Page 312 - Rock Mechanics For Underground Mining
P. 312

ENERGY, MINE STABILITY, MINE SEISMICITY AND ROCKBURSTS


                                        Using these definitions and a suitable analytical or computational model of a mine
                                        structure, it is possible, in theory at least, to assess the stability of an equilibrium
                                                                                          ¨
                                        state, by notional probing to determine the algebraic value of W.
                                          Unstable equilibrium in a rock mass leads to unstable deformation, seismic events
                                        and seismic emissions from the source of the instability. Where a seismic event results
                                        in damage to rock around mine excavations it is conventionally called a rockburst.
                                        It is generally recognised (Gibowicz, 1988) that there are two modes of rock mass
                                        deformation leading to instability and mine seismicity. One mode of instability in-
                                        volves crushing of the rock mass, and typically occurs in pillars or close to excavation
                                        boundaries. The second mode involves slip on natural or mining-induced planes of
                                        weakness, and usually occurs on the scale of a mine panel or district rather than on
                                        the excavation or pillar scale for the first mode.



                                        10.7 Instability due to pillar crushing

                                        Conditions for the crushing mode of instability in a mine structure arise in the post-
                                        peak range of the stress–strain behaviour of the rock mass. This aspect of rock de-
                                        formation under load has been discussed in section 4.3.7. Cook (1965) recognised
                                        that rockbursts represent a problem of unstable equilibrium in a mine structure. He
                                        subsequently discussed the significance, for mine stability, of the post-peak behaviour
                                        of a body of rock in compression (Cook, 1967b). In the discussion in section 4.3.7,
                                        the term ‘strain-softening’ was used to denote the decreasing resistance of a specimen
                                        to load, at increasing axial deformation. It appears that much of the macroscopic soft-
                                        ening that is observed in compression tests on frictional materials can be accounted
                                        for by geometric effects. These are associated with the distinct zones of rigid and
                                        plastic behaviour which exist in the cracked rock in the post-peak state (Drescher and
                                        Vardoulakis, 1982). Notwithstanding the gross simplification involved in the strain-
                                        softening model of rock deformation, it is useful in examination of the mechanics of
                                        unstable deformation in rock masses.
              Figure 10.17  (a) Schematic repre-  The simplest problem of rock stability to consider is loading of a rock specimen in
              sentation of the loading of a rock spec-  a conventional testing machine, as was discussed in an introductory way in section
              imen in a testing machine; (b) load–
                                        4.3.7. The problem is represented schematically in Figure 10.17a, and has been dis-
              displacement characteristics of spring
                                        cussed in detail by Salamon (1970). Figure 10.17b illustrates the load–displacement
              and specimen; (c) specimen stiffness
              throughout the complete deformation  performance characteristics of the testing machine (represented as a spring) and the
              range (from Salamon, 1970).  specimen. Adopting the convention that compressive forces are positive, the load
                                        (P) – convergence (S) characteristics of the rock specimen and the spring may be
                                        expressed by

                                                                     P r = f (S)                     (10.75)

                                        and

                                                                    P s = k(  − S)                   (10.76)

                                        where the subscripts r and s refer to the rock and spring respectively, and   is the
                                        displacement of the point O 1 on the spring. The specification of spring performance
                                        in equation 10.76 implies that spring stiffness k is positive by definition.

                                        294
   307   308   309   310   311   312   313   314   315   316   317