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Fundamentals of Rock Mechanics Fundamentals of Rock Mechanics Fourth Edition J. C. Jaeger, N. G. W. Cook, and R. W. Zimmerman Blackwell Publishing © 2007 Blackwell Publishing BLACKWELL PUBLISHING 350 Main Street, Malden, MA 02148-5020, USA 9600 Garsington Road, Oxford OX4 2DQ, UK 550 Swanston Street, Carlton, Victoria 3053, Australia The right of J.C. Jaeger, N.G.W. Cook, and R.W. Zimmerman to be identified as the Authors of this Work has been asserted in accordance with the UK Copyright, Designs, and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs, and Patents Act 1988, without the prior permission of the publisher. First edition published 1969 by Methuen Reprint published 1971 by Chapman and Hall Second edition published 1976 by Chapman and Hall Third edition published 1979 Fourth edition published 2007 by Blackwell Publishing Ltd 1 2007 Library of Congress Cataloging-in-Publication Data Jaeger, J.C. ( John Conrad), 1907Fundamentals of rock mechanics – J.C. Jaeger, N.G.W. Cook, and R.W. Zimmerman. – 4th ed. p. cm. Includes bibliographical references and index. ISBN-13: 978-0-632-05759-7 (pbk.: alk. paper) ISBN-10: 0-632-05759-9 (pbk.: alk. paper) 1. Rock mechanics. I. Cook, Neville G.W. II. Zimmerman, Robert W. III. Title. TA706.J32 2007 624.1’513–dc22 2006036480 A catalogue record for this title is available from the British Library. Set in 10.5/12.5pt Dante by Newgen Imaging Systems (P) Ltd, Chennai, India Printed and bound in Singapore by Markono Print Media Pte Ltd The publisher’s policy is to use permanent paper from mills that operate a sustainable forestry policy, and which has been manufactured from pulp processed using acid-free and elementary chlorine-free practices. Furthermore, the publisher ensures that the text paper and cover board used have met acceptable environmental accreditation standards. For further information on Blackwell Publishing, visit our website: www.blackwellpublishing.com Contents Preface to the Fourth Edition 1 Rock as a Material 1.1 Introduction 1.2 Joints and faults 1.3 Rock-forming minerals 1.4 The fabric of rocks 1.5 The mechanical nature of rock ix 1 1 2 4 6 7 2 Analysis of Stress and Strain 2.1 Introduction 2.2 Definition of traction and stress 2.3 Analysis of stress in two dimensions 2.4 Graphical representations of stress in two dimensions 2.5 Stresses in three dimensions 2.6 Stress transformations in three dimensions 2.7 Mohr’s representation of stress in three dimensions 2.8 Stress invariants and stress deviation 2.9 Displacement and strain 2.10 Infinitesimal strain in two dimensions 2.11 Infinitesimal strain in three dimensions 2.12 Determination of principal stresses or strains from measurements 2.13 Compatibility equations 2.14 Stress and strain in polar and cylindrical coordinates 2.15 Finite strain 9 9 10 17 23 27 32 35 38 41 43 49 3 Friction on Rock Surfaces 3.1 Introduction 3.2 Amonton’s law 3.3 Friction on rock surfaces 3.4 Stick–slip oscillations 3.5 Sliding on a plane of weakness 3.6 Effects of time and velocity 65 65 66 67 70 73 76 55 56 57 60 vi contents 4 Deformation and Failure of Rock 4.1 Introduction 4.2 The stress–strain curve 4.3 Effects of confining stress and temperature 4.4 Types of fracture 4.5 Coulomb failure criterion 4.6 Mohr’s hypothesis 4.7 Effects of pore fluids 4.8 Failure under true-triaxial conditions 4.9 The effect of anisotropy on strength 80 80 80 85 87 90 94 97 100 103 5 Linear Elasticity 5.1 Introduction 5.2 Stress–strain relations for an isotropic linear elastic solid 5.3 Special cases 5.4 Hooke’s law