a 61 m (200 ft) high concrete arch structure completed in 1954, failed in 1959 as the result of a wedge of rock in the left abutment sliding following build up of excessive uplift water pressures (Jaeger, 1963). The Teton Dam, a 93 m (305 ft) high central-core earthfill structure, failed in 1976 during filling of the reservoir partly as the result of erosion of fill in the key trench by water flowing from open joints in the rock foundation (US Department of the Interior, 1980). 7.1.2 Foundation design for gravity and embankment dams The general requirements for the design of rock foundations for gravity and embankment dams are stability against sliding and overturning, acceptable levels of differential deformation, and control of seepage and erosion. Depending on the type of dam

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Figure 7.2 Time of dam deteriorations and failures after completion of construction (after Kaloustian, 1984): (1) deteriorations due to loss of strength; (2) dam failures; and (3) deteriorations due to seepage and uplift.

and the geological conditions of the foundation, it is usual that differing levels of effort are directed to these design tasks (Bieniawaski and Orr, 1976). Stability against sliding, both within the foundation, and at the interface between the dam and the foundation, is usually of more concern for gravity dams than earthfill dams. Overturning is only of concern for gravity dams, together with the development of tensile stresses at the heel and high compressive stresses at the toe induced by the moments. Methods of calculating the factor of safety against sliding and overturning, and examples of remedial measures taken to prevent sliding are discussed in Section 7.2 and 7.3. Deformation of the rock foundations is usually not of concern for embankment dams because the structure can accommodate some differential deformation that may occur at the boundary between materials with different moduli. However, in concrete dams, differential deformation of the foundation and abutments may be of concern if this induces excessive stress levels in the concrete (see Fig. 3.2 and Section 3.2).

Seepage in foundations, and particularly at the contact between the dam and the foundation, is of most concern in embankment dams where uncontrolled seepage can result in scour of the core material. Methods of preparing rock foundation surfaces are discussed in Section 7.5, and procedures for grouting and drainage are presented in Section 7.7. 7.1.3 Loads on dams The resultant of the wide variety of loads that may act on a dam must be resisted by the foundation with no risk of sliding or overturning, and without excessive deformation. The following is a summary of typical load conditions, with particular emphasis on gravity dams. 1. The dead weight consists of the dam structure plus appurtances such as intakes, gates and bridges. For concrete dams, the unit weight of concrete is approximately 23 kN/m3 (146 lb/

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS

ft3). 2. Water exerts both external forces on the dam, and internal forces in the foundation and abutments. The external water forces are made up of the head of water acting on the upstream face (either normal operating level or peak maximum flood), the tail water where water is ponded downstream of the dam, and loads on sloping or horizontal surfaces. The water forces are modified by wave action, reservoir set up due to steady winds blowing up the reservoir, ice loading at the crest of the dam, and the possible accumulation of silt behind the dam (Thomas, 1976). Horizontal silt pressure, including the effect of the water, is equivalent to a fluid with a density up to 13.5 kN/m3 (86 lb/ft3); verticalsilt pressure is equivalent to a soil with a wet density up to 19 kN/m3 (121 lb/ ft3). Themagnitude of ice forces, which act at the dam water surface level, should be appropriate for the climatic conditions at the site, and will depend on such factors as the thermal expansion of the ice and the wind drag. 3. Internal water forces comprise uplift forces in the foundation and abutments, the magnitude of which depends on the characteristics of the dam and the foundation, as well as condition of the dam-rock contact. The uplift pressures will also be influenced by any provisions for grout curtains and drainage, and their long term reliability. 4. Thermal expansion in concrete gravity dams where the monolith joints are grouted, can create a thrust across the joints and result in twist effects and additional loading of the foundation. These conditions are usually most severe during construction (Jansen, 1988). 5. The effect of seismic forces in foundation design is accounted for, as a first approximation, by applying an additional external force to the structure acting through the center of gravity of the section in a downstream direction. This force is equal to the product of the weight of the dam and a seismic coefficient, the value of which depends on the

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seismicity of the site. An additional seismic force is the hydrodynamic force produced by the reaction of the water on the dam. This technique is known as pseudo-static seismic analysis and is used to assess the overturning and sliding stability of gravity dams. 7.1.4 Loading combinations In selecting loads for design purposes, combinations of loads are used that have a reasonable probability of simultaneous occurrence. Combinations of transitory loads, each of which has only a remote probability of occurrence at any given time, and have negligible probability of simultaneous occurrence are not considered as a reasonable basis for design (US Department of the Interior, 1976). The following load combinations are normally considered for the design of concrete gravity dams (Jansen, 1988), with factors of safety as discussed in Section 7.2.5. • Case I—construction condition: dam completed but no water in the reservoir and no tailwater; wind load on the downstream face. • Case II—construction condition with earthquake: earthquake acceleration in the downstream direction; no reservoir, tailwater or wind loads. • Case in—normal operating condition: pool elevation at top of closed spillway gates or at spillway crest where spillway is ungated; minimum tailwater; dead load and uplift. Earth, silt and ice pressures, as applicable; temperature load if monolith joints are grouted. • Case IV—flood condition: reservoir and tail water at maximum flood pool elevations. Tailwater pressures against spillway sections should be based on the discharge height against the dam expected with the type of energy dissipater provided (however, full tailwater pressure should be used in uplift determination); dead load and uplift, earth, silt and temperature loads are considered where applicable. Normally

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Figure 7.3 Foundation for spillway structure containing a fault plane that dips downstream and daylights in the downstream excavation (after Nieble and Neto, 1983).

all spillway gates will be open during the maximum design flood, but some gates may be closed during lesser floods, depending on the operating plan. • Case V—normal operating condition with earthquake: earthquake acceleration in the upstream direction; other normal operating loads, except no ice pressure. 7.2 Sliding stability The water impounded in a reservoir induces a horizontal force on the dam structure that must be resisted by the shear strength of the rock in the foundation to prevent sliding type failure (Fig. 7.3). Other structures that may be subjected to sliding failure are spillways and gravity intake structures which are often perched high on the abutment of the main dam where the topography drops off steeply downstream. A powerhouse located immediately downstream may require a deep excavation forming a high face below the intake structure, and there may be a potential for a sliding failure if downstream dipping geological features daylight in this face. Possible stabilization measures include excavating additional rock to lower the foundation

as could be done for the structure shown in Fig. 7.3, or joining the intake structure to the powerhouse to form a unit with a greater resistance to the horizontal thrust of the reservoir water (Deere, 1976). If these conditions cannot be met, an underground powerhouse may be required. The following discussion on sliding stability mainly relates to gravity dams because this is often an important design aspect for this dam type. 7.2.1 Geological conditions causing sliding The ability of the rock in the foundation to resist sliding failure depends on the orientation and continuity of faults, joints and bedding planes in the foundation, the shear strength of these discontinuities, and the uplift pressures generated by the head of water in the reservoir (Wahlstrom, 1974; Rescher, 1981). Examples of geological conditions in which sliding is possible are shown in Fig. 7.4. The examples in Fig. 7.4 show that there are a wide variety of geological conditions that can result in sliding failure of dams. The one common condition in all six cases is the presence of a weak plane that daylights at the ground surface downstream of the dam. However, the presence of low strength, near-

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS

horizontal discontinuities that do not daylight downstream of the dam may result in excessive displacement of the foundation; Fig. 7.8 shows examples of stabilization measures undertaken in these geological conditions. In general, stability conditions are unfavorable if the discontinuities are continuous and planar, contain a low strength or brittle infilling, and have positions and orientations that form a wedge of rock that can slide from the foundation. 7.2.2 Shear strength The shear strength of a potential sliding surface is expressed in terms of the cohesion and friction angle of the surface (see equation 3.12). The stability analysis should examine the shear strength properties of planes of weakness in the rock, as well as the rock-concrete interface. • Rock shear strength Shear strength parameters are determined either by laboratory or in situ testing as described in Section 4.5.2. However, reliable measurement of cohesion values of low strength infilling material will usually require in situ testing where the tests can be made of the undisturbed discontinuity. The shear strength values used in design may include or exclude cohesion, and may be either the peak or residual friction angles. It would be appropriate to use the peak friction angle if the discontinuity had no history of displacement, and the construction process would not result in any significant relaxation and movement of the surface. Also, may include the effect of the friction angle surface roughness i, if it is considered that the roughness of the discontinuity will contribute to (see Section 3.4). the total friction angle, The most conservative strength parameters would be to assume cohesion of zero and a residual friction angle (Hoek and Londe, 1974). Deere (1976) suggests that the factor of safety against sliding should be checked for both peak and residual values and recommends that the

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factor of safety should be not less than 1.1 for the residual friction angle. • Rock-concrete shear strength The shape of the Mohr envelope for these surfaces has been found to be significantly non-linear with some tensile strength (for intact surfaces) and a decreasing friction angle at higher normal stress values. The development of this envelope requires testing of cores containing the rock-concrete interface in direct tension, triaxial extension and triaxial compression (Lo et al., 1991a). Sampling of the rock-concrete contact was carried out on seven existing dams founded on rock in Ontario and the following shear strength parameters obtained for 16 sets of samples (Lo et al., 1991b): Tension Cohesion Friction angle

0–450 kPa (65 psi) 0–900 kPa (130 psi) 32°–54°.

Stability analyses of the dams were carried out and in some cases it was found that the factor of safety against sliding was less than 1.0 if cohesion was assumed to be zero. As all the dams were operating satisfactorily it was concluded that a tensile strength and cohesion were operative over a significant portion of the bearing area. 7.2.3 Water pressure distributions Uplift water pressure on potential sliding surfaces in the foundation will vary from the full reservoir head at the upstream end of the foundation, to zero, or the tailwater head, if any, at the downstream end. The distribution of this head along sliding surface will depend on the presence and performance of grout curtains and drain holes in the foundation, as well as the stress condition on the plane. Measurement of actual uplift pressures in foundations of a number of US Bureau of Reclamation dams where drains are operational, shows that the values are often less than the theoretical distribution assumed for design (US Department of the Interior, 1951).

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Figure 7.4 Geological conditions in dam foundations that can result in sliding failures (after Wahlstrom, 1974): (a) brittle jointed sandstone containing beds of clay shale dipping upstream and daylighting beyond the toe of the dam; (b) horizontally bedded limestone with clay shale seams that daylight downstream of the dam; (c) fractured crystalline rock containing a fault with low strength clay infilling that dips upstream; (d) conjugate joint sets with orientations that will result in easy shear dislocation of the rock mass; (e) sedimentary rocks dipping downstream intersected by a fault that daylights beyond the toe of the dam; and (f) folded sequence of sedimentary rocks containing clay shale beds.

Uplift pressures used in design are based on observations of piezometric measurements made in existing dams, which show that drains are usually effective in reducing the uplift pressure at the row of drains to a value equal to between one half and one third of the head difference between the upstream and downstream ends of the foundation.

Therefore, a reasonable assumption for the pressure distribution would be two straight line segments (lines a in Fig. 7.5). A more conservative assumption, for the condition of the drains being inoperative, would be a constant decrease in head (line b in Fig. 7.5). The uplift water pressure head ux along the line of

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS

the foundation drains is (7.1) where ut and uh are the pressure heads respectively at the downstream (toe) and upstream (heel) ends of the foundation with width B; x is the distance of the drains from the heel, and R is the proportional reduction in head at the drains. Having calculated the value of ux, the total uplift force U per unit length of the foundation is ( 7 . 2 ) The structure shown in Fig. 7.5 is a spillway with the gate closed; water forces external to the structure comprise the driving forces on the gate and

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upstream face of the apron D, D', a vertical force on the apron V, and an inclined force on the ogee D?. The direction of all these forces is at right angles to the face on which they act, and they are resolved into their vertical and horizontal components for design purposes. Note that when the gate is open the driving force is diminished to D', D?, but flow over the spillway can produce negative (uplift) pressures along the crest of the ogee. 7.2.4 Stability analysis The analysis of stability conditions of a sliding failure of a gravity dam foundation follows the principles of the limit equilibrium analysis of sliding blocks as described in Section 6.2. Limit equilibrium analysis consists of calculating the

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INTRODUCTION

Figure 7.5 Spillway structure showing external water pressures acting on the ogee and gate, drainage and grout holes, and uplift pressure distributions in the foundation.

resisting and displacing forces acting on the sliding surface, with the ratio of these two forces being the factor of safety of the foundation. Figures 7.6(a) and (b) show two different sliding failure modes that may take place in a dam foundation. In both cases, the dam length is much greater than its width and so a two-dimensional analysis can be carried out on a unit length of the dam. The equations defining the factor of safety for each condition are as follows (Nicholson, 1983). In Fig. 7.6 (a) sliding can take place either along the horizontal base of the dam (1), or along a planar discontinuity that daylights in a face downstream of the dam (2). The factor of safety FS against sliding on any horizontal plane (surface 1) is (7.3) where c is the cohesion and

is the friction angle

of the sliding surface, and A1 is its surface area; ?V1 is the vertical force comprising the weight of the structure, u1 is the water uplift force; ?H1 is the net horizontal force due to the reservoir, and tailwater pressures if any, acting on the upstream and downstream faces of the dam respectively, plus other external forces such silt, ice and wind loads as appropriate. The water uplift force is calculated from equation 6. 9 where hw is the total head between the reservoir level and the sliding surface. For a dam with a vertical upstream face, the water produces only a while for a sloping horizontal force upstream dam face, the water force acting on this face has a vertical component which increases the normal force on the sliding plane and improves the shear resistance. For a non-horizontal sliding surface (Fig. 7.6(a),

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS

225

Figure 7.6 Modes of sliding failure in foundations of gravity dams (after Underwood and Dixon, 1976): (a) sliding failure on continuous planes in a foundation; and (b) sliding failure with passive wedge at the toe of the dam.

surface (2) with dip of—?p) the factor of safety is calculated using equation 7.4 in which the total vertical and horizontal forces are resolved into normal and shear forces acting on the sliding surface. The uplift force u2 acts normal to the sliding plane and must be resolved into its vertical and horizontal components. The factor of safety FS against sliding is (7.4) Note that the angle ?p is positive if the foundation dips upstream, and negative if it dips downstream. In Fig. 7.6(b) the dam has been recessed into the foundation so that there is a passive wedge of rock at the toe of the dam which provides a resisting force in addition to the shear strength of the base of the dam. Using limit equilibrium methods, the f actor of safety of the combined surface is given by:

(7.5) where i is the subscript associated with n planar segments making up the critical potential failure surface, each with dip ?i and area Ai; Hi and Vi are respectively the horizontal and vertical components of any forces acting on plane i; ui is the uplift water force on segment i; and (7.6) Because ??i is a function of FS, calculation of the factor of safety is an iterative process requiring first an initial estimate of FS, which is refined with each successive iteration. Calculation of the factor of safety is facilitated by drawing a free body diagram of each wedge showing the magnitude and direction of all the applied and resulting forces acting on it.

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Figure 7.7 Sliding failure in horizontally bedded foundation with buckling of slab at toe (after Underwood and Dixon, 1976).

Where the dam is recessed dam into rock containing well defined sets of discontinuities, the dip angle ?2 of the base of the passive wedge may be defined by the structural geology. However, in closely fractured rock, for example, where the sliding plane is not defined by a pre-existing plane of weakness, ? 2 is given by (7.7) The angle is the developed angle of internal friction which is equal to (7.8) Note that, for the failure condition shown in Fig. 7.6 (b), the two components of the resisting force may not be additive if the two surfaces have different shear stiffnesses. For example, if the base of the dam is a rough rock surface with good cohesion between the rock and the concrete, while the base of the passive wedge is a continuous smooth joint, then the base of the dam will have a greater shear stiffness than the joint (see inset Fig. 7.6(b)). Therefore, a small shear displacement d will develop most of the shear resistance along the base of the dam, with relatively little shear resistance being developed on the base of the wedge (i.e. . Where the sliding surfaces have significantly different stiffnesses, consideration should be given to ignoring the shear strength of the less stiff surface. For foundations comprising a number of polygons

formed by sets of discontinuities, a method of analysis method has been developed in which sliding takes place both on the base and the sides of each block. This analysis method allows the incorporation of differing shear strength parameters on each sliding surface, and external water uplift, foundation loads and reinforcement forces at specified locations and inclinations (US Army Corps of Engineers, 1989). Figure 7.7 shows a dam recessed into a horizontally bedded foundation rock where resistance to sliding is provided by the buckling strength of these slabs of rock, in addition to the shear strength of the base of the dam. From the Euler formula for buckling beams, the approximate buckling resistance fr is given by (Underwood and Dixon, 1976): (7.9) where E is the deformation modulus of the intact rock; A is the cross-sectional area of the strut (for a unit length of the foundation, A equals the thickness of the strut); L is the length of the strut; and D/2 is the least radius of gyration or half strata thickness. The approximate overall factor of safety of sliding for the condition shown in Fig. 7.7 is (7.10) where c and are the shear strength components on the base of the dam, and A1 is the area of the foundation. The magnitude of the buckling

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227

resistance will be very sensitive to any fractures in the strut that would open as soon as the strut started to buckle. Therefore, if the rock contains vertical jointing it is likely that fr will be significantly diminished from that given in equation 7.9 and some judgement will be required to determine a realistic value for the length of the strut L, and the effect of relative stiffnesses as discussed above (see Fig. 7.6(b)). Note that for the conditions shown in both Figs. 7.6 (a) and (b) an improvement in sliding resistance can be achieved by installing tensioned rock anchor downstream of the toe of the dam. For example, the factor of safety against sliding of the spillway of the Elkhart Dam in Indiana in the United States was increased by installing an anchored thrust block at the toe of the structure. The rock anchors were installed at a dip of 70° in an upstream direction and tensioned against the top of the thrust block to provide both a vertical and horizontal force. The sliding stability was calculated by considering the horizontal component of the anchor force as a passive force that was added to the numerator (shear resistance) of equation 7.3 (Jansen, 1988). Where practical, installation of the reinforcement such that the dam is tied directly to the foundation, rather than downstream of the dam, will allow the performance of the reinforcement to be more reliably predicted.

be studied by carrying out sensitivity analyses to determine, for example, that a factor of safety of 2.0 under static conditions does not drop below 1.3 under seismic loading conditions. This issue can be studied in more detail using reliability analysis in which all the variable parameters are defined as distribution functions in order to calculate a distribution function for the coefficient of reliability, or probability of failure (see Sections 1.6 and 6.2.2). As discussed in Section 7.1.1 and shown in Fig. 1.9, analysis of dam failures indicates that the present probability of failure for rock foundations is about 10−5 per dam year and foundation designs carried out using probabilistic methods should aim to achieve this level of reliability. This information can then be used in risk analysis to evaluate the consequence of failure for various options, and selection of an appropriate design. The US Army Corps of Engineers (1981) has established a factor of safety of 2.0 for normal static loading conditions, and 1.3 for seismic loading conditions. These factors of safety are accepted provided that a monitoring system is installed to measure structural movements and uplift pressures, and that the instrumentation and drainage is maintained. In circumstances where the long term maintenance of the dam is less certain than those under the jurisdiction of the Corps of Engineers, the use of higher factors of safety may be considered.

7.2.5 Factor of safety

7.2.6 Examples of stabilization

In using limit equilibrium analysis to calculate the sliding stability of a gravity dam, it is necessary to select a factor of safety to which to design the foundation. One of the factors that may influence the selection of an appropriate factor of safety for a particular dam is the degree of uncertainty in the load and strength values that are used in the design. The design values that are often least well defined are the cohesion on either the rock-concrete contact or a geological feature, uplift forces in the foundation, and earthquake accelerations. The influence of the variation in design parameters can

The following are examples of dams where remedial work, in addition to drainage and grouting, has been carried out to prevent sliding in the foundation. In all these cases the analysis principles demonstrated in Fig. 7.6 can be applied, with the details of the stabilization procedure varied to suit conditions at each site (Fig. 7.8). • Concrete shear keys The 180 m (590 ft) high Itaipu Dam in Brazil is a hollow concrete gravity dam founded on a series of basalt flows. Within the foundation there occurs a series of sub-horizontal flow contacts containing contact breccia. In order to

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INTRODUCTION

prevent sliding failure on these contacts, concrete shear keys were constructed to increase both the shear strength and the shear stiffness of the contacts. They were formed by excavating eight tunnels at about 16 m (52 ft) centers, both parallel and normal to the dam axis, and filling them with concrete. The tunnels were 2.5 m (8.2 ft) wide and 3.5–7 m (11.5–23 ft) high so as to cut through the weak layer and into sound rock above and below. A cross section is shown in Fig. 7.8(a). The total area of the shear key is 125m×150m (410×490 ft). A system of drainage tunnels surrounds the square grid of shear keys to minimize the build up of water pressure (Abrahao et al., 1983). • Bored concrete piles The spillway structure of the Gezouba Project in China is a 35 m (115 ft) high concrete gravity structure founded on a horizontally bedded sequence of sandstones, siltstones and claystone (Fig. 7.8(b)). These rock types are all of low strength and highly deformable. The shear strength of the foundation was improved by installing a pattern of 20 m (65.6 ft) deep bored concrete piles downstream of the dam (Xu et al., 1983). • Concrete ballast The Morris Shepard Dam Texas is a 57 m (187 ft) high, flat slab buttress dam founded on low permeability shale. In 1986 movement monitoring results and observations of cracks in the upstream and downstream spillway foundations showed that the structure had slid a distance of about 115 mm (4.53 in) since construction in 1941. Remedial work consisted of installing 145 pressure relief wells because there had been no drainage in the original construction, and placement of 60000m3 (78500yd3) of concrete in the hollow core of the spillway. The combination of reduced uplift pressures and increased weight of the dam had the effect of increasing the net vertical force and thus the shear strength of the slip planes in the foundation (ENR, 1988). • Excavation and concreting The Liu-Jia-Xia dam on the Yellow River in China is a 147 m (482 ft) high concrete gravity dam founded on an extensively faulted and folded micaceous and hornblende schist. During construction of the

foundations selective excavation and concreting was carried out in a number of fault zones to improve both the bearing capacity and shear strength of the rock mass. On the right abutment, poor rock was excavated to a depth of 25 m (82 ft), and in the main fault zone a 3×4 m (10×13 ft) shaft, 15m (50 ft) deep was excavated and then back-filled with concrete followed by extensive grouting (Fu et al., 1983). • Tensioned anchors The Inguri Dam in Russia is a 271.5 m (891 ft) high arch dam founded on limestone and dolomite with the beds dipping downstream at an angle of 50°–70°. The founda tion rock also contains six sets of closely spaced joints. Stabilization of the foundation consisted of excavating a network of tunnels in the fault zones and back-filling these with concrete. A concrete slab was then poured on the rock surface at the toe of the dam and tensioned anchors installed to provide an additional restraining force (Mgalobelov and Lomov, 1979). Tensioned anchors were also used in the construction of the Karakaya Dam in Turkey which is a 173 m (568 ft) high concrete arch dam constructed in a narrow gorge with approximately 60° side slopes. The foundation rock is a highly metamorphosed gneiss containing faults and schistosity that dip out of the sides of the gorge at angles of between 40° and 80° to form a series of potentially unstable wedges in the abutments. These wedges were stabilized by installing multistrand anchors each stressed to 170 t. In the right abutment a total of 1200 anchors where installed and a fewer number in the left abutment where the geological conditions were more favorable to stability (Gavard and Gilg, 1983). Tensioned anchors have also been installed in a number of concrete gravity dams to improve their stability in the event of earthquake loading (see Section 7.6). 7.3 Overturning and stress distributions in

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Figure 7.8 Examples of methods of preventing sliding failure of gravity dam foundations: (a) concrete shear key in brecciated zone of foundation of Itaipu Dam (Abrahao et al., 1983); (b) concrete bored piles installed across lowstrength beds in dam foundation (Xu et al., 1983). 1. Grout curtain 2. Drain holes 3. Consolidation grouting 4. Goodquality basalt 5. Brecciated and faulted zone 6. Concrete shear key 7. Low-strength bed 8. Bored concrete piles.

foundations In concrete gravity dams the resultant load on the foundation is inclined in the downstream direction which induces both an overturning moment, and a non-uniform stress distribution in the foundation rock. Consequently, two components of the design of gravity dams are analysis of the stability of the structure against overturning, and a comparison of the stress levels in the foundation with the allowable bearing capacity of the rock. A further component of the stress analysis is to

examine the deformation of the foundation under the action of the applied loads, and to determine if these deformations result in the development of excessive stress levels in the concrete. This condition may be most severe if the foundation contains rocks of significantly different deformation moduli resulting in the development of high stress gradients in the concrete at the boundaries of rock types (see Fig. 3.2).

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Figure 7.9 Approximate method of calculating overturning stability and foundation stress distributions for concrete gravity dams (after Underwood and Dixon, 1976).

7.3.1 Overturning Stability against overturning is determined by calculating the resultant of the forces acting on the foundation, and ensuring that this resultant acts within the middle third of the base (Fig. 7.9). The resultant acts through the centre of gravity CG of the structure and is the vector sum of the vertical and horizontal forces. The total vertical force ∑V is the sum of the weight of the structure, the vertical components of water forces acting on inclined surfaces, and uplift forces. The total horizontal force ∑H is the sum of the water forces on the upstream and downstream faces together with silt, ice and wind forces as appropriate. These forces are used to calculate the overturning moment M and the loading eccentricity, e equal to (7.11) from which the stress distribution in the foundation can be estimated (see Section 7.3.2 below). The effect of earthquakes on overturning can be determined by adding a pseudo-static force to the resultant force vector. The horizontal pseudostatic

force is equal to the product of the weight of the dam and the seismic coefficient, and the vertical upwards pseudo-static force can be taken as one third of the horizontal force (see Section 7.4). This will have the effect of decreasing the vertical force and increasing the moment, resulting in an increase in the eccentricity, e. For stability against overturning under earthquake loading conditions, it is usually considered satisfactory that the resultant lie within the base of the structure (Jansen, 1988). In practice, it is unlikely that bodily overturning of a gravity dam will occur because other failures will occur before this can take place. These failures will comprise crushing of the toe material and cracking of the upstream material resulting in increased uplift pressure and a reduction in shear resistance. 7.3.2 Stress and strain in foundations The stress distribution along a dam foundation can be calculated, as a first approximation, from the sum of the stress produced by the weight of the structure, and the stresses due to the moments. This method gives a straight line distribution between the

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS

toe and the heel of the dam. Assuming that the length of the dam is considerably greater than the width, the maximum and minimum stresses are defined as: (7.12a) and (7.12b) where ?V is the sum of vertical forces, e is the eccentricity of foundation loading and B is the width of foundation. If the resultant load lies within the middle third of the stresses are entirely the base compressive, while if the resultant lies outside the tensile stresses are induced middle third at the heel (see also Section 5.5.4). If the stress at any portion on the foundation bearing surface is tensile, it is usually assumed that over this portion of the base of the dam the uplift pressure is the full hydrostatic head, and the cohesion is zero. The stress levels defined by equations 7.12a and 7.12b can be compared with allowable bearing capacity of the rock to estimate if excessive deformation will occur (see Section 5.2.2). This analysis would involve defining the strength of the rock mass in terms of the compressive strength of the intact rock, and rock mass strength parameters m and s (Table 3.7). In general it is found that the very significant loads produced by the weight of the dam and the impounded water can induce stress changes in the foundation rock to a depth about equal to the height of the dam. Section 5.5.3 provides some guidelines as to how structural geology may influence the distribution of induced stresses in the foundation. This information would be of importance, for example, in determining the depth to which an inverted pendulum should be installed in order to ensure that the lower end was in rock undisturbed by the structure. The assumptions made in equations 7.12 are that the foundation is homogeneous, elastic and planar and that the dam is rigid, which may be realistic in some circumstances. However, at dam sites with complex geological conditions and/or irregular topography, it

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is not possible to use elastic theory to calculate the stress distributions and deformations. In these circumstances numerical methods are usually used to identify areas of either tensile stress, or high compressive stress, which exceed the allowable stresses in the concrete or rock (Itasca Corp., 1996; Zienkiewicz, 1988; Wittke et al., 1972). An important feature of numerical modeling of rock is the ability to include discontinuities and determine whether there will be shear movement or seperation as a result of the applied structural loads. The following are a number of examples of studies of stress and strain in dam foundations where the geological structure was incorporated in the analysis. (a) Finite element analysis of stress distribution Finite element analysis was used to determine the stresses in the foundation of a gravity dam (Fig. 7.10). The calculated stress levels were compared with the rock mass strength, as defined by cohesion and friction angle, to determine a factor of safety for each element. The analysis showed a significant zone where the factor of safety was less than the required value of 1.5. Remedial work for the foundation consisted of installing fully grouted, untensioned steel dowels which were assumed to have the effect of increasing the cohesion of the rock mass. (b) 3DEC analysis of displacement in jointed rock Analyses were carried out to examine the influence of discontinuites in the foundation on the performance of the Cambambe Dam and the Funcho Dam in Portugal (Lemos, 1996). Fig. 7.11 shows the model of the 85 m high Cambambe concrete arch dam founded on siltstones and sandstones which contain three joint sets, with slightly different orientations in the left and right banks. Of particular importance to deformation behavior of the foundation was a set of sub-horizontal, clay filled joints with friction angles in the range 12– 16°. These foundation conditions and the dam were modeled using the program 3DEC, a threedimensional version of the UDEC program

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Figure 7.10 Results of finite element analysis to calculate stress levels and factors of safety in foundation of a gravity dam (Egger and Spang, 1987).

(Universal Distinct Element Code) (Itasca, 1996) with the purpose of comparing the computed deflection of the structure with that measured in a physical model. The dam was modeled using 174 three-dimensional quadratic finite elements which allowed the shape of the curved shell to be accurately defined, and to reproduce the bending behavior for elasto-plastic analysis. The foundation was modeled as 904 discrete elements, with their shapes and orientation defined by the discontinuties. In the analysis the elements were assumed to be deformable in order to model the rock mass deformability and its effect on stresses induced in the dam. The element sizes were four times those in the physical model and in order to model the deformation accurately the stiffnesses

were reduced by a factor of four. Compatibility at the interface between the dam and its foundation was achieved by dividing the quadratic elements into eight triangles and by adding a slave node at the face centres. The properties of the materials making up the model are listed in Table 7.2. The effect of water pressure in the foundation, which influences sliding behavior, can be modeled in 3DEC by assuming that the blocks are impervious and all flow takes place in the joints (Damjanac, 1996). However, this is demanding of computer time, and for the model in Fig. 7.11 a simplified procedure was used based on an equivalent continuum model using rock mass permeability values from in situ tests. The displacement of the dam calculated by 3DEC,

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Figure 7.11 Three-dimensional 3DEC analysis of concrete arch dam, and foundation containing three joint sets, to compare calculated displacement with physical model (Lemos, 1996).

using the rock mass properties listed in Table 7.2, closely matched those in the physical model and

showed that sliding on the low strength joints did not occur until the loads were well in

Table 7.2 Rock and concrete properties used in 3DEC analysis of arch dam (Lemos, 1996) Parmeter

Concrete

Rock/Concrete interface

Intact rock

Joint

Clay infilling

Young’s modulus (GPa) Poisson’s ratio Cohesion (MPa) Tensile strength (MPa) Friction angle (°) Dilation angle (°) Normal stiffness (GPa/m) Shear stiffness (GPa/m)

31 0.2 12 10 37 0 – –

– – 10 6 30 –

51 0.2 – – –

– – 0 – 30 0 1.0 0.50

– – 0 – 15 – – –

–

excess of the design load. A similar modeling technique was used for the 43 m high Funcho arch dam which is founded on interbedded shale and graywacke striking parallel to the valley and dipping at about 40–60°. The deformation moduli of the foundation rock varied from 1 GPa (145 ksi)

– –

for the shale in the right bank to 25 GPa (3600 ksi) for the graywacke in the left bank. Both the 3DEC model and the monitoring of the structure showed strains of up to 10 mm in a direction towards the lower modulus rock in the right bank. A feature of the 3DEC analysis, which was not an

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Figure 7.12 Two-dimensional finite element model of a horizontal section of Cannelles Dam showing the orientations of the principal joint sets and the stabilization of the abutments (Alonso and Carol, 1985).

issue in the studies reported by Lemos (1996) because arch dams cannot withstand large motions, is the ability to model displacement resulting from shearing and separation of the discontinuities. (c) Finite element analysis of abutments in jointed work The Cannelles concrete arch dam in Spain is constructed in a steep sided canyon on a limestone foundation. The limestone is strong, but contains a persistent set of discontinuities that have a near vertical dip, strike parallel to the canyon walls and have an infilling of clay and irregular limestone

concretions with widths of between 10 and 300 mm (0.4 and 11.8 in). An extensive in situ testing program was carried out to determine the shear strength parameters of the infilled discontinuities. Stability analysis of the abutments was carried out using of two-dimensional finite element model in a horizontal plane assuming plane strain con ditions (Fig. 7.12). The analysis required a detailed description of the shear behavior of the discontinuities, the input parameters being the peak and residual shear strengths, the change in strength with shear displacement, and the normal and shear

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS

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Figure 7.13 Strain measurements along boreholes M1 and M2 showing opening of discontinuities in the heel of the dam as a result of increase in water level from 2137 to 2161 m (Kovari and Peter, 1983).

stiffnesses. The analysis investigated the stability of the abutments and stabilization measures required to prevent movement along the joints. These stabilization measures consisted of tunnels filled with concrete at a number of levels in the abutments, and a counterfort wall on the right abutment (Alonso and Carol, 1985). (d) Three-dimension finite element analysis of arch dam abutments A three-dimensional finite element analysis of jointed rock was used in the design of the Longton 220 m (722 ft) high arch dam in China (Carrere et al., 1987). The model incorporated the dam and the topography, as well as the major geological features such as gouge-filled faults with low friction angles. The stress analysis showed that it was necessary to stiffen certain faults in the abutments with concrete filled galleries to keep stresses and strains in the dam within acceptable limits. (e) Open joints in foundation upstream of dam The Albigna concrete gravity dam in Switzerland is founded on a strong granite which contains a set of persistent, healed discontinuities that dip downstream at an angle of about 60° (Fig. 7.13). It was discovered from monitoring of the deflection of

the crest of the dam, as well as seepage measurements, that the foundation was undergoing elastic-plastic deformation as a result of the opening of the downstream dipping discontinuities. Measurements with a sliding micrometer showed the extent to which the two discontinuities closest to the heel of the dam opened when the reservoir level was raised by 30 m (98 ft) to full storage level. Remedial work for this condition comprised emptying the reservoir, cleaning of rock surfaces upstream of the dam, and sealing the discontinuities with a neoprene sheet 240 m long and 12 m wide (790 by 40 ft) (Kovari and Peter, 1983). 7.4 Earthquake response of dams 7.4.1 Introduction The three main hazards to dams from earthquakes are: 1. fault movement in the dam foundation;

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2. ground motion in the foundation; 3. wave action in the reservoir. Displacement of a fault running through the foundation is likely to result in severe damage or even collapse of the dam. For this reason, detailed geological investigations are carried out for dams in seismic regions to identify potentially active faults and site the dam at a safe distance from such features, or design the dam to accommodate displacement. Both numerical and physical models have been used to study fault displacement in dam foundations. For example, a 1:250 physical model of a 185 m high arch dam in Greece which incorporated a joint system showed that up to 1 m of movement could occur without damage to the structure. There are at least two dams, the Morris Dam in California and the Clyde Dam in New Zealand, in which the plane of an underlying fault has been extended through the entire dam section in the form of a sliding joint. In both cases the joints are vertical and are designed for displacements of up to 2 m, although up to 1990 no movement had been detected (National Research Council, 1990). Ground motion can induce excessive stresses and displacements in both the dam and its foundation resulting in slope failures of embankment dams, and cracking of concrete dams. For dams founded on rock it is important to analyze the structural geology to identify blocks of rock in the foundation or abutments that may move when subjected to earthquake loading. A third cause of damage is the occurrence of landslides or rock falls into the reservoir that create water waves (seiche) resulting in a rise in water level that may overtop the dam. The following are two examples of earthquake induced dam failures. The San Fernando Dam in California is a 44 m high hydraulic earthfill dam. In 1971 a 6.5 Richter magnitude earthquake centered approximately 8 km from the dam caused a rotational slip failure of the downstream face and part of the crest; fortunately, enough of the upstream half of the dam remained in place to contain the water (Jennings, 1971). The Konya Dam in India is a 91 m high concrete gravity dam which was

damaged by a Richter magnitude 6.5 earthquake that generated in the dam a peak acceleration of approximately 50% of gravity. The dam sustained a horizontal crack near the upper third point and many of the appurtenances were damaged (Housner, 1970; Chopra and Chakrabati, 1973). The San Fernando Dam in California is in an area of high seismicity where extensive studies of earthquakes have been made. The experience gained from the San Fernando Dam and other well documented seismic events, have been used to significantly improve the design and construction procedures for all structures, including dams, in areas where earthquakes are common. However, the Konya Dam in India is in an area of low seismic activity and it is believed that the earthquake was related to reservoir filling. Other dams in low seismic areas have also recorded earthquakes during reservoir filling. For example, the 128 m (420 ft) high Kariba Dam Dam on the Zambezi River in central Africa, which is in a nonseismic area, recorded nine earthquakes with Richter magnitudes 5.1–6.1 over a three month period as the reservoir reached full impoundment (Rothe, 1969). Also, the Hsinfengkiang Dam in China, which is a 91 m (300 ft) high buttress dam, was damaged by a magnitude 6.1 earthquake in 1962; the damage consisted of a horizontal crack about 15 m (50 ft) below the crest (Sheng et al., 1970). These events show that the possible occurrence of earthquakes in areas of low seismicity should be considered in the design of major dams. 7.4.2 Measured motions of foundation rock For dams located in mountainous terrain, seismic design should take into account the possible spatial variation in the ground motions from the valley floor to high in the abutments. Although there are few ground motion records on the walls of canyons and most were of low intensity, many of the records that do exist show significant variation in the motions. For example, during a 1984 earthquake in Japan, ground motions were measured for the Nagawado

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS

(arch) Dam which is 155 m high and has a crest length of 355.5 m. The following are some of the accelerations measured at different points on the dam and in its foundation and abutments: 1. foundation at depth of 17 m below base of dam —0.029g at right angles to the dam axis and 0. 016g parallel to the dam axis; 2. deep in right abutment at elevation of 25 m above base of dam—0.021g at right angles to dam axis and 0.018g parallel to dam axis; 3. deep in right abutment at elevation of crest of dam—0.026g at right angles to dam axis and 0. 031g parallel to dam axis; 4. crest of dam at midspan—0.197g peak radial acceleration; 5. crest of dam at quarter point from left abutment —0.245g peak radial acceleration. Other records have shown that the ratio of the horizontal peak velocity at the crest level of the dam to that at the base of the dam is generally greater than unity. Motions recorded at the Ambiesta (arch) Dam in Italy in 1976 showed a base to crest velocity ratio of 3.1–1.9, at the Chirkey (arch) Dam in Russia the base to crest velocity ratio was 1.6, and at the Pacoima Dam in California the acceleration at the crest level was about twice that at the base. Such non-uniform motions can have a significant effect on the stresses generated in the concrete dam compared with uniform motions (National Research Council, 1990). However, these are all low intensity motions and it is not known if there will be a different response in the case of stronger motions. 7.4.3 Sliding stability and overturning under seismic loads For concrete gravity dams the stability against sliding can be determined by limit equilibrium methods, and the stress distribution in the foundation can be estimated by taking moments (see Section 7.3). As a first approximation, the effect of earthquake loading on sliding stability and stress

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distribution can be determined by pseudo-static analysis, but this is only applicable for particularly stiff dams with heights less than 30 m (100 ft). Where applicable, the analysis procedure consists of applying a constant force as an external load acting through the center of gravity of the structure. This force can be applied in a horizontal direction only, but if it is considered that the horizontal and vertical motions will be in phase, then both horizontal and vertical forces could be applied to the structure. This can produce a resultant force acting in a downstream direction, above the horizontal, which is the direction most detrimental to stability. The magnitude of the inertial force Qi is given by (Jansen, 1988): (7.13) where a is the seismic coefficient expressed as a fraction of the gravitational acceleration; and W is the weight of the dam. A significant component of the forces influencing the stability of a gravity dam is the pore water pressure in the foundation. However, it is usually assumed that the pore water pressure is constant for both static and seismic loading for the following reasons. During seismic events, as the dam moves upstream, the upstream portion of the dam carries the inertia load in compression resulting in higher pore pressures, while the stresses in the downstream portion of the dam tend towards tension causing reduction in pore pressures. When the movement of the dam reverses, pore pressures tend to be reduced in the upstream portion and increased in the downstream portion. Since the increase in pore pressures in the compressive zones is usually accompanied by a larger increase in total stress, higher pore pressures do not significantly affect stability during seismic loading. Should cracking occur in the upstream face during an earthquake, it is usually assumed that the oscillations occur quickly enough that there is no significant penetration of water into the cracks (National Research Council, 1990). In addition to the force due to acceleration of the dam, it is necessary to add a hydrodynamic force resulting from the reaction of the impounded water

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INTRODUCTION

Figure 7.14 Value of hydrodynamic pressure coefficient ke for sloping dam faces (Jansen, 1988).

on the dam. This hydrodynamic force can be calculated from the Westergaard formula as follows (Westergaard, 1933): (7.14) (7.15) where Qe is the horizontal hydrodynamic force down to depth y; Me is the moment at depth y due to Qe; hw is the total height of water at the dam face; Ce is the factor depending principally on the height of the dam and the earthquake period te in seconds (te is often assumed as 1 s) and is equal to (7.16a)

(7.16b) The factor ke accounts for any slope on the face of

the dam and varies from 1 for a vertical face to 0 for a horizontal face (Fig. 7.13). Pseudo-static analysis is an approximation for examining stability conditions of a foundation subjected to earthquake motions. It will usually produce a conservative design because the short duration transient earthquake force is modeled as a constant, uni-directional force. Advantages of pseudo-static analysis are that the acceleration values are taken directly from the building codes, and the calculation method is relatively straight forward. 7.4.4 Finite element analysis Dynamic response of dams can be carried out using finite element analysis to calculate stresses and strains in the dam and its foundation, induced by earthquake accelerations in the foundation. Figure 7.15 shows an example of a threedimensional dynamic analysis of a concrete gravity dam using the program ABAQUS (Hibbitt, Karlsson and Sorensen, Inc., 1987). The model incorporates the foundation and abutments of the

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS

dam so as to account correctly for the differing properties of the soil in the right abutment and the rock in the foundation and left abutment. The main purpose of this analysis was to determine the stress levels in the concrete which were found to be highest at the crest where the greatest strains were induced. Stress levels in the foundation rock were substantially less than the rock strength, and there was no significant displacement of the foundation rock. Details of the dynamic finite element analysis method, which are beyond the scope of this book, are described by Chopra (1978), Fenves and Chopra (1984, 1987), Fok et al., (1986) and Jansen (1988). A component of these analyses that is of significance to the calculated stresses in the dam is the interaction between the dam and the deformation of the foundation rock. This is because dams, and particularly arch dams, partly resist the reservoir water pressures as well as thermal and earthquake forces by transmitting these forces to the foundation and the canyon walls. The effect of including the dam-foundation interaction, in comparison with modelling the dam with a rigid foundation, is to reduce the maximum principal stresses throughout the dam monolith. It is usually assumed that the deformation modulus of the foundation rock is constant for both static and seismic loading conditions. Finite element analysis was also used to determine the displacement of a wedge of rock in a dam foundation when subjected to a Richter magnitude 6. 5 earthquake represented by three synthetic accelerograms (Scott and Dreher, 1983). The factor of safety at each time step was calculated by limit equilibrium methods and was only found to drop below 1.0 on two occasions during the earthquake for durations of 0.05 s (Fig. 7.16). If the maximum dam loads and the peak inertial forces had been used in a pseudo-static analysis,the factor of safety would have been less than 1.0 and the conclusion might have been that the foundation was unstable. The displacement of the rock wedge during this 0. 05 s period was calculated to be 7.9 mm (0.31 in). The analyses can account for the effect of the rate

239

of shear displacement on the shear strength of the rock discontinuities (Crawford and Curran, 1982). The analysis results shown in Fig. 7.16 are based on work done at the proposed Auburn Dam in California, where the foundation contains a potentially active fault (US Department of the Interior, 1978). 7.4.5 Earthquake displacement analysis Calculation of the factor of safety against sliding by pseudo-static limit equilibrium methods for earthquake loading conditions (see Section 7.4.2) is usually a conservative method of analysis. Failure does not necessarily occur when the dynamic transient stress reaches the strength of the rock, and if the factor of safety drops below 1.0 at some time, and on some portions of the foundation, it does not necessarily imply a serious problem. What really matters is the magnitude of permanent displacement caused at the times that the factor of safety is less than 1.0 (Lin and Whitman, 1986). A method of calculating displacement as the result of earthquake motions has been developed by Newmark (1965). The principle of Newmark’s method is illustrated in Fig. 7.17 which shows the displacement of a block when the base is subjected to a uniform horizontal acceleration pulse of magnitude ag and duration t0. The velocity of the foundation is a function of the time t and is designated y(t), and its velocity at time t is y. Assuming a frictional contact between the block and the base, the velocity of the block will be x, and the relative velocity between the block and the base will be u where (7.17) The resistance to motion is accounted for by the inertia of the block. The maximum force that can be used to accelerate the block is the shearing resistance on the base of the block which . This limiting force is has a friction angle of proportional to the weight of the block W and is of , corresponding to a yield magnitude , as shown by the acceleration ay of dashed line on the acceleration plot (Fig. 7.17(b)).

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INTRODUCTION

Figure 7.15 Example of dynamic, three-dimensional analysis of a concrete gravity dam (B.C.Hydro, Sandwell Inc.): (a) dam model from downstream perspective; and (b) vertical section through crest of dam showing deflected shape under dynamic loading (deflection at magnification of 44).

The shaded area shows that the ground acceleration

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS

241

Figure 7.16 Calculation of factor of safety against time for a rock wedge in a dam foundation under earthquake loads (Scott and Dreher, 1983): (a) geology of foundation; and (b) variation of factor of safety with ground motion history.

pulse exceeds the acceleration of the block, resulting in slippage. Figure 7.17(c) shows the velocities as a function of time for both the ground and the block accelerating forces. The maximum velocity for the ground accelerating force has a magnitude v which remains constant after an elapsed time of to. The magnitude of the ground velocity vg is given by (7.18) while the velocity of the block vb is

(7.19) After time tm the two velocities are equal and the block comes to rest with respect to the foundation, . The value of tm is that is, the relative calculated by equating the ground velocity v to the velocity of the block to give the following expression for the time tm: (7.20) The displacement dm of the block relative to the

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INTRODUCTION

Figure 7.17 Displacement of rigid block on moving base (Newmark, 1965): (a) block on moving base; (b) acceleration plot; and (c) velocity plot.

ground at time tm is obtained by computing the area of the shaded region on Fig. 7.17(c) as follows:

(7.21)

Equation 7.21 gives the displacement of the block in response to a single acceleration pulse (duration to, magnitude ag) that exceeds the yield acceleration , assuming infinite ground displacement. The equation also shows that the displacement is proportional to the square of the ground velocity.

While equation 7.21 applies to a block on a horizontal plane, a block on a sloping plane will slip at a lower yield acceleration and show greater displacement depending on the direction of the acceleration pulse. For a cohesionless surface where the factor of safety of the block FS is equal to and the applied acceleration is horizontal, Newmark shows that the yield acceleration ay, is given by (7.22) where is the friction angle of sliding surface, and ? p is the dip angle of this plane. Note that for . Also equation 7.22 shows

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS

that for a block on a sloping surface, the yield acceleration is higher when the acceleration pulse is in the downdip direction compared with the pulse in the updip direction. The displacement of a block on an inclined plane can be calculated by combining equations 7.21 and 7.22 as follows:

In an actual earthquake, the pulse would be followed by a number of pulses of varying magnitude, both positive and negative, which will produce a series of displacement pulses. This method of displacement analysis can be applied to the case of a transient sinusoidal acceleration (a(t)g) illustrated in Fig. 7.18 (Goodman and Seed, 1966). If during some period of the acceleration pulse the shear stress on the sliding surface exceeds the shear strength, displacement will take place. Displacement will, of course, take place much more readily in a down slope direction, which is illustrated in Fig. 7.18 where the shaded areas are the portion of each pulse in which movement takes place. For the conditions illustrated in Fig. 7.18, it is assumed that the yield acceleration diminishes with displacement, that is, Integration of the yield portions of the acceleration pulses give the velocity of the block. It will start to move at time t1 when the yield acceleration is exceeded, and the velocity will increase up to time t2 when the acceleration drops below the yield acceleration. The velocity drops to zero at time t3 as the acceleration direction begins to change from up slope to down slope. Integration of the velocity pulses gives the displacement of the block, with the duration of each displacement pulse being (t3—t1). The simple displacement models shown in Figs 7.17 and 7.18 have since been developed to model displacement due to actual earthquake motions more accurately. For example, Sarma (1975) used several non-rectangular pulses to model ground motion. Also, Franklin and Chang (1977) examined the effect of erratic ground motion on predicted displacement, and have drawn up a series of design

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charts from which displacement of embankments can be calculated. In addition, Jibson et al. (1998) have developed maps showing the probabilistic hazard from landslides induced by earthquakes, based on the shaking intensity and ground acceleration, slope angle and rock mass strength. Where these techniques are used to evaluate the possible permanent deformations of embankment dams and soil slopes, they are applicable where the soils are not vulnerable to major strength loss, or to the development to high excess pore water pressures at the anticipated level of shaking. 7.5 Preparation of rock surfaces An important aspect of dam construction is the careful preparation of the bearing surface to ensure that the contact is watertight and that the rock has adequate bearing capacity. Exposure of the final rock surface should also be an opportunity to carry out detailed geological mapping to check on interpretations made during the investigation and design phases of the project. For embankment dams the importance of good surface preparation cannot be over emphasized because this may be the main path for water seepage once impoundment begins. The bearing surface should be free of irregularities to minimize the risk of localized arching in the fill, and differential strain and cracking in the embankment. Also, open discontinuities underlying erodible material in the fill should be sealed to prevent erosion. It is believed that a cause of failure of the Teton Dam in Idaho was inadequate sealing of open discontinuities in the foundation (US Dept. of the Interior, 1980). For concrete dams, foundation treatment is required to remove material with insufficient bearing capacity or shearing resistance, and to seal discontinuities to prevent either excessive seepage or erosion of weak infilling materials. The following are some examples of preparation work that may be required to the surface of a rock foundation prior to starting construction of the dam (Fig. 7.19).

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INTRODUCTION

Figure 7.18 Integration of accelerograms to determine downslope movement (Goodman and Seed, 1966).

7.5.1 Shaping For earthfill dams it is desirable to have a reasonably uniform rock surface that is free of irregular knobs, cavities and overhangs, or excessive changes in slope (Pratt et al., 1972). The shaping work can involve both dental concrete to fill voids or overhangs, and careful blasting for rock removal. In general, slopes should be trimmed to maximum angles in the range of 1:1 to 2V:1H. Where possible, it is desirable to shape both the foundation and the abutments so that dam is pressed into rather than pulled away from the contact surfaces under the reservoir load. If blasting is required for any of this work, extreme care must be exercised to prevent damage to the foundation rock from excessive explosive charges (controlled blasting is discussed in Chapter 10). As an example of quantifying shaping work, at the Cat Arm earthfill dam in Newfoundland, Canada, the specifications including the following

provisions in the foundation (Humphries, 1987; Thomas, 1976).

preparation

1. General abutment slope should not be steeper than 4H:3V. 2. For steps up to 3 m high, slope should not be steeper than 3V:1H. 3. For steps up to 5 m high, slope should not be steeper than 2V:1H. 4. For (1) and (2), when normal to the dam axis, the foundation must not present a smooth continuous surface for more than 30% of the core width. For concrete dams, the foundation should be reasonably level and if the natural surface dips downstream it may be necessary to cut a series of steps, dipping upstream, to improve the shearing resistance of the surface. Surfaces that have been polished by glacial action, for example, should be roughened by light blasting or chipping. Steps or abrupt changes in elevation of the foundation should

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS

245

Figure 7.19 Preparation of rock foundation surfaces for embankment dam.

not be located close to block joints so as to avoid creating thin wedges under a portion of the block (Jansen, 1988). 7.5.2 Cleaning and sealing The final foundation surface should be cleaned of all loose and broken rock with particular attention paid to zones and seams of weak rock. This usually requires the use of air and water jets with sufficient pressure to break up and move unsuitable materials. For embankment dams, faults and seams of weak or weathered rock are usually cleaned out to a depth of not less than three times their width and then backfilled with concrete or slush grout. The concrete should be highly plastic, and the aggregate dimensions not more than about one third of the crack width. Placement of the concrete should be carried out using a tremie pipe extending to the bottom of the fracture, and not poured or brushed in from the surface. As an example of sealing deep fractures, at the Normandy Dam in Tennessee, four open joints extending to 30 m (100ft) below the surface were

sealed by drilling a series of closely spaced, 0.92 m (3 ft) diameter holes which were then filled with concrete. In addition, all weathered rock at the surface was removed and the exposed discontinuities carefully sealed (Spearman, 1976). Another method to seal narrow, continuous fractures, that has been used at the Mintang Project in Taiwan, is to wash out low strength infillings with high pressures water jets to depths of several tens. of meters, and then fill the open seams with grout (Hoek, 1986; Cheng, 1987). Cutoff trenches are frequently used to control seepage in the foundation of embankment dams. Where blasting must be used for excavation of a key trench, carefully aligned blast holes, light charges and appropriate detonation sequences must be used to prevent fracturing and loosening of the surrounding rock (see Chapter 10). Heavy blasting could result in increased permeability of the foundation rock and limit the effectiveness of the cutoff. The base width of a cutoff trench is usually between one half and one quarter of the height of the dam, and the slopes should be flat enough to ensure that there is no arching in the fill (Jansen, 1988).

