Reliability Analysis of Rock Wedges

Abstract

The stability analyses of tetrahedral wedges in rock slopes are commonly conducted using the versatile sequential vectorial operations or stereographic projection methods. This paper presents an alternative approach using closed-form equations, for cases where the upper ground surface dips in the same direction as the slope face. The equations allow determination of kinematic admissibility, the modes of sliding (whether along two planes or a single plane), and the corresponding factor of safety. Since the factor of safety does not reflect the uncertainty of parameters, the Hasofer-Lind second moment reliability index is explored. Useful insights are obtained based on the perspective of an ellipsoid expanding in the original space of the random variables. The proposed perspective also suggests a practical method of computing the reliability index using the Solver tool available in a spreadsheet software. First-order probability bounds based on reliability indices of a tetrahedral wedge are in good agreement with the results of Monte Carlo simulation. The need to account for multiple failure modes and to consider all surfaces bounding the failure domain is demonstrated.