Rock Mechanics.pdf - Mining and Blasting

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Figure 13.16 Representation of a partial extraction operation (a) in terms of an equivalent volume, total area extraction (b). DESIGN OF A STOPE-AND-PILLAR LAYOUT single-phase mining operation, the mechanical integrity of the pillar support is assured, and volume extraction ratio is maximised. A graphical, heuristic procedure is used to demonstrate how this objective may be realised. Considering a representative element of a mine structure, shown in Figure 13.16a, the volume Ve of coal extracted from a block of plan dimensions wo + wp, and working height h,is Ve = h[(wo + wp) 2 − w 2 p ] (13.19) To obtain the same extraction volume Ve by complete extraction over the area of the element, i.e. over (wo + wp) 2 , a stope height he, called the equivalent working height, could be mined. This situation is illustrated in Figure 13.16b. The equivalent working height is given by the expression or he(wo + wp) 2 = Ve = h[(wo + wp) 2 − w 2 p ] he = h[1 − (wp/(wo + wp)) 2 ] (13.20) The yield of a naturally supported operation can be measured conveniently in terms of the equivalent working height, he, of an associated, fictitious operation in which extraction is complete over the area of a representative element of the deposit. Thus, any change in stoping geometry which increases the equivalent working height represents an increase in the yield performance of the operation. The effect of varying 387
Figure 13.17 Relation between yield of an orebody (given as equivalent working height, he), room span and real working height (after Salamon, 1967). PILLAR SUPPORTED MINING METHODS the mining geometry may be assessed by considering an arbitrarily thick orebody, selecting particular stope spans and working heights, and calculating pillar dimensions (as discussed in option (ii) in the preceding design exercise) to achieve a required factor of safety for the pillar-supported structure. Salamon carried out this type of exercise, for the field conditions of a mining depth of 152 m, and a required factor of safety of 1.6. The results of this exercise are presented in Figure 13.17, in which equivalent working height is shown as a function of actual working height, for selected stope spans. The observation from the plots is that independent increases in stope span wo and real working height h both lead to increased equivalent working height, and therefore to increased yield from the orebody. The significant engineering inference is that recovery from an orebody may be maximised, while assuring the integrity of the support system, if the following conditions are met simultaneously: (a) the maximum (i.e. complete) thickness of the orebody is mined; (b) the maximum room span consistent with assuring local stability of wall rock is mined. These conclusions may appear self-evident. The reality is that they are a direct result of the nature of the pillar strength formula. A different relation between pillar strength and pillar shape and dimensions could conceivably have led to different geometric requirements for maximising volumetric yield from an orebody. Having shown how maximum mineral potential of an orebody can be achieved in a pillar-supported operation, it is useful to explore the way in which maximum yield varies with geomechanical setting. The volumetric extraction ratio R can be seen, from Figure 13.16b, to be given by the ratio of equivalent working height he and orebody thickness M; i.e. introducing equation 13.20 388 R = he/M = h/M[1 − (wp/(wo + wp)) 2 ] (13.21)
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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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Page 357 and 358: Figure 11.26 Resin grouted rockbolt
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Page 361 and 362: ROCK SUPPORT AND REINFORCEMENT Tabl
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Page 365 and 366: MINING METHODS AND METHOD SELECTION
Page 367 and 368: Figure 12.2 Elements of a supported
Page 375 and 376: Figure 12.6 Schematic layout for bi
Page 377 and 378: Figure 12.8 Layout for shrink stopi
Page 379 and 380: Figure 12.9 Schematic layout for VC
Page 381 and 382: Figure 12.11 Key elements of longwa
Page 383 and 384: Figure 12.13 Mining layout for tran
Page 387 and 388: 13 Figure 13.1 Schematic illustrati
Page 389 and 390: Figure 13.3 Layout of barrier pilla
Page 391 and 392: Figure 13.5 Principal modes of defo
Page 393 and 394: Figure 13.8 Geometry for tributary
Page 395 and 396: PILLAR SUPPORTED MINING METHODS str
Page 397 and 398: Figure 13.10 Distribution of vertic
Page 399 and 400: Figure 13.12 Pillar behaviour domai
Page 401 and 402: PILLAR SUPPORTED MINING METHODS Lun
Page 403: Figure 13.15 Options in the design
Page 407 and 408: Figure 13.19 Model of yield of coun
Page 409 and 410: Figure 13.20 North-south vertical c
Page 411 and 412: Figure 13.23 Stope-and-pillar layou
Page 413 and 414: Figure 13.25 Calibrated stability c
Page 415 and 416: PILLAR SUPPORTED MINING METHODS wor
Page 417 and 418: Figure 13.28 Pillar performance, de
Page 419 and 420: Figure 13.29 (a) Stope and pillar l
Page 421 and 422: Figure 13.31 (a) Plane strain analy
Page 423 and 424: PILLAR SUPPORTED MINING METHODS Pan
Page 425 and 426: 14 Artificially supported mining me
Page 427 and 428: ARTIFICIALLY SUPPORTED MINING METHO
Page 431 and 432: Figure 14.2 Simplified view of stru
Page 435 and 436: Figure 14.5 Confined block model fo
Page 437 and 438: Figure 14.7 Crown and sidewall stre
Page 443 and 444: Figure 14.10 Sublevel open stoping
Page 445 and 446: Figure 14.12 Some applications of c
Page 447 and 448: 15 Longwall and caving mining metho
Page 449 and 450: Figure 15.2 Shear stress drop in th
Page 451 and 452: LONGWALL AND CAVING MINING METHODS
Page 453 and 454: 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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LONGWALL AND CAVING MINING METHODS
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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
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Figure 17.4 Reflection of a cylindr
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BLASTING MECHANICS means that no ci
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Figure 17.8 Layout of blast holes i
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Figure 17.9 Influence of field stat
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Figure 17.11 Generation of surface
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BLASTING MECHANICS The components o
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BLASTING MECHANICS amplitudes of th
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BLASTING MECHANICS 17.9 Evaluation
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Figure 17.15 (a) Schematic cross se
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BLASTING MECHANICS in Figure 17.17,
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MONITORING ROCK MASS PERFORMANCE (a
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MONITORING ROCK MASS PERFORMANCE su
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MONITORING ROCK MASS PERFORMANCE Ta
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Figure 18.2 The Distometer ISETH, a
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Figure 18.5 Self-inductance multipl
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MONITORING ROCK MASS PERFORMANCE is
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Figure 18.9 Biaxial vibrating wire
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MONITORING ROCK MASS PERFORMANCE me
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Figure 18.12 Cross section at 6650N
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Figure 18.13 Examples of convergenc
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Figure 18.15 Longitudinal section l
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Figure 18.16 (Cont.) MONITORING ROC
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Appendix A Basic constructions usin
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Figure A.3 Determining the angle be
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APPENDIX A USE OF HEMISPHERICAL PRO
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APPENDIX B STRESSES AND DISPLACEMEN
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Figure A.6 Axisymmetric tunnel prob
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Figure A.9 Bolt load-extension curv
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APPENDIX D LIMITING EQUILIBRIUM ANA
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ANSWERS TO PROBLEMS 2 (a) 0.087 - 0
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ANSWERS TO PROBLEMS 3 wp = 38.6 m,
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REFERENCES Symp. & 17th Tunn. Assn
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REFERENCES Brady, B. H. G. and Bray
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REFERENCES Collier, P. A. (1993) De
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REFERENCES Drescher, A. and Vardoul
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REFERENCES Gustafsson, P. (1998) Wa
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REFERENCES Hood, M. and Brown, E. T
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REFERENCES Kaiser, P. K. and Tannan
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REFERENCES Lorig, L. J. and Brady,
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REFERENCES Ortlepp, W. D. (1994) Gr
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REFERENCES Rojas, E., Molina, R. an
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REFERENCES Spottiswoode, S. M. and
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REFERENCES Villaescusa, E., Windsor
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Index Page numbers appearing in bol
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INDEX Coulomb (cont.) parameters 96
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INDEX Excavation (cont.) support ra
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INDEX Jaeger’s plane of weakness
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INDEX Panel caving 470-2, 473, 474,
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INDEX Seismic (cont.) moment 306, 3
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INDEX Strength (cont.) residual 86,
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INDEX United States (USA) 395, 396,
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