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Rocks, such as shales, which deteriorate on exposure to the atmosphere, and to wetting and drying cycles, should be protected during foundation preparation. One means of doing this is to make the overall excavation to just above final grade and then to remove the remaining rock progressively as the dam is constructed. Alternatively, the rock could be shotcreted as soon as it is exposed. In rockfill dams, air and water will continue to circulate in the voids in the fill at the foundation level, and soft rocks may continue to deteriorate after completion of the dam. In these circumstances, the rock surface can be sealed with shotcrete. For concrete gravity dams, the US Bureau of Reclamation provides the following recommendation for the required depth of excavation of steeply dipping, transverse (upstreamdownstream aligned) discontinuities in the foundations of concrete dams (Golze, 1977): or (7.22a) or or (7.22b) where d is the depth cleaning; b is the width of fracture; and H is the height of dam above general foundation level. 7.5.3 Rebound Geological processes such as erosion, or excavation as part of the construction work, can result in rebound of the foundation. Rebound occurs predominantly in weak rock such as shales, and the open discontinuities may be filled with weathering products or river silt. Another cause of rebound is high horizontal stress in the rock that is relieved when the excavation for the foundation reduces the vertical stress. The effects of rebound can include differential movement of the structure, as well as

the creation of fractures in the foundation with low shear strength and high permeability. The following are three examples of remedial work carried out in the case of rebound. At the Peace Canyon Project in British Columbia the work comprised excavation and structural grouting (Lauga and Taylor, 1983), at the Garrison Dam in North Dakota periodic regrouting was performed (Lane, 1955), and at the Oahe Dam in South Dakota deep rock anchors were installed and the dam redesigned with increased articulation to accommodate movement (Underwood et al., 1964). 7.5.4 Solution cavities Cavities may exist in the foundations of dams constructed on soluble rocks such as limestone, gypsum, anhydrite, and calcium carbonate (James and Kirkpatrick, 1980). Such cavities can cause excessive leakage as occurred at the Keban in Turkey (Bosovic et al., 1981), or solution of these materials can result in failure such as is suspected to have occurred at the Quail Creek reservoir in Utah where gypsum was found in the foundation (ENR, 1989). Solution cavities can be sealed with cement grout or concrete, provided that the exploration program has adequately defined the extent of the cavities (see also Section 5.3). For example, at the Keban Dam, the large size of the cavities required that they first be filled with rock, gravel, sand and clay before injecting grout. The Zimapan Dam in Mexico was constructed in karstic terrain and mapping carried out in a system of tunnels driven into the abutments identified nearly 2100 discontinuities, of which about 9% were open with an average width of about 500 mm (Fig. 7.20). The grouting procedure was first to clean clay infilling material from the solution cavities, and then seal the outlet in the wall of the tunnel with a grout plug before filling the cavity with grout using an injection hose. Following this work, additional grout holes were drilled surrounding the karstic zone to treat the rock mass,

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Figure 7.20 Grouting procedures of Zimapan Dam: (a) layout of grouting tunnels in abutments and typical curtain grout holes; and (b) grouting of solution cavities intersected in tunnel (Foyo et al., 1997). 1. Access tunnel 2. Shaft 3. Diversion tunnel 4. Grout tunnel 5. Bedding 6. Karst feature 7. Grout hole 8. Grout curtain 9. Drain hole 10. Cement plug 11. Injection hose

and to create the grout curtain (Foyo et al., 1997). The design of the grout curtain was based on the principle of the grout intensity number GIN which is defined as the product of the final grout pressure (bars) and the maximum cement absorption (liters (Lombardi and per linear meter), or Deere, 1993). For this project a GIN of 2000 bar lm-1 was used which balanced the requirements to grout open discontinuities with low pressure, and fine discontinuities with high pressure while avoiding the risk of hydrofracturing. 7.6 Foundation rehabilitation As increasing numbers of dams reach or exceed their design life, there is a corresponding need for inspections to identify deterioration, and then to carry out required rehabilitation work, as well as upgrading to meet new operating and safety standards. As an example of the scope of such

inspection and remediation programs, the California Division of Safety of Dams carried out an evaluation of the seismic stability of more than 1200 dams under their jurisdiction (Babbitt, 1993). It was found that there was a need for upgrading of a total of 94 dams, of which eight required grouting and drainage of the foundation. Other types of remediation ranged from increasing freeboard, buttressing of both concrete gravity and embankment dams, and in nine cases constructing replacement dams. There will often be some uncertainty in the condition of dams with ages of several decades because, for example, the design and as-built drawings, as well as the maintenance records may be missing or incomplete. Furthermore, a visual inspection of the dam, together with an examination of the instrumentation records, if any, may not provide much definitive information on the distribution of water uplift pressures on the base of the dam, or weathering of rock in the foundation. In

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order to quantify this uncertainty, prob abilistic methods of analysis have been developed which address both the stability mechanics and the degree of uncertainty in the design parameters (ICOLD, 1993). Section 1.6.4 discusses methods of calculating the probability distribution of the factor of safety of a structure from which the coefficient of reliability can be calculated. This analysis may show for example, that two structures have the same deterministic factor of safety. However, if the stability of one is less certain as shown by a lower coefficient of reliability CR then this would have the higher priority for remedial work. A similar procedure has been used to evaluate the stability of concrete gravity navigation structures, in which a reliability index was calculated in order to rank their stability conditions (Wolff, 1993). It is also important that the safety of the dam with respect to both its probability of failure and the consequence of failure meet the general standard of the industry. Figure 1.9 shows that dams are generally designed so that the annual probability of failure causing damage is in the range, or better, of 10−4 for a loss of life of 10, and 10−5 for loss of life of 100. The following are some examples of remedial work that has been undertaken for dam foundations. 7.6.1 Monitoring The most common instrumentation that is installed in dam foundations are piezometers to measure the distribution of water uplift pressures, and instruments such as extensometers, inclinometers and tiltmeters to measure displacement. An important development regarding dam safety is automation which allows readings to be taken at specified intervals and the results transmitted to a remote location for interpretation and analysis (Myers and Marilley, 1997; Elliott, 1997). If a reading exceeds a pre-determined threshold, the system controlling the instrumentation can be designed to set off alarms and increase the frequency of the readings. Factors to consider in the design of automated monitoring systems include the

power availability (solar, power grid), distance of monitoring personnel from site (travel time to check alarmed condition), site security (vandalism, wild animal interference), natural hazards (snow avalanches, forest fires) and consequences of failure (facilities in downstream flood path). There are a number of manufacturers of automated monitoring systems and it is generally recommended that well-proven commercial instrumentation be used rather than one-off custom equipment. Instrumentation in dams is often subjected to a wide range of temperature and humidity and even the best systems require ongoing maintenance by experienced personnel in order to produce reliable readings over a long time period. If there is a tendency for the system to produce false alarms, its credibility will be slowly eroded and there is the danger that a real emergency will be ignored. 7.6.2 Grouting, sealing and drainage Dams designed with a grouting/inspection gallery in the lower part of the structure will allow a grouting program to be carried out during the operation of the dam in order to decrease the permeability or to improve the rock modulus. However, drilling holes from the crest of the dam into a small target in the foundation, which will require accurate drilling with close control of deviation, may not be feasible, particularly in embankment dams with sloping cores. One of the difficulties in grouting a foundation under full head conditions is that high gradients and flows in the rock may carry away the grout before it has time to set, even if fast setting grout is used. For example, at the Stewartville Dam in Ontario, Canada which is founded on limestone containing micaceous material it was necessary to carry out remedial work 1, 18, 20, 34 and 41 years after the reservoir was first filled. This work comprised cement and cement-asphalt grouting, and placing an upstream low permeability blanket (Lo et al., 1991b). Similarly, at the Albigna Dam in

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Switzerland it was necessary to drain the reservoir in order to place a neoprene sheet on the foundation immediately upstream of the structure to control water pressure induced movement (see Section 7.3.2). If possible, it is preferable to lower the water in the reservoir to below the level that is being treated. Because grouting of the foundation of an existing dam is likely to reduce the effectiveness of the drains, these should be re-drilled at the end of the grouting operation. Monitoring of piezometers in the foundation, as well as seepage rates, may also show that water pressures in the foundation are rising to unacceptable levels indicating that the effectiveness of the drains is diminishing. Under these circumstances remedial work could include drilling new holes from the drainage gallery, or cleaning the existing holes with water jets or brushes. 7.6.3 Anchoring Permanent post-tensioned anchors have been used in the United States since the 1970’s to help existing dams meet contemporary safety standards. The most common usage of anchors has resulted from dam safety re-analysis based on new criteria for the PMF (Peak Maximum Flood) and the MCE (Maximum Credible Earthquake) (Powell and Pearson, 1993). Dams designed in the first half of this century generally do not meet the new standards and owners are required by law to take appropriate remedial action. Anchors have been used in dam-raising operations where they have proved more economical in resisting the increased overturning moments than placing additional concrete mass. Typical application of anchors include resistance to overturning, sliding and earthquake forces (Bruce, 1993a). Details of anchor design and construction are discussed in Chapter 9; particularly important features of anchors for dams are corrosion protection of all components and a comprehensive and well documented testing program.

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A typical application of post-tensioned anchors is at the Stewart Mountain in Arizona which is a thin arch concrete dam with a maximum height of 64.6 m (212 ft) and a width varying from 10.4 m (34 ft) at the base to 2.4 m (8 ft) at the crest (Bianchi and Bruce, 1993; Bruce et al., 1991). The dam foundation is a strong pre-Cambrian quartz diorite cut by irregular but strong granite dykes. Threedimensional finite element stability analysis of seismic loading conditions showed that there was a need to improve the strength of the arch dam because of the poor quality of the horizontal construction joints between concrete pours. In addition, it was necessary to install anchors to stabilize the left thrust block to prevent sliding failure at or just below the structure/foundation contact where the rock was fractured, sheared and weathered. The anchors installed in the concrete arch comprised a bundle of 22, 15.2 mm (0.6 in) diameter epoxy coated strands each with a design load of 2.8 MN (630 kips) which was about 50% of the guaranteed ultimate tensile strength (GUTS). The bond lengths varied from 9.1 to 14 m (30–46 ft) and the free stressing length varied up to 67.7 m (222 ft). A total of 62 tendons were installed at 2.4 m (8 ft) centers along the crest of the dam in 254 mm (10 in) diameter holes drilled with a down-the-hole hammer (Fig. 7.21). Of particular importance for the drilling was accurate hole alignment which was achieved by first installing a carefully aligned 1.5 m (5 ft) long guide tube at the collar, and then measuring the hole deviation at 3 m (10 ft) intervals. 7.6.4 Scour protection High velocity, turbulent flow such as occurs during spillway operation can result in scour that can loosen and remove blocks from spillway chutes, tunnels and foundations, possibility resulting in steepening and eventually undermining of the structures (Burgi and Eckley, 1987; Annandale et al., 1996a; Perlea et al., 1997). The susceptibility of

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a foundation to scour can be estimated from a comparison between the erosive power of the water and the resistance of the rock to scour, such that the threshold of scour is when the erosive power just equals the scour resistance. As discussed below, the erosive power is a function of the water flow characteristics in plunge pools and spillway chutes, while the erosion resistance is a function of four quantifiable properties of the rock mass. This matter is also discussed in Section 6.7.2 regarding the scour of bridge piers. (a) Erosive power action of water Scour can result where water flow over irregular surfaces is accompanied by eddies and turbulence resulting in fluctuating pressures at the surface over which it is flowing. The action of these forces, together with the hydrostatic forces in the cracks, causes a tugging and pulling of the rock which can loosen and remove blocks from the surface over which the water is flowing. The erosive power of water per unit flow width P can be related to the magnitude of fluctuating pressures and the resulting rate of energy dissipation, or stream power, by the following equation: (7.23) where ?w is the unit weight of water; q is the unit discharge and ?E is the energy loss (Annandale, 1995). Examples of turbulent flow resulting in energy dissipation are headcuts where a spillway discharges over a drop structure into a plunge pool, hydraulic jumps where flow undergoes an abrupt change in slope, where there are changes in bed slope causing separation of the flow from the bed, and open channel flow. In all four cases, theoretical relationships backed-up by experimental data, have been developed between the energy loss, and the flow characteristics and bed geometry. Details of these relationships, which are beyond the scope of this book, will depend on the particular conditions at each site and should be verified by specialists in the field of hydraulic engineering. (b) Scour resistance of rock In order to quantify the susceptibility of rock masses to scour, an erodibility index Kr has been

developed in which the relevant character of the rock mass is calculated as the product of four parameters (Annandale, 1995): (7.24) This method of calculating the erodibility index is a modification of the Q-system for assessing sup port requirements for tunnels that uses properties of the rock mass that are readily measured in the field. The four properties of the rock mass that are used to assess its resistance to scour are the strength of the intact rock Ms, the mean block size as determined by the joint spacing Kb, the shear strength of the discontinuity surfaces Kd and the shape of the blocks and the dip of the discontinuity set relative to the flow direction Js. Section 6.7.2 describes in detail the method of calculating Kr, and provides tables relating properties of the rock mass to values for these dimensionless parameters. (c) Stream power-scour resistance relationship The relationship between the scour resistance of rock and soil materials and the energy dissipation of water flowing over a variety of hydraulic structures has been determined empirically by studying field conditions. The results of 137 such observations are shown in Fig. 6.12 in which the sites where scour did and did not occur are distinguished. The dashed line is the approximate threshold of scour for this data, and the relationship between the erodibility index Kr and the rate of energy dissipation per unit width of flow p (kW/m2) is: (7.25) Equation 7.25 and the information presented in Fig. 6.12 can be used as a guideline in assessing the susceptibility of a facility to scour. Where there is a risk of scour, preventative measures include modifying the designs to reduce turbulent flows to acceptable levels, or protecting the rock with reinforced concrete aprons or rip rap. 7.7 Grouting and drainage Grouting of dam foundations to reduce the permeability of the rock, and sometimes to improve

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Figure 7.21 Section through arch of Stewart Mountain Dam showing typical multi-strand anchor installation (Bianchi and Bruce, 1993). 1. Full reservoir level. 2. Normal tailwater. 3. Arch section. 4. Silt. 5. Alluvium and fill. 6. Bedrock foundation. 7. 22 Strand bundled tendon. 8. Bond length (9–14 m).

the modulus, is widely practised and for many structures it is essential for both safety and economic performance. Grouting involves the injection of liquids into discontinuities and voids in the rock which then set to form a stable and resistant component of the rock mass. By suitable location of injection drill holes, injection pressures

and the properties of the injection fluid, it is possible to form a continuous curtain, blanket or bulb of grouted rock and improve the properties of the rock mass by a desired amount. Figure 7.22 shows an example of the use of grouted zones under a buttress dam (Jaoui et al., 1982), while Fig. 7.20 shows a more extensive grouting operation of both

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the foundation and the abutments. 7.7.1 Grouting functions Grouting can fulfill one or more of the following functions, depending on the use of the dam and the geological conditions of the foundation (Casagrande, 1961). (a) Consolidation grouting Improvement of the modulus of the rock will reduce deformation under load. Since the modulus of the rock mass is highly dependent on the closure and displacement of discontinuities, filling these with a stable grout will have a significant effect on the modulus (Kikuchi et al., 1995). Consolidation grouting is most commonly used in the foundation of concrete dams, which are sensitive to differential movement. Consolidation grouting was carried out in the abutments of the Cabril arch dam in Portugal which was founded on strong, unaltered granite but was experiencing deformation of the cantilevers. The grouting was successful in reducing the maximum deflection from 65 mm to 50 mm (2.6–2 in), an improvement of nearly 25% (Serafim, 1964). (b) Permeability control This is used to reduce seepage quantities and uplift pressure. For rocks in which the intact rock is impervious, seepage is concentrated in the discontinuities and filling the discontinuities with a stable grout will substantially reduce the rock mass permeability. This may involve the formation of a continuous curtain over the full length of the dam and into the abutments, and the curtain may comprise a single row, or multiple rows of holes. (c) Uplift control A low permeability grout curtain in combination with a line of drain holes downstream of the curtain will significantly reduce uplift pressures in the foundation. Reduced uplift pressures will im prove the factor of safety against sliding. Reference to Fig. 7.5 shows the range of uplift water pressures that may exist depending on the efficiency of the grout curtain and drain holes. (d) Erosion control

High pressure gradients and seepage velocities that develop in dam foundations can erode low strength, unconsolidated infillings, as well as closely fractured or weak rock at the base of the core. This is an unstable situation because as erosion occurs the seepage quantities and scour will increase, and eventually the integrity of the dam may be threatened. Grouting for erosion control will require that the holes be carefully placed to intersect the discontinuities that are of concern and to ensure that the consolidation of the infilling is as continuous as possible. For grouting to fulfill these four functions, there needs to be: 1. complete filling of discontinuities and voids; 2. high mechanical strength of the grout; 3. good bond to rock; 4. resistance of the grout to chemical leaching; 5. predictability of the grouting process; 6. limited travel of the grout to avoid losses. The following is a general description of usual grout practices that will produce the desired results. There are no standard grouting procedures because for each installation, procedures must be modified to suit the geological conditions at the site. 7.7.2 Grout types This discussion of grouting methods is mainly concerns cement-water grouts because these are the materials most often used in rock foundations. However, a wide variety of other grouts are available for special applications. For example, hot asphalt has been used to seal solution cavities in the limestone foundation of the Stewartville Dam in Ontario under full head conditions in which the flow quantities were so high that cement grout could not be retained long enough to set in the large cavities (Lukajic et al., 1985). Also, sealing of large cavities with high turbulent flows has been achieved using organic foams containing polyurethane (Cambefort, 1977), and fine (0.05–0.1 mm wide) cracks have

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Figure 7.22 Example of consolidation and curtain grouting installations in the foundation of a buttress dam (Jaoui et al., 1982). 1. Consolidation grouting. 2. Grout curtain. 3. Drain holes. 4. Grouting and drainage gallery.

been sealed with silicate based grouts in the foundation of a landfill containment facility where acid leachate would have dissolved cement grout (Graf et al., 1985). It is likely that chemical grouts will become common in sealing containment facilities for hazardous wastes where leakage tolerances are very low and fine discontinuities have to be sealed. The use of cement grout is not appropriate where the discontinuity width is less than about 0.25 mm, or three times the maximum particle size of the cement, otherwise rapid blinding of the discontinuity occurs (Karol, 1986). Under these conditions, it may be possible to use ultra-fine cements together with a superplasticizer to keep the

cement particles dispersed and prevent the formation of flocs (Weaver, 1993). Alternatively, chemical grouts such as silicates, resins and acrylamides may be used; these grouts will penetrate fine fractures, are resistant to acid attack, have fast set times, and will set without shrinkage. Their main disadvantage is high cost. 7.7.3 Mechanism of grouting When grout is pumped down a drill hole that intersects a series of discontinuities, the extent to which they are filled with grout will depend on physical properties of the grout, namely the

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cohesion (or yield point of visco-plastic fluid) and viscosity of the grout mix. Viscosity determines the rate at which grout flows from a hole under a given pressure (the time required to fill the fracture), and cohesion determines how far the grout will travel and limits the extent of the grouted zone (Deere and Lombardi, 1985). These two properties have to be balanced to produce the properties most suitable to the site conditions. For example, when grouting fine fractures, a low cohesion grout (with high water content) will flow a considerable distance from the hole, but the grout may be discontinuous and of low strength, and form an ineffective seepage barrier. Once a cement grout has been pumped into a crack it should form a solid that entirely fills the space with no shrinkage. However, while the chemical action of cement hydration requires a water:cement ratio of 0.45:1 by volume (or 0.3:1 by weight), water in excess of this is required for making the grout workable and transporting and placing it. Some of this excess water will be retained in the set grout, but much of it must be removed as the grout sets. This process is known as bleeding. It takes place as the movement of the grout in a crack slows so that the cement particles settle and water collects above the surface of the cement. Unless this bleed water can be removed and replaced with more cement, an effective seal will not be formed. Figure 7.23 shows three stages of grout penetration in a horizontal crack. At the start of grouting (a), the grout travels from the hole freely along the open crack under the pressure from the grout hole. As the pressure in the grout builds up, the limit of penetration is reached and there is no further motion of the grout (b). At this time, bleed starts in a lateral direction, because bleeding in a vertical direction is limited, to form a discontinuous grout filling (c). The diagram demonstrates that vertical fractures, in which the bleed water can rise to the surface, can be more readily grouted than horizontal fractures (Houlsby, 1985). The extent to which grouts bleed is related to the water:cement (w:c) ratio of the placement mix. At a w:c ratio of 2:1 (by volume) which is commonly used in grouting operations, after a period of about

one hour 35% of the volume is filled with water, with only 65% of the fracture containing grout. For much thinner mixes with w:c ratios of 12:1, bleeding takes place within 15 minutes and the bleed water volume occupies about 85% of the volume of the fracture. In order to minimize settlement of the cement, bentonite is often added to the mix in the proportion of 2–4% bentonite by weight of cement (see Section 7.7.6). 7.7.4 Drilling method Grout holes can be drilled by either percussion or diamond methods. Percussion drilling is faster and cheaper than rotary drilling and produces satisfactory results as long as precautions are taken that the holes are parallel so that there are no gaps in the curtain caused by excessive hole deviation. If the length of the holes exceeds about 8–10 m (26– 33 ft) it is recommended that the orientation of the holes be measured and if deviation is excessive, modified drilling methods could be used. The advantages of diamond drilling are that fractures in the core can be examined which can be useful in the planning of grouting operations, and a cleaner and straighter hole is obtained. It is usual that a minimum of 10% of grout holes are diamond drilled to obtain geological information. Hole diameters have little effect on the results of grouting and they are usually in the range 40– 50 mm (1.5–2 in). It is most important that the walls of the drill holes are thoroughly cleaned of drill cuttings that block fractures intersected in the walls and would prevent grout penetration. It has been found that water is significantly better than air in cleaning cuttings from drill holes, so water circulation is preferable to air circulation for removing cuttings. Also, if the hole intersects a fracture into which the circulation water is lost, the drilling should be stopped as soon as possible to minimize the risk of the fracture becoming clogged with cuttings. Grouting would then be carried out to seal the fracture before recommencing drilling (Weaver, 1991).

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS

Additional information on drilling methods is discussed in Sections 4.3 and 10.2. 7.7.5 Hole patterns The two categories of grouting to seal seepage, namely blanket and curtain grouting, require different patterns of holes which depend on the geometry of the dam, the geology of the foundation and the degree of water tightness that must be achieved. Figure 7.24 shows the arrangement of drill holes for blanket and curtain grouting used to seal the fractured and faulted sandstones, siltstones, mudstones and shales in the foundation of the Wimbleball Dam in the UK. In total, the blanket and curtain grouting involved almost 94 000 m (310 000 ft) of drilling and the injection of 3500 t of grout (Bruce and George, 1982). For both curtain and blanket grouting, the first requirement of laying out grout holes is that they be oriented to intersect the main water bearing discontinuity set(s) in the foundation. For example, if there is a set of persistent, steeply dipping discontinuities aligned at right angles to the dam axis, the grout holes would be drilled at a dip of about 60° to 70° and a trend parallel to the dam axis. Vertical grout holes would be appropriate for sets of horizontal discontinuities in the foundation. (a) Blanket grouting The rock immediately under the dam may be more permeable than the rock at depth as the result of blasting damage during surface preparation, and stress relief causing opening of discontinuities. This is also the area where high hydraulic gradients are developed, so particular attention is required to sealing this region of the foundation. For embankment dams, blanket grouting consists of drilling holes on a square pattern to cover the entire area of the core so that the combination of the blanket and curtain grouting form a ‘T’ under the dam (Sherard et al., 1963). This minimizes the risk of seepage paths being developed over the top of the grout curtain which can result in scour of the core material.

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(b) Curtain grouting In theory, the effectiveness of a grout curtain in reducing uplift pressures is improved if it is inclined at about 15° upstream so that the seepage path is lengthened compared with a vertical curtain. However, this does require more careful control of drill hole alignment to ensure that the holes are parallel and lie in the same plane. The following is a general plan for laying out curtain grout holes, the details of which would depend on the geological condition and degree of water tightness needed (Deere, 1976). 1. Drill exploration holes using coring equipment to a depth equal to the full head H on about 30 m (100 ft) spacing. The core will provide information on the general geology of the foundation from which the details of the grouting plan can be drawn up. Conduct permeability measurements to assess the grouting requirements and methods. 2. Drill primary grout holes to a depth of H/2 to 2H/3; hole spacings may range from 3–20 m (10–65 ft). 3. Drill secondary grout holes on split spacing so there is progressive closure of the curtain. These holes may be drilled to a shallower depth than the primary holes if the rock becomes tighter with depth. 4. If additional grouting is needed, tertiary and possibly quartenary holes are drilled on split spacings (Bruce and George, 1982). Alternatively, a second row of grout holes is drilled at a distance of about 2m (6 ft) downstream following the same layout as the primary and secondary holes. Close spacing will be required in low permeability rock because the grout will penetrate a shorter distance in the narrow fractures. Generally, the wider fractures are grouted with the primary and secondary holes, while the finer fractures are grouted with the tertiary holes. The final spacing of the grout holes will depend on the permeability criterion established for the foundation, and the

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Figure 7.23 Grout penetration of horizontal fractures: ph is the pressure in the grout hole; d is the distance along crack (Houlsby, 1985): (a) start of grouting; (b) grout reaches limit of penetration for the particular pressure and water:cement ratio used; and (c) grout stiffens, radius of pressure transmission contracts and bleed pockets develop.

development of a continuous curtain or blanket. The grouting operation is evaluated by conducting variable head tests in open holes to measure the permeability of the rock mass (see Section 4.4.2), or monitoring grout takes. Selection of an acceptable permeability criterion for the foundation depends on both the value of the water lost by leakage, as well as the type of dam (see Fig. 7.26 and Section 7.7.10). As shown in the procedure described in the previous paragraphs, the general approach to effective grouting is to drill holes at a progressively closer spacing, or to drill multiple rows of holes, until the permeability criterion is

achieved. 7.7.6 Grout mixes Where cement grouts are used, the possible mixes that can be used range from 1:1 to as high as 10:1 (water:cement ratio). The low-ratio, thick grouts are used to fill wide fractures and voids, while very thin, high ratio grouts have been used when sealing fine fractures where there is concern regarding the penetration of thicker grouts. The use of thick grouts to seal tight fractures will

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS

result in little penetration into the rock surrounding the hole because of the high cohesion of the mix. However, it is likely that the grout that does penetrate the fracture will be of good quality, so a pattern of closely spaced holes would be required to seal a tight rock mass effectively. Conversely, low cohesion, high w:c ratio grouts will penetrate greater distances in tight fractures, but a continuous seal may not be formed. As discussed in Section 7.7.3, thin grouts have a high proportion of excess water when they set and so much of the volume filled by the mix will consist of water which must be bled off to form a tight seal. Both Deere and Houlsby (1982) recommend the use of thicker, ‘stable’ mixes in which there is minimal settling of the cement grains. Houlsby’s criteria for grout mixes are as follows. A starter mix is selected based on previous experience, permeability tests and information on fracture width and orientation. Once grouting has started, successively thicker mixes may be used depending on how well the hole has accepted the grout. At most sites, a ratio of 2:1 w:c ratio (by volume) is suitable for a starter mix, except in the following cases: • For fractures with widths of 0.75 mm (0.03 in) or finer, start with a mix of 3:1. • For fractures with widths of 1.2–2.5 mm (0.5– 0. 1 in), start with a mix of 1:1. Note, equivalent water:cement (w:c) ratios are: • (2:1) by volume=(1.3:1) by weight; • (1:1.5) by volume=(1:1) by weight; and • (1:1) by volume=(0.67:1) by weight. Bentonite is often used in cement grouts to reduce the sedimentation of the cement particles so that there is less tendency for fractures to be partially filled with poor quality grout. The proportion of bentonite added to the mix is usually in the range of 2–4% of the weight of cement. It has also been found that the main effect of bentonite is to increase

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the cohesion which limits the penetration distance. However, the use of fluidizers such as Intraplast (Sika) enhances the penetration of grout into fine fractures without the w:c ratio having to be increased (Deere and Lombardi, 1985). 7.7.7 Grout strength It is considered that a minimum strength of about 9 MPa (1300 p.s.i.) is required for grout to be able to resist high hydraulic gradients without scour or piping (Deere, 1982). This strength range is approximately equivalent to that of weak concrete. It is likely that this minimum strength will also be required for consolidation grouting where the grout is being employed to improve the modulus of the rock mass. While bentonite is used to reduce the sedimentation of cement grouts, it has the disadvantage that it will reduce the strength of the grout. Laboratory studies of grout strengths show that for thin mixes at a w:c ratio of about 6:1 by volume, the bentonite lowered the strength by about 50–75% , while for thicker mixes at a w:c ratio of about 2:1, the strength was reduced by about 25% (Burgin, 1979). Samples with a w:c ratio of 1.5:1 gave 28 day strengths of about 9 MPa (1300 p.s.i.), at bentonite contents of between 2% and 8% . At this w:c ratio there was little influence of the bentonite content on the grout strength. 7.7.8 Grout pressures Pressures used for grouting should be sufficient to inject grout into the fractures in the foundation rock, and achieve some radial penetration. This pressure should be less than that required to fracture the rock because it is not desirable to create new fractures that may not then be completely fil led with grout. One of the factors that determines the quantity of grout take is the pressure drop in the grout along the fracture. Once this pressure drop equals the applied pressure in the hole, there will be

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Figure 7.24 Arrangement of blanket and curtain grouting for buttress dam (Bruce and George, 1982): (a) plan and elevation along line of grout curtain; and (b) section through typical buttress showing relative location of blanket and curtain grouting, and pressure relief wells.

no further take and grouting is halted because progressively increasing the pressure to induce further grout take may force open fractures in the rock. In tight rock it is unnecessary to maintain the pressure while the grout sets because the grout will not flow out of the fracture once it has been injected to refusal. However, if open voids are being grouted the pressure should be maintained until the grout has taken its initial set.

A chart relating grout pressure to depth below the ground surface and the strength of rock is given in Fig. 7.25 (Houlsby, 1977a). This chart shows that pressures as great as two or three times the overburden pressure can be used in strong rock (lines 3 and 4 on Fig. 7.25). However, grout pressures should be less than the overburden pressure in very weak and fractured rock to minimize the development of new fractures, and in

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS

horizontally bedded rock where the grout could cause heaving at the surface. It is possible to apply sufficient pressure to open fractures and increase the distance of grout penetration without causing hydrofracturing of the rock. This approach is based on the ‘rule of thumb’ that the maximum pressure is equal to one bar per meter of depth (line 1 in Fig. 7.25), and has been used successfully in grouting strong rock. A more conservative approach with respect to prevention of hydrofracturing is to use a maximum pressure of one p.s.i. per foot of depth (line 5 in Fig. 7.25) which may limit the grout penetration (Weaver, 1993). Another factor to consider in determining grout pressures is increasing pressure with each stage of grouting. Deere and Lombardi (1985) suggest that the pressures p used in each stage of grouting could be as follows, depending on site conditions: 1. 2. 3. 4.

primary: p; secondary: 1.5p; tertiary: 2p; quartenary: 2.5p.

7.7.9 Grouting procedures Grouting is usually carried out in stages using inflatable or expansion packers to isolate sections of the hole. This procedure ensures that the full length of the hole is grouted and avoids the situation that may develop if the full length of the hole were to be grouted in one operation, where most of the grout is pumped into one open fracture and no grout is injected into the tighter fractures. The length of hole that is grouted in any stage is determined by positioning the packer so that individual fractures can be grouted as desired. Grouting lengths vary from as short as 3m (10 ft) to as long as 10 m (33 ft), with shorter lengths being used closer to the rock surface and in more fractured rock. The grout is injected into the hole at the predetermined pressure and grouting is continued until there is ‘refusal’ in grout take. That is, grouting should not be stopped until there has been

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no measurable take over a five to ten minute period so that the grout that has been injected into the fracture has been packed tight. This procedure will promote and maintain the full penetration of the grout, particularly if the applied pressure has been sufficient to open the fractures, which may not be the case if the pressure was cut off while the hole was still taking grout. Grouting can either be carried out from the top down, or the bottom up depending on the condition of the rock. In poor rock where the drill holes will not stay open, grouting is carried out from the top which requires that the hole be progressively deepened with each stage of grouting. A packer is used to isolate each section of the hole so that higher pressures can be used at depth without fracturing the near-surface rock. The disadvantage of this procedure is that the drilling costs are high because the drill rods have to be removed and the grout tubes and packers lowered into the hole for each section of grouting. The advantage is that the grouting can be stopped if the rock permeability increases with depth to a value less than the minimum required value. In good quality rock, the grout hole can be drilled to full depth and then grouted from the bottom up using packers to isolate successive sections of the hole (Bruce, 1993b). 7.7.10 Permeability criteria for grouted rock When planning a grouting program it is important to determine the level of permeability that is required to suit both the function of the dam, and its safe operation. For example, where the function of the dam is flood control, seepage through the foundation is acceptable as long as it does not compromise the safety of the structure due to scour or piping of loose discontinuity infillings. Where there is a significant economic value to the water stored in the reservoir, and particularly where water is pumped into the reservoir, seepage losses are much less acceptable. The permeability of the rock mass after grouting can be measured either by

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1. One bar per meter depth 2. pB=4D 3. pB=3D 4. pB=2D 5. One p.s.i per foot depth 6. pB=1.5D 7. pB=1D pB=is the pressure at the bottom of the stage Figure 7.25 Typical permissible grout pressures for various foundation condition (after Houlsby, 1977a).

conducting variable head tests in test holes and calculating the permeability (Section 4.4.2), or by monitoring the grout take expressed in weight of cement per unit length of hole. Permeability criteria, as suggested by Houlsby (1977a), for grout curtains in the foundations of a variety of dam types are shown in Fig. 7.26. Permeability values can be expressed in units of both lugeons and m/s, assuming 1 lugeon is equivalent to 1.3×10−7 m/s. Lugeon values vary from less than 1 for rock with occasional tight fractures, to as much as 100 for rock containing fractures with widths up to approximately 6 mm (0. 25 in). Details of field test methods to measure

permeability are provided in Section 4.4. As shown in Fig. 7.25, the permeability criteria range from 1 lugeon where seepage must be minimized, to as high as 5 to 7 lugeons where seepage is permitted and the foundation comprises sound rock in which there is no risk of piping. The original lugeon test was conducted at a pressure of 10 bar (150 p.s.i.) and 1 lugeon equals a water take of 1 liter/m length of hole/minute (Houslby, 1977b). This pressure level is now considered to be too high because fracturing of the rock may occur at these pressures. For tests conducted at lower pressures, a modified lugeon value can be calculated by multiplying the measured water take by the ratio:

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS

10 bar/Test pressure. An alternative permeability criterion is based on grout take expressed in weight of cement take per unit length of drill hole. Deere (1976) suggests that grout take should be no more than 12.5– 25 kg/m (8–16 lb/ft) to achieve adequate sealing of high dams. The advantage of using grout take as the permeability criterion is that the effectiveness of the grout seal can be determined during grouting operations with no need to perform additional tests. However, the disadvantage is that the grout take depends to some degree on injection pressures and mix ratios, and more closely controlled permeability measurements can be made using permeability tests employing water. 7.7.11 Monitoring grouting operations The installation of an efficient grout curtain depends to a large degree on precise control and monitoring of the grouting process. Precise control of the grout mix and injection pressure will allow, for example, the water:cement ratio and pressure to be decreased if a wide fracture is encountered in which take would be excessive at high injection pressure and water:cement ratio. Similarly, accurate records of grout take, preferably plotted graphically, provide information that can be used to evaluate the grouting program and determine where extra holes are required to produce an effective seal. Equipment is now available to control and monitor automatically the following functions of grouting operations in up to six holes simultaneously (Demming et al., 1985): 1. 2. 3. 4. 5. 6.

cement weight per hour; pressure; flow; flow/pressure; total bag rate for the hole; water take in volume per minute during water pressure test.

Water:cement ratios can be keyed into the

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computer, and nuclear densometers and magnetic flow meters on the line monitor actual densities and quantities allowing close control of the grouting operation. The system also has the capability to generate reports showing, in the form of histograms, results of all the units listed above. The control and monitoring equipment, together with the mixers and pumps, is contained in a steel shipping container that can readily be moved around the site. In many installations, the pumping equipment is on the surface and the grouting operation is in a tunnel or gallery deep in the foundation with a telephone for communication. 7.7.12 Leaching Because grouts are subject to chemical leaching, their long term stability must be considered in design, and their performance monitored during operations. Leaching corrosion of cement grout is caused by the dissolution and removal of hardened cement compounds by seepage water (Petrovsky, 1982). The main component of hydrated cement is lime (CaO) which can comprise 60– 65% of the total cement volume in the form of free calcium hydroxide (Ca(OH)2) and hydrated calcium compounds such as silicates, aluminates and alumino-ferrites. These hydrated compounds remain stable in the calcium hydroxide solution at concentrations of about 1300 mg CaO/l and a pH of 12.0. Leaching of calcium hydroxide is accompanied by the hydrolysis of the hydrated cement compounds and the release of lime to the seepage water. The reduction of CaO content in the cement grout leads to gradual decomposition of the cement binder and deterioration of the grout. The removal of 25% of the lime from the grout can reduce its strength by as much as 50%. In permeable cement grout, there are three stages of leaching as follows. 1. First, the rapid dissolution of the free calcium hydroxide. This occurs at the onset of the leaching process and the concentration of

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Figure 7.26 Suggested permeability criteria for rock foundations (after Houlsby, 1977a).

calcium in the seepage water is at its highest point. 2. Second, lime is liberated from the hydrated calcium compounds by the hydrolytic action of

the seepage water, and the calcium concentration in the seepage water diminishes. 3. Third, the calcium hydroxide and the hydrated compounds are dissolved from the deeper

FOUNDATIONS OF GRAVITY AND EMBANKMENT DAMS

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Figure 7.27 Leaching intensity for dam grout curtains (Petrovsky, 1982). Dam 1:36 m high, 513 m long; 6 m deep grout curtain with holes on 1.5 m centres. Total grout take=51 tonnes. Dam 2:124 m high, 1072 m long; 60 m deep grout curtain with holes on 3–5 m centers. Total grout take=2500 tonnes. Dam 3:65 m high, 391 m long; 40 m deep grout curtain with holes on 0.5–1.4 m centers. Total grout take= 12 000 tonnes.

zones in the grout. During this leaching stage, the concentration of the calcium in the seepage water is low and remains relatively constant. Petrovsky describes a nine year monitoring program of grout curtains on three concrete gravity dams in Russia. By measuring the calcium content of the water flowing in the drain holes it was possible to calculate the weight of calcium lost from the curtains. The gradients of the grout loss lines in Fig. 7.27 show that the rate of loss was significantly higher at dam 2 which was 4 years old, than in dams 1 and 3 which were between 12 and 16 years old. This indicates that the leaching rate decreases with time, and that leaching process was in the secondary stage (as defined in the previous paragraphs) at dam 2, while it was in the tertiary stage at dams 1 and 3. While it was considered that the rate of loss was not significant when compared with the quantity of grout in the curtains, if the leaching were to be concentrated in a few high flow zones, the grout curtain could be weakened at these points.

In any foundation where a grout curtain is installed to control seepage and/or uplift, it is important that the performance of the curtain is monitored by measuring seepage volumes in the drainage system, and by installing piezometers to measure water pressures in the foundation. If increases in uplift pressures and seepage quantities can be attributed to deterioration in the grout curtain, then additional grouting can readily be carried out if there are galleries in the foundation or base of the dam. 7.7.13 Drainage When grout curtains are installed in dam foundations, they usually incorporate drains holes located downstream of the curtain. The functions of these holes are to provide a low pressure outlet for seepage water, and to provide a monitoring point of pressures and seepage quantities in the foundation. Pressures can be measured by fitting pressure gauges to pipes sealed into the collars of the holes, and seepage quantities can be monitored by V-notch

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weirs at the discharge point in the gallery. Drain holes are, of course, drilled after grouting is complete to minimize the risk of filling the holes with grout, and are oriented such that they inter sect the water bearing discontinuities. The holes may be aligned either vertically, or dipping downstream so that they are not drilled into the grout curtain. The drain hole diameter should be a minimum of about 75 mm (3 in) and the spacing of may be in the range 1.5–5 m (5–16 ft), with narrower spacing being used in rock containing impersistent discontinuities. As a general rule, hole depths vary from 20 to 40% of the water head, and from 35 to 70% of the grout curtain depth (Golze, 1977). Another factor that may be considered in planning the location of the drain holes, particularly for arch dams, is that the compressive stresses induced in the foundation by the weight of the dam may close discontinuities and reduce permeability resulting in the development of increased uplift pressures towards the downstream toe of the dam. Under these conditions the drain holes may be inclined upstream but should not intersect open discontinuities at the upstream toe where the water thrust on the dam may produce tensile stresses in the rock (ICOLD, 1993). The drain holes may be uncased in sound rock, or cased with perforated plastic casing in fractured rock. The casing will keep the hole open and control loosening of the rock in the walls of the hole. Provision should also be made for cleaning or redrilling holes in the event they become blocked by bacterial growth, for example. 7.8 References Abrahao, R.A., Silveira, J.F. and de Barros, F.P. (1983) Itaipu main dam foundations: design and performance during construction and preliminary filling of the reservoir. 5th Int. Cong. on Rock Mech., Melbourne, ISRM, pp. C191–7. Annandale, G.W. (1995) Erodibility. J. Hydraulic Research, 33(4), 471–93. Annandale, G.W., Abt, S.R., Ruff, J. and Wittler, R. (1996a) Scour damage. The Military Engineer, Soc. of American Military Eng., 88(580), 34–5. Alonso, E.E. and Carol, I. (1985) Foundation analysis of an arch dam. Comparison of two modelling techniques: no tension and jointed rock material. Rock Mech. and

Rock Eng., 18(3), 187–204. Babbitt, D.H. (1993) Improving seismic safety of dams in California. Proc. Specialty Conf. on Geotechnical Practice in Dam Rehabilitation, ASCE Geotech. Special Pub. No. 35, Raleigh, NC, pp. 365–72. Bianchi, R.H. and Bruce, D.A. (1993) Use of posttensioned anchorages on the arch portion of the Stewart Mountain Dam, Arizona. Proc. Specialty Conf. on Geotechnical Practice in Dam Rehabilitation, ASCE Geotech. Special Pub. No. 35, Raleigh, NC, pp. 791–802. Bieniawski, Z.T. and Orr, C.M. (1976) Rapid site appraisal for dam foundations by the geomechanics classification. ICOLD, Trans. 12th Int. Congress on Large Dams, Mexico, Vol. II, Q46, R32, ICOLD (www.icold-cigb.org.1) pp. 483–500. Bosovic, A., Badanur, H., Nonveiller, E. and Pavlin, B. (1981) The Keban Dam foundation on karstified limestone. Bull. Int. Assoc. of Eng. Geol., 24, 45–51. Bruce, D.A. (1993a) Stabilization of concrete dams by post-tensioned rock anchorages: the state of American practice. Proc. Specialty Conf. on Geotechnical Practice in Dam Rehabilitation, ASCE Geotech. Special Pub. No. 35, Raleigh, NC, pp. 320–32. Bruce, D.A. (1993b) Review of drilling and grouting methods of existing embankment dams. Proc. Specialty Conf. on Geotechnical Practice in Dam Rehabilitation, ASCE Geotech. Special Pub. No. 35, Raleigh, NC, pp. 803–19. Bruce, D.A., Fiedler, W.R. and Triplett, R.E. (1991) Anchors in the desert. Civil Engineering, 61(12), 40–43. Bruce, D.A. and George, C.R. F. (1982) Rock grouting at Wimbleball Dam. Geotechnique, 32(4), 323–48. Burgi, P.H. and Eckley, M.S. (1987) Repairs at Glen Canyon Dam. Concrete International, March, 24–31. Burgin, C.R. (1979) Investigations of the Physical Properties of Cement-bentonite Grouts for Improvement of Dam Foundations. Thesis, University of Florida, partial requirement for MSc degree. Cambefort, H. (1977) The principles and applications of grouting. Q. J. Eng. Geol., 10, 57–95. Carol, I. and Alonso, E.E., (1985) A new joint element for the analysis of fractured rock. Proc. 5th Int. Cong. on Rock Mech., Melbourne, ISRM, pp. F147–51. Carrere, A., Nury, C. and Pouyet, P. (1987) The contribution of a non-linear, three dimensional finite element model to the evaluation of the appropriateness

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of a geologically complex foundation for a 220 m high arch dam in Longton, China (in French). Proc. 6th Int. Cong. Rock Mech., Montreal, ISRM, pp. 305–311. Casagrande, A. (1961) Control of seepage through foundations and abutments of dams. Geotechnique, XI, 161–182. Cheng, Y. (1987) New development in seam treatment of Feitsui Arch Dam foundation, Taiwan. Proc. 6th Int. Cong. Rock Mech., Montreal, ISRM, pp. 319–326. Chopra, A.K. (1978) Earthquake resistant designs of concrete gravity dams. J. Structural Div. ASCE, 104 (ST6), 953–971. Chopra, A.K. and Chakrabati, P. (1973) The Konya Earthquake and the damage to Konya Dam. Bull. of the Seismological Soc. of Amer., 63(2), 381–97. Crawford, A.M. and Curran, J.H. (1982) The influence of rate- and displacement-dependent shear resistance of rock slopes to seismic loads. Int. J. Rock Mech. Min. Sci. & Geomech. Abstr., 19, 1–8. Deere, D.U. (1976) Dams on rock foundations—some design questions. Specialty Conf. on Rock Eng. for Foundations and Slopes, Boulder, CO, ASCE, Geotechnical Eng. Div., Vol. 2, pp. 55–86. Deere, D.U. (1982) Cement-bentonite grouting for dams. Grouting in Geotechnical Engineering, Proc. of Conf. sponsored by Geotechnical Eng. Div., ASCE, New Orleans, pp. 279–300. Deere, D.U. and Lombardi, G. (1985) Grout slurries thick or thin? Proc. of Session ‘Issues in Dam Grouting’, Denver, Colorado, ASCE, Geotechnical Eng. Div., pp. 156–164. Demming, M., Rogers, J.L. and Tula, A. (1985) Computer applications in grouting. Proc. of Session Issues in Dam Grouting, Denver, Colorado, ASCE, Geotechnical Eng. Div., pp. 123–131. Egger, P. and Spang, K. (1987) Stability investigations for ground improvement by rock bolts at a large dam. Proc. 6th Int. Cong. Rock Mech., Montreal, ISRM, pp. 349–354. Elliott, J.F. (1997) Monitoring pre-stressed structures. Civil Engineering, ASCE, New York, July, 61–3. Engineering News Record (1988) Brakes put on slipping spillway. ENR, June, 24–6. Engineering News Record (1989) Foundation problems are blamed for reservoir embankment failure. ENR, January, 10–11. Fenves, G. and Chopra, A.K. (1984) EAGD-84: A Computer Program for Earthquake Analysis of Concrete Gravity Dams. Report No. UCB/EERC-84/

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11, Earthquake Engineering Research Center, University of California, Berkeley, CA. Fenves, G. and Chopra, A.K. (1987) Simplified earthquake analysis of concrete dams. ASCE, J. Structural Eng., 113(8), 1688–708.

Fok, K.L., Hall, J.F. and Chopra, A.K. (1986) EACD-3D: A Computer Program for Three Dimensional Earthquake Analysis of Concrete Dams. Report No. UCB/EERC-86/09, Earthquake Engi neering Research Center, University of California, Berkeley, CA. Forster, J.W. (1986) Geological problems overcome at Revelstoke. Water Power and Dam Construction, July, 53–8, August, 42–5. Foyo, A., Tomillo, C., Maycotte, J.I. and Willis, P. (1997) Geological features, permeability and groutabilty characteristics of the Zimapan Dam foundation, Hidalgo State, Mexico. Engineering Geology, 46, 157–74. Franklin, A.G. and Chang, F.K. (1977) Earthquake Resistance of Earth and Rock-fill Dams. Report 5: Permanent Displacement of Earth Embankments by Newmark Sliding Block Analysis. US Army Engineer Waterways Experiment Station, Vicksburg, Miss., Miscellaneous Paper S-71–17. Fu, B.-J., Zhu, Z.-J. and Li, G.-Z. (1983) Analytical experience on the stability of the high dam foundation of the Liu-Jia-Xia hydropower station. 5th Int. Cong. on Rock Mech., Melbourne, ISRM, pp. C199–203. Gavard, M. and Gilg, B. (1983) Stability analysis of the excavation of the Karakaya arch dam and power plant. 5th Int. Cong. on Rock Mech., Melbourne, ISRM, pp. C219–25. Golze, A.R. (1977) Handbook of Dam Engineering. Van Nostrand Reinhold, New York. Goodman, R.E. and Seed, H.B. (1966) Earthquake induced displacements of sand embankments. ASCE, 92, SM2, 125–46. Graf, E.D., Rhoades, D.J. and Faught, K.L. (1985) Chemical grout curtains at Ox Mountain dams. Proc. of Session Issues in Dam Grouting, Denver, Colorado, ASCE, Geotechnical Eng. Div., pp. 92–9. Hibbitt, Karlsson and Sorensen, Inc. (1987) ABAQUS Three Dimensional Finite Element Analysis. Providence, Rhode Island. Hoek, E. (1986) Personnel communication. Hoek, E. and Londe, P. (1974) Surface workings in rock. Proc. 3rd Int. Cong. on Rock Mech., Denver, ISRM, Vol. 2, pp. 613–54.

266

INTRODUCTION

Houlsby, A.C. (1977a) Engineering of grout curtains to standards. ASCE, Geotech. Div., 103(GT9), pp. 953–71. Houlsby, A.C. (1977b) Routine interpretation of the lugeon water-test. Q. J. Eng. Geol., 9, 303–13. Houslby, A.C. (1982) Optimum water:cement ratios for rock grouting. Grouting in Geotechnical Engineering, Proc. of Conf. sponsored by the Geotechnical Engineering Division, ASCE, New Orleans, pp. 317–31. Houlsby, A.C. (1985) Cement grouting: water minimizing practices. Proc. of Session on Issues in Dam Grouting, Denver, Colorado, ASCE, Geotechnical Eng. Div., pp. 34–75. Housner, G.W. (1970) Seismic events at Konya Dam, rock mechanics theory and practice. Proc. 11th Symp. on Rock Mech. American Institute of Mining, Metallurgical and Petroleum Engineers, New York. Humphries, R.W. (1987) Filter design, foundation treatment and hydraulic fracturing of dams founded on rock. Proc. South-east States Geotechnical Conference, Nashville, TN. ICOLD (1979) Deterioration cases collected and their preliminary assessment. Trans. ICOLD, 1, 2. ICOLD (1993) Rock foundations for dams. ICOLD Bulletin, 88, Paris. ICOLD (1995) Dam failures statistical analysis. International Commission on Large Dams (ICOLD), Bulletin 99, Paris. Itasca Consulting Group (1996) Universal Distinct Element Code (UDEC), Version 3.0. Minneapolis, Minnesota. Jaeger, C. (1963) The Malpasset Report. Water Power, 15 (2), 55–61. James, A.N. and Kirkpatrick, I.M. (1980) Design of foundations of dams containing soluble rocks and soils. Q. J. Eng. Geol., 13, 189–98. Jansen, R.B. (1988) Advanced Dam Engineering for Design, Construction, and Rehabilitation. Van Nostrand Reinhold, New York. Jaoui, A., Islah, M., Garnier, G., Gavard, M. and Gilg, B. (1982) The Tamzaourt-Dam, a buttress dam with particular foundation problems. 14th Cong. on Large Dams, Rio de Janiero, ICOLD, Vol. II, Q53, R3, pp. 37–48. Jennings, P.C. (Ed.) (1971) Engineering Features of the San Fernando Earthquake. California Institute of Technology, Pasadena, California. Jibson, R.W., Harp, E.L. and Michael, J.A. (1998) A

Method for Producing Digital Probabilistic Seismic Landslide Hazard Maps: An Example from the Los Angeles, California, Area. US Geological Survey, Denver, Open-File Report 98–113, pp. 17. Kaloustian, E.S. (1984) Statistical analysis of distribution of concrete dam foundation failures. Proc. Int. Conf. on Safety of Dams, Coimbra, Portugal, Balkema, Rotterdam, pp. 311–319. Karol, R.H. (1986) Chemical and Microfine Grouting. Workshop on Remedial Seepage Control, US Army Engineer Waterways Experiment Station, October. Kikuchi, K., Mito, Y. and Adachi, T. (1995) Case study of the mechanical improvement of rock masses by grouting. Proc. Int. Workshop on Rock Foundation, Tokyo, Japan, Balkema, Rotterdam, pp. 393–7. Kovari, K. and Peter, G. (1983) Continuous strain monitoring in the rock foundation of a large dam. Rock Mech. and Rock Eng., 16, 157–71. Lane, K.S. (1955) Designing for foundation movements at Garrison Dam. 5th Congress on Large Dams, ICOLD, Paris. Lane, R.G.T. (1963) The jetting and grouting of fissured quartzite at Kariba. Conf. on Grouts, British National Society on Soil Mechanics, London, pp. 85–90. Lauga, H. and Taylor, H. (1983) Gravity dam on horizontally bedded sedimentary rock. Proc. 7th Pan American Conf. on Soil Mechanics and Foundation Eng., Vancouver, pp. 77–91. Lemos, J.V. (1996) Modelling of arch dams on jointed rock foundations. Proc. ISRM Int. Symp. Eurock ‘96, Turin, September, ed. G.Barla, Balkema, Rotterdam, Vol. 1, pp. 519–26. Lin, J.-S. and Whitman, R.V. (1986) Earthquake induced displacement of sliding blocks. J. Geotech. Eng. Div., ASCE, 112(1), 44–59. Lo, K.Y., Ogawa, T., Lukajic, B. and Dupak, D.D. (1991a) Measurement of strength parameters of concrete-rock contact at the dam-foundation interface. Geotechnical Testing J., 14(4), 383–94. Lo, K.Y., Ogawa, T., Lukajic, B., Smith, G.F. and Tang, J.H.K. (1991b) The evaluation of stability of existing concrete dams on rock foundations and remedial measures. Proc. 17th Int. Cong., Int. Commission on Large Dams, Vienna, Austria, pp. 963–90. Lombardi, G. and Deere, D. (1993) Grouting design and control using the GIN principle. Water Power Dam Construction, Sutton, UK, June, 15–22. Lukajic, B., Smith, G. and Deans, J. (1985) Use of asphalt in treatment of dam foundation leakage,

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Stewartville Dam. Specialty Conf. on Rock Eng. for Foundations and Slopes, Boulder, CO, ASCE, Geotechnical Eng. Div., Vol. 2, pp. 76–91. Mgalobelov, Y.B. and Lomov, I.E. (1979) Stabilization of the Inguri arch dam rock foundation. 4th Int. Cong. on Rock Mech., Montreux, ISRM, pp. 433–8. Myers, B.K. and Marilley, J.M. (1997) Automated monitoring of Tolt Dam. Civil Engineer, ASCE, March, 44–6. National Research Council (1990) Earthquake Engineering for Concrete Dams: Design, Performance and Research Needs. National Academy Press, Washington, DC. Newmark, N.M. (1965) Effect of earthquakes on dams and embankments. Geotechnique, 15(2), 139–60. Nicholson, G.A. (1983) Design of Gravity Dams on Rock Foundations: Sliding Stability Assessment by Limit Equilibrium and Selection of Shear Strength Parameters. Technical Report GL-83–13, Geotechnical Laboratory, US Army Engineer Waterways Experiment Station, Vicksburg, MS. Nieble, C.M. and Neto, S.B. (1983) Conceptual geomechanical models: their evolution during the design and construction of dams. Proc. 5th Int. Cong. Rock Mech., Melbourne, ISRM, pp. C213–17. Perlea V.G., Mathews, D.L. and Walberg, F.C. (1997) Rock erosion of unlined spillway chute. Int. Commission on Large Dams 19th Congress, Florence, Q. 75, R. 11, pp. 153–72. Petrovsky, M.B. (1982) Monitoring of grout leaching at three dam curtains in crystalline rock foundations. Proc. Conf. on Grouting in Geotechnical Engineering, New Orleans, ASCE, Geotechnical Eng. Div., pp. 105–19. Powell, C. and Pearson, R. (1993) Coolidge Dam abutment stability and stabilization. Proc. Specialty Conf. on Geotechnical Practice in Dam Rehabilitation, ASCE Geotech. Special Pub. No. 35, Raleigh, NC, pp. 834–49. Pratt, H.K., McMordic, R.C. and Dumas, R.M. (1972) Foundations and Abutments—Bennett and Mica Dams. J. Geotech. Div., ASCE, 98, SM 10, 1053–72 . Rescher, O.J. (1981) Geomechanische Modelluntersuchungen fur die Grundung von Talsperren (Foundation problems of large dams— geomechanical model tests), Rock Mech., 14, 117–66. Rocha, M. (1974) Present possibilities of studying foundations of concrete dams. Proc. 3rd Int. Cong. Rock Mech., Denver, pp. 879–97.

