Rock Mechanics.pdf - Mining and Blasting

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2 Stress and infinitesimal strain 2.1 Problem definition The engineering mechanics problem posed by underground mining is the prediction of the displacement field generated in the orebody and surrounding rock by any excavation and ore extraction processes. The rock in which excavation occurs is stressed by gravitational, tectonic and other forces, and methods exist for determining the ambient stresses at a mine site. Since the areal extent of any underground mine opening is always small relative to the Earth’s surface area, it is possible to disregard the sphericity of the Earth. Mining can then be considered to take place in an infinite or semi-infinite space, which is subject to a definable initial state of stress. An understanding of the notions of force, stress and strain is fundamental to a proper and coherent appreciation of the response of a rock mass to mining activity. It was demonstrated in Chapter 1 that excavating (or enlarging) any underground opening is mechanically equivalent to the application, or induction, of a set of forces distributed over the surfaces generated by excavation. Formation of the opening also induces a set of displacements at the excavation surface. From a knowledge of the induced surface forces and displacements, it is possible to determine the stresses and displacements generated at any interior point in the rock medium by the mining operation. Illustration of the process of underground excavation in terms of a set of applied surface forces is not intended to suggest that body forces are not significant in the performance of rock in a mine structure. No body forces are induced in a rock mass by excavation activity, but the behaviour of an element of rock in the periphery of a mine excavation is determined by its ability to withstand the combined effect of body forces and internal, post-excavation surface forces. However, in many mining problems, body force components are relatively small compared with the internal surface forces, i.e. the stress components. Some mine excavation design problems, such as those involving a jointed rock mass and low-stress environments, can be analysed in terms of block models and simple statics. In most deep mining environments, however, the rock mass behaves as a continuum, at least initially. Prediction of rock mass response to mining therefore requires a working understanding of the concepts of force, traction and stress, and displacement and strain. The following discussion of these issues follows the treatments by Love (1944) and Jaeger (1969). In the discussion, the usual engineering mechanics convention is adopted, with tensile normal stresses considered positive, and the sense of positive shear stress on any surface determined by the sense of positive normal stress. The geomechanics convention for the sense of positive stresses will be introduced subsequently. 2.2 Force and stress The concept of stress is used to describe the intensity of internal forces set up in a body under the influence of a set of applied surface forces. The idea is quantified by defining the state of stress at a point in a body in terms of the area intensity of forces 17
Figure 2.1 (a) A finite body subject to surface loading; (b) determination of the forces, and related quantities, operating on an internal surface; (c) specification of the state of stress at a point in terms of the traction components on the face of a cubic free body. STRESS AND INFINITESIMAL STRAIN acting on the orthogonally oriented surfaces of an elementary free body centred on the point. If a Cartesian set of reference axes is used, the elementary free body is a cube whose surfaces are oriented with their outward normals parallel with the co-ordinate axes. Figure 2.1a illustrates a finite body in equilibrium under a set of applied surface forces, Pj. To assess the state of loading over any interior surface, Si, one could proceed by determining the load distribution over Si required to maintain equilibrium of part of the body. Suppose, over an element of surface A surrounding a point O, the required resultant force to maintain equilibrium is R, as shown in Figure 2.1b. The magnitude of the resultant stress r at O, or the stress vector, is then defined by R r = lim A→0 A If the vector components of R acting normally and tangentially to A are N, S, the normal stress component, n, and the resultant shear stress component, , atO are defined by N S n = lim , = lim A→0 A A→0 A The stress vector, r, may be resolved into components tx, ty, tz directed parallel to a set of reference axes x, y, z. The quantities tx, ty, tz, shown in Figure 2.1b are called traction components acting on the surface at the point O. As with the stress vector, the normal stress, n, and the resultant shear stress, , the traction components are expressed in units of force per unit area. A case of particular interest occurs when the outward normal to the elementary surface A is oriented parallel to a co-ordinate axis, e.g. the x axis. The traction components acting on the surface whose normal is the x axis are then used to define three components of the state of stress at the point of interest, 18 xx = tx, xy = ty, xz = tz (2.1)
Page 1 and 2: Rock Mechanics
Page 3 and 4: Rock Mechanics for underground mini
Page 5 and 6: Contents Preface to the third editi
Page 7 and 8: CONTENTS 9 Excavation design in blo
Page 9 and 10: CONTENTS ix Appendix A Basic constr
Page 11 and 12: PREFACE TO THE THIRD EDITION Mining
Page 13 and 14: PREFACE TO THE SECOND EDITION In th
Page 15 and 16: PREFACE TO THE FIRST EDITION design
Page 17 and 18: ACKNOWLEDGEMENTS Safety in Mines Re
Page 19 and 20: Figure 1.1 (a) Pre-mining condition
Page 21 and 22: ROCK MECHANICS AND MINING ENGINEERI
Page 25 and 26: Figure 1.4 Principal features of a
Page 27 and 28: 10 Figure 1.5 Definition of activit
Page 31 and 32: Figure 1.7 Components and logic of
Page 33: ROCK MECHANICS AND MINING ENGINEERI
Page 37 and 38: Figure 2.2 Free-body diagram for es
Page 39 and 40: STRESS AND INFINITESIMAL STRAIN As
Page 41 and 42: STRESS AND INFINITESIMAL STRAIN In
Page 43 and 44: Figure 2.3 Free-body diagram for de
Page 45 and 46: Figure 2.5 Problem geometry for det
Page 47 and 48: Figure 2.7 Rigid-body rotation of a
Page 49 and 50: STRESS AND INFINITESIMAL STRAIN the
Page 51 and 52: STRESS AND INFINITESIMAL STRAIN str
Page 53 and 54: ⎡ ⎢ ⎣ xx yy zz xy yz zx STRES
Page 55 and 56: Figure 2.11 Cylindrical polar coord
Page 57 and 58: STRESS AND INFINITESIMAL STRAIN fre
Page 59 and 60: Figure 2.13 Construction of a Mohr
Page 61 and 62: 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
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ROCK MASS STRUCTURE AND CHARACTERIS
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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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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,
Page 641 and 642:
INDEX Seismic (cont.) moment 306, 3
Page 643 and 644:
INDEX Strength (cont.) residual 86,
Page 645:
INDEX United States (USA) 395, 396,
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