Rock Mechanics.pdf - Mining and Blasting

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PROBLEMS flow and return on the high initial investment. This may have at least three undesirable consequences: it could lead to the development of an uneven profile in the cave back and the possible arrest of caving as a result of the new, uneven distribution of stresses; in weak materials, if draw is continued or if a path for the gravity flow of fines is established, it could lead to chimneying through the orebody (see Chapter 16) and early dilution; and if a group of drawpoints is drawn excessively with respect to the rate of caving, or if cave propagation is arrested and draw is continued, an air gap may be created providing the potential for a damaging air blast to be generated should a major collapse of the cave back occur. A fuller discussion of the factors influencing draw control and draw control practices is given by Brown (2003). The manual and empirical methods formerly used for modelling draw and developing draw control procedures are now being replaced by computer based modelling and optimisation procedures (e.g. Diering, 2000, Guest et al., 2000). Problems 1 Figure (a) below shows the rectangular cross section of a deep underground excavation. The height of the excavation is small compared with its width, and its length, perpendicular to the section, is large. The principal in situ stresses are pxx and pzz. For these conditions, the elastic stresses in the rock surrounding the excavation are well represented by the expressions: where xx = d − e sin + pxx − pzz zz = d + e sin xz =−ecos d = rpzz √ cos r1r2 − 1 2 (1 + 2) e = a2 rpzz sin (r1r2) 3/2 = 3 2 (1 + 2) Figure (b) shows the dimensions and relative positions of two such excavations produced by the longwall mining of two parallel tabular orebodies. (a) If pzz = 32 MPa and pxx = 40 MPa, show that each of the excavations is outside the other’s 5% zone of influence. (b) Calculate the state of stress at F which is midway between B and C. 481
LONGWALL AND CAVING MINING METHODS (c) Using equation 10.84, calculate the mining-induced elastic displacements of the upper and lower surfaces at the midpoint of each of the excavations if G = 16 GPa and = 0.20. 2 A 1.0 m thick, flat-lying, metalliferous orebody of large areal extent is to be extracted by a longwall method. The in situ vertical stress at the mining depth is 85 MPa, and Young’s modulus and Poisson’s ratio of the rock are 48 GPa and 0.20, respectively. (a) Calculate the critical span of a longwall face under these conditions. What total amount of energy is released per unit length of stope and per unit volume of extraction, for this critical span? What values do these quantities approach as the span increases above the critical? (b) Partial extraction is to be used to control the energy release rates in this case. Using equations 10.88 and 15.1, write down an expression for the total energy released per unit volume of extraction when the orebody is mined in a number of parallel panels of span, l, spaced on centres of S as in Figure 15.5a. Determine values of l and S that will restrict this energy release rate to 15 MJ m −3 and maintain an extraction ratio of at least 0.80. In order to ensure the long-term stability of the pillars it is necessary that they have width to height ratios of at least 20. 3 A 2.5 m thick horizontal coal seam at a depth of 230 m is to be extracted by a series of parallel longwall panels with a single row of pillars between them as shown in Figure 15.7. The roadways are to be 4.5 m wide and the weighted unit weight of the overburden materials is = 25 kN m −3 . The distribution of vertical stress with distance, x, from the pillar rib side is of the type illustrated in Figure 15.9 with the width of the yield zone xb = 10 m and the peak stress yy = 12 MPa. The vertical stress, zz, decays with distance into the solid coal away from the yield zone according to the equation where v is the in situ vertical stress. 482 (zz − v) = (yy − v) exp{(xb − x)/12}
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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
Page 447 and 448: 15 Longwall and caving mining metho
Page 449 and 450: Figure 15.2 Shear stress drop in th
Page 451 and 452: LONGWALL AND CAVING MINING METHODS
Page 455 and 456: Figure 15.6 Hydraulic prop reaction
Page 457 and 458: 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 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: 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 and 510: MINING-INDUCED SURFACE SUBSIDENCE f
Page 511 and 512: Figure 16.8 Relation between stope
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
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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
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,
Page 645:
INDEX United States (USA) 395, 396,
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