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Rothe, J.P. (1969) Earthquake and reservoir loadings. Proc. 4th World Conf. on Earthquake Engineering, International Association for Earthquake Engineering. Sarma, S.K. (1975) Seismic stability of earth dams and embankments. Geothechnique 25(4), 743–61. Scott, G.A. and Dreher, K.J. (1983) Dynamic stability of concrete dam foundations. Proc. 5th Int. Cong. Rock Mech., Melbourne, ISRM, pp. C227–33. Seed, H.B., Duncan, J.M. and Idris, I.M. (1975) Criteria and methods for static and dynamic analysis of earth dams. In Naylor, D.J., Stagg, K. and Zienkiewicz, O.C. (eds), Criteria and Assumptions for Numerical Analysis of Dams, Swansea, University College, pp. 564–88. Serafim, J.L. (1964) The behaviour of arch dams and their foundations. Proc. 8th Int. Cong. on Large Dams, Edinburgh, ICOLD, Discussion on Q.29, Vol. V. Sheng, C.-K., et al. (1970) Earthquakes induced by reservoir impounding and their effects on the Hsinfengkiang Dam. Proc. 10th Int. Conf. on Large Dams, Madrid, ICOLD. Sherard, J.L., Woodward, R.J., Gizienski, S.F. and Clevenger, W.A. (1963) Earth and Earth-Rock dams. Wiley, New York, pp. 509–62. Spearman, E.L. (1976) Foundation investigation and treatment for TVA dams. Proc. of Specialty Conf. on Rock Eng. for Foundations and Slopes, Boulder, CO, ASCE, Geotechnical Eng. Div., pp. 101–13. Thomas, H.H. (1976) The Engineering of Large Dams. Wiley, New York, pp. 55–8. Underwood, L.B. and Dixon, N.A. (1976) Dams on rock foundations. Specialty Conf. on Rock Eng. for Foundations and Slopes, Boulder, CO, ASCE, Geotechnical Eng. Div., Vol. 2, pp. 125–46. Underwood, L.B., Thorfinnson, S.T. and Black, W.T. (1964) Rebound in redesign of Oahe Dam hydraulic Structures. J. Soil Mech. and Foundation Div., ASCE, 90, SM3. US Army Corps of Engineers (1981) Sliding Stability of Concrete Structures. Technical Letter No. 1110–2– 256. US Army Corps of Engineers (1989) Re-evaluation of the Sliding Stability of Concrete Structures on Rock with Emphasis on European Experience. US Army Eng. Waterways Experiment Station, Vicksberg, MS, Technical Report REMR-GT-12. US Department of the Interior, Bureau of Reclamation (1951) Design Criteria for Concrete Gravity and Arch Dams. Eng. Monograph No. 19. US Department of the Interior, Bureau of Reclamation,

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(1976) Design Manual for Concrete Gravity Dams. A Water Resources Technical Publication. US Department of the Interior, Bureau of Reclamation (1978) Foundation Studies (Design and Analysis of Auburn Dam, Vol. II). US Department of the Interior, Teton Dam Failure Review Group (1980) Failure of Teton Dam, Final Report. Supt. of Documents, US Govt Printing Office, Washington, DC. Wahlstrom, E.E. (1974) Dams, dam foundations and reservoir sites. (Developments in Geotechnical Engineering, Vol. 6), Elsevier S.P. C., Amsterdam, Oxford, New York. Weaver, K.D. (1991) Dam Foundation Grouting. ASCE, New York. Weaver, K.D. (1993) Some considerations for remedial grouting for seepage control. Proc. Specialty Conf. on Geotechnical Practice in Dam Rehabilitation, ASCE Geotech. Special Pub. No. 35, Raleigh, NC, 256–67.

Westergaard, H.M. (1933) Water pressures on dams during earthquakes. Trans, ASCE, 98, 418–33. Wittke, W., Rodatz, W. and Wallner, M. (1972) Three dimensional calculation of the stability of caverns, slopes and foundations in anisotropic, jointed rock, by means of the finite element method. Deutsche Geotechnik, 1(1). Wolff, T.F. (1993) Reliability analysis of navigation structures. Proc. Specialty Conf. on Geotechnical Practice in Dam Rehabilitation, ASCE Geotech. Special Pub. No. 35, Raleigh, NC, pp. 159–73. Xu, L.X., Gong, Z.X. and Lin, W.P. (1983) Sliding stability of foundation rock with shear zones. 5th Int. Cong. on Rock Mech., Melbourne, ISRM, pp. C205– 208. Zienkiewicz, O.C. (1988) The Finite Element Analysis in Engineering Science, 3rd edn, McGraw Hill, New York.

8 Rock socketed piers

8.1 Introduction Socketed piers are constructed in drill holes extending below the structure to depths where sound rock, that can sustain the applied loads, is encountered. They are used where there is no suitable bearing material at the surface and it is uneconomical to excavate this low strength material, and for conditions where structural loads are substantial and permissible settlements small. Loads on drilled piers are usually vertical and compressive. However, inclined and uplift loads can be accommodated with the use of suitable designs and construction methods. Figure 8.1 shows a worm’s eye view of common applications of deep foundations where one high rise building is supported by belled caissons and another by piles bearing on, or socketed into the bedrock. In both these cases, the load is supported in a combination of side-wall shear and end bearing and the full length of the pier is utilized. Another application for drilled piers is to transfer the structural load to a specified depth by ensuring there is no side-wall shear developed. Figure 8.2 shows an example of this type of construction to transfer the building load in piers adjacent to the tunnel to a depth below the invert and avoid inducing stresses on to the tunnel lining. A similar application is shown in Fig. 1.2(c). 8.1.1 Types of deep foundations The essential difference between piles and drilled

piers is in the method of construction. Piles are installed by driving or vibrating the structural member and displacing the ground, while piers are installed by drilling a hole which is then filled with concrete. Drilled piers may be installed entirely in stiff, cohesive soil, or drilled through the soil to end bearing on rock, or drilled (socketed) to some depth into the rock. 8.1.2 Investigations for socketed piers Drilling large diameter holes in rock is expensive and it is important for economy that the length and diameter of the socket are minimized. This will usually require that a thorough investigation of subsurface conditions be carried out to determine the depth to sound rock and the quality of the rock which will be supporting the load. Of particular importance is the identification of geological features such as zones of shattered or weak rock, and clay-filled seams. Where piers are being installed in karstic formations, drilling will usually be required at most or all pier locations to locate possible solution features. These exploration drill holes would have to extend as far as 3 m (10 ft), or two to three times the socket diameter, below the planned bearing level for the end of the socket to ensure that there are no cavities in the bearing area. On one highway project, in a narrow gorge where the rock type was a strong limestone, the piers had to be extended to depths as great as 60 m (200 ft) below the planned depth before competent rock was encountered in which to drill a 2 m (6 ft) deep

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Figure 8.1 Typical installations of belled and rock socketed drilled piers (Macaulay, 1976. Reprinted by permission of Houghton Mifflin Co.).

socket (Kay, 1989). Foundation construction in karstic formations is also discussed in Section 5.3.

Information is also required on the compressive strength of the rock to determine the bearing

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Figure 8.2 End-bearing drilled pier transfers applied load to rock below tunnel invert.

capacity, and the modulus to determine the settlement characteristics. Compressive strength can be measured with laboratory tests on rock cores from which design values for bearing capacity and shear strength can be determined. However, modulus values used in design are the rock mass modulus and it may be necessary to carry out in situ testing, such as pressuremeter tests, to establish design values. Alternatively, a method of relating rock mass modulus to geological characteristics is described in Section 3.2. Information on ground water is also useful in assessing likely construction conditions. The position of the water table will determine whether the shaft will be wet or dry, and the permeability of the rock will determine whether wet shafts can be pumped dry. This information should be evaluated

during design because if it is likely that the shaft will be flooded, then inspection and cleaning of the walls and base of the shaft will be difficult. Consequently, conservative side-wall strength values would be used to account for possible accumulations of cuttings and drill mud on bearing surfaces. 8.2 Load capacity of socketed piers in compression Drilled piers can be designed to support the applied load in: 1. side-wall shear comprising adhesion or skin friction on the wall of the socket; or 2. end bearing on the material below the tip of the

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pier; or 3. a combination of both. Situations where support is provided solely in sidewall shear are where the base of the drilled hole cannot be cleaned so that it is uncertain that any end bearing support will be developed. Alternatively, where sound bed rock underlies low strength overburden material, it may be possible to achieve the required support in end bearing on the rock only, and assume that no support is developed in the overburden. However, where the pier is drilled some depth into sound rock, a combination of sidewall shear and end bearing can be assumed (Kulhawy and Goodman, 1980). 8.2.1 Mechanism of load transfer The relative magnitude of the support developed in side-wall shear and end bearing depends on the following factors. First, the moduli of the materials in which the pier is socketed and that of the pier itself, second, the magnitude of loading in relation to the side-wall shear strength, and third, the method of construction. The mechanism of load transfer and settlement of a socketed pier, and the distribution of support between the sidewalls of the shaft and end bearing is illustrated in Fig. 8.3. In this model all the shaft resistance is replaced by a spring with stiffness ks, and all the end bearing is replaced with a second spring of stiffness kb. The support provided in side-wall shear Qs and end bearing Qb are each equal to the product of the displacement and the (Winterkorn and spring stiffness, i.e. Fang, 1975). In the first case, much of the support is developed in the upper part of the pier, that is, the side-wall resistance per unit displacement is much greater than the end bearing force developed for the same displacement. Thus the spring constant ks is stiffer than the spring constant at the base kb. The deflection of the pier is a combination of elastic shortening of the pier and deflection of the tip. Because most of the deflection occurs in the upper

part of the pier, that is, ds is greater than db, the portion of support developed in side-wall shear is much greater than that developed in end bearing. In the second case, material with very low bearing capacity occurs at the base of the pier, such that the spring constant kb is much less stiff than the spring constant ks. Provided that the applied load does not exceed the shear strength of the side-walls, most of the displacement will occur in the upper part of the pier and the major portion of the load will be carried in side-wall shear. In the third case, the pier has been drilled through material with a low modulus to end bearing on material with much higher modulus, so the spring constant kb is much greater than the spring constant ks. In this case, much of the displacement will occur due to elastic shortening of the pier, and a relatively small amount due to deflection of the high modulus material below the base of the pier. Under these conditions, most of the load is carried in end bearing. 8.2.2 Shear behavior of rock sockets Both theoretical and field studies of the performance of rock-socketed piers show that the major portion of the applied load is usually carried in side-wall shear. The peak shear stress t developed on the walls of the shaft is assumed to behave as a Mohr-Coulomb material as follows: (8.1) where c is the cohesion between the rock and the concrete, a is the normal stress at the rock-concrete is the friction angle of the rock interface, and surface. If the displacement of the pier exceeds the elastic limit of the interface so that the cohesion is lost and the friction angle is diminished to the residual value , the available shear strength is now given by (8.2) Normal stress at the rock-concrete interface is induced by two mechanisms. First, application of a compressive load on the top of the pier results in

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Figure 8.3 Simplified support mechanism for socketed piers showing components of load carried in side shear (Qs and end bearing (Qb) (Winterkorn and Fang, 1975).

elastic dilation of the concrete, and second, shear displacement at the rough surface of the drill hole results in mechanical dilation of the interface. If the stiffness of the material surrounding the socket with respect to normal displacement is constant, then the normal stress will increase with increasing applied load, and there will be a corresponding increase in the shear strength. The degree of mechanical dilation that occurs is

related to the roughness of the walls of the socket, as well as the strength of the rock that forms the irregularities. As shown in equation 3.13, these irregularities tend to be sheared off as the normal stress increases. Therefore, for rock that is significantly weaker than concrete, the roughness of the surface may have little influence on the shear stress developed on the walls of the pier. Simulations of the behavior of rock sockets have

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been carried out in laboratory tests using a constant stiffness direct shear machine (Ooi and Carter, 1987). The test samples consisted of 76 mm (3 in) diameter sandstone cores with concrete cast on one end. The interface between the rock and the concrete consisted of either a smooth surface cut with a diamond saw, or a series of asperities with wavelengths ranging from 10 to 15 mm (0.4–0.6 in) and an amplitude of 2.5 mm (0.1 in). The equivalent roughness angle i of the asperities ranges from 18° to 28°. The uniaxial compressive strengths of the sandstone and concrete were respectively 15–20 MPa (2200– 2900 p.s.i.) and 40 MPa (5800 p.s.i.). The effect of bonding of the concrete to the rock was examined by casting the concrete directly to the rock surface on some of the samples, and by placing a plastic film on the surface of other samples which acted as a bond breaker. Two plots of Ooi and Carter’s test results show (a) typical shear stress-shear displacement curves, and (b) a summary of the relationship between shear and normal stresses for both peak and residual strengths for all rough surfaces, both bonded and unbonded (Fig. 8.4). Note that in Fig. 8.4(b) the ratio of normal and shear stress scales is about 3.5. The conclusions that can be drawn from the test results are as follows. 1. There is a distinct peak shear stress that occurs at a shear displacement of less than 1 mm (0. 04 in) and the residual shear strength occurs at a displacement of about 2–5 mm (0.08–0.2 in). 2. Cohesive bonding between the concrete and the rock has a significant effect on the peak and residual shear strengths as indicated by curve 1 (bonded) and 2 (unbonded). 3. A rough rock-concrete interface has a considerably higher shear strength than a smooth interface (compare curves 1 and 3). 4. The peak shear strength, at low normal stresses, is almost an order of magnitude higher than the residual shear strength (Fig. 8.4(b)), indicative of the significant loss of support that occurs when the bond is broken.

8.2.3 Factors affecting the load capacity of socketed piers Figure 8.5 shows the results of load tests carried out on a socketed pier installed through hard silty clay into highly weathered siltstone at a site in Singapore (Chang and Wong, 1987). These results illustrate typical performance of socketed piers. That is, the distribution of the axial load is highly non-uniform, and the larger portion of the load is carried in the stronger rock while the portion of the load carried in end bearing is relatively small. The performance of rock socketed piers has been studied in laboratory tests, in analytical studies using finite element analysis and in full scale load tests. The laboratory work has studied model piers and has tested the rock-concrete interface to determine the factors that influence the shear resistance (Ladanyi and Domingue, 1980; Pells et al., 1980). The finite element analyses have investigated the influence of socket geometry (length to diameter ratio), and the relative moduli between the concrete and the rock in the walls and base of the socket on both load capacity and displacement (Rowe et al., 1978; Donald et al., 1980; Rowe and Pells, 1980). In many of the full scale load tests, measurements have been made of the portion of the load carried in side shear and that in end bearing. This had been achieved by constructing piers with soft material such as styrofoam at the base to eliminate end bearing, and by casing the socket to eliminate side-wall shear (Seychuck, 1970; Glos and Briggs, 1983). The results of this investigation work have shown that the following factors have a significant influence on the load capacity and settlement of the pier: (a) the geometry of the socket as defined by the length to diameter ratio; (b) the modulus of the rock both around the socket and below the base; (c) the strength of the rock in the walls of the socket and below the pier; (d) the condition of the side-walls with respect to roughness, and the presence of drill cuttings or

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Figure 8.4 Shear behavior of rock-concrete joints tested in constant normal stiffness apparatus (Ooi and Carter, 1987): (a) typical shear stress-displacement curves; and (b) peak and residual strength envelopes.

bentonite cakes; (e) the condition of the end of the pier with respect to the removal of drill cuttings and other loose material from the bottom of the socket; (f) layering in the rock and the presence of seams with differing strengths and moduli.

(g) settlement of the pier in relation to the elastic limit of side-wall shear strength. (h) creep of the material at the rock-concrete interface resulting in increasing settlement with time.

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Figure 8.5 Typical distributions of socket Qs and base Qb loads in rock-socketed piers (Chang and Wong, 1987).

(a) Effect of socket geometry The geometry of a rock socket, which is defined by the length to diameter ratio, has a significant effect on the load capacity of the pier. As the ratio increases from 0, the portion of the load carried in end bearing diminishes and progressively more of the load is carried in side-wall shear. This is illustrated in Fig. 8.6 where, for the condition that the rock has a higher modulus than the pier, almost all the load is carried in side-wall shear at an L/B ratio of 4, while only 50% of the load is carried in side-wall shear at an L/B ratio of 1 (Osterberg and Gill, 1973). The implication of this behavior is that short sockets rely on sound rock at the base of the pier to provide a substantial portion of the support whereas, in long rock sockets, little of the load reaches the base. The typical distributions of load shown in Fig. 8.6 have been confirmed by instrumenting production piers and measuring the stress both at the base and at intervals down the socket for installations is very weak shale (Horvath et al., 1989) and in karstic dolomite (Tang et al., 1994). Section 8.2.3(g) discusses how the loads in the base and socket

change with time after completion of construction. (b) Effect of rock modulus As shown in equations 8.1 and 8.2 the shear stress developed on the side-walls of a socket is partially dependent on the normal stress acting on the rock surface, with the magnitude of this normal stress being directly related to the stiffness of the surrounding rock. Loading of the pier results in some displacement at the rock-concrete interface and for a rough interface surface, where the strength of the rock is such that the asperities are not sheared off, dilation occurs which increases the normal stress at the surface. This increase in normal stress ? s is given by the following equation (Seidel and Haberfield, 1994): (8.3) where E(m) and v(m) are respectively the rock mass modulus and Poison’s ratio and r and ?r respectively are the radius of the pier and the change in radius due to dilation. Another possible method of increasing the normal stress is to use nonshrink cement in the pier to eliminate the shrinkage that occurs as normal cement sets.

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Figure 8.6 Distribution of side-wall shear stress in relation to socket length and modulus ratio (after Osterberg and Gill, 1973).

The relationship in equation 8.3 is illustrated in Fig. 8.6 which shows the distribution of shear stress along the walls of the socket. Where the rock has a the higher modulus than the concrete socket is confined and high normal stresses are developed on the side-wall. As a consequence, a major portion of the load is carried in the upper part of the socket. In contrast, where the rock has a the lower modulus than the concrete normal stresses are diminished and less of the load is carried in shear on the sides of the socket. For the conditions shown in Fig. 8.6, the effect of a reduction in the modulus by one order of magnitude causes the shear stress to be more uniformly distributed down the socket and the base load to increase from about 8% to 30% of the applied load.

The stress distribution down the socket is also influenced by the deformation modulus of the rock at the base of the pier. If the rock has a very low modulus then it will support a negligible portion of the load. Figure 8.7 illustrates two different stress distributions depending on the relative modulus of the rock in the socket, and that below the base. The pier with the low modulus rock in the base has a reduced bearing capacity compared with the pier with sound rock in the base. (c) Effect of rock strength The shear strength developed on the side-walls of sockets and the bearing capacity of the rock below the base of the pier are related to the strength of the rock mass. Where the rock is weaker than the concrete, shear zones will develop down the sides of the socket at a diameter slightly greater than the

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Figure 8.7 Effect of rock modulus at base of pile on distribution of side-wall shear stress (Osterberg and Gill, 1973).

asperities on the walls of the hole. With increasing strength of the rock, the shear strength that can be sustained in the walls of the socket is increased, and when the rock is stronger than the concrete, the limiting shear strength is the strength of the concrete. Figure 8.8 shows the results of load tests on full scale piers. The full line shows the relationship between the ultimate average shear stress tult developed in the side-wall and the uniaxial compressive strength su(r) of the rock, and the dashed line shows the same relationship with a factor of safety of 2.5 applied to the shear stress. The capacity of the walls of the shaft to sustain the applied vertical load is expressed in terms of the adhesion factor a which is given by the ratio t/su(r). For piers installed in the very weak to moderately weak sedimentary rocks, the adhesion factor for ultimate shear stress conditions was found to be (Fig. 8.8). Application of a factor of safety of 2.5 to these results provides an approximate allowable adhesion factor of Further information on the value of allowable adhesion values is provided by test results of full scale piers in weathered sedimentary and granitic rocks in Singapore. It was found that for

rock with compressive strengths in the range 1–5 MPa (145–725 p.s.i.) the allowable adhesion factor (Lueng, 1996) was given by (note: adhesion values given for compressive strength in MPa). The bearing capacity of the base of the pile is related to both the rock strength and the geometry of the socket (Fig. 8.9). Where the base of the pier is at, or close to, the ground surface (Fig. 8.9(a)), a wedge type of failure is developed and the pier undergoes both vertical displacement and rotation. Where the depth of embedment is greater than twice the diameter of the socket (Fig. 8.9(b)) a punching type failure occurs and a truncated conical plug of fractured rock is formed below the base (Williams et al., 1980). Allowable side-wall and end-bearing stress values for use in design of piers are given in Section 8.3. (d) Condition of side walls The laboratory tests of rock-concrete shear strength behavior (Fig. 8.4) clearly show the difference in

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Figure 8.8 Relationship between compressive strength of rock in socket and side-wall shear resistance, or adhesion factor (Williams and Pells, 1981, courtesy of Research Journals. National Research Council Canada). su(r): rock unconfinedcompressive strength; tult: ultimate side-wall shear stress.

shear strength of rough and smooth sockets. Sample 1 in which grooves had been cut on the rock surface shows higher peak and residual stresses than sample 3 which was a saw-cut surface. Similar results had been found in full-scale tests as shown in Fig. 8.10 (Horvath et al., 1983). These tests were conducted in very weak mudstones with uniaxial compressive strengths of about 7 MPa (1000 p.s.i.); RQD values ranged from 29% to 88% and occasional clay seams up to 37 mm (1.5 in) thick were encountered. The sockets were 710 mm (28 in) in diameter and 1.37 m (4.5 ft) long. The sockets were drilled with an auger to produce a relatively smooth side-wall surface. In half of the test sockets grooves were cut which were between 10 and 30 mm (0.4–1.2 in) deep (in the radial direction) and about 10 mm (0.4 in) long (in the axial direction). The load-displacement curves in Fig. 8.10 show that the effect of the grooves is to reduce the displacement by a small amount in the elastic range, but there is significantly less total displacement. In general, the effect of grooving the walls of the socket is to reduce brittle failure, that is, the large displacement that occurs once the elastic range has been exceeded. In production shafts grooves can be cut with a

grooving tool suitable for the rock conditions. For example, the sockets in a very weak sequence of mudstones, siltstones and sandstones with compressive strengths ranging from 3.2 to 11.6 MPa (460–16700 p.s.i.) for the Northumberland Straight bridge in Canada were roughened with rectangular grooves 240 mm (9.45 in) high and 110 mm (4.3 in) deep on a vertical spacing of 1 m (3.3 ft) (Walter et al., 1997). Another significant effect on shear strength of sockets is the presence of loose drill cuttings and bentonite cakes on the side walls of the sockets (Fig. 8.11). Drill cuttings may be removed by washing the socket with water jets, but bentonite cakes are more difficult to dislodge. Where bentonite is used to stabilize the walls of the socket, there is likely to be a cake of bentonite between the rock surface and the concrete. The cake was found to be as thick as 40 mm in sockets excavated in mudstone, while in other cases, the cake was paper thin and did not effect pier performance (Williams and Pells, 1981). To take into account the possible effect of bentonite on the walls of the socket, these tests indicate that the design bond strength should be reduced to about 25% of the value assumed for a

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Figure 8.9 Typical failure mechanism for end-bearing piles (Williams et al., 1980): (a) base of pier bearing at ground surface; and (b) socketed pier with length/diameter>2. 1. Original position of pier. 2. Position of pile after failure of base. 3. Original ground surface. 4. Heave and cracking to 1–1.6 m from pier. 5. Passive zone containing heaved slabs. 6. Plastic zone showing intense fracturing with slickensided surfaces. 7. Conical zone relatively unsheared. 8. Intact rock. 9. Truncated conical plug. 10. Loading column with base plate. 11. Steel casing with concrete base plate.

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Figure 8.10 Comparison of load-displacement behavior for augered and grooved sockets (Horvath et al., 1983, courtesy of Research Journals. National Research Council Canada).

load tests to verify performance. An alternative to bentonite slurries for maintaining wall stability is to use polymer slurries. Polymers do not form mudcakes and so there is improved load transfer at the rock-concrete interface compared with shafts drilled with bentonite. The action of polymer slurries is to increase the effective stress at the borehole wall by increasing the viscosity of the filtrate while a hydraulic gradient is maintained between the slurry column and the water in the rock discontinuities. This action enhances hole stability as long as the pressures in the slurry column exceed the hydrostatic ground water pressure in the formation. However, a possible detrimental effect of polymer slurries is the deposition of drill cuttings in the base of the pier if the suspended solids are not in stable suspension, and settle after clean out is completed (O’Neill and Hassan, 1994). (e) Condition of end of socket If it is assumed in design that load is carried in end bearing, it is essential that the end of the socket be thoroughly cleaned of all drill cuttings and loose rock. If there is a low modulus material in the base of the socket, considerable displacement of the pier

will have to take place before end bearing is mobilized. It is likely that this displacement will cause the peak side-wall shear strength to be exceeded so that the actual bond strength will be the residual shear strength resulting in a diminished load capacity of the pier. Where it is not possible to clean and inspect the end of the socket, it may be necessary to assume that there is no end bearing; this requires that the socket be made long enough to carry the full load in sidewall shear. (f) Layering in the rock Layers of weak, low modulus rock both in the socket and below the base of the pier may influence the load bearing capacity of the pier. In some cases occasional layers may be beneficial to the performance of the pier if they form grooves that increase the effective roughness of the walls of the socket. However, the other effect of low-modulus layers is to reduce both the shear strength and the modulus of the rock mass which will reduce the load capacity of the pier. The effective side-wall shear resistance t* and modulus E* of the layered rock mass can be calculated as the weighted average

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Figure 8.11 Influence of side-wall condition on socket shear strength (Williams and Pells, 1981, courtesy of Research Journals. National Research Council Canada).

of the two materials as follows (Rowe and Armitage, 1987; Thorne, 1980): (8.4) (8.5) where p is the proportion of the shaft which consists of low strength material; ts, Es are the side-wall shear resistance and modulus of low strength material; and tr, Er are the side-wall shear resistance and modulus of the higher strength material. Where the pier will be loaded partially or totally in end bearing, it is important that any low strength layers below the end of the socket are identified. In some cases it may be necessary to drill exploration holes at some or all pier locations to determine the position and thickness of such seams, and also establish criteria for acceptable rock below the socket (Gill, 1980). Soft seams located at distances greater than about three socket diameters below the end of the socket, will probably have little effect on bearing capacity. However, the effect of seams located in the immediate end bearing area of the

socket should be evaluated by the use of equations 8.4 and 8.5, or numerical analysis to examine the specific effect of such layers. (g) Creep One of the few available records of the load and displacement performance over time of socketed piers is provided by Tang et al. (1994) and Drumm (1998). This study examined three piers drilled through residual soil with thickness ranging from 3. 07 m to 17.8 m (10.1–58.7 ft) and socketed into hard, grey dolomite containing enlarged joints and etched pits which formed extremely irregular pinnacles. The depth of the rock sockets ranged from 8.97 to 6.4 m (29.5–21 ft) and the axial design load varied from 10 600 to 12 600 kN (2380–2830 kips) (Fig. 8.12). Figure 8.12 (a) shows the stresses at the top and base of one pier for a period of 2000 days and Fig. 8.12(b) shows the change in the distribution of stresses down the shaft over the same time period. The proportion of the load carried in end loading

LOAD CAPACITY OF SOCKETED PIERS IN COMPRESSION

varied from 14% to 19% of the load at the top of the pier. While the strain gauges in shaft showed increasing load with time, the load cell at the base showed mininal load increase after construction was complete. Similar performance has been reported by Ladanyi (1977) for a 0.89 m (35 in) diameter pier socketed to a depth of 4.57 m (15 ft) in horizontally bedded, fractured shale. The total applied load was 9.15 MN (2060 kips) and the design values for side-wall shear resistance and end bearing were 1.035 MPa (150 p.s.i.) and 4.83 MPa (700 p.s.i.) respectively. The load in end bearing was monitored over a period of nearly four years and the results showed that this load increased by about 65% after the end of construction. However, at the end of this period only about 10% of the applied load was being carried in end bearing. The likely mechanism for the change in load with time is the gradual shedding of the side-wall resistance in the more highly stressed upper part of the socket, with a corresponding increase in the base load. This load adjustment takes place at stresses which are well below the peak stress so there is no significant displacement of the pier. 8.2.4 Socketed piers in karstic formation Where socketed piers are to be installed in karstic formations, the detailed geology must be investigated to ensure that the end is not bearing on a rock pinnacle, or thin seam of rock above a cavity. If cavities are suspected, exploration drill holes would be required, with a hole at every pier, extending to below the planned bearing level, if conditions vary across the site. This may result in different designs being prepared for each pier to suit the local geological conditions. If the bearing surface at the tip is sloped, the bearing capacity may be improved by cutting a bench, or by installing steel dowels into holes drilled into sound rock (Sowers, 1976). Alternatively, the hole can be extended to more competent rock. Cutting a bench will often require dewatering of the caisson, which

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may be difficult where the upper part of the hole passes through soil which could blow in if a steep hydraulic gradient is developed. See also Section 5.3 for more detailed discussions on foundation construction in karstic terrain. 8.3 Design values: side-wall resistance and end bearing Rock socketed piers can be designed to carry compressive loads in side-wall shear only, or end bearing only, or a combination of both. The most important factors that influence the design procedure are the strength, degree of fracturing and modulus of the rock, the condition of the walls and base of the socket, and the geometry of the socket. 8.3.1 Side-wall shear resistance In determining the load capacity in side-wall shear, the simplifying assumption is made that the shear stress t is uniformly distributed down the walls of the socket and the allowable load capacity is given by the following equation: (8.6) where Q is the total applied load; ta is the allowable side-wall shear stress; B is the diameter of socket, and L is the length of socket. The diameter of the socket is usually determined by the type of drilling equipment that is available, and the length is selected so that average side-wall shear stress is not greater than the allowable shear stress, and that the design settlement is not exceeded. An approximate correlation between the observed side-wall shear stress, expressed in terms of the adhesion factor and the strength of the rock in the sockets of test piers is shown in Fig. 8.8. These results, together with additional tests, have been used to develop the following equations relating the approximate allowable side-wall resistance ta (in MPa) and unconfined compressive rock strength su(r) (in MPa) for smooth and grooved sockets (Rowe and

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Figure 8.12 Variation in load distribution in socketed pier with time: (a) shaft stress versus time in relation to construction progress; and (b) vertical stress distribution and geological profile of socketed pier (data provided by E. Drumm, University of Tennessee, 1998).

Armitage, 1987). For clean sockets, with side-wall undulations between 1 mm and 10 mm deep and less than 10

mm wide (0.04–0.4 in deep, <0.4 in wide):

LOAD CAPACITY OF SOCKETED PIERS IN COMPRESSION

(8.7a) or (8.7b) For clean sockets, with side-wall undulations greater than 10 mm deep and 10 mm wide (>0.4 in deep, >0.4 in. wide): (8.8) Values for the adhesion factor a (t/(su(r)) as defined in Fig. 8.8, may be available from test piers at the site or from tests in similar geological conditions. The factor of safety FS included in equations 8.7 and 8.8 relates the ultimate to the allowable shear resistance, and takes into account the many factors that can influence the side-wall shear resistance as discussed in Section 8.2.3, as well as uncertainty in the construction quality. As shown in Fig. 8.8, a factor of safety of 2.5 relates the ultimate to allowable stress values in these test piers. However, where the rock is closely fractured so that the rock mass in the walls of the socket tends to be loose and have a low deformation modulus, the values for ta should be reduced from the value given in equations 8.7 and 8.8. This will allow for the lower confining pressures developed around the socket. A limited amount of test data indicates that ta should be reduced by as much as 40% where the modulus of the rock mass is approximately one fifth of the modulus of the intact rock (Williams and Pells, 1981). Use of equations 8.7 and 8.8 with an appropriate factor of safety will usually result in the pier behaving elastically with minimal risk of excessive settlement. The small difference between these two equations shows that the roughness of the side-walls has little influence on the shear resistance when the applied shear stresses are well within the elastic limit (see Fig. 8.10). The main value of roughened sockets is in minimizing settlement if this is critical to performance of the pier. At sites where there are a large number of piers to be installed, or in geological conditions where there

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is little previous experience in this type of installation, load tests are often justified to determine actual design values for side wall shear strength. The tests may save significant construction costs if the test strength is shown to be higher than the conservative value assumed in the design. For example, load tests using an Osterburg hydraulic cell to apply the load were carried out on a 0.91 m (3 ft) diameter pier installed in a very weak sequence of mudstones, siltstones and sandstones for the Northumberland Strait bridge (Walter et al., 1997) In order to test two rock types within a single pier, the pier was cast with a styrofoam plug in the base and the Osterburg cell was located between the upper and lower test sections of the concrete pier. The procedure was to first test the upper, shorter test section, then to cast an additional concrete plug on the top of the socket and re-apply the load to test the lower section. Tests were carried out to find the working and ultimate shear strengths, as well as cyclic tests to check that there was no loss of adhesion with expected ice loading conditions. The test results confirmed that the working strengths were close to those found for similar materials, and the final design socket length was about 55% of the length calculated in the preliminary design. 8.3.2 End-bearing capacity As illustrated in Fig. 8.9, a highly loaded, endbearing socket may fracture a cone of rock beneath the end of the pier which will result in excessive settlement. However, tests piers have been loaded to base pressures as high as three and even ten times the compressive strength of the rock without collapse (Williams, 1980). Test results demonstrate that allowable load capacity Qa, which includes a factor of safety of about 2–3, at the base of the pier is (Rowe and Armitage, 1987): (8.9) where su(r) is the uniaxial compressive strength of rock at the base of pier; and B is the diameter of

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ROCK SOCKETED PIERS

base of pier. Equation 8.9 is applicable provided that the following three conditions are met: 1. The base of the socket is at least one diameter below the ground surface. 2. The rock to a depth of at least one diameter below the base of the socket is either intact or tightly jointed (no compressible or gouge filled seams). 3. There are no solution cavities or voids below the base of the pier. For conditions where the rock below the base of the pier contains horizontal or near horizontal seams infilled with material of lower strength than the bearing rock, the allowable end-bearing capacity is reduced from that given in equation 8.9 and can be found from: (8.10) where (8.11)

and for socket length L, diameter B, (8.12) The characteristics of the seams are defined by their spacing S and thickness t if filled with rock debris or soil. The term K' is applicable for , and .The factor K' includes a nominal factor of safety of 3 against the lowerbound bearing capacity of the rock foundation (Canadian Geotechnical Society, 1992).

8.4 Axial deformation 8.4.1 Settlement mechanism of socketed piers This section describes procedures for calculating the vertical settlement of socketed piers for three different construction methods: 1. side-wall resistance only; 2. end bearing only; 3. combined side-wall resistance and end bearing. The design methods can accommodate rock with differing moduli in the socket and base of the pier, as well as sockets which are recessed below the surface. The settlement calculations have been developed from finite element analyses (Pells and Turner, 1979; Rowe and Armitage, 1987), the results of which have been checked against settlements of full scale load tests (Horvath et al., 1989; Chiu and Donald, 1983). Axial deformation of a socketed pier, with increasing load, is a three stage process as follows. 1. Deformation starts with elastic compression of the pier where it is not bonded to the rock, and elastic shear strain at the rock-grout interface. Under these conditions the deformation is small and the major portion of the applied load is carried in side-wall shear. The pier exhibits elastic behavior during this stage of the loading. 2. Slippage starts at the rock-concrete interface and an increasing portion of the load is transferred to the base of the pier. 3. At increasing displacement, the rock-concrete bond is broken and a constant frictional shear resistance is developed on the walls of the socket; an increasing load is carried in end bearing. At this level of displacement, slip occurs on the wall of socket and the side-wall resistance exhibits plastic behavior.

LOAD CAPACITY OF SOCKETED PIERS IN COMPRESSION

Although methods of calculating vertical displacement have been developed for both elastic and plastic behavior of socketed piers (Rowe and Armitage, 1987), the usual design practice is to assume elastic conditions that occur at small settlements. In calculating elastic settlement it is assumed that the pier consists of an elastic inclusion welded into the surrounding rock and that no slip occurs at the rock-concrete interface. Under these conditions, the displacements are small, and end bearing resistance is not fully mobilized. As illustrated in Fig. 8.13, there are a number of different socket conditions depending on the geology of the site and the construction method of the pier. The condition of the socket determines the load transfer mechanism from the head of the pier to the side walls and base, and calculation of settlement requires the use of influence factors appropriate for each condition. Influence factors are provided for the following four socket conditions: 1. side-wall shear resistance only (Figs. 8.14, 8.15); 2. end bearing only (Fig. 8.16); 3. side-wall resistance and end bearing for a socket in a homogeneous rock (Fig. 8.17); 4. side-wall resistance and end bearing where the rock in the walls and the base have differing moduli (Fig. 8.17). 8.4.2 Settlement of side-wall resistance sockets Socketed piers that support the applied load in sidewall resistance only may be constructed where the base of the drill hole cannot be cleaned out effectively, or where the rock in the base has little bearing capacity, such as karstic limestone or very weak shale. The general equation for settlement d of the top of a socketed pier with side shear resistance, at the surface of a semi-elastic half space is: (8.13) where Q is the applied load; B is the diameter of socket; Em(s) is the modulus of deformation of rock

287

mass in the shaft; and I is the settlement influence factor given in Fig. 8.14. Values of the rock mass deformation modulus have been back-analyzed from observations of the settlement of socketed piers and the following correlation between the modulus and the uniaxial compressive strength of the rock su(r), incorporating a factor of safety of approximately 2, has been proposed (Rowe and Armitage, 1987): (8.14) Note that in making an assessment of the value of the rock modulus, the degree of fracturing of the rock mass must be considered. Reference to Fig. 3.10 shows the relationship between the characteristics of the rock mass and the modulus of deformation; more highly fractured rock will be able to deform more readily and there will be less confinement on the socket. Where the rock is highly fractured, judgment will be required to assess whether it is necessary to reduce the rock mass modulus calculated using equation 8.14. Settlement calculated using equation 8.13, with the value of the influence factor I being related to the socket geometry L/B and the modulus ratio R, given in Fig. 8.14. These values have been calculated for a Poisson’s ratio of 0.25; it has been found that variations in the Poisson’s ratio in the range 0.1–0.3 for rock and 0.15–0.3 for the concrete have little effect on the influence factors. The values for the influence factors shown in Fig. 8.14 assume that the socket is fully bonded from the rock surface. However, influence factors will be reduced where the pier is recessed below the ground surface because the rock around the socket is more confined and the normal stress at the concrete surface is increased. Recessed sockets are formed by casing the upper part of the hole, or for conditions where the socket passes through a layer of weathered rock where there is little or no side-wall shear resistance developed. For a recessed socket, the settlement is given by (8.15) where RF is a reduction factor given in Fig. 8.15.

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Figure 8.13 Summary of methods of calculating elastic settlement of side-wall sockets, end bearing piers and complete socketed piers.

8.4.3 Settlement of end loaded piers Where the shaft of the pier is cased such that no

side-wall shear is developed and the load is entirely

LOAD CAPACITY OF SOCKETED PIERS IN COMPRESSION

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Figure 8.14 Elastic settlement influence factors for side-wall resistance socketed pier (Pells and Turner, 1979, courtesy of Research Journals. National Research Council Canada).

supported in end bearing, the settlement is calculated in a similar manner to that of a footing on the surface. However, the settlement of the pier will be less than that of a footing at the surface because the rock in the bearing area below the base of the pier is more highly confined than the surface rock. This confinement is accounted for by applying a reduction factor to the settlement equation. The value of the reduction factor depends on the ratio of the depth of embedment D to the diameter of the pier B, and the relative stiffness of the pier and the rock. If the ratio of the pier modulus to the rock , then modulus is greater than about 50 the pier can be considered to be a rigid footing, while if the ratio is less than 50, the pier can be considered as a flexible footing. Values of the socketed piers: reduction factor are given in Fig. 8.16 for both flexible and rigid circular footings; these reduction factors are for the average settlement of the footing. Using the reduction factors given in Fig. 8.16, the equation for the settlement of an end bearing pier, including the elastic compression of the pier itself is (8.16) where Ec is the concrete modulus; RF' is the

reduction factor for an end bearing socket; D is the depth of pier; Cd is the shape and rigidity factor as given in Table 5.6 (since piers are usually circular in shape, the values for Cd for average settlement are 0. 85 of flexible footing, and 0.79 for a rigid footing). Q is the foundation load; Em(b) is the deformation modulus of the rock mass in the pier base; B is the pier diameter, and v is the rock mass Poisson’s ratio. 8.4.4 Settlement of socketed, end bearing piers Reference to Fig. 8.6 shows that a portion of the load on a socketed pier is carried in end bearing, and that the end bearing load is related to the socket geometry and the rock modulus. For these conditions, settlement is calculated using equation 8. 13, using influence factors for an end bearing socketed pier given in Fig. 8.17. These curves have been developed for elastic behavior with no slip along the side-walls (Rowe and Armitage, 1987). The three sets of curves in Fig. 8.17 show the effect on the influence factors of differing moduli between the rock in the base, and the rock in the socket (Em(b)/ Em(s)). Comparison of Fig. 8.17 (for

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Figure 8.15 Reduction factors for calculation of settlement of recessed sockets (Pells and Turner, 1979, courtesy of Research Journals. National Research Council Canada).

Figure 8.16 Reduction factors for calculation of average settlement of end bearing sockets (Pells and Turner, 1979, courtesy of Research Journals. National Research Council Canada).

with Fig. 8.14 shows that the influence factor for a side-wall shear/end-bearing socket has a larger value than a socket with no end bearing which demonstrates that a pier with end bearing on a

clean, sound rock surface will settle less than a pier with side-wall resistance only. The three sets of curves in Fig. 8.17 also show that settlement will diminish with increasing modulus of the rock at the

LOAD CAPACITY OF SOCKETED PIERS IN COMPRESSION

base. Where a portion of the applied load is carried in end bearing, it is necessary to check that this load does not exceed the bearing capacity of the rock in the

base. The percentage of the load carried in end bearing can be determined from the lower half of Fig. 8.17, from which the pressure on the rock in the base of the pier can be calculated.

EXAMPLE 8.1 DESIGN OF ROCK SOCKETED PIERS

The following are examples of the design procedures for the different types of socketed piers discussed in this chapter. Consider a pier with a diameter B of 1.5 m and a vertical compressive load Q of 10 MN. Assume that the concrete has a modulus Ec of 20 GPa, and that the compressive strengths of the rock in the socket and base of the pier are as follows: socket compressive strength=2 MPa base compressive strength=20 MPa base Poisson’s ratio=0.25. SIDE-WALL SHEAR RESISTANCE ONLY Assume that the hole is drilled with an auger and that the rock is sufficiently massive that it is not required to use bentonite to stabilize the walls of the hole. Furthermore, equipment is not available to groove the walls so the drill hole has no significant roughness. For the

condition that the base of the socket cannot be cleanedso that no end bearing will be developed, it is necessarythat the socket be long enough to carry the full appliedload in side-wall shear. From equation 8.7 the workingbond stress for rock with a compressive strength of 2MPa and a smooth, clean socket is 0.35 MPa. The required socket length L is calculated from equation 8.6as follows, assuming that the average bond stress developed over the full length of the socket is 0.35 MPa:

The settlement of the head of the pier, assuming elastic behavior is calculated from equation 8.13, using Fig. 8.14 to determine the influence factor I and equation 8.14 to determine the rock modulus . In Fig. 8.14 the ratio and the length-to-diameter , which gives an influence factor of 0.26. The settlement is given by: ratio L/B is

where

291

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Figure 8.17 Elastic settlement influence factors and end-bearing ratios for complete socketed piers (after Rowe and Armitage, 1987, courtesy of Research Journals. National Research Council Canada).

If the pier is cased through an upper 3 m thick layer of soil (new total length=9 m), then the settlement calculation is modified as follows. A reduction factor RF is applied to the elastic settlement of the socket as given in Fig. 8.15. For a value of D/B of and a modulus ratio, for RF is approximately 0.8. Therefore the elastic settlement of the socket is:

, the value

To this settlement must be added the elastic compression of the recessed, 3 m length of the pier which is equal to 0.9 mm. END BEARING PIER Assume that the purpose of the pile is to transfer the applied load to the rock at a depth of 6 m below the ground surface as shown, for example, in Fig. 8.2. In these circumstances the socket would be cased through the rock and the entire load would be carried in end bearing. The applied bearing pressure s on the end of the pier is:

LOAD CAPACITY OF SOCKETED PIERS IN COMPRESSION

As shown in equation 8.9, the allowable bearing pressure, including a factor of safety against fracture of the rock of about 3, for an end bearing pier is equal to the uniaxial compressive strength of the rock. The compressive strength of the rock below the base of the pier is 20 MPa so the entire applied load of 10 MN can be safely carried in end bearing. The settlement of an end bearing pile is calculated from equation 8.16, using Fig. 8.16 to determine the reduction factor RF. The ratio of the concrete modulus to the modulus of the rock below the base is i.e. less than 50, so it can be assumed that the base of the pier will act as a flexible footing. The reduction factor for a flexible footing on a rock with a Poisson’s ratio of 0.25 and a depth to diameter ratio, , is 0.7. The settlement is calculated as follows

These calculations show that settlement due to compression of the pier is small compared with the compression of the rock below the base. SOCKETED AND END-BEARING PIER For a pier fully socketed into the rock, the end of which is bearing on a clean, sound rock surface, the load will be supported in both side-wall shear and end bearing. Under these conditions the socket length can be significantly shorter than where the load is supported only in side-wall shear. A design procedure for this type of pier is first to select a socket length which is less than that required to carry the full applied load in side-wall shear resistance, and then use Fig. 8.17 to determine the settlement influence factor and the end-bearing load. For a socket length of 4 m, L/B is 2.7 and from the upper half of Fig. 8.17(a) the influence factor I is about 0.18 when . The settlement is calculated from equation 8.13 as:

The portion of the load carried in end bearing can also be determined from Fig. 8.17(a). By down to intersect extending a vertical line from the point on the horizontal axis where the ratio Qb/Q is found to have a value of about 40%. the line representing the ratio Therefore, the load carried in end bearing is 4 MN and the load carried in side-wall shear is 6 MN. Having determined the socket length to achieve a specified settlement, the final task is to ensure that the side-wall and end bearing stresses do not exceed allowable values as specified by equations 8.7 and 8.9 respectively. An alternative design procedure is to calculate an influence factor from an allowable settlement value and then use Fig. 8.17 to determine the required socket length. Inspection of Fig. 8.17 shows that it will not always be possible to achieve an intersection between the Ec/Em(s) lines and the horizontal line drawn from the required value of the influence factor. If there is no intersection between the horizontal line

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ROCK SOCKETED PIERS

drawn from the I axis and the modulus ratio curve Ec/Em(s), then the design value for the influence factor cannot be achieved. It is then necessary to modify the design as follows. For conditions where the design influence factor is too small for an intersection point, it would be necessary to increase the allowable settlement, or decrease the pier load by installing more piers. For conditions where the design influence factor is too high for an intersection point, this would indicate that the allowable settlement is high and slip will occur along the shaft. If the load on the pier is high enough to cause slip, then the pier will no longer behave elastically and plastic shear will occur along the socket. If the value for I is too low to achieve an intersection, then the required settlement is too small for the conditions and either a greater settlement must be accepted or a larger pile diameter used.

8.4.5 Socketed piers with pre-load applied at base The application of a pre-load stress at the base of an end bearing socketed pier has the effect of reducing settlement, and this technique may be used where the rock is poor or where settlement tolerances are minimal. The upward movement of the pier when the pre-load is applied at the base causes a reduction of the load supported by shaft resistance and a more uniform distribution of load down the shaft, the effect of which is to improve the load-settlement behavior. Pre-loading the base of a pier will have no significant effect on the load capacity unless consolidation grouting of the rock below the base of the pier is carried out. Pre-loads have been produced by installing a load cell at the base of test piers (Horvath et al., 1983; Meyer and Schade, 1995), and by pressure grouting the base (Simons, 1963; Taylor, 1975). In the project described by Meyer and Schade, an Osterburg hydraulic cell was placed in the base of piers up to 1.32 m (52 in) diameter drilled into soil which were then loaded to compress the material beneath the base of the pier. This procedure also tested the side-wall shear of the piers which showed that it was possible to reduce the length of the socket by about 10 m (30 ft) from that assumed in the design. Furthermore, the piers supported the 8.9 MN (2000 kip) service load with only 12 mm (0.5 in) of settlement. In the project described by Taylor, pressure grouting was used at a site where six out of a total of 22 piers were socketed into a volcanic agglomerate

comprising basalt gravel and boulders in a matrix of weathered ash, while the remainder were end bearing on sound basalt. The piers in the agglomerate were belled to increase the bearing capacity and then the base was pressure grouted to limit settlement. The pressure grouting procedure was to place a layer of clean gravel at the base of each pier, and then cast the concrete with grout pipes extending through the pier to the base. Grout was pumped into the gravel at the base, before application of the structural load, at a pressure equal to the maximum calculated bearing stress, including earthquake loading. Some uplift of the piers was observed during grouting, but this was limited by the side-wall shear resistance of the socket. The objective of this procedure was to induce settlement in the base of the pier prior to application of the structural load. This was considered to be successful in that settlements of the piers socketed into the agglomerate was no greater than that of the piers founded on sound basalt. 8.5 Uplift Uplift loads on socketed piers can result where elevated structures are subjected to horizontal loads. Examples of structural uplift loads are tall transmission towers where the tower forms a point of intersection between two sections of tangent line, and some members of dock structures that must withstand ship impacts. Another condition where uplift forces may be

LOAD CAPACITY OF SOCKETED PIERS IN COMPRESSION

developed are piers drilled through expansive soils and then socketed into rock. Swelling of the soil can grip and lift the shaft developing tensile stresses in the pier. Swelling pressures in clay can be as high as 2 MPa (300 p.s.i.), and free swell of such a soil may amount to 20% or more of the thickness of the zone of active heaving. There are examples of unreinforced pier shafts breaking in tension in areas where swelling soils are prevalent, with the break often occurring immediately above the base or underream (Woodward et al., 1972). Figure. 8.18 shows a design suitable for use in areas of swelling clays. The reinforcement for the pier consists of a concrete-filled steel pipe which has the capacity to carry the applied compressive load. The outside of the pipe down to the bottom of the expansive layer is coated with bituminous mastic. When the pier is gripped and lifted by the expansive clay, the mastic coating flows and the upward force in the pier is limited to the shear strength of the mastic. In many circumstances where substantial uplift loads occur, the most economical design is often the installation of tensioned anchors as described in Chapter 9. The advantage of the use of tensioned anchors is that they can be installed in smaller diameter holes than socketed piers and by applying a pre-load, the uplift displacement can be controlled. Socketed piers can be designed to resist uplift forces either by enlarging or belling the base, or by developing sufficient side-wall shear resistance. While belling the base of a pier is common in soils, this can be an expensive and difficult operation in rock. Moreover, since a significant amount of sidewall shear resistance is developed in rock sockets, it is usually more economical to deepen the socket than to construct a shorter, belled socket 8.5.1 Uplift resistance in side-wall shear Uplift load tests have been performed on side-wall resistance socketed piers to determine their load displacement behavior and the ultimate load capacity (Webb and Davies, 1980; Kulhawy, 1985; Garcia-Fragio et al., 1987). The results of tension

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tests conducted by Webb and Davis on concrete piers socketed into very weak sandstone have been compared with the results of compression tests (refer to Fig. 8.10). The two sets of curves have similar shapes within the linear elastic range. However, as the uplift load increases and the side-wall bond begins to break down, the tension pier undergoes large deformations and eventually fails, compared with the compression pier where settlement is limited because an increasing proportion of the load is taken in end bearing. The results of load-displacement tests performed on tension piers can be used to calculate the shear stress developed on the side-wall, and the actual displacement can be compared with the theoretical displacement calculated from elastic theory for compression piers. The tests by Webb and Davies indicate that equation 8.7 can be used to estimate side-wall shear strength for tensile loads provided that there is no tendency for a cone of rock at the surface to break out around the pier; this requires a length:diameter ratio of at least two (see Section 9.3.4). The measured displacements of the piers tested in tension by Webb and Davies have been compared with theoretical settlements for compression tests calculated from elastic theory using equation 8.13 (for fully bonded sockets), and equation 8.15 (for recessed sockets), and the influence factors given in Figs 8.14 and 8.15 respectively. It is found that the measured displacement of the socket, taking into account the elongation of the shaft, is within about 30% of the displacements calculated by elastic theory for compression piers. An example of a full scale testing program of uplift capacity of concrete piers socketed into rock is described by Yoshii (1995) for a transmission line project constructed in steep, mountainous terrain. The towers were 110 m (360 ft) high and the four supporting piers were each 20 m (66 ft) deep and up to 3.5 m (11.5 ft) in diameter. The sockets were excavated by pipe clamshell and manual labour. The loads on the foundations were due to the tower and cable weights, the cable tension and wind forces which produced a combination of

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Figure 8.18 Design of belled pier for relief or uplift due to expansion of upper clay layer; the outer layer of concrete is expected to break in tension near the bottom of the expansive layer. (by Raba-Kistner Consultants Inc. (Woodward et al., 1972)). Note: Pipe must develop sufficient bond below rock level to transfer column load and uplift forces to concrete shaft and footing.

compressive, uplift and lateral loading. Part of the design work comprised uplift tests on test piers 8 m (26 ft) long and 2.5 m (8.2 ft) in diameter, with the load applied with a hydraulic jack installed within the base of the pier. The rock in the socket was a weathered granite with a cohesion of 2–20 kPa (0.3– 2.9 p.s.i.) and a friction angle of about 45°. The tests showed that the socket behaved elastically up to the design load of 11 MN, and achieved an ultimate load of 17 MN (3820 kips). The average shear stresses generated on the walls of the socket at these two loads were 175 kPa and 270 kPa respectively (25 and 39 p.s.i.). These stresses for piers in very weak rock can be compared with allowable and ultimate shear stresses presented in Fig. 8.8 (compression) and Table 9.2 (tension). In conclusion, it is suggested that preliminary design of tension piers, or piers that are only occasionally subjected to tensile loads, can be carried out using the equations that have been developed for the design of compression piers.

