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Ground Engineering - Principles andPractices for Underground Coal Mining
J.M. Galvin
Ground Engineering -Principles and Practicesfor Underground CoalMining
J.M. GalvinManly, NSW, Australia
ISBN 978-3-319-25003-8 ISBN 978-3-319-25005-2 (eBook)DOI 10.1007/978-3-319-25005-2
Library of Congress Control Number: 2015958095
Springer Cham Heidelberg New York Dordrecht London# Springer International Publishing Switzerland 2016This work is subject to copyright. All rights are reserved by the Publisher, whether the whole orpart of the material is concerned, specifically the rights of translation, reprinting, reuse ofillustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way,and transmission or information storage and retrieval, electronic adaptation, computer software,or by similar or dissimilar methodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names areexempt from the relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information inthis book are believed to be true and accurate at the date of publication. Neither the publisher northe authors or the editors give a warranty, express or implied, with respect to the materialcontained herein or for any errors or omissions that may have been made.
Cover illustration: Longwall face at Angus Place Colliery, Australia (photograph by PeterCorbett, permission granted by Centennial Coal)
Printed on acid-free paper
Springer International Publishing AG Switzerland is part of Springer Science+Business Media(www.springer.com)
Every effort has been made to contact the copyright holders of the figures and tableswhich have been reproduced from other sources. Anyone who has not been properlycredited is requested to contact the publishers, so that due acknowledgment may bemade in subsequent editions.
Foreword
Underground coal mining in Australia began at Newcastle, New South Wales,
in the early 1800s. For almost a century, mining was by traditional hand
working methods until the first mechanised coal cutter was introduced in
1890. More highly productive mechanised longwall mining was introduced
in 1963 and is now the predominant method of Australian underground coal
production. In common with underground mining in other parts of the world,
during its 200 year history, underground coal mining in Australia has experi-
enced a number of major disasters involving fatalities. However, particularly
in recent decades, the Australian mining industry has a proud record of having
reduced progressively the overall numbers and unit rates of fatalities and
serious injuries arising from underground ground control issues.
Nevertheless, the issue of safety in underground coal mines remains of
concern to the industry itself, to mining regulators, to those working in the
industry in a range of capacities and to the community at large. Despite the
advances that have been made in mine geotechnical engineering over the last
50 years through research and development and through advances in mining
practice, it is widely accepted that the ground engineering and associated risk
management aspects of underground coal mining still require the develop-
ment of deeper basic understandings and the implementation of those
understandings in mining practice. In response to these concerns, the industry
developed the view, largely through its Australian Coal Research Associa-
tion Program (ACARP), supported by the Minerals Council of Australia
(MCA), that a handbook on ground engineering risk management in under-
ground coal mining should be prepared.
The question of who should be commissioned to write such a handbook or
textbook (as it became) gave the industry very little pause for thought. In
terms of his depth and breadth of knowledge, his experience and his standing
in the industry, Emeritus Professor Jim Galvin was the obvious choice.
After completing degrees in Science and Mining Engineering at the
University of Sydney in 1973 and 1975, respectively, Jim Galvin worked
in the South African mining industry where he obtained his PhD in mining
rock mechanics from the University of the Witwatersrand in 1981. He went
on to serve as Head of the Coal Strata Control Section of the South African
Chamber of Mines Research Organisation. In 1982 he returned to Australia
where he gained practical experience in all aspects of underground coal
v
mining from face worker to mine manager. During this time, he served as a
Member of the NSW Mines Rescue Service. Jim was appointed Professor of
Mining Engineering at the University of New South Wales in 1993 and
served as Head of School from 1995 to 2003. He now has an extensive
private consulting practice. Jim was elected a Fellow of the Australian
Academy of Technological Sciences and Engineering in 2009.
Throughout his career, Jim has had a special interest in risk management,
particularly as it applies to workplace health and safety and the environment.
He has served in a range of expert capacities at state, national and international
levels in mine accident investigations, in planning enquiries, in the provision of
expert evidence, in review roles for mining companies and regulators and in
delivering courses and keynote lectures. These roles include serving as Chair
of the Victorian Government’s mining Technical Review Board; an Indepen-
dent Advisor to the Health, Safety and Environment Committee of the Board
of BHP Billiton; Safety Advisor to the Board of Solid Energy, New Zealand; a
Statutory Member of the NSW Planning Assessment Committee; an Interna-
tional Expert Reviewer for the Mine Health and Safety Council of
South Africa; and Chair of the Continuing Professional Development Com-
mittee of the Mine Managers Association of Australia.
During the course of the preparation of this book, I had the opportunity to
review every chapter and to discuss with Jim several of the important questions
that his text addresses. In my opinion, the book provides an outstanding,
detailed and much needed, account of ground engineering principles and
their application in underground coal mining practice in Australia and interna-
tionally. A particular strength of the book is the way in which good under-
ground coal mining practice is identified and discussed within an
understandable and logical applied mechanics framework. It provides a fine
example of what good mining engineering should be. As my fellow reviewer,
Emeritus Professor Horst Wagner, has said, “a particular and unique aspect of
the book is the link between ground engineering and risk management......there
is no comparable text which covers ground engineering principles and under-
ground coal mining practice in such a comprehensive way”.
