Page 295 - Rock Mechanics For Underground Mining

ENERGY TRANSMISSION IN ROCK

The mining consequence of the excess energy can be perceived from the localised
superposition of the associated dynamic stresses on the equilibrium static stresses.
Even when the local static stress concentration may not be sufficient to cause failure
in the rock mass, superposition of the dynamic stresses related to the excess energy
may be sufficient to induce adverse mechanical response in the medium. Three simple
modes of adverse response may be identified immediately: the combined dynamic
and static stresses may exceed the strength of the rock mass; reduction of the normal
stress on a plane of weakness reduces the shear resistance of the surface, and may lead
to slip; tensile stresses may be induced, causing local relaxation in the rock structure.
All of these response modes may be expressed as deteriorating ground conditions in
the periphery of the mine opening.
This discussion suggests that, in the design of an opening, attention should be paid
to both static and dynamic loading of rock around the excavation and in the zone
of influence. Although the static stress distribution around an opening is determined
readily, the potential for extensive rock mass disintegration under static conditions is
indicated conveniently by the released energy W r . Further, although dynamic stresses
are not readily computed, the excess energy W e is readily determined from excavation-
induced tractions and displacements, and can serve as a useful index of dynamic
stresses. In practice, the excess energy and the released energy are closely related in
magnitude. The conclusion is that released energy constitutes a basis for excavation
design, since it is indicative of both static and dynamic stresses imposed by excavation.
This principle seems to be particularly appropriate in mining, where static stresses
frequently approach the in situ strength of the host rock mass and the extent of rock
mass failure needs to be considered.

10.3 Energy transmission in rock

Impulsive changes in the state of loading in a rock mass are associated with events such
as sudden crushing of pillars, sudden slip on planes of weakness, or sudden loading
or unloading of the surface of a blast hole or an excavation. Such changes result
in generation and transmission of body waves in the medium. As will be discussed
later, energy transmission in rock is accompanied by energy absorption, related to
both the microscopic and macroscopic structure of rock. However, a damped, elastic
progressive wave represents a fair conceptual model of energy transmission in a
rock mass. It is therefore useful to consider initially the mechanics of elastic wave
propagation in a medium. This topic is considered in detail by Kolsky (1963).

10.3.1 Longitudinal wave in a bar
Longitudinal wave propagation in a cylindrical bar is the simplest (one-dimensional)
case of elastic energy transmission. Transient motion in a suspended bar may be
initiated by an impulse applied at one end. A wave travels along the bar, as illustrated
in Figure 10.6a, resulting in a transient longitudinal displacement, u x (t), at any point.
To establish the nature of the transient motion and the associated transient state of
stress, it is necessary to take account of the inertial effects associated with induced
particle motion. An element of the bar of mass dM, shown in Figure 10.6b, is subject
to a longitudinal acceleration ¨ u x (t). To take account of the impulsive displacement of

277