Rock Mechanics

Frontispiece Post-pillar mining in ajointed and faulted rock mass at theDolphin Mine, King Island, Australia(photograph by permission of King Is-land Scheelite and CSIRO Division ofGeomechanics).

RockMechanicsfor underground miningThird edition

B. H. G. BradyEmeritus Professor, The University of Western Australia, and ConsultingEngineer, Montville, Queensland, Australia

E. T. BrownEmeritus Professor, The University of Queensland, and Senior Consultant,Golder Associates Pty Ltd, Brisbane, Australia

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Second edition 1993Third edition 2004

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Published by Springer,

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1985, 1993, 2004, 2006 B.H.G. Brady and E.T. BrownReprinted with corrections 2006

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ISBN-10 1-4020-2064-3 (PB)

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ISBN-10 1-4020-2116-X (e-book)ISBN-13 978-1-4020-2116-9 (e-book)

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Contents

Preface to the third edition xiPreface to the second edition xiiiPreface to the first edition xvAcknowledgements xvii

1 Rock mechanics and mining engineering 1

1.1 General concepts 11.2 Inherent complexities in rock mechanics 41.3 Underground mining 61.4 Functional interactions in mine engineering 91.5 Implementation of a rock mechanics programme 13

2 Stress and infinitesimal strain 17

2.1 Problem definition 172.2 Force and stress 172.3 Stress transformation 192.4 Principal stresses and stress invariants 232.5 Differential equations of static equilibrium 252.6 Plane problems and biaxial stress 262.7 Displacement and strain 292.8 Principal strains 332.9 Strain compatibility equations 342.10 Stress-strain relations 342.11 Cylindrical polar co-ordinates 372.12 Geomechanics convention 392.13 Graphical representation of biaxial stress 41Problems 43

3 Rock mass structure and characterisation 46

3.1 Introduction 463.2 Major types of structural features 473.3 Important geomechanical properties of discontinuities 513.4 Collecting structural data 573.5 Presentation of structural data 693.6 The hemispherical projection 713.7 Rock mass classification 77Problems 82

4 Rock strength and deformability 85

4.1 Introduction 854.2 Concepts and definitions 86

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CONTENTS

4.3 Behaviour of isotropic rock material in uniaxialcompression 87

4.4 Behaviour of isotropic rock material in multiaxialcompression 99

4.5 Strength criteria for isotropic rock material 1054.6 Strength of anisotropic rock material in triaxial compression 1174.7 Shear behaviour of discontinuities 1204.8 Models of discontinuity strength and deformation 1304.9 Behaviour of discontinuous rock masses 133Problems 139

5 Pre-mining state of stress 142

5.1 Specification of the pre-mining state of stress 1425.2 Factors influencing the in situ state of stress 1435.3 Methods of in situ stress determination 1475.4 Presentation of in situ stress measurement results 1565.5 Results of in situ stress measurements 159Problems 161

6 Methods of stress analysis 165

6.1 Analytical methods for mine design 1656.2 Principles of classical stress analysis 1666.3 Closed-form solutions for simple excavation shapes 1736.4 Computational methods of stress analysis 1786.5 The boundary element method 1796.6 The finite element method 1836.7 The distinct element method 1896.8 Finite difference methods for continuous rock 1926.9 Linked computational schemes 195

7 Excavation design in massive elastic rock 197

7.1 General principles of excavation design 1977.2 Zone of influence of an excavation 2017.3 Effect of planes of weakness on elastic stress distribution 2047.4 Excavation shape and boundary stresses 2097.5 Delineation of zones of rock failure 2137.6 Support and reinforcement of massive rock 217Problems 221

8 Excavation design in stratified rock 224

8.1 Design factors 2248.2 Rock mass response to mining 2258.3 Roof bed deformation mechanics 2278.4 Roof design procedure for plane strain 2308.5 Roof beam analysis for large vertical deflection 235

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CONTENTS

9 Excavation design in blocky rock 242

9.1 Design factors 2429.2 Identification of potential block failure modes – Block Theory 2439.3 Symmetric triangular roof prism 2559.4 Roof stability analysis for a tetrahedral block 2619.5 Design practice in blocky rock 2639.6 Stope wall design – the Mathews stability chart method 266

