Rock Mechanics

TITLES OF RELATED INTEREST

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Rock Mechanics For Underground Mining

B. H. G. Brady Division of Geomechanics, CSIRO, Australia

E.IBrown Imperial College of Science and Technology, London

London GEORGE ALLEN & UNWIN Boston Sydney

©B. H. G. Brady & E. T. Brown, 1985 This book is copyright under the Berne Convention. No reproduction without permission. All rights reserved.

George Allen & Unwin (publishers) Ltd, 40 Museum Street, London WCIA lLU, UK

George Allen & Unwin (Publishers) Ltd, Park Lane, Hemel Hempstead, Herts HP2 4TE, UK

Allen & Unwin Inc., Fifty Cross Street, Winchester, Mass. 01890, USA

George Allen & Unwin Australia Pty Ltd, 8 Napier Street, North Sydney, NSW 2060, Australia

First published in 1985

ISBN-13: 978-94-011-6503-7 001: 10.1007/978-94-011-6501-3

e-ISBN-13: 978-94-011-6501-3

British Library Cataloguing in Publication Data

Brady, B.H.G. Rock mechanics for underground mining.

1. Mining engineering 2. Rock mechanics l. Title 624.1'5132 TN275

Library of Congress Cataloging in Publication Data

Brady, B. H. G. (Barry H. G.) Rock mechanics for underground mining.

Bibliography: p. Includes index. 1. Rock mechanics. 2. Mining engineering. I. Brown, E. T. II. Title. TA706.B73 1985 622'.2 84-11160 ISBN-13: 978-94-011-6503-7

Artwork drawn by Oxford Illustrators Ltd Set in 10 on 12 point Times Roman by Mathematical Composition Setters Ltd, Salisbury, Wiltshire and printed in Great Britain by William Clowes Limited, Beccles and London

Preface

Rock mechanics is a field of applied science which has become recognised as a coherent engineering discipline within the last two decades. It consists of a body of knowledge of the mechanical properties of rock, various techniques for the analysis of rock stress under some imposed perturbation, a set of established principles expressing rock mass response to load, and a logical methodology for applying these notions and techniques to real physical prob­lems. Some of the areas where application of rock mechanics concepts have been demonstrated to be of industrial value include surface and subsurface construction, mining and other methods of mineral recovery, geothermal energy recovery and subsurface hazardous waste isolation. In many cases, the pressures of industrial demand for rigour and precision in project or process design have led to rapid evolution of the engineering discipline, and general improvement in its basis in both the geosciences and engineering mechanics. An intellectual commitment in some outstanding research centres to the proper development of rock mechanics has now resulted in a capacity for engineering design in rock not conceivable two decades ago.

Mining engineering is an obvious candidate for application of rock mechanics principles in the design of excavations generated by mineral extrac­tion. A primary concern in mining operations, either on surface or underground, is loosely termed 'ground control', i.e. control of the displace­ment of rock surrounding the various excavations generated by, and required to service, mining activity. The particular concern of this text is with the rock mechanics aspects of underground mining engineering, since it is in under­ground mining that many of the more interesting modes of rock mass behaviour are expressed. Realisation of the maximum economic potential of a mineral deposit frequently involves loading rock beyond the state where intact behaviour can be sustained. Therefore, underground mines frequently represent ideal sites at which to observe the limiting behaviour of the various elements of a rock mass. It should then be clear why the earliest practitioners and researchers in rock mechanics were actively pursuing its mining engineer­ing applications.

Underground mining continues to provide strong motivation for the advancement of rock mechanics. Mining activity is now conducted at depths greater than 4000 m, although not without some difficulty. At shallower depths, single mine excavations greater than 350 m in height, and exceeding 500000 m 3 in volume, are not uncommon. In any engineering terms, these are significant accomplishments, and the natural pressure is to build on them. Such advances are undoubtedly possible. Both the knowledge of the mechanical properties of rock, and the analytical capacity to predict rock mass performance under load, improve as observations are made of in-situ rock behaviour, and as analytical techniques evolve and are verified by practical application.

vii

PREFACE

This text is intended to address many of the rock mechanics issues arising in underground mining engineering, although it is not exclusively a text for mining education. It consists of four general sections, viz. general engineering mechanics relevant to rock mechanics; mechanical properties of rock and rock masses; underground design and design of various types and associated com­ponents of a mine structure; and several topics related to rock mechanics prac­tice. The material presented is an elaboration of a course of lectures originally prepared for undergraduate rock mechanics instruction for mining students at the Royal School of Mines, Imperial College, London. Some subsequent addi­tions to this material, made by one of the authors while at the University of Minnesota, are also included. The authors believe that the material is suitable for presentation to senior undergraduate students in both mining and geological engineering, and for the initial stages of post-graduate instruction in these fields. It should also be of interest to students of other aspects of geomechanics, notably civil engineers involved in subsurface construction, and engineering geologists interested in mining and underground excavation design. Practising mining engineers and rock mechanics engineers involved in mine design may use the book profitably for review purposes, or perhaps to obtain an appreciation of the current state of engineering knowledge in their area of specialisation.

