5
Strain is a change in the relative configuration of points within a solid. One
can study finite strain or infinitesimal strain-both are relevant to the
deformations that occur in the context of the principles of rock mechanics
and their engineering applications. Large-scale strain can be experienced
underground as illustrated in Fig. 5.1, where there is severe deformation
around a coal mine access tunnel. When such displacements are very small,
one can utilize the concept of infinitesimal strain and develop a strain
tensor directly analogous to the stress tensor. Thus, we will first discuss
finite strain and then infinitesimal strain.
5.1 Finite strain
Strain may be regarded as normalized displacement. If a structure is
subjected to a stress state, it will deform. However, the magnitude of the
deformation is dependent on the size of the structure as well as the
magnitude of the applied stresses. In order to render the deformation as a
scale-independent parameter, the concept of strain (which in its simplest
form is the ratio of displacement to the undeformed length) is utilized. Such
displacements can also occur naturally in rock masses through the
application of tectonic stresses resulting from past and present geological
processes. Some excellent examples are shown in Ramsey and Huber
(1983).
The displacements, whether natural or artificial, can be complex; an
example is shown schematically in Fig. 5.2. It should also be noted that
strain is a three-dimensional phenomenon that requires reference to all
three Cartesian co-ordinate axes. However, it is instructive, in the first
instance, to deal with two-dimensional strain: once the fundamental
concepts have been introduced, three-dimensional strain follows as a
natural progression.
In order to provide a structure for our analysis of two-dimensional strain,
we will consider the separate components of strain. There are normal
strains and shear strains, as illustrated in Fig. 5.3.
As with normal stress and shear stress components, it is much easier to