10 Energy, mine stability, mine seismicity and rockbursts 271

10.1 Mechanical relevance of energy changes 27110.2 Mining consequences of energy changes 27510.3 Energy transmission in rock 27710.4 Spherical cavity in a hydrostatic stress field 28510.5 General determination of released and excess energy 28910.6 Mine stability and rockbursts 29310.7 Instability due to pillar crushing 29410.8 Thin tabular excavations 29910.9 Instability due to fault slip 30110.10 Characterisation of seismic events 304

11 Rock support and reinforcement 312

11.1 Terminology 31211.2 Support and reinforcement principles 31311.3 Rock–support interaction analysis 31711.4 Pre-reinforcement 32211.5 Support and reinforcement design 32611.6 Materials and techniques 338

12 Mining methods and method selection 347

12.1 Mining excavations 34712.2 Rock mass response to stoping activity 34912.3 Orebody properties influencing mining method 35212.4 Underground mining methods 35512.5 Mining method selection 368

13 Pillar supported mining methods 370

13.1 Components of a supported mine structure 37013.2 Field observations of pillar performance 37213.3 Elementary analysis of pillar support 37513.4 Design of a stope-and-pillar layout 38413.5 Bearing capacity of roof and floor rocks 39013.6 The Elliot Lake room-and-pillar mines 39113.7 Stope-and-pillar design in irregular orebodies 39613.8 Open stope-and-pillar design at Mount Charlotte 403

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CONTENTS

13.9 Yielding pillars 404Problems 406

14 Artificially supported mining methods 408

14.1 Techniques of artificial support 40814.2 Backfill properties and placement 41014.3 Design of mine backfill 41614.4 Cut-and-fill stoping 41814.5 Backfill applications in open and bench stoping 42314.6 Reinforcement of open stope walls 427

15 Longwall and caving mining methods 430

15.1 Classification of longwall and caving mining methods 43015.2 Longwall mining in hard rock 43015.3 Longwall coal mining 44015.4 Sublevel caving 45315.5 Block caving 465Problems 481

16 Mining-induced surface subsidence 484

16.1 Types and effects of mining-induced subsidence 48416.2 Chimney caving 48616.3 Sinkholes in carbonate rocks 49516.4 Discontinuous subsidence associated with caving

methods of mining 49616.5 Continuous subsidence due to the mining of

tabular orebodies 506

17 Blasting mechanics 518

17.1 Blasting processes in underground mining 51817.2 Explosives 51817.3 Elastic models of explosive–rock interaction 52117.4 Phenomenology of rock breakage by explosives 52217.5 Computational models of blasting 52717.6 Perimeter blasting 52717.7 Transient ground motion 53217.8 Dynamic performance and design of underground excavations 53617.9 Evaluation of explosive and blast performance 538

18 Monitoring rock mass performance 543

18.1 The purposes and nature of monitoring rockmass performance 543

18.2 Monitoring systems 54418.3 Examples of monitoring rock mass performance 558

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CONTENTS

Appendix A Basic constructions using thehemispherical projection 568

A.1 Projection of a line 568A.2 Projection of the great circle and pole to a plane 568A.3 Determination of the line of intersection of two planes 569A.4 Determination of the angle between two lines in a plane 570A.5 Determination of dip direction and true dip 571A.6 Rotation about an inclined axis 572

Appendix B Stresses and displacements induced by point andinfinite line loads in an infinite, isotropic, elastic continuum 574

B.1 A point load (the Kelvin equations) 574B.2 An infinite line load 575

Appendix C Calculation sequences for rock–supportinteraction analysis 575

C.1 Scope 575C.2 Required support line calculations 575C.3 Available support line calculations 577

Appendix D Limiting equilibrium analysis of progressivehangingwall caving 580

D.1 Derivation of equations 580D.2 Calculation sequence 584

Answers to problems 585References 589Index 614

ix

Preface to the third edition

Sometimes it is suggested that mining engineering and its supporting engineeringsciences have reached a state of maturity. However, this proposition is inconsistentwith major developments in the twenty years that have elapsed since the preparation ofthe first edition of this book, and the ten years since it has been subject to any substantialrevision. Over those periods, innovations and improvements in engineering practicein mining and mining rock mechanics, and advances in the engineering science ofrock mechanics, have been extraordinary. For these reasons the third edition, whichresults from comprehensive and thorough revision of the earlier editions, has involvedthe replacement or substantial modification of the equivalent of about half of the textand figures of those versions of the book.

