Rock Mechanics.pdf - Mining and Blasting

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STRENGTH CRITERIA FOR ISOTROPIC ROCK MATERIAL Table 4.1 Constants in Bieniawski’s empirical strength criterion (after Bieniawski, 1974). Rock type A B norite 5.0 0.8 quartzite 4.5 0.78 sandstone 4.0 0.75 siltstone 3.0 0.70 mudstone 3.0 0.70 Using a boundary element analysis to calculate the elastic stresses induced around the raise as the pillar was progressively mined, he found that fracture of the rock could be accurately modelled using equation 4.23 with A = 3.0, k = 0.75 and c = 90 MPa which is approximately half the mean value of 170 MPa measured in laboratory tests. Hoek and Brown (1980) found that the peak triaxial compressive strengths of a wide range of isotropic rock materials could be described by the equation 1 = 3 + m c 3 + s 20.5 c (4.25) where m varies with rock type and s = 1.0 for intact rock material. On the basis of analyses of published strength data and some interpolation and extrapolation based on practical experience, Marinos and Hoek (2000) have suggested that the constant m for intact rock, mi, varies with rock type in the manner shown in Table 4.2. A normalised peak strength envelope for sandstones is shown in Figure 4.30. The grouping and analysis of data according to rock type has obvious disadvantages. Detailed studies of rock strength and fracture indicate that factors such as mineral composition, grain size and angularity, grain packing patterns and the nature of cementing materials between grains, all influence the manner in which fracture initiates and propagates. If these factors are relatively uniform within a given rock type, then it might be expected that a single curve would give a good fit to the normalised strength data with a correspondingly high value of the coefficient of determination, r 2 . If, on the other hand, these factors are quite variable from one occurrence of a given rock type to another, then a wider scatter of data points and a poorer fit by a single curve might be anticipated. For sandstones (Figure 4.30) where grain size, porosity and the nature of the cementing material can vary widely, and for limestone which is a name given to a wide variety of carbonate rocks, the values of r 2 are, indeed, quite low. Despite these difficulties and the sometimes arbitrary allocation of a particular name to a given rock, the results obtained initially by Hoek and Brown (1980) and updated by Marinos and Hoek (2000), do serve an important practical purpose. By using the approximate value of mi found to apply for a particular rock type, it may be possible to carry out preliminary design calculations on the basis of no testing other than a determination of a suitable value of c made using a simple test such as the point load test. A value of c is required as a scaling factor to determine the strength of a particular sample of rock. Thus although the same value of mi may apply to granites from different localities, their strengths at different confining pressures may differ by a factor of two or three. 113
ROCK STRENGTH AND DEFORMABILITY Table 4.2 Variation of the constant mi for intact rock by rock group (after Hoek, 2003). Porphyries ∗Conglomerates and breccias may present a wide range of mi values depending on the nature of the cementing material and the degree of cementation, so they may range from values similar to sandstone, to values used for fine grained sediments (even under 10). ∗∗These values are for intact rock specimens tested normal to bedding or foliation. The value of mi will be significantly different if failure occurs along a weakness plane. 114
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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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ROCK MASS STRUCTURE AND CHARACTERIS
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Page 81 and 82: Figure 3.17 Sample number vs. preci
Page 83 and 84: Figure 3.19 Diagrammatic illustrati
Page 87 and 88: Figure 3.20 Computerised depiction
Page 89 and 90: Figure 3.23 Stereographic projectio
Page 91 and 92: Figure 3.26 Polar stereographic net
Page 93 and 94: Figure 3.28 Contours of pole concen
Page 99 and 100: Figure 3.30 Geological Strength Ind
Page 103 and 104: Figure 4.1 Idealised illustration o
Page 105 and 106: ROCK STRENGTH AND DEFORMABILITY wit
Page 107 and 108: Figure 4.4 Influence of end restrai
Page 109 and 110: ROCK STRENGTH AND DEFORMABILITY whe
Page 111 and 112: Figure 4.8 Principle of closed-loop
Page 113 and 114: Figure 4.12 Two classes of stress-
Page 115 and 116: Figure 4.14 Point load test apparat
Page 117 and 118: Figure 4.15 Biaxial compression tes
Page 119 and 120: Figure 4.18 Results of triaxial com
Page 121 and 122: ROCK STRENGTH AND DEFORMABILITY was
Page 123 and 124: Figure 4.23 Coulomb strength envelo
Page 125 and 126: Figure 4.25 Extension of a preexist
Page 127 and 128: Figure 4.29 The three basic modes o
Page 129: Figure 4.30 Normalised peak strengt
Page 133 and 134: Figure 4.32 The normality condition
Page 135 and 136: Figure 4.33 Variation of peak princ
Page 137 and 138: Figure 4.35 Direct shear test confi
Page 139 and 140: Figure 4.37 Shear stress-shear disp
Page 141 and 142: Figure 4.40 Peak and residual effec
Page 143 and 144: Figure 4.43 Effect of shearing dire
Page 145 and 146: Figure 4.45 Relations between norma
Page 147 and 148: Figure 4.47 Coulomb friction, linea
Page 149 and 150: ROCK STRENGTH AND DEFORMABILITY whe
Page 151 and 152: Figure 4.49 Composite peak strength
Page 153 and 154: Figure 4.50 Hoek-Brown peak strengt
Page 155 and 156: Figure 4.52 Determination of the Yo
Page 157 and 158: ROCK STRENGTH AND DEFORMABILITY 4 A
Page 159 and 160: 5 Pre-mining Figure 5.1 Method of s
Page 161 and 162: Figure 5.2 The effect of irregular
Page 163 and 164: PRE-MINING STATE OF STRESS surround
Page 165 and 166: PRE-MINING STATE OF STRESS induced
Page 167 and 168: Figure 5.5 (a) Definition of hole l
Page 169 and 170: Figure 5.6 (a) Core drilling a slot
Page 171 and 172: Figure 5.7 Principles of stress mea
Page 173 and 174: PRE-MINING STATE OF STRESS strength
Page 175 and 176: PRE-MINING STATE OF STRESS A second
Page 177 and 178: PRE-MINING STATE OF STRESS by the e
Page 179 and 180: PRE-MINING STATE OF STRESS extend i
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PRE-MINING STATE OF STRESS (d) Dete
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METHODS OF STRESS ANALYSIS quantita
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METHODS OF STRESS ANALYSIS It is in
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Figure 6.2 A thick-walled cylinder
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METHODS OF STRESS ANALYSIS For the