I congratulate Emeritus Professor Jim Galvin for an outstanding achieve-
ment. I recommend this book unreservedly to all those having responsibility
for identifying and managing ground control-related risk issues in under-
ground coal mines, including mine managers, planners, operators, geotech-
nical engineers (including consultants), mining regulators, academics and
especially mining engineering students. It is my hope that the rational
approaches discussed in this book will replace the largely empirical methods
used for coal mine excavation design in Australia and internationally.
Golder Associates Pty Ltd., Brisbane, Australia Edwin T. Brown AC
University of Queensland, Brisbane, Australia
President of the International Society for
Rock Mechanics, 1983–1987
9 March 2015
vi Foreword
Preface
Ground engineering is a critical component in designing and conducting
mining operations that are safe, efficient and economically viable. Its contri-
bution is characterised by pervasive uncertainty due to an incomplete knowl-
edge of material properties, behaviour mechanisms, loading environments
and the strength of rock structures. Consistent with international standards,
the effect of this uncertainty on achieving objectives constitutes risk. This
means that ground engineering should be practised within a risk management
framework that aims to both prevent unwanted outcomes and mitigate their
consequences to an acceptable level. To be successful, this process requires
knowledge of fundamental scientific and engineering principles relevant to
ground behaviour; knowledge of mining systems, practices and hazards; and
an understanding of risk management principles, supported by experience
and skill.
This text has its origins in a request from the Australian coal mining
industry to develop a ground control risk management handbook from the
perspective of both an academic and a mine operator and, in the process, to
clarify a range of conflicting and confusing advice to the industry regarding
ground control practices. It soon became apparent that in order to achieve this
goal in a manner that was objective and consistent with risk management
processes, there was a need to re-establish the basic principles of rock
behaviour and to apply these to practical mining situations. This task evolved
into one of writing a textbook that aims to provide ground engineering
principles and practices associated with underground coal mining at a tech-
nical level and in a language and format appropriate to ground control
practitioners and to those that engage with these practitioners.
The text is written by a mining engineer with a specialist knowledge in
rock mechanics and risk management and who has had practical experience,
responsibility and accountability for the design and management of large
underground coal mines and for the consequences of loss of ground control.
Hence, its audience is wide ranging and includes geoscience and engineering
undergraduates, postgraduate students in ground engineering programmes,
mine managers, mine site ground control officers and geotechnical engineers,
consultants, equipment suppliers, risk managers and the legal profession.
Where appropriate, readers are directed to sources of more detailed or
specialist knowledge.
vii
Chapter 1 defines ground engineering and provides an overview of the
mine design process and the framework for risk management. After
introducing basic coal mining systems and associated terminology, Chap. 2
presents the fundamental physical and applied mechanics principles that
underpin ground engineering in general and not just in underground coal
mining. These principles are applied and developed further in the next three
chapters by considering how the rock mass responds, firstly, to the formation
of a single excavation (Chap. 3), then to formation of pillar systems as a
consequence of forming multiple excavations (Chap. 4), followed by consid-
eration of interactions between mine workings in the same seam and in
adjacent seams (Chap. 5).
Inevitably, the rock mass needs to be supported and reinforced around the
perimeter of excavations in order to improve its internal load carrying
capacity, to restrict convergence at the mining horizon and to prevent falls
of ground. A review of ground support and reinforcement systems, the
mechanics of their behaviour and the manner in which they modify rock
mass response is presented in Chap. 6. This and the principles developed in
earlier chapters provide the basis for reviewing a number of design
approaches and options for ground support in Chap. 7.
Chapters 8 and 9 are concerned, respectively, with ground control
principles and practices relating specifically to pillar extraction and to
longwall mining. Principles and practices relating to bord and pillar mining
layouts are encompassed in earlier chapters, particularly Chap. 4 which deals
with coal pillar systems.
A range of hazards are common to all forms of underground coal mining
and these are addressed in Chaps. 10 and 11. Chapter 10 is confined specifi-
cally to the effects, impacts and consequences of ground movement, or
subsidence, on the interburden between mine workings and the surface and
on the surface. Chapter 11 presents a wide range of other hazards and
emphasises the need for a cross-disciplinary approach when addressing
some of these.
Throughout these first 11 chapters, reference is made regularly to
elements of risk management. The text concludes by bringing the entire
ground engineering process and its management together in Chap. 12 under
a risk management framework. Ground Control Management Plans
(GCMPs) give effect to the risk management process. The generic structure
of a GCMP is presented and supported with six appendices of associated
information. Extracts from actual GCMPs are presented in both Chap. 12 and
some of the appendices. This includes examples of procedures required to
support a GCMP, such as Trigger Action Response Plans (TARPs) and a
Change Management procedure. The chapter concludes with a review of
aspects of instrumentation and monitoring essential to monitoring for effec-
tiveness and change and to responding in an appropriate and timely manner
to variances from planned performance.
This text deliberately does not suggest the use of specific design
procedures. There are a number of fundamental reasons for taking this
approach. Some of the more important are, firstly, there are few, if any,
design procedures that are entirely accurate or that apply to all
viii Preface
circumstances. Secondly, a range of design approaches to a problem are often
available. Thirdly, ground engineering is an evolving discipline and not only
may better design procedures evolve in time to come, but some that are
considered acceptable today may subsequently be found to be flawed or to
have additional limitations. Fourthly, the reader is encouraged to understand
and to critically evaluate the relevance and reliability of design approaches
for themself, consistent with the philosophy of risk assessment. In some
cases, this may require seeking third-party advice.