However, for piers with substantial tensile loads, or dynamic tensile loads, full scale load tests may be performed to determine the allowable side-wall shear resistance and the load-displacement behavior. 8.5.2 Uplift resistance of belled piers In weak rock it is possible to bell the base of the pier either to increase the bearing capacity of a compression pier, or to resist uplift in the case of a tension pier. The uplift capacity of a socketed pier is calculated as follows (FHWA, 1988) and is based on the breakout theory for discs (Vesic, 1971). The side-wall shear resistance above the bell should be discounted, and the pier should be designed as an anchor, for which the net upward bearing capacity is (8.17) where Ab, the area of bearing surface of the bell is

LOAD CAPACITY OF SOCKETED PIERS IN COMPRESSION

given by (8.18) Bb is the diameter of bell, Bs is the diameter of shaft, Nu is the uplift bearing capacity factor and tb is the shear strength of rock mass (see equation 3.15). The value of the uplift bearing capacity factor Nu depends on the ratio z/Bb, where the dimension z is defined in Fig. 8.19. This assumes that the base of the layer of expansive soil acts as a free surface: When and when These values for Nu are for intact or slightly fractured rock; for closely fractured rock Nu should be reduced by an appropriate amount determined by the designer (FHWA, 1988). 8.6 Laterally loaded socketed piers Lateral loads on socketed piers may be derived from wind pressures, current forces from flowing water, wave action, earthquakes, and in the case of bridges, centrifugal forces and braking forces from moving vehicles (Fig. 8.20). Other causes of lateral loading are impacts from ships in the case of docks and dolphins, and rock and soil pressures where the pier is used to reinforce a slope (Oak-land and Chameau, 1989). The capacity of a socketed pier to withstand lateral loads depends on the rigidity of the pier, as well as the load-deformation characteristics and formation thicknesses of the rock and soil in which the pier is socketed (Carter and Kulhawy, 1992). For a pier that passes through a soft soil and is then socketed in sound rock, even a short embedment length in the rock can have a significant effect on the lateral deformation. Poulos (1972) describes a method of calculating the displacement of laterally loaded piles using elastic theory. This analysis examines the difference in deflection between pinned-tip piles that bear on the rock surface and are

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free to rotate but not translate, and fixed-tip piles that are socketed into the rock and neither rotate or translate. The analysis shows that the lateral deflection for fixed-tip piles can be considerably less than that of pinned-tip piles. For a pier that is fully embedded in rock with a higher modulus than that of the pier material, the lateral deformation at the rock surface will be primarily a function of the pier modulus and deformation is likely to be minimal. This is generally a stable condition, except where the rock contains shallow dipping fractures forming blocks that could move under the application of the horizontal load (refer to Fig. 8.25). The force exerted on the blocks of rock can be calculated using p-y curves (see Section 8.6.1). The results can be used to determine the required capacity of rock anchors that should be installed to prevent movement. 8.6.1 Computing lateral deflection with p-y curves The most widely used procedure for designing laterally loaded piers is the p-y method. The following is a description of the principle of this method; analyses usually involve the use of computer programs such as COM624 (FHWA, 1986) and LATPILE (University of British Columbia, 1985) which use similar algorithms. Details of the analysis procedure and applications of these programs, which is beyond the scope of this book, are provided in the program documentation. Application of a lateral load to a socketed pier must result in some lateral deflection. The lateral deflection will, in turn, cause a reaction in the surrounding rock and soil that acts in the opposite direction to the deflection. The magnitude of the reaction in the rock or soil is a function of the deflection, and the deflection is dependent on the soil-rock reaction. Thus, calculating the behavior of a socketed pier under lateral load involves the solution of a soil-rock-structure interaction problem. In this solution, two conditions must be satisfied: the equations of equilibrium, and

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Figure 8.19 Belled piers to resist uplift forces due to (a) expansive soils, (b) tensile loads.

compatability between deflection and soil-rock reaction. This method of analysis can be extended beyond the elastic range to analyze movements where the soil or rock yields plastically and ultimately fails in shear. This can be modeled using p-y curves which represent: 1. the lateral deformation y of the soil and rock at any given depth below the ground surface; and 2. horizontally applied rock and soil reactions p (units kN/m or lbf/ft) ranging from zero to the stage of yielding of the rock-soil in ultimate shear when the deformation increases without any further increase in the load. The p-y curves are independent of the dimensions, shape and stiffness of the pier and represent the deformation of a discrete slice of the soil and rock surrounding the pier that is unaffected by loading above and below it (Tomlinson, 1977). A model for a laterally loaded socketed pier

demonstrating the concept of p-y curves is shown in Fig. 8.21. Each layer of soil and rock has been replaced with a spring, and the load-deformation behavior of each spring is represented by a p-y curve (Fig. 8.21(b)). The rock or soil reaction p (force per unit length down the socketed pier) is a function of the lateral deflection y. The p-y curves in Fig. 8.21(b) show the yielding and increasing modulus of the soil in the portion of the pier drilled through soil, and the higher modulus, elastic behavior of the rock in the socket. The deflected shape of the pier is superimposed on the p-y curves, and the deformation modulus of the soil is given by the secant to the p-y curve at the corresponding deflection. Figure 8.21 (c) shows that the modulus is defined as the ratio and the modulus increases with depth. The deflection of the pier can be modeled most accurately by defining a p-y curve at the top and bottom of each layer since the program interpolates soil behaviour between each pair of given points. The general behavior of a socketed pier under lateral

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Figure 8.20 Typical conditions resulting in lateral loads on socketed piers: (a) socketed piers installed to stabilize failing slope; and (b) loadings on single-column support for a bridge (FHWA-IP-84–11).

load can be obtained by solving the following differential equation (Hetenyi, 1946): (8.19) where Qx is the axial load on the pier; y is the lateral deflection of the pier at a point x along the length of the shaft; p is the lateral soil reaction per unit length of pier; EI is the flexural rigidity of pier with modulus E and moment of inertia I; I equals pr4/4 for circular pier with radius r; and W is the distributed horizontal load along the length of the shaft. Other beam formula which are used to calculate the shear stress in the pier V, the bending moment M, and the slope of the elastic curve S are (8.20) (8.21)

(8.22) Calculation of the deflected shape of a laterally loaded pier, as well as the shear and bending moment in the pile involves an iterative process comprising the following steps. 1. The deflected shape of the pier is assumed by the computer. 2. The p-y curves are entered with the deflections and a set of modulus values is obtained. 3. With the modulus values, the differential equations defining the behavior of the pier are solved to obtain a new set of deflections. 4. Steps 2 and 3 are repeated until the deflections obtained are within the given tolerances of the values obtained from the previous computation. 5. Bending moment, shear and other aspects of the behavior of the pier are then computed.

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Figure 8.21 Model of a socketed pier under lateral load showing the concept of soil response: (a) reaction of rock and soil layers replaced by springs; (b) stress-strain curves; (c) increase in modulus with depth.

The procedure for constructing p-y curves for clays and granular soils, above and below the water table, for both static and dynamic loading, as well as for weak rock, has been developed by Reese (Reese et al., 1974; FHWA, 1986; Reese, 1997). The procedure consists of first calculating the ultimate resistance pult of the soil and rock, and then calculating the modulus from laboratory tests,or using empirical relationships between rock mass characteristics and modulus (Fig. 3.10). Alternatively, p-y curves can be obtained from the results of in situ pressuremeter tests (Atukorala et al., 1986; Briaud et al., 1982, 1983), and from inclinometer measurements (Brown and Zhang, 1994). 8.6.2 p-y curves for rock There are few records of p-y curves for rock, probably because once the rock strength is greater then that of the concrete, the pier is essentially fixed

at the top of rock and the design issue relates to the stability of the rock socket rather than the modulus (see Section 8.6.3). However, the results of a limited number of tests of installations in very weak rock have been used in the development of a preliminary procedure for drawing up p-y curves for weak rock based on the following concepts and procedures (Reese, 1997). 1. The geological structure of the rock mass can significantly influence its behavior, which must be taken into account in the application of the procedures described in this section. 2. The p-y curves for rock and the bending stiffness EI for the pile must both reflect nonlinear behavior in order to predict loadings at failure. of the p-y curves must be 3. The initial slope predicted because small lateral deflections of piles in rock can result in resistances of large magnitudes. For a given value of compressive is assumed to increase with strength, depth below the ground surface.

LOAD CAPACITY OF SOCKETED PIERS IN COMPRESSION

4. The modulus of the rock mass Em, for may be taken from the correlation with initial slope of a pressuremeter curve. Other correlations between the rock mass rating RMR for rock masses and the in situ modulus of deformation are shown in Fig. 3.10 and equation 3.5. 5. The ultimate resistance pult for the p-y curves will rarely, if ever, be developed in practice, but the prediction of pult is necessary in order to reflect non-linear behavior. 6. The component of the resistance related to the depth below the surface is considered to be small in comparison with that from the compressive strength, and therefore the weight of the rock is neglected. 7. The compressive strength of the intact rock used for computing the value for pult may be obtained from tests of intact samples. 8. The assumption is made that fracturing will occur at the rock surface under small deflections. Therefore, the compressive strength of the intact rock is reduced by a factor ar to account for the fracturing. The value for ar is assumed to be 0.33 for RQD values of 100% and to increase linearly to 1.0 at RQD of 0%. This relationship between ar and RQD accounts for the likely brittle failure and significant loss of strength of massive rock when strained, compared with the greater amount of deformation that may occur prior to failure for fractured rock (i.e. low RQD). If the RQD is 0% the compressive strength may be taken directly from the pressuremeter curve. (a) Ultimate resistance of rock The ultimate resistance pult of the rock when subject to lateral loading in a drilled socket is based upon limit equilibrium and increases in value with depth below the surface of the rock. The value for pult is given by (Reese, 1997): (8.23) or

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(8.24) where ar is the strength reduction factor; su(r) is the compressive strength of the intact rock, usually lower bound and will vary with depth as appropriate for site conditions; xr is the depth below the surface of the rock; and B is the pier diameter. (b) Slope of initial portion of p-y curve For a beam resting on an elastic, homogeneous, isotropic solid, the relationship between the modulus of the rock mass Emi over the initial part of the p-y curve, and the initial slope of the curve is given by (8.25) where ki is a dimensionless constant derived from experiment and assumes that the depth below the rock surface has a similar effect on ki as for pult. For the initial portion of the p-y curve up to point A (see Fig. 8.22), values for ki are given by: (8.26) or (8.27) Equations 8.26 and 8.27 which have been developed from experimental data show that the initial portions of the p-y curves are very stiff, which is consistent with the very low deflections observed during the initial loads. (c) Calculation of p-y curves The p-y curves for weak rock have three portions as shown in Fig. 8.22. The procedure for devel oping these curves is to calculate first pult using equation 8.23 or 8.24 appropriate for the depth, and then the initial slope of the curve using equation 8.26 or 8.27. The three portions of the p-y curve are defined by the following equations. The initial straight line portion is given by: (8.28) while the curved portion is given by (8.29) and the horizontal portion by (8.30)

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Figure 8.22 Typical p-y curve for weak rock.

where (8.31) and km is a constant ranging from 5E–4 to 5E–5. Based on the very limited number of case studies, it has been found that km has values of 5E–4 for vuggy limestone, and 5E–5 for sandstone containing very closely spaced discontinuities. These tests are described in more detail in (d) below. The value for the deflection yA defining the limit of the linear portion of the p-y curve is found by solving for the intersection of equations 8.28 and 8.29 and is given by (8.32) The equations described in this section are based on limited data and should be used with an appropriate factor of safety for conditions where the geology differs significantly from that at the test sites. Where possible, full-scale load tests should be carried out to confirm these calculations. Also, the assumed linear relationship between p and y should be valid for static loading and if resistance is due lateral stresses only (Reese, 1997). (d) Examples of p-y curves from full scale tests

Figure. 8.23 shows the results of two lateral load tests on pier socketed into very weak rock, and the general trend of the p-y curves for these materials calculated using the procedures discussed in Section 8.6.2 (a), (b) and (c) above. For each test, py curves for depths below the top of bedrock (xr) of 1 m and 3 m (3.28 and 6.56 ft) are shown to illustrate the effect of depth on the lateral resistance of these materials. That is, both the ultimate lateral increase resistance pult and the initial modulus with depth. A summary of test methods and site conditions, and values for the design parameters, is as follows. 1. 1.22 m (48 in) diameter pier drilled to a total depth of 17.53 m (57.7 ft), with a 13.32 m (43.7 ft) long socket into brittle, vuggy lime-stone; the RQD was assumed to be close to zero. The maximum horizontal load was 670 kN (150 kips) and the deflection of the pier was measured at the point of application of the load and at the top of rock (FHWA, 1984; Reese, 1997). The maximum deflection was 18 mm (0. 71 in) at the point of load application (3.5 m (11.5 ft) above the rock level), and 0.54 mm (0. 0213 in) at rock level. The design parameters

LOAD CAPACITY OF SOCKETED PIERS IN COMPRESSION

defining the p-y curves are shown in Fig. 8.23 (a). 2. 2.25 m (88.6 in) diameter piers drilled to a depth of 12.5 and 13.8 m (41 and 42.3 ft) into dense, fractured sandstone with RQD ranging from 0 to 80%. An inclinometer casing was cast into the pier to measure the deflection as the horizontal load was applied, and the deflected shape was then used to derive p-y curves by making a best fit to the data using a preselected analytical function for the p-y relationship (Brown and Zhang, 1994; Reese, 1997). The maximum applied load was 6450 kN (1450 kips) and the maximum deflection at the top of the pier was 6 mm (0.24 in). The design parameters defining the p-y curves are shown in Fig. 8.23(b). (e) Example of analysis of laterally loaded socketed pier The results of an analysis of a laterally loaded socketed pier using the program LATPILE are shown in Fig. 8.24. The depth of the overburden is 6 m, and the socket depth in rock is 2 m, for a total pier depth of 8 m. The p-y curves at the top and bottom of the overburden, and in show the significantly the rock different resistance provided by the overburden and the rock. The three pairs of curves in the lower part of Fig. 8.24 show the displacement, moment and shear force distributions down the pier, and the effect on these parameters of the 2 m long socket. For these particular conditions, the overburden is sufficiently stiff to provide considerable resistance to the lateral loads, and the socket has only a minor effect in reducing the displacement, moment and shear. 8.6.3 Socket stability under lateral load An important aspect of the design of rock socketed piers under lateral load is the stability of the rock in the socket. Figure 8.25 shows two examples of rock wedges formed (a) by a single pier located on a

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slope face, and (b) at the base of a vertical wall supported by a row of piers. The stability of rock socket will be highly dependent on the structural geology of rock because this will define the shape and dimensions of the wedge, as well as the shear strength parameters of the sliding surfaces. Of particular importance is the presence of discontinuities that are oriented to form the base of the wedge. In Fig. 8.25(a) a joint that dips either into or out of the slope could develop an unstable wedge, and this condition is exacerbated if the rock contains a vertical conjugate joint set that forms release surfaces on the sides of the wedge. In full scale load tests (Maeda, 1983; Yoshii, 1995) in which the pier was socketed into a weathered, rhyolitic tuffy breccia with no continuous joints, the dip angle of the base of the wedge ψp was found to be (Fig. 8.25(a)): (8.33) where ψf is the dip of the slope face and is the friction angle of the rock in the socket. Note that a negative value for ψp indicates that the base of the wedge is inclined above the horizontal. The tests by Maeda also showed that the angle defining the width of the wedge is approximately equal to 45°. Figure 8.25(b) shows a vertical wall with a horizontal surface at the base. In this case discontinuities dipping away from the wall will not ‘daylight’ and a potentially unstable wedge will not be formed. However, joints dipping towards the wall do form a wedge and stability calculations by Greenway et al. (1986) showed that the capacity of the socket to sustain lateral loads is a minimum when the dip of the fractures ψp is in the range of about 5° to 30°. The stability of the rock sockets with the geometries shown in Fig. 8.25 can be analyzed using the principles described in Chapter 6. This analysis involves resolving all forces acting on the wedge into vectors parallel and normal to the sliding surface, from which the resisting and displacing forces and the factor of safety are calculated. In the case of the wedge in Fig. 8.25(a) a conservative

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assumption would be that no shear stresses are developed on the two sides of the wedge and that the resistance would be developed solely on the base. The normal stress on the base would be calculated for the weight of the entire wedge. In contrast, for the wedge in Fig. 8.25(b), the factor of safety could be calculated for a unit length of the wedge, again assuming that no shear resistance is developed on the end faces. Potentially unstable wedges in the socket area could be reinforced with tensioned rock bolts anchored below the base of the socket. The shear force determined by the program LATPILE would be used to determine the magnitude of the displacing force acting on the wedge and calculate the reinforcing force required to retain the wedge of rock. 8.7 References American Petroleum Institute (1979) Recommended practice for planning, designing and constructing fixed offshore platforms. Report No. API-RP2A, Washington, DC, 10th Edition. Atukorala, U.D., Byrne, P.M. and She, J. (1986) Prediction of ‘p-y’ Curves from Pressuremeter Tests. Soil Mechanics Series 108, Civil Engineering Department, University of British Columbia. Barton, Y.O. and Pande, G.N. (1982) Laterally loaded piles in sand: centrifuge tests and finite element analyses. Numerical Models in Geomechanics, Balkema, Rotterdam, pp. 749–58 Briaud, J.-L., Smith, T.D. and Meyer, B.J. (1982) Pressuremeter gives elementary model of laterally loaded piles. Int. Symp. on in situ Testing of Rock and Soils, Paris, May. Briaud, J.-L., Smith, T.D. and Meyer, B.J. (1983) Laterally loaded piles and the pressuremeter: comparison of existing methods. ASTM Special Technical Publication on the Design and Performance of Laterally Loaded Piles and Pile Groups, June. Brown, D.A. and Zhang, S. (1994) Determination of p-y curves in fractured rock using inclinometer data. Proc. Int. Conf. Design and Construction of Deep Foundations, US Federal Highway Administration, Orlando, FL, pp. 857–71. Canadian Geotechnical Society (1985) Canadian

Foundation Engineering Manual, 2nd edn, BiTech Publishers, Vancouver, British Columbia. Carter, J.P. and Kulhawy, F.H. (1992) Analysis of laterally loaded shafts in rock. J. Geotechncial Eng., 118(6), ASCE, 839–55. Chang, M.F. and Wong, I.H. (1987) Shaft friction of drilled piers in weathered rock. Proc. 6th Int. Conf. on Rock Mech. Montreal, ISRM, pp. 313–18. Chiu, H.K. and Donald, I.B. (1983) Prediction of the performance of side resistance piles socketed in Melbourne mudstone. Proc. International Cong. on Rock Mech., Melbourne, ISRM, pp. C235–243. Donald, I.B., Chiu, H.K. and Sloan, S.W. (1980) Theoretical analysis of rock socketed piles. Proc. International Conf. on Structural Foundations on Rock, Sydney, pp. 303–16. Drumm, E.C. (1998) Personal communication. Federal Highway Administration (US) (1986) Behavior of Piles and Pile Groups Under Lateral Load. FHWA/ RD-85–106, Federal Highway Administration, Dept. of Research, Development and Technology, McLean, Virginia. Federal Highway Administration (US) (1988) Drilled shafts: Construction Procedures and Design Methods. FHWA-HI-88–042, Federal Highway Administration, Dept. of Research, Development and Technology, McLean, Virginia. Garcia-Fragio, A., James, E., Romana, M. and Simic, D. (1987) Testing the Axial Capacity of Steel Piles Grouted into Rock. Int. Soc. Rock Mechanics, Montreal, pp. 267–71. Gill, S.A. (1980) Design and construction of rock sockets. Proc. International Conf. on Structural Foundations on Rock, Sydney, pp. 241–52. Glos, G.H. and Briggs, O.H. (1983) Rock sockets in soft rock. J. Geotech. Eng. Div., ASCE, 109(4), 525–35. Greenway, D.R., Powell, G.E. and Bell, G.S. (1986) Rock-socketed caissons for retention of an urban road. Proc. of Conf. on Rock Engineering and Excavation in an Urban Environment, Hong Kong, Inst. Mining and Met., pp. 173–80. Hetenyi, M. (1946) Beams on Elastic Foundations. The University of Michigan Press, Ann Arbor, Michigan. Horvath, R.G., Kenney, T.C. and Kozicki, P. (1983) Methods of improving the performance of drilled piers in weak rock. Can. Geotech. J., 20, 758–72. Horvath, R.G., Schebesh, D. and Anderson, M. (1989) Load-displacement behaviour of socketed piers— Hamilton General Hospital. Canadian Geotechnical

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Figure 8.23 p—y curves for very weak rocks determined from lateral load tests on rock socketed piers (adapted from Reese, 1997). Journal, 26, 260–8.

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Figure 8.24 Illustration of a laterally loaded pier showing deflection, moment and shear force computed by program LATPILE. Kay, G.B. (1989) Personal communication. Kulhawy, F.H. (1985) Drained uplift capacity of drilled shafts. Proc. XI Int. Conf. on Soil Mech. and Foundation Eng., San Francisco, pp. 1549–52.

Kulhawy, F.H. and Goodman, R.E. (1980) Design of foundations on discontinuous rock. Proc. International Conf. on Structural Foundations on Rock, Sydney, Australia, pp. 209–220.

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Figure 8.25 Stability of rock sockets under lateral loading: (a) wedge formed by single laterally loaded socket located on slope (after Maeda, 1983); and (b) wedge formed at base of vertical wall supported by a row of socketed piers (after Greenway et al., 1986). Ladanyi, B. (1977) Friction and end bearing tests on bedrock for high capacity socket design: Discussion. Can. Geotech. J., 14, 153–5. Ladanyi, B. and Domingue, D. (1980) An analysis of bond strength for rock socketed piers. Proc. Int. Conf. on Structural Foundations on Rock, Sydney, pp. 363–73. Lueng, C.F. (1996) Case studies of rock socketed piles. J.

Southeast Asian Geotechnical Soc., 27(1), 51–67. Macaulay, D. (1976) Underground. Houghton Mifflin Co., Boston, MA. Maeda, H. (1983) Horizontal behavior of pier foundation on a soft rock slope. Int. Congress of Rock Mechanics, Melbourne, ISRM, pp. C181–4. Matlock, H. (1970). Correlations for laterally loaded piles in soft clay. Proc. 2nd Annual Offshore Technology

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Conf., Paper 1204, Vol. 1, Houston, pp. 577–94. Meyer, B.J. and Schade, P.R. (1995) Touchdown for the O-cell test. Civil Engineering, ASCE, February, 57–9. Oakland, M.W. and Chameau, J.-L. (1989) Analysis of drilled piers used for slope stabilization. Transportation Research Record 1219, Transportation Research Board, Washington, DC, pp. 21–32. O’Neill, M.W. and Hassan, K.M. (1994) Drilled shafts: effects of construction on performance and design criteria. Proc. Int. Conf. Design and Construction of Deep Foundations, US Federal Highway Administration, Orlando, FL, pp. 137–87. Ooi, L.H. and Carter, J.P. (1987) Direct shear behavior of concrete-sandstone interfaces. Proc. 6th Int. Conf. on Rock Mech., Montreal, ISRM, pp. 467–70. Osterberg, J.O. and Gill, S.A. (1973) Load transfer mechanisms for piers socketed in hard soils or rock. Proc. 9th Canadian Sym. on Rock Mech., Montreal, pp. 235–62. Pells, P.J. N., Rowe, R.K. and Turner, R.M. (1980) An experimental investigation into side shear for socketed piles in sandstone. Proc. Int. Conf. on Structural Foundations on Rock, Sydney, pp. 291–302. Pells, P.J. N. and Turner, R.M. (1979) Elastic solutions for the design and analysis of rock socketed piles. Can. Geotech. J., 16, 481–7. Poulos, H.G. (1972). Behavior of laterally loaded piles: III —socketed piles. J. Soil Mech. and Foundation Div., ASCE, 98, SM4, 342–60. Reese, L.C. (1997) Analysis of laterally loaded piles in weak rock. J. Geotechnical and Geoenvironmental Eng., 123(11), ASCE, 1010–17. Reese, L.C., Cox, W.R. and Koop, F.D. (1974) Analysis of laterally loaded piles in sand. 6th Annual Offshore Technology Conference, Houston, Texas, Paper, No. 2079. Rowe, R.K. and Armitage, H.H. (1987) Theoretical solutions for the axial deformation of drilled shafts in rock. Can. Geotech. J., 24, 114–25 and 126–42. Rowe, R.K., Booker, J.R. and Balaam, N. (1978) Application of the initial stress method to soilstructure interaction. Int. J. of Numer. Meth. in Eng., 12(5), 873–80. Rowe, R.K. and Pells, P.J. N. (1980) A theoretical study of pile-rock socket behavior. Proc. Int. Conf. on Structural Foundations on Rock, Sydney, pp. 253–64. Seidel, J.P. and Haberfield, C.M. (1994) A new approach to the prediction of drilled pier performance in rock. Proc. Int. Conf. Design and Construction of Deep

Foundations, US Federal Highway Administration, Orlando, FL, pp. 556–85. Seychuck, J.L. (1970) Load tests on bedrock. Can. Geotech. J., 7, 464–70. Simons, H. (ed.) (1963) The Bridge Spanning Lake Maracaibo in Venezuela. Bauverlag GmbH., WeisenBaden, pp. 22–59. Sowers, G.F. (1976). Foundation bearing in weathered rock. Proc. of Specialty Conf. on Rock Eng. for Foundations and Slopes, Boulder, CO., ASCE, Geotech. Eng. Div., Vol. II, pp. 32–41. Tang, Q., Drumm, E.C. and Bennett, R.M. (1994) Response of drilled shaft foundations in karst during construction loading. Proc. Int. Conf. Design and Construction of Deep Foundations, US Federal Highway Administration, Orlando, FL, pp. 1296–309. Taylor, P.W. (1975) Pre-loaded pier foundations for city building. New Zealand Eng. 15, pp. 320–5. Thorne, C.P. (1980) The capacity of piers drilled in rock. Proc. Int. Conf. on Structural Foundations on Rock, Sydney, pp. 223–33. Tomlinson, M.J. (1977) Pile Design and Construction Practice. ICE, Cement and Concrete Association, London. University of British Columbia (1985) Deflections of Laterally Loaded Piles, LATPILE.PC. Civil Engineering Program Library, UBC, Vancouver. Vesic, A.S. (1971) Breakout resistance of objects embedded in the ocean bottom. J. Soil Mech. and Foundation Div., ASCE, 97, SM9 (Proc. Paper 8372), 1183–205. Walter, D.J., Burwash, W.J. and Montgomery, R.A. (1997) Design of large-diameter drilled shafts for the Northumberland Straight bridge project. Canadian Geotech. J., 34, 580–7. Webb, D.L. and Davies, P. (1980) Ultimate tensile loads of bored piles socketed into sandstone rock. Proc. Int. Conf. on Structural Foundations on Rock, Sydney, pp. 265–70. Williams, A.F. (1980) The Design and Performance of Piles Socketed in Weak Rock. PhD Thesis, Monash University, Melbourne. Williams, A.F., Johnston, I.W. and Donald, I.B. (1980) The design of socketed piles in weak rock. Proc. Int. Conf. on Structural Foundations on Rock, Sydney, pp. 327–47. Williams, A.F. and Pells, P.J. N. (1981) Side resistance rock sockets in sandstone, mudstone and shale. Can. Geotech. J., 18, 502–13.

LOAD CAPACITY OF SOCKETED PIERS IN COMPRESSION

Winterkorn, H.F. and Fang, H.-F. (1975) Foundation Engineering Handbook. Van Nostrand Reinhold, New York, pp. 601–15.

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Woodward, R.J., Gardner, W.S. and Greer, D.M. (1972) Drilled Pier Foundations. McGraw-Hill, New York, pp. 84–91.

9 Tension foundations

9.1 Introduction In contrast to that of soil, the relatively high shear and tensile strengths of rock allows rock foundations to support substantial tension (uplift) loads. These loads are transferred from the structure to the foundation rock by steel anchors, comprising rigid bars or flexible strands. The anchors are secured with cement or epoxy grout in a hole drilled into the foundation, and the head of the anchor is then embedded in, or bolted to, the structure. In applications where movement of the structure must be limited, the anchors are prestressed. This method of support, which mobilizes a mass of rock in the foundation to resist the uplift, is often a more efficient support method for tensile loads than attaching the structure to a mass of concrete with a weight equal to the applied load. Figure 9.1 shows the main support towers of a suspension bridge, and an internal view of one of the anchor chambers. Each cable consists of 20 strands which are anchored with 12 m (40 ft) long anchors installed into a pattern of holes drilled into the rock. The anchors are secured with mechanical expansion shells, and then pretensioned against the reaction plate in the anchor chamber so that there would be no movement of the anchorage when the suspension cables were loaded. At the completion of installation, the anchor holes were fully grouted to protect the cables against corrosion. Note that this installation was carried out in the 1960’s; although the anchors are performing satisfactorily, present practice would be to use grout anchorages rather than mechanical expansion shells, and to use

a more reliable method of corrosion protection. Figure 9.2 as well as Fig. 1.2(d) show other applications of rock anchors to support tensile loads and demonstrates the wide range of loading conditions that can be accommodated by rock anchors. In all these applications, the general design and construction procedure comprises drilling a hole, or holes, where possible in a direction parallel to the direction of the applied load to a depth where rock is encountered, and then anchoring a rigid steel bar or cable in the hole. This installation can be as simple as a length of reinforcing steel fully grouted into the hole, or as complex as a bundle of high strength steel cables with two layers of corrosion protection which is anchored in the lower part of the hole with cement grout and then tensioned. The choice of anchor type will depend on such factors as the magnitude and duration of the load, the potential for corrosion, the rock conditions in the anchor zone, and physical constraints such as construction access. The examples shown in Fig. 9.2 illustrate some different conditions for anchor installations. In Fig. 9.2(a) the anchors to secure the rock fall protection roof would have to be of low capacity because it would be necessary to use a lightweight drill that could be lifted into position on the slope face, and a cable anchor that could be readily inserted in the uphole. In contrast, the anchors through the gravity dam (Fig. 9.2(b)) could be of much larger capacity because a barge-mounted drill could be used to drill large diameter holes, and a high capacity cable anchor assembly could be lifted into place using a helicopter or crane.

ANCHOR MATERIALS AND ANCHORAGE METHODS

This chapter discusses the following four aspects of the design and construction of tensioned anchors: 1. the different types of anchors and anchorage systems that are available on the market, and their applications; 2. design methods to determine the load capacity of anchors; 3. causes of corrosion and methods of corrosion protection for permanent protection; 4. test methods used during construction to verify anchor performance and capacity. The anchors described are mainly suitable for installations in rock. Descriptions of anchors systems suitable for installation in soil, which usually require the use of such techniques as belled or pressure grouted anchors, may be found in pub lications by Hanna (1982) and Federal Highway Administration (1982). 9.2 Anchor materials and anchorage methods The anchors used for the typical applications shown in Figs 9.1 and 9.2 are generally fabricated from rigid steel bars or strand, and anchored with cement or epoxy grout. This section describes the materials that are available from some specialist manufacturers of anchor products and the conditions in which they are most often used. These products are suitable for ‘permanent’ anchors, the performance of which must meet the following criteria. 1. A high degree of reliability is required for both the materials from which the tieback and head components are fabricated and the completed installation. 2. The applied structural loads may be either static or cyclic, and may be as high as 5 MN (≈1000 kips). 3. Deformation tolerances are low and must be predictable. 4. The service life should not be less than about

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50 years. In order to meet these requirements, the materials must be of very high quality and the installation and testing procedures be designed so that the performance of every anchor can be verified. The reason for this high level of quality control is that once the anchors are installed, it is virtually impossible to inspect or replace them without excavating the foundation. There are many types of rock bolts available on the market that are used in the mining industry and for temporary support in tunnels. These products include various types of rigid bolts with wedge type anchorages, and bolts such as Swellex (Atlas Copco) and Split Set (Ingersoll Rand) which are malleable and deform as they are installed. Generally these bolts have lengths up to about 3 m, are not corrosion protected and are designed to yield at high loads. While these properties are suitable for the conditions for which they are designed, their performance will not meet the requirements for permanent anchors listed in the previous paragraph. Consequently they are not discussed in this book. 9.2.1 Allowable working loads and safety factors The allowable working load of an anchor is the design load that the anchor is required to sustain under normal service conditions; higher loads may be acceptable as long as they only occur infrequently and are within limits as specified below. The allowable working load is expressed as a percentage of the specified characteristic strength of the steel. The characteristic strength is the guaranteed limit below which not more than 5% of the test results fall; none of the test results are less than 95% of the characteristic strength. The characteristic strength of the steel may be either the guaranteed ultimate tensile stress (GUTS) or the yield stress. The yield stress is the stress at which the permanent strain reaches 0.1% (known as the 0.1% offset stress), and is equivalent to about 85% of the ultimate tensile stress. These values are supplied by

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Figure 9.1 Suspension bridge across the Peace River in northern British Columbia, Canada (courtesy of the British Columbia Ministry of Transportation and Highways): (a) view of bridge with anchor chamber in foreground; and (b) interior view of anchor chamber showing connections between the 20 individual strands and the head of the rock anchors.

the tendon manufacturer as part of the product

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Figure 9.2 Typical applications of rock anchors to support tension loads: (a) anchored roof to protect roadway from rock falls; (b) permanent tie-downs installed to improve overturning resistance of dam; and (c) rock anchors providing support for tensioned cable.

specification, and it is usually possibly to obtain a mill certificate which gives the strength results for the particular batch of steel from which the bar or tendon was manufactured. Figure 9.3 shows typical load extension curves for a seven-wire strand and a prestressing bar and defines both the yield and ultimate loads. The allowable working load is generally taken to be between 50% and 62.5% of the ultimate tensile strength, i.e. the factor of safety against failure of the anchor material is between 2 and 1.6. Littlejohn and Bruce (1975b) provide an extensive review of safety factors used in practice and specified in codes by such countries as Britain, France, Germany and Switzerland. The factors of safety used and

specified vary from as low as 1.43 to as high as 2. 27, but the trend appears to be to use a factor of safety of 2 for most permanent applications. As described in Section 9.5, the procedure for testing the performance of anchors requires the application of an overload which can readily be accommodated if the working load is 50% of the ultimate strength; the maximum test load should not exceed the yield load of the steel. This margin of safety also allows the application of occasional overloads during the service life to stress levels up to about 60% of the ultimate strength.

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Figure 9.3 Typical stress-strain curves for 32 mm diameter prestressing bar and 13 mm diameter strand (after Libby, 1977).

9.2.2 Steel relaxation A property of steel which may be of significance to the performance of tensioned anchors is stress relaxation. Tensioned anchors may lose load with time as a result of both steel relaxation, as described in this section, and creep of the anchorage as described in Section 9.3.7. The factors that influence steel relaxation are the stress level, the service temperature, time after stressing, and in the case of strand, the tendency of the strand to unwind. At stress levels up to 50% of the ultimate strength, relaxation is negligible and if an overload is applied during testing this will reduce the tendency of the strand to relax during service. For stress levels of 75% of the ultimate strength and temperatures of 20° C, a load loss of 5–10% of the applied stress occurs in ordinary stress relieved steel, while in ‘stabilized’ strand the load loss is reduced to 1.5%. Figure 9.4 shows the relationship between the stress

relaxation, as a percentage of the initial stress, and time for steel bar, wire and strand. This graph shows that the major part of the relaxation takes place in the first 100 hours. However, the relaxation will continue with time, although at a decreasing rate, and the relative relaxations ?t at times t of 1, 100, 1000 and 250 000 hours are The equation defining the loss of stress due to relaxation at normal ambient temperatures is as follows (Libby, 1977): (9.1) where ?sr is the relaxation stress loss at time t hours after stressing; si is the initial stress, and sy is the 0. 1% offset stress. Note that this equation is only applicable when the ratio si/sy is equal to or greater than 0.55, because when the initial stress is less than 0.55 of the 0.1% offset stress, relaxation is negligible. In situations where these levels of relaxation are

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Figure 9.4 Relaxation of tendon steel and bar from initial stress of 0.7 ultimate tensile strength (after Littlejohn and Bruce, 1975a). 1. Range of values for stress relieved wires. 2. Alloy steel wires. 3. Range of values for stress relieved strands. 4. Range of values for 19-wire strand (not stress relieved). 5. Stabilized strand.

unacceptable, restressing at a time of 1000 hours will reduce the further relaxation to about one quarter of its normal value at an initial stress of 70% of GUTS. Another method of reducing relaxation is to overload the anchor at the time of initial stressing and hold this stress for a period of up to 10 minutes which disposes of the rapid initial relaxation (Littlejohn and Bruce, 1976). It is also found that the relaxation rate increases rapidly at temperatures over 20° C which may be of significance in some applications. 9.2.3 Strength properties of steel bar and strand The properties of steel bar and strand anchors that are required for design are the yield stress, the ultimate tensile stress, the elastic modulus and the relaxation characteristics. While the manufacturer’s specifications should be checked for the actual properties of any product, the information given in Table 9.1, which lists the properties for some widely distributed products, can be used as a guideline for preliminary design.

9.2.4 Applications of rigid bar anchors The types of steel bars used as rock anchors include deformed reinforcing steel, continuously threaded bar such as Dywidag Threadbar or Williams allthread bar, and hollow core rock bolts such as Williams bar. In almost all applications, deformed bar is used because of the improved steel-grout bond strength in comparison with smooth bar. Figure 9.5 shows two typical installations of bar anchors and illustrates both mechanical wedge and grout type anchorages. The Dywidag threadbar has a smooth plastic sheath on its upper end where no bond is developed (Fig. 9.5(a)). When the bar is fully grouted this arrangement forms an bond length lb over which a rock-grout-steel bond operates, and a free stressing length lf which allows strain in the bar during tensioning. The features of continuously threaded bar are that it can be cut to any desired length and the threads can withstand rough handling in the field without damage. The cement grouted anchorage can be used in both weak and strong rock with the length of the anchorage being adjusted according to the strength of the rock (see Section 9.4). The value of the free

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stressing length is the ability of this length of the bar to strain in response to changing loads in the anchor. Note that this type of installation would not be considered to have sufficient corrosion protection for most permanent installations. The hollow core bolt (Fig. 9.5(b)) is anchored with a mechanical rock anchor. This type of anchor is set by drilling a hole with a diameter that is just large enough to grip the cone, and then torquing the bar to draw the cone into the shell and force the two

halves of the shell against the wall of the drill hole. The advantage of mechanical anchors is that the bolt can be installed and tensioned in one operation, which is in contrast to grouted anchors that cannot be tensioned until the grout has set after a period of several days. The hole through the center of the bar is used to grout the bolt either immediately before, or after tensioning. In a down hole, the grout is pumped

Table 9.1 Properties of common types of bar used for permanent rock anchors Product

Yield stress (1% offset) MPa (kips/in2)

Ultimate tensile stress GUTS MPa (kips/in2)

Elastic modulus GPa (p.s.i)

Reinforcing steel 400 grade Dywidag 420/500 grade Dywidag 835/1030 grade Williams hollow core bar Prestressing strand, 7-wire. 15 mm dia.

400 (58) 420 (61) 835 (121) 371 (54) 1570 (228)

600 (87) 500 (72) 1030 (149) 501 (73) 1770 (257)

201 (29×106) 201 (29×106) 205 (29.7×106) 207 (30×106) 193 (28×106)

down the bar until grout return is obtained at the collar of the hole, while in an uphole, the grout is pumped up a tube sealed into the collar until return is obtained through the center hole. This grouting system eliminates the use of grout tubes attached to the bar which can be damaged during installation of the bar. For permanent installations, the anchors are always grouted because the mechanical anchor will slip in time as a result of corrosion of the wedge and creep of the highly stressed rock around the anchor. A significant difference between the two types of anchor shown in Fig. 9.5 is the manner in which the tensioning force is retained in the bar. In the fully bonded Williams bar, the nut and reaction plate are effectively superfluous once the grout has reached its full strength because the steel is bonded to the rock over the full length of the anchor. In contrast, for bars with a free stressing length (in the case of the Dywidag bar) the maintenance of the prestress depends on the integrity of the anchor nut and plate because there is no bond developed in the free stressing length. Therefore it is important that good corrosion protection be provided for the heads of anchors with free stressing lengths. Moreover, the rock under the bearing plate should be protected from weathering, where appropriate, because if the

highly stressed rock under the plate were to break down, the tension in the bolt would be lost. Reinforcing steel is used where the primary function of the anchors is to secure a footing to a rock surface and the loading conditions consist of purely compressive loads, or uplift and/or shear loads only occur infrequently. The installation procedure would be to drill a pattern of holes in the rock foundation, anchor the reinforcing bar with cement grout, and then cast the footing with the exposed part of the anchors embedded in the concrete. In the example shown in Fig. 9.2(c), the anchors could either be embedded in the concrete to form a passive anchor, or they could be sleeved through the concrete and then pre-stressed against the top surface of the concrete footing. For a discussion on the performance of passive and prestressed foundations see Section 9.3. Rigid bar anchors are commonly installed where the design working load is in the range of about 100– 600 kN (22–135 kips), and where the required length is less than about 8 m (25 ft). The advantages of bar anchors are the ease of handling short lengths which can be coupled together as required, and locking off the applied stress using a threaded nut which can be reset if the bar is later retensioned.

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Figure 9.5 Typical bar anchors with grout and mechanical anchors (courtesy Dywidag Systems Int. and Williams Form Hardware and Rock Bolt Co.): (a) Dywidag continuous threadbar with grouted anchor and smooth sheath on free stressing length; and (b) Williams hollow core bar with mechanical anchor showing alternative grouting methods for upholes and downholes.

The disadvantages of bar anchors are their limited load capacity (it is impractical to bundle bars to form higher capacity anchors), and the difficulty of handling long, continuous lengths. Where long anchors are required and access space is restricted, couplings can be used to join short sections of bar. However, for long anchors, continuous strand may be preferred to coupled rigid bars because of the time

required during installation to couple the bars and install corrosion protection on the couplings. 9.2.5 Applications of strand anchors Figure 9.6 shows the components of a multistrand tendon with a corrosion protection system

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comprising a grouted corrugated sheath on the bond length, and polypropylene sheaths with a corrosion inhibiting grease on each strand in the unbonded length. In the bond length, the strands are separated by spacers and the entire anchor assembly is centered in the drill hole with centering sleeves so that all components of the anchorage assembly are fully encased in grout. The usual procedure is to grout the corrugated sheath on to the strand in an assembly yard and then transport the assembled anchor to the site for installation. Care is taken not to bend the bonded length which would result in cracking and weakening of the grout. Where it is necessary to bend the anchor during installation because of space limitations, grouting both inside and outside the sheath can be performed after the assembly has been placed in the hole. This requires that the anchor be fabricated with two grout tubes, one inside and one outside the corrugated sheathing, or both inside the sheathing but with one extending through the end cap for grouting the annulus. The tensioned strand is secured at the head of the anchor by pairs of tapered wedges that grip the cable with a serrated inner surface and are held in place by tapered holes in the anchor plate (Fig. 9.7). The wedges are pushed into the holes in the anchor plate once the strand has been tensioned to the lockoff load. The required load capacity of the anchor is obtained by assembling a bundle of strands as shown in Fig. 9.6. An upper limit for the number of strands that can be readily made into a bundle is about 25 strands which has an ultimate load capacity in excess of 4 MN (900 000 lb), and requires a drill hole with a diameter of at least 200 mm (8 in). Because it is not possible to join lengths of strand, the entire anchor assembly, with the corrosion protective sheaths, has to be fabricated in one piece, the weight of which can be considerable. Therefore, when determining the number of strand to make up a bundle, an important consideration is the method of installation. For example, in vertical or steeply inclined down-holes, a heavy anchor can often be lowered into the hole using a crane or helicopter,

while in horizontal or up-holes it would be preferable to use a greater number of anchors, each with fewer strands to facilitate their being pushed up the hole. 9.2.6 Cement grout anchorage Anchorage methods for tie-backs include mechanical wedges, resin grout and cement grout, of which cement grout is the most common for per manent installations and is used for a wide variety of applications. Epoxy resin and mechanical wedge anchors can be used to secure low capacity rock bolts, that is loads of up to about 200 kN (45 000 lb), and with lengths not more than about 8 m (25 ft). The advantages and disadvantages of these three types of anchorages are discussed in the following sections. The advantages of cement grout anchorage are the availability and low cost of the materials, simple installation procedures, and its suitability for a wide range of soil and rock conditions. In addition, cement provides an environment that protects the steel bar or strand from corrosion, and when properly installed the strength of the grout will improve rather than deteriorate with time. The disadvantages are that careful quality control is required during mixing and placing, that in fractured rock it may flow into even fine fractures (width greater than about 0.25 mm) resulting in an incompletely filled hole, and the set grout is brittle and can be damaged by movement during installation and stressing. The procedure for the design and installation of a grout anchor is as follows. (a) Hole diameter For economy, the hole diameter must be as small as possible, while providing a sufficiently thick annulus of grout to transmit the shear stresses from the steel to the surrounding rock. The hole diameter should also be large enough that the anchor can be readily inserted without having to resort to hammering or driving. In fractured rock, fragments of rock may be dislodged from the walls of the hole

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Figure 9.6 Typical multi-strand anchor with corrosion protection comprising grouted corrugated sleeve, polypropylene sheath and full grout embedment (courtesy Lang Tendons).

as the anchor is pushed forward and the anchor

could become jammed part way into the hole if the

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Figure 9.7 Head of multi-strand anchor showing tapered wedges gripping the strand and seated in tapered holes in the bearing plate.

hole diameter is too small. Usual practice in the selection of the drill hole diameter is to ensure that the ratio of the diameters of the anchor da and hole dh falls within the following approximate range: (9.2) The low end of this range would be used in strong, massive rock while the high end would be used in fractured rock. For example, a bundled anchor with a diameter of 100 mm could be installed in a 200 mm diameter hole in fractured rock, or a 150 mm diameter hole in massive rock. The use of ratios higher than 2.5 is possible, but the larger hole diameter will be more costly to drill, and require a higher compressed air quantity to flush the cuttings from the hole. (b) Bond length The most important factors influencing the selection

of the bond length is the strength and fracture characteristics of the rock in the bond zone. The results of load tests on anchors installed in a wide variety of rock conditions have provided approximate values for the allowable working bond stress at the rock-grout interface. The working bond stress, which is related to the unconfined compressive strength of the rock, has values which range from about 350 kPa (50 p.s.i.) for weak rock to a high of 1400 kPa (200 p.s.i.) for strong rock. If it is assumed that the shear stress is uniformly distributed along the full length of the anchor, the required bond length can be calculated from the working bond stress and the area of the periphery of the drill hole in the bond zone. Further details on the procedure for calculating the required bond length is given in Section 9.3.2 which describes the design of rock anchors.

ANCHOR MATERIALS AND ANCHORAGE METHODS

(c) Grout mix The required properties of grout used to anchor tensioned bars are first that it is strong enough to withstand the high stresses that are developed around the anchor, second that it does not degrade with time, and third that it is non-corrosive so that it does not affect the properties of the steel. Another consideration is that it must be of a consistency that will permit it to be readily placed in long, small diameter holes. In designing a grout mix to meet these requirements, the factors to consider are the water:cement ratio (w:c), the required setting time, and the use of additives to reduce shrinkage and segregation, and to improve workability (see (d) below). The use of grout mixes containing sand or fine aggregate is usually not recommended because these granular materials tend to block grout tubes. The cement used in grouts can be ordinary Portland cement (Type I), sulphate resisting cement (Type II), or hi-early (rapid setting) cement (Type III) (Bruce et al., 1996). Type I is used for most applications, with the following possible exceptions. If the rock contains sulfide minerals such as pyrite, or if the anchor is exposed to sea water, sulfate resisting Type II cement would be required. Where the sulfate content exceeds 2000 ppm, Type V cement should be used which has a high resistance to sulfate. Type III cement would be used where support must be provided shortly after installation; the setting time can be reduced from about five or six days for Type I cement, to three or four days for Type III. One of the difficulties in using Type III cement is that its working time is limited in warm weather. High alumina cement should be avoided because a high water:cement ratio is required for pumpability which may produce a low quality grout. Water used in grout should generally meet drinking water standards, except for the presence of bacteria. Contaminants that can be harmful to the performance of grout are sulfates, sugars and suspended matter (e.g. algae), and chlorides should be avoided where the grout will be in direct contact with the steel. The concentrations of these substances should be less than 0.1% in the case of

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sulfates, and less than 0.5% in the case of chlo rides. The water:cement ratio (by weight) used in the grout mix has a significant influence in the performance of grout: high water contents result in reduced strengths and durability, increased shrinkage and excessive bleed as shown in Fig. 9.8. These properties relate to both the bond strength of the grout and the protection it provides against corrosion of the steel. For example, excessive grout bleed will result in segregation and the presence of water in the upper part of the anchor zone. It is found that a w:c ratio of between 0.4 and 0.45 will produce a grout that can be readily pumped down small diameter grout tubes and will produce a strong, continuous grout column. The setting time of grout is important in scheduling tensioning operations, and in quickly providing support in emergency situations. Figure 9.9 shows the comparative setting times for a number of grout products. On projects where a substantial number of anchors are being installed, crushing tests on 50 mm (2 in) cubes of grout can be carried out to determine the compressive strength at 7 and 28 days. Strengths of 20 MPa (3000 p.s.i.) at 7 days, and 30 MPa (4300 p.s.i.) at 28 days are generally required, and a minimum strength at the time of stressing of 20 MPa (3000 p.s.i.) is recommended. On smaller projects where there is insufficient time to carry out such testing, the strength of the grout is effectively determined by load-deformation measurements made during tensioning of the anchor. (d) Admixtures While grout mixes comprising only cement and water are generally satisfactory for anchoring projects, non-shrink grouts formulated by grout manufacturers specifically for anchor installations are also available. These pre-mixed products will provide a more uniform and higher quality grout than may be produced by field mixing of the ingredients, and the non-shrink properties will enhance both the bond strength and the encapsulation of the anchor. The use of admixtures is usually restricted to compounds that control bleed, improve flowabil

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Figure 9.8 Effect of water content on the compressive strength, bleed and flow resistance of grout mixes (Littlejohn and Bruce, 1975b).

ity, reduce water content and retard set; a common non-shrink agent is Intraplas N (Sika Products) that is added to the mix at about 1% of the cement weight. However, accelerators, expansion agents and admixtures containing chlorides or sulfides, or aluminum powder should be avoided. Admixtures should only be used where tests have shown that they will have no long term effect on the performance of the anchor system, such as degradation of the grout or corrosion of the steel. Expanding grouts should only be used to fill voids such as under the trumpet at the head of the anchor. Where the expansion of the grout is due to the generation of gases during setting, the grout is likely to be porous and may then not be an effective barrier to water and moisture. In mixing grouts containing additives, the materials should be added in the following order: watercement-additives. Mixing should be carried out continuously using a high speed shear type mixer equipped with a recirculating chamber. Grout which

has not been used within 30 minutes after mixing is unsuitable because the process of setting has proceeded too far and the additives are no longer effective. (e) Grout pressures Rock anchors are usually grouted at atmospheric pressure. Pressure grouting is only used where the rock is sufficiently loose and fractured that the grout will be forced into the rock mass to consolidate and strengthen it, and form a mass of grouted rock integral with the anchor zone. Depending on the degree to which the rock is fractured, the effect of pressure grouting may be to increase the capacity of the anchorage by as much as 100%. A common procedure for pressure grouting is to install the anchor with two sets of grout tubes. The tube for primary grout extends to the distal end of the anchor zone and is used to fill the entire hole with grout as shown by the return of grout at the vent tube sealed in the collar of the hole. The tube

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Figure 9.9 Relationship between grout compressive strength and time of curing for various anchor grouts (Ocean Construction Products).

for pressure grouting, known as a tube en machette, is usually about 8–10 mm in diameter with holes drilled through it at regular intervals in the anchor zone. The holes are covered with a flexible rubber sleeve and fixed to the pipe to form a one-way valve system. Once the primary grout has attained an initial set, the secondary grout is pumped through the secondary grout tube to fracture the primary grout and penetrate the rock. This operation can be repeated a number of times and produce a significant improvement in anchor capacity. The pressure used for secondary grouting would depend on the grout take and the pressure should only be sufficient to cause the grout to penetrate existing fractures in the rock. Care should be exercised that the pressure does not exceed the confining pressure of the rock surrounding the anchor zone, because this could result in fracture of the rock and reduction in the strength of the rock

mass. (f) Centralizers It is important that the bar (or strand bundle) be fully embedded in a continuous and uniform grout column to develop a high strength bond in the anchor zone, and provide corrosion protection for the steel. This is achieved by installing centralizer sleeves at intervals along the bond zone which hold the anchor away from the walls of the drill hole and achieve a minimum grout cover of about 15 mm (0. 6 in). These centralizers are plastic ‘springs’ attached to the anchor with wire that are able to deform as they are pushed into the drill hole to accommodate variations in drill hole diameter (Fig. 9.10). The spacing between centralizers is usually between 0.5 and 3 m (1.5–10 ft), depending on the flexibility of the anchor and curvature of the drill hole.

