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Once the shear strength of the discontinuities (persistent discontinuities) or equivalent discontinuities (non-persistent discontinuities containing rock bridges) have been defined, the directional strength of the rock mass can be defined as follows.
As discussed by Jennings (1972), these equations contain a number of important implied assumptions and become much more complex in the case of non-coplanar discontinuities and/or a rock mass with two discontinuity sets parallel to the slope orientation
is the coefficient of continuity along the rupture plane given by:
In this case the equivalent strength parameters can be computed (Jennings 1972):
The definition of these equivalent shear strength parameters can be done using closed-form solutions (e.g. Jennings 1972). The simplest case is a planar rupture through coplanar joints and rock bridges, as shown in Figure 5.44.
Figure 5.41: Polar plots illustrating the effect of discontinuity sets parallel to the slope in the shear strength of the rock mass. The magnitude of the shear strength for a given orientation q is equal to the radial distance from the origin to the red curve
Unless the effect of rock bridges is accounted for, the shear strength of the discontinuities will be underestimated. Detailed discussions can be found in Jennings (1970, 1972), Einstein et al. (1983) and Wittke (1990). In a rock slope with non-persistent discontinuities a step- path failure surface will occur through a combina- tion of discontinuities and rock bridges (Figure 5.43). An ‘equivalent discontinuity’ can be assigned to this step-path failure (Figure 5.43) and allocated ‘equivalent’ shear strength parameters.
if the discontinuities are non-persistent and their continuity is interrupted by rock bridges (see Figures 5.42 and 5.43) their shear strength will increase considerably.
if the discontinuities are persistent and can be assumed continuous for the slope being studied then the shear strength of the discontinuities can be assessed as described in section 5.3, and values for the cohesion and friction angle of the discontinui- ties can be defined;
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