Analysis of stepped-path sliding with three joint sets

Sliding along a stepped path formed by two or more joint sets is more common than an ongoing discontinuity in rock slopes. The solution to the problem of sliding along a stepped path formed by two joint sets (i.e. one major and one cross joint set) has been studied previously. However, exists no work exists on the analysis of stepped path sliding with three joint sets.

To solve the problem of stepped path sliding incorporating three joint sets two approaches are described in this paper. In the first approach a simulation model which generates possible stepped paths is proposed. In the second approach the problem is first separated into two sub-problems (namely, major joint with one of the cross joints as subproblem no. 1, and major joint with the other cross joint as sub-problem no. 2) for which the probability of failure can be easily obtainable, and then the probability of failure for three-joint case is calculated using the results of two sub-problems. Formulations for the second approach, which is much simpler than the first one, is given and used to solve some example problems. Results indicate that the inclusion of a second cross joint set increases the probability of failure.