Engineering Rock Mechanics

Substituting these into the Mohr-Coulomb criterion, I TI = cw + on tan &,

and rearranging gives

where cw and &,, are the cohesion and the angle of friction for the discon-
tinuity @.e. plane of weakness), and pW is illustrated in Fig. 8.4. The plot of
the equation in Fig. 8.4 shows the minimum strength and also the angles
at which the sample strength becomes less than that of the intact rock.
An alternative presentation is via the Mohr's circle representation, as
shown in Fig. 8.5. The Mohr-Coulomb failure loci for both the intact rock
and the discontinuity are shown. We also show three Mohr's circles, A, B
and C, representing the lowest strength, an intermediate case and the
highest strength.

Circle A represents the case when the failure locus for the discontinuity

is just reached, i.e. for a discontinuity at the angle 2pwO = 90" + h".

Circle B is a case when failure can occur along the discontinuity for a

range of angles, as indicated in the figure.

Circle C represents the case where the circle touches the intact rock

failure locus, i.e. where failure will occur in the intact rock if it has not

already done so along the discontinuity.

The importance of these different failure mechanisms will be made clear in
later chapters, when we consider the stresses around excavations in rock
containing discontinuities. According to the circumstances, failure can either
occur along the discontinuities or through the intact rock, depending on the
relative orientations of the principal stresses and the discontinuities.

z = c + on tan+

,-Intact rock

, , ,

't , , ,

2p, = 90 + +w Range of angles 2p, =^90 + +

Figure 8.5 Mohr's circle representation of the possible modes of failure for rock

containing a single plane of weakness.