172 Anisotropy and inhomogeneityMoreover, if the semi-variogram statistic is obtained for different dir-
ections, the anisotropy of the rock mass inhomogeneity can also be
studied.
Case (i): nugget effect. No correlation between sample values. Consist-
ent inhomogeneity across the site. Independent isolated values, like
nuggets. This is the model assumed in conventional statistics.
Case (ii): hear effect. There is some basic variation with repeated samples
(i.e. as evidenced at h = 0). Correlation then linearly decreases with
sample separation distance.
Case (iii): 'spherical' semi-variogam. At sample separations less than the
range (the range is the sample separation distance, h, for which there
is a correlation), there is some correlation between the sample values:
this is the region of correlation. The correlation reduces rapidly as h
increases.
Case (iv): 'Gaussian' semi-variogram. Similar to Case (iii) but the region of
better correlation extends to about half the range.
(b) Case (i): not at all; Case (ii): about 25 m; Case (iii): about 10 m; Case
(iv): about 25 m.
The semi-variogram methodology using data from known locations
and the associated geostatistical techniques such as kriging to predict
rock property values in other locations was originally developed for
characterizing and predicting ore grades for mining. This question and
answer have been included to illustrate the potential value of geostat-
istical techniques for characterizing rock mass property data: it is a tool
ideally suited for rock characterization but currently is under-used.10.3 Additional points
In terms of the DIANE nature of real rock masses, almost all rock
masses are fractured and hence Discontinuous. The fractures are critical
because mechanical failure usually occurs through the presence of a
major low-strength feature, such as reactivation of movement on a
fracture, rock blocks moving, or the influence of water in the fractures.
We should always assume that the rock mass is fractured.
Similarly, it should be assumed that the rock mass is Inhomogeneous,
unless there is some evidence that the degree of inhomogeneity is not
significant for the rock engineering design study underway. The best
method of characterizing and simplifying inhomogeneity is to divide the
rock mass into structural domains such that the property values can be
assumed essentially constant within a domain, and the best method for
the choosing of structural domains is commonsense geology supported
by sampling and geostatistics.
Remember also that Anisotropy is often 'built into' the parameters
being used. We saw that stress and strain, represented by second-order
tensors, have principal axes. Thus, the possibility of an anisotropic stress
state is automatically included in the definition of stress with the three
principal stresses acting in mutually orthogonal directions. Similarly, in