In all cases, critical designs should be subjected to peer review as part of
the risk assessment process. Notwithstanding this, aspects of a number of
design procedures have been discussed to help the end-user to better under-
stand the degree of confidence to be placed in them and in identifying the
types of controls and contingencies that may need to be implemented to
manage unplanned outcomes. These aspects all reflect the opening statement
in that ground engineering is characterised by pervasive uncertainty.
It cannot be over emphasised that, first and foremost, the moral and
professional responsibility of those involved in ground engineering is to
safeguard the health and safety of mine personnel and the general public.
The most important measure of sound ground engineering is that everyone
returns home from work safe and well.
Manly, NSW, Australia J.M. Galvin
December 2015
Preface ix
Acknowledgements
The production of this book would not have been possible without substantial
financial assistance from the Australian Coal Association Research Program
(ACARP). This was complemented with support from ACARP staff, notably
Roger Wischusen, Anne Mabardi and Nicole Youngman. The Minerals
Council of Australia (MCA) also provided financial assistance towards
publication costs. The complete work was independently peer reviewed by
Emeritus Professor Ted Brown AC and by Emeritus Professor Horst Wagner,
both of whose advice, encouragement and ongoing interest proved invalu-
able. Select topics were also peer reviewed by the following academic
and professional colleagues: Professor Ismet Canbulat, Dr Winton Gale,
Professor Ian Johnson, Dr Colin Mackie, Mr Bernie McKinnon, Dr Ken
Mills, Dr Paul O’Grady, Emeritus Professor Frank Roxborough AM,
Mr Arthur Waddington, and Dr John Watson. Many other international
colleagues in academia and in the mining industry contributed select advice,
diagrams and photographs. The author expresses his appreciation to these
organisations and individuals.
A wide range of historical material was offered to the author to support the
writing of this text. This was complemented with the author’s archive of
photographs, plans and reports collected over four decades. Every endeavour
has been made to identify the original owner of this information and to obtain
their permission to reproduce it. This was not always possible, however, and
the author apologies for any oversight. A high reliance has been placed on
photographs since a picture is worth a thousand words, especially when
dealing with underground environments. Some pictures depict a good situa-
tion but others do not. Therefore, unless specifically requested to do so, the
source and location of many pictures have not been identified in the text,
albeit permission had been received to republish them.
The following organisations and individuals provided significant informa-
tion and technical assistance: Anglo American, Mr Ian Anderson, Mr James
Barbato, BHP Billiton, BHP Billiton Mitsubishi Alliance, Professor Naj
Aziz, Dr Baotang Shen, Mr Alan Broome, Mr Roger Byrnes, Professor
Ismet Canbulat, Centennial Coal, Coal Services Pty Ltd, Mr Peter Corbett,
Mr Jason Emery, Mr Phil Enright, Dr Essie Esterhuizen, Mr Richard
Everleigh, Dr Winton Gale, Mr Les Gardner, Glencore, Dr Peter Hatherly,
Mr Bruce Jack, Mr Don Kay, Dr Chris Mark, Mr Phil McCarthy,
xi
Mr John McKendry, Mr Bernie McKinnon, Mine Subsidence Engineering
Consultants, Ms Carol Mische, Mr Andrew Myors, Dr Paul O’Grady,
Mr Dan Payne, Dr Philip Pells, SCT Operations Pty Ltd, Mr Jim Sandford,
Mr John Sherrill, Adjunct Professor Tim Sullivan, and Emeritus Professor
Horst Wagner.
The author acknowledges the assistance of Mr Christopher Cassar,
Mr Duncan Chalmers, Mr Carlos Cortez, Mr Roger Davis, Mr Daniel Hart,
Ms Sandee Johnson, Ms Simone Kalin, Ms Joanne Lloyd, Dr Colin Mackie,
and Ms Anna Mills in preparing select figures. Particular thanks are
expressed to Ms Margarita Mitchell for undertaking the bulk of the drafting
in the final manuscript.
Most importantly, this work could not have been completed without the
support, patience and assistance of my wife, Elizabeth. This is greatly
appreciated.
