Development of a probabilistic kinematic wedge sliding analysis procedure and application to a rock slope at a hydropower site in China

In performing kinematic wedge stability analysis, in practice, it is usually assumed that the wedge is a “Standard Wedge” (the term is explained in the paper) sliding along the line of intersection of the two discontinuity planes. Intersection of two discontinuities with the lower and upper rock slope surfaces can result in forming Standard Wedges, Overlying Wedges and No Wedges. Vector procedures are developed in the paper to differentiate the aforementioned formation modes for the wedges. Vector procedures are then given to calculate the sliding modes, sliding directions, maximum safe slope angles and factor of safety for the Standard and Overlying wedges. Procedures are also given to incorporate the variability of discontinuity orientations and strength and to calculate the instability cumulative probabilities corresponding to different cut slope dip angles. All these procedures are incorporated in a computer code, named PKWSAC. The developed procedure and the computer program were then validated by applying them to three examples and comparing the results obtained through this procedure with the results obtained through Lucas’ stereographic procedure [Lucas JM (1980) Int J Rock Mech Min Sci Geomech Abstr 17:57–61]. The validated procedure was then applied to a rock slope at a hydropower site in China to perform both deterministic and probabilistic kinematic wedge stability analyses. The paper also shows a comparison between the deterministic and probabilistic analyses results.