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.
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