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Figure 6.3 Problem geometry, coordi
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Figure 6.4 Problem geometry, coordi
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METHODS OF STRESS ANALYSIS When the
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Figure 6.5 Superposition scheme dem
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METHODS OF STRESS ANALYSIS The disc
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Figure 6.7 Development of a finite
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METHODS OF STRESS ANALYSIS Solution
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Figure 6.8 A simple finite element
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Figure 6.9 A schematic representati
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METHODS OF STRESS ANALYSIS block ce
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METHODS OF STRESS ANALYSIS where ˚
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METHODS OF STRESS ANALYSIS The prin
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EXCAVATION DESIGN IN MASSIVE ELASTI
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Figure 7.2 A logical framework for
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Figure 7.3 (a) Axisymmetric stress
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Figure 7.6 A plane of weakness, ori
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Figure 7.8 A flat-lying plane of we
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Figure 7.10 Shear stress/normal str
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Figure 7.12 Ovaloidal opening in a
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Figure 7.15 States of stress at sel
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Figure 7.16 Prediction of the exten
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Figure 7.18 Contour plots of princi
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Figure 7.19 Problem geometry for de
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8 Excavation Figure 8.1 An excavati
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EXCAVATION DESIGN IN STRATIFIED ROC
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Figure 8.4 Experimental apparatus f
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Figure 8.7 Free body diagrams and n
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Figure 8.8 Assumed distributions of
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Figure 8.9 Flow chart for the deter
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Figure 8.10 Normalised arch thickne
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EXCAVATION DESIGN IN STRATIFIED ROC
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Figure 8.11 Normalised deflection a
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9 Excavation Figure 9.1 Generation
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Figure 9.3 (a) A finite, non-tapere
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(a) (b) Figure 9.4 (a) Vertical cro
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(a) (b) (c) EP EP Reference circle
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Figure 9.10 JP 100 is the only JP w
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Figure 9.12 Traces of the views of
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EXCAVATION DESIGN IN BLOCKY ROCK In
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Figure 9.14 Free-body diagrams of a
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EXCAVATION DESIGN IN BLOCKY ROCK di
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Figure 9.16 Symmetrical wedge in th
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Figure 9.17 (a) Geometry for determ
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Figure 9.18 Problem geometry demons
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Figure 9.20 Cut-and-fill stope mine
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Figure 9.22 Chart to determine fact
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EXCAVATION DESIGN IN BLOCKY ROCK Th
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Figure 10.1 (a) Pre-mining state of
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Figure 10.3 (a) Dynamic loading of
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Figure 10.5 (a) Pre-mining and (b)
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Figure 10.6 Problem definition and
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ENERGY, MINE STABILITY, MINE SEISMI
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Figure 10.9 Force and stress compon
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Figure 10.12 Distribution of radial
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Figure 10.15 Problem geometry for d
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Figure 10.17 (a) Schematic represen
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Figure 10.20 Elastic/post-peak stif
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Figure 10.24 Relation between frequ
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Figure 10.28 Six possible ways that
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Figure 10.29 First motions for P an
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11Rock support and reinforcement 11
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Figure 11.1 (a) Hypothetical exampl
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Figure 11.4 Non-linear support reac
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Figure 11.5 Idealised elastic-britt
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Figure 11.6 Calculated required sup
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ROCK SUPPORT AND REINFORCEMENT The
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Figure 11.9 Ground reaction curves
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Figure 11.12 Use of grouted reinfor
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ROCK SUPPORT AND REINFORCEMENT If,
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Figure 11.16 Local reinforcement ac
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Figure 11.18 Typical working sketch
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Figure 11.19 Permanent support and
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Figure 11.22 Basis of natural coord
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Figure 11.24 Distributions of (a) s
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Figure 11.26 Resin grouted rockbolt
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Figure 11.28 Alternative methods of
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ROCK SUPPORT AND REINFORCEMENT Tabl
