Implications for in situ stress 83
and for orthotropy (T,, =The reader should note that, in order to simplify these relations, use has
been made of various complementary Poisson's ratios (e.g. vlz instead of
vz1EI/Ez). These equations are from Amadei ef al. (1983) and demonstrate
conclusively that, for certain combinations of the respective elastic
constants, the horizontal components can be significantly different. In fact,
an orthotropic model is probably a much better representation of a
discontinuous rock mass with three perpendicular discontinuity sets than
an isotropic model.
A final point is that, given the 21 independent components of the
compliance matrix, the correct engineering approach to the problem of
modelling rock masses would be to establish to what extent the compliance
matrix can validly be simplified. In other words, the logic would be to assume
complete anisotropy unless we have reason to assume otherwise.
However, because of cost constraints and the practicalities of engineering,
of the order of 99% of all analyses that have been conducted have contained
the assumption that the rock mass is fully isotropic with only two elastic
constants. In the majority of the remaining cases, transverse isotropy has
been assumed; and in a few isolated examples, orthotropy (with nine elastic
constants) has been assumed. To the authors' knowledge, no one has either
measured the 21 constants or conducted an analysis assuming a
compliance matrix with non-zero components. There are lessons here
concerning the relation between rock mechanics and its application to rock
engineering, i.e. the theory and the practice.