Rock Wedge Stability Analysis by a Level III Reliability Method

In fractured rock masses, discontinuities control the mechanical response of rock slopes. They even define the geometry of a potential failure, known a kinematically controlled failure. Hence, a proper characterization and description are needed to assess their stability. Accordingly, in this work, a reliability assessment of rock wedges' stability was performed by a Monte Carlo simulation. The orientation of discontinuities was modeled as a random variable that follows the rotationally symmetric Fisher distribution. We developed an algorithm to define the modes of failure based on the orientation of planes, which was articulated within a methodology to compute the factor of safety of rock wedges explicitly. The algorithm systematically defines a set-up of joint planes. Then it verifies the relative location of the slope orientation on that set-up, which is related to the mode of failure of the rock wedge. The proposed algorithm was validated by comparison against commercial software; both yielded the same results. Besides, the probability of failure and the factor of safety probability function of removable wedges were computed for different concentration parameters. Reliability assessment showed the importance of properly characterizing the variability of joint orientation since the concentration highly influences the computed probability of failure. In addition, a proper definition of removable wedges by kinematic analysis is required before computing the factor of safety because many combinations of planes do not lead to unstable wedges, which reduces the probability of failure. Otherwise, it is overestimated. Finally, we recommend further work on rock wedge reliability assessment involving rotational nonsymmetric distribution.