Rock Mechanics.pdf - Mining and Blasting

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AN INFINITE LINE LOAD B.2 An infinite line load For a line load, of intensity px per unit length, applied at the xy co-ordinate origin, in the x direction, and tensile normal stresses reckoned positive, etc. px x xx =− 4(1 − ) r 2 2 2x (1 − 2) + r 2 px x yy =− 4(1 − ) r 2 −(1 − 2) + 2y2 r 2 px y xy =− 4(1 − ) r 2 2 2x (1 − 2) + r 2 2 px x ux = − (3 − 4) ℓn r 8G(1 − ) r 2 px xy u y = 8 G(1 − ) R2 where r 2 = x 2 + y 2 . Appendix C Calculation sequences for rock–support interaction analysis C.1 Scope The stepwise calculation sequences presented in this appendix permit rock–support interaction analyses to be carried out for the axisymmetric problem defined in Figure A.6. Further details of these analyses are given by Daemen (1975), Hoek and Brown (1980), and Brown et al. (1983). C.2 Required support line calculations Solution using the elastic-brittle rock mass behaviour model of Figure 11.5 Input data c = uniaxial compressive strength of intact rock pieces; m, s = material constants for the original rock mass; E, = Young’s modulus and Poisson’s ratio of the original rock mass; mr, sr = material constants for the broken rock mass; f = gradient of −ε p 3 vs. εp 1 line (Figure 11.5); p = hydrostatic field stress; ri = internal tunnel radius. 575
Figure A.6 Axisymmetric tunnel problem showing the development of a plastic zone around the tunnel. APPENDIX C ROCK–SUPPORT INTERACTION ANALYSIS Calculation sequence (1) M = 1 2 (2) G = m 4 2 E 2(1 + ) + mp c 1/2 + s − m 8 (3) For pi p − Mc, deformation around the tunnel is elastic, i ri = (p − pi) 2G (4) For pi < p − Mc, plastic deformation occurs around the tunnel ue re = Mc 2G (5) p − Mc N = 2 + mr c sr m2 1/2 r (6) re pi = exp N − 2 + ri mr c sr m2 1/2 r (7) 576 i ri = Mc G( f + 1) ( f − 1) + 2 re ri f +1
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Rock Mechanics
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Rock Mechanics for underground mini
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Contents Preface to the third editi
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CONTENTS 9 Excavation design in blo
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CONTENTS ix Appendix A Basic constr
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PREFACE TO THE THIRD EDITION Mining
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PREFACE TO THE SECOND EDITION In th
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PREFACE TO THE FIRST EDITION design
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ACKNOWLEDGEMENTS Safety in Mines Re
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Figure 1.1 (a) Pre-mining condition
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ROCK MECHANICS AND MINING ENGINEERI
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Figure 1.4 Principal features of a
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10 Figure 1.5 Definition of activit
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Figure 1.7 Components and logic of
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Figure 2.1 (a) A finite body subjec
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Figure 2.2 Free-body diagram for es
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STRESS AND INFINITESIMAL STRAIN As
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STRESS AND INFINITESIMAL STRAIN In
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Figure 2.3 Free-body diagram for de
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Figure 2.5 Problem geometry for det
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Figure 2.7 Rigid-body rotation of a
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STRESS AND INFINITESIMAL STRAIN the
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STRESS AND INFINITESIMAL STRAIN str
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⎡ ⎢ ⎣ xx yy zz xy yz zx STRES
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Figure 2.11 Cylindrical polar coord
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STRESS AND INFINITESIMAL STRAIN fre
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Figure 2.13 Construction of a Mohr
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STRESS AND INFINITESIMAL STRAIN fun
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3 Rock Figure 3.1 Sidewall failure
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Figure 3.2 Jointing in a folded str
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Figure 3.5 Diagrammatic longitudina
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Figure 3.7 Discontinuity spacing hi
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Figure 3.9 Illustration of persiste
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Figure 3.11 Typical roughness profi
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ROCK MASS STRUCTURE AND CHARACTERIS
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Figure 3.17 Sample number vs. preci
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Figure 3.19 Diagrammatic illustrati
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Figure 3.20 Computerised depiction
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Figure 3.23 Stereographic projectio
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Figure 3.26 Polar stereographic net
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Figure 3.28 Contours of pole concen
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Figure 3.30 Geological Strength Ind
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Figure 4.1 Idealised illustration o
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ROCK STRENGTH AND DEFORMABILITY wit
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Figure 4.4 Influence of end restrai
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ROCK STRENGTH AND DEFORMABILITY whe
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Figure 4.8 Principle of closed-loop
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Figure 4.12 Two classes of stress-
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Figure 4.14 Point load test apparat
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Figure 4.15 Biaxial compression tes
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Figure 4.18 Results of triaxial com