The following sources are thanked for permission to reproduce previously
published material:
Taylor and Francis Group (Figures 1.1, 2.5, 2.17(b)); H. Bock (Figure 1.2);
International Society for Rock Mechanics (Figure 1.2); ACIRL (Figures
1.5, 3.11, 3.18(b), 3.18(c), 3.18(d), 3.19(b), 3.19(c), 3.21, 5.6, 8.16(a),
9.6); South African Council for Scientific and Industrial Research – CSIR
(Figures 2.9, 2.14, 2.15, 2.16, 3.1, 3.9, 3.20, 3.26, 3.30, 3.31, 3.35, 4.20,
4.21, 4.24, 5.16, 6.7(f), 6.21, 6.22, 6.23, 8.8(a), 8.12, 8.32, 10.14(b),
10.17, 11.16, 12.10); B.H.G. Brady and E.T. Brown (Figures 2.12, 2.13,
2.24, 12.9); McGraw Hill (Figure 2.17(a)); B. J. Madden (Figure 2.19,
Table 7.8(c)); C.R. Windsor (Figures 2.24, 6.30; Table 6.3); E. Hoek
(Figures 2.5, 2.17(b), 2.27); Elsevier (Figures 2.51, 3.14, 6.30); Southern
African Institute of Mining and Metallurgy (Figures 3.13, 3.24, 3.30, 3.31,
4.26, 5.3, 6.53(e), 9.10); Mine Subsidence Engineering Consultants
(Figures 3.18(a), 3.19(a), 10.19, 10.24, 10.26); P.J. Hatherly (Figures
3.18(b), 3.18(c), 3.18(d), 3.19(b), 3.19 (c), 12.17); University of New
South Wales (Figures 3.8, 3.33, 3.34, 3.36, 3.37, 4.6(a), 4.7, 4.9, 4.13,
4.30, 4.32, 4.35, 6.10, 6.49, 8.8(b), 8.9, 8.10, 8.15(b), 8.20, 9.32, 10.25,
10.28, 11.3, 11.7, 11.8(a), 12.14; Table 7.8(d)); NSW Government
(Figures 3.34, 3.36, 3.37, 4.6(a), 4.31, 10.3, 10.4, A8.3; Table A11.3);
Z.T. Bieniawski (Figure 4.23); G.S. Esterhuizen (Figures 4.26, 4.37,
8.22); AMIRA International (Figure 4.27); Springer (Figures 4.33, 7.2);
Australasian Institute of Mining and Metallurgy (Figures 5.22(a), 6.3, 6.4,
6.52, 8.11, 8.16(b), 9.33, 10.20); Strata Worldwide (Figures 6.5, 6.10);
P. Schubert (Figures 6.26, 6.27, 6.28); P.J.N. Pells (Figures 6.29, 6.34(b));
SCT Operations Pty Ltd (Figures 6.40(a), 12.11, 12.12, 12.15); University
of Wollongong (Figure 6.40(b)); Illawarra Branch of the Australasian
Institute of Mining and Metallurgy (Figures 6.50, 8.19(c), 10.6); Maney
Publishing (Figure 6.49(c)); R. Campbell (Figures 6.50, 6.51); W.J. Gale
(Table 6.6, Figures 9.4, 9.5, 9.19, 9.20, 9.21, 10.8, 10.9, 10.10, 12.19);
D.J. Hutchinson and M.S. Diederichs (Figure 7.6); Australian
Geomechanics Society (Table 7.7; Figures 10.20, 12.8); Sandvik Mining
(Figure 8.4); Cardno MM&A (Figures 8.13, 8.15(a)); Solid Energy New
xii Acknowledgements
Zealand (Figure 8.17(b)); R. Everleigh (Figures 9.11, 9.12, 9.13, 9.14);
Geological Society of Australia Inc. – Queensland Division (Figure 9.25
(b)); G. Klenowski (Figure 9.25(b)); South African National Institute of
Rock Engineering (Figure 9.25(c)); I.R. Forster (Figures 10.3, 10.4;
Tables A11.2, A11.3); K.W. Mills (Figures 10.6, 10.11, 10.22, 10.31,
10.34, 11.2(a), 11.2(b)); H. Guo (Figure 10.7); B. McKinnon (Figure
10.13(c)); G.J. Cole-Clark (Figure 10.14); Mine Subsidence Technologi-
cal Society (Figures 10.14, 10.22, 10.27, 10.29, 10.37); B.K. Hebblewhite
(Figure 10.18)); J. Barbato (Figures 10.19, 10.24, 10.26, 10.27); D.R. Kay
(Figure 10.29); A.R. Pidgeon (Figure 10.37); G. Taylor (Figure 11.7);
T. Lu (Figure 12.18); Queensland Government (Figures A8.1, A8.2);
R. Byrnes (Table A11.1); NSW Mines Subsidence Board (Table A12.2);
A.A. Waddington (Tables A12.3, A12.4).
