Problem definition

The engineering mechanics problem posed by underground mining is the prediction

of the displacement field generated in the orebody and surrounding rock by any

excavation and ore extraction processes. The rock in which excavation occurs is

stressed by gravitational, tectonic and other forces, and methods exist for determining

the ambient stresses at a mine site. Since the areal extent of any underground mine

opening is always small relative to the Earth’s surface area, it is possible to disregard

the sphericity of the Earth. Mining can then be considered to take place in an infinite

or semi-infinite space, which is subject to a definable initial state of stress.

An understanding of the notions of force, stress and strain is fundamental to a proper

and coherent appreciation of the response of a rock mass to mining activity. It was

demonstrated in Chapter 1 that excavating (or enlarging) any underground opening is

mechanically equivalent to the application, or induction, of a set of forces distributed

over the surfaces generated by excavation. Formation of the opening also induces a set

of displacements at the excavation surface. From a knowledge of the induced surface

forces and displacements, it is possible to determine the stresses and displacements

generated at any interior point in the rock medium by the mining operation.

Illustration of the process of underground excavation in terms of a set of applied

surface forces is not intended to suggest that body forces are not significant in the

performance of rock in a mine structure. No body forces are induced in a rock mass

by excavation activity, but the behaviour of an element of rock in the periphery of

a mine excavation is determined by its ability to withstand the combined effect of

body forces and internal, post-excavation surface forces. However, in many mining

problems, body force components are relatively small compared with the internal

surface forces, i.e. the stress components.

Some mine excavation design problems, such as those involving a jointed rock

mass and low-stress environments, can be analysed in terms of block models and

simple statics. In most deep mining environments, however, the rock mass behaves

as a continuum, at least initially. Prediction of rock mass response to mining therefore

requires a working understanding of the concepts of force, traction and stress,

and displacement and strain. The following discussion of these issues follows the

treatments by Love (1944) and Jaeger (1969).

In the discussion, the usual engineering mechanics convention is adopted, with

tensile normal stresses considered positive, and the sense of positive shear stress on

any surface determined by the sense of positive normal stress. The geomechanics

convention for the sense of positive stresses will be introduced subsequently.

Rock Mechanics

B. H. G. Brady