Rock Mechanics.pdf - Mining and Blasting

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CHIMNEY CAVING can be cumbersome. However, the simple example of a rectangular stope in a horizontal orebody with no groundwater pressures gives a ready solution that may be used for purposes of illustration. From two equations of the form of equation 16.4 giving the vertical shear resistance developed on the faces of the block, the total shear resistance is found as or Q = Q = 2(a + b)A 1−B c h 0 (kz − tm) B dz 2(a + b)A1−B c [(kh − tm) k(1 + B) 1+B −|tm| 1+B ] The weight of the block is W = abh, and so, at limiting equilibrium, the factor of safety against vertical sliding is F = 2(a + b)A1−B c 2 abhk(1 + B) [(kh − tm) 1+B −|tm| 1+B ] (16.9) For poor quality rock masses of the type commonly involved in chimney caving, tm ≈ 0. In this case, equation 16.9 reduces to F = 2(a + b)k Bh B A1−B c 1−Bab(1 + B) (16.10) This result shows that the factor of safety decreases as the stope dimensions increase, the mining depth decreases, k decreases, the rock mass quality decreases, the uniaxial compressive strength of the intact rock decreases and as the unit weight of the overburden increases. As an example of the application of equation 16.10, consider the hypothetical case of a shallow abandoned room-and-pillar coal mine. The overburden is a very poor quality argillaceous rock mass with = 0.023 MN m −3 , A = 0.050, B = 0.539 and c = 15 MPa. The room span is a = b = 10 m, and the depth of the roof below surface is h = 30 m. For k = 1.0, equation 16.10 gives F = 1.61. The factor of safety reduces to unity when h is reduced to 12.4 m. Hoek (1989) carried out an analysis of the stability of a rectangular crown pillar which is similar to the analysis presented here. He allowed for the presence of a water table within the crown pillar and for the ratios of the horizontal and vertical in situ stresses to be different for the two pairs of vertical faces of the rectangular block. Hoek (1989) used the Hoek-Brown non-linear strength criterion and allowed the parameters involved in the solution, other than the dimensions of the pillar, to vary according to a normal distribution. He then carried out a simulation to investigate the influence on the calculated factor of safety of the pillar height, the Rock Mass Rating, RMR, the material constant mi in the Hoek-Brown criterion, the intact rock strength, c, the water table depth and the two k factors. Bétourney (1994) and Bétourney et al. (1994) presented a limiting equilibrium analysis and some numerical modelling results for the progressive chimney caving mechanism illustrated in Figure 16.3 which they refer to as chimneying disintegration failure. They also analysed the case of up-dip chimneying in an inclined orebody. The 493
Figure 16.8 Relation between stope span, L, rock mass cohesion, cm, and factor of safety, F, for chimneying disintegration stability analysis (after Bétourney, 1994). MINING-INDUCED SURFACE SUBSIDENCE approach used is to approximate successive internal failure surfaces by circular arcs which represent lines of active earth pressure. In the vertical caving case shown in Figure 16.3, each rupture line is composed of symmetric circular arcs intersecting at an apex which is a point of passive earth pressure. The equilibrium of each successive volume of rock is assessed using the method of slices developed for slope stability analysis (see Hoek and Bray, 1981, Mitchell, 1983). Bétourney (1994) and Bétourney et al. (1994) reported the results of their analyses as a relation between stope span, L, rock mass cohesion, cm, and factor of safety, F, for a particular value of rock mass unit weight, , as shown in Figure 16.8. They found that for the chimneying disintegration mechanism to occur, the block size and the degree of interlocking, and hence the cohesion, of the rock mass needed to be low. Bétourney (1994) applied this approach to the back analysis of the failures at the Brier Hill Mine (Rice, 1934) and the Athens Mine as illustrated in Figure 16.4 (Allen, 1934, Boyum, 1961). It must be emphasised that the limiting equilibrium analyses presented here provide only approximate solutions for particular types of chimney caving. They are not applicable to the case in which caving occurs by progressive unravelling of discrete blocks of strong rock. They apply best to those cases in which geological planes of weakness form the vertical boundaries of the caving block, and those in which the 494
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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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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
Page 459 and 460: Figure 15.8 Vertical stress redistr
Page 461 and 462: Figure 15.11 Distribution of observ
Page 463 and 464: Figure 15.13 Plan view of microseis
Page 465 and 466: Figure 15.16 Ground-support interac
Page 467 and 468: Figure 15.18 Roadway support and re
Page 469 and 470: LONGWALL AND CAVING MINING METHODS
Page 475 and 476: Figure 15.25 Comparison of isolated
Page 477 and 478: Figure 15.26 Geometry of a sublevel
Page 479 and 480: Figure 15.28 Theoretical determinat
Page 481 and 482: Figure 15.31 Deterioration of a cro
Page 483 and 484: Figure 15.32 Distinct element simul
Page 487 and 488: Figure 15.34 Extended Mathews stabi
Page 489 and 490: Figure 15.36 Comparison of postand
Page 493 and 494: Figure 15.39 Idealised plan illustr
Page 495 and 496: Figure 15.41 Idealised vertical sec
Page 497 and 498: Figure 15.42 Vertical slice through
Page 501 and 502: 16 Figure 16.1 Trough subsidence ov
Page 503 and 504: MINING-INDUCED SURFACE SUBSIDENCE c
Page 505 and 506: Figure 16.4 North-south section, At
Page 507 and 508: Figure 16.6 (a) Rectangular block g
Page 509: MINING-INDUCED SURFACE SUBSIDENCE f
Page 513 and 514: MINING-INDUCED SURFACE SUBSIDENCE M
Page 515 and 516: MINING-INDUCED SURFACE SUBSIDENCE
Page 517 and 518: Figure 16.14 Chart developed to est
Page 519 and 520: Figure 16.16 Progressive hangingwal
Page 521 and 522: Figure 16.19 Idealised model used i
Page 523 and 524: Figure 16.21 Longitudinal section,
Page 525 and 526: MINING-INDUCED SURFACE SUBSIDENCE t
Page 527 and 528: MINING-INDUCED SURFACE SUBSIDENCE w
Page 529 and 530: MINING-INDUCED SURFACE SUBSIDENCE F
Page 531 and 532: Figure 16.25 Subsidence troughs pre
Page 533 and 534: Figure 16.28 Predicted and measured
Page 535 and 536: 17 Blasting mechanics 17.1 Blasting
Page 537 and 538: Figure 17.1 An empirical matching o
Page 539 and 540: 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,
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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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