Acknowledgements xiii
Contents
1 Scope of Ground Engineering . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 What Is Ground Engineering . . . . . . . . . . . . . . . . . . . . 2
1.2 Peculiarities of Ground Engineering . . . . . . . . . . . . . . . 5
1.3 State of The Art . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.4 Risk Management . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.5 The Impact of Risk Management and Technology . . . . . 8
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Fundamental Principles for Ground Engineering . . . . . . . . . 13
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2 Characteristics of Underground Coal Mining . . . . . . . . . 14
2.2.1 Geological Setting . . . . . . . . . . . . . . . . . . . . . 14
2.2.2 Mine Access . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.3 Mine Roadways . . . . . . . . . . . . . . . . . . . . . . 15
2.2.4 Mining Methods . . . . . . . . . . . . . . . . . . . . . . 17
2.3 Rock Mass Fabric . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.4 Physical Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.5 Material Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.5.1 Load-Displacement . . . . . . . . . . . . . . . . . . . . 21
2.5.2 Stress-Strain . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.5.3 Stiffness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.5.4 Strength . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.5.5 Stored Energy and Seismicity . . . . . . . . . . . . 25
2.5.6 Poisson’s Effect . . . . . . . . . . . . . . . . . . . . . . 26
2.5.7 Cohesion and Friction on a Fracture
Surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.5.8 Post-peak Strength Behaviour . . . . . . . . . . . . 28
2.6 Rock Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.6.1 Specifying Stresses within Rock . . . . . . . . . . 28
2.6.2 Strength of Rock . . . . . . . . . . . . . . . . . . . . . . 31
2.6.3 Equivalent Modulus of Strata . . . . . . . . . . . . . 36
2.6.4 Failure Criteria . . . . . . . . . . . . . . . . . . . . . . . 36
2.6.5 Effective Stress . . . . . . . . . . . . . . . . . . . . . . . 40
2.6.6 Primitive, Induced, Resultant
and Field Stress . . . . . . . . . . . . . . . . . . . . . . 41
2.6.7 Field Stress in Coal . . . . . . . . . . . . . . . . . . . . 43
xv
2.6.8 Field Shear Strength . . . . . . . . . . . . . . . . . . . 44
2.6.9 Reduction in Confinement . . . . . . . . . . . . . . . 45
2.6.10 Rock Mass Classification Systems . . . . . . . . . 46
2.6.11 Failure Mode . . . . . . . . . . . . . . . . . . . . . . . . 51
2.6.12 Ground Response Curve . . . . . . . . . . . . . . . . 52
2.7 Analysis Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 53
2.7.1 Empirical Methods . . . . . . . . . . . . . . . . . . . . 54
2.7.2 Analytical Methods . . . . . . . . . . . . . . . . . . . . 55
2.7.3 Numerical Methods . . . . . . . . . . . . . . . . . . . . 55
2.7.4 Safety Factor . . . . . . . . . . . . . . . . . . . . . . . . 58
2.7.5 Statistical and Probabilistic Analysis . . . . . . . 59
2.8 Statics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 64
2.8.2 Basic Definitions and Principles . . . . . . . . . . . 64
2.8.3 Transversely Loaded Beams . . . . . . . . . . . . . 67
2.8.4 Axially Loaded Columns . . . . . . . . . . . . . . . . 69
2.8.5 Eccentrically Loaded Columns . . . . . . . . . . . 72
2.8.6 Beam-Columns Subjected to Simultaneous
Axial and Transverse Loading . . . . . . . . . . . . 74
2.8.7 Thin Plate Subjected to Axial
and Transverse Load . . . . . . . . . . . . . . . . . . . 74
2.8.8 Linear Arch Theory . . . . . . . . . . . . . . . . . . . . 75
2.8.9 Classical Beam Theory Applications
in Ground Engineering . . . . . . . . . . . . . . . . . 76
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
3 Excavation Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.2 Excavation Response . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.3 Caving Mechanics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
3.3.1 Basic Principles . . . . . . . . . . . . . . . . . . . . . . 85
3.3.2 Strong Massive Strata . . . . . . . . . . . . . . . . . . 100
3.3.3 Span Design . . . . . . . . . . . . . . . . . . . . . . . . . 106
3.4 Elevated Horizontal Stress . . . . . . . . . . . . . . . . . . . . . . 109
3.5 Shallow Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.5.1 Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
3.5.2 Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
4 Pillar Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
4.2 Functional, Risk Based Approach to Pillar Design . . . . . 123
4.3 Pillar Working Stress . . . . . . . . . . . . . . . . . . . . . . . . . . 125
4.3.1 Pillar System Stiffness . . . . . . . . . . . . . . . . . . 125
4.3.2 Regular Bord and Pillar Layouts . . . . . . . . . . 127
4.3.3 Irregular Bord and Pillar Layouts . . . . . . . . . . 130
4.4 Pillar System Strength . . . . . . . . . . . . . . . . . . . . . . . . . 132
4.4.1 Defining Pillar Strength and Failure . . . . . . . . 132
4.4.2 Geological Factors . . . . . . . . . . . . . . . . . . . . 133
xvi Contents
4.4.3 Geometric Factors . . . . . . . . . . . . . . . . . . . . . 136
4.4.4 Scale Factors . . . . . . . . . . . . . . . . . . . . . . . . 140
4.4.5 Determining Pillar Strength . . . . . . . . . . . . . . 140
4.5 Quantifying Design Risk . . . . . . . . . . . . . . . . . . . . . . . 150
4.5.1 Probabilistic Stability Prediction . . . . . . . . . . 150
4.5.2 Probabilistic Design . . . . . . . . . . . . . . . . . . . 153
4.5.3 Summary Points . . . . . . . . . . . . . . . . . . . . . . 154
4.6 Pillar Failure Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 154