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Figure 11.31 Toussaint-Heintzmann y
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MINING METHODS AND METHOD SELECTION
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Figure 12.2 Elements of a supported
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Figure 12.6 Schematic layout for bi
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Figure 12.8 Layout for shrink stopi
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Figure 12.9 Schematic layout for VC
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Figure 12.11 Key elements of longwa
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Figure 12.13 Mining layout for tran
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13 Figure 13.1 Schematic illustrati
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Figure 13.3 Layout of barrier pilla
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Figure 13.5 Principal modes of defo
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Figure 13.8 Geometry for tributary
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PILLAR SUPPORTED MINING METHODS str
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Figure 13.10 Distribution of vertic
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Figure 13.12 Pillar behaviour domai
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PILLAR SUPPORTED MINING METHODS Lun
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Figure 13.15 Options in the design
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Figure 13.17 Relation between yield
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Figure 13.19 Model of yield of coun
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Figure 13.20 North-south vertical c
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Figure 13.23 Stope-and-pillar layou
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Figure 13.25 Calibrated stability c
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PILLAR SUPPORTED MINING METHODS wor
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Figure 13.28 Pillar performance, de
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Figure 13.29 (a) Stope and pillar l
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Figure 13.31 (a) Plane strain analy
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PILLAR SUPPORTED MINING METHODS Pan
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14 Artificially supported mining me
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ARTIFICIALLY SUPPORTED MINING METHO
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Figure 14.2 Simplified view of stru
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Figure 14.5 Confined block model fo
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Figure 14.7 Crown and sidewall stre
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Figure 14.10 Sublevel open stoping
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Figure 14.12 Some applications of c
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15 Longwall and caving mining metho
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Figure 15.2 Shear stress drop in th
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LONGWALL AND CAVING MINING METHODS
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Figure 15.6 Hydraulic prop reaction
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Figure 15.7 Development and extract
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Figure 15.8 Vertical stress redistr
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Figure 15.11 Distribution of observ
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Figure 15.13 Plan view of microseis
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Figure 15.16 Ground-support interac
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Figure 15.18 Roadway support and re
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Figure 15.25 Comparison of isolated
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Figure 15.26 Geometry of a sublevel
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Figure 15.28 Theoretical determinat
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Figure 15.31 Deterioration of a cro
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Figure 15.32 Distinct element simul
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Figure 15.34 Extended Mathews stabi
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Figure 15.36 Comparison of postand
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Figure 15.39 Idealised plan illustr
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Figure 15.41 Idealised vertical sec
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Figure 15.42 Vertical slice through
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16 Figure 16.1 Trough subsidence ov
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MINING-INDUCED SURFACE SUBSIDENCE c
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Figure 16.4 North-south section, At
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Figure 16.6 (a) Rectangular block g
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MINING-INDUCED SURFACE SUBSIDENCE f
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Figure 16.8 Relation between stope
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MINING-INDUCED SURFACE SUBSIDENCE M
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MINING-INDUCED SURFACE SUBSIDENCE
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Figure 16.14 Chart developed to est
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Figure 16.16 Progressive hangingwal
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Figure 16.19 Idealised model used i
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Figure 16.21 Longitudinal section,
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MINING-INDUCED SURFACE SUBSIDENCE t
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MINING-INDUCED SURFACE SUBSIDENCE w
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MINING-INDUCED SURFACE SUBSIDENCE F
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Figure 16.25 Subsidence troughs pre
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Figure 16.28 Predicted and measured
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17 Blasting mechanics 17.1 Blasting
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Figure 17.1 An empirical matching o
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Figure 17.2 A finite difference mod
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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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