Throughout the text, and particularly in those sections concerned with excavation design and design of a mine structure, reference is made to compu­tational methods for the analysis of stress and displacement in a rock mass. The use of various computation schemes, such as the boundary element, finite element and distinct element methods, is now firmly and properly embedded in rock mechanics practice. The authors have not listed computer codes in this book. They are now available in most program libraries, and are transported more appropriately on magnetic tape than as listings in text.

The preparation of this book was assisted considerably by the authors' colleagues and friends. Part of the contribution of Dr John Bray of Imperial College is evident in the text, and the authors record their gratitude for his many other informal contributions made over a period of several years. Dr John Hudson of Imperial College and Gavin Ferguson of Seltrust Engineering Ltd read the text painstakingly and made many valuable suggestions for improvement. Professor Charles Fairhurst supported preparation activities at the University of Minnesota, for which one of the authors is personally grateful. The authors are also indebted to Moira Knox, Carol Makkyla and Colleen Brady for their work on the typescript, to Rosie and Steve Priest who prepared the index, and to Laurie Wilson for undertaking a range of tedious, but important, chores. The authors are also pleased to be able to record their appreciation of the encouragement and understanding accorded them by the publisher's representatives, Roger Jones, who persuaded them to write the book, and Geoffrey Palmer, who expertly supervised its production. Finally, they also thank the many individuals and organisations who freely gave per­mission to reproduce published material.

viii

B.H.G.B. E.T.B.

Acknowledgements

We would like to thank the following people and organisations for permission to reproduce previously published material:

King Island Scheelite and CSIRO Division of Geomechanics (Frontispiece); Soc. Min. Engrs (1.4 & 5, 13.15, 16 & 17, 14.8 & 9, 15.11, 13, 14,25,26,27 & 30, 16.10, Tables 12.1 & 15.2); G. V. Borquez (1.4); J. C. Folinsbee (1.5); M. H. de Freitas (3.2); Elsevier (3.3, 4.8); Gold Fields of S. Afr. (3.5); Pergamon Press (3.7, 8, 9, 10, 11, 12, 16, 17 & 21,4.11, 12, 13, 19,21 & 43, 11.1, 15.17, 19,20, 17.7); Z. T. Bieniawski (3.30, Tables 3.5 & 6); Instn Min. Metall. (3.31,4.17,8.7 & 8, 11.13 & 23,16.13 & 14,18.5,6,7,8 & 19, A3.5, Tables 3.8 & 9, 11.2); ELE Int. (4.14); Figure 4.20 reprinted from Q. Colo School Mines 54(3) 177-99 (1959) by L. H. Robinson by permission of the Colorado School of Mines; Figure 4.30b-d reproduced from J. Engng Industry 89, 62-73 (1967) by permission of R. McLamore, K. E. Gray and Am. Soc. Mech. Engrs; Australasian Inst. Min. Metall. (4.33 & 35); Thomas Telford (4.34 & 36); R. E. Goodman (4.41,42 & 44); N. G. W. Cook (1O.~4); W. D. Ortlepp (11.25); Chamber of Mines of S. Afr. (11.26); H. O. Hamrin and Soc. Min. Engrs AIME (12.1,2,5,6,7,8,9, 10, 11 & 12); Dravo Corp (12.3); I. A. Goddard (13.15, 16 & 17); Mount Isa Mines (14.8 & 9): M. D. G. Salamon (15.2, 18.13 & 14, Table 18.2); Instn Min. Engrs (15.3 & 7, 16.24); B. N. Whittaker (15.3, 7 & 10); National Coal Board and A. H. Wilson (15.4 & 5, Table 15.1); National Coal Board (15.6, 16.17, 18, 19, 20 & 23); L. J. Thomas (15.8 & 9); Figure 15.23 reproduced from Storage in excavated rock caverns (M. Bergman (ed.» by permission of Pergamon Press; Figure 15.28 is reproduced from Proc. 4th Canadian rock mech. symp. (1968) by permis­sion of the Minister of Supply and ServiCes Canada; Mining Journal and G. A. Ferguson (15.29); University of Toronto Press (16.8); D. S. Berry (16.21); K. Kovari and A. A. Balkema, Rotterdam (18.4); P. Londe and Am. Soc. Civ. Engrs (18.5); Glotzl Gesellschaft fUr Baumesstechnik mbH (18.6); Am. Min. Congr. (18.9); D. H. Laubscher (Tables 11.3, 12.1, 15.2); Mining Journal (Table 11.4); E. G. Thomas and the Australian Mineral Foundation (Tables 14.1 & 2).