4.6.1 Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154
4.6.2 Conventional Failure Mode . . . . . . . . . . . . . . 154
4.6.3 Dynamic Confined Core Failure . . . . . . . . . . . 156
4.7 The Complexity of Pillar Behaviour . . . . . . . . . . . . . . . 158
4.8 Pillar Design Considerations . . . . . . . . . . . . . . . . . . . . 162
4.8.1 Empirical Data Regime . . . . . . . . . . . . . . . . . 162
4.8.2 Stiff Superincumbent Strata . . . . . . . . . . . . . . 164
4.8.3 Foundation Behaviour . . . . . . . . . . . . . . . . . . 164
4.8.4 Seam Specific Strength . . . . . . . . . . . . . . . . . 170
4.8.5 Ground Response Curve . . . . . . . . . . . . . . . . 170
4.8.6 Correlations Between Safety Factor
and Performance Probability . . . . . . . . . . . . . 171
4.8.7 UNSW Pillar Design Methodology . . . . . . . . 172
4.8.8 Diamond Shaped Pillars . . . . . . . . . . . . . . . . 174
4.8.9 Irregular Pillar Shapes . . . . . . . . . . . . . . . . . . 174
4.8.10 Highwall Mining . . . . . . . . . . . . . . . . . . . . . . 175
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
5 Interaction Between Workings . . . . . . . . . . . . . . . . . . . . . . . 181
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
5.2 Workings in the Same Seam . . . . . . . . . . . . . . . . . . . . . 182
5.2.1 Framework . . . . . . . . . . . . . . . . . . . . . . . . . . 182
5.2.2 Pillar Systems . . . . . . . . . . . . . . . . . . . . . . . . 183
5.2.3 Roadways . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
5.2.4 Panels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
5.2.5 Interaction Between Roadways
and Excavations . . . . . . . . . . . . . . . . . . . . . . 193
5.3 Multiseam Workings . . . . . . . . . . . . . . . . . . . . . . . . . . 196
5.3.1 Framework . . . . . . . . . . . . . . . . . . . . . . . . . . 196
5.3.2 Pillar Systems . . . . . . . . . . . . . . . . . . . . . . . . 196
5.3.3 Extraction Panels . . . . . . . . . . . . . . . . . . . . . 199
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
6 Support and Reinforcement Systems . . . . . . . . . . . . . . . . . . . 211
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
6.2 Primary Characteristics . . . . . . . . . . . . . . . . . . . . . . . . 212
6.3 Standing Support . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
6.3.1 Props . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
6.3.2 Timber Chocks . . . . . . . . . . . . . . . . . . . . . . . 216
6.3.3 Cementitious Chocks . . . . . . . . . . . . . . . . . . . 221
6.3.4 Steel Arches and Sets . . . . . . . . . . . . . . . . . . 222
6.3.5 Pillars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
Contents xvii
6.4 Tendon Support and Reinforcement . . . . . . . . . . . . . . . 223
6.4.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
6.4.2 Functions of Tendons . . . . . . . . . . . . . . . . . . 227
6.4.3 Anchorage of Tendons . . . . . . . . . . . . . . . . . 239
6.4.4 Practical Considerations . . . . . . . . . . . . . . . . 253
6.5 Surface Restraint Systems . . . . . . . . . . . . . . . . . . . . . . 258
6.5.1 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
6.5.2 Cross Supports . . . . . . . . . . . . . . . . . . . . . . . 258
6.5.3 Screens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261
6.5.4 Membranes and Liners . . . . . . . . . . . . . . . . . 263
6.6 Spiling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263
6.7 Strata Binders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264
6.8 Void Fillers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 265
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
7 Ground Support Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
7.2 Roof Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272
7.2.1 Failure Modes . . . . . . . . . . . . . . . . . . . . . . . 272
7.2.2 Generic Design Approaches . . . . . . . . . . . . . . 273
7.3 Theoretical Roof Support Design Aspects . . . . . . . . . . . 282
7.3.1 Classical Beam Theory . . . . . . . . . . . . . . . . . 282
7.3.2 Contribution of Long Central Tendons . . . . . . 284
7.3.3 UCS – E Correlations . . . . . . . . . . . . . . . . . . 287
7.3.4 Rock Mass Classification Systems . . . . . . . . . 287
7.3.5 Reinforcement Density Indices . . . . . . . . . . . 288
7.3.6 Numerical Modelling . . . . . . . . . . . . . . . . . . 289
7.4 Summary Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . 289
7.5 Operational Roof Support Design Aspects . . . . . . . . . . . 290
7.5.1 Roadway Span . . . . . . . . . . . . . . . . . . . . . . . 290
7.5.2 Timing of Installation . . . . . . . . . . . . . . . . . . 292
7.5.3 Role and Timing of Centre Tendons . . . . . . . . 292
7.5.4 Effectiveness of Pretension . . . . . . . . . . . . . . 294
7.5.5 Stress Relief . . . . . . . . . . . . . . . . . . . . . . . . . 294
7.5.6 Coal Roof . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
7.5.7 Floor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 295
7.5.8 Monitoring at Height . . . . . . . . . . . . . . . . . . . 296
7.5.9 Mining Through Cross Measures . . . . . . . . . . 296
7.6 Rib Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296
7.6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 296
7.6.2 Risk Profile . . . . . . . . . . . . . . . . . . . . . . . . . . 297
7.6.3 Rib Composition . . . . . . . . . . . . . . . . . . . . . . 297
7.6.4 Rib Behaviour . . . . . . . . . . . . . . . . . . . . . . . 298
7.6.5 Design Considerations . . . . . . . . . . . . . . . . . . 303
7.6.6 Support Hardware Considerations . . . . . . . . . 304
7.6.7 Operational Considerations . . . . . . . . . . . . . . 305