One of the key drivers for many significant developments in fundamental rock me-chanics over the period has been the mining industry’s recognition of the economicreturns of better understanding and more rigorous application of the governing sci-ences embedded in its industrial operations and processes. The result has been somenotable advances in mining engineering practice, involving improvements in miningmethods in particular. For example, caving methods are now more widely appliedas understanding of their scientific basis has improved and their economic and oper-ational advantages have been realised. Whereas sublevel caving was once regardedin some places as a method of marginal interest, the advent of very large scale sub-level caving, made possible in part by improved drilling technology and in part byunderstanding of the governing rock mechanics, it is now an attractive proposition formany orebodies. Similarly, block caving is now conducted efficiently and reliably inorebody settings that would have been inconceivable two decades ago. At the sametime, methods such as overhand cut-and-fill stoping and shrink stoping have declinedin application, replaced in part by open stoping and bench-and-fill stoping, where largescale mechanisation, improved backfill technology, reliable rock mass reinforcementof stope walls and the intrinsic advantages of non-entry methods of working have ledto superior economics and enhanced operational safety.

The scope of developments in mining rock mechanics science and practice has beenas impressive as that in mining engineering. Perhaps the most significant advance hasbeen the resolution of some longstanding issues of rock fracture, failure and strengthand their relation to the modes of deformation and degradation of rock around miningexcavations. The fact that the key research on this topic was conducted at the Under-ground Research Laboratory of Atomic Energy of Canada Limited demonstrates theextent to which mining rock mechanics has benefited from fundamental research inother fields of rock engineering. The mechanics of blocky rock has also been a field ofimpressive development, particularly in regard to formulation of a broad spectrum ofmethods of analysis of block jointed rock and their application in excavation engineer-ing and support and reinforcement design. More generally, improved understandingof the mechanics of discontinuous rock has had a profound effect on simulation ofcaving mechanics and therefore on the design and operation of block caving andsublevel caving mines.

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PREFACE TO THE THIRD EDITION

Mining-induced seismicity and the related phenomenon of rockbursts have becomemore prevalent in hard rock mining. Developments in mineworthy seismic equipmentand associated data recording, processing and analysis hardware and software havecontributed greatly to measurement, characterisation and management of the problem.These developments have been complemented by measures in excavation designand extraction sequencing which have done much to mitigate the serious operatingproblems which can occur in seismically active, rockburst prone mines. In large-scaleopen stope mining, Canadian developments based on pillarless stoping, formulationof extraction sequences which promote the evolution and uniform displacement of aregular mine stress abutment, and the extensive use of cement-stabilised backfill, havebeen successful in managing an acute mining challenge. Notably, these measures havebeen based on sound conceptual and analytical models of the relation of damagingseismicity to induced stress, geological structure, potential rock displacements andstrain energy release during mining.

Some remarkable developments in computational methods have supported theseimprovements in rock mechanics practice. Many mining rock mechanics problemsare effectively four-dimensional, in that it is the evolution of the state of stress over thetime scale of the mining life of the orebody which needs to be interpreted in terms ofthe probable modes of response of the host rock mass. The computational efficiencyof tools for three-dimensional stress analysis now permits modelling of key stages ofan extraction sequence, for example, as a matter of routine rock mechanics practice.Similarly, computer power and efficient algorithms provide a notable capacity tosimulate the displacement and flow of rock in cave mining and to support design ofoptimum caving layouts.

Notwithstanding these developments, it is encouraging to note continued attentionto formal mathematical analysis in solution of rock mechanics problems. The resultsof such analysis provide the canonical solutions for the discipline of rock mechanicsand ensure a sound base for both the science and engineering practice.

In preparing this extensive revision, the authors have been fortunate to have thesupport of many colleagues and several organisations. In particular, they would liketo record the helpful advice and comment of colleagues on possible improvementsin earlier editions of the book and in identifying inevitable errors in the text. Theyacknowledge the generous assistance of the Brisbane office of Golder Associates inproviding facilities and many helpful services, particularly in assistance with draft-ing of the figures for this edition. One of the authors was supported for part of thework of revision by The University of Western Australia, and the other by the JuliusKruttschnitt Mineral Research Centre of The University of Queensland. This support,including the associated library services, is acknowledged with gratitude. The authorsthank the many individuals and organisations who generously gave permission to usepublished material. Finally, they record the encouragement of publisher’s represen-tative, Petra van Steenbergen, and her patient assistance and advice during this majorundertaking.