ix

Contents

Preface

Acknowledgements

List of tables

1 Rock mechanics and mining engineering 1 .1 General concepts 1.2 Inherent complexities in rock mechanics 1.3 Underground mining 1.4 Functional interactions in mine engineering 1.5 Implementation of a rock mechanics programme

2 Stress and infinitesimal strain 2.1 Problem definition 2.2 Force and stress 2.3 Stress transformation 2.4 Principal stresses and stress invariants 2.5 Differential equations of static equilibrium 2.6 Plane problems and biaxial stress 2.7 Displacement and strain 2.8 Principal strains, strain transformation, volumetric

strain and deviator strain 2.9 Strain compatibility equations 2.10 Stress-strai n relations 2.11 Cylindrical polar co-ordinates 2.12 Geomechanics convention for displacement,

strai n and stress 2.13 Graphical representation of biaxial stress Problems

3 Rock mass structure 3.1 Introduction 3.2 Major types of structural features 3.3 Important geomechanical properties of discontinuities 3.4 Collecting structural data 3.5 Presentation of structural data 3.6 The hemispherical projection 3.7 Rock mass classification Problems

4 Rock strength and deformability 4.1 Introduction

xi

page vii

ix

xvii

1

4 6

11 14

17 17 18 19 23 26 27 29

34 35 35 38

40 42 44

48 48 49 53 59 69 70 77 84

86 86

CONTENTS

4.2 Concepts and definitions page 87 4.3 Behaviour of isotropic rock material in uniaxial

compression 88 4.4 Behaviour of isotropic rock material in multiaxial

compression 100 4.5 Strength criteria for isotropic rock material 105 4.6 Strength of anisotropic rock material in triaxial

compression 113 4.7 Shear behaviour of discontinuities 115 4.8 Behaviour of discontinuous rock masses 126 Problems 131

5 Pre-mining state of stress 135 5.1 Specification of the pre-mining state of stress 135 5.2 Factors influencing the in-situ state of stress 136 5.3 Methods of in-situ stress determination 140 5.4 Presentation of in-situ stress measurement results 146 5.5 Results of in-situ stress measurements 149 Problems 150

6 Methods of stress analysis 153 6.1 Predictive methods for mine design 153 6.2 Principles of classical stress analysis 154 6.3 Closed-form solutions for simple excavation shapes 161 6.4 Computational methods of stress analysis 167 6.5 The boundary element method 168 6.6 The finite element method 173 6.7 The distinct element method 180 6.8 Hybrid computational schemes 183

7 Excavation design in massive elastic rock 184 7.1 General design methodology 184 7.2 Zone of influence of an excavation 186 7.3 Effect of planes of weakness on elastic stress

distribution 189 7.4 Excavation shape and boundary stresses 194 7.5 Delineation of zones of rock failure 199 7.6 Support and reinforcement of massive rock 202 Problems 206

8 Excavation design in stratified rock 209 8.1 Design factors 209 8.2 Rock mass response to mining 210 8.3 Roof bed deformation mechanics 212 8.4 Roof design procedure for plane strain 214 8.5 Roof design for square and rectangular

excavations 219 8.6 Improved design procedures 222

XII

CONTENTS

9 Excavation design in jointed rock page 223 9.1 Design factors 223 9.2 Identification of potential failure modes 224 9.3 Symmetric triangular roof prism 227 9.4 Asymmetric triangular roof prism 231 9.5 Roof stability analysis for a tetrahedral wedge 234 9.6 Pragmatic design in jointed rock 236

10 Energy changes accompanying underground mining 240 10.1 Mechanical relevance of energy changes 240 10.2 Mining consequences of energy changes 244 10.3 Spherical cavity in a hydrostatic stress field 245 10.4 General determination of released energy 251 10.5 Thin tabular excavations 254 10.6 Cut-and-fill stopi ng 258

11 Rock support and reinforcement 260 11.1 Terminology 260 11.2 Support and reinforcement principles 261 11.3 Rock-support interaction analysis 265 11.4 Pre-rei nforcement 270 11.5 Support and reinforcement design 272 11.6 Materials and techniques 279

12 Mining methods and method selection 292 12.1 Mining excavations 292 12.2 Rock mass response to stoping activity 294 12.3 Orebody properties influencing mining method 298 12.4 Underground mining methods 301 12.5 Mining method selection 313

