Rock Mechanics.pdf - Mining and Blasting

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Figure 10.22 Representation of a narrow mine opening as a narrow slot. THIN TABULAR EXCAVATIONS the presence of natural discontinuities. This is demonstrated in Figure 10.20, where the stiffness ratios for various jointed specimens are seen to be quite different from that for an unjointed specimen. As demonstrated in Figure 10.21, various joint patterns lead to a positive value of a pillar stability index, for a pillar width/height ratio of 0.5. It can be readily inferred, from the shape of the accompanying plots in Figure 10.21, that stable post-peak behaviour is assured at higher pillar width/height ratios. The results as presented imply that the natural discontinuities in a rock mass have a dominant effect on the post-peak deformation properties of the medium, and may control the potential for mine global instability. In general, joint sets and other features oriented to favour slip during the process of development of new fractures in a pillar can be expected to lead to stable yield of the pillar. Analysis of mine stability for geometrically irregular mine structures is not amenable to simplification in the way described for the structures developed in stratiform orebodies. It is possible that a general computational method for global stability analysis may be formulated by incorporation of the localisation theories of Rudnicki and Rice (1975) and Vardoulakis (1979) in some linked computational scheme. 10.8 Thin tabular excavations Interest in thin, tabular excavations arises since they are common and industrially important sources of ore. They are generated when coal seams or reef ore deposits are mined by longwall methods. Energy release has been studied extensively in relation to the mining of South African gold reefs, where, at the mining depths worked, static stresses are sufficient to cause extensive rock mass fracture around production excavations. Many of the original ideas associated with energy release evolved from studies of problems in deep mining in South Africa. For example, Hodgson and Joughin (1967) produced data on the relation between ground control problems in and adjacent to working areas in stopes and the rate of energy release. Some of these notions of the mining significance of energy release appear to have developed from macroscopic application of the principles of Griffith crack theory. The conventional treatment of a thin tabular excavation such as that by Cook (1967a), considers it as a parallel-sided slit, as shown in Figure 10.22. Sneddon (1946) showed that the mining-induced displacements of points on the upper and 299
ENERGY, MINE STABILITY, MINE SEISMICITY AND ROCKBURSTS lower surfaces of the excavation are given by u y =±[(1 − )/G]p[(L 2 /4) − x 2 ] 1/2 (10.84) where the negative sign corresponds to the upper excavation surface, and L is the stope span. Using the methods described previously, it is readily shown that the released energy and the excess energy are given by Wr = We = [(1 − )/8G]L 2 p 2 (10.85) Bray (1979) showed that the increase in static strain energy, Ws, is also given by equation 10.85. The expressions for Wr, We and Ws (equation 10.85) apply up to the stage where the excavation remains open, i.e. until convergence between the footwall and hangingwall sides of the stope produces contact. This occurs when the convergence at midspan is equal to the mined stope height H. From equation 10.84, the critical span L0 at which contact occurs is given by or H = [2(1 − )/G]pL0/2 L0 = GH/(1 − )p (10.86) At this stage, the released energy Wr and stored strain energy Ws are given by Wr = Ws = (/8)pL0 H As was noted earlier, the total released energy and strain energy increase are of limited practical significance, since a complete stope is not generated instantaneously. Mining interest is, instead, in the energy changes for incremental extension of the stope. Thus, while a stope remains open dWr/dL = [(1 − )/4G]Lp 2 (10.87) For stoping spans greater than the critical span L0, Bray (1979) showed that Wr approaches asymptotically to the expression while Ws approaches the maximum value Wr = LHp (10.88) Ws max = HL0 P/4 (10.89) Therefore the incremental rates of energy storage and release are given by dWr/dL = Hp dWs/dL = 0 (10.90) The nature of equations 10.90 indicates the key mechanical principle involved in longwall mining. If it were possible to mine a narrow orebody as a partially closed, 300
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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
Page 265 and 266: (a) (b) (c) EP EP Reference circle
Page 267 and 268: Figure 9.10 JP 100 is the only JP w
Page 269 and 270: Figure 9.12 Traces of the views of
Page 271 and 272: EXCAVATION DESIGN IN BLOCKY ROCK In
Page 273 and 274: Figure 9.14 Free-body diagrams of a
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Page 277 and 278: Figure 9.16 Symmetrical wedge in th
Page 279 and 280: Figure 9.17 (a) Geometry for determ
Page 281 and 282: Figure 9.18 Problem geometry demons
Page 283 and 284: Figure 9.20 Cut-and-fill stope mine
Page 285 and 286: Figure 9.22 Chart to determine fact
Page 287 and 288: EXCAVATION DESIGN IN BLOCKY ROCK Th
Page 289 and 290: Figure 10.1 (a) Pre-mining state of
Page 291 and 292: Figure 10.3 (a) Dynamic loading of
Page 293 and 294: Figure 10.5 (a) Pre-mining and (b)
Page 295 and 296: Figure 10.6 Problem definition and
Page 297 and 298: ENERGY, MINE STABILITY, MINE SEISMI
Page 299 and 300: Figure 10.9 Force and stress compon
Page 307 and 308: Figure 10.12 Distribution of radial
Page 309 and 310: Figure 10.15 Problem geometry for d
Page 311 and 312: Figure 10.17 (a) Schematic represen
Page 315: Figure 10.20 Elastic/post-peak stif
Page 319 and 320: Figure 10.24 Relation between frequ
Page 325 and 326: Figure 10.28 Six possible ways that
Page 327 and 328: Figure 10.29 First motions for P an
Page 329 and 330: 11Rock support and reinforcement 11
Page 331 and 332: Figure 11.1 (a) Hypothetical exampl
Page 333 and 334: Figure 11.4 Non-linear support reac
Page 335 and 336: Figure 11.5 Idealised elastic-britt
Page 337 and 338: Figure 11.6 Calculated required sup
Page 339 and 340: ROCK SUPPORT AND REINFORCEMENT The
Page 341 and 342: Figure 11.9 Ground reaction curves
Page 343 and 344: Figure 11.12 Use of grouted reinfor
Page 345 and 346: ROCK SUPPORT AND REINFORCEMENT If,
Page 347 and 348: Figure 11.16 Local reinforcement ac
Page 349 and 350: Figure 11.18 Typical working sketch
Page 351 and 352: Figure 11.19 Permanent support and
Page 353 and 354: Figure 11.22 Basis of natural coord
Page 355 and 356: Figure 11.24 Distributions of (a) s
Page 357 and 358: Figure 11.26 Resin grouted rockbolt
Page 359 and 360: Figure 11.28 Alternative methods of
Page 361 and 362: ROCK SUPPORT AND REINFORCEMENT Tabl
Page 363 and 364: Figure 11.31 Toussaint-Heintzmann y
Page 365 and 366: MINING METHODS AND METHOD SELECTION
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Figure 12.2 Elements of a supported
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MINING METHODS AND METHOD SELECTION
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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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