Effect of discontinuities on the proximate state of stress 65could well be a good representation for rocks containing three mutually
perpendicular sets of discontinuities. It can be seen from the expressions
for k in Fig. 4.18 that the horizontal stress components can be different for
certain values of the elastic constants in the orthotropic case.
It is a consequence of the assumption of transverse isotropy that the two
horizontal principal stresses will be equal. However, in the case of
orthotropy, the horizontal stresses can take on different values. Thus, it is
in this last case that we find the conditions as encountered in the natural
rock mass. In fact, there is nothing surprising about having one component
of the horizontal stress field being much higher than the other; the apparent
inconsistency lies in the oversimplication of the rock mass as a purely
isotropic material. This subject will be amplified in Chapter 8 on rock
masses.
4.8.4 Discontinuities
The discussion in the earlier sections was about accuracy and precision, i.e.
bias and spread in the measurements. We noted that, in the case of the
vertical stress component, the prediction based on the overlying rock
weight was more or less accurate-in the sense that the prediction was a
good fit to the data-but there was a spread in the results. The situation
with the horizontal stress component was more complicated because of the
unexpectedly high values of the horizontal stress components and the large
spread of values. One of the most important factors causing the spread of
results in both cases is the fact that the rock is not a continuum. All rocks
are fractured on various scales, so the rock mass is a discontinuum and the
internal stress distribution reflects this geometry. Thus, we must ask the
questions: ’To what extent is the stress state affected in the region of a rock
fracture?’, ‘How is this affected by scale?’, and ’How does this affect the
results of a stress determination programme?’ These are the subject of the
discussion presented in the next section.
4.9 Effect of discontinuities on the proximate
state of stress
In Fig. 4.19 we show just one example of the influence that a rock fracture
can have on the overall stress state, in this case illustrated for a plane strain
case and a far-field hydrostatic (i.e. q = o2 = os) stress state. It is clear from
the figure that both the principal stress orientations and magnitudes are
dramatically perturbed by the presence of the fracture. Note also that we
have purposely not included any absolute scale in this figure. The elastic
modelling used here could represent a fracture of any scale, from a very
small flaw in a crystal, through a single rock joint in an otherwise
unfractured rock mass, to a fault in a tectonic plate. This has major
consequences for stress determination strategies and interpretation of
results. Clearly, for a discontinuity of the order of 10 km long, all stress
measurements in an adjacent proposed engineering site would be
affected by the presence of the discontinuity-but perhaps this is the stress
state that should be measured. Conversely, the single rock fracture could