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Figure 4.13 Axial force–axial displacement curve obtained for Tennessee Marble with post-peak unloading and reloading (after Wawersik and Fairhurst, 1970). BEHAVIOUR OF ISOTROPIC ROCK MATERIAL IN UNIAXIAL COMPRESSION Marble which was unloaded and then reloaded from a number of points in the postpeak range. Several points should be noted about the behaviour observed. (a) On reloading, the curve eventually joins that for a specimen in which the axial displacement increases monotonically with time. (b) As displacement continues in the post-peak region, the proportion of the total displacement that is irrecoverable increases. (c) The unloading–loading loop shows some hysteresis. (d) The apparent modulus of the rock which can be calculated from the slope of the reloading curve, decreases with post-peak deformation and progressive fragmentation of the specimen. If rock specimens are subjected to loading and unloading cycles in the pre-peak range, some permanent deformation and hysteresis are generally observed. This is often associated with ‘bedding-down’ effects, and for this reason, the ISRM Commission (1979) recommends that ‘it is sometimes advisable for a few cycles of loading and unloading to be performed’. 4.3.9 The point load test Sometimes the facilities required to prepare specimens and carry out uniaxial compression tests to the standard described above are not available. In other cases, the number of tests required to determine the properties of the range of rock types encountered on a project may become prohibitive. There may be still further cases, in which the uniaxial compressive strength and the associated stress–strain behaviour need not be studied in detail, with only an approximate measure of peak strength being required. In all of these instances, the point load test may be used to provide an indirect estimate of uniaxial compressive strength. This account is based on the ISRM Suggested Method for determining point load strength (ISRM Commission, 1985). 97
Figure 4.14 Point load test apparatus (photograph by ELE International Ltd). ROCK STRENGTH AND DEFORMABILITY In this test, rock specimens in the form of core (the diametral and axial tests), cut blocks (the block test) or irregular lumps (the irregular lump test) are broken by a concentrated load applied through a pair of spherically truncated, conical platens. The test can be performed in the field with portable equipment or in the laboratory using apparatus such as that shown in Figure 4.14. The load should be applied at least 0.5D from the ends of the specimen in diametral tests, where D is the core diameter, and equivalent distances in other tests as specified by the ISRM Commission (1985). From the measured value of the force, P, at which the test specimen breaks, an Uncorrected Point Load Index, Is, is calculated as Is = P D2 (4.5) e where De, the equivalent core diameter, is given by the core diameter, D, for diametral tests, and by 4A/ for axial, block and lump tests, where A is the minimum cross sectional area of a plane through the specimen and the platen contact points. The index, Is, varies with De and so size correction must be applied in order to obtain a unique point load strength index for a particular rock sample for use for strength classification. Wherever possible, it is preferable to carry out diametral tests on 50–55 mm diameter specimens. The size-corrected Point Load Strength Index, Is(50), is defined as the value of Is that would have been measured in a diametral test with D = 50 mm. The results of several series of tests carried out by a number of 98
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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
Page 63 and 64: 3 Rock Figure 3.1 Sidewall failure
Page 65 and 66: Figure 3.2 Jointing in a folded str
Page 67 and 68: Figure 3.5 Diagrammatic longitudina
Page 69 and 70: Figure 3.7 Discontinuity spacing hi
Page 71 and 72: Figure 3.9 Illustration of persiste
Page 73 and 74: Figure 3.11 Typical roughness profi
Page 75 and 76: ROCK MASS STRUCTURE AND CHARACTERIS
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: Figure 4.12 Two classes of stress-
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 and 130: Figure 4.30 Normalised peak strengt
Page 131 and 132: ROCK STRENGTH AND DEFORMABILITY Tab
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
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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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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
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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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