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Figure 9.10 Dywidag bar anchor and corrugated sheathing, with two types of centralizer sleeves to hold bar from walls of drill hole.

9.2.7 Resin grout anchorage Resin anchorages are used for the installation of rigid bars with maximum lengths of about 7–8 m (23–26 ft), and maximum tensile loads of about 200 kN (45000lb). The anchorage is a two component system usually consisting of a viscous liquid resin and a catalyst that are packaged together in plastic ‘sausage’ cartridges about 200 mm (8 in) long and 20 mm (0.75 in) in diameter (Fig. 9.11). When the

two components are mixed by driving and spinning the bolt through the cartridges and shredding the plastic sheath, they set to form a rigid, nondegrading solid that anchors the steel bar in the hole. The setting time for the resin varies from about 1 minute to as much as 90 minutes depending on the reagents. The setting time is dependent on the temperature; fast setting resin sets in 4 minutes at a temperature of -5°C (23°F), and 25 seconds at 35°C (95°F). The resins have a limited shelf life and the expiry date should be checked at the start of the

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325

Figure 9.11 Resin cartridges; the white strip down the side of the cartridges is the hardener.

project. The principal advantage of the resin anchorage is the simplicity and speed of installation, with support being provided within minutes of spinning the bolt. The disadvantages are the limited length and tension load of the bolt, and the fact that only bars can be used. Another disadvantage is that corrosion protective sheaths cannot be used with a resin anchorage because they will be damaged when the bar is spun to mix the resin. The corrosion resistance of resin grouted anchors is limited because it is not possible to ensure that the bar is completely encapsulated in resin. Also, the shredded plastic sleeve may be a pathway for water to reach the unprotected bar. The corrosion protection systems for permanent anchors discussed in Section 9.4.4 provide a more reliable level of protection than that of resin anchorages. The installation procedure is to place in the drill hole a sufficient number of resin cartridges to fill the annular space around the anchor. It is important that the hole diameter is within the tolerances specified by the cartridge manufacturer because if the hole is too large mixing of the resin will be inadequate. This usually precludes the use of coupled bolts because the hole size required to accommodate the couplings will be too large for

complete resin mixing. This drawback may be overcome by reducing the hole diameter in the bond zone to be anchored with resin, and then using cement grout in the upper part of the hole with the larger diameter. Test have shown that the optimum annulus thickness for resin grout is about 3 mm (1/8 in) (Ulrich et al., 1990). The bar is spun as it is driven through the cartridges, and the spinning is continued for about 30 seconds after the bar has reached the end of the hole. The speed of rotation should be at least 60 revolutions per minute to achieve full mixing of the resin, and shred the plastic cartridges. This is accomplished by coupling the bolt to the drill chuck with a dolly and rotating the bolt with the drill, or using a torque wrench. When using fully threaded bars, the direction of rotation should auger the resin into the anchor zone; the opposite rotation may result in the distal end of the bolt being ungrouted as the resin is augered out of the hole. With bolt lengths greater than about 7–8 m (23–26 ft), most drills cannot rotate a fully embedded bolt at the required speed which limits the maximum bolt length. If the bolt is fully embedded in fast setting resin, it cannot be tensioned and the bolt acts as a passive anchor, or dowel. However, a tensioned bolt can be

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installed by using a fast setting resin (2–4 minute setting time) in the distal end of the hole, and a slower setting resin (15–30 minute setting time) in the remainder of the hole. The bolt is tensioned after the fast resin has set but before the slower resin has hardened. When all the resin has set, a fully grouted tensioned anchor is created which will continue to function even if the plate and nut at the surface are lost. 9.2.8 Mechanical anchorage The photograph in Fig. 9.12 shows the details of a Williams mechanical anchor, and the full installation is shown in Fig. 9.5(b). The components of the mechanical anchor are a pair of wedges that slide over a tapered cone threaded on the end of the bar. The installation procedure is to drill a hole to a specified diameter so that the wedge is gripped by the walls of the hole. When the bolt is torqued, the cone moves up the bar and expands the wedges against the walls of the hole to anchor the bar. Note that the surfaces of the wedges are smooth because this produces a uniform pressure on the rock, in comparison with serrated surfaces which crush and break the rock possibly resulting in reduced load capacity of the anchorage. The advantage of mechanical anchors is that installation is rapid, although not as rapid as resin anchors, and tensioning can be carried out as soon as the anchor has been set. They can also be used where flowing water precludes the use of cement anchorages. The disadvantage of the mechanical anchor is that it can only be used in medium to strong rock in which the anchor will grip, and the maximum working tensile load is in the range 150– 300 kN (35 000–70 000 lb). Mechanical anchors for permanent installations must always be fully grouted because creep and corrosion of the anchorage will result in loss of support with time. Grouting can be carried out either using a grout tube attached to the bar before installation, or in the case of the Williams bar, through the center hole until there is grout return at the collar.

9.3 Design procedure for tensioned anchors When a tensile load is applied to a rock anchor, this load is supported by the mass of rock in which the anchor is embedded (see the three examples in Fig. 9.2). The mechanism by which the load is transmitted from the steel bar or strand to the surrounding rock depends upon the following factors. 1. The applied load is transmitted from the steel anchor to the rock in the walls of the drill hole by the shear stresses developed at the steelgrout and grout-rock interfaces. 2. Stresses are developed between the rock in the immediate vicinity of the anchor and the surrounding rock. The capacity of the rock to withstand these stresses is significantly influenced by the orientation of discontinuities in the rock. 3. If the applied load acts in a direction above the horizontal, the mass of rock in which the bolt is anchored acts as a gravity restraining force (Figs 9.2(b) and (c)). Where the load acts below the horizontal (Fig. 9.2(a)), the cone of rock must be self supporting. The following is a description of these components of anchor performance. 9.3.1 Mechanics of load transfer mechanism between anchor, grout and rock When a tensile load is applied to a steel bar or cable that is anchored in rock with a column of grout (either cement or epoxy resin), shear stresses are developed at both the steel-grout and grout-rock interfaces (Fig. 9.13). The distribution of these stresses along the length of the anchor has been studied in laboratory model tests (Farmer, 1975), full-scale field tests (Golder Associates, 1983), and numerical analysis (Russell, 1968; Coates and Yu, 1971; Wijk, 1978). All these results show that under elastic conditions, the shear stress distribution is

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327

Figure 9.12 Wedge-type mechanical anchor (courtesy of Williams Form Hardware and Rockbolt Co.).

non-linear with high stresses concentrated at the top of the bond length which diminish rapidly down the hole. The shear stress distribution tx at the steel-grout interface along a fully bonded tensioned anchor, assuming that the steel, grout and rock all behave elastically and there is no slippage at the interface, can be defined by the following equation (Farmer, 1975):

where r1 is the radius of bolt; s0 is the normal stress applied at the proximal end (closest to the rock surface) of bond length; x is the distance from the proximal end of bond length;

The curve in Fig. 9.13 shows a typical distribution for the shear stress in terms of the dimensionless ratios tx/s0 and x/r1. This curve has been developed for a 30 mm (1.2 in) diameter bar grouted with epoxy resin resin into a 40 mm (1.6 in) diameter drill hole. The elastic moduli of the epoxy and steel are 2 GPa and 200 GPa (0.29×106 and 29×106 p.s.i.) respectively. Equation 9.3, which defines an exponential decay in the shear stress, can be used as a guideline to determine the length of bond required to dissipate the full applied tension within the anchorage. The shear stress is diminished to 1 % of its value at the top of the anchorage when ? is equal to 4.6, so the bond length lb to effectively dissipate the applied stress is equal to

(9.4)

(9.6)

(9.3)

for

i.e. thin grout annulus, or (9.5)

for

i.e. thick grout annulus; is the elastic modulus of the grout, Eb is the elastic modulus of bolt, and r2 is the radius of the drill hole.

Integration of equation 9.3 allows calculation of the total load Q carried by the anchorage between any two points (x1 and x2) along the bond length as follows:

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Figure 9.13 Distribution of shear stress along the length of the anchor zone of a tensioned anchor (after Farmer, 1975).

(9.7)

Equation 9.7 can be used to calculate the load carried between any two points along the bond The load carried by the length, x1 and and full length of the bond length, i.e. is approximately equal to the product of the applied tensile stress and the cross-sectional area of is small when the bar, assuming that the term A value of the parameter ? has been found from a

series of tests on bar anchors in which strain gauges were attached on the bond length at values of x equal to 0.3, 1.52, 3.05, 5.18 and 7.62 m (1– 25 ft). The anchors were installed in rock comprising alternating layers of closely fractured argillite and moderately fractured quartzite. With reference to Fig. 9.13, the values for the loads, stresses and dimensions were as follows:

The strain gauges showed a typical highly non-linear stress distribution along the bond length with the stress in the bar diminishing to zero at 2.1 and 3.7 m at the lowest and highest test loads respectively. It was found that values for the parameter ? of about 0.

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329

Figure 9.14 Variation in distributions of tensile stress along length of anchor zone with increasing applied load.

03–0.05 gave a close match between the measured loads along the bond zone and those predicted by equation 9.7. The shear stress distribution curve shown in Fig. 9.13 assumes no slippage at the interface and elastic behavior over the full length of the anchorage. However, as the applied stress is increased, the shape of the shear stress distribution curve becomes more linear and a greater portion of the load is carried at the distal end of the anchor (Fig. 9.14). As the load is further increased, the bond at the proximal end of the bond length will start to fail. Once the bond has been broken, the shear strength will be equal to the friction of the surface. General design practice is to select a combination of applied load and anchorage dimensions such that there is no slippage, and that the shear stress does not reach the distal end of the anchorage. That is, the applied load for the conditions shown in Fig. 9.14, would be between Q1 and Q2. The shear stresses developed at the steel-grout-rock interfaces along the bond length will result in a change in the stress field in the material around the anchorage. Figure 9.15 shows the results of model tests of a tensioned anchor in sand where the bond length is at some distance below the ground surface

(Hobst and Zajic, 1977). The contours of vertical stress show that there is a zone of compression at the proximal end and above the bond length, and a zone of dilation at the distal end and below the anchor. This stress distribution shows the value of having the bond length embedded at some depth below the surface to contain the zone of compressed rock. An anchor with the top of the bond length at the ground surface would have diminished capacity because the compressed rock would not be confined. Also,the zone of dilated rock shows how nearby structures may be influenced by a tensioned anchor. 9.3.2 Allowable bond stresses and anchor design The typical distributions of shear stresses along the anchor length shown in Figs 9.13 and 9.14 demonstrate the non-linear nature of this distribution. However, the exact form of this distribution is difficult to predict for the wide range of conditions that may exist within a tensioned anchor. For this reason a simplifying assumption is made for design purposes, namely that the shear stress is uniformly distributed along the bond length. The magnitude of this average shear stress for both the rock-grout and grout-steel interfaces

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Figure 9.15 Results of model tests of tensioned anchor in cohesionless sand showing distribution of vertical stress contours and zones of compression and dilation (Hobst and Zajic, 1977).

has been established empirically from the results of tests on full-scale and laboratory anchors. Calculation of the bond length is a two stage process that ensures that the working bond stresses are not exceeded at either the rock-grout or the grout-steel interfaces. First, the bond length and drill hole diameter are selected such that the average shear stress at the rock-grout interface is less than or equal to the working bond strength. Second, the length of the anchor is checked against the required design development length of the steel which is the length of embedment required to support the applied tensile load. Assuming that the shear stress is uniformly distributed on the surface of the drill hole forming

the bond length, the bond length lb is calculated from (9.8) where Q is the applied tensile load at the head of anchor; d is the diameter of drill hole, and τa is the working bond strength of rock-grout interface. From equation 9.8 a combination of bond length and drill hole diameter is selected such that the shear stress at the rock-grout interface is less than or equal to the working bond stress. Equation 9.8 indicates that in design, the average bond stress can be matched to the working bond stress by increasing the bond length, or the hole diameter as required.

ANCHOR MATERIALS AND ANCHORAGE METHODS

However, a practical limit on the bond length is in the range 8–10 m (26–33 ft), with usual rock drilling equipment limiting the drill hole diameter to about 150 mm (6 in). If a longer bond length than 8– 10 m is required, additional, lower capacity anchors should be installed. The reason for this restriction is that the peak stress is developed at the proximal end of the bond and if this stress is greater than the ultimate bond strength, failure of the grout in the proximal end of the bond will occur regardless of the bond length. An approximate relationship between the rockgrout bond strength and the uniaxial compressive strength of the rock has been developed from the results of load tests on anchors installed with cement grout anchorages in a wide range of rock types and strengths (Littlejohn and Bruce, 1977). Values for the design, or working τa, and ultimate τu bond strengths for cement grout are given by equations 9. 9 and 9.10 respectively:

331

(9.9) and (9.10) where σu(r) is the uniaxial compressive strength of the rock in the bond zone, or that of the weakest rock in the bond zone if the rock is layered. Values of τa, assuming a factor of safety of 3 applied to τu, which have been used for a variety of rock types and rock strengths for cement grout are shown in Table 9.2 (PTI, 1996; Littlejohn and Bruce; 1977). Some judgement should be used in the application of equation 9.8 and Table 9.2 to ensure that the bond stress value is suitable for the actual conditions that may be encountered. Unfavourable conditions necessitating a low value of τa would include a smooth hole surface produced by rotary drilling

Table 9.2 Approximate relationship between rock type and working bond shear strength for cement grout anchorages

Rock type Granite, basalt Dolomitic limestone Soft limestone Slates, strong shales Weak shales Sandstone Concrete Weak rock Medium rock Strong rock

Working bond stress τa at rock-grout interface MPa

p.s.i.

0.55–1.0 0.45–0.70 0.35–0.50 0.30–0.45 0.05–0.30 0.30–0.60 0.45–0.90 0.35–0.70 0.70–1.05 1.05–1.40

80–150 70–100 50–70 40–70 10–40 40–80 70–130 50–100 100–150 150–200

compared with percussion drilling, a zone of loose, fractured rock in the bond length, drill cuttings smeared on the walls of the hole, holes from which the drill cuttings cannot be completely cleaned, or flowing water. Favorable bond conditions may occur where the rock comprises strong rock with narrow layers of weaker rock, or in strong basalt containing vesicles; in both conditions irregularities in the wall of the hole enhance bonding. Because the actual conditions in the hole are likely to be unknown,

usual practice is to conduct performance tests on selected anchors to ensure that the anchor meets specified acceptance criteria (see Section 9.5). For the resin products that are widely available, ultimate rock-resin bond strengths vary from about 4.8 MPa (700 p.s.i.) for installations in very strong granite with compressive strengths in the range of 80–100 MPa (12 000–15 000 p.s.i.) to 1 MPa (150 p.s.i.) in weak mudstones and siltstones with compressive strengths in the range 5–5.5 MPa (700–

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800 p.s.i.). Based on these values, it is possible to produce ultimate anchorage strengths of approximately 200 kN (45 000 lb) with bond lengths of 0.3 m (12 in) and 1.4 m (55 inches) respectively for these two classes of rock strengths. The second step in the anchor design is to check that the shear stress developed at the steel-grout bond interface does not exceed the working bond stress (British Standards Institution, 1985). Values for bond stresses have been derived from pull-out tests conducted in concrete to determine development lengths of bar and strand. Development lengths, which are the embedment lengths required to develop the full strength of the bar are defined by the following equations (Canadian Portland Cement Association, 1984).

projects, although a factor of safety up to about 1.5 may be used in poor anchoring conditions. Such conditions include variable grout thickness in the annulus where the anchor cannot be accurately centered in the hole, or a low strength grout because of flowing water in the bond zone or where the grout is contaminated with drill cuttings. 9.3.3 Prestressed and passive anchors

Where rock anchors are used to support tension loads, there are two different design methods that can be used—prestressed or passive anchors (Fig. 9.17). The advantages of using prestressed anchors are that the deflection of the head of the anchor is minimal on the application of the structural load, and they can have a somewhat 1. For 35 mm diameter bars and smaller: greater load capacity. This is of particular (9.11)importance in the case of anchors subjected to cyclic loads which could experience fatigue failure but not less than if not prestressed. (9.12)Figure 9.17 demonstrates the mechanism by which 2. For 45 mm diameter bars: tie-down anchors support tensile loads. In Fig. 9.17 (a), the anchor comprises two components: a bond (9.13) length lb and a free stressing length lf. Over the bond length, bond is developed between the steel and the 3. For 55 mm diameter bars: cement grout which secures the tie-down in the (9.14)hole, while in the free stressing length, which is ungrouted or encased in a smooth plastic sheath, no 4. For prestressing strand bond is developed. When a reaction plate is (9.15)installed at the rock surface and a tensile load is applied to the head of the anchor, a zone of rock between the reaction plate and the bond length is compressed. This also develops shear stresses at the where ld is the development length (mm); Ab is the boundary between the compressed zone and the cross-sectional area of bar (mm2); sy is the specified surrounding rock. Under these conditions, the yield strength of non-pre-stressed reinforcement capacity of the anchor to sustain pull-out forces (MPa); suc is the specified compressive strength of depends on the shear stress in the bond length, as grout (MPa); and db is the nominal diameter of bar well as the shear strength of the rock at the or strand (mm). The relationship between bar boundaries of the zone of compressed rock diameter and working development length as (Fig. 9.17(a)). In the case of anchors installed below defined by equations 9.11–9.15 is shown in the horizontal, there is additional uplift capacity in Fig. 9.16. the weight of the rock mobilized between the bond Equations 9.11–9.15 define working development length and the reaction plate. Also, the capacity of lengths which should be suitable for most anchoring

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333

Figure 9.16 Working development lengths for steel bar and strand anchored in cement grout; lengths calculated from equations 9.11–9.15.

the anchor is enhanced where the most highly stressed portion of the rock mass at the upper end of the bond zone is below the ground surface and is confined by the surrounding rock. Figure 9.17(b) shows an anchor which is bonded over its full length and no prestress is applied—this is sometimes referred to as a passive anchor. In this case, the application of the structural load causes shear stresses to be developed in the bond zone at the ground surface. Since this rock is unconfined, and may also be weathered and/or fractured by blasting in the preparation of the foundation, its capacity to withstand the concentrated stresses at the upper end of the anchor is less than that of the embedded anchor. The result is likely to be partial debonding of the anchor and displacement as the load is applied. Another important difference between the prestressed and passive anchors is the displacement of the head of the anchor on the application of the structural load. This is illustrated in the model shown in Fig. 9.18, where the bond is replaced with a spring of stiffness kb and the shear strength of the rock in which the anchor is embedded is replaced with a spring of stiffness kr. The tensile load Q supported by the anchor is equal to the product of the spring stiffness and the displacement d. In the case of a prestressed anchor (Fig. 9.18(a)), the displacement of the head of the anchor, at loads up

to the level of the pre-load Qp, will be limited to the small deformation of the surrounding rock, . Once the structural load exceeds the prestress load, the displacement of the head of the anchor will be equal to elastic elongation of the freestressing length plus the small amount of deformation in the rock surrounding the bond zone. The displacement db of a passive anchor (Fig. 9.18 (b)) will be primarily the result of strain of the upper end of the bond zone at the ground surface. Because the upper end of the bond zone is unconfined, the displacement db will exceed the displacement dr of the more highly confined . As the load is prestressed anchor, i.e. increased, a progressively longer portion of the anchor zone is stressed and the displacement db increases. The relative load-displacement behavior of prestressed and passive anchors is illustrated in Fig. 9.19. 9.3.4 Uplift capacity of rock anchors Figure 9.20 illustrates two common uplift loading conditions for rock anchors—a pure tension load (a), and a combination of tension and moment (b). An example of an anchor loaded in pure tension is the support for a guy wire where the wire and the anchor are co-linear, while a combination of

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Figure 9.17 Mechanism of support of tension loads by (a) prestressed and (b) passive anchors.

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335

Figure 9.18 Simplified model of support mechanism of (a) prestressed and (b) passive anchors.

tower subjected, for example to wind loads, is anchored with bolts in a circular or square pattern around the base. Much of the work in developing design procedures for these loading conditions has been carried out by electrical utilities for the design of foundations for transmission towerss (EPRI, 1983; Ghosh, 1976). These are tall structures that do not produce high bearing pressures, but must withstand significant moments induced by wind loads and tension in the conductors, particularly when they are coated with ice. The different design procedures used for these two loading conditions is described in the following sections. (a) Pure tension loading There are several possible failure modes for anchors loaded in pure tension (Fig. 9.20(a)). Failure may occur in the steel, or in the bond at either the rockgrout or the grout-steel interfaces, or a cone of rock with its apex near the mid-point of the anchor zone

may be pulled out. Design against failure of the anchor at the grout interfaces requires that the length of the bond zone, and the diameters of the bar and drill hole are proportioned such that the average shear stress is less than the working bond shear strength. Values for working rock-grout bond shear strength are given in Table 9.2 and formulae for development lengths of embedded bars and strand are given by equations 9.11–9.15. After the bond length required to resist bond failure has been determined, the next step is to check that the anchor will mobilize a sufficient volume of rock to support the applied load. The results of uplift tests on rock anchors show that the mass of rock mobilized around the anchor is approximately conical, with the dimensions and shape of the cone being dependent on the structural geology of the site. A simplifying assumption can be made that the apex angle is 90°, and that the position of the apex

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Figure 9.19 Typical relative load-deflection performance of prestressed and passive anchors.

Figure 9.20 Types of loading conditions for uplift anchors: (a) pure uplift load; and (b) combined compression and moment load.

is at the mid-point of the bond length (Fig. 9.20(a)). The weight of the cone can be calculated from these dimensions, but test results show that the maximum uplift load that is actually supported is as low as seven and as high as 56 times the weight of the cone (Saliman and Schaefer, 1968; Littlejohn et al., 1977a). The difference between the cone weight and the actual uplift capacity is that the support is provided by the strength of the rock on the surface of the cone. This clearly demonstrates that using only the weight of the cone for uplift resistance

produces a very conservative design. A precise design method for the capacity of uplift anchors cannot readily be developed because the dimensions of the wedge, as well as the strength of the rock on the surface of the cone are difficult to define. Littlejohn and Bruce (1975a) have made a survey of cone dimensions used on about twenty projects around the world which shows that the apex angle varies from 60° to 90°, and that the position of the apex varies from the top to the bottom of the bond length. Narrow apex angles

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Figure 9.21 Influence of structural geology on the shape of cones of rock mobilized by uplift anchors: (a) wide cone formed in horizontal bedded formation; (b) narrow cone formed along vertical joints; and (c) surface of cone formed along conjugate joints.

(60°) are used in weak rock, and in strong rock that the apex angle may be as great as 120° (Radhakrishna and Klym, 1980). The shape of the rock cone is also strongly influenced by the structural geology in the bond length as illustrated in Fig. 9.21. The most favorable case is that of continuous structure aligned at right angles to theanchor (Fig. 9.21(a)), and the least favorable angle is where the structure is aligned parallel to the anchor (Fig. 9.21(b)). It is considered that the most likely location of the apex of the cone is the midpoint of the bond because the shear stress is concentrated in the upper half of the bond length. The rock strength that operates on the surface of the cone can only be estimated because the failure mechanism consists of a complex combination of shear and tensile movements related to the details of the geological structure relative to the direction of the applied load. The range of rock fracture

mechanisms that may occur is illustrated in Fig. 9.21. As it would not be possible to simulate this failure mechanism in laboratory scale tests, the strength developed on the surface of the cone is best determined from the results of full-scale uplift tests. Where load tests are not possible, the strength of the rock under these load conditions can be estimated from equation 9.16 which gives the tensile strength of fractured rock (Hoek, 1983) (st is a negative number): (9.16) where st is the working tensile strength on surface of cone, su(r) isthe unconfined compressive strength of rock; m, s are rock mass strength constants (see Table 3.7) and FS is the factor of safety applied to the rock strength. A limited number of results of tests on uplift anchors (Saliman and Schaefer, 1968; Littlejohn et al., 1977a; Ismael, 1982) indicates that

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Figure 9.22 Cone of rock mobilized by tie-down anchor to resist uplift load.

equation 9.16 gives reasonable values for the strength of fractured rock in tension. The value assumed for the factor of safety in equation 9.16 would depend on the fracture intensity of the rock and the orientation of the discontinuities with respect to the anchor. It is estimated that the value of FS may vary from 2 for massive rock with the predominant discontinuity set at right angles to the anchor, to 4 for closely fractured rock, or where the discontinuities are parallel to the anchor. Where a large number of anchors are to be installed on a project and there are substantial savings to be realized in having the bond length as short as possible, it would usually be appropriate to conduct a test program to verify the rock strength. The capacity of an anchor loaded in tension against failure of the cone of rock depends upon the combined weight of rock in the cone and the rock strength on the surface of the cone (Fig. 9.22). The buoyant weight Wc of the cone is (9.17) and the resisting force f(r) developed on the curved surface area of the cone is (9.18) The capacity of the rock cone to resist the tension

force Q depends on the direction of the force. If Q acts vertically upwards the weight improves the load capacity, while if Q acts vertically downwards the weight diminishes the load capacity. Therefore, the uplift capacity Q is given by (9.19) In equations 9.17–9.19, ? is the apex angle of cone, D is the depth of apex below ground surface, Dw is the depth of water table below ground surface, ?r is the rock unit weight, ?w is the water unit weight, ?c is the angle between vertical upwards direction and load direction, and FS is the factor of safety applied to the load. (b) Combined moment and tension loading The load condition shown in Fig. 9.20(b) comprises a combination of a moment M, and an vertical force Q applied to the tower structure which is anchored with a group of bolts arranged in a circular pattern around the base (Fig. 9.23). A full scale test of this loading condition has been carried out by Radhakrishna and Klym (1980) and the method of calculating the support has been reported by Ismail (1982). A structure subjected to vertical and moment loads induces a distribution of stresses in the foundation which can be approximated by the method shown in Fig. 9.23. The moment applied to the structure is resisted by a force couple composed of tension T

ANCHOR MATERIALS AND ANCHORAGE METHODS

and compression C forces. The tensile force is mobilized by the rock anchors and the compression force is mobilized by the rock on which the tower is founded. The distance between these forces is defined by a lever arm am which depends upon the load distribution in the foundation and the geometry of the anchor layout. Where the bolts are laid out in a circular pattern and the distribution of the stresses across the base of the tower is triangular, the lever arm is found to be about 0.7 times the diameter of the anchor bolt circle. This value for the lever arm is in agreement with the theoretical value for the case of a triangular stress distribution in a steel ring subjected to bending. The stability of the structure is calculated from the weight of the truncated cone of rock mobilized in the foundation, and the strength of the rock on a portion of the cone surface that is subjected to uplift. Assume that the apex angle of the rock cone is 90° so that the truncated cone has the dimensions shown in the lower diagram on Fig. 9.23. The weight of the mass of rock in the truncated cone is given by

(9.20)

, where D is depth of the truncated cone for and d is the diameter of the circle of anchor bolts. For a symmetrical distribution of the tension and compression forces in the foundation, only the rock on the surface of the uplift half of the cone will be mobilized to resist the applied loads. The surface area of one half of the truncated cone, ignoring the

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horizontal base of the cone, is (9.21) and the resisting force generated on this surface is (9.22) where st is the tensile strength of the rock on the surface of the cone as defined by equation 9.16. The vertical force on the wedge is the total of the applied vertical force Q and the tension force T induced by the moment. The magnitude of the force T is determined by taking moments about the axis of rotation such that (9.23) Therefore the load capacity of the tower foundation is given by (9.24) Note that the sign of the force Q depends on its direction and is defined as follows: +Q vertical force upwards in same direction as tension force induced by the moment; -Q vertical force downwards. Equation 9.24 can be solved to find the length of bolt required to mobilize a cone of rock with dimensions sufficient to support the combined loads, with the required capacity of the bolts depending on the bolt pattern selected. It is also necessary to check that the compressive stresses induced on the outer edge of the foundation do not exceed the bearing capacity of the rock.

EXAMPLE 9.1 VERTICAL UPLIFT LOADING

Consider an anchor loaded with a vertical uplift force of 250 kN (56.2 kips) installed in a horizontally

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Figure 9.23 Truncated cone of rock mobilized by group of anchors to resist combined uplift and moment loading: (a) dimensions of truncated cone; (b) plan of anchors; (c) triangular stress distribution; and (d) section through uplift portion of cone.

bedded limestone with a uniaxial compressive strength of 30 MPa (4350 p.s.i.) (moderately weak rock)

ANCHOR MATERIALS AND ANCHORAGE METHODS

and a fracture spacing of about 0.5 m (1.6 ft). The load is coincident with the axis of the bolt so there are no moments generated in the anchor. The water table is 0.5 m below the ground surface . Determine the length of passive, fully grouted anchor required to support this load. The first step in the design is to determine the diameter of the steel bar that will have a working load of 250 kN. A 25 mm (1 in) diameter, continuously threaded bar with an ultimate tensile stress of 1030 MPa (150 k.s.i.) will have an ultimate strength of 506 kN (114 kips) and a working strength, at 50% of the ultimate strength, of 253 kN (57 kips) (see Table 9.1). This bar will support the uplift force. From equation 9.9 and Table 9.2, the working bond strength at the rock-grout interface for limestone with a compressive strength of 30 MPa (4350 p.s.i.) will be in the range 700 kPa-1 MPa (100–145 p.s.i.). Assume a value for the working bond strength of 800 kPa (116 p.s.i.) for design purposes. If the 25 mm diameter bar da is installed in a 50 mm (2 in) diameter drill hole dh, the value of the ratio dh/da is 2 (see equation 9.2). Assuming that the bolt is anchored with cement grout, and the shear stress is uniformly distributed along the bond, it can be determined from equation 9.8 that the required bond length is 2 m (6.6 ft). From equation 9.11 the required development length is 1.75 m (5.75 ft). This shows that the rock-grout bond strength, which is less than the grout-steel bond, governs the bond length determination. The uplift capacity is the sum of the weight of the cone of rock mobilized by the anchor, and the strength developed on the surface of the cone as defined by equation 9.19. If the density of the rock is 25 kN/m3 (160 lb/ft3) and the apex angle is 90°, and the depth is 1 m (apex at mid-point of bond), the buoyant weight of the cone is 24.9 kN (5.6 kips). The surface area is 4.4m2 (47.4 ft2). From table 3.7, the constants m, s defining the rock mass strength are and and from equation 9.16, the working rock strength in tension on the surface of the cone, assuming FS equals 2 is about 10 kPa (1.5 p.s.i.). The total uplift resistance is the sum of cone weight of 24.9 kN (5.6 kips) and the tensile strength of the cone surface of 44 kN (9.9 kips) which is less than the design load of 250 kN. If the bolt length is increased to 4m (13.1 ft) so that the cone depth is 2 m (6.6 ft), then the cone weight increases to 186 kN (41.8 kips) and the surface area of the cone increases to 17.7m2 (190.5ft2). The total resistance is 363 kN (82 kips) which exceeds the design load. These figures show that the very low tensile strength generates more uplift capacity than the weight of the cone of rock.

EXAMPLE 9.2 UPLIFT-MOMENT LOADING

To illustrate the design of a combined uplift and moment loading, consider a tower with an uplift load of 250 kN (56.2 kips) and a moment of 500 kNm (369 kip-ft). The base of this tower has a diameter of 2 m (6.6 ft) and is anchored with eight bolts equally spaced around the base. The rock properties are identical to those described in Example 9.1. The first step is to calculate the depth of the truncated rock cone that must be mobilized to support this loading condition. The tension force is calculated from equation 9.23 to be 750 kN (168.6 kips) and the total uplift force is 1000 kN (224.8 kips). If it is assumed that the depth below the surface of the truncated cone is 3.0 m and the water table is again 0.5 m below ground surface

341

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TENSION FOUNDATIONS

then the weight of the 45° truncated cone is calculated from equation 9.20 to be 1219 kN (274 kips). From equation 9.21 the surface area of one half of the truncated cone is 33 m2 (355 ft2), and the resisting force due to the tensile strength of the rock is 330 kN (74 kips). From equation 9.24 the total resisting force exceeds the uplift force by a factor of safety of 1.47 [(1219+250)/1000]. The load on each bolt is calculated as follows. The applied uplift load is uniformly distributed on each bolt and is equal to (7 kips). The uplift force generated by the moment is concentrated on the edge of the foundation and is distributed between three bolts (Fig. 9.23(b)). The load on each bolt is approximately (56 kips) and the total force on each bolt is 281 kN (63 kips). For steel with an ultimate tensile strength of 1030 MPa (150 k.s.i.), a 30 mm diameter bar will have an ultimate strength of 728 kN (164 kips). If the maximum working load is 364 kN (82 kips) at 50% of the ultimate strength, a 30 mm bar has adequate capacity for these loads, with allowance for some nonuniformity in loading. The load on each anchor can be more accurately calculated by integrating to find the portion of the force supported by each bolt.

9.3.5 Group action

9.3.6 Cyclic loading of anchors

Where a number of anchors are required to support the structural load, the combined effect of the group of anchors must be evaluated. As shown in Fig. 9.23, the cones of rock mobilized by each anchor interact where the bolts are closely spaced to form a single truncated cone. In order to prevent excessive stress concentrations being developed around the anchors that could fracture the rock, and minimize the risk of drills holes intersecting, it is usual practice to specify both a minimum spacing and a stagger between the bond zones. While there are no codes defining spacing and stagger, one commonly used criteria for the minimum spacing is that it should be the lesser value of four times the diameter of the bond zone or 1.2 m (4 ft) (PTI, 1996). Also, the South African Code of Practice (1972) recommends that for anchors spaced at less than 0.5 times the bond length, the stagger between alternate anchors should be 0.5 times the anchor length. Anchors can also be staggered by installing them at different angles. This is particularly important where there is a persistent set of discontinuities; the anchors should be oriented so that they cross the discontinuities and are not all aligned either parallel or perpendicular to the discontinuity sets.

Conditions that could result in cyclic loading on tensioned anchors may include tidal movement, and wind and traffic loading (Madhloom, 1978; Al Mosawe, 1979). Where the anchorage is in closely fractured rock, the cyclic loading may cause loosening and dilation of the rock mass, and eventual reduction in the capacity of the anchor. The installation of prestressed anchors under these conditions will maintain the interlock between the blocks of rock in the anchor zone and minimize the risk of movement of the anchorage. In addition, placement of the top of the bond zone at some depth below the rock surface will provide confinement to the rock in the most highly stressed area of the rock and minimize the risk of loosening of the rock mass. Section 9.3.3 discusses the applications of prestressed and passive anchors. 9.3.7 Time-dependent behavior and creep On many projects that rely on tensioned anchors for permanent support, there is a requirement for long term monitoring of both the load in selected anchors, and the deformation of the structure. These two sets of information will be of value in determining the cause of any displacement or

ANCHOR MATERIALS AND ANCHORAGE METHODS

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Figure 9.24 Long-term load monitoring of anchors (Littlejohn and Bruce, 1979).

change in load. For example, movement in a direction that lengthens the anchor together with an increase in load would indicate that the anchor is holding, but there is insufficient anchoring force to prevent movement of the structure. A monitoring specification has been prepared by the Bureau Securitas (1972) which specifies both the number of anchors that must be monitored and the monitoring frequency as follows. 1. Number of anchors to be monitored 10% of total anchors installed for 1–50 anchors 7% of total anchors installed for 51–500 anchors 5% of total anchors installed for >500 anchors 2. Frequency of monitoring First year, every three months Second year, every six months Third to tenth year, once a year 3. Load change tolerance A change in load greater than 20% of the design should be investigated. Time-dependent behavior of rock anchors will result from both relaxation of the steel bar or strand, and creep of the grout and rock in the bond length. As discussed in Section 9.2.2, relaxation of the steel

will be negligible if the applied load is not more than about 50% of the ultimate strength. At applied loads in excess of 50% of the ultimate strength, relaxation will be limited if the anchor is restressed at a time of 1000 hours. Figure 9.24 shows a typical plot of load loss against time for anchors comprising 12×15.2 mm (0.6) diameter Dyform strand with an 8 m (26 ft) long bond zone in a 140 mm (5.5 in) diameter drill hole. The design loads were in the range 2172–2337 kN (488–525 kips) (Littlejohn and Bruce, 1979). In another test, monitoring was carried out over a period of five years (248 weeks) of the load in a number of cement grouted, 36 mm diameter bar anchors loaded to 80% of the ultimate strength of the bar. The results showed a relatively rapid loss of load of about 5-7% of the applied load in the first six months, followed by a decreased rate of load loss in the subsequent months with a total loss of load of 7–9% at the end of five years (Benmokrane and Ballivy, 1991). Additional tests have shown that the load is generally stable or decreases very slowly after the first six months, with the majority of the load being lost in the first one or two months (FHWA, 1982; Golder Associates, 1989). In comparison with the creep rates for bare strand shown in Fig. 9.24, it has been found that epoxycoated filled strand exhibits creep rates that are an order of magnitude higher, although the total

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elongation was within acceptable limits (Bruen et al., 1996). A possible cause of this creep movement may be deformation of the epoxy between the strands (see Section 9.5.3, Acceptance Criteria). 9.3.8 Effect of blasting on anchorage Blasting may sometimes take place close to tensioned anchors and it will be necessary to design the blasting procedure so that there is no damage to the anchors. Damage that can be caused by blasting may include fracture of the grout in the bond zone, overstressing of the bar of strand, and disturbance of the head of the anchor. Methods of protecting anchors against these causes of damage are described below. (a) Blast damage to bond Detonation of an explosive confined in a drill hole will generate a shock wave in the surrounding rock that will have sufficient energy within a distance of about 40–50 borehole diameters to fracture the rock (refer to Fig. 10.13). At greater distances, the shock wave will generate ground vibrations that may have sufficient magnitude to fracture the grout in the anchorage zone. The resilience of cement grouted anchors to blasting is demonstrated in hard rock mining operations where it is common practice to mine upwards through pre-placed passive anchors. Despite the high level of explosive energy to which these anchors are subjected, they are still effective in supporting the mine roof. A specific testing program of the performance of resin anchored rock bolts located close to blasts has been carried out in a tunnel in Wales (Little-john et al., 1989; Rodger et al., 1996). The tests showed that all deformations in the bolts were elastic and there was no resin-bolt debonding or loss of load for ground accelerations in the range 10–640 g. These accelerations were developed by explosive loads per delay in the range 16.5–35.8 kg (36–79 lb) detonated at distances as close as 1 m (3.3 ft) from the bolts. Section 10.3.4 discusses methods of calculating blast vibration levels. While grouted bolts are able to sustain load when

subjected to blast induced vibrations, it is likely that the grout, which is brittle, is cracked by the ground motion and may then be more susceptible to corrosion. Where corrosion of the steel is of concern, the provision of a grouted sheath that is more resilient than the grout alone, will improve corrosion resistance. (b) Overstressing of bar or strand Passage of the shock wave through the rock causes dilation and compression of the rock mass which will alter the strain in the anchor. This strain will be transient if the rock behaves elastically. However, if the magnitude of the shock wave is sufficient to permanently open discontinuities which are intersected by the anchor, there will be a corresponding permanent increase in the stress in the anchor. In the tunnel blasting tests described in (a) above, it was found that the dynamic stress induced in the bolts was about twice the level for fully grouted, untensioned bolts than for prestressed bolts anchored with two speed resin. This indicates that confinement of the rock by the tensioned bolts helps to limit the deformation of the rock mass and corresponding strain in the steel. For example, in a 6 m (19.7 ft) long bolt tensioned to 100 kN (22.5 kips) subjected to a peak particle acceleration of 345 mm/sec (13.5 in/ sec) and a maximum acceleration of 130g, the peak dynamic stress in the bolts reached a level of 13% in excess of the prestress. An approximate relationship between the peak dynamic load (expressed as a percentage of the prestress load) and the blast parameters for the tunnel in Wales was found to be (9.25) where R is the distance between the blast (m) and the bolt and W is the explosive weight detonated per delay (kg) (Littlejohn, 1993). Another example of stresses induced in tensioned anchors by blasting is given by Littlejohn et al. (1977b) where both the transient and permanent stress in anchors installed in the footwall of a coal mine were monitored. The anchors had working

ANCHOR MATERIALS AND ANCHORAGE METHODS

loads of 1500 kN (337 kips) and free stressing lengths of 12 m (39 ft), and were located parallel to the rows of blast holes. A row of nine blast holes, each loaded with 32 kg (70 lb) of explosive and located 5 m (16 ft) from the row of anchors, was detonated on a single delay. Detonation of this explosive charge caused an instantaneous increase in anchor load of 100 kN (7%) and a permanent increase of load of 64 kN (4%). (c) Flyrock damage Where there is a possibility of damage to the head of a prestressed anchor from flyrock, either the blast should be covered with blasting mats or the head protected in an appropriate manner. This is particularly important in the case of strand because the wedges are highly stressed and sensitive to damage. 9.3.9 Anchors in permafrost Extensive rock bolting has been carried out in permafrost using both cement and resin anchorages. The general method used in all these installations is to heat the ground around the bond length sufficiently to melt the permafrost during the time that the cement or resin is setting. When the permafrost reforms, the ground expands to develop a contact pressure between the ground and the grout that enhances the bond strength (Kast and Skermer, 1986). Using this method the cement or resin sets normally and the bond strengths developed are comparable to those obtained in unfrozen ground. Tests have been conducted in 8 m (26 ft) deep holes in sound, frozen rock using a neat Ciment Fonduwater grout mix heated to about 13°C (55°F); Ciment Fondu has a high heat of hydration which counteracts the cooling effect of the ground. The bar was heated prior to installation and the permafrost around the hole was melted by circulating steam. It was found that the temperature in the grout was maintained above freezing for up to 18 hours, which compared with a setting time of the grout of about 5 hours. Pull tests indicated that an ultimate rock-grout bond strength of about 1 MPa

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(145 p.s.i.) was developed, while the steel-grout bond strength was as high as 7 MPa (1015 p.s.i.). These bond values are similar to those for anchors in weak rock (see Table 9.2). Resin has also been used for anchors installations in permafrost with ground temperatures down to −30° C. The procedure was to circulate hot water in the hole to melt the ice around the hole, and to heat the bar and resin to about 35°C (95°F). The bar was then installed in the normal manner and the resin sets before the temperature of the ground adjacent to the resin dropped below the freezing level (Kast, 1989). A detailed testing program of anchors installed in permafrost has also been carried out by Johnston and Ladanyi (1972). The material in the bond zone comprised varved silt and clay, containing ice lenses 2–8 mm (0.8–0.3 in) thick, at an overall ground temperature of about −0.5°C (31°F). The grout mix used for the anchorage consisted of high early strength cement (Type III), sand and water mixed in the proportions 1:1:0.5. The grout temperature when placed was between 5 and 14°C (40–55°F). At the completion of the test program all the anchors were recovered and is was found that the grout was hard and the particles well bonded, and the surface in contact with the frozen soil was not flaky or powdery. Although the primary purpose of this program was to conduct creep tests, it appears that the working bond strength for these conditions was about 0.1 MPa (14.5 p.s.i.). 9.4 Corrosion protection The protection of permanent anchors, and sometimes temporary anchors, against corrosion is one of the most important aspects of their design and construction. Current practice is to provide a corrosion protection system, appropriate for the site conditions, for all permanent anchors, as well as for temporary anchors where the environment is corrosive and there is a chance of failure during their service life. Permanent anchors are defined as those with a service life exceeding 24 months (PTI,

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1996). The importance of corrosion protection is demonstrated in the results of a survey of failure of anchorage systems caused by corrosion (Littlejohn, 1987). A total of 35 cases of corrosion failure have been reported in the literature, of which 11 were temporary anchors; the time to failure varied from six months to 31 years. These failures could be divided into the following three categories: 1. corrosion of the bond zone (2 failures); 2. corrosion of the free stressing length (21 failures); 3. corrosion of the head (19 failures). While these failures are only a small fraction of the millions of anchor projects that have been installed, corrosion is just about the only cause of failure once the system has been installed and tested. Research on corrosion of rock bolts in Finland and Sweden has shown that there can be defects in the grout encapsulation of cement grouted anchors, particularly in and under the head area where the corrosion protection may be incomplete (Baxter, 1997). Furthermore, for resin anchored bolts encapsulation of the steel can be incomplete due to poor mixing, the presence of the shredded plastic sheath in the resin and the inability to center the bar in the hole. The process of corrosion is complex and not clearly understood, particularly in the highly variable conditions that may occur below the ground surface. For this reason corrosion protection measures are almost always provided on permanent anchors. 9.4.1 Mechanism of corrosion The mechanism of corrosion of prestressing steel is predominantly an electrolytic reaction in which three conditions must be present. First, the steel strand or bar must be in contact with an electrolyte, which in rock anchors is usually water. Second, the electrolyte must be in contact with an anode and a cathode, and third, there must be direct metallic

connection between the anode and cathode (Fig. 9.25). A film of water is sufficient to develop corrosion, and the corrosion risk increases in flowing water where the corrosion products are carried away to expose a new surface to attack. Humidity is an even more dangerous condition because of the ample supply of oxygen to the corrosion site (Littlejohn and Bruce, 1977). Where these three conditions exist, corrosion will occur if a current flows between the anode and the cathode. The rate of corrosion is proportional to the magnitude of the current, and corrosion occurs as the metal ions go into solution at the anode. There are two mechanisms which will develop a current flow. First, a galvanic micro-cell is set up where the cathode has a higher electrical potential relative to the electrolyte than the anode resulting in the development of a potential difference between the anode and the cathode (Fig. 9.25(a)). Second, where stray direct currents are present in the soil, the steel offers a low resistance path and a portion of the current may leak into the anchor (Fig. 9.25(b)). Where the current leaves the steel and discharges back into the soil or electrolyte, an anode is formed and corrosion pits will firm at this point (FHWA, 1982). Potential stray current sources are electrified railways, welding operations, cathodic protection rectifiers and electroplating plants. Galvanic micro-cells may develop under a variety of circumstances, all of which meet the three conditions for corrosion listed in the previous paragraphs. Any one, or a combination of the conditions described below may occur around an anchor and result in corrosion (Hanna, 1982). 1. Inhomogeneities within the metal Impurities and regions of varying composition will have different electric potentials with the result that a current flow is generated between different regions within the metal. 2. Defects at the metal surface Cracks in the metal surface, which may develop when the steel is stressed, form discontinuities in any protective layer and the crack becomes an anodic zone where corrosion may initiate.

ANCHOR MATERIALS AND ANCHORAGE METHODS

3. Bimetallic cells Where two metals are in contact, the difference in electric potential be tween the metals generates a current. The morereactive cell acts as the anode and, under theright conditions, corrosion occurs at the anode. 4. Oxygen supply Where there is a high oxygen concentration at the surface, the metal becomes cathodic and sites of low oxygen concentration become anodic. The magnitude of the current generated is related to the difference in oxygen concentration. 5. Hydrogen concentration A variation in hydrogen ion concentration, or pH, produces an electrical differential and the formation of a galvanic micro-cell. 9.4.2 Types of corrosion Corrosion can occur as general corrosion on the entire surface of the steel, as local corrosion forming pitting and crevices, and as hydrogen embrittlement. General corrosion results where the anode and cathode are approximately equal in area, and can be beneficial where it forms a thin, continuous and stable coating that protects the steel from further attack. Local corrosion is associated with defects and inhomogeneities in the steel, and also where stressing produces breaks in a protective surface layer. Hydrogen embrittlement occurs where the steel molecular structure is disrupted and weakened by the absorption into the metal lattice of atomic hydrogen. The conditions under which these types of corrosion develop are discussed below (FHWA, 1982; Reeves, 1987). (a) Pitting corrosion Pitting corrosion results from intense local attack in an electrolyte. It is one of the most destructive forms of corrosion because the pit will reduce the cross-sectional area of the highly stressed steel member. Furthermore, once initiated, the corrosion process within the pit produces a condition that stimulates further corrosion. The galvanic cell shown in Fig. 9.25(a) shows the conditions that

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produce pitting corrosion. The chloride ions locally weaken the passive film protecting the steel and an anodic zone is developed where metal ions go into solution. These ions react with the water to produce a variety of iron oxide corrosion products (rust). As the process continues, the pH of the cathode increases due to the accumulation of hydroxyl ions. Simultaneously, the pH is lowered within the pit because corrosion products retard the diffusion of oxygen into the pit, while chloride ions migrate into the pit. The rate of corrosion increases as the pH decreases. (b) Stress corrosion Stress corrosion cracking is an anodic corrosion process with the crack forming at anodic sites. The formation of a crack in a steel under high tensile load exposes a fresh metal surface to attack and the reduction in cross-sectional area may eventually result in brittle failure of the anchor. There is some indication that high strength steels with a yield stress above 1240 MPa (180 000 p.s.i.), or a Rockwell C hardness greater than 40 are susceptible to stress corrosion cracking (Uhlig, 1971). (c) Hydrogen embrittlement Hydrogen embrittlement occurs when atomic hydrogen resulting from a corrosion reaction or cathodic polarization enters the metal lattice at cathodic zones. At a void in the metal, the atomic hydrogen will combine to form molecular hydrogen in a process that generates internal stresses and reduces the ductility of the steel. Sulfide ions at the cathode zone accelerate hydrogen embrittlement by ‘poisoning’ the steel surface enabling the atomic hydrogen to penetrate the metal more easily. Hydrogen embrittlement may not be visible on the steel surface, and can occur slowly resulting in failure of the anchor long after installation. (d) Bacterial corrosion Wet clays, marshes and organic soils below the water table often contain sulfate-reducing anaerobic bacteria that will accelerate steel corrosion in deaerated soils. These bacteria exist where sulfates, moisture and organic matter are present, and are most active at pH levels between 6.2 and 7.8. They do not survive at high pH levels. The bacterial

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Figure 9.25 Representation of corrosion mechanisms: (a) galvanic micro-cell developed at steel surface (Hanna, 1982); and (b) stray-current corrosion (FHWA, 1982).

corrosion process involves the reduction of sulfates to sulfides with hydrogen supplied by the steel and the formation of rust and weak, porous ferrous sulfide. This corrosion may be general, or local to form pits.

(e) Corrosion in grout Embedding an anchor in grout produces alkaline, high-pH conditions and the formation of a galvanic micro-cell involving oxygen. Local concentrations of oxygen at the anode lead to general corrosion and

ANCHOR MATERIALS AND ANCHORAGE METHODS

the formation of a layer of hydrous ferrous oxide. This is a passive layer that is insoluble in solutions with a pH above 4.5. As the pH of the grout is above 12.5, the ferrous oxide inhibits further corrosion. However, the protective environment provided by the grout will be diminished if the grout is cracked or porous allowing penetration of chemicals, such as chloride (Cl−), sulfite (SO), sulfate (SO3) and carbonate (CO3) ions that will neutralize the alkaline conditions. Studies of diffusion rates of chlorides through cement grout, with subsequent corrosion of the steel, can be used to estimate the service life of anchors protected solely with cement grouts (Chakravorty et al., 1995). Protective systems comprising both cement grout, and plastic sheathes that are resistant to cracking and prevent moisture infiltration of the more brittle grout, are discussed in Section 9.4.4. Steel corrosion within a grout column is a dangerous condition because the products of corrosion occupy a greater volume than the original metal and large bursting pressures are developed. These pressures may be great enough to break up the grout column and can lead to loss of bonding. 9.4.3 Corrosive conditions Investigation programs for anchoring projects will usually include a study of the potential for corrosion of the anchors. Because there are many different types of corrosion as described in the previous section, there are also many different geological and ground water conditions that cause corrosion. Furthermore, conditions may change with time as a result of changes in land use and such events as chemical spills. Consequently it is difficult to determine definitively the corrosive nature of a site and general practice is to provide corrosion for all permanent anchor systems. The following list describes conditions that will usually create a corrosive environment (Hanna, 1982; PTI, 1996): 1. soils and rocks which contain chlorides;

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2. seasonal changes in the ground water table; 3. anchorages in marine environments where they are exposed to sea water which contains chlorides and sulfates; 4. fully saturated clays with high sulfate content; 5. anchorages passing through different ground types which possess different chemical characteristics; 6. peat bogs, organic fills containing humic acid; 7. acid mine or industrial waste. The corrosive environments described above can be quantified in terms of the pH value and the resistivity of the site. In highly acidic ground (pH<4), corrosion by pitting is likely, while in a slightly alkaline ground (pH between 6.2 and 7.8), sulfatereducing bacteria flourish. Soil resistivity is related to corrosion potential by the magnitude of the current that can flow between the steel and the soil. The lower the resistivity of a soil, the larger the current flow and the greater the corrosion potential. In general the degree of corrosiveness decreases as follows (King, 1977):

As a guideline on corrosive conditions, ground should be considered aggressive and permanent anchors should be protected against corrosion if it has one or more of the following conditions (PTI, 1996): 1. pH<4.5; 2. resistivity<2000 ohm cm; 3. sulfides present; 4. stray currents present; 5. chemical attack has occurred to other buried structures. The type of steel used for the anchor also has an influence on corrosion potential. It is found that quenched and tempered prestressing steels are susceptible to hydrogen embrittlement corrosion and should not be used for permanent anchors.

