166 Anisotropy and inhomogeneityin a specific horizontal direction. We also noted that properties such as the
rock mass deformability and permeability will be functions of the discon-
tinuity frequency, and hence will be anisotropic in nature. In the case of
discontinuity frequency, we showed explicitly the variation with direction.
For deformability, the architecture of the elastic compliance matrix takes into
account the linking between stresses and strains and hence also explicitly
quantifies some anisotropy. It was also explained in Chapter 9 that
permeability is a second-order tensor with three principal permeabilities,
again explicitly characterizing some anisotropy via the tensor. Figures
illustrating these concepts have been included in Chapters 7-9.
However, not all rock properties have anisotropy incorporated into their
characterization. For example, as was asked at the beginning of the chapter,
how do we characterize the anisotropy of compressive strength?
Compressive strength is usually assumed to be a scalar value, which is by
definition directionless: measurements of compressive strength should be
qualified with information on the direction of loading relative to the rock
structure.
Figure 10.2 demonstrates the anisotropy of compressive strength
recorded for a series of tests performed on a slate. In this case, the
anisotropy can be characterized through application of the single plane of
weakness theory (discussed in Chapter S), which does have directionality
built into its formulation.
One should be very careful with the measurement of any assumed scalar
property in rock mechanics and rock engineering, because there is no in-
built directionality in the characterization of such a property. The three
most frequently measured parameters in rock mechanics and rock engi-
neering are discontinuity frequency, RQD and point load strength. These
are almost always (but incorrectly) assumed to be scalar properties (and
hence imply isotropy), whereas, they are actually higher-order parameters
(implying anisotropy).
Where it is economically viable, rock masses should always be assumed
to be anisotropic unless it can be demonstrated that isotropy is a sufficient-
ly accurate representation for the particular rock mass and engineering
objective.
10.3 Inhomogeneity
The word 'inhomogeneity' is derived from the two Greek words homos
(meaning the same, with the Latin prefix in- forming the negative) and
genos (meaning kind). Anisotropy means having different properties in
different directions at a certain location, with the location unspecified. Now
we consider inhomogeneity, which means having different properties at
different locations given Q certain measurement direction. If the measurement
direction is not specified, then a compound of the two aspects could occur.
We saw that anisotropy is intrinsic to the very definition of many
geotechnical parameters. This is not the case for inhomogeneity, and so we
must have recourse to statistical and geostatistical techniques. Under-
standing the inhomogeneity of rock can be important. Indeed, in many
cases, we may be interested in the extreme values rather than the mean