170 Anisotropy and inhomogeneity
Unifmdy rlodDlll orisnutioor
Ncgauve cxpocn(i.l CYC lengths
Isotropic linearly increasing joint frequenciesU"if0d)r Radom Idoms
Ncguiivc exposotill u.ce lcogtbs
3 joint seb(b) Statistically inhomogeneous. having
radial 1inc.r driR
Figure 10.4 Computer-generated rock jointing patterns (from LaPointe and
Hudson, 1985). (a) Statistically homogeneous. (b) Statistically inhomogeneous,
having radial linear drift.requirements, but the possibilities for extending the classical solutions in
this way are limited. This not only applies to the anisotropy of the material
properties, but also to anisotropy of the problem geometry.
With reference to the plane strain solution for the stresses around
underground excavations, there are 'classical' solutions for circular and
elliptical openings and, through the use of complex variables, various
pseudo-rectangular shapes. However, extensions to, for example, the inter-
action between two parallel openings are not possible-this is the realm of
engineering approximations. Thus, it is unlikely that our four main 'problem
attributes' can be incorporated as extensions of classical solutions.
Over the last two decades, there has been development in computer-
based numerical solutions which are specifically designed to deal with
more complex geometry and material properties. These techniques include
finite difference, finite element, boundary element and distinct element
formulations, providing the capability of incorporating discontinuousness,
anisotropy, inhomogeneity and more complex constitutive behaviour. With
this capability, the types of rock properties that can occur need to be studied
further.
An initial step in dealing with the four attributes is to consider the
distinction between rock properties at a point and rock properties over a
volume. In other words, there are some properties, such as density, which
can be considered as essentially point properties and do not depend on the
discontinuites. There are other properties, such as secondary permeability,
which are dictated by the presence of discontinuities and cannot be consider-
ed as point properties: these are associated with a certain volume of rock. In
Table 10.1, we present examples of both point and volume properties.
The distinction between the two types of property is not cut and dried.
For example, the state of stress in a rock mass is, of course, influenced by
the discontinuites; but considering the definition of stress at a point (which