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

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Preface to the second edition

Since the publication of the first edition, several developments in rock mechanics haveoccurred which justified a comprehensive revision of the text. In the field of solidmechanics, major advances have been observed in understanding the fundamentalmodes of deformation, failure and stability of rock under conditions where rockstress is high in relation to rock strength. From the point of view of excavation designpractice, a capacity for computational analysis of rock stress and displacement ismore widely distributed at mine sites than at the time of preparing the first edition. Inrock engineering practice, the development and demonstration of large-scale groundcontrol techniques has resulted in modification of operating conditions, particularlywith respect to maintenance of large stable working spans in open excavations. Eachof these advances has major consequences for rock mechanics practice in mining andother underground engineering operations.

The advances in solid mechanics and geo-materials science have been dominatedby two developments. First, strain localisation in a frictional, dilatant solid is nowrecognised as a source of excavation and mine instability. Second, variations indisplacement-dependent and velocity-dependent frictional resistance to slip are ac-cepted as controlling mechanisms in stability of sliding of discontinuities. Rockburstsmay involve both strain localisation and joint slip, suggesting mitigation of this per-vasive mining problem can now be based on principles derived from the governingmechanics. The revision has resulted in increased attention to rockburst mechanicsand to mine design and operating measures which exploit the state of contemporaryknowledge.

The development and deployment of computational methods for design in rockis illustrated by the increased consideration in the text of topics such as numericalmethods for support and reinforcement design, and by discussion of several casestudies of numerical simulation of rock response to mining. Other applications ofnumerical methods of stress and displacement analysis for mine layout and designare well established. Nevertheless, simple analytical solutions will continue to beused in preliminary assessment of design problems and to provide a basis for engi-neering judgement of mine rock performance. Several important solutions for zoneof influence of excavations have been revised to provide a wider scope for confidentapplication.

Significant improvements in ground control practice in underground mines arerepresented by the engineered use of backfill in deep-level mining and in applicationof long, grouted steel tendons or cable bolts in open stoping. In both cases, theengineering practices are based on analysis of the interaction between the host rockand the support or reinforcement system. Field demonstration exercises which validatethese ground control methods and the related design procedures provide an assuranceof their technical soundness and practical utility.

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PREFACE TO THE SECOND EDITION

In the course of the revision, the authors have deleted some material they consideredto be less rigorous than desirable in a book of this type. They have also correctedseveral errors brought to their attention by a perceptive and informed readership, forwhich they record their gratitude. Their hope is that the current version will be subjectto the same rigorous and acute attention as the first edition.

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

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Preface to the first edition

Rock mechanics is a field of applied science which has become recognised as acoherent engineering discipline within the last two decades. It consists of a body ofknowledge of the mechanical properties of rock, various techniques for the analysis ofrock stress under some imposed perturbation, a set of established principles express-ing rock mass response to load, and a logical scheme for applying these notions andtechniques to real physical problems. Some of the areas where application of rock me-chanics concepts have been demonstrated to be of industrial value include surface andsubsurface construction, mining and other methods of mineral recovery, geothermalenergy recovery and subsurface hazardous waste isolation. In many cases, The pres-sures of industrial demand for rigour and precision in project or process design haveled to rapid evolution of the engineering discipline, and general improvement in itsbasis in both the geosciences and engineering mechanics. An intellectual commitmentin some outstanding research centres to the proper development of rock mechanicshas now resulted in a capacity for engineering design in rock not conceivable twodecades ago.

Mining engineering in an obvious candidate for application of rock mechanicsprinciples in the design of excavations generated by mineral extraction. A primaryconcern in mining operations, either on surface or underground, is loosely termed‘ground control’, i.e. control of the displacement of rock surrounding the variousexcavations generated by, and required to service, mining activity. The particularconcern of this text is with the rock mechanics aspects of underground mining engi-neering, since it is in underground mining that many of the more interesting modes ofrock mass behaviour are expressed. Realisation of the maximum economic potentialof a mineral deposit frequently involves loading rock beyond the state where intactbehaviour can be sustained. Therefore, underground mines frequently represent idealsites at which to observe the limiting behabiour of the various elements of a rockmass. It should then be clear why the earliest practitioners and researchers in rockmechanics were actively pursuing its mining engineering applications.

Underground mining continues to provide strong motivation for the advancementof rock mechanics. Mining activity is now conducted at depths greater than 4000 m,although not without some difficulty. At shallower depths, single mine excavationsgreater than 350 m in height, and exceeding 500 000 m3 in volume, are not uncommon.In any engineering terms, these are significant accomplishments, and the naturalpressure is to build on them. Such advances are undoubtedly possible. Both theknowledge of the mechanical properties of rock, and the analytical capacity to predictrock mass performance under load, improve as observations are made of in-siturock behaviour, and as analytical techniques evolve and are verified by practicalapplication.