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ROCK STRENGTH AND DEFORMABILITY was
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Figure 4.23 Coulomb strength envelo
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Figure 4.25 Extension of a preexist
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Figure 4.29 The three basic modes o
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Figure 4.30 Normalised peak strengt
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ROCK STRENGTH AND DEFORMABILITY Tab
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Figure 4.32 The normality condition
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Figure 4.33 Variation of peak princ
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Figure 4.35 Direct shear test confi
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Figure 4.37 Shear stress-shear disp
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Figure 4.40 Peak and residual effec
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Figure 4.43 Effect of shearing dire
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Figure 4.45 Relations between norma
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Figure 4.47 Coulomb friction, linea
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ROCK STRENGTH AND DEFORMABILITY whe
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Figure 4.49 Composite peak strength
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Figure 4.50 Hoek-Brown peak strengt
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Figure 4.52 Determination of the Yo
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ROCK STRENGTH AND DEFORMABILITY 4 A
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5 Pre-mining Figure 5.1 Method of s
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Figure 5.2 The effect of irregular
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PRE-MINING STATE OF STRESS surround
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PRE-MINING STATE OF STRESS induced
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Figure 5.5 (a) Definition of hole l
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Figure 5.6 (a) Core drilling a slot
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Figure 5.7 Principles of stress mea
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PRE-MINING STATE OF STRESS strength
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PRE-MINING STATE OF STRESS A second
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PRE-MINING STATE OF STRESS by the e
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PRE-MINING STATE OF STRESS extend i
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PRE-MINING STATE OF STRESS (d) Dete
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METHODS OF STRESS ANALYSIS quantita
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METHODS OF STRESS ANALYSIS It is in
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Figure 6.2 A thick-walled cylinder
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METHODS OF STRESS ANALYSIS For the
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Figure 6.3 Problem geometry, coordi
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Figure 6.4 Problem geometry, coordi
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METHODS OF STRESS ANALYSIS When the
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Figure 6.5 Superposition scheme dem
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METHODS OF STRESS ANALYSIS The disc
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Figure 6.7 Development of a finite
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METHODS OF STRESS ANALYSIS Solution
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Figure 6.8 A simple finite element
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Figure 6.9 A schematic representati
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METHODS OF STRESS ANALYSIS block ce
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METHODS OF STRESS ANALYSIS where ˚
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METHODS OF STRESS ANALYSIS The prin
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EXCAVATION DESIGN IN MASSIVE ELASTI
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Figure 7.2 A logical framework for
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Figure 7.3 (a) Axisymmetric stress
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Figure 7.6 A plane of weakness, ori
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Figure 7.8 A flat-lying plane of we
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Figure 7.10 Shear stress/normal str
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Figure 7.12 Ovaloidal opening in a
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Figure 7.15 States of stress at sel
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Figure 7.16 Prediction of the exten
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Figure 7.18 Contour plots of princi
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Figure 7.19 Problem geometry for de
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8 Excavation Figure 8.1 An excavati
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EXCAVATION DESIGN IN STRATIFIED ROC
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Figure 8.4 Experimental apparatus f
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Figure 8.7 Free body diagrams and n
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Figure 8.8 Assumed distributions of
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Figure 8.9 Flow chart for the deter
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Figure 8.10 Normalised arch thickne
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EXCAVATION DESIGN IN STRATIFIED ROC
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Figure 8.11 Normalised deflection a
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9 Excavation Figure 9.1 Generation
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Figure 9.3 (a) A finite, non-tapere
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(a) (b) Figure 9.4 (a) Vertical cro
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(a) (b) (c) EP EP Reference circle
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Figure 9.10 JP 100 is the only JP w
