Engineering Rock Mechanics

Stress-controlled instability mechanisms 357

Figure 19.18 Elliptical openings in transversely isotropic rock.

Slip on pre-existing discontinuities. Another possibility is that the rock has
been weakened by the presence of a pre-existing discontinuity. Assume
that this discontinuity does not affect the elastic constants in any way, and
so the usual CHILE assumption is valid, but the strength of the rock is
reduced on the discontinuity. The extent of any potential zone of instability
can be established by considering whether the induced stresses locally
satisfy the discontinuity shear strength criterion.
In Fig. 19.20, there is a discontinuity in the vicinity of a circular opening.
The specific procedure is then to take a point on the discontinuity to start
(for computational convenience, we have chosen the closest point on the
discontinuity to the centre of the opening), evaluate the stress components
at the point using the Kirsch equations, transform these components into
normal and shear stress components acting on the discontinuity, and finally
substitute them into the Mohr-Coulomb (or any other suitable) criterion.
This procedure enables a graph of the ratio of actual strength to required
strength versus the parameter d to be drawn, and an example (for a
cohesionless discontinuity) is also shown in Fig. 19.20.
From this curve, there is an indication of the location and intensity of the
damage the discontinuity might sustain as a result of the engineering. In
the graph, the line representing tan 4 is drawn and hence the extent of
the zone of potential slip is studied. The length of the zone will depend on