7.6.8 Summary Conclusions . . . . . . . . . . . . . . . . . . 306
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
xviii Contents
8 Pillar Extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
8.2 Attributes of Pillar Extraction . . . . . . . . . . . . . . . . . . . . 310
8.3 Basic Pillar Extraction Techniques . . . . . . . . . . . . . . . . 313
8.3.1 Design and Support Terminology . . . . . . . . . . 313
8.3.2 Total Extraction Methods . . . . . . . . . . . . . . . 316
8.3.3 Partial Extraction Methods . . . . . . . . . . . . . . 328
8.4 Ground Control Considerations . . . . . . . . . . . . . . . . . . 333
8.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 333
8.4.2 Regional Stability . . . . . . . . . . . . . . . . . . . . . 333
8.4.3 Panel Stability . . . . . . . . . . . . . . . . . . . . . . . 343
8.4.4 Workplace Stability . . . . . . . . . . . . . . . . . . . 352
8.5 Operating Discipline . . . . . . . . . . . . . . . . . . . . . . . . . . 356
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356
9 Longwall Mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
9.2 Panel Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 360
9.2.1 Basic Longwall Mining Methods . . . . . . . . . . 360
9.2.2 Gateroad Direction and Layout . . . . . . . . . . . 362
9.2.3 Chain Pillar Life Cycle . . . . . . . . . . . . . . . . . 363
9.2.4 Chain Pillar Design . . . . . . . . . . . . . . . . . . . . 364
9.2.5 Chain Pillar/Gateroad Behaviour . . . . . . . . . . 367
9.3 Longwall Powered Supports . . . . . . . . . . . . . . . . . . . . . 374
9.3.1 Development . . . . . . . . . . . . . . . . . . . . . . . . 374
9.3.2 Basic Functions . . . . . . . . . . . . . . . . . . . . . . 378
9.3.3 Static and Kinematic Characteristics . . . . . . . 379
9.4 Operational Variables . . . . . . . . . . . . . . . . . . . . . . . . . 386
9.4.1 Cutting Technique and Support
Configuration . . . . . . . . . . . . . . . . . . . . . . . . 386
9.4.2 Powered Support System Maintenance . . . . . . 387
9.4.3 Face Operating Practices . . . . . . . . . . . . . . . . 388
9.5 Longwall Face Strata Control . . . . . . . . . . . . . . . . . . . . 390
9.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 390
9.5.2 Coal Face . . . . . . . . . . . . . . . . . . . . . . . . . . . 390
9.5.3 Floor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391
9.5.4 Immediate and Upper Roof Strata . . . . . . . . . 392
9.6 Installation Roadways . . . . . . . . . . . . . . . . . . . . . . . . . 398
9.7 Pre-driven Roadways Within a Longwall Block . . . . . . 403
9.7.1 Generic Types and Mining Practices . . . . . . . 404
9.7.2 Pre-driven Longwall Recovery Roadways . . . 405
9.8 Longwall Face Recovery . . . . . . . . . . . . . . . . . . . . . . . 412
9.9 Other Longwall Variants . . . . . . . . . . . . . . . . . . . . . . . 414
9.9.1 Longwall Top Coal Caving . . . . . . . . . . . . . . 414
9.9.2 Miniwall . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
Contents xix
10 Overburden Subsidence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421
10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 422
10.2 Generic Behaviours . . . . . . . . . . . . . . . . . . . . . . . . . . . 422
10.3 Sub-surface Subsidence . . . . . . . . . . . . . . . . . . . . . . . . 423
10.3.1 Fundamentals . . . . . . . . . . . . . . . . . . . . . . . . 423
10.3.2 Subsurface Effects . . . . . . . . . . . . . . . . . . . . 427
10.3.3 Impacts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
10.4 Surface Subsidence . . . . . . . . . . . . . . . . . . . . . . . . . . . 441
10.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 441
10.4.2 Sinkhole and Plug Subsidence . . . . . . . . . . . . 441
10.4.3 Classical Subsidence Behaviour . . . . . . . . . . . 442
10.4.4 Site-Centric Subsidence . . . . . . . . . . . . . . . . . 447
10.4.5 Prediction of Classical Surface Subsidence . . . 453
10.4.6 Prediction of Site-Centric Subsidence . . . . . . . 462
10.4.7 Surface Subsidence Impacts . . . . . . . . . . . . . . 464
10.4.8 Mitigation and Remediation . . . . . . . . . . . . . . 468
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 472
11 Operational Hazards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477
11.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
11.2 Windblast . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
11.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 478
11.2.2 Behaviour Features . . . . . . . . . . . . . . . . . . . . 478
11.2.3 Risk Management of Windblasts . . . . . . . . . . 481
11.3 Feather Edging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
11.4 Top Coaling and Bottom Coaling . . . . . . . . . . . . . . . . . 484
11.5 Dipping Workings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
11.6 Inrush . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
11.6.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
11.6.2 Critical Factors and Considerations . . . . . . . . 487
11.7 Flooded Workings . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489
11.8 Bumps and Pressure Bursts . . . . . . . . . . . . . . . . . . . . . 490
11.8.1 Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . 490
11.8.2 Pressure Burst Failure Mechanisms . . . . . . . . 492
11.8.3 Seismic Events Associated with Rock
Failure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
11.8.4 Seismic Events Associated with
Discontinuities . . . . . . . . . . . . . . . . . . . . . . . 496
11.8.5 Risk Management of Pressure Bursts . . . . . . . 496
11.9 Gas Outbursts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 500
11.9.1 Definition . . . . . . . . . . . . . . . . . . . . . . . . . . . 500