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9.4.4 Corrosion protection methods A number of rock bolt and rock anchor manufacturers have developed proprietary rock corrosion protection systems that have been thoroughly tested in a wide range of applications and can be used with confidence for permanent anchors. A partial list of these manufacturers include Dywidag, Freyssinet and Williams Form Hardware and Rock Bolt Co. While the basic method of protection for all these systems is very simple, installa tion requires close attention to detail to ensure that every part of the anchor will be permanently protected. PTI (1996) classifies corrosion protection systems as either Class I or Class II. For Class I anchors the bond length is encapsulated in a grout-filled sheath or is coated with epoxy, while for Class II anchors the bare strand or bar is embedded in grout. In both cases the unbonded length is encapsulated in a sheath filled with a corrosion inhibitor or a heat shrink sleeve, and the head comprises a trumpet filled with corrosion inhibitor and the exposed head is covered for permanent anchors. Figure 9.26 illustrates an anchor with Class I corrosion protection, while Fig. 9.5 illustrates anchors with Class II corrosion protection. Table 9.3 lists the conditions under which anchors with Class I and II protection systems may be used. The general requirements of a corrosion protection system are as follows. 1. There will be no break down, cracking or dissolution of the protection system during the service life of the anchor.

2. The fabrication of the protection system can be carried out either in a plant or on site in such a manner that the quality of the system can be verified. 3. The installation and stressing of the anchor can be carried out without damage to the protection system. 4. The materials used in the protection system must be inert with respect to both the steel anchor and the surrounding environment. The material most commonly used for corrosion protection is cement grout, primarily because it creates a high pH environment that passivates the steel by forming a surface layer of hydrous ferrous oxide. In addition, cement grout is inexpensive, simple to install, has sufficient strength for most applications, and has a long service life. The greatest drawback to grout is its tendency to crack, particularly when loaded in tension or bending. Because of the brittle nature of grout, it is usual that the protection system comprises a combination of grout and a plastic sleeve. In this way, the grout produces the high pH environment around the steel, while the plastic sleeve provides protection against cracking of the grout. In order to minimize the formation of shrinkage cracks that would reduce the corrosion resistance of the grout, it is common practice to incorporate additives in the grout mix to eliminate shrinkage and reduce bleed (see Section 9.2.6). A corrosion protection system that can be used for both bar anchors and strand is shown in Fig. 9.26; the components and installation procedure are as follows.

Table 9.3 Conditions for which Class I and II corrosion protection systems may be used (modified from PTI, 1996) Class I Double corrosion protection

Class II Single corrosion protection

Permanent anchors (working life>24 months); and ground conditions aggressive or unknown; and serious consequences of failure; or Permanent anchors (working life>24 months); and ground conditions aggressive or unknown; and consequences of failure not serious; and incremental

Temporary anchors (working life<24 months); and ground conditions aggressive; or Permanent anchors; and ground conditions nonaggressive; and consequences of failure not serious; and incremental placement costs expensive.

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Figure 9.26 Corrosion protection system for anchors comprising two grout layers, a corrugated plastic sheath, and a grease-filled sleeve for the head (courtesy Dywidag Systems Int.).

Class I Double corrosion protection placement costs inexpensive.

1. A corrugated sheath made of high density polyethylene (HDPE) is grouted over the full length of the bar. This operation can be carried out before the bar is inserted in the hole by placing the bar on an inclined surface with the head up and then pumping grout through the grout cap so that the sheath is filled from the

Class II Single corrosion protection

bottom upwards. Alternatively, the sheath can be grouted after installation in the hole through a grout tube sealed inside the sheath. In the bond zone the corrugated sheath transmits the shear stresses from the steel through the two layers of grout to the rock. 2. A smooth plastic sheath, coinciding with the

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free stressing length, is placed over the corrugated sheath. The ends of the smooth sheath are sealed with heat shrink tubing to prevent grout from entering the annular space between the sheaths. 3. Any couplings in the bar are protected with heat shrink tubing. 4. Centralizing sleeves are attached to the bond zone at intervals of about 1 m to produce a uniform thickness of grout in the annulus. 5. Two tubes are attached to the sheathing. In an uphole the grout tube is attached to the head while the vent tube extends to the top (distal) of the anchor. In a down hole, the grout tube extends to the lower (distal) end of the anchor and the vent tube is attached to the head. The completed assembly is lowered into the drill hole, taking care not to bend the bar or crack the grout by using a rigid cradle set at the same inclination as the drill hole. 6. The reaction plate with holes for the grout and vent tubes is installed. Attached to the under side of the plate is a steel tube with a seal between the plate and the plastic sheathing. 7. The hole is grouted through the grout tube until grout return is obtained in the vent tube. 8. After stressing, an anti-corrosion grease is pumped through a nipple in the plate to protect the length of the bar between the plate and the plastic sheathing. Also, a cap filled with grease is installed to protect the nut or wedges from corrosion. The corrosion protection system shown in Fig. 9.26 will provide three layers of protection—two layers of grout and the plastic sheathing. However, the portion of the anchor immediately below the head is especially vulnerable to corrosion because, in order to permit stressing and installation of the locking nut or strand wedges, it cannot be grouted prior to stressing. Protection of the head is particularly important because this portion of the anchor is often exposed to the atmosphere, and on marine and river structures the heads will be subjected to fluctuating water levels and humid air. The head is protected

with an anti-corrosive grease which can accommodate movement of the head due to temperature fluctuations and cyclic loading; grout would crack under these conditions. An alternative to a grouted corrugated sleeve over the full length of a strand anchor is to encase the free stressing length in a polypropylene sheath packed with anti-corrosion grease which is then embedded in grout (see Fig. 9.6). This system will provide the same level of protection as that shown in Fig. 9.26 but the light weight and flexibility of the polypropylene sheath facilitates handling in the field. Corrosion protection systems other than grout are also available. For example, stainless prestressing steels are available (George Clark Ltd, Sheffield UK), but their cost would prohibit their use except in highly corrosive atmospheres with serious consequences for failure. Galvanized or epoxy coated bars are also available. Epoxy coatings will meet requirements for Class I protection where the coating thickness for the bar is in the range 0.18–0.3 mm (ASTM A775), or 0.64–1.14 mm for strand (ASTM A882). Fiberglass bars may be an alternative in highly corrosive conditions. Rock bolts anchored with resin cartridges are widely used in civil engineering projects (see Section 9.2.7), but the corrosion protection provided by the in situ mixed resin is likely to be inferior to that of cement grout encapsulation (Baxter, 1997). The reason for this situation is that the resin does not provide a high-pH environment such as cement grout, and it is not possible to center the bar in the hole and to have control over the uniform distribution of resin within the annulus between the walls of the hole and the bar. Moreover, the plastic sheath in which the resin components are packaged are shredded, but remain mixed with the resin and are likely to be a conduit for the passage of water from the rock to the steel. 9.3.5 Corrosion monitoring For installations supported with permanent anchors,

ANCHOR MATERIALS AND ANCHORAGE METHODS

particularly where there is a serious consequence of failure, it is useful to have a means of monitoring corrosion of the steel. At present (1998) corrosion monitoring is rarely carried out. The requirements for a system for long term corrosion monitoring are that it must be stable, compact so that an oversize hole is not required for installation, and is not destructive to the anchor. One monitoring system that should meet these requirements is manufactured by Vetek Corporation. The system comprises an electrode of silver-silver chloride inside a plastic braid that is wrapped around the steel anchor, but is not electrically connected to it. The bolt with the electrode can then be installed in the HDPE plastic sheath in the normal manner. The condition of the steel is monitored by measuring the electric potential between the anchor and the electrode using a remote readout unit. The system can be automated to trigger an alarm if the potential drops below a pre-set limit. 9.5 Installation and testing The materials from which the anchor is fabricated, and procedures used for installation and testing, are usually specified in the contract documents. These specifications must strike a balance between a ‘method’ specification that defines all the materials and procedures that must be used by the contractor, and a ‘performance’ specification that simply defines the end product. If only specialist anchor contractors are invited to bid, then a performance specification can be prepared that specifies the capacity of the anchor, the minimum free stressing length, the level of corrosion protection, and the acceptance criteria with respect to load testing. This gives the contractor the flexibility to select the drilling method, anchor materials and length of anchorage that will be both economical, and achieve the required performance. If there is open bidding on the contract so that inexperienced contractors may perform the work, it would be necessary to write a method specification that defines all aspects of the contract. A successful anchoring project can

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require the use of special drilling, grouting and testing equipment, as well as close attention to all the details of the installation, and for these reasons specialist contractors are preferred on large anchoring projects. Components of an anchoring project that are usually specified are the free stressing length and the working load, the permeability of the rock in the bond length, the load testing requirements, and the acceptance criteria for these tests. This section discusses the testing procedures used to verify the performance of the anchor, while methods of drilling and grouting are usually left to the discretion of the contractor, and are discussed in Chapter 10. 9.5.1 Water testing It is important that the grout does not leak into the rock surrounding the anchor hole because this may result in a partially grouted anchor. Cement grout may flow into fractures with apertures greater than about 0.25 mm (0.01 in) and it will be necessary to seal such fractures prior to installing the anchor. The water tightness of the drill hole can be tested by filling the hole with water and subjecting it to a pressure of 35 kPa (5 p.s.i.) in excess of the hydrostatic head as measured at the top of the hole. The rate at which the water level falls in the hole is observed and the hole is acceptable if the seepage rate does not exceed 9.5 l (2.5 gal) over a 10 minute period (PTI, 1996); time should be allowed for the rock in the walls of the hole to be saturated. If this rate is exceeded, then it is necessary to grout the hole using a low water: cement ratio grout or a sanded grout, let the grout set for a period of about 8–24 hours, and then redrill the hole. Drilling should be carried out while the grout strength is still considerably less than that of the rock so that the drill steel will not deviate off the hole alignment. The water tightness test would then be repeated to ensure that the fractures had been sealed, and if necessary the hole is regrouted and redrilled. As an alternative to filling the entire hole with

354

TENSION FOUNDATIONS

water, packers could be used to isolate the bond zone to determine seepage conditions only in this area where complete grouting is required. This procedure would be required where the rock is fractured in the portion of the hole where the free stressing length is located and complete grouting may not be necessary. Holes that are flowing under artesian pressures may also need sealing after drilling if it is not possible to control the flow by applying a back pressure during grouting of the anchor. Failure to seal a flowing hole may result in grout being washed from the hole and the formation of a poor quality anchorage. The procedure for grouting a flowing hole would be to seal a pair of tubes into the collar, with the grout tube extending to the bottom of the hole and a vent tube at the ground surface. A grout pressure in excess of the water inflow pressure could be maintained until the grout had set by extending the grout tubes vertically to develop the required hydrostatic head. Alternately, drain holes could be drilled to lower the water pressure prior to installing the anchor. A more difficult circumstance to overcome is where ground water flow through the rock around the bond zone is fast enough to carry away the grout before it has time to set. Where such conditions are possible, a careful ground water investigation may be justified because rapid water flow may preclude the use of grouted anchors. 9.5.2 Load testing The stressing procedure for all permanent anchors incorporates tests to evaluate their performance and ensure that they meet specified acceptance criteria. The tests comprise applying a load to the bar or strand with a hydraulic jack, and monitoring the extension of the anchor by measuring the movement of the head. Figure 9.27 shows a typical set up for a load test of a bar anchor. The test equipment comprises a coupling and extension rod which passes through the hollow ram jack, and is secured with a nut on the top of the jack. The lower part of the jack has a hydraulic wrench to tighten

the nut when the design load has been reached. Prior to starting testing, the hydraulic system should be calibrated in a compression testing machine to relate gauge pressure to applied load. Movement of the head of the anchor is measured, to the nearest 0.025 mm (0.001 in), with a dial gauge mounted on a reference point which is independent of the anchor. If the dial gauge is mounted on the bearing plate, the measured movement may be in error due to the displacement of the plate as the load is applied. The usual procedure is to mount the dial gauge on a tripod set up on the ground at a distance of about 1 m (3 ft) from the head of the anchor (Fig. 9.27). The purpose of making load-extension measurements is to ensure that the anchor is behaving elastically, that there is no loss of load with time, and that the required volume of rock to support the applied load is being mobilized by the anchor. This behavior is evaluated by carrying out four types of tests (PTI, 1996): 1. performance tests; 2. proof tests; 3. creep tests; 4. lift-off tests The performance and creep tests are a detailed examination of the load-extension behavior. They are carried out on the first two to five anchors, and on a minimum 2% of the remaining anchors. Proof and creep tests are carried out on all remaining the anchors. For any anchor that fails either test, an additional two performance tests are performed, and the failed anchor is either improved to meet the required load, or is replaced. A lift-off test is performed on every anchor. (a) Performance tests The performance test comprises a cyclic loading procedure in the following sequence with an extension measurement being made at each increment (Fig. 9.28): AL, 0.25P, AL, 0.25P, 0.5P, AL,

ANCHOR MATERIALS AND ANCHORAGE METHODS

355

Figure 9.27 Hydraulic jack set up for stressing a bar anchor; the jack incorporates a wrench for tightening the nut. The dial gauge to measure displacement of the head is mounted on a tripod which is an independent reference point.

0.25P, 0.5P, 0.75P, AL, 0.25P, 0.5P, 0.75P, P, AL, 0.25P, 0.5P, 0.75P, P, 1.2P, AL, 0.25P, 0.5P, 0.75P, P, 1.2P, 1.33P—hold for creep test, AL, P—lock-off. where AL is the alignment load required to take out slack out of the system, and P is the design (lockoff) load. The application of an overload is an important part of checking that the anchor has capacity in excess of the design load. However, the value of the maximum load must be compared with the yield strength of the steel to ensure that it does not exceed 80% of the elastic limit of the steel. (b) Proof tests The loading sequence for a proof test is as follows: AL, 0.25P, 0.5P, 0.75P, P, 1.2P, 1.33P,

–hold for creep test, AL(optional), P—lock off This loading sequence is equivalent to the last cycle of the performance test shown on Fig. 9.28. (c) Creep tests At the applied maximum load of 1.33P in both the performance and proof tests, creep extension readings are taken at intervals of 1, 2, 3, 4, 5, 6 and 10 minutes. If the total creep movement between 1 and 10 minutes exceeds 1 mm (0.04 in), the test load should be maintained for an additional 50 minutes and the extension recorded at 20, 30, 40, 50 and 60 minutes. (d) Lift-off tests When the anchor has been locked off at the design load, the jack pressure is reduced to zero and then reapplied to determine the load at which the nut or wedges are lifted off the bearing plate. This test is performed on every anchor.

356

TENSION FOUNDATIONS

Figure 9.28 Results of anchor performance test showing load-displacement measurements, and permanent (?p) and elastic (?e) displacement.

9.5.3 Acceptance criteria An anchor is acceptable if the results of the performance, proof, creep and lift-off tests meet three acceptance criteria recommended by the PTI (1996) for permanent anchors; these are as follows: 1. The total elastic extension measured in performance or proof tests should exceed 80% of the theoretical elastic elongation of the free stressing length, and be less than the theoretical elastic elongation of the free stressing length plus 50% of the bond length (Fig. 9.29). 2. The creep extension should not exceed 1 mm (0.04 in) during the period of 1–10 minutes. If this value is exceeded, then the total creep extension within the period 6–60 minutes should not exceed 2 mm (0.08 in) (Fig. 9.30). 3. The lift-off should be within 5% of the specified transfer load. The first criterion ensures that the rock mass between the head and the bond length is mobilized by the applied load, and that the major portion of the bond stress is developed in the top half of the

anchorage. This criterion is shown graphically in Fig. 9.29 where the elastic ?e and permanent ?p portions of the measured extension are plotted against load for the performance test shown in Fig. 9.28. An anchor meets the acceptance criterion if the elastic extension line falls between the two dashed lines designated (a) and (b). The acceptance criteria extension limits are calculated using the elastic modulus of the steel (see Table 9.1) and the cross-section area of the bar or strand bundle, together with the appropriate bond and free stressing lengths. It is generally found that creep in rock anchors is small and that conducting long term creep tests is not warranted. If creep exceeds the limit in criterion 2, the anchor is unacceptable because this is an indication of failure of the bond rather than the creep of the surrounding rock. Where an anchor fails to meet the acceptance criterion, it may be possible to improve the bond if there are secondary grout tubes through which pressure grouting can be carried out. If this is not possible a replacement anchor would have to be installed. As discussed in Section 9.3.7, creep of epoxy filled strand may be greater than that of bare strand, and the acceptance criterion should be adjusted accordingly. At a test

ANCHOR MATERIALS AND ANCHORAGE METHODS

357

Figure 9.29 Permanent and elastic displacement of anchor in comparison with acceptance criteria.

load of 80% of the ultimate strength, creep movements are estimated to be 0.015% , or higher, of the apparent free stressing length during the 6–10 minute log cycle. When conducting lift-off tests on strand anchors, care should be taken not to loosen the wedges and re-grip the strand at a different position. Proper seating of the wedges requires that they be embedded into the steel, and indentations in the steel will act as stress concentrators that should not be located below the bearing plate. 9.6 References Al-Mosawe, M.J. (1979) The Effect of Repeated and Alternating loads on the Behaviour of Dead and Prestressed Anchors in Sand. Thesis, University of Sheffield, England. Baxter, D.A. (1997) Rockbolt corrosion under scrutiny. Tunnels and Tunnelling International, London, July, 35–8. Benmokrane, B. and Ballivy, G. (1991) Five year monitoring of load losses on prestressed cementgrouted rock anchors. Can. Geotech. J., 28, 668–77. British Standards Institution (1985) The Structural Use of

Concrete. BS 8110, Part 1, London. Bruce, D.A., Greene, B. and Schaffer, A. (1996) Unique cofferdam construction: Pt. Marion Lock and Dam, Pennsylvania. Ground Engineering, April, 41–4. Bruen, M.P., Pansic, N. and Schwartz, M.I. (1996) Creeping suspicion. ASCE, Civil Engineering, May, 60–3. Bureau Securitas (1972) Ground Anchors. French Code of Practice, Editions Eyrolles, Recommendations TA72. Canadian Portland Cement Association (1984) Concrete Design Handbook. CPCA, Ottawa, pp. 178–81. Chakravorty, M., Frangopol, D.M., Mosher, R.L. and Pytte, J.E. (1995) Time-dependent reliability of rockanchored structures. Reliability Eng. and System Safety, 47, 231–36. Coates, D.F. and Yu, Y.S. (1971) Rock Anchor Design Mechanics. Canada Dept. of Energy Mines and Resources, Research Report No. R233. Dywidag Canada, Ltd (1993) Dywidag Rock AnchorMono-bar, Bundle Anchor, Epoxy Anchor. Dyckerhoff & Widmann AG, Munich, W. Germany. Electric Power Research Institute (1983) Transmission Line Structure Foundations for Uplift-compression

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Figure 9.30 Results of creep test showing measured extension over a 10 minute period compared with acceptance criterion of 1 mm. Loading. EPRI EL-2870, Project 1493–1 EPRI, Palto Alto, CA. Farmer, I.W. (1975) Stress distribution along a resin grouted anchor. Int. J. Rock Mech. &; Geomech. Abstr., 12, 347–51. Federal Highway Administration (US) (1982) Tiebacks. Report No. FHWA/RD-82/047, Washington, DC. Ghosh, R.S. (1976) Reinforced Concrete Footing Anchored in Rock. Ontario Hydro Research Division Report No. S76–4-K, Toronto, Canada. Golder Associates (1983) Project files: full scale load tests on instrumented anchors. Golder Associates (1989) Project files: long term monitoring results. Hanna, T.H. (1982) Foundations in Tension—Ground Anchors. Trans Tech/McGraw-Hill, ClausthalZellerfeld, Germany. Hobst, L. and Zajic, J. (1977) Anchoring in Rock. Elsevier, Amsterdam, pp. 38–43. Hoek, E. (1983) Strength of jointed rock masses. Geotechnique 33, 3, 187–223.

Ismael, N.F. (1982) Design of shallow rock-anchored foundations. Can. Geotech. J., 19, 463–71. Johnston, G.H. and Ladanyi, B. (1972) Field tests of grouted rock anchors in permafrost. Can. Geotech. J., 9, 176–94. Kast, G. (1989) Personal communication. Kast, G, and Skermer, N. (1986) DEW Line anchors in permafrost. Geotech. News, 4(4), 30–3. King, R.A. (1977) A Review of Soil Corrosiveness with particular Reference to Reinforced Earth. Transport and Road Research Laboratory, Crowthorne, UK, Supplementary Research Report No. 316. Libby, J.R. (1977) Modern Prestressed Concrete. Van Nostrand Reinhold, New York. Littlejohn, G.S. (1987) Ground anchorages: corrosion performance. Proc. Inst. of Civil Eng., Part 1, Vol. 82, pp. 645–62. Littlejohn, G.S. (1993) Overview of rock anchorages. Comprehensive Rock Engineering, Pergamon Press, UK, Vol. 4, Ch. 15, pp. 413–50. Littlejohn, G.S. and Bruce, D.A. (1975a) Rock anchors —

ANCHOR MATERIALS AND ANCHORAGE METHODS

state of the art. Part 1: Design. Ground Eng., 8(4), 41–8. Littlejohn, G.S. and Bruce, D.A. (1975b) Rock anchors state of the art. Part 2: Construction. Ground Eng., 8(4), 36–45. Littlejohn, G.S. and Bruce, D.A. (1976) Rock anchors — state of the art. Part 3: Stressing and testing. Ground Eng., 9(5), 331–41. Littlejohn, G.S. and Bruce, D.A. (1977) Rock anchors design and quality control. Proc. 16th Symp. on Rock Mechanics, U. of Minnesota, pp. 77–88. Littlejohn, G.S. and Bruce, D.A. (1979) Long-term performance of high capacity rock anchors at Devonport. Ground Eng., 12(7), 25–33. Littlejohn, G.S., Bruce, D.A. and Deppner, W. (1977a) Anchor field tests in carboniferous strata. Specialty Session No. 4, 9th International Conf. on Soil Mechanics an Foundation Eng., Tokyo, pp. 82–6. Littlejohn, G.S., Norton, P.J. and Turner, M.J. (1977b) A study of rock slope reinforcement at Westfield (Scotland) open pit and the effect of blasting on prestressed anchors. Proc. Conf. on Rock Eng. University of Newcastle upon Tyne, Vol. 1, pp. 293–310. Littlejohn, G.S., Rodger, A.A., Mothersille, D.K. V. and Holland, D.C. (1989) Dynamic response of rock bolts. Proc. 2nd Int. Conf. on Foundations and Tunnels, (2), Engineering Technics Press, pp. 57–64. Madhloom, A. (1978) Repeated loading of piles in sand. Thesis, University of Sheffield, England. PostTensioning Institute (1996) Recommendations for Prestressed Rock and Soil Anchors, 3rd edn, Phoenix., AZ.

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Radhakrishna, H.S. and Klym, T.W. (1980) Behavior of rock anchored foundations subject to shear and moment loads. IEEE Trans. on Power Apparatus and Systems, Vol. PAS-99, No 2, pp. 760–4. Reeves, R.B. (1987) Corrosion protection of permanent tiebacks. Speciality Conf. on Rock Fall Mitigation, Region 10, Federal Highway Administration, Portland, Oregon. Rodger, A.A., Littlejohn, G.S., Xu, H. and Holland,D. C. (1996) Instrumentation for monitoring the dynamic and static behaviour of rock bolts in tunnels. Proc. Inst. Civil Eng., 119, 146–55. Russell, J.R. (1968) Stress distributions around rock bolts: elastic stresses. Proc. 10th Symp. on Rock Mech., Austen, Texas, pp. 661–6. Saliman, R. and Schaefer, R. (1968) Anchored footings for transmission towers. ASCE Annual Meeting and National Meeting on Structural Engineering, Pittsburgh, PA, Sept. 3-Oct. 4, Preprint 753. South African Code of Practice (1972) Lateral Support in Surface Excavations. The South African Institution of Civil Engineers, Johannesburg. Uhlig, H.H. (1971) Corrosion and Corrosion Control. Wiley, New York, p. 134. Ulrich, B.F., Wuest, W.J. and Stateham, R.M. (1990) Relationship between annulus thickness and the integrity of resin-grouted roof bolts. Report of Investigations 9253, United States Bureau of Mines, Washington, DC. Wijk, G. (1978) A theoretical remark on the stress field around prestressed rock bolts. Int. J. Rock Mech. & Geomech. Abstr. 15, 289–294.

10 Construction methods in rock

10.1 Introduction The construction of foundations on rock will usually involve one or more of the following three tasks. 1. First, there is likely to be some rock excavation either by blasting, or a non-explosive method such as ripping or splitting, which must be done with care to avoid damaging the bearing rock. 2. Second, some reinforcement of the foundation may have to be installed to ensure the long-term stability of the structure. 3. Third, a suitable bearing surface or excavation for the structure will have to be prepared. Often these construction tasks will be performed by an independent contractor whose performance will depend to some degree on the specifications to which he is working. Therefore, the construction of a stable foundation will depend not only on the preparation of reliable designs, but also on contract documents that clearly define the work required and the rights and responsibilities of the owner and contractor, and provide a fair level of compensation. It is also important that the assumption of risk in the performance of the work should be appropriately apportioned between the owner and the contractor. For example, if an excavation is to be made below the water table where subsurface conditions are uncertain, requesting a lump sum price would probably result in high bids because the contractors would have to include contingencies to cover their risk. An alternative would be to obtain unit prices for spec

ified work items and then pay for the work actually carried out. This chapter describes common construction methods for rock excavations, and discusses the principles involved in the preparation of contract documents. 10.2 Drilling On most rock foundation projects there is a requirement to drill holes for such purposes as geological investigation, blasting, the installation of anchors or socketed piers, and the set up of instrumentation. An example of the versatility in drilling equipment is shown in Fig. 10.1 where a ‘bencher’ is drilling holes for rock bolts in a vertical cliff face. The bencher comprises a pneumatic percussion drifter mounted on a boom equipped with a chain feed; the boom is attached to the cliff face with a rock anchor. The drillers are suspended on heavy duty canvas belts attached with carabiners to steel core, hemp ropes which are specifically designed for this type of work. Their supplies are carried in a ‘spider’ (in the foreground) which is an aluminium basket equipped with a pneumatic hoist motor; a steel hoist rope attached to a pin above the crest of the cliff allows the spider to be raised and lowered on the face. Drilling methods that are commonly used on rock construction projects are diamond, percussion, rotary and auger drilling, with diameters ranging from 50 mm (2 in) to 1.2 m (48 in). In selecting the drilling equipment appropriate for the site

CONSTRUCTION METHODS IN ROCK

361

Figure 10.1 Rock bolt holes being drilled in the face of a vertical cliff with a pneumatic bencher drill (photograph by D.Wood).

conditions, the following factors should be considered: 1. recovery of intact samples; 2. length of hole; 3. diameter of hole; 4. directional tolerance; 5. site access; 6. strength and degree of fracturing of the rock; 7. depth and condition of overburden; 8. availability of drilling water; 9. condition of wall of hole; 10. drilling rates and costs.

This section describes common drilling methods and the conditions in which they may be used; information on drilling equipment and methods may be obtained from handbooks (ADITC, 1997) and product literature published by drill manufacturers such as Atlas Copco, Boyles Bros. Drilling Co., Gardner-Denver, Longyear, Sandvik and Tamrock. General descriptions of drilling equipment and operations are included in publications by the Federal Highway Administration (1982) and Society of Mining Engineers (1973).

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Figure 10.2 Diesel-powered surface diamond drill (courtesy of JKS Boyles, 1989).

10.2.1 Diamond drilling The primary use of diamond drilling is investigation work to recover intact core for the study of site geology, and to obtain samples for laboratory strength testing (see Section 4.3). Diamond drills may also be used in construction where it is necessary to drill long, accurately aligned holes, or where access space is limited and it is not possible to use percussion drills. Because diamond drills rely on rotational speed and thrust rather than impact force to cut the rock, diamond drills have smaller dimensions than percussion drills, and are capable of drilling to greater depth. Diamond drill holes can reach depths in excess of 1000 m (3000 ft). The deviation of diamond drilled holes is less than that of percussion drilled holes because diamond drill rods are stiffer than percussion drill rods, and diamond drills develop a steady thrust compared with the impact forces in a percussion drill. With the use of appropriate casing and drilling muds,

diamond drill holes can be put down in highly fractured ground which would cave if drilled with a percussion drill. The disadvantages of diamond drilling are the low advance rates and high cost relative to percussion drills. Also, the diamond bit cuts a hole with a smooth wall surface which will result in a lower bond strength for rock anchors compared with the relatively rough surface produced by percussion drills. The main components of a diamond drill comprise a power unit which may be a diesel or compressed air motor, and a drill head that is powered from the motor through a gear box and gear train (Fig. 10.2). The function of the drill head is to rotate the drill string, supply thrust to the drill bit and to advance the rods as the drill bit cuts the hole. The drill string comprises lengths of drill rod which are flush coupled and have a diameter slightly smaller than the hole diameter, a core barrel which retains the drill core as the hole advances, and the drill bit on the lower end of the core barrel. The cutting face of

CONSTRUCTION METHODS IN ROCK

the drill bit is impregnated with diamonds set in a metal alloy matrix, and the cutting action is achieved by applying a high rotational speed (about 2000 rpm) and low thrust (30–70 kN, or 6700–16 000 lb). During drilling it is essential that the bit is flushed continually with water or drilling mud to cool the bit, remove the cuttings and reduce friction between the drill string and the walls of the hole. Where drilling fluid circulation is lost, casing or muds are used to seal fractures and zones of broken, permeable ground. Usual practice is to advance casing through the overburden and seat the casing shoe in bedrock to form a watertight seal through the permeable upper formations. If the drill fluid is lost in a fracture intersected in the bedrock, various types of muds can be used to form a cake on the walls of the hole, or the fracture can be sealed with grout. However, if it is later planned to conduct permeability tests in the hole, it is necessary to

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employ muds that will break down a few days after use, and can be washed out of the hole to leave the walls of the hole uncontaminated. In North America, diamond coring equipment dimensions are designated by letters as shown in Table 10.1. For example, NQTT refers to: N size core, Q designates wire line equipment, and TT designates a triple-tube core barrel. Wire line equipment, which is used for deep drill holes, has a double tube core barrel consisting of an inner core barrel that is retrieved with an overshot assembly lowered down the hole on a steel cable, or wireline (Fig. 10.3). This system allows the core barrel to be retrieved at the end of every drill run without the time-consuming process of pulling the rods. A triple-tube core barrel contains a split inner tube that is pumped out of the core barrel without disturbing the core. The split tube is placed on a cradle and the top half of the tube is

Table 10.1 Dimensions of diamond drilling equipment (Boart Longyear Inc.) Hole diameter

Core diameter

Casing OD*

mm

mm

(in)

mm

(in)

mm

(in)

(1.06) (1.32) (1.78) (2.41) (3.27)

57.1 73.0 88.9 114.3 –

(2.25) (2.87) (3.5) (4.5)

44.5 55.6 69.9 88.9 117.5

(1.75) (2.19) (2.75) (3.5) (4.63)

(in)

AQ 48.0 (1.89) 26.9 BQTT 60.0 (2.36) 33.5 NQTT 75.7 (2.98) 45.1 HQTT 96.0 (3.78) 61.1 PQTT 122.7 (4.83) 83.0 *Wire line series dimensions, AW, BW, NW, HW.

removed, making it possible to log the core with minimal disturbance. In comparison, the core is removed from a double-tube core barrel by pumping or hammering, which inevitably results in disturbance to the core. In very weak, fractured rock a system can be used in which the inner tube of the triple-tube barrel is lined with a clear plastic sleeve. The core slides into the sleeve as the drill advances. When the inner tube is opened, the core is contained in the plastic tube where it can be logged, photographed, and stored with minimal disturbance.

Drill rod OD

10.2.2 Percussion drilling Percussion drilling is the most common method of rock drilling because of its relatively low cost, and the high production rates that can be achieved (Fig. 10.4). While the predominant use of this equipment is for drilling blast holes, it is also used to drill holes for rock anchors, socketed piers and drainage. The two main categories of percussion drills are pneumatic and hydraulic, with the drifter either being on the surface (conventional jack hammer or airtrac), or in the hole (down-the-hole (DTH) drills). The common range of hole diameters for this equipment is from 35 mm (1.5 in) to 150

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mm (6 in) for surface drills, and from 100 mm (4 in) to 200 mm (8 in) for DTH drills. The maximum length of holes drilled with surface mounted drifters is limited to about 30–40 m (100–120 ft), although efficiency starts to diminish at depths greater than about 20 m (65 ft). This depth limitation is the result of the difficulty in flushing cuttings from the hole, the reduction in efficiency as a result of loss of energy in the drill string, as well as the excessive deviation. However, DTH drills can drill holes to depths of about 300 m (1000 ft), because there is no loss of energy in the drill string. (a) Surface percussion drills The principle of percussion drilling is to apply a series of impact forces to a tungsten carbide drill bit with sufficient energy to crush and break the rock. With each impact, the bit is rotated to expose a new face to the bit, while the cuttings are continuously flushed from the hole with air or water. The minimum flushing or bailing velocity for cleaning the cuttings is 1000–2000 m/min (3000–7000 f.p.m.). Thus the drilling rate depends on the following factors: the impact energy, the thrust on the drill rods, the rotation speed, the rate at which the cuttings are flushed from the hole, the condition of the rock, and the hole dimensions. All these factors are considered in the selection of the most appropriate method of drilling for each project. In both pneumatic and hydraulic percussion drills, impact is applied by means of a reciprocating piston which strikes the bit or drill steel and produces a series of high-energy stress waves that are transmitted to the bit. The impact rate is in the range 2000–3500 blows per minute. The reciprocating action of the piston is controlled by valves that introduce compressed air or hydraulic fluid alternately at each end of the cylinder (Fig. 10.5). The shock wave travels down the drill steel at a speed of about 5000 m/s (the speed of sound in steel), and the shape of the shock wave depends on the shape and impact velocity of the piston. A pneumatic drill produces a shock wave that has a high peak stress, while the shock wave produced by a hydraulic drill is more uniform (Fig. 10.6). The result is that a hydraulic drill can

produce a shock wave with higher total energy, and therefore a higher penetration rate, than a pneumatic drill. If a pneumatic drill were to produce a shock wave with the same total energy as the hydraulic drill, overstressing and breakage of the drill rods would occur. Rotation of the drill steel is either dependent or independent of the movement of the piston. With dependent rotation, the drill rod is rotated on the backstroke of the piston by a rifle bar. A system of ratchet and pawls allows the piston to travel forward without rotation on the forward stroke while the fluted rifle bar is positioned for the next stroke (Fig. 10.7). Therefore the speed of rotation, which is usually in the range of about 50–100 rpm, cannot be changed to suit varying rock conditions. Independent rotation is achieved by a motor that operates independently of the movement of the piston, and is both reversible and has variable torque. The advantages of hydraulic drills over pneumatic drills are the greater penetration rates (up to 50% higher), greater control of the drilling functions, and reduced noise and exhaust mist. However, the disadvantages of hydraulic drills are their higher capital cost and more expensive maintenance. (b) Down-the-hole (DTH) drills Drills with the drifter mounted at the surface require that the impact energy produced by the piston be transmitted down the drill rods to the bit. There is a significant loss of energy in the drill string that becomes greater as the hole depth increases. The efficiency of the drill can be significantly improved by mounting the drifter in the hole immediately behind the bit which allows both larger diameter and deeper holes (at least 300 m, or 1000 ft) to be drilled. Other advantages of the DTH drills are lower noise levels, and reduced wear on the drill rods. However, the disadvantages are that the minimum hole diameter is limited by the cylinder dimensions to about 100 mm (4 in). Also, in short holes the penetration rate of a DTH drill is less than that of a surface mounted drill because of the smaller cylinder diameter of the DTH drifter. In highly fractured rock, DTH drills should be used

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365

Figure 10.3 Diagram of wire-line core barrel. (courtesy of JKS Boyles).

with care because caving of the hole can result in loss of the drifter. 10.2.3 Rotary drills Rotary drilling is a versatile drilling method that can be used to drill holes from 75 mm (3 in) to 560 mm (22 in) in diameter, and, in the case of oil wells, up to several thousand meters deep. The components

of a rotary drill are a surface drive unit, which may be a standard diamond drill or a larger truck mounted diesel unit, that applies a torque and thrust to the drill string and bit. The thrust applied to the bit may be as high 500 kN (110 000 lb) in hard rock in order to achieve contact pressures which are high enough to break the rock. The rotation of the bit, at a speed of between 30 and 120 rpm, continuously exposes the bit to a fresh rock face. Rotary drills can be employed in very soft rock

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Figure 10.4 Tracked drill equipped with surface mounted hydraulic drifter (Tamrock Drills).

Figure 10.5 Working principle of a hydraulic drifter (Tamrock (1983)). The piston is shown at the front end of its stroke. Oil enters drifter through the high-pressure port (1) and flows to the front part of cylinder (2). The piston is forced backwards and at the same time oil enters the distribution chamber (3), pushing the distributor (4) to the rear position. A portion of the oil enters the high-pressure accumulator (5) that is filled with nitrogen. The nitrogen is compressed and accumulates energy. The oil in the rear of the cylinder escapes through port (6) to the return port (7). The low-pressure accumulator (8) prevents shock loads in the return hose.

using drag bits, and in very hard rock using roller cone bits equipped with tungsten carbide inserts (Fig. 10.8). In soft rock the bit scrapes the rock, while in hard rock the torque and thrust applied to the bit produces a crushing and chipping action. The

cuttings are cleaned from the hole by either air or water which is forced down the drill rods and exhausted up the annulus between the drill rods and the wall of the hole. The primary applications of rotary drills are in oil

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367

Figure 10.6 Impulse curves for (a) hydraulic and (b) pneumatic drifters (Atlas Copco).

wells, and for large diameter blast holes in open pit mines. They may be used in geological exploration to advance the hole through materials such as boulder till and rock where there is no requirement to obtain intact samples. Examination of the cuttings and recording the advance rate will give an indication of the geological conditions, but would not be a substitute for continuous sampling. 10.2.4 Overburden drilling Where holes must be advanced through a considerable thickness of overburden overlying the bedrock, it is often necessary to install casing to prevent the hole from caving. Where the overburden is soft soil, the casing can be pushed or driven, but in situations where the overburden is dense soil or contains boulders, it will be necessary to advance the casing by drilling. Drilling economies can be realized if the casing installation and rock drilling can be carried out in one operation using the same drill rig. Drilling systems that can perform these dual operations are diamond drilling, or two percussion methods, namely the Tubex system manufactured by Sandvik, and drills manufactured by the Klemm and Barber companies.

The Tubex bit, which is used with either surface mounted or down-the-hole percussion drills, comprises a reamer mounted on a cam behind a tungsten carbide insert pilot bit (Fig. 10.9). When a torque is applied to the drill rods the reamer expands the pilot hole to a diameter just larger than the casing and the shoulder on the guide advances the casing. When the casing has been seated in bedrock and the torque is reversed, the reamer contracts and the bit can be withdrawn through the casing. Hole diameters drilled with Tubex bits are shown in Table 10.2. The Klemm and Barber drills use a two-tube drilling system to advance the casing and the drill string independently. The Barber drill uses a rotary casing driver to advance the casing equipped with a tungsten carbide studded shoe through materials ranging from sand and gravel to boulders. A top drive simultaneously advances a drill string equipped with a down-the-hole hammer, drag bit or roller cone bit that drills either inside or ahead of the casing. Once the casing has been seated in the bedrock and the overburden drilling is complete, the hole in the rock can be drilled to depths of several hundred meters. Cuttings are cleaned from the hole using air or water pumped down the drill rods and returned in the space be

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Figure 10.7 Pneumatic, surface mounted, rifle-bar rotated percussion drill showing rotation mechanism comprising ratchet and pawls (courtesy Ingersoll-Rand Co. and Society of Mining Engineers, 1973). Table 10.2 Drill hole diameters for Tubex drilling Drill bit number Tubex 90 Tubex 115 Tubex 140 Tubex 165 Tubex 190 Tubex 215 Tubex 240 Tubex 365

Casing ID (overburden)

Hole diameter (rock)

mm

(in)

mm

(in)

102 126 152 181 205 241 260 387

(4) (5) (6) (7.1) (8.1) (9.5) (10.25) (15.25)

85 110 128 152 165 203 229 356

(3.34) (4.31) (5) (6) (6.5) (8) (9) (14)

tween the rods and the casing. Holes can be drilled with diameters up to 1 m (40 in).

10.2.5 Large diameter drilling Large diameter (in the approximate range 0.6–3 m or 2–10 ft) drill holes may be required for such purposes as detailed in situ inspections of dam

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369

Figure 10.8 Rotary tricone drill bits: (a) soft-formation, (b) medium-formation, (c) hard-formation, (d) tungsten carbide inserts for very hard formation (courtesy Hughes Tool Co. and Society of Mining Engineers, 1973).

foundations, or the installation of rock socketed piers. Holes of these dimensions can be drilled with augers (in soft rock) or percussion methods where no core recovery is required, or by the Calyx method if there is a need to recover core.

Augers are used in overburden and soft rock with compressive strengths up to 30 MPa (4350 psi) where the material is strong enough for the walls of the hole to stand unsupported. The advantages of augering are the high penetration rates, the low

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Figure 10.9 Tubex drilling system for setting casing through overburden (courtesy Atlas Copco). 1. Shoulder. 2. Bit tube. 3. Guide. 4. Reamer. 5. Pilot bit.

noise levels, and that no flushing medium is required to remove cuttings from the hole. In short holes, continuous flight augers are used where the excavated material is brought to the surface by the rotating flights and the drill string is not brought to the surface until the hole is complete. For larger holes, the 2–3 m (6–10 ft) long auger is lowered into the hole on the drill string (Fig. 10.10). When the hole has been advanced a short distance the auger is retracted with the excavated material and discharged by reversing the rotation direction. For large diameter holes in strong rock, a specialty drill called the ‘super drill’ can be used (Fig.10.11). This is a large size DTH hammer equipped with a button bit that can drill holes with diameters up to about 0.75 m (30 in) and to depths of several hundred meters. This drill can be used to install rock socketed piers and holes for high capacity multi-strand tensioned anchors. Where core samples are required, the Calyx drilling system provides core with a diameter up to 3 m (10 ft), and a clean hole that is suitable for geological mapping. The drill consists of a blunt nosed steel barrel that is rotated in the hole. The cutting medium

is steel shot which is poured or injected into the hole and is trapped beneath the blunt bottom of the barrel. The tumbling and rolling action of the shot cuts the rock. Alternatively, the lower edge of the barrel can be equipped with tungsten carbide teeth that can cut even strong rock, although the rate of advance will be slow. The core, which is removed about every meter, must be broken off the bottom of the hole. This can be accomplished by driving a wedge between the core and the wall of the hole, or by detonating a ring of primacord around the lower end of the core. The core, or pieces of core, are then removed by drilling a hole in the top and installing an eye so that the core can be lifted out with a crane. 10.2.6 Directional drilling An important advance in drilling technology is the ability to control the direction of drill holes. Directional drilling allows holes to be drilled in both rock and soil with lengths of up to about 2000 m (5500 ft) in which both the path that the drill

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371

Figure 10.10 Auger drilling holes for rock-socketed piers for a bridge foundation (diagram courtesy of Atlas Copco).

follows, and the end point, can be specified to

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Figure 10.11 0.6 m (2 ft) diameter superdrill for drilling socket holes in hard rock (Ingersoll Rand Co.)

tolerances of about 1% of the length of the hole. This allows, for example, curved holes to be drilled to bypass obstructions, or long straight holes to be drilled which would otherwise wander off line. Applications of directional drilling include controlling the direction of deep investigation and drainage holes, drilling multiple holes from a single set up, and some instrumentation installations. Directional drilling could also be used where there is no access to a location where a straight hole can be drilled, where a precise exit point is required, or to place instrumentation cables in a secure hole under a structure (National Research Council, 1994). Directional drilling technology was developed in the oil industry where several production wells are frequently drilled from the same surface location. Figure 10.12 shows an example of an oil well drilling rig being used to drill a 500 m (1650 ft) long hole for a telephone cable under a major highway. The entry point for the hole is at an angle

of 60° and is located on a steep valley slope, while the exit point is horizontal and located in the floor of the valley. The components of the directional drilling system used with the drill rig shown in Fig. 10.12 are as follows. 1. A roller cone drill bit (refer to Fig. 10.8). 2. A head assembly containing a low speed (70– 150 rpm), high torque rotary motor which directly drives the bit. Behind the motor there is a bent sub which allows a bend of up to 2° to be set between the head and the drill string. The direction of the hole is controlled by setting the direction and angle of the bend in the sub. 3. A string of standard drill rods. The rods do not rotate during drilling but are used to apply a thrust to the bit, to convey drilling mud to the rotary mud motor and the drill bit, and to set the direction of the bent sub. The rotary motor is powered by the mud pumped down the drill

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373

Figure 10.12 Directional drilling system drilling 200 mm (8 in) diameter hole under highway to exit in valley floor (Sierra Drilling).

rods, which then passes through the bit to clean the cuttings from the hole. An efficient and accurate method of detecting the position of the drill hole is the MWD (measurement while drilling) method. The MWD system comprises a 10 m (31 ft) long, non-magnetic stainless steel drill collar located behind the head assembly and bent sub. Within this collar are housed magnetometers, which detect the azimuth of the collar relative to the earth’s magnetic field, and accelerometers which detect dip of the collar relative to the earth’s gravitational field. Electrical output from the magnetometers and accelerometers is encoded into a binary signal that is pulsed up the mud column to the surface. By frequent monitoring of the azimuth and dip readings, it is possible to calculate the position of the end of the drill hole and its position relative to the required alignment. If a change in direction is required, the drill string is

rotated to reset the orientation of the bent sub. The precision with which a hole can be directed along a specified path depends on the accuracy with which its position can be determined, and the minimum radii through which it can be turned. The minimum radius for a 75 mm (3 in) diameter drill hole is about 100 m (300 ft) and the hole can be drilled as a continuous curve, or a series of curves and tangents. Experience has shown that it is possible to achieve directional control of ±2–3 m (6– 10 ft) over a hole length of 500 m (1650 ft). 10.3 Blasting and non-explosive rock excavation Rock excavation is often required on rock foundation projects to remove, for example, material that may not have sufficient bearing capacity, or to form a level bearing surface. While blasting is the most common rock excavation method because of

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its relatively low cost, non-explosive excavation methods such as ripping, splitting and the use of hydraulic breakers are suitable where the rock is weak, or there is a need for very precise control of either excavation limits, and/or ground vibration levels. The requirements of any excavation method are the use of procedures that break the rock efficiently, while controlling damage to the rock in the bearing surface, of the slopes above and below the foundation, and any nearby structures. This section describes the basics mechanics of blasting, and how they may be applied to the design of blasts where there is a need to control rock fragmentation and ground vibrations. Also discussed are non-explosive excavation techniques suitable for rock foundation projects. 10.3.1 Rock fracture by explosives Blasting operations comprise the following three tasks: 1. drilling blast holes which have an appropriate diameter, and are laid out in a regular pattern as defined by the burden and spacing; 2. loading the holes with a suitable type and quantity of explosive; 3. detonating the holes in a precise sequence. The design of all these parameters depends on the mechanism by which rock is broken by explosives, and an understanding of the rock fracture mechanism as described below is essential to the design of blasts. When an explosive is detonated, it is converted within a few microseconds from a solid to a high temperature gas. When confined in a blasthole, this very rapid reaction causes pressures that can reach 100 000 atmospheres to be exerted against the walls of the borehole. The explosive energy is transmitted into the rock mass in the form of a shockwave which travels at a velocity of several thousand meters per second. Rock breakage, which depends

on both the energy of the shock wave, and to a greater extent on the gas pressure, is a three stage process as follows: first, crushing occurs in the immediate vicinity of the borehole; second, radial fractures are developed; and third, movement of the fractured rock mass takes place towards the free face (Fig. 10.13). The following is a more detailed description of the rock fracture mechanism illustrated in Fig. 10.13 (FHWA, 1985; Hemphill, 1981). As the shock wave enters the rock surrounding the borehole, the material is crushed in compression for a distance of one to two borehole diameters (Fig. 10.13(a)). However this effect is limited because, with the expansion of the compressive wave front, the stress level quickly decays below the dynamic compressive strength of the rock. At this stage the high gas pressure and the expansion of the borehole develops fractures aligned parallel to the borehole axis in the form of a series of radial cracks that may extend to distances up to 40–50 borehole diameters (Fig. 10.13(b)). If there is a free face within a distance of about 30 borehole diameters of the hole, a portion of the shock wave is reflected from the face and this results in some spalling of rock on the free face (Fig. 10.13(b)). Furthermore, the relief provided by the free face, combined with the force exerted by the expanding high pressure gas, causes movement of the rock that has been weakened and broken into wedge shaped pieces by the formation of the radial cracks. This movement of the rock mass extends the radial cracks to the free face resulting in fragmentation of the rock mass (Fig. 10.13(c)). This mechanism of rock fracture clearly shows the importance of the presence of a free face, at the correct distance from the blast hole, for efficient blasting operations. If the hole is located in a large volume of rock with no free face, there will be no breakage other than the crushing and formation of the radial cracks, and possibly some cratering at the surface. On the other hand, if the hole is too close to the face, the explosive energy will not be confined by the rock, resulting in venting of the high pressure gases and the creation of excessive flyrock and noise.

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375

Figure 10.13 Mechanism of rock breakage by explosives: (a) crushing and formation of radial fractures; (b) rock spalling on free face; and (c) movement of fractured rock at free face.

The distance between the nearest free face and the blast hole is termed the burden, which is approximately related to the explosive diameter by the following empirical relationship (FHWA, 1985):

(10.1a) where Be is the burden distance in meters; SGe is the explosive specific gravity; SGr is the rock specific gravity; and de is the explosive diameter in mm.

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Alternatively, (10.1b) where Be is in feet and de is in inches. In a blast consisting of a number of multi-hole rows, it is necessary that the holes be detonated in a sequence starting with the holes closest to the free face. With a suitable delay interval between rows, there is sufficient time for fracture and displacement of the rock in each row to form a free face for the succeeding row. If this interval is too short, the result is excessive airblast and rock fracture behind the blast holes, while if the interval is too long, the muck pile is scattered. An appropriate delay interval in milliseconds is about 10–12 times the burden in meters (i.e. 30 ms delays for a 3 m burden). 10.3.2 Controlled blasting In making a rock excavation for a foundation it is often necessary to use controlled blasting procedures that limit damage to the rock in the bearing surface and any surrounding rock cuts. Excessive blast damage can result in reduced bearing capacity, and instability of slopes above or below the foundation. Figure 10.14 shows a photograph of a rock cut in very strong granite in which excessive blasting energy in the upper part of the cut has severely fractured the rock, while controlled blasting in the lower half has formed a vertical, stable face. Controlled blasting involves drilling closely spaced, carefully aligned drill holes, which are loaded with a light explosive charge, and detonated in a specified sequence with respect to the main blast. The principle of controlled blasting is closely related to the mechanism of rock fracture described in Section 10.3.1. An explosive load is used that generates a shock wave and gas pressure that is just sufficient to break the rock between drill holes, but not cause crushing or develop radial fractures in the rock behind the face. This is achieved by two methods. First, an explosive is used with a relatively

low detonation velocity of about 2800 m/s (9200 ft/ s) which is approximately one half the velocity of high strength nitroglycerin based gelatin dynamites. Second, the explosive diameter is less than that of the drill hole so there is an air gap between the explosive and the rock in the walls of the drill hole. The dimensions of the air gap are given by the decoupling ratio which is the ratio of the borehole diameter to the explosive diameter. At a decoupling ratio of 2, the pressure level in the borehole is about an order of magnitude less than that when the explosive is packed into the hole, i.e., at a decoupling ratio of 1. Rock fracture along a required design line is achieved when a low energy shock wave produced by a low strength, decoupled explosive intersects a nearby drill hole. The hole acts as a stress concentrator, and is reflected from this free face. Under the right conditions this will result in the formation of a clean fracture between the holes with no cracking of the rock behind the face (Langefors and Kihlstrom, 1967). There is some flexibility allowed in the detonation of the final line holes: they can be detonated on the same delay, or on different delays without significantly effecting the final result. Also, they can be detonated before or after the holes in the main blast (see below). Where there is a need for very closely controlled blasting, one or more unloaded holes can be drilled between the loaded holes to ‘guide’ the fracture along the required line. The general objective in the design of a controlled blast is for the distribution of explosive energy on the face to be as uniform as possible. This is achieved by drilling accurately aligned and evenly spaced holes, and by distributing the explosive up the full length of the hole using small diameter and/or spaced charges. To minimize poor results caused by deviation of the drill holes, the maximum depth of drill holes is usually limited to about 8 m (26 ft). Three common methods of controlled blasting are preshearing, trim blasting and line drilling. The main features of these three methods are described below, together with approximate equations for the hole spacing and explosive charge. These equations

CONSTRUCTION METHODS IN ROCK

377

Figure 10.14 Comparison of rock conditions on presheared (lower) and heavily blasted (upper) rock faces.

should be considered as guidelines because it is essential that the strength of the rock mass and character of the discontinuities be taken into account when designing a blast. (a) Preshearing In preshearing, the row of holes along the final face are detonated before the main blast, or on the first delay interval of the main blast. This forms a fracture, coincident with the final row of drill holes, which inhibits the extension of the radial cracks from the main blast. The row of preshear holes can either be detonated on the same delay, or on separate delays if there is a need to control ground vibrations in the area outside the blast.

