Bayesian-based probabilistic kinematic analysis of discontinuity-controlled rock slope instabilities

Discontinuity-controlled rock slope instability analysis is a difficult problem in the field of geotechnical engineering. Many random discontinuities existing in rock masses will negatively influence rock slope stabilities. This study is aimed to determine the failure angle (apparent angle of the sliding surface in the direction of the cut face) of potentially unstable blocks in discontinuity-controlled rock slopes in Dalian, China. For this purpose, a detailed discontinuity survey was conducted in seven exploratory trenches and two outcrops. Possible failure modes of the slope were predicted. Thus, according to theories of kinematics and probability statistics, it is possible to determine the failure angle of potentially unstable blocks with a new method that combines the results of Bayesian inference, probabilistic kinematic analysis and stereographic projection. Bayes' formula was used to estimate the scