Rock Mechanics.pdf - Mining and Blasting

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ROOF BEAM ANALYSIS FOR LARGE VERTICAL DEFLECTION and from equation 8.29, dxx dzn =−2Er zn z 2 on 1 + 3 16 s2 z (8.34) Introducing equation 8.34 in equation 8.33, and satisfying the inequality condition of equation 8.32, dMR dzn The inequality is satisfied if = 1 2 nt2 Er zn 2 1 − 3 zon < 0 (8.35) 3 1 + zon > zn > zon √3 16 s2 z (8.36) Hence, the maximum resisting moment, corresponding to the minimum height of a stable arch and the maximum vertical deflection of the arch, is given by and from equation 8.16, zn = min zn = zon √3 max n = zon − min zn = zon − zon √3 = 0.42zon (8.37) (8.38) From equation 8.27, this value of n corresponds to an outer fibre elastic strain given by 2 3 εxx = r 3 1 + 16s2 (8.39) z In some numerical studies using UDEC, Sofianos considered deflection and moment arm in the arch at the condition of bucking. The comparison shown graphically in Figure 8.11 indicates a very good correspondence between the deflection and arch height at buckling calculated using equations 8.37 and 8.38 and from the numerical analysis, for a wide range of normalised beam spans. For stability against buckling, the maximum resisting moment must be greater than the deflecting moment, or from equations 8.19 and 8.13, MR = 1 2 xxnt 2 min zn ≥ 1 8 qs2 = MA = MR (8.40) FSb where q is the distributed load on the beam. Substituting in equation 8.40 the expressions for xx and min zn (equations 8.29 and 8.37) yields the following expression governing elastic stability and buckling of the voussoir arch, for known values of n and r: 3 √ 3 1 + 16 3Qnsn s2 z = 8rn 1 F Sb ≤ 1 (8.41) 239
Figure 8.11 Normalised deflection and arch lever arm versus normalised span, from numerical simulation for E = 16 GPa and = 30 kN/m 3 (after Sofianos, 1996). EXCAVATION DESIGN IN STRATIFIED ROCK Using r = 1/2.6n from equation 8.25, FoSb = 0.59/ 3 Qnsz 1 + 16s2 z ≈ 3.15/Qns 3 z = 3.15zonqns 4 z (8.42) This shows that the factor of safety against buckling instability is inversely proportional to the fourth power of the roof span. Further, for a given room span, the minimum roof bed thickness corresponding to a factor of safety of unity is given by tmin = s 1/3 Qn 3.15 zon (8.43) Comparison of UDEC numerical studies of the beam thickness at buckling with results calculated from equation 8.43 (Sofianos, 1996) shows good correspondence between the two different approaches. 8.5.6 Beam failure by crushing at hinges The maximum values of compressive stress in the arch occur at the hinge points at the top centre of the span and at the lower edges of the contacts of the beam with the abutments. Although Sofianos (1996) proposes an analysis in terms of allowable strains, the most direct method of assessing the possibility of local crushing of the hinges is to compare the local compressive stress with a measure of rock strength. To do this, equation 8.31 may be used to estimate a value of the arch deflection z, which provides directly a value of and, from equation 8.16, a value for the equilibrium moment arm of the arch, z. The required value xx may then be evaluted directly from equation 8.14. As noted previously, care must be taken in selecting a suitable value for the rock mass compressive strength c to be used in assessing the potential for failure by local crushing. The Factor of Safety against crushing at the beam hinge points, FoScrush,is given by 240 FoScrush = c xx (8.44)
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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
Page 205 and 206: Figure 6.8 A simple finite element
Page 207 and 208: Figure 6.9 A schematic representati
Page 209 and 210: METHODS OF STRESS ANALYSIS block ce
Page 211 and 212: METHODS OF STRESS ANALYSIS where ˚
Page 213 and 214: METHODS OF STRESS ANALYSIS The prin
Page 215 and 216: EXCAVATION DESIGN IN MASSIVE ELASTI
Page 217 and 218: Figure 7.2 A logical framework for
Page 219 and 220: Figure 7.3 (a) Axisymmetric stress
Page 221 and 222: Figure 7.6 A plane of weakness, ori
Page 223 and 224: Figure 7.8 A flat-lying plane of we
Page 225 and 226: Figure 7.10 Shear stress/normal str
Page 227 and 228: Figure 7.12 Ovaloidal opening in a
Page 229 and 230: Figure 7.15 States of stress at sel
Page 231 and 232: Figure 7.16 Prediction of the exten
Page 233 and 234: Figure 7.18 Contour plots of princi
Page 235 and 236: Figure 7.19 Problem geometry for de
Page 241 and 242: 8 Excavation Figure 8.1 An excavati
Page 243 and 244: EXCAVATION DESIGN IN STRATIFIED ROC
Page 245 and 246: Figure 8.4 Experimental apparatus f
Page 247 and 248: Figure 8.7 Free body diagrams and n
Page 249 and 250: Figure 8.8 Assumed distributions of
Page 251 and 252: Figure 8.9 Flow chart for the deter
Page 253 and 254: Figure 8.10 Normalised arch thickne
Page 255: EXCAVATION DESIGN IN STRATIFIED ROC
Page 259 and 260: 9 Excavation Figure 9.1 Generation
Page 261 and 262: Figure 9.3 (a) A finite, non-tapere
Page 263 and 264: (a) (b) Figure 9.4 (a) Vertical cro
Page 265 and 266: (a) (b) (c) EP EP Reference circle
Page 267 and 268: Figure 9.10 JP 100 is the only JP w
Page 269 and 270: Figure 9.12 Traces of the views of
Page 271 and 272: EXCAVATION DESIGN IN BLOCKY ROCK In
Page 273 and 274: Figure 9.14 Free-body diagrams of a
Page 275 and 276: EXCAVATION DESIGN IN BLOCKY ROCK di
Page 277 and 278: Figure 9.16 Symmetrical wedge in th
Page 279 and 280: Figure 9.17 (a) Geometry for determ
Page 281 and 282: Figure 9.18 Problem geometry demons
Page 283 and 284: Figure 9.20 Cut-and-fill stope mine
Page 285 and 286: Figure 9.22 Chart to determine fact
Page 287 and 288: EXCAVATION DESIGN IN BLOCKY ROCK Th
Page 289 and 290: Figure 10.1 (a) Pre-mining state of
Page 291 and 292: Figure 10.3 (a) Dynamic loading of
Page 293 and 294: Figure 10.5 (a) Pre-mining and (b)
Page 295 and 296: Figure 10.6 Problem definition and
Page 297 and 298: ENERGY, MINE STABILITY, MINE SEISMI
Page 299 and 300: 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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ENERGY, MINE STABILITY, MINE SEISMI
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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
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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
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
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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
Page 635 and 636:
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,
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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