Rock dynamics
73 and time-
dependent
aspects
In this chapter we will be discussing a variety of effects related to the
different strain rates that occur throughout the range of rock mechanics
processes and rock engineering applications. Following the introduction,
highlighting the wide time ranges over which these effects are manifested,
we discuss the basic theory of rock dynamics, obtaining dynamic rock
properties and the relevance of the ideas in engineering.
13.1 Introduction
In Chapter 6, it was noted that the compressive strength is the maximum
stress that can be sustained by a specimen of rock. Let us now say that
the compressive strength is reached at 0.1% strain, i.e. 0.001. If this strain
is developed in 1 p-for example, during an explosion-the strain rate is
1 x lo3 s-’. If, on the other hand, this strain is developed over a period of
30 years, the average strain rate is of the order of 1 x 10-l’ s-’. Between these
two extremes, there are 15 orders of magnitude of strain rate, and so, if the
rock exhibits any time-dependent behaviour, we would not expect to be
able to use the same rock properties for an analysis of both cases. In Fig.
13.1, we illustrate two manifestations of these extremes of strain rate. Fig.
13.l(a) shows hackle marks that develop on rock fracture surfaces formed
during high strain rate failure, in this case on the surface of a blast-induced
fracture. Fig. 13.1@) shows the effect of the gradual deterioration, and
subsequent failure, of the pillars in an old mine in chalk beneath a main
road.
Within the rock mechanics principles, it is necessary to be able to account
for time-dependent behaviour. In the development and discussion of the
elastic compliance matrix in Chapter 5, when we considered the addition
of the component strains caused by the component stresses, no time-
dependent behaviour was incorporated. Indeed, one aspect of the theory
of elasticity is that there is no time component and that all strain energy
is recoverable, i.e. all strain energy introduced into a material through
loading will be subsequently liberated on unloading. However, when
time dependency is involved, there is always hysteresis in the