This text is intended to address many of the rock mechanics issues arising in under-ground mining engineering, although it is not exclusively a text on mining applica-tions. It consists of four general sections, viz. general engineering mechanics relevantto rock mechanics; mechanical properties of rock and rock masses; underground

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PREFACE TO THE FIRST EDITION

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 anelaboration of a course of lectures originally prepared for undergraduate rock mechan-ics instruction for mining students at the Royal School of Mines, Imperial College,London. Some subsequent additions to this material, made by one of the authorswhile at the University of Minnesota, are also included. The authors believe that thematerial is suitable for presentation to senior undergraduate students in both miningand geological engineering, and for the initial stages of post-graduate instruction inthese fields. It should also be of interest to students of other aspects of geomechanics,notably civil engineers involved in subsurface construction, and engineering geol-ogists interested in mining and underground excavation design. Practising miningengineers and rock mechanics engineers involved in mine design may use the bookprofitably for review purposes, or perhaps to obtain an appreciation of the currentstate of engineering knowledge in their area of specialisation.

Throughout the text, and particularly in those sections concerned with excavationdesign and design of a mine structure, reference is made to computational methods forthe analysis of stress and displacement in a rock mass. The use of various computationschemes, such as the boundary element, finite element and distinct element methods,is now firmly and properly embedded in rock mechanics practice. The authors havenot listed computer codes in this book. They are now available in most programlibraries, and are transported more appropriately on magnetic storage media than aslistings in text.

The preparation of this book was assisted considerably by the authors’ colleaguesand friends. Part of the contribution of Dr John Bray of Imperial College is evidentin the text, and the authors record their gratitude for his many other informal con-tributions made over a period of several years. Dr John Hudson of Imperial Collegeand Gavin Ferguson of Seltrust Engineering Ltd read the text painstakingly and mademany valuable suggestions for improvement. Professor Charles Fairhurst supportedpreparation activities at the University of Minnesota, for which one of the authorsis personally grateful. The authors are also indebted to Moira Knox, Carol Makkylaand Colleen Brady for their work on the typescript, to Rosie and Steve Priest whoprepared the index, and to Laurie Wilson for undertaking a range of tedious, but im-portant, chores. The authors are also pleased to be able to record their appreciation ofthe encouragement and understanding accorded them by the publisher’s representa-tives, Roger Jones, who persuaded them to write the book, and Geoffrey Palmer, whoexpertly supervised its production. Finally, they also thank the many individuals andorganisations who freely gave permission to reproduce published material.