The approximate explosive load per unit length of drill hole we to produce a clean presplit line without damage to the wall is given by equation 10.2. The actual explosive load should be adjusted to account for the rock strength and degree of fracturing: (10.2) where dh is the drill hole diameter (mm or in). Using this explosive load, the appropriate hole spacing on the preshear line is about 10–12 times the hole diameter. (b) Trim blasting

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In trim blasting, the final row of holes is detonated last in the sequence, either as the last row in a production blast, or after the production blast. Thus the trim blast removes rock broken by the main blast and forms a stable face along the trim line. The spacing between trim blast holes can be slightly greater than that for presplit holes because in the case of trimming there is a free face to provide relief for the blast. In the layout of trim blast holes, approximate dimensions for the spacing and burden are 16 and 20 times the drill hole diameter respectively. The explosive load can be estimated from equation 10.2. The choice between the use of preshear and trim blasting is often decided by operational conditions. First, for a preshear the total burden should be at least 2–3 times the hole depth to ensure there is an adequate mass of rock to confine the explosive force; instances of displacement of the entire by the preshear have been recorded. Second, the ground vibration levels at some distance from the blast produced by preshearing can be greater than those produced by trim blasting because of the greater confinement of the final line explosive. Third, trim blasting is often preferred in closely fractured rock; in preshear blasting the minimal relief for the explosive gases can cause damage to the rock behind the final line. (c) Line drilling Line drilling involves drilling a line of closely spaced, carefully aligned holes along the final wall line, and loading every second or third hole with explosive. The unloaded holes act as stress concentrators causing a fracture to form preferentially between the holes during the passage of the shock wave produced by adjacent loaded holes. Although this method of controlled blasting is expensive because of the quantity of careful drilling required, it can produce stable rock faces cut to close-dimensional tolerances. A particular use of line drilling is for the excavation of tight corners (Fig. 10.15). In the case of both convex and concave slopes, unloaded line holes are drilled in the corner area to act as guides for the shock wave produced by the presplit holes. On the

concave slope (Fig. 10.15(a)), a loaded hole is required to break the confined rock in the corner, while on the convex slope (Fig. 10.15(b)) all the holes in the corner are unloaded because there is ample relief in this situation (Du Pont, 1964). 10.3.3 Blasting horizontal surfaces A common operation on rock foundation projects is excavation to create a level bearing area for the structural footing. The two main requirements of the blasting operation under these conditions are that the final surface be within close elevation tolerances, and that there be minimal damage to the bearing rock. If there is excessive overblasting, cleaning of the rock surface of broken rock will be a time-consuming operation, and extra concrete will be needed to fill the overbreak. On the other hand, under-excavation will require expensive trim blasting of the high points to bring the surface to grade. One method of producing a stable bearing surface close to the required grade is to use inclined, rather than vertical blast holes (Fig. 10.16). Usual blasting practice is to use vertical holes which are sub-drilled to below the required final excavation level. The cratering effect at the bottom of each blast hole then produces a rock surface that is at no point higher than the required grade. The sub-drill depth for vertical holes is about one third of the burden distance. However, with the use of holes inclined towards the free face, the sub-drill depth can be reduced and the irregularity of the rock surface diminished. In addition, there is greater relief on inclined holes than vertical holes with the result that there is less damage to the rock in the foundation area. The disadvantages of inclined holes are the slight extra drilling length, the greater difficulty in controlling hole direction, and the increased possibility of hanging the drill steel in the hole, especially when drilling broken ground.

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Figure 10.15 Layout of preshear and line holes to excavate rock in tight corners: (a) pattern when excavation is inside preshear plane; and (b) pattern when excavation is outside preshear plane.

10.3.4 Ground vibration control As the shock wave produced by the detonation of an explosive spreads out into the rock in the direction

away from the free face, its energy will diminish below that required to break the rock. However, the energy level will still be sufficient to generate ground vibrations that may propagate to considerable distances from the blast. Any

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Figure 10.16 Comparison of extent of over-excavation when using vertical and inclined blast holes to excavate foundation: (a) inclined blast holes; and (b) vertical blast holes.

structures located within this vibration area will be subjected to this motion and may be damaged if the vibration levels exceed certain thresholds. In addition, humans are very sensitive to ground vibrations and may be disturbed at distances considerably greater than those which cause damage to structures. This section describes methods of determining ground vibration levels and provides damage thresholds for a number of types of structures. (a) Calculation of ground vibrations

The detonation of an explosive charge near a free surface generates two body waves and one surface wave as a result of the elastic response of the rock. The faster of the two waves propagated within the rock is called the primary or P wave which is a compressive wave that produces particle motion in the direction of propagation. The slower body wave is called the secondary or S wave which is a shear wave that produces motions perpendicular to the direction of propagation. The surface wave, which is slower than either the P or S wave, is named after Rayleigh who proved its existence, and

CONSTRUCTION METHODS IN ROCK

is known as the R wave. In terms of vibration damage, the R wave is the most important because it propagates along the ground surface, and because its amplitude decays more slowly with distance travelled than either the P or S wave. The wide variations in geometrical and geological conditions on typical blasting sites preclude the calculation of ground vibration levels by means of elastodynamic equations. Therefore, the most reliable predictions are given by empirical relationships developed from the measurement of vibration levels produced by full-scale blasts. The potential of damage to a structure from blast vibrations is related to the response of the structure to passing vibrations. Damage occurs when differential movement between structural members or between different points in the same structural member causes strains to develop which, in turn, cause cracking (Dowding, 1985). The strain induced in a structure is related to both the magnitude, and to the frequency of the vibration. Numerous studies have examined the level of ground vibrations that induces damage in structures, and particularly residential structures. These studies have shown that damage potential can be most readily correlated with the particle velocity (Siskind et al., 1976; Siskind et al., 1980; Stagg et al., 1984). The particle velocity is a measure of the velocity of particles of ground during passage of the shock wave, and not the propagation velocity of the shock wave itself. The stress wave has three components—vertical, longitudinal and transverse—and it is necessary to measure all three components and use the greatest, termed the peak particle velocity (PPV), to assess damage potential. The magnitude of the PPV is related to the both the radial distance from the blast Re and the explosive weight detonated per delay W by: (10.3) where ke and ße are constants which have to be determined by measurements of vibrations at each is known as particular blast site; the term

381

the scaled distance. Equation 10.3 plots as a straight line on log-log paper in which ke is the intercept on the velocity axis at a scaled distance of 1.0, and ße is the slope of the line (Fig. 10.17). The results of vibration measurements for surface blasts show that values of the constants ke and ße are as follows (Oriard, 1971): Units: PPV—mm/s; Re—m; We—kg Units: PPV—in/s; Re—ft; We—lb. For preshear blasts where the explosive is more highly confined, the constant ke can reach values 6400 (metric) or 800 (imperial). Equation 10.3 can be solved to predict ground vibration levels for a particular blast. Alternatively, the maximum allowable explosive weight per delay can be calculated to minimize the risk that vibration levels will exceed a certain thresh old level at a specified distance from the blast. Where equation 10.3 shows that vibrations will be close to critical levels, it is preferable to measure actual vibrations to establish reliable values for the constants ke and βe. (b) Vibration damage thresholds Vibration measurement programs have determined the threshold vibrations levels that may result in damage to structures of various types, as well as the vibration levels that are perceptible and objectionable to humans (Table 10.3). The velocity of 50 mm/s (2 in/s) is used as a damage threshold for a wide range of structures and is accepted as a practical limit in many blasting operations. For the results shown in Fig. 10.17, in order to maintain the PPV below 50 mm/s it is necessary that the scaled distance exceed 6.35 m/ kg½. That is, at a distance of 20 m (65 ft) from the blast, the maximum explosive weight detonated per delay should be 9.9 kg (22 lb). The frequency of the ground vibrations is also of importance in assessing damage potential. If the principal frequency, that is, the frequency of greatest amplitude pulse, is approximately equal to the

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Figure 10.17 Typical plot of measured peak particle velocity versus scaled distance for a series of blasts.

natural frequency of the structure, then there is a greater risk of damage than if the principal and natural frequencies are significantly different (Dowding, 1985). The natural frequency of twostorey residential buildings is in the range 5–20 Hz, and the natural frequency decreases with increasing

height of the structure. The principal frequency of a blast will vary with such factors as the type of blast, the distance between the blast and the structure, and the material through which the ground vibrations travel. Typical construction

Table 10.3 Peak particle velocity damage threshold levels Threshold velocity Description of effect of ground vibrations due to blasting mm/s

(in/s)

3–5 (0.12–0.2) Vibrations perceptible to humans 33–50 (1.3–2) Vibrations objectional to humans 50 (2) Limit below which risk of damage to structures, even old buildings, is very slight (<5%). Also, no damage to underground utilities. 250 (10) Damage to restrained, monolithic concrete walls.

blasts produce vibrations with principal frequencies

in the range of about 50–100 Hz. It is found that

CONSTRUCTION METHODS IN ROCK

383

large quarry blasts produce vibrations with lower principal frequencies than construction blasts, that principal frequencies decrease with increasing distance due to frequency attenuation, and that vibrations measured on rock have higher frequencies than those measured in soil. 10.3.5 Vibrations in uncured concrete On some construction projects there may be a need to carry out blasting operations close to uncured concrete. Under these circumstances, explosive charge weights per delay should be designed to keep ground vibrations to within limits which are determined by the age of the concrete, the distance of the concrete from the blast, and the type of structure. Figure 10.18 and Table 10.4 show an approximate relationship between allowable peak particle velocity levels and the concrete age (Oriard and Coulson, 1980). At ages less than four hours, the concrete has not yet set and somewhat higher vibration levels are permissible than during the period of between 4 and 24 hours when the concrete is taking its initial set. The two sets of vibration limits shown in Fig. 10.18 also show that mass concrete (i) is able to withstand higher vibrations than structural walls and slabs (ii); structural walls of freshly poured concrete are particularly sensitive to vibrations. Figure 10.18 shows that, for the same time after batching, allowable vibration levels are greater for distances of 0–15 m (50 ft)—lines marked ‘a’— than for distances greater than 75 m (250 ft)—lines marked ‘b’. The reason for this is that concrete can

Table 10.4 Illustration of particle velocity and distance criteria for blasting near uncured concrete Time from batching (hours) Nonstructural fill and mass concrete mm/s Structural walls, structural concrete slabs (in/s) mm/s (in/s) 0–4 4–24 24–72 72–168 168–240 over 240

100 (4) df 25 (1) df 40 (1.5) df 75 (3) df 200 (8) df 375 (15) df

50 (2) df 6 (0.25) df 25 (1) df 50 (2) df 125 (5) df 250 (10) df

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Figure 10.18 Approximate maximum allowable vibration levels in uncured concrete (Oriard and Coulson, 1980): (i) non-structural fill, mass concrete; and (ii) structural concrete walls and slabs.

Time from batching (hours) Nonstructural fill and mass concrete mm/s Structural walls, structural concrete slabs (in/s) mm/s (in/s) df=distance factor to account for frequency attenuation =1.0 when distance is 0–15 m (0–50 ft) =0.8 when distance is 15–50 m (50–150 ft) =0.7 when distance is 50–80 m (150–250 ft) =0.6 when distance is over 80 m (over 250 ft)

better withstand high frequency vibrations because low frequencies induce greater deflections in the structure. Vibration frequencies decrease as the distance from the blast increases because there is attenuation of frequency with distance. The result of this frequency attenuation is that, at equal curing times, higher vibration levels are permitted at closer distances as shown by the two series of lines marked ‘a’ and ‘b’ on Fig. 10.18.

In critical conditions it is recommended that vibrations and strength tests be conducted to confirm the performance of the concrete and the relationships given in Fig. 10.18. 10.3.6 Non-explosive excavation Where an excavation must be made to close

CONSTRUCTION METHODS IN ROCK

dimensional tolerances, or where vibration levels must be restricted to very low levels, it may be appropriate to use non-explosive excavation methods rather than blasting. Four common methods are ripping, impact hammers, hydraulic splitters, and expansion compounds. Ripping with a ripping tooth mounted on a bulldozer is the most efficient non-blasting excavation method, but can only be used in areas that are large enough, such as a dam foundation, for the equipment to operate. Also, the degree of fracturing and strength of the rock must be suitable for the equipment to be used. A common method of assessing the suitability of ripping as an excavation method is to compare the seismic velocity of the rock (see Section 4.1.2) with rippability charts for a range of bulldozer sizes (Caterpillar Inc., 1997). These charts have been developed from extensive field testing, and show, for example, that a D-8R dozer (228 kW or 305 hp) can rip rock with seismic velocities up to 1500–1800 m/s (5000 to 6000 ft/s), while for a D-10R dozer (425 kW or 570 hp) the upper limit for ripping is a seismic velocity of about 2100–2400 m/s (7000 to 8000 ft/s). A more comprehensive method of assessing rippability is to determine the excavatability index which is the product four parameters related to the rock strength Ms, the block size Kb, the orientation and spacing of the discontinuities Kd, and the shear strength of the discontinuities Js (Kirsten, 1982). The excavatability index Kr is calculated from (10.4) These four parameters are identical to those used to assess the susceptibility of rock to scour as discussed in Section 6.7.2. This is appropriate because the mechanisms of scour and ripping are

385

similar in that they involve the application of a force to remove particles of in situ rock. Magnitudes for the four parameters can be determined from Tables 6.2–6.5 which assign numerical values to geological characteristics of the rock mass. For example: 1. for a moderately weak rock, 2. with three joints sets and an RQD of 50%, 3. with tight but smooth planar discontinuities and slightly altered rock surfaces, 4. with the closer joint spacing dipping in the direction of ripping at 45° and slabby rock with an aspect ratio of 1:4, 5. Field tests have shown that the limits to ripping in terms of the Kr values for equipment with the following flywheel powers are as in Table 10.5. It is suggested that these categories of Kr be used as a guideline in selecting excavation methods to suit different sizes of equipment, and that the procedure should be calibrated to suit local conditions. In contrast to ripping, an hydraulic impact hammer mounted on an excavator boom can operate in more restricted areas and excavate to very close tolerances with minimal damage to the rock beyond the excavation limits. Impact hammers can break even very strong rock provided that it contains discontinuities which can be exploited by the chisel to loosen and move blocks. Section 10.5.3 discusses the relationship between rock mass strength characteristics and the appropriate method of excavation.

Table 10.5 Limits to ripping in terms of excavatability index Kr Kr

Limits to ripping

0.1–10

Can be ripped by dozers with flywheel powers in the range 100–150 kW (135–200 hp), e.g. Caterpillar D6D/D7G; 10–1000 Can be ripped by dozers with flywheel powers in the range 225–300 kW (300–400 hp), e.g. Caterpillar D8K/D9H; >1000 Extremely difficult ripping even by dozers with flywheel powers of 520 kW (700 hp), e.g. Caterpillar D10.

Excavation with both hydraulic splitters and

expansion agents involves drilling closely spaced

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holes (about 150–200 mm, or 6–8 in, spacing) along the required excavation .line, and then applying a high internal pressure to the boreholes. In the case of the hydraulic splitter the internal pressure is generated by a wedge that is pushed by hydraulics between two tapered platens. In the case of expansive cement, the pressure is developed when the cement is mixed with water and confined in a borehole. This pressure is sufficient to generate fractures that will preferentially form between the drill holes that act as stress concentrators. These methods produce the best results in massive rock or concrete; in fractured rock it can be difficult to control the direction of the cracks. The advantages of hydraulic splitters and expansion agents are lack of noise and vibration, and the generally precise control over excavation limits. The disadvantages are that both these methods are slow and costly and are not suitable for the excavation of large volumes of rock. Most chemical expansion agents require a period of about 5–12 hours to break the rock. 10.4 Bearing surface improvement and rock reinforcement Prior to construction of a footing it may be necessary to take steps, depending on the geological and geometrical conditions at the site, to prepare a suitable bearing surface, and reinforce the bearing rock. The purpose of this work would be to ensure that the rock has adequate bearing capacity, and that there is no excessive movement or weathering of the foundation rock during the design life of the structure. In addition to stabilization work carried out at the time of construction, remedial work may also be necessary during operation of the structure. Remedial work is most often required in climates where the rock is subjected to frequent freeze-thaw cycles, heavy precipitation, or where the rock is susceptible to weathering. Figure 10.19 shows examples of a variety of surface preparation and reinforcement measures that may be applicable on rock construction projects (Wyllie,

1979, 1991, 1995; Cheng, 1987; Romana and Izquierdo, 1987; FHWA, 1982). In Fig. 10.19 the footing is located on a bench cut into a steep rock face. The rock contains a set of joints that dips out of the slope face at an angle of about 30° and there is a potential for sliding failures on these surfaces. The rock also contains a fault that is parallel to the major joint set, and weathering of the broken rock below the fault has formed a cavity in the rock face. In the bearing area there is a seam of crushed and sheared rock that dips at an angle of about 65° into the face. The block formed by the intersection of the fault and the seam of sheared rock will be potentially unstable under the loads applied by the structure. The following is a brief description of the stabilization work ((1)–(9)) illustrated in Fig. 10.19; design procedures for this work are provided in Chapters 5, 6 and 9. 10.4.1 Trim blasting (1) The formation of a planar, level bearing surface may require controlled blasting or a non-explosive excavation method. Where possible, the bearing surface should be at right angles to the direction of the applied load so there is no tendency of the footing to slide. Also, there should be no irregular protrusions or cavities so that the bearing pressure will be uniform across the full area of the footing, with no stress concentrations induced in the footing. 10.4.2 Surface preparation (2) Following excavation of the rock, the bearing surface should be thoroughly cleaned of all broken, loose and weathered rock using high pressure air or water hoses. Levelling of the base of a blasted excavation with a dozer will rarely produce an adequate structural bearing surface because cavities in the excavated surface will be filled with broken rock that cannot be compacted by the low bearing pressure of the tracks.

CONSTRUCTION METHODS IN ROCK

387

Figure 10.19 Surface preparation and reinforcement of rock foundation. 1. Trim blast to create level bearing surface. 2. Loose and broken rock cleaned from bearing surface. 3. Lean concrete fill in seam of weak rock. 4. Shotcrete with drain holes to control rock weathering and frost action. 5. Pins to prevent loosening and movement of jointed rock. 6. Tensioned rock anchors to reinforce crest of foundation. 7. Tensioned, multi-strand anchors installed to prevent shear failure on fault dipping out of slope face. 8. Concrete buttress to support cavity. 9. Drain hole to prevent build up of water pressure behind buttress.

In some circumstances it may be necessary to roughen smooth and planar bearing surfaces if there is a risk of the footing sliding on this surface. An hydraulic impact hammer may be an appropriate means of removing blocks of rock to roughen the

surface.

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10.4.3 Dental concrete (3) If the bearing surface is intersected by a seam of crushed or faulted rock, this can be sub-excavated to a depth equal to at least twice its width and then back filled with lean concrete. This procedure will probably be satisfactory where the fault width is not more than about one quarter to one third of the footing width. If the fault width is greater than one third of the footing width, the design bearing pressure should be reduced accordingly, and a more extensive dental concreting program may be required. Alternatively, the footing could be reinforced to bridge over the low bearing pressure area. 10.4.4 Shotcrete (4) Shotcrete is pneumatically applied, fine aggregate mortar (less than 13 mm or 1/2 in aggregate size) that is usually placed in a 75–100 mm (3–4 in) thick layer (ACI, 1996). When applied on surface excavations, the primary functions of shotcrete are to prevent loosening and weathering of the surface rock; negligible support of the overall slope is provided. The effectiveness of shotcrete depends to a large degree on the condition of the rock surface to which it is applied. The surface should be free of organic matter, soil and broken rock, and should also be damp to ensure good adhesion between the shotcrete and the rock. The shotcrete applications shown in Fig. 10.19 will prevent the seepage of runoff water and frost heave under the footing, and also prevent loosening of the rock along the crest of the bench on which the footing is located. It is important that there be holes through the shotcrete to prevent build up of water pressures. In massive rock the drain holes should be drilled before the shotcrete is applied so that the holes can be located to intersect discontinuities along which seepage water is flowing. The holes are plugged with rags or wooden plugs while the shotcrete is applied. For all permanent applications shotcrete should be reinforced to reduce the risk of cracking and

spalling. The two most common types of reinforcement are welded wire mesh and steel fibers. Wire mesh is the more common reinforcement method, but the advantages of using steel fiber reinforcing are the faster application time and production of a superior product on irregular rock surfaces. (a) Wire mesh reinforcing Welded wire mesh is usually fabricated from 3.5 mm (0.13 in or 10 gauge) diameter wire on minimum 100 mm (4 in) centers and is attached to the rock surface with threaded pins, complete with a nut and washer. The pins are grouted into holes drilled in the rock on about 1–2 m (3–6 ft) centers, and located at low points to hold the mesh close to the rock face so that the mesh will be entirely encased in shotcrete. Wire mesh can only be used on reasonably uniform surfaces because its stiffness prevents it from being closely attached to irregular surfaces. Weld mesh is generally preferable to the more flexible chain link mesh because the 50 mm (2 in) opening size of chain link mesh is too small for complete penetration of the aggregate with the result that voids may be formed behind the mesh. An alternative method of installing mesh is to place it between two layers of shotcrete, with the first layer creating a smoother surface to which the mesh can be closely attached. (b) Steel fiber reinforcing The installation of mesh on to rock faces to provide reinforcement for shotcrete is time consuming and labor intensive. In comparison, shotcrete containing steel fibers as the reinforcement medium can be applied in a single pass. For applications on irregular surfaces the extra cost of the fibers and wear to the pump and hoses usually more than compensates for the saving in installation time of mesh. Fibers are manufactured from high strength carbon steel with lengths of 30–38 mm (1.2–1.5 in) and an equivalent diameter of 0.5 mm (0.02 in), and are deformed or have crimped ends to resist pullout. The principal function of the fibers is to increase significantly the tensile and post-crack strength of the shotcrete compared with nonreinforced shotcrete (Fig. 10.20).

CONSTRUCTION METHODS IN ROCK

389

Figure 10.20 Load-deformation characteristics of steel-fiber reinforced shotcrete. 1. without fibers 2. 1% vol. fibers 3. 2% vol. fibers 4. 3% vol. fibers

Shotcrete properties are specified as follows. 1. Compressive strength is usually about 20 MPa (2900 p.s.i.) at 3 days and 30 MPa (4350 p.s.i.) at 7 days. 2. First crack flexural strength is 4.5 MPa (650 psi) at 7 days. 3. The toughness index determines the post-crack strength. The procedure for calculating the toughness indices I5 and I10 is shown on Fig. 10.20; toughness indices of are suitable for most applications. Shotcrete is tested by cutting samples from a 0.6 m (24 in) square by 0.1 m (4 in) thick test panel that is shot at the same time and with the same mix and pump as the production shotcrete. The samples are tested in a compression machine to determine the compressive strength, and in bendingto determine the flexural strength and the I5 and I10 toughness indices (ASTM, 1985). Steel fiber reinforced shotcrete can be applied using standard shotcrete equipment, although the wear to

the pump and hose is somewhat greater than when used to place non-fiber mix. Pumping of steel-fiber mix requires that the fibers be uniformly distributed in the shotcrete mix to avoid balling that would block the pump or produce a partially reinforced product. The usual procedure is to add the fibers in the ready mix plant, either to wet mix in a mixer truck, or to dry mix which is packaged in bags. The properties of shotcrete are enhanced by the use of micro-silica which is added to the mix as a partial replacement for cement (USBM, 1984). Silica fume is an ultra fine powder with a particle size approximately equal to that of cigarette smoke. When added to shotcrete, silica fume reduces rebound, allows thickness of up to half a meter to be applied in a single pass, and covers surfaces on which there is running water. There is also an increase in the long term strength in most cases. Typical shotcrete mixes for wet and dry processes are shown in Table 10.6. The wet mix is used where the shotcrete can be supplied to the site in readymix trucks, while dry mix is supplied in bags (1 m3 capacity) and the water is added at the nozzle under the control of the nozzleman. When using dry mix, better results are achieved if the mix is pre-

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moisturized to about 4% water content before it is placed in the pump. 10.4.5 Shear keys (5) Where there is a possibility of blocks sliding on discontinuties dipping out of the slope face, the slope can be stabilized with shear keys installed at the toe of the blocks. The function of the keys is to prevent movement of blocks on the face because

progressive loosening and loss of interlock on the discontinuity surfaces could result in a much larger failure. The required size of a key to support a block, which depends upon the block dimensions, the dip and shear strength properties of the sliding plane, can be determined by limit equilibrium methods (see Chapter 6). In these calculations it can be assumed that the key supplies a resisting force, acting up the sliding plane, that is equal to the shear strength of the steel. The

Table 10.6 Typical shotcrete mix proportions, at the nozzle (Wood, 1998) Material

Wet mix

Dry mix

Plain kg/m3

(lb/ft3)

% by wt.

Silica fume

Plain

kg/m3

kg/m3

(lb/ft3)

% by wt. kg/m3 (lb/ft3) % by wt.

425

(26)

18.0

375

(23)

16.0

–

–

0.0

50

(3.1)

2.1

495

(31)

21.0

490

(30)

20.9

1215

(75)

51.5

1205

(75)

51.4

60

(3.7)

2.5

60

(3.7)

2.6

165 –

(10.2) –

7.0 –

165 –

(10.2) –

7.0

–

–

–

–

–

–

–

–

–

–

100.0

2345

(lb/ft3)

% by wt.

400 (25) 17.0 350 (22) 15.0 Portland cement, Type 10 Silica – – 0.0 47 (2.9) 2.0 fume 460 (28) 19.6 485 (30) 20.8 Coarse aggregate , <10 mm* Concrete 1260 (78) 53.7 1215 (75) 52.1 sand* Steel 57 (3.5) 2.4 57 (3.5) 2.4 fibers Water 170 (10.5) 7.2 177 (11) 7.6 Water Yes – Yes – – reducing admixture Superplas – – – Yes – – ticizer Yes – Yes – – Airentraining admixture Total 2347 100.0 2331 100.0 * Proportions based on “specific surface dry” aggregates.

working strength of steel in shear is about 25% of the yield tensile strength. The keys comprise a row of steel reinforcing bars fully grouted into holes drilled to a depth of about 0. 3–0.6 m (1–2 ft). The diameter of the bars may range from about 25 to 50 mm (1–2 in) and the spacing

2360

Silica fume

100.0

depends on the support force required. The bars are fully encased in concrete, both to protect the steel from corrosion, and to provide continuous support that will prevent movement of the block. Shear keys are usually only used to support blocks up to about 2 m (6 ft) thick; it is more efficient to support larger

CONSTRUCTION METHODS IN ROCK

blocks with tensioned rock bolts which provide both a resisting force and normal force on the sliding plane. 10.4.6 Rock bolts (6)

391

these anchors is the determination of the length required to ensure that they are anchored below the depth of the deepest potential failure plane. This would require both careful mapping of the rock face and a vertical diamond drill hole to identify all possible faults with this orientation.

The rock bolts shown in Fig. 10.19 are installed just below the crest of the bench on which the footing is located. The function of these bolts is to prevent loosening and movement of the rock in this area which is both highly stressed, and susceptible to relaxation because of its proximity to the vertical face. Movement of the rock in this area could result in loss of support along the outer edge of the footing. These bolts could be either tensioned or untensioned depending on the geological conditions. If the rock contains sets of joints dipping out of the face and there has already been some movement on these joints, tensioned bolts would probably be required to increase the shear strength of the surface. However, if the rock is generally massive and undisturbed, the installation of untensioned, fully grouted bolts to minimize long term loosening of the rock may be satisfactory. Details of design and installation procedures for rock bolts are given in Chapter 9.

The concrete buttress shown in Fig. 10.19 has been constructed to fill a cavity in the rock face that has developed as the result of weathering of the fractured rock below the fault plane. The buttress fulfills two functions: first to retain and protect the area of weak rock, and second to support the overhang. The loads on the buttress are low so it is not necessary that the concrete be reinforced. However, in order that the buttress prevent relaxation of the rock, it should be founded on a clean rock surface and anchored to the base using steel pins to prevent sliding. Also, the top should be poured so that it is in continuous contact with the underside of the overhang. In order to meet this second requirement, it may be necessary to place the last pour through a hole drilled downwards into the cavity from the rock face, and use a non-shrink agent in the pour.

10.4.7 Tensioned rock anchors (7)

10.4.9 Drain holes (9)

The tensioned rock anchors shown in Fig. 10.19 are installed to prevent a sliding type failure of the wedge of rock formed by the intersection of the fault dipping out of the slope face, and the subvertical seam of fractured rock. Because of the high probability of movement of this wedge under the applied structural loads, it would be necessary that the anchors be installed and tensioned prior to construction of the footing. This procedure would prestress the foundation by providing normal and shear stresses on the potential sliding plane and prevent movement when the structural load is applied. A very important aspect of the design of

It is possible that ground water seepage will be concentrated at the fault zone and the underlying area of fractured rock. If this is the case, drain holes would be required through the buttress to ensure that water pressures do not build up behind the concrete. It is usual for drain holes to be cased with a perforated plastic pipe to prevent caving. The orientation and position of the drain holes should be selected so that they intersect the major discontinuities that are carrying the water. Since most intact rock has essentially zero permeability, holes which do not intersect discontinuities will not be effective drains. For the conditions shown in

10.4.8 Concrete buttress (8)

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Fig. 10.19, drain holes inclined at the same angle as the fault would produce limited drainage compared with the flatter hole shown which intersects a number of these features. 10.5 Contracts and specifications The success of a construction project can often depend as much on the contract and specifications that define the work, as the design of the project itself. The importance of contracts is first that they define the work to be performed, and second that they are legal documents that prescribe the rights and responsibilities of the owner and the contractor. The contract must also comply with all laws which may be applicable to the project. While most construction contracts have the same basic format, every project requires a set of documents that specifically addresses the particular conditions of the work. Some of the basic decisions that are required in preparing the documents are the type of contract, i.e., unit or fixed price contracts, whether bids will be open to all contractors or only to selected contractors (prequalification), and whether end-product or method specifications will be prepared. This section discusses these aspects of contract specifications with particular reference to projects involving rock excavation. Also, the discussion is mainly directed to North American contracting practices (Berman and Crossland, 1972; Crimmins et al., 1972). 10.5.1 Components of contract documents Contract documents usually consist of the following principal components (Merritt, 1976): 1. 2. 3. 4. 5. 6.

advertisement for bids; information to bidders; proposal form; contract-agreement form bond forms; general provisions;

7. special provisions; 8. technical specifications. All these items, apart from the last two, will generally have similar formats regardless of the construction project and the type of contract. As a guideline in preparing contracts, most government agencies, utilities and corporations have drawn up standard documents which they have found to be applicable to the type of work in which they are involved. The following is a summary of the items that are included in the general and special provisions, and the technical specifications. (a) General and special provisions The general provisions set out the rights and responsibilities of the parties to the contract (owner and contractor) and the surety, the requirements governing their business and legal relationships, and the authority of the engineer. Where the general conditions are standard documents that are published by the contracting agency, and it is necessary to make modifications, additions or deletions to suit the requirements of the project, these items constitute the special provisions. Particular items that are usually included in the general provisions are as follows: 1. Definitions and abbreviations of terms used in the specifications. 2. Bidding requirements which include prequalification, delivery of proposal, bonding and, for public agencies, a noncollusion affidavit. Prequalification is documentary evidence of capability and financial standing, or particular experience in a portion of the work such as socketed piers or high tension anchors. 3. Contract and subcontract procedure which includes award and execution of the contract, requirements for contract bond, submission of progress schedule, recourse for failure to execute the contract, and provisions for subletting contracts. 4. Scope of work is a description of the work to be performed, and such items as work space available for equipment and materials, final site

CONSTRUCTION METHODS IN ROCK

5.

6.

7.

8.

clean up, and maintenance of traffic where required. Also, a limit is set on the deviation of actual quantities from estimated quantities without change in the contract price (see Section 10.5.3(d)). Control of work which includes the authority of the engineer, the plans, specifications and working drawings. Also included are procedures for inspection and testing of the work, handling of defective work, contractor’s claims for change orders, and final acceptance of the completed work. Legal and public relations covers all provisions for legal relations between the contractor and owner, and between the contractor and the general public. Also covered are liability and insurance provisions, and compliance with applicable laws such as public safety, explosives and blasting, accident prevention, public safety, public utilities and pollution abatement. Prosecution and progress includes provisions for commencement and completion of the work, suspension of the work, unavoidable delays, default of the contract, liquidated damages and extension of time. Measurement and payment includes provisions for measurement of quantities, scope of payment, payment for changes in plans, procedures for partial and final payment, termination of contractor’s responsibility, and guarantee against defective work.

(b) Technical specification The technical specifications give details of the general and special conditions affecting the performance of the work, materials to be used, construction details, measurement of quantities under the scheduled items of work, and the method of payment for these items. 10.5.2 Types of contract Factors to consider in the selection of the most

393

appropriate type of contract for a project are the certainty with which site conditions and quantities can be defined, the required flexibility in the construction work, and the time available to prepare and negotiate a contract. Fundamental to the selection of the appropriate type of contract is determining how the risk should be shared between the owner and the contractor; this depends on the uncertainties that may be encountered during the course of the work. The basic contract types are unit-price and lump sum, with various types of negotiated contracts that may be used under special circumstances. The following are descriptions of common types of contract and the conditions in which they may be applicable for foundation projects involving rock excavation and support. (a) Unit-price contract This is the most common type of contract for rock excavation work, and is used when it is not possible to delineate on the drawings the exact quantities to be included in the contract. The terms of this contract provide that the owner will pay to the contractor a specified amount of money for each unit of work completed. The units of work may be any items whose quantities can be measured such as cubic meters of rock, lineal meter of rock bolt, or cubic meters of grout. Payments are usually made by the owner at specified intervals during construction, with the amount of each payment depending on the value of the work completed during the prior time period. (b) Lump-sum contract If the owner knows exactly the quantities of work to be accomplished, and these quantities can be accurately shown on the drawings, a lump-sum contract can be let. Payments are usually made on a monthly basis with the amount of each payment depending on the value of work completed in the prior time period. Note that a lump-sum contract can be let with a portion of the work such as grouting awarded on a unit price basis. While the majority of projects involving rock excavation are bid as either unit price or lump sum contracts, some major infrastructure projects are bid on the basis of design-build or build-operate-

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transfer (BOT) as discussed below. (c) Design-build contract In design-build projects the owner will define such criteria as the location of a bridge, its required capacity, the construction schedule and the design standards that it should meet. The contractors then form teams with engineering companies to produce the designs that meet both the project requirements, and suit their experience and available equipment. The advantages of the design-build process are that overall procurement time is reduced and that there should be cost savings in that the construction method and materials are not restricted to those selected by an independent designer. However, for successful design-build projects it is essential that the criteria are carefully defined and that they are then fulfilled in the actual construction. (d) BOT contracts BOT projects, and their many variations, expand the scope of the design-build concept and require the construction consortium to finance, design, build and then operate the facility while collecting a fee (such as a toll on a bridge). The fee must cover the total of the capital cost of construction as well as operating costs, and return a reasonable profit. The magnitude of the fee, which may be limited in the contract terms, must be set at a level that will attract a sufficient number of users; this often requires variable pricing depending on demand. At the end of a specified concession period, which may be in the range 20–30 years, ownership of the facility is transferred back to the government agency (Levy, 1996). 10.5.3 Rock excavation and reinforcement specifications The specifications for projects involving rock excavation and reinforcement must include provisions for the uncertainties inherent in these projects. Typical of the uncertainties in the geotechnical aspects of a project are the depth to bedrock, ground water inflow quantities, and the presence of seams of weak or fractured rock. It is unlikely that a representative sampling of these

conditions will be provided by surface mapping and some investigative drilling. Some of the methods which can be used to address these uncertainties in the contract are discussed in this section. (a) Geotechnical data The technical specifications for a rock excavation project should include a geotechnical report describing the geology, ground water and material properties of the site. This information is sometimes divided into factual data and interpretative data as follows. Factual data comprise surface mapping results, drill logs and the results of in situ and laboratory tests, with no projections or interpretation of the data. Interpretative data may show such information as projection of data between drill holes, a range of possible ground water inflow rates, stable slope angles of excavations and the support methods that may be required. The purpose of providing two sets of data is to differentiate clearly between data that have been verified, and interpretations of this data based on judgement and previous experience at this and similar sites. The reports should clearly state the limitations of the data provided. For example, freezing temperatures and heavy rain may change conditions from those described in the report, and interpolations of data between drill holes may not be precise. (b) Definition of rock and soil The ratio of excavation costs between rock and soil may vary from as low as 2 for bulk excavation, to as high as 15 for sites with small rock quantities to be excavated to tight tolerances. Although some contracts classify all materials to be excavated as ‘common’, frequently there are different unit rates for excavation quantities of rock and soil and this requires that the contract contains a definition of these materials for payment purposes. This can readily be accomplished at sites where overburden (soil) overlies sound bed rock and the boundary between the two materials can be determined by mapping, drilling and geophysics. However, where there is a continuous gradation between ‘rock’ and ‘soil’, or the boundary is highly irregular; it is often difficult to draw up an unambiguous definition that

CONSTRUCTION METHODS IN ROCK

395

Figure 10.21 Possible excavation methods related to strength and degree of fracturing of rock (modified from US Dept of Navy, 1982). Note: Rock strength classifications refer to ranges listed in Table 3.6.

clearly distinguishes between the two materials. The ease with which rock can be excavated depends on both the strength of the intact material and the degree of fracturing, so both these properties should be incorporated in any definitions of materials that are included in the contract. Figure 10.21 shows an approximate relationship between the method of excavation—digging, ripping or blasting—and the material properties as defined by the strength of the intact rock and the fracture frequency (see Section 4.3.1). This chart shows, for example, that even very weak rock may need to be blasted if the discontinuities are very widely spaced so that there are no blocks that can be loosened and removed by the excavating equipment. The boundaries shown on this chart depend, of course, on the excavation equipment used by the contractor, and some

calibration in local conditions will be required before it can be used with confidence to define materials for payment purposes. Section 10.3.6 discusses a more comprehensive method of classifying rock in relation to the method of excavation. An alternative material classification, that defines the material according to the equipment with which it can be excavated, has been drawn up by the US Bureau of Reclamation. This classification, which is given in full below, can be used as a guideline in preparing a classification to suit local conditions. ‘Except as otherwise provided in these specifications, material excavated will be measured and classified in excavation, to the lines shown on the drawings or as provided in

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these specifications, and will be classified for payment as follows: Rock excavation. For purposes of classification of excavation, rock is defined as sound and solid masses, layers or ledges of mineral matter in place and of such hardness and texture that it: 1. Cannot be effectively loosened or broken down by ripping in a single pass with a late model tractor-mounted ripper equipped with one digging point of standard manufacturer’s design adequately sized for use with and propelled by a crawler type tractor rated between 210- and 240-net flywheel horsepower, operating in low gear, or 2. In areas where it is impractical to classify by use of a ripper described above, rock excavation is defined as sound material of such hardness and texture that it cannot be loosened and broken down by a 6-pound drifting pick. The drifting pick shall be class D, Federal Specification GGG-H-506d, with handle not less than 34 inches in length. 3. All boulders or detached pieces of solid rock more than 1 cubic yard in volume will be classified as rock excavation. Common excavation. Common excavation includes all material other than rock excavation. All boulders or detached pieces of solid rock less than 1 cubic yard in volume will be classified as common excavation.’ (c) Risk On most projects involving rock excavation there is likely to be some uncertainty as to the conditions that will be encountered: a single persistent discontinuity may cause failure of a slope designed at a steep angle, or a zone of faulted rock may be encountered in the bearing area of a foundation. It is usually considered that is beneficial, to both the cost and progress of the project, that there is an apportionment of risk for these uncertainties

between the owner and the contractor. The sharing of risk is most conveniently accommodated by the type of contract that is used on the project. For example, in circumstances where there is uncertainty as to the conditions that may be encountered, the contractors will submit high bids if they have to assume all the risk for construction costs regardless of the conditions encountered. However, if the owner is prepared to cover some of the risk by paying specified unit prices for items for which the quantities are uncertain, the total cost of the project is likely to be lower. For example, the documents may simply state that a foundation excavation shall have certain minimum dimensions and consist of ‘sound rock’, for which a lump sum payment will be made. In these circumstances, the contractors assume all the risk and their bid must cover contingencies for such factors as dewatering, slope support and improvement of the rock if it has inadequate bearing capacity. However, if unit prices are paid for approved quantities of all these items, the total contract price is likely to be lower because the contractors have greater assurance that they will be paid for the work performed. (d) Variation in quantities It is rarely possible to define precisely in the contract the quantities of all items on the project. Quantities that are often difficult to define are rock and common excavation, rock bolt lengths, and shotcrete and grouting volumes. While the use of a unit price contract allows flexibility in payment for actual quantities, it is also desirable to have a mechanism for protection against ‘unbalanced’ bids. An unbalanced bid is a high unit price with a substantial profit margin that is bid for an item that only has a small quantity in the contract. Therefore, the price of this item will not significantly affect the total bid price. However, if during construction the actual quantity of this unit becomes much greater than that originally estimated, there may be substantial increases in the overall project cost. Protection against unbalanced bids can be provided by including a clause in the contract that requires that the unit prices be renegotiated if the actual

CONSTRUCTION METHODS IN ROCK

quantity differs from the estimated quantity by more than say 20%. This clause will also protect the contractor in the event that the actual quantity is substantially less than the estimate and the bid price is insufficient to cover the mobilization costs. (e) Prequalification On rock excavation projects it may be desirable to have the work performed by a contractor who is experienced, for. example, in presplit blasting and control of ground vibrations. This may be achieved by including in the bidding requirements a clause specifying that the contractor supplies documentary evidence of previous experience in this work, and that the personnel with this experience will be working on the project. This process of prequalification may not be possible on projects for some government agencies who have to accept bids from all contractors. In these circumstances it may be necessary to prepare specifications that are somewhat more detailed than on contracts where only experienced contractors are invited to submit bids. An additional type of prequalification involves only inviting selected contractors with particular experience in certain specialist operations to bid on a project. For example, there are only a limited number of contractors experienced in the

397

installation of high tension anchors, and only these contractors may be invited to submit bids for the work. However, in these circumstances the contractor may also be given the responsibility of determining the bond length and the procedures for achieving the required load capacity, while the designer only specifies the minimum working load and the free stressing length. In this way the contractor assumes some risk on the project in return for not having to bid on an open contract. Other specialist operations that may not be put out to open bidding are shotcreting, grouting and high scaling. (f) End-product and method specifications A factor to consider in the preparation of a contract is the extent to which the methods to be used by the contractor will be prescribed in the documents. That is, whether ‘end-product’ or ‘method’ specifications will be prepared. In most cases it is preferable to prepare end-product specifications, which specify the structure that is to be built, so that the construction methods and equipment that are employed by the contractors are left to their discretion. Method specifications would only be required where an unusual structure is to be built, and/or where the contractors have little experience in the required construction procedures. Method

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Figure 10.22 Process for resolution of construction disputes involving a Disputes Review Board, DRB (Stanley, 1989).

specifications result in the majority of the risk being assumed by the designer and the owner. (g) Dispute Review Board In order to reduce the often lengthy and costly resolution of construction claims in the courts, there is increasing support for an alternative method using a Dispute Review Board (Coffee, 1988; ASCE, 1989). The Board is usually composed of three members, one chosen by the owner, one by the contractor and a third who chairs the group, who is chosen by the two members themselves. The Board meets at the site once every three months approximately, and also receives copies of progress reports in order to stay informed about the job and areas of potential dispute. Figure 10.22 shows the mechanism for resolution of a dispute involving the DRB, together with the maximum times permitted for each of the activities. The operation and functions of the Board are defined in the contract documents. The objective of this process is to resolve disputes as they occur, when the facts and the personnel involved are readily available. Furthermore, the work continues while the dispute is resolved, so the schedule is maintained, the job is completed and final payment made promptly. (h) Partnering

Partnering is not a contract, but a culture and management style that requires a particular approach to reduce the effects of any disputes (Atkinson and Knowles, 1996). The aim is to produce teamwork between the participants and reduce confrontation, together with a dispute resolution process that develops trust between the all the stakeholders involved on the project. The stages in implementing a partnering program are as follows. 1. Pre-bid meeting A pre-bid meeting instigated by the owner sets out the procedures for the partnering process, and engenders a trust and commitment to the process by all parties. 2. Audit An audit of all the stakeholders’ management systems is carried out to produce a Project Quality Plan, and evaluate whether their culture will allow them to participate fully in the partnering process. 3. Specification The owner’s commitment to partnering needs to be reflected in the bid documents. This will include a clear statement of the objectives of the process, a schedule of meetings and workshops and a description of the Dispute Resolution process. 4. Award of contract Following the award of the

CONSTRUCTION METHODS IN ROCK

contract, the owner and contractor each appoint a partnering leader, partnering workshops are organized, and a facilitator who will help to implement partnering is named. 5. Partnering workshops Early in the project all decision making personnel from the main organizations are involved in workshops in which the potential problems are examined and an agreed Project Mission Statement is developed. 6. Partnering agreements The result of the workshops is the preparation of a Partnering Agreement that states the objectives of the project, and defines the communication and dispute resolution processes. The agreement can then be used to evaluate the performance of the partnering as the project proceeds. 7. Dispute resolution The resolution of disputes as described in (g) above is a well proven procedure for rapidly and economically settle disputes and avoid claims. Projects involving excavations and construction in rock are inherently uncertain because of the natural variability in rock characteristics, and it is beneficial to use a system to resolve conflicts efficiently to the satisfaction of all parties. 10.6 References American Concrete Institute (1996) Specification for Shotcrete. ACI 506.2–95. American Society of Civil Engineers, (1989) Avoiding and resolving disputes in underground construction. ASCE Technical Committee on Contracting Practices, Underground Technology Research Council, June. ASTM (1985) Flexural Toughness and First-crack Strength of Fiber-reinforced Concrete (Using Beam with Third-point Loading). ASTM standards Vol. 04. 02, C 1018–85. Atkins, K.P. and Sowers, G.F. (1984) Tunneling under building with thin rock cover. J. Geotech. Eng., ASCE, 110(3), 311–17. Atkinson, D. and Knowles, J.R. (1996) Partnering: the stakeholder ethos. Tunnels and Tunnelling, May, 45–6. Atlas Copco (1978) Product Manual, 3rd edn, Atlas Copco AB, Stockholm. ADITC (Australian Drilling Industry Training Committee Ltd) (1997) Drilling—Manual of methods, applications

399

and management. CRS Lewis Publishers, Baton Rouge, FL. Berman, T. and Crossland, S.H. (1972) Construction Business Handbook, McGraw-Hill, NewYork, Ch.14. Boyles Bros Drilling Co. (1988) Product data. Caterpillar Inc. (1997) Caterpillar Performance Handbook, Edition 28. Peoria, IL. Cheng, Y. (1987) New development in seam treatment of the Feitsui arch Dam foundation. Proc. of Int. Conf., Montreal, Int. Soc. of Rock Mechanics, pp. 319–26. Coffee, J.D. (1988) Dispute review boards in Washington State. Amer. Arbitration Assoc. J., December. Crimmins, R., Samuels, R. and Monahan, B.P. (1972) Construction Rock Work Guide. Wiley-Interscience, New York. Dowding, C.H. (1985) Blast Vibration Monitoring and Control. Prentice-Hall, Englewood Cliffs, NJ. Du Pont of Canada (1964) Controlled Blasting. Wilmington, Delaware. Federal Highway Administration (US) (1982) Tiebacks. FHWA, US Department of Transportation, Report No. FHWA/RD-82/047. Federal Highway Administration (US) (1985) Rock Blasting. FHWA, US Department of Transportation, Contract No. DTFH 61–83-C-00110. Federal Highway Administration (US) (1989) Rock Slopes: Design, Excavation, Stabilization. FHWA, US Department of Transportation. Golder Associates (1989) Project files. Hemphill, G.B. (1981) Blasting Operations. McGrawHill, New York. Kirsten, H.A. D. (1982) A classification system for excavation of natural materials. The Civil Engineer in South Africa, July, 292–303. Langefors, U. and Kihlstrom, B. (1967) The Modern Technique of Rock Blasting, Wiley, New York. Levy, S.M. (1996) Build, Operate, Transfer. Wiley, New York. McGregor, K. (1967) The Drilling of Rock. CR Books, London Merritt, F.S. (ed.) (1976) Standard Handbook for Civil Engineers, McGraw-Hill, New York, Ch. 3–4. National Research Council (1994) Drilling and Excavation Technologies for the Future. National Academy Press, Washington, DC. Oriard, L.L. (1971) Blasting effects and their control in open pit mining. Proc. Second Int. Conf. on Stability in Open Pit Mining, Vancouver, AIME, New York, pp. 197–222.

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Oriard, L.L. and Coulson, J.H. (1980) TVA Blast Vibration Criteria for Mass Concrete. Minimizing Detrimental Construction Vibrations, ASCE, Preprint 80–175, pp. 103–23. Romana, M. and Izquierdo, F.A. (1987) Reinforcement of slopes under Denia Castle, Spain. Proc. of Int. Conf., Montreal; Int. Soc. of Rock Mech., pp. 485–9. Siskind, D.E., Stachura, V.J. and Raddiffe, K.S. (1976) Noise and Vibrations in Residential Structures from Quarry Production Blasting. US Bureau of Mines, Report of Investigations 8168. Siskind, D.E., Stagg, M.S., Kopp, J.W. and Dowding, C.H. (1980) Structure Response and Damage Produced by Ground Vibrations from Surface Blasting. US Bureau of Mines, Report of Investigations 8507. Society of Mining Engineers (1973) Mining Engineering Handbook, Vol. 1. SME of AIME, New York, Ch. 11. Stagg, M.S., Siskind, D.E., Stevens, M.G. and Dowding, C.H. (1984) Effects of Repeated Blasting on a Wood Frame House. US Bureau of Mines, Report of Investigations 8896.

Stanley, E.M. (1989) Dispute review boards, a better way. Civil Engineering ASCE, New York, December, pp. 58–60. Tamrock, (1983) Handbook of Underground Drilling, Tamrock Drills, Finland US Bureau of Mines (1984) Selected Pneumatic Gunites for use in Underground Mines: a Comparative Engineering Analysis. USBM, Dept. of the Interior, Information circular 8984. US Department of Navy (1982) Design Manual 7.1, Soil Mechanics, NAVFAC DM-7.1, Alexandria, Virginia. Wood, D.F. (1998) Personnal communication. Wyllie, D.C. (1979) Fractured bridge supports stabilized under traffic. Railway Track and Structures, Jully, pp. 29–32. Wyllie, D.C. (1991) Rock slopes stabilization and protection measures. 34th Ann. M. AEG, Chicago, October. Wyllie, D.C. (1995) Stability of foundations on jointed rock—case studies. Proc. Int. Workshop on Rock Foundations, Japan, A.A.Balkema, pp. 253–8.

APPENDIX I Stereonets for hand plotting of structural geology data

I.1 Introduction

I.3 Plotting great circles

Analysis of the orientation of structural geology data involves first plotting poles representing the dip and dip direction of each discontinuity. This plot will help to identify discontinuity sets, for which both the average orientation and the scatter (dispersion) can be calculated. The second step in the analysis is to plot great circles representing the average orientation of each set, major discontinuities such as faults, and the dip and dip direction of the cut face. Hand plotting of structural data can be carried out on the stereonets provided in this Appendix. Figure I.1 shows a polar net while Fig. I.2 is equatorial net and Fig. I.3 shows the relationship between these two projections.

Great circles are plotted on the equatorial net (Fig. I.2), but they cannot be plotted directly on this net because the true dip can only be scaled off the horizontal axis. The plotting procedure for great circles consists of the following steps in which shallow dipping planes plot close to the periphery of the net, and steeply dipping planes plot as larger radius circles close to the center.

I.2 Plotting poles Poles can be plotted on the polar stereonet (Fig. I.1) on which the dip direction is indicated on the periphery of the circle, and the dip is measured along radial lines with zero degrees at the center. The procedure for plotting poles is to lay a sheet of tracing paper on the printed polar net and mark the north direction and each quadrant position around the edge of the outer circle. A mark is then made to show the pole which represents the orientation of each discontinuity as defined by its dip and dip direction. Poles for shallow dipping discontinuities lie close to the center of the circle, and poles of steeply dipping discontinuities lie close to the periphery of the circle.

1. Lay a piece of tracing paper on the net with a thumb tack through the center point so that the tracing paper can be rotated on the tracing paper. 2. Mark the north direction of the net on the tracing paper. 3. Locate the dip direction of the plane on the scale around the circumference of the net and mark this point on the tracing paper. Note that the dip direction scale on the equatorial net for plotting great circles starts at the north point at the top of the circle and increases in a clockwise direction. 4. Rotate the tracing paper until the dip direction mark coincides with the horizontal axis of the net, that is the 90° or 180° points of the dip direction scale. 5. Locate the arc on the net corresponding to the dip of the plane and trace this arc on to the paper. Note that a horizontal plane has a great circle at the circumference of the net, and a vertical plane is represented by a straight line passing through the center of the net.

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APPENDIX I

Figure I.1 Polar equal area stereonet for plotting poles (drawn by C.M. St John, Royal School of Mines, London).

6. Rotate the tracing paper so that the two north points coincide and the great circle is oriented correctly. I.4 Lines of intersection The intersection of two planes is a straight line which defines the direction in which a wedge formed by these two planes will slide. The

procedure for determining the orientation of the line of intersection between two planes is as follows. 1. Locate the line of intersection between the two planes which is represented by the point at which the two great circles intersect. 2. Draw a line from the center of the net through the point of intersection and extend it to the circumference of the net. 3. The trend of the line of intersection is given by

APPENDIX I

403

Figure I.2 Equatorial equal area net for plotting poles and great circles (drawn by C.M. St John, Royal School of Mines, London).

the position where the line drawn in Step 2 intersects the scale on the circumference of the net. 4. Rotate the tracing paper until the line drawn in Step 2 lies over one of the horizontal axes of the net (dip directions 90° or 180°). 5. The plunge of the line of intersection is read off the scale on the horizontal axis with a

horizontal plunge having a point of intersection at the circumference and a vertical plunge at the center of the net. I.5 Reference Hoek, E. and Bray, J. (1981) Rock Slope Engineering, 3rd edn, IMM, London.

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APPENDIX I

Figure I.3 Polar and equatorial projections of a sphere (Hoek and Bray, 1981).

APPENDIX II Quantitative description of discontinuities in rock masses

II. 1 Introduction This appendix provides details of the parameters used in geological mapping and diamond drilling for the quantitative description of rock masses. The information provided is based entirely on the procedures drawn up by the International Society of Rock Mechanics (ISRM, 1981), and which are discussed in more detail in Sections 4.2 and 4.3 of this book. The objective of using the ISRM procedures for geological mapping and drill core logging are as follows. First, these procedures are quantitative, so that each parameter is measured and the results can be used either directly, or interpreted, for use in design. Second, the use of standardized procedures allows different personnel to work to the same standards, and to produce comparable information. The following is a description of the parameters that describe the rock mass, together with tables listing values used to quantify these parameters. Also provided are mapping forms that can be used to record both geological mapping and oriented core logging. Further information on geological characterization and methods of data collection are discussed in Chapter 4. II.2 Rock mass characterization parameters Figure II.1 illustrates the parameters that characterize the rock mass, and Fig. II.2 shows how they can be divided into six classes related to the rock material and its strength, the discontinuity

characteristics, infilling properties, the dimensions and shape of the blocks of rock, and ground water conditions. Each of the parameters in Fig. II.2, (A) to (M), is discussed below. II.2.1 Rock material description (A) Rock type The value of including the rock type in describing a rock mass is that this defines the process by which the rock was formed. For example, sedimentary rocks such as sandstone usually contain well ordered sets of discontinuities because they are laid down in layers, and are medium to low strength because they have usually only been subject to moderate heating and compression. Also, the rock type gives an indication of the properties of the rock mass from general experience of their engineering performance. For ex ample, granite tends to be strong and massive and resistant to weathering, in comparison to shale which is often weak and fissile, and can weather rapidly when exposed to wetting and drying cycles. The three primary characteristics of rock that are used to define its type are (see Table II.1): 1. color, as well as whether light or dark minerals predominate; 2. texture or fabric ranging from crystalline, granular or glassy; 3. grain size that can range from clay particles to gravel (Table II.2).

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APPENDIX II

Figure II.1 Diagram illustrating rock mass properties.

(B) Rock strength The compressive strength of the rock comprising the walls of a discontinuity is an important component of shear strength and deformability, especially if the walls are in direct rock to rock contact as in the case of unfilled joints. Slight shear displacement of individual joints caused by shear stresses within the rock mass often results in very small asperity contact areas and actual stresses locally approaching or exceeding the compression strength of the rock wall materials, hence the asperity damage. The wall strength is quantified in the determination of shear strength as the joint compressive strength (JCS) as discussed in

Section 3.4.2(b). Table II.3 defines ranges of rock material strength with a corresponding grade (R6 etc.) related to simple field identification procedures. (C) Weathering Rock masses are frequently weathered near the surface, and are sometimes altered by hydrothermal processes. The weathering (and alteration) generally affects the walls of discontinuities more than the interior of rock blocks. This results in a wall strength some fraction of what would be measured on the fresher rock found in the interior of the rock blocks, for example that sampled by drill core. A description of the state of weathering or alteration

APPENDIX II

407

Figure II.2 List of parameters describing rock mass characteristics.

both for the rock material and for the rock mass is

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APPENDIX II

therefore an essential part of the description of wall strength. There are two main results of weathering: one dominated by mechanical disintegration, the other by chemical decomposition including solution. Generally, both mechanical and chemical effects act together, but, depending on climatic regime, one or other of these aspects may be dominant. Mechanical weathering results in opening of discontinuities, the formation of new discontinuities by rock fracture, the opening of grain boundaries, and the fracture or cleavage of individual mineral grains. Chemical weathering results in discoloration of the rock and

leads to the eventual decomposition of silicate minerals to clay minerals: some minerals, notably quartz, resist this action and may survive unchanged. Solution is an aspect of chemical weathering which is particularly important in the case of carbonate and saline minerals. The relatively thin ‘skin’ of wall rock that affects shear strength and deformability can be tested by means of simple index tests. The apparent uniaxial compression strength can be estimated both from Schmidt hammer tests and from scratch and geological hammer tests, since the

Table II.1 Rock type classification

Note: Numbers can be used to identify rock types on data sheets (see Appendix III). Reference: Geological Society Engineering Group Working Party (1977) Table II.2 Grain size scale Description Boulders Cobbles Coarse gravel Medium gravel Fine gravel Coarse sand Medium sand Fine sand Silt, clay

Grain size mm

(in)

200–600 60–200 20–60 6–20 2–6 0.6–2 0.2–0.6 0.06–0.2 <0.06

(7.9–23.6) (2.4–7.9) (0.8–0.24) (0.2–0.8) (0.1–0.2) (0.02–0.1) (0.008–0.02) (0.002–0.008) (<0.002)

Table II.3 Classification of rock material strengths Grade Description R6

Extremely strong rock

R5

Very strong rock

R4

Strong rock

R3

Medium weak rock

Field identification Specimen can only be chipped with geological hammer. Specimen requires many blows of geological hammer to fracture it. Specimen requires more than one blow with a geological hammer to fracture it. Cannot be scraped or peeled with a pocket knife; specimen can be fractured with single firm blow of

Approximate range of compressive strength MPa

(p.s.i)

>250

(>36000)

100–250

(15 000–36 000)

50–100

(7000–15 000)

25–50

(3500–7000)

APPENDIX II

Grade Description

R2

Weak rock

R1

Very weak rock

R0 S6 S5 S4

Extremely weak rock Hard clay Very stiff clay Stiff clay

S3

Firm clay

S2

Soft clay

S1

Very soft clay

Field identification

Approximate range of compressive strength

geological hammer. Can be peeled with a pocket knife; shallow indentations made by firm blow with point of geological hammer. Crumbles under firm blows with point of geological hammer; can be peeled by a pocket knife. Indented by thumbnail. Indented with difficulty by thumbnail. Readily indented by thumbnail. Readily indented by thumb but penetrated only with great difficulty. Can be penetrated several inches by thumb with moderate effort. Easily penetrated several inches by thumb. Easily penetrated several inches by fist.

latter have been roughly calibrated against a large body of test data. Mineral coatings will affect the shear strength of discontinuities to a marked degree if the walls are planar and smooth. The type of mineral coatings should be described where possible. Samples should be taken when in doubt. Table II.4 defines grades of rock weathering.

409

MPa

(p.s.i)

5–25

(725–3500)

1–5

(150–725)

0.25–1 >0.5 0.25–0.5 0.1–0.25

(35–150) (>70) (35–70) (15–35)

0.05–0.1

(7–15)

0.025–0.05

(4–7)

<0.025

(<4)

II.2.2 Discontinuity description (D) Discontinuity type The discontinuity type is useful in the description of the rock mass because each type has properties

Table II.4 Weathering and alteration grades Grade Term I II

III

IV

V VI

Fresh

Description

No visible sign of rock material weathering; perhaps slight discoloration on major discontinuity surfaces. Slightly weathered Discoloration indicates weathering of rock material and discontinuity surfaces. All the rock material may be discolored by weathering and may be somewhat weaker externally than in its fresh condition. Moderately weathered Less than half of the rock material is decomposed and/or disintegrated to a soil. Fresh or discolored rock is present either as a continuous framework or as corestones. Highly weathered More than half of the rock material is decomposed and/or disintegrated to a soil. Fresh or discolored rock is present either as a discontinuous framework or as corestones. Completely weathered All rock material is decomposed and/or disintegrated to soil. The original mass structure is still largely intact. Residual soil All rock material is converted to soil. The mass structure and material fabric are destroyed. There is a large change in volume, but the soil has not been significantly transported.

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APPENDIX II

that influence the behavior of the rock mass. For example, faults can have lengths of several kilometers and contain low strength gouge, while joints lengths usually do not exceed a few meters and they often contain no infilling. Section 2.1.1 describes the characteristics of the most common types of discontinuities which include faults, bedding, foliation, joints, cleavage and schistosity. (E) Discontinuity orientation The orientation of a discontinuity in space is described by the dip of the line of steepest declination measured from horizontal, and by the dip direction measured clockwise from true north. Example: dip direction (α)/dip (ψ) (025°/45°). The orientation of discontinuities relative to an engineering structure largely controls the possibility of unstable conditions or excessive deformations developing. The importance of orientation increases when other conditions for deformation are present, such as low shear strength and a sufficient number of discontinuities or joint sets for slip to occur. The mutual orientation of discontinuities will determine the shape of the individual blocks comprising the rock mass. (F) Roughness The wall roughness of a discontinuity is a potentially important component of its shear strength, especially in the case of undisplaced and interlocked features (e.g. unfilled joints). The importance of wall roughness declines as aperture, or infilling thickness, or the degree of any previous displacement increases. In general terms the roughness of discontinuity walls can be characterized by undulations and asperities. Large scale undulations, if interlocked and in contact, cause dilation during shear displacement since they are too large to be sheared off. Asperities are small scale roughness that tends to be damaged during shear displacement unless the discontinuity walls are of high strength and/or the stress levels are low, so that dilation can also occur on these small scale features. In practice, undulations affect the initial direction of shear displacement relative to the mean discontinuity plane, while asperities affect the shear

strength that would normally be sampled in a laboratory or medium scale in situ direct shear test. If the direction of potential sliding is known, roughness can be sampled by linear profiles taken parallel to this direction. In many cases the relevant direction is parallel to the dip (dip vector). In cases where sliding is controlled by two intersecting discontinuity planes, the direction of potential sliding is parallel to the line of intersection of the planes. In the case of arch dam abutment stability, the direction of potential sliding may have a marked horizontal component. If the direction of potential sliding is unknown, but nevertheless of importance, roughness must be sampled in three dimensions instead of two. This can be done with a compass and disk-clinometer (Fig. 4.6). Dip and dip direction readings can be plotted as poles on equal-area nets. Alternatively, discontinuity surfaces can be contoured relative to their mean planes using photogrammetric methods. This can be a useful technique if the critical surfaces are inaccessible. The purpose of all roughness sampling methods is for the eventual estimation or calculation of shear strength and dilation. Presently available methods of interpreting roughness profiles and estimating shear strength include measuring the i value (or inclination) of the irregularities, or the joint roughness coefficient JRC of the surface (Fig. II.3). The contribution of the surface roughness to the total friction angle of a surface is discussed in more detail in Section 3.4.2. Descriptive terms that can be used to define roughness are a combination of small scale features (several centimeters dimensions): rough, smooth, slickensided, and larger scale features (several meters dimensions): stepped, undulating, planar. These terms can then be combined to describe decreasing levels of roughness as in Table II.5. (G) Aperture Aperture is the perpendicular distance separating the adjacent rock walls of an open discontinuity, in which the intervening space is air or water filled. Aperture is thereby distinguished from the

APPENDIX II

Figure II.3 Roughness profiles and corresponding range of JRC values associated with each one (ISRM, 1981).

411

412

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Table II.5 Descriptive terms for roughness Level

Description

I II III IV V VI VII VIII IX

Rough, stepped Smooth, stepped Slickensided, stepped Rough, undulating Smooth, undulating Slickensided, undulating Rough, planar Smooth, planar Slickensided, planar

width of a filled discontinuity. Discontinuities that have been filled (e.g. with clay) also come under this category if filling material has been washed out locally. Large aperture can result from shear displacement of discontinuities having appreciable roughness and waviness, from tensile opening, from outwash, and from solution. Steep or vertical discontinuities that have opened in tension as a result of valley erosion or glacial retreat may have very large apertures. In most sub-surface rock masses apertures are small and will probably be less than half a millimeter, compared to the tens, hundreds or even thousands of millimeters width of some of the outwash or extension varieties. Unless discontinuities are exceptionally smooth and planar it will not be of great significance to the shear strength that a ‘closed’ feature is 0.1 mm wide or 1.0 mm wide. However, indirectly as a result of hydraulic conductivity, even the finest may be significant in changing the effective normal stress and therefore also the shear strength. Unfortunately, visual observation of small apertures is inherently unreliable since, with the possible exceptions of drilled holes and bored tunnels, visible apertures are bound to be disturbed apertures, either due to disturbance by blasting, or due to surface weathering effects. The influence of apertures is best assessed by water permeability testing. Apertures are recorded from the point of view of both their loosening and conducting capacity. Joint water pressure, inflow of water and outflow of

storage products (both liquid and gas) will all be affected by aperture. Apertures can be described by the terms listed in Table II.6. II.2.3 Infilling description (H) Infilling type and width Infilling is the term for material separating the adjacent rock walls of discontinuities, e.g. calcite, chlorite, clay, silt, fault gouge, breccia etc. The perpendicular distance between the adjacent rock walls is termed the width of the filled discontinuity, as opposed to the aperture of a gapped or open feature. Owing to the enormous variety of occurrences, filled discontinuities display a wide range of physical behavior, in particular as regards their shear strength deformability and permeability. Short-term and long-term behavior may be quite different such that it is easy to be misled by favorable short-term conditions. The wide range of physical behavior depends on many factors of which the following are probably the most important: 1. mineralogy of filling material (Table II.1); 2. grading or particle size (Table II.2); 3. over-consolidation ratio; 4. water content and permeability (Table II.11); 5. previous shear displacement; 6. wall roughness (Fig. II.3 and Table II.5);

APPENDIX II

7. width (Table II.6);

Table II.6 Aperture dimensions Aperture (mm)

Description

<0.1 0.1–0.25 0.25–0.5 0.5–2.5 2.5–10 >10 1–100 100–1000 >1 m

Very tight Tight Partly open Open Wide Moderately wide Very wide Extremely wide Cavernous

Every attempt should be made to record the above factors, using quantitative descriptions where possible, together with sketches and/or color photographs of the most important occurrences. Certain index tests are suggested for a closer investigation of major discontinuities considered to be a threat to stability. In special cases the results of these field descriptions may warrant the recommendation for large scale in situ testing, at least in the case of dam foundations or major slopes. II.2.4 Rock mass description (I) Spacing The spacing of adjacent discontinuities largely controls the size of individual blocks of intact rock. Several closely spaced sets tend to give conditions of low mass cohesion whereas those that are widely spaced are much more likely to yield interlocking conditions. These effects depend upon the

413

8. fracturing or crushing of wall rock.

‘Closed’ features

‘Gapped’ features

‘Open’ features

persistence of the individual discontinuities. In exceptional cases a close spacing may change the mode of failure of a rock mass from translational to circular or even to flow (e.g. a ‘sugar cube’ shear zone in quartzite). With extremely close spacing the orientation is of little consequence as failure may occur through rotation or rolling of the small rock pieces. As in the case of orientation, the importance of spacing increases when other conditions for deformation are present, i.e. low shear strength and a sufficient number of discontinuities or joint sets for slip to occur. The spacing of individual discontinuities and associated sets has a strong influence on the mass permeability and seepage characteristics. In general, the hydraulic conductivity of any given set will be inversely proportional to the spacing, if individual joint apertures are comparable. Spacing can be described by means of terms listed in Table II.7.

Table II.7 Spacing dimensions Description

Spacing, mm

Extremely close spacing Very close spacing Close spacing Moderate spacing Wide spacing Very wide spacing

<20 20–60 60–200 200–600 600–2000 2000–6000

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APPENDIX II

Description Extremely wide spacing

(J) Persistence Persistence implies the areal extent or size of a discontinuity within a plane. It can be crudely quantified by observing the discontinuity trace lengths on the surface of exposures. It is one of the most important rock mass parameters, but one of the most difficult to quantify in anything but crude terms. The discontinuities of one particular set will often be more persistent than those of the other sets. The minor sets will therefore tend to terminate against the primary features, or they may terminate in solid rock. In the case of rock slopes and dam foundations it is of the greatest importance to attempt to assess the degree of persistence of those discontinuities that are unfavorably orientated for stability. The degree to which discontinuities persist beneath adjacent rock blocks without terminating in solid rock or terminating against other discontinuities determines the degree to which failure of intact rock would be involved in eventual failure. Perhaps, more likely, it determines the degree to which ‘down-stepping’ would have to occur between adjacent discontinuities for a failure surface to develop. Persistence is also of the greatest importance to tension crack development behind the crest of a slope. Frequently, rock exposures are small compared with the area or length of persistent discontinuities, and the real persistence can only be guessed. Less frequently it may be possible to record the dip length and the strike length of exposed discontinuities and thereby estimate their persistence along a given plane through the rock Table II.8 Persistence dimensions

Spacing, mm >6000

mass using probability theory. However, the difficulties and uncertainties involved in the field measurements will be considerable for most rock exposures encountered (see also Section 2.6.2). Persistence can be described by means of terms listed in Table II. 8. (K) Number of sets Both the mechanical behavior and the appearance of a rock mass will be dominated by the number of sets of discontinuities that intersect one another. The mechanical behavior is especially affected since the number of sets determines the extent to which the rock mass can deform without involving failure of the intact rock. The appearance of the rock mass is affected since the number of sets determines the degrees of overbreak that tends to occur with excavation by blasting (Fig. II.4). The number of sets of discontinuities may be a dominant feature of rock slope stability, though traditionally the orientation of discontinuities relative to the face is considered of primary importance. However, a large number of sets having close spacing may change the potential mode of slope failure from translational or toppling to rotational/circular. In the case of tunnel stability three or more sets will generally constitute a three-dimensional block structure having a considerable more ‘degrees of freedom’ for deformation than a rock mass with less than three sets. For example, a strongly foliated phyllite with just one closely spaced joint set may give equally good tunneling conditions as a massive granite with three widely spaces joint sets. The amount of overbreak in a tunnel will usually be strongly dependent on the number of sets.

Persistence

Dimensions, m

Very low persistence Low persistence Medium persistence High persistence Very high persistence

<1 1–3 3–10 10–20 >20

APPENDIX II

415

Figure II.4 Examples illustrating the effect of the number of joint sets on the mechanical behavior and appearance of rock masses (ISRM, 1981).

The number of joint sets occurring locally (for example along the length of a tunnel) can be described according to the following scheme: I massive, occasional random joints; II one joint set; III one joint set plus random; IV two joint sets; V two joint sets plus random; VI three joint sets; VII three joint sets plus random; VII four or more joint sets; I

IX crushed rock, earth-like. Major individual discontinuities should be recorded on an individual basis. (L) Block size and shape Block size is an extremely important indicator of rock mass behavior. Block dimensions are determined by discontinuity spacing, by the number of sets, and by the persistence of the discontinuities delineating potential blocks. The number of sets and the orientation determine the shape of the resulting blocks, which can take the approximate form of cubes, rhombohedrons,

416

APPENDIX II

tetrahedrons, sheets etc. However, regular geometric shapes are the exception rather than the rule since the joints in any one set are seldom consistently parallel. Jointing in sedimentary rocks usually produces the most regular block shapes. The combined properties of block size and interblock shear strength determine the mechanical behavior of the rock mass under given stress conditions. Rock masses composed of large blocks tend to be less deformable, and in the case of underground construction, develop favorable arching and interlocking. In the case of slopes, a small block size may cause the potential mode of failure to resemble that of soil (i.e. circular/ rotational) instead of the translational or toppling modes of failure usually associated with discontinuous rock masses. In exceptional cases ‘block’ size may be so small that flow occurs, as with a ‘sugar-cube’ shear zone in quartzite. Rock quarrying and blasting efficiency are likely to be largely a function of the natural in situ block size. It may be helpful to think in terms of a block size distribution for the rock mass in much the same way that soils are categorized by a distribution of particle sizes. Block size can be described either by means of the average dimension of typical blocks (block size index Ib), or by the total number of joints intersecting a unit volume of the rock mass (volumetric joint count Jv, Table II.9). Rock masses Rock masses can be described by the following adjectives, to give an impression of block size and shape (Fig. II.5): I massive=few joints or very wide spacing; II blocky=approximately equidimensional; III tabular=one dimension considerably smaller than the other two; IV columnar=one dimension considerably larger than the other two; V irregular=wide variations of block size and shape; VI crushed=heavily jointed to ‘sugar cube’.

II.2.5 Ground water (M) Seepage Water seepage through rock masses results mainly from flow through water conducting discontinuities (‘secondary’ permeability). In the case of certain sedimentary rocks the ‘primary’ permeability of the rock material may be significant such that a proportion of the total seepage occurs through the pores. The rate of seepage is roughly proportional to the local hydraulic gradient and to the relevant directional permeability, proportionality being dependent on laminar flow. High velocity flow through open discontinuities may result in increased head losses due to turbulence. The prediction of ground water levels, likely seepage paths, and approximate water pressures may often give advance warning of stability or construction difficulties. The field description of rock masses must inevitably precede any recommendation for field permeability tests so these factors should be carefully assessed at this early stage. Irregular ground water levels and perched water tables may be encountered in rock masses that are partitioned by persistent impermeable features such as dykes, clay filled discontinuities or impermeable beds. The prediction of these potential flow-barriers and associated irregular water tables is of considerable importance, especially for engineering projects where such barriers might be penetrated at depth by tunneling, resulting in high pressure inflows. Seepage of water caused by drainage into an engineering excavation may have far reaching consequences in cases where a sinking ground water level would cause settlement of nearby structures founded on overlying clay deposits. The approximate description of the local hydrogeology should be supplemented with detailed observations of seepage from individual discontinuities or particular sets, according to their relative importance to stability. A short comment concerning recent precipitation in the area, if known, will be helpful in the interpretation of these observations. Additional data concerning ground

APPENDIX II

417

Figure II.5 Sketches of rock masses illustrating block shape. (a) blocky; (b) irregular; (c) tabular; and (d) columnar (ISRM, 1981).

water trends, and rainfall and temperature records will be useful supplementary information. In the case of rock slopes, the preliminary design estimates will be based on assumed values of effective normal stress. If, as a result of field observations, one has to conclude that pessimistic assumptions of water pressure are justified (i.e. a tension crack full of water with zero exit pressure at the toe of the unfavorable discontinuity) then this will clearly have the greatest consequences for

design. So also will the field observation of rock slops and tunnel portals through ice wedging and/ or increased water pressure caused by ice-blocked drainage paths are serious seasonal problems in many countries. Seepage from individual unfilled and filled discontinuities or from specific sets exposed in a tunnel or in a surface exposure can be assessed according to the following descriptive terms in Table II.10 and II.11.

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APPENDIX II

In the case of a rock engineering construction which acts as a drain for the rock mass, for example a tunnel, it is helpful if the overall flow into individual Table II.9 Block dimensions

sections of the structure are described. This should ideally be performed immediately after excavation as ground water levels, or the rock

Description

Jv (joints/m3)

Very large blocks Large blocks Medium-sized blocks Small blocks Very small blocks

<1.0 1–3 3–10 10–30 >30

Table II.10 Seepage quantities in unfilled discontinuities Seepage rating Description I II III IV V VI

The discontinuity is very tight and dry, water flow along it does not appear possible. The discontinuity is dry with no evidence of water flow. The discontinuity flow is dry but shows evidence of water flow, i.e. rust staining etc. The discontinuity is damp but no free water is present. The discontinuity shows seepage, occasional drops of water, but no continuous flow. The discontinuity shows a continuous flow of water. (Estimate liters/min and describe pressure i.e. low, medium, high).

Table II.11 Seepage quantities in filled discontinuities Seepage rating Description I II III IV V VI

The filling materials are heavily consolidated and dry, significant flow appears unlikely due to very low permeability. The filling materials are damp, but no free water is present. The filling materials are wet, occasional drops of water. The filling materials show signs of outwash, continuous flow of water (estimate liter/min). The filling materials are washed out locally, considerable water flow along out-wash channels (estimate liter/min and describe pressure, i.e. low medium, high). The filling materials are washed out completely, very high water pressures experienced, especially on first exposure (estimate liter/ min and describe pressure).

Table II.12 Seepage quantities in rock mass (e.g. tunnel wall) Seepage rating Description I II III IV V

Dry walls and roof, no detectable seepage. Minor seepage, specify dripping discontinuities. Medium inflow, specify discontinuities with continuous flow (estimate liter/min/ 10 m length of excavation). Major inflow, specify discontinuities with strong flows (estimate liter/ min/10 m length of excavation). Exceptionally high inflow, specify source of exceptional flows (estimate liter/min/10 m length of excavation).

APPENDIX II

mass storage, may be depleted rapidly. Descriptions of seepage quantities are given in Table II.12. A field assessment of the likely effectiveness of surface drains, inclined drill holes, or drainage galleries should be made in the case of major rock slopes. This assessment will depend on the orientation, spacing and apertures of the relevant discontinuities. The potential influence of frost and ice on the seepage paths through the rock mass should be assessed. Observations of seepage from the surface trace of discontinuities may be misleading in freezing temperatures. The possibility of iceblocked drainage paths should be assessed from the point of view of surface deterioration of a rock excavation, and from the point of view of overall stability. II.3 Field mapping sheets The two mapping sheets included with this appendix provide a means of recording the qualitative geological data described in Section II.2 above. Sheet 1 Rock mass description sheet describes the rock material in terms of its colour, grain size and strength, the rock mass in terms of the block shape, size, weathering and the number of discontinuity sets and their spacing. Sheet 2 Discontinuity survey data sheet describes the characteristics of each discontinuity in terms of its type, orientation, persistence, aperture/width, filling, surface roughness and water flow. This sheet can be used for recording both outcrop (or tunnel) mapping data, and oriented core data (excluding persistence and surface shape). II.4 References International Society for Rock Mechanics (1981b) Suggested Methods of the Quantitative Description of Discontinuities in Rock Masses (ed. E.T.Brown), Pergamon Press, Oxford, UK.

419

420

APPENDIX II

APPENDIX II

421

APPENDIX III Conversion factors

Imperial unit Length mile foot inch Area square mile acre square foot square inch Volume cubic yard cubic foot cubic inch

Imp. gallon pint US gallon

SI unit

SI unit symbol Conversion factor (Imperial Conversion factor (SI to to SI) Imperial)

kilometer meter millimeter millimeter

km m mm mm

square kilometer km2 hectare ha hectare ha square meter m2 square meter m2 square millimeter mm2 cubic meter cubic meter liter cubic millimeter cubic centimeter liter cubic meter liter liter cubic meter liter

Mass ton tonne ton (2000 lb) (US) kilogram ton (2240 lb) (UK)

m3 m3 liter mm3 cm3 m3 l l m3 l t kg

1 mile=1.609 km 1 ft=0.3048 m 1 ft=304.80 mm 1 in=25.40 mm

1 km=0.6214 mile 1 m=3.2808 ft 1 mm=0.003 281 ft 1 mm=0.039 37 in

1 mile2=2.590 km2 1 mile2=259.0 ha 1 acre=0.4047 ha 1 acre=4047 m2 1 ft2=0.092 90 m2 1 in2=645.2 mm2

1 km2=0.3861 mile2 1 ha=0.003 861 mile2 1 ha=2.4710 acre 1 m2=0.000 247 1 acre 1 m2=10.7643 ft2 1 mm2=0.001 550 in2

1 yd3=0.7646 m3 1 ft3=0.028 32 m3 1 ft3=28.32 1 1 in3=16 387 mm3 1 in3=16.387 cm3 1 in3=0.016 39 1 1 gal=0.004 56 m3 1 gal=4.546 l 1 pt=0.568 l 1 US gal=0.0038 m3 1 US gal=3.8 l

1 m3=1.3080 yd3 1 m3=35.3150 ft3 1 liter=0.035 31 ft3 1 mm3=61.024×10−6 in3 1 cm3=0.061 02 in3 1 liter=61.02 in3 1 m3=220.0 gal 1 liter=0.220 gal 1 liter=1.7606 pt 1 m3=263.2 US gal 11=0.264 US gal

1 ton=0.9072 tonne 1 ton=907.19 kg = 1016.1 kg

1 tonne=1.1023 ton 1 kg=0.001 102 ton = 0.000 984 ton

423

Imperial unit

SI unit

SI unit symbol Conversion factor (Imperial Conversion factor (SI to to SI) Imperial)

kip

kilogram

kg

1 kip=453.59 kg

pound kilogram Mass density ton per cubic yard (2000 kilogram per cubic meter lb) (US) tonne per cubic meter ton per cubic yard (2240 lb) (UK) pound per cubic foot kilogram per cubic meter tonne per cubic meter pound per cubic inch gram per cubic centimeter tonne per cubic meter Force ton force (2000 lb) (US) kilonewton ton force (2240 lb) (UK) kip force kilonewton pound force newton tonf/ft (2000 lb) (US) kilonewton ton f/ft (2240 lb) (UK) pound force per foot Hydraulic conductivity centimeter per second foot per year foot per second Flow rate cubic foot per minute

cubic foot per second gallon per minute Imperial unit

1 kg=0.002 204 6 kip

kg

1 lb=0.4536 kg

1 kg=2.2046 lb

kg/m3

1 ton/yd3=1186.49 kg/m3

t/m3

1 ton/yd3=1.1865 t/m3 1 ton/yd3=1328.9 kg/m3

kg/cm3 t/m3 g/cm3

1 lb/ft3=16.02 kg/m3 1 lb/ft3=0.01602 t/m3 1 lb/in3=27.68 g/cm3

1 kg/m3=0.000 842 8 ton/ yd3 1 t/m3=0.8428 ton/yd3 1 kg/m3=0.000 75 ton/ yd3 1 kg/cm3=0.062 42 lb/ft3 1 t/m3=62.42 lb/ft3 1 g/cm3=0.036 13 lb/in3

t/m3

1 lb/in3=27.68 t/m3

1 t/m3=0.036 13 lb/in3

kN kN N kN/m

1 tonf=8.896 kN =9.964 kN 1 kipf=4.448 kN 1 lbf=4.448 N 1 ton f/ft=29.186 kN/m

per meter newton per meter

N/m

=32.68 kN/m 1 lbf/ft=14.59 N/m

1 kN=0.1124 tonf (US) =0.1004 tonf (UK) 1 kN=0.2248 kipf 1 N=0.2248 lbf 1 kN/m=0.034 26 tonf/ft (US) =0.0306 tonf/ft (UK) 1 N/m=0.068 53 lbf/ft

meter per second meter per second meter per second

m/s m/s m/s

1 cm/s=0.01 m/s 1 ft/yr=0.9665×10−8 m/s 1 ft/s=0.3048 m/s

1 m/s=100 cm/s 1 m/s=1.0346×108 ft/yr 1 m/s=3.2808 ft/s

cubic meter per second

m3/s

1 m3/s=2119.093 ft3/min

liter per second cubic meter per second liter per second liter per second

l/s m3/s l/s l/s

1 ft3/min=0.000 471 9 m3/s 1 ft3/min=0.4719 l/s 1 ft3/s=0.028 32 m3/s 1 ft3/s=28.32 l/s 1 gal/min=0.075 77 l/s

SI unit

Pressure, Stress ton force per square kilopascal foot (2000 lb) (US) ton force per square

SI unit symbol Conversion (Imperial to SI) kPa

1 l/s=2.1191 ft3/min 1 m3/s=35.315 ft3/s 1 l/s=0.035 31 ft3/s 1 l/s=13.2 gal/min

factor Conversion factor (SI to Imperial)

1 tonf/ft2=95.76 kPa

1 kPa=0.01044 ton f/ft2

1 tonf/ft2=107.3 kPa

1 kPa=0.00932 ton/ft2

424

Imperial unit

SI unit

SI unit symbol Conversion (Imperial to SI)

foot (2240 lb) (UK) pound force per pascal Pa square foot kilopascal kPa pound force per pascal Pa square inch kilopascal kPa Weight density* pound force per cubic kilonewton per cubic kN/m3 foot meter Energy foot lbf joules J * Assuming a gravitational acceleration of 9.807 m/s2

factor Conversion factor (SI to Imperial)

1 lbf/ft2=47.88 Pa 1 lbf/ft2=0.047 88 kPa 1 lbf/in2=6895 Pa 1 lbf/in2=6.895 kPa

1 Pa=0.020 89 lbf/ft2 1 kPa=20.89 lbf/ft2 1 Pa=0.000 1450 lbf/in2 1 kPa=0.1450 lbf/in2

1 lbf/ft3–0.157 kN/m3

1 kN/m3=6.37 lbf/ft3

1 ft.lbf=1.355 J

1 J=0.7376 ft.lbf

Index

Acid leachate 234 Active/passive wedges 137 Adit 93, 122, 128 Air photograph 93, 95 Alignment studies 94 Allowable bearing pressures 135 see also Bearing capacity Anhydrite 83, 228 Anisotropic rock 59, 126 Anode 320 Aperture 102, 328, 381 Artesian pressure 328 Arylamide grout 235fc Asperities 69, 76, 102, 106 rock socket 253 Asphalt 234 Attenuation blasting 353, 355 seismic waves 97 Atterburg limits 83 Australia 136

Bearing surface improvement 225, 356 Bedding 25, 94, 95, 113, 119, 125 Bell solution 139, 142 Bending failure 143 Bentonite 71, 114, 116, 151, 239, 258 Beta distribution 20 Bieniawaski, Z.T. 60, 203 Blasting 7, 194, 226, 227, 345 burden 347 preshear 348 controlled blasting 347 corners 349 damage 113, 347 damage thresholds 353 free face 346 ground vibration control 349 horizontal surfaces 349 line drilling 349 modulus test 119, 122 preshearing 348 rock anchor damage 318 rock fracture mechanism 345, 346 scaled distance 352 shockwave 346 sub-drill 349 trim blasting 348, 356 vibration frequency 353 vibration particle velocity 352 vibrations in uncured concrete 353 Blasting mats 319 Block size/shape 103, 385 Borehole surveying 111 Borehole video camera 111 Boussinesq equations 166 Brazilian tension test 71, 80 Breccia 71, 211 Bridge

Back analysis 50, 65, 76 Basalt 69, 211, 272 Base shear 9 Bearing capacity 131, 133, 138 bedded formations 142 building codes 133 dipping formations 140 fractured rock 136 karstic formations 144 layered formations 143 recessed footing 139, 142 slab 144 sloping ground 139 wedge 141 Bearing capacity factors 139 425

426

INDEX

arch 1 exploration 93 foundation failure 5 scour of foundations 195 settlement 12 calculations of 159 suspension 11, 131, 136, 287 Britain 136, 164, 290 Buckling failure 143 Building codes 133, 142 foundation design, seismic 9 loads 8 Bulk modulus 97 Burger substance 85, 164 Calcite 71, 82 Calcium carbonate 5, 228 Calcium hydroxide 243 California 10, 58, 194, 219, 220, 223, 229 Canada 9, 16, 53, 83, 136, 200, 226, 230, 258 Carbonation 82, 83 Cathode 320 Cement grout 234 leaching 243 piezometer 114, 117 Centre of gravity 188 Centrifugal force 173, 274 Chalk 69 China 88, 211, 218, 219 Chloride 298, 323 Chlorite 83 Clay 71, 83, 144, 215, 217, 272, 324 classification 378 Claystone 82, 211 Cleavage 26 Coal 319 Coal mining 164 Coecient of reliability 18, 23, 230 Cohesion 66, 70, 71, 76, 192, 194, 215 grout 237 in situ test 128 sliding stability 180 wedge 186 Com624, 275 Compass 110, 111 geological 29, 104, 105, 370 Compressive strength 48

asperities 70 bearing capacity 137 classification 61, 375 fractured rock 64 intact rock 63 point load strength 63 rock anchor bond 306 rock socket 257, 264 shotcrete 359 testing 51 Compressive wave 97 Concrete arch dam 231 bearing surface improvement 227 blasting damage 353 buttress 361 dam abutment reinforcement 218 properties 217 scour protection 199, 233 Conglomerate 69 Consolidation 163 Contracts blasting 364 build-operate-transfer 363 components of contract documents 362 definition of rock and soil 364 design-build 363 Dispute Review Board 367 end product 362, 367 factual data 364 general and special provisions 362 interpretative data 364 lump-sum 363 measurement and payment 363 method specifications 361, 367 partnering 368 prequalification 366 ripping 364 risk 366 rock excavation and reinforcement 364 technical specification 363 types of contract 363 unit price 363 variation in quantities 366 Correction factor borehole jack 121 footing shape 138 settlement 158 Corrosion 7

INDEX

bacterial corrosion 323 cables 287 hydrogen embrittlement 323 in grout 323 monitoring 327 pitting corrosion 321 rock anchors 320 stress corrosion 322 Corrosive environment 323 Creep 80, 83, 87 carbonate 84 components (four) 84 constants 88 ductile rock 5 heave 83 in situ measurement 86 long term 88 mechanisms 84 modulus test 54 rock anchors 332 rock sockets 261 salt 85 sandstone 85 shale 85 shear loading 88 stress dependent 5, 163 weathering 48 Curved shear strength envelope 79 Cut and cover 131 Cyclic loading 50, 89, 317 Dam 1, 2 arch 200, 202, 215, 216 buttress 202 dam-foundation interaction 221 earthquake response 218, 220 see also Pseudo-static analysis factor of safety 210 and sliding 207, 210 failures and deteriorations 4, 201 finite element analysis 221 gravity 202 overturning 213 stress distribution 214, 215 hydrodynamic force 220 ice forces 204, 208 in situ testing 119 loading combinations 204 loads 203

probability analysis 230 reliability 201 reservoir filling 219 seismic upgrading 229 silt forces 204, 208 sliding joint 219 stability against sliding/overturning 203, 220 tailwater 204, 208 thermal expansion 204 water forces 203 wind forces 204, 208 Dam failure floods 202 reservoir filling 202 seepage and uplift 203 seismic events 202 time of failure 203 Dam foundations blasting 227 bored concrete piles 211 buckling strength 210 cleaning and sealing 226 concrete ballast 211 concrete shear keys 211, 217, 218 cuto trench 227 displacement (earthquake) 221, 224 drainage 207, 211, 244 drains, bacterial growth 244 dynamic pore pressure 220 erosion 202, 225 excavation and concreting 211 factor of safety 215 finite element analysis 215, 218 flow net 13 grout 229, 233 internal water forces 204 investigation/design 200 monitoring 230 neoprene sheet 218 open joints 218, 227 permeability 116

Dam foundations (contd.) preparation of rock surfaces 218, 225 rebound 228 recessed foundation 209 rehabilitation 229 rock anchor 210, 212, 228, 231 rock-concrete shear strength 205, 207, 216 rock shear strength 205

427

428

INDEX

seepage 218 seismic forces 204 seismic ground motion 219 shaping 225 sliding failure 204, 207, 208 slush grout 227 solution cavities 228 stabilization 211 water pressure 207, 214, 244 Dam performance statistics 201 Dam rehabilitation anchoring 231 grouting 230 monitoring 230 scour protection 231 Dams Albigna dam 218, 230 Ambiesta dam 220 Auburn dam 223 Cabril arch dam 233 Cambambe dam 215 Cannelles dam 217 Cat Arm dam 226 Chirkey dam 220 Clyde dam 219 Elkhart dam 210 Funcho dam 216 Garrison dam 228 Gezouba project 211 Ghe Zhou gravity dam 88 Gordon dam 51 Hsinfengkiang dam 219 Inguri dam 212 Itaipu dam 211 Karakaya dam 213 Kariba dam 219 Keban dam 228 Konya dam 219 Liu-Jia-Xia dam 211 Long Valley dam 10 Longton arch dam 218 Malpasset dam 5, 203 Mintang project 227 Morris dam 219 Morris Shepard dam 211 Nagawado dam 219 Normandy dam 227 Nukui arch dam 128 Oahe dam 228

Pacoima dam 220 Peace Canyon project 228 Quail Creek 228 Revelstoke gravity dam 200 San Fernando dam 219 Stewart mountain 231 Stewartville dam 230, 234 Teton dam 203, 225 Wimbleball dam 236 Zimapan dam 228 Darcy’s law 112 Debris flow 95 Deere, D.U. 205, 206 Deformation modulus 48, 50, 56, 216 anisotropic rock 58 back analysis 51 borehole jack 121 definition 51 dilatometer 120 fractured rock 57, 58 in situ testing 119 intact rock 51, 57 plate load test 122 radial jacking test 125 rock mass 58, 60 rock socket 256 settlement 160, 162 size eect 56 weak rock 55 Degree of fracturing 97 Delphi panel 18 Dental concrete 226, 358 Deterministic analysis 15, 179 Development length 307 Diamond drilling 93, 106, 109, 117, 361 Dilation angle 217 Dilatometer 86 Diorite 231 Dip 28, 102, 104, 379, 381 Dip direction 28, 102, 104, 379, 381 Direct shear test 74–6, 128 Discontinuity aperture 381 daylight 27, 38, 40, 177, 205, 280 dispersion 40 displaced 73 frequency 106 infilling 71, 205 length (probability distribution) 42

INDEX

mapping 44 number of sets 103, 385 orientation 28, 379 and scour 198 orthogonal 26, 33, 95, 100 persistence 103, 383 roughness 69 sets 33, 196 spacing 46, 58, 103, 105, 383 probability distribution 43 type 378 undisplaced 73–4 Dolomite 82, 212, 261 Dowels 215 Drainage 116, 244, 328, 361 shotcrete 358 Drill core 111, 133 orientation 109 photograph 106 recovery 107 Drilling 106, 334 auger 342 bencher 334 calyx 106, 111, 342 cased holes 342 Christienson-Hugel 110 clay impression core barrel 109 diamond drilling 106, 107, 109, 147, 335 directional drilling 343 down-the-hole (DTH) drill 337, 338 drill string vibration 111 drilling mud 336 feed rate 111 fluid pressure 111 hole alignment 231 integral sample 109 large diameter drilling 342 overburden drilling 340 percussion drilling 111, 147, 235, 334, 337 rotary drill 340 super drill 343 tool thrust 111 tool torque 111 triple tube core barrel 107, 336 Tubex system 341 Dynamic compaction 151 Dywidag threadbar 292, 324 Earthquake 56, 173, 182, 231, 274

building foundation 9 displacement analysis 195, 223 fault displacement 218 force modification factor 9 ground motion variation 219 hydrodynamic force 220 importance factor 10 reservoir filling 219 seismic response factor 9 stability analysis 194 zonal velocity ratio 9 see also Pseudo-static seismic analysis Eccentricity 173 Elastic material 53 Elastic modulus 120 Electrolyte 320 Epoxy 231 Erodibility index 232 Erosion 225, 228 Expansion agents (rock breakage) 356 Explosives 112, 346, 352 Extensometer 230 Factor of safety 15, 66 3-d slope 188 dam foundations 211 bearing capacity 138 design values 16 deterministic 23 planar failure 179 rock sockets 263, 264 toppling failure 191 uplift 313 wedge failure 185 Failure type circular 36, 191 planar 36, 38, 177 sliding 205, 206 toppling 36, 38, 188 wedge 25, 35, 36, 38, 183, 283 Fatigue 89 Fault 94, 95 bridge foundation 1 dam foundation 212, 218, 219 definition 25 geophysics 97 ground water 119 infilling 71, 103 mapping 104

429

430

INDEX

Fibre glass rock anchors 327 Fill loads 9 Finite dierence analysis 163 Finite element analysis borehole jack 121 dam foundation 217, 231 dynamic 221 layered foundation 143 rock socket 254, 265 settlement 160 FLAC 159, 163 Flatjack 122, 126 Flexural strength, shotcrete 359 Flood 231 Flow net 15 Flyrock 319 Flysch 55 Foliation 26, 113 Foundation failures 4, 201 France 5, 203, 290 Friction angle back analysis 76 dam foundation 215 infilling 71 limit equilibrium 40 Mohr-Coulomb material 66 Newmark analysis 223 residual 71 rock type 66 sliding stability 180 stability analysis 192 stress distribution 171 toppling failure 191 wedge 186 Friction cone 40 Geological mapping 99, 104, 374 Geophysics 96, 147 explosive 97 ground penetrating radar 99, 147 resistivity 98 seismic 97 Germany 29, 290 Gneiss 53, 69, 213 Goodman, R.E. 159, 171, 187, 188, 225 Goodman jack tests 53 Grain size 85, 375 Granite 69, 82, 99, 131 Graywacke 216

Great circle 30, 35, 370 Ground water 13, 112 mapping 104, 387 rock socket 251 tension crack 181, 186 toppling 190 Grout 7, 82, 116, 228, 230, 233 blanket grouting 236 bleeding 235 cohesion 237 consolidation grouting 233 curtain grouting 237 drilling method 235 erosion control 234 fluidizers 239 grouting procedures 240 hole patterns 236, 237 leaching 243 mechanism of 235 mixes 237 monitoring 241 overburden pressure 239 permeability control 233 criteria 241 pressure 239 strength 239 types of 234 uplift control 233 viscosity 235 Gypsum 5, 82, 83, 228 Halite 5, 82 Heat shrink tubing 326 Heave 83, 83 Helicopter 287 Hoek back analysis 76 dam foundation 205 foundation failure 143 tensile strength 80, 313 wedge failure 186 Hoek-Brown strength criterion 65, 76, 137, 142 Hong Kong 140 Hydration 82, 83 Hydraulic impact hammer 7, 355 Hydraulic jack 122 Hydraulic splitter 7, 356 Hydrofracture 239

INDEX

Hysteresis 52 Illite 83 Impression packer 111 In situ testing 93, 119, 217 Inclinometer 230 Industrial waste 324 Inelastic rock 163 Infilling 70, 71 classification 382 dam foundation 227 in situ test 128 mapping 103 normally-, over-consolidated 74 permeability 113 scour 197 Instrumentation 230 International Society of Rock Mechanics 100, 374 Italy 220 Japan 29, 95, 128, 136, 195, 219 Joint 26 Joint compressive strength (JCS) 70, 376 Joint roughness coecient (JRC) 70, 102, 105 Kaolinite 82, 83 Karst 94 Karstic formation 4, 144 characteristics 145 dam foundation 228 deep foundations 151 foundation type 148, 149 foundation treatment 151 geophysics 96 ground penetrating radar 99 rock socketed pier 6, 249, 263 sealing 228 Key block theory 187 Kinematic analysis 38 Kulhawy, F.H. 159 Landfill 234 Landslide 94, 95, 219 LATPILE 275 Leaching 243 Lime 243 Limestone 13, 55, 69, 71, 82, 145, 152, 212, 217, 228, 230, 234, 249 Limit equilibrium analysis 179, 207, 210

431

Limit states design 16 Line mapping 104 Line of intersection 35, 40, 183, 372, 381 Linear variable dierential transformer (LVDT) 52, 74, 120 Load dead load 138 highway bridge 10 impact 10 live load 138 railway bridge 10 Load factor 17 Load-deformation behaviour, fractured rock 53 Lognormal distribution 43 Lugeon 241 Mapping 93 Mapping sheets 388, 389 Margin of safety 20 Marl 55, 68 Mexico 228 Mica 59, 68, 82 Modulus of elasticity 120 Mohr diagram 71 Mohr-Coulomb material 66, 180, 253 Monitoring 230 Monte Carlo analysis 21, 40, 183 Montmorillonite 71, 83 Mudstone 83, 258 Multi-position extensometers 122, 125 Negative exponential distribution 43 Neoprene 230 New York 133 Newmark, N.M. 223 Nitrogen 117 Non-explosive excavation 345, 355 Non-shrink grout 298 Normal distribution 20 Olivine 83 Oolite 144 Orthogonal joint sets 26 Osterburg hydraulic cell 264, 272 Overturning moment 173 Oxidation 82, 83 Packer 117, 240, 328 Peck, R.B. 133 Permanent deformation 54

432

INDEX

Permeability 13 anisotropic rock 113 Darcy’s law 112 discontinuity aperture 102 drainage 361 drilling 111 falling head tests 237 infilling 103 mapping 104 measurement 116 piezometers 113 primary permeability 112 pump test 119 secondary permeability 113 shape factor 118 UDEC 215 variable head test 117 Persistence classification 384 mapping 44 Perspex 109 Photograph 110 Phyllite 59 Piezometer 113, 117, 230, 231 electrical transducers 115 multiple standpipe 115 multi-port (MP) 115 pneumatic 114 standpipe 114 time lag 114 Piles 88, 152, 249 Pin piles 153 Pins (rock reinforcement) 360 Plate load test 53, 55, 87, 122 correction factor 124 Plate tectonics 195 Plunge 29, 373 Point load test 63 Poisson’s ratio 52, 53, 97, 120, 160 Pole density 32 Pole plot 31, 370 Polyethylene (HDPE) 326 Polypropylene 327 Polyurethane 234 Porosity 97 Portugal 215, 217 Potentiometer 120 Pre-load 272 Pressure gradient 112

Probabilistic analysis 18, 183 Probability 40, 385 density function 183 detection of sink holes 147 distributions 19, 42 of failure 18, 21, 36, 202, 230 Pseudo-static seismic analysis 194 bridge 182, 192 dam 223 gravity dam 204, 213, 220, 221 Punching failure 143 p-y curves 275 Pyrrotite 82 Radial stress 172 Railway 10 Rayleigh wave 97, 351 Rebound 228 Recessed footing 138, 209 Reconnaissance 93 Reinforcement of rock 7, 356 Release surface 177, 183 Reliability analysis 18 Residual soil 147 Resin anchor 301, 304 Resin grout 235 Resistivity 98 Retaining-wall instability 6 Reynolds number 113 Rigidity factor 155 Rip rap 199, 233 Ripping 355 River hydraulics 95 Rock anchor 1, 182, 361 acceptance criteria 330 allowable working load 290 anchor materials 289 bearing capacity 142 bond length 297 cement admixtures 298 cement grout anchorage 292, 296 cement grout mix 297 centralizers 300 Ciment Fondu 319 corrosion failure 302, 320 mechanism 320 protection 293, 324 types 321 corrosive conditions 323

INDEX

creep 302, 317, 330, 332 cyclic loading 317 dam 210, 228, 231 displacement of the head 308 drilling 335 eect of blasting 318 embedment length 307 failure 7 galvanized 327 group action 316 grout bleed 298 grout pressures 300 guaranteed ultimate tensile strength 290 hole diameter 296 lift-o test 330 load transfer mechanism 303 load-extension measurement 329 mechanical anchor 292, 302 moment/tension loads 314 optimum plunge angle 186 passive 308 performance test 329 permafrost 319 polypropylene sheath 294 pre-stressed 307 proof test 330 resin anchor 300, 320 rock cone 310, 313 seepage 328 shear stress distribution 303 Split Set bolts 290 stagger 4 steel relaxation 290, 317 steel/grout bond 307 strand anchors 293 strength properties 292 Swellex bolts 290 tie-down 174 toppling 191 tube en machette 300 uplift capacity 308 water testing 328 working bond strength 306, 320 yield stress 290 Rock mass 65 Rock mass rating (RMR) 60 Rock mass strength 48 Rock socketed pier 3 belling 273, 274

433

bentonite 258 condition of end of socket 260 condition of side walls 258 creep 261 eect of rock modulus 255 eect of rock strength 257 eect of socket geometry 255 end-bearing capacity 264 factor of safety 263 failure 6 influence factors 265, 269 investigation 249 karstic formation 151, 263 lateral load 274, 280 lateral stability 280 load capacity 251, 254 load transfer 251 pre-load 272 p-y curve 276, 277 recessed socket 267 reduction factor 267 rock layering 261 settlement end bearing 267 socketed 269 settlement mechanism 265 settlement side wall 265 side-wall shear resistance 253, 263, 265 uplift load 272, 273, 274 Rock type 100, 374 Roughness angle 74 classification 381 discontinuity 102 infilling 103 measurement 105 rock socket 253 scour resistance 197 RQD 106, 133, 196, 258, 278, 279, 280, 355 Russia 212, 220, 244 Salt 163 Sandstone 53, 69, 80, 83, 131, 156, 159, 211, 215, 253, 273 Saponite 83 Sarma 225 Schist 55, 59, 68, 159, 211 Schistosity 26 Scour 4, 112, 198 dam foundation 203, 231

434

INDEX

energy dissipation 232 erosive power of water 195, 232 foundation stability 5, 195 grout strength 239 Q-system 232 resistence of rock 196 rock susceptibility 355 sealing grout 234 water action 13 Sculpting (of rock) 7 Sea water 298, 323 Seed 225 Seepage 13, 15, 112, 116 blasting 148 classification 386, 387 dam failure 202

Seepage (contd.) embankment dam 225 grouting 233, 236 leaching 243 mapping 34, 104 permeability criteria 241 weathering 82 Seiche 219 Seismic codes 195 Seismic upgrading 229 Sensitivity analysis 17 Serpentine 83 Settlement 4, 131 allowable 11 arch bridge 1 bridges 12, 50 buildings 50 compressible bed within sti formation 156 compressible layer on rigid base 156 deformation modulus 28 dierential 11, 50 elastic 54 elastic rock 155 geological conditions 133 ground subsidence 164 homogeneous, isotropic rock 155 inclined, variable thickness beds 159 layered formation 155 sliding 154 sti layer overlying compressible formation 158 time dependent 154, 163 transversely isotropic rock 159 Shale 55, 59, 68, 82, 83, 131, 144, 156, 159, 216, 227,

228, 261 Shape factor permeability 118 settlement 156 Shear modulus 58, 97, 120, 121, 161 Shear strength 48, 66, 69, 112, 119 discontinuities 66 fractured rock 75 steel 360 Sheeting joint 6 Shotcrete 82, 228, 358 mix 359 silica fume 359 steel fibre reinforcing 358 wire mesh reinforcing 358 Silicate grout 234 Siltstone 69, 211, 215, 254 Sine wave 111 Singapore 254, 257 Site selection 93 Size eects 56, 64 Slate 69 Sliding stability 133 Solution cavity detection 147 Sowers, G.F. 144, 153 Spacing (of discontinuities), classification 384 Spain 135, 136 Spread footing 2, 62 Stability of foundations 2, 5, 13, 27, 177 Stainless prestressing steels 327 Stereo net 31, 38, 104, 106, 109, 370 data selection 33 Stereographic projection 29 Stiness 58, 120, 161, 216, 218 Stiness ratio 172 Stochastic model (discontinuities) 36 Strain gauges 52 Strength testing in situ 49–50 laboratory 49 Stress distribution 164 distributed loads 167 eccentrically loaded footings 173 elastic isotropic rock 166 layered formations 168 line load 168 transversely isotropic rock 171 Stress field 83 Stress relief 83, 113, 228

INDEX

Strike 28 Structural geology 7, 93, 177, 312, 370 Styrofoam 9, 264 Subsidence 164 Sulphates 298 Sulphide 83 Survey 110 Swelling 82 chemical reaction 83 clay 82 hydration 82 pressures 82 Switzerland 218, 230, 290 Sylvite 82 Talus 95 Tar sand 163 Tensile strength 48, 79–80, 144, 217 fractured rock 313 Tension crack 95 Tension foundation 4 Terrestrial photograph 95 Terzaghi, K. 137 Terzaghi correction 105 Test pit 106 Texture 375 Three-dimensional stability analysis 187 Tiltmeter 230 Time-dependent properties 80 Toppling 188 see also Failure type Transmission tower 11, 272, 309 Trend 29, 372 Triangular distribution 20 Tunnel 125, 249 seepage 389 UDEC 159, 215 United States of America 8, 136, 203, 210, 231 University of California, Berkeley 50 Variable head test 116 Vermicullite 83

Visco-elastic material 87, 163 Viscous flow 85 V-notch weir 244 Wall strength 102 Water jets 227 Water sampling 115 Water table 97, 118 Weathering 4, 48 bearing capacity 135, 163 chemical 376, 379 classification 80, 379 decomposition 82 disintegration 80 geophysics 96 mapping 102 mechanical 376, 379 settlement 156 Wedge rock socket, lateral load 283 see also Failure type Well sounder 114 Williams all-thread bar 292 Williams hollow core bar 302 Window mapping 104 Wire-line 109 Worked examples bearing capacity 142 rock anchor (uplift, moment loading) 315 settlement elastic rock 158 fractured rock 162 socketed piers 269 stability analysis planar failure 182 wedge failure 187 XSTABL 193 XSTABL stability analysis 193 Yield acceleration 224 Young’s modulus 53

435