13 Naturally supported mining methods 316 13.1 Components of a supported mine structure 316 13.2 Field observations of pillar performance 318 13.3 Tributary area analysis of pillar support 320 13.4 Design of a stope-and-pillar layout 325 13.5 Bearing capacity of roof and floor rocks 331 13.6 Stope-and-pillar design in irregular orebodies 333 13.7 Global stability of a supported mine structure 342 13.8 Yielding pillars 349 Problems 349

14 Artificially supported mining methods 351 14.1 Techniques of artificial support 351 14.2 Backfill properties and placement 353 14.3 Cut-and-fill stoping 357 14.4 Backfill applications in open stoping 363

xiii

CONTENTS

15 Longwall and caving mining methods page 369 15.1 Classification of longwall and caving mining methods 15.2 Longwall mining in hard rock 15.3 Longwall coal mining 15.4 Sublevel caving 15.5 Block caving Problems

16 Mining-induced surface subsidence 16.1 Types and effects of mining-induced subsidence 16.2 Chimney caving 16.3 Sinkholes in carbonate rocks 16.4 Discontinuous subsidence associated with caving

methods of mining 16.5 Continuous subsidence due to the mining of

tabular orebodies

17 Blasting mechanics 17.1 Blasting processes in underground mining 17.2 Explosives 17.3 Energy transmission in rock 17.4 Elastic models of explosive-rock interaction 17.5 Phenomenology of rock breakage by explosives 17.6 Computational models of blasting 17.7 Transient ground motion 17.8 Perimeter blasting

18 Monitoring rock mass performance 18.1 The purposes and nature of monitoring rock mass

performance 18.2 Monitoring systems 18.3 Examples of monitoring rock mass performance

Appendix 1 Basic constructions using the hemispherical projection

A 1.1 Projection of a line A1.2 Projection of the great circle and pole to a plane A 1.3 Determination of the line of intersection of two planes AlA Determination of the angle between two lines in a plane A1.5 Determination of dip direction and true dip Al.6 Rotation about an inclined axis

Appendix 2 Stresses and displacements induced by point and infinite line loads in an infinite, isotropic, elastic

369 369 372 382 392 402

405 405 407 415

416

423

433 433 433 436 445 446 451 452 454

459

459 461 474

484

484 484 485 486 487 488

continuum 490

A2.1 A point load (the Kelvin equations) 490 A2.2 An infinite line load 491

xiv

CONTENTS

Appendix 3 Calculation sequences for rock-support interaction analysis

A3.1 Scope A3.2 Required support line calculations A3.3 Available support line calculations

Appendix 4 limiting equilibrium analysis of progressive hangingwall caving

A4.1 Derivation of equations A4.2 Calculation sequence

Answers to problems

References

Index

xv

page 491

491 492 496

499 499 503

504

507

520

Tables

3.1 Classification of discontinuity spacing 3.2 Classification of discontinuity persistence 3.3 Classification of discontinuity roughness 3.4 Values of cf>(z) for the normal distribution 3.5 Geomechanics classification of jointed rock masses 3.6 The effects of joint strike and dip in tunnelling 3.7 Determination of rock maS>ll rating 3.8 Modified geomechanics classification scheme 3.9 Assessment of joint condition 3.10 Total possible percentage reductions to ratings for

classification parameters 4.1 Constants in Bieniawski's empirical strength criterion 4.2 Approximate strength criteria for intact rock and jointed

rock masses 11.1 Required support line calculations for sample problem 11.2 Rockbolt parameter design rules for rock masses 11.3 Guide for support of mining excavations based on modified

geomechanics classificatjon 11.4 Comparison of dry- and wet-mix shotcreting processes 12.1 Caving performance of various geomechanical classes of

rock masses 13.1 Exponents determining pillar strength from its volume and

shape 14.1 Size analyses of sandfills prepared from mill tailings 14.2 Typical strength parameters for cemented sandfill 14.3 In-situ properties of composite backfills 15.1 Calculation of distributions of vertical stress at rib sides 15.2 Fragment sizes expected from the block caving of orebodies 18.1 Absolute stress measurements at the panel 10 crown pillar,

NBHC Mine 18.2 Radiated seismic energy and mining-induced energy change

at ERPM

xvii

page 55 56 56 63 79 80 81 82 83

84 110

128 268 275

276 287

315

324 353 354 356 375 401

475

478

Frontispiece Post-pillar mining in a jointed and faulted rock mass at the Dolphin Mine, King Island, Australia (photograph by permis­sion of King Island Scheelite and CSIRO Division of Geomechanics).