Page 35 - Rock Mechanics For Underground Mining

2 Stress and infinitesimal strain

2.1 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 there-
fore 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.

2.2 Force and stress

The concept of stress is used to describe the intensity of internal forces set up in a
body under the influence of a set of applied surface forces. The idea is quantified by
defining the state of stress at a point in a body in terms of the area intensity of forces
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