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Figure 9.12 Traces of the views of
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EXCAVATION DESIGN IN BLOCKY ROCK In
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Figure 9.14 Free-body diagrams of a
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EXCAVATION DESIGN IN BLOCKY ROCK di
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Figure 9.16 Symmetrical wedge in th
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Figure 9.17 (a) Geometry for determ
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Figure 9.18 Problem geometry demons
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Figure 9.20 Cut-and-fill stope mine
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Figure 9.22 Chart to determine fact
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EXCAVATION DESIGN IN BLOCKY ROCK Th
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Figure 10.1 (a) Pre-mining state of
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Figure 10.3 (a) Dynamic loading of
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Figure 10.5 (a) Pre-mining and (b)
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Figure 10.6 Problem definition and
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ENERGY, MINE STABILITY, MINE SEISMI
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Figure 10.9 Force and stress compon
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Figure 10.12 Distribution of radial
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Figure 10.15 Problem geometry for d
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Figure 10.17 (a) Schematic represen
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Figure 10.20 Elastic/post-peak stif
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Figure 10.24 Relation between frequ
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Figure 10.28 Six possible ways that
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Figure 10.29 First motions for P an
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11Rock support and reinforcement 11
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Figure 11.1 (a) Hypothetical exampl
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Figure 11.4 Non-linear support reac
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Figure 11.5 Idealised elastic-britt
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Figure 11.6 Calculated required sup
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ROCK SUPPORT AND REINFORCEMENT The
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Figure 11.9 Ground reaction curves
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Figure 11.12 Use of grouted reinfor
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ROCK SUPPORT AND REINFORCEMENT If,
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Figure 11.16 Local reinforcement ac
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Figure 11.18 Typical working sketch
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Figure 11.19 Permanent support and
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Figure 11.22 Basis of natural coord
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Figure 11.24 Distributions of (a) s
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Figure 11.26 Resin grouted rockbolt
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Figure 11.28 Alternative methods of
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ROCK SUPPORT AND REINFORCEMENT Tabl
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Figure 11.31 Toussaint-Heintzmann y
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MINING METHODS AND METHOD SELECTION
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Figure 12.2 Elements of a supported
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Figure 12.6 Schematic layout for bi
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Figure 12.8 Layout for shrink stopi
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Figure 12.9 Schematic layout for VC
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Figure 12.11 Key elements of longwa
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Figure 12.13 Mining layout for tran
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13 Figure 13.1 Schematic illustrati
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Figure 13.3 Layout of barrier pilla
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Figure 13.5 Principal modes of defo
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Figure 13.8 Geometry for tributary
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PILLAR SUPPORTED MINING METHODS str
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Figure 13.10 Distribution of vertic
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Figure 13.12 Pillar behaviour domai
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PILLAR SUPPORTED MINING METHODS Lun
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Figure 13.15 Options in the design
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Figure 13.17 Relation between yield
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Figure 13.19 Model of yield of coun
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Figure 13.20 North-south vertical c
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Figure 13.23 Stope-and-pillar layou
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Figure 13.25 Calibrated stability c
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PILLAR SUPPORTED MINING METHODS wor
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Figure 13.28 Pillar performance, de
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Figure 13.29 (a) Stope and pillar l
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Figure 13.31 (a) Plane strain analy
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PILLAR SUPPORTED MINING METHODS Pan
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14 Artificially supported mining me
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ARTIFICIALLY SUPPORTED MINING METHO
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Figure 14.2 Simplified view of stru
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Figure 14.5 Confined block model fo
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Figure 14.7 Crown and sidewall stre
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Figure 14.10 Sublevel open stoping