11.9.2 Behaviour Features . . . . . . . . . . . . . . . . . . . . 501
11.9.3 Risk Management of Outbursts . . . . . . . . . . . 501
11.10 Mining Through Faults and Dykes . . . . . . . . . . . . . . . . 503
11.11 Frictional Ignition Involving Rock . . . . . . . . . . . . . . . . 508
11.12 Backfilling of Bord and Pillar Workings . . . . . . . . . . . . 509
11.13 Roof Falls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512
11.13.1 Effect on Pillar Strength . . . . . . . . . . . . . . . . 512
11.13.2 Roof Fall Recovery . . . . . . . . . . . . . . . . . . . . 513
xx Contents
11.14 Experimental Panels . . . . . . . . . . . . . . . . . . . . . . . . . . 515
11.15 Alternative Rock Bolt Applications . . . . . . . . . . . . . . . 519
11.16 Convergence Zones and Paleochannels . . . . . . . . . . . . . 519
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 520
12 Managing Risk in Ground Engineering . . . . . . . . . . . . . . . . . 525
12.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 526
12.2 Ground Control Management Plan . . . . . . . . . . . . . . . . 527
12.2.1 Basis for a Ground Control
Management Plan . . . . . . . . . . . . . . . . . . . . . 527
12.2.2 Structure of a Ground Control
Management Plan . . . . . . . . . . . . . . . . . . . . . 528
12.2.3 Competencies . . . . . . . . . . . . . . . . . . . . . . . . 528
12.3 Risk Analysis Foundations . . . . . . . . . . . . . . . . . . . . . . 532
12.4 Types of Risk Assessment . . . . . . . . . . . . . . . . . . . . . . 533
12.5 Risk Assessment Process . . . . . . . . . . . . . . . . . . . . . . . 535
12.5.1 Context . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535
12.5.2 Team Composition . . . . . . . . . . . . . . . . . . . . 536
12.5.3 Controls . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537
12.5.4 Other Process Considerations . . . . . . . . . . . . . 537
12.6 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538
12.6.1 Hazard Plans . . . . . . . . . . . . . . . . . . . . . . . . 538
12.6.2 Trigger Action Response Plans . . . . . . . . . . . 538
12.6.3 Review . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539
12.6.4 Change Management . . . . . . . . . . . . . . . . . . . 540
12.6.5 Other Implementation Considerations . . . . . . . 541
12.6.6 Determining Acceptable Levels of Risk . . . . . 541
12.6.7 Reviewing a Risk Assessment . . . . . . . . . . . . 542
12.7 Monitoring . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543
12.7.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543
12.7.2 Monitoring Strategy . . . . . . . . . . . . . . . . . . . 544
12.7.3 Sensory Monitoring . . . . . . . . . . . . . . . . . . . . 545
12.7.4 Monitoring with Instrumentation . . . . . . . . . . 546
12.7.5 Displacement Monitoring Instrumentation . . . 547
12.7.6 Stress Monitoring Instrumentation . . . . . . . . . 552
12.7.7 Other Instrumentation . . . . . . . . . . . . . . . . . . 557
12.7.8 Field Monitoring Practices . . . . . . . . . . . . . . . 560
12.8 Concluding Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 562
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 563
Appendix 1: Brief History of Key Developments in Ground
Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 567
Appendix 2: Equivalent Moduli for a Stratified Rock Mass . . . . . 573
Appendix 3: Basic Statics Formulations for a Clamped
and a Simply Supported Beam Subjected to Transverse Load . . . 575
Appendix 4: Foundation Behaviour . . . . . . . . . . . . . . . . . . . . . . . 579
Contents xxi
Appendix 5: Formulae for Calculating Load on a Pillar
Based on Abutment Angle Concept for the Most
General Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593
Appendix 6: Timber Prop Performance Parameters . . . . . . . . . . 595
Appendix 7: Standard Work Procedure for Setting
a Timber Prop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 597
Appendix 8: Derivation of Geometric Relationship
for Deflection of a Chord . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 601
Appendix 9: Three Major Incidents in Australia Related
to the Design of Pillar Extraction Panels . . . . . . . . . . . . . . . . . . . 603
Appendix 10: Advantages, Disadvantages and Operational
Aspects Relating to Mobile Roof Supports . . . . . . . . . . . . . . . . . . 611
Appendix 11: A Selection of Design Requirements
and Guidelines Relating to Controlling Surface and Aquifer
Water Inflow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613
Appendix 12: A Selection of Classification Schemes Relating
to Subsidence Impacts on Structures . . . . . . . . . . . . . . . . . . . . . . 617
Appendix 13: Examples of Risk Management Based Statutory
Requirements Relevant to Developing Ground Control
Management Plans . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625
Appendix 14: Sources of Information Relevant to Managing
Risk in Ground Engineering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629
Appendix 15: Guidelines for Developing a Mine Safety
Management System and a Principal Hazard Management
Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633
Appendix 16: An Example of a Trigger Action Response
Plan (Ground Management on a Longwall Face) . . . . . . . . . . . . . 639
Appendix 17: An Example of a Change Management Policy
Pertaining to Ground Engineering . . . . . . . . . . . . . . . . . . . . . . . . 641
Appendix 18: An Example of a Ground Control Monitoring
Plan Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 645
xxii Contents
Glossary of Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653
Glossary of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671
Contents xxiii