Rock Mechanics.pdf - Mining and Blasting

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Figure 11.13 Rockbolt design to support the weight of a roof beam in laminated rock. SUPPORT AND REINFORCEMENT DESIGN local support and reinforcement to support individual blocks or loosened zones on an excavation boundary; general or systematic reinforcement in which the objective is to mobilise and conserve the inherent strength of the rock mass; and support and reinforcement system designed to resist the dynamic loading associated with rock burst conditions. Static design analyses for the first two applications will be discussed here. The more complex case of dynamic or rockburst loading will be considered in section 15.2.3. 11.5.2 Local support and reinforcement Two types of design analysis will be presented here. The first type involves simple static limiting equilibrium analyses which essentially treat the system components as rigid bodies and use simplified models of system mechanics. The second type are more rigorous and comprehensive analyses which take into account the deformation and slip or yield of the support and reinforcing system elements and the rock mass. Design to suspend a roof beam in laminated rock. As illustrated in Figure 11.13 rockbolts may be used to suspend a potentially unstable roof beam in laminated rock. The anchorage must be located outside the potentially unstable zone. If it is assumed that the weight of the rock in the unstable zone is supported entirely by the force developed in the rockbolts then or T = Ds 2 s = T D 1 2 (11.8) where T = working load per rock bolt, = unit weight of the rock, D = height of the unstable zone, and s = rockbolt spacing in both the longitudinal and transverse directions. 327
ROCK SUPPORT AND REINFORCEMENT If, for example, T = 10 tonne = 100 kN, = 25 kN m−3 and D = 4 m, equation 11.8 gives s = 1.0 m. In this application, care must be taken to ensure that the bolt anchors have an adequate factor of safety against failure under the working load, T . This design method is conservative in that it does not allow for the shear or flexural strength of the strata above the abutments. Lang and Bischoff (1982) extended this elementary analysis to incorporate the shear strength developed by the rock mass on the vertical boundaries of the rock unit reinforced by a single rockbolt. The rock is assumed to be destressed to a depth, D, as in Figure 11.13, but variable vertical stresses, v, and horizontal stresses, k v, are assumed to be induced within the de-stressed zone. Typically, k may be taken as 0.5. The shear strength developed at any point on the perimeter of the reinforced rock unit is given by c + kv, where c is the cohesion and = tan is the coefficient of friction for the rock mass. Lang and Bischoff’s analysis leads to the result T = AR k 1 − c R 1 − exp(−kD/R) 1 − exp(−kL/R) (11.9) where T = rockbolt tension, A = area of roof carrying one bolt (= s 2 for a s × s bolt spacing), R = shear radius of the reinforced rock unit, = A/P, where P is the shear perimeter (= 4s for a s × s bolt spacing), = a factor depending on the time of installation of the rockbolts ( = 0.5 for active support, and = 1.0 for passive reinforcement), and L = bolt length which will often be less than D, the height of the de-stressed zone of rock. Lang and Bischoff suggest that, for preliminary analyses, the cohesion, c, should be taken as zero. Design charts based on equation 11.9 show that, particularly for low values of , the required bolt tension, T , increases significantly as L/s decreases below about two, but that no significant reduction in T is produced when L/s is increased above two. This result provides some corroboration of Lang’s empirical rule that the bolt length should be at least twice the spacing. For a given set of data, equation 11.9 will give a lower required bolt tension than that given by equation 11.8. Clearly, Lang and Bischoff’s theory applies more directly to the case of the development of a zone of reinforced, self-supporting rock, than to the simpler case of the support of the total gravity load produced by a loosened volume of rock or by a roof beam in laminated rock. Design to support a triangular or tetrahedral block. In Chapter 9, the identification of potential failure modes of triangular and tetrahedral blocks was discussed, and analyses were proposed for the cases of symmetric and asymmetric triangular roof prisms. These analyses take account of induced elastic stresses and discontinuity deformability, as well as allowing for the self-weight of the block and for support forces. The complete analysis of a non-regular tetrahedral wedge is more complex. An otherwise complete solution for the tetrahedral wedge which does not allow for induced elastic stresses is given by Hoek and Brown (1980). The analyses presented in Chapter 9 may be incorporated into the design procedure. Consider the two-dimensional problem illustrated in Figure 11.14 to which the analysis for an asymmetric triangular prism may be applied. If it is assumed that the normal stiffnesses of both discontinuities are much greater than the shear stiffnesses, 328
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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
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
Page 307 and 308: Figure 10.12 Distribution of radial
Page 309 and 310: Figure 10.15 Problem geometry for d
Page 311 and 312: Figure 10.17 (a) Schematic represen
Page 315 and 316: Figure 10.20 Elastic/post-peak stif
Page 319 and 320: Figure 10.24 Relation between frequ
Page 325 and 326: Figure 10.28 Six possible ways that
Page 327 and 328: Figure 10.29 First motions for P an
Page 329 and 330: 11Rock support and reinforcement 11
Page 331 and 332: Figure 11.1 (a) Hypothetical exampl
Page 333 and 334: Figure 11.4 Non-linear support reac
Page 335 and 336: Figure 11.5 Idealised elastic-britt
Page 337 and 338: Figure 11.6 Calculated required sup
Page 339 and 340: ROCK SUPPORT AND REINFORCEMENT The
Page 341 and 342: Figure 11.9 Ground reaction curves
Page 343: Figure 11.12 Use of grouted reinfor
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Page 349 and 350: Figure 11.18 Typical working sketch
Page 351 and 352: Figure 11.19 Permanent support and
Page 353 and 354: Figure 11.22 Basis of natural coord
Page 355 and 356: Figure 11.24 Distributions of (a) s
Page 357 and 358: Figure 11.26 Resin grouted rockbolt
Page 359 and 360: Figure 11.28 Alternative methods of
Page 361 and 362: ROCK SUPPORT AND REINFORCEMENT Tabl
Page 363 and 364: Figure 11.31 Toussaint-Heintzmann y
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
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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
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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
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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,
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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