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Figure 14.12 Some applications of c
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15 Longwall and caving mining metho
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Figure 15.2 Shear stress drop in th
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LONGWALL AND CAVING MINING METHODS
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Figure 15.6 Hydraulic prop reaction
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Figure 15.7 Development and extract
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Figure 15.8 Vertical stress redistr
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Figure 15.11 Distribution of observ
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Figure 15.13 Plan view of microseis
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Figure 15.16 Ground-support interac
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Figure 15.18 Roadway support and re
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Figure 15.25 Comparison of isolated
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Figure 15.26 Geometry of a sublevel
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Figure 15.28 Theoretical determinat
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Figure 15.31 Deterioration of a cro
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Figure 15.32 Distinct element simul
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Figure 15.34 Extended Mathews stabi
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Figure 15.36 Comparison of postand
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Figure 15.39 Idealised plan illustr
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Figure 15.41 Idealised vertical sec
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Figure 15.42 Vertical slice through
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16 Figure 16.1 Trough subsidence ov
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MINING-INDUCED SURFACE SUBSIDENCE c
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Figure 16.4 North-south section, At
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Figure 16.6 (a) Rectangular block g
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MINING-INDUCED SURFACE SUBSIDENCE f
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Figure 16.8 Relation between stope
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MINING-INDUCED SURFACE SUBSIDENCE M
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MINING-INDUCED SURFACE SUBSIDENCE
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Figure 16.14 Chart developed to est
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Figure 16.16 Progressive hangingwal
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Figure 16.19 Idealised model used i
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Figure 16.21 Longitudinal section,
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MINING-INDUCED SURFACE SUBSIDENCE t
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MINING-INDUCED SURFACE SUBSIDENCE w
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MINING-INDUCED SURFACE SUBSIDENCE F
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Figure 16.25 Subsidence troughs pre
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Figure 16.28 Predicted and measured
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17 Blasting mechanics 17.1 Blasting
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Figure 17.1 An empirical matching o
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Figure 17.2 A finite difference mod
Page 541 and 542: Figure 17.4 Reflection of a cylindr
Page 543 and 544: BLASTING MECHANICS means that no ci
Page 545 and 546: Figure 17.8 Layout of blast holes i
Page 547 and 548: Figure 17.9 Influence of field stat
Page 549 and 550: Figure 17.11 Generation of surface
Page 551 and 552: BLASTING MECHANICS The components o
Page 553 and 554: BLASTING MECHANICS amplitudes of th
Page 555 and 556: BLASTING MECHANICS 17.9 Evaluation
Page 557 and 558: Figure 17.15 (a) Schematic cross se
Page 559 and 560: BLASTING MECHANICS in Figure 17.17,
Page 561 and 562: MONITORING ROCK MASS PERFORMANCE (a
Page 563 and 564: MONITORING ROCK MASS PERFORMANCE su
Page 565 and 566: MONITORING ROCK MASS PERFORMANCE Ta
Page 567 and 568: Figure 18.2 The Distometer ISETH, a
Page 569 and 570: Figure 18.5 Self-inductance multipl
Page 571 and 572: MONITORING ROCK MASS PERFORMANCE is
Page 573 and 574: Figure 18.9 Biaxial vibrating wire
Page 575 and 576: MONITORING ROCK MASS PERFORMANCE me
Page 577 and 578: Figure 18.12 Cross section at 6650N
Page 579 and 580: Figure 18.13 Examples of convergenc
Page 581 and 582: Figure 18.15 Longitudinal section l
Page 583 and 584: Figure 18.16 (Cont.) MONITORING ROC
Page 585 and 586: Appendix A Basic constructions usin
Page 587 and 588: Figure A.3 Determining the angle be
Page 589 and 590: APPENDIX A USE OF HEMISPHERICAL PRO
Page 591: APPENDIX B STRESSES AND DISPLACEMEN
Page 595 and 596: Figure A.9 Bolt load-extension curv
Page 597 and 598: APPENDIX D LIMITING EQUILIBRIUM ANA
Page 603 and 604: ANSWERS TO PROBLEMS 2 (a) 0.087 - 0
Page 605 and 606: ANSWERS TO PROBLEMS 3 wp = 38.6 m,
Page 607 and 608: REFERENCES Symp. & 17th Tunn. Assn
Page 609 and 610: REFERENCES Brady, B. H. G. and Bray
Page 611 and 612: REFERENCES Collier, P. A. (1993) De
Page 613 and 614: REFERENCES Drescher, A. and Vardoul
Page 615 and 616: REFERENCES Gustafsson, P. (1998) Wa
Page 617 and 618: REFERENCES Hood, M. and Brown, E. T
Page 619 and 620: REFERENCES Kaiser, P. K. and Tannan
Page 621 and 622: REFERENCES Lorig, L. J. and Brady,
Page 623 and 624: REFERENCES Ortlepp, W. D. (1994) Gr
Page 625 and 626: REFERENCES Rojas, E., Molina, R. an
Page 627 and 628: REFERENCES Spottiswoode, S. M. and
Page 629 and 630: REFERENCES Villaescusa, E., Windsor
Page 631 and 632: Index Page numbers appearing in bol
Page 633 and 634: INDEX Coulomb (cont.) parameters 96
Page 635 and 636: INDEX Excavation (cont.) support ra
Page 637 and 638: INDEX Jaeger’s plane of weakness
Page 639 and 640: INDEX Panel caving 470-2, 473, 474,
Page 641 and 642: INDEX Seismic (cont.) moment 306, 3
Page 643 and 644:
INDEX Strength (cont.) residual 86,
Page 645:
INDEX United States (USA) 395, 396,
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