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Page 1: Ground Engineering - Principles and Practices for ...3A978-3-319-25005-2%2F1.pdf · (MCA), that a handbook on ground engineering risk management in under-ground coal mining should

Ground Engineering - Principles andPractices for Underground Coal Mining

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J.M. Galvin

Ground Engineering -Principles and Practicesfor Underground CoalMining

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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.

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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Glossary of Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653

Glossary of Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671

Contents xxiii