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 (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 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 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.

LOAD CAPACITY OF SOCKETED PIERS IN COMPRESSION

281

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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ROCK SOCKETED PIERS

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 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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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

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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.

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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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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

ANCHOR MATERIALS AND ANCHORAGE METHODS

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.

ANCHOR MATERIALS AND ANCHORAGE METHODS

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

ANCHOR MATERIALS AND ANCHORAGE METHODS

337

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

339

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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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