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

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Acknowledgements

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

Mount Isa Mines Limited (Cover photograph); King Island Scheelite and CSIRO Di-vision of Geomechanics (Frontispiece); Soc. Min. Met. & Expl. (Figures 1.4, 1.5,11.25, 11.27, 12.1, 12.2, 12.3, 12.5, 12.6, 12.7, 12.8, 12.9, 12.11, 12.12, 12.13,13.26, 13.30, 15.20, 15.22, 15.41, Table 11.2); G. V. Borquez (Figure 1.4); J. C.Folinsbee (Figure 1.5); E. Hoek (Figures 3.1, 3.30, 4.51, Table 4.2); M. H. de Freitas(Figure 3.2); Elsevier/ Pergamon (Figures 3.3, 3.7, 3.8, 3.9, 3.10, 3.11, 3.12, 3.16,3.17, 3.21, 3.24.8, 4.11, 4.12, 4.13, 4.10, 4.21, 4.28, 4.46, 4.48, 4.52, 4.53, 6.11, 7.1,8.7, 8.8, 8.9, 8.10, 8.11, 9.13, 9.16, 11.1, 11.8, 11.16, 11.17, 11.19, 15.10, 15.11,15.12, 15.13, 15.14, 15.19, 15.27, 15.28, 15.32, 16.25, 16.26, 17.3); S. Afr. Inst. Min.Metall. (Figures 3.4, 10.27, 13.10, 13.14, 13.17, 13.18, 15.4, 15.6); Goldfields of S.Afr. (Figure 3.5); Julius Kruttschnitt Mineral Research Centre (Figures 3.14, 15.34,15.35, 15.39, 15.40, 15.42); Somincor (Figure 3.20); Rocscience Inc. (Figure 3.29);Z. T. Bieniawski (Tables 3.5, 3.6); Am. Soc. Civ. Engrs (Figure 4.9); ELE Int. (Figure4.14); Inst. Mats, Mins & Min./Instn Min. Metall. (Figures 4.17, 9.20, 12.10, 14.11,15.8, 15.15, 15.29, 16.16, 16.17, 16.19, 16.20, 16.28, 18.12); Figure 4.20 reprintedfrom Q. Colo. School Mines, 54(3): 177-99 (1959), L. H. Robinson, by permission ofthe Colorado School of Mines; Springer Verlag (Figure 4.29); NRC Canada (Figures4.31, 7.17); Figure 4.33 reproduced from J. Engng Industry, 89: 62–73 (1967) bypermission of R. McLamore, K. E. Gray and Am. Soc. Mech. Engrs; Aus. Inst. Min.Metall. (Figures 4.36, 4.38, 11.9, 13.25, 15.25, 15.31, 15.36, 15.37); Thomas Telford(Figures 4.37, 4.39); John Wiley (Figures 4.45, 9.3, 9.5, 9.8, 9.9, 9.10, 9.11, 9.12);Univ. Toronto Press (Figures 4.51, 13.27, 13.28, 18.1b, 18.13, 18.14, 18.16, 18.17);J. R. Enever (Figure 5.8); C. R. Windsor (Figure 5.11); World Stress Map Project(Figure 5.12); Assn Engrg Geologists (Figure 8.6); Canadian Institute of Mining,Metallurgy and Petroleum (Figures 9.21 (from CIM Bulletin, Vol. 82, No. 926),9.22 (from CIM Bulletin, Vol. 88, No. 992), 9.23 (from CIM Bulletin, Vol. 88,No. 992), 9.24 (from CIM Bulletin, Vol. 82, No. 926), 9.25 (from CIM Bulletin,Vol. 93, No. 1036), 13.6 (from CIM Bulletin, Vol. 90, No. 1013), 13.12 (from CIMBulletin, Vol. 90, No. 1013), 13.13 (from CIM Bulletin, Vol. 90, No. 1013), 13.29(from CIM Bulletin, Vol. 89, No. 1000), 16.21); G. E. Blight and Am. Soc. Civ.Engrs (Figure10.5c and d, 14.4); N. G. W. Cook (Figure 10.24); J. R. Rice andBirkhauser Verlag (Figure 10.25); P. Duplancic (Figure 10.26); Birkhauser Verlag(Figures 10.28, 10.29); W. H. Freeman (Figure 10.30); Swets & Zeitlinger/A. A.Balkema (Figures 11.11, 11.28, 13.31, 13.32, 14.10, 14.12, 15.33, 16.3, 16.8, 17.17,18.1a, 18.4, 18.9, 18.10, Tables 3.5, 3.6); Itasca (Figures 11.20, 11.21, 11.22); W. D.Ortlepp (Figure 11.30); J. M. Galvin (Figure 13.11); D. G. F. Hedley (Figures 13.20,13.21, 13.22, 13.23, 13.24); I. A. Goddard (Figure 13.26); Kluwer AcademicPublishers (Figures 14.3. 14.5); V. A. Koskela (Figure 14.10); P. Lappalainen(Figure 14.12); E. G. Thomas and Australian Mineral Foundation (Tables 14.1, 14.2);

xvii

ACKNOWLEDGEMENTS

Safety in Mines Research Advisory Committee (Figure 15.1); J. A. Ryder (Figures15.2, 15.3); M. D. G. Salamon (Figure 15.5); M. Colwell (Figure 15.7); Aspermont(Figure 15.15); L. J. Thomas (Figure 15.17); B. K. Hebblewhite (Figures 15.18,15.19); G. A. Ferguson and Mining Journal (Figure 15.38); A. Karzulovic(Figures 16.11, 16.12, 16.13, 16.14); National Coal Board (Figures 16.22, 16.27); D.S. Berry (Figure 16.23); New South Wales Dept. Mineral Resources (Figure 16.29);C. K. McKenzie and Julius Kruttschnitt Mineral Research Centre (Figures 17.14,17.15, 17.16); C. K. McKenzie (Figure 17.17); K. Kovari (Figure 18.4); P. Londe andAm. Soc. Civ. Engrs. (Figure 18.5); Slope Indicator Co. (Figure 18.6); Geokon Inc.(Figures 18.7, 18.8); H. F. Bock (Figure 18.20); Int. Soc. Rock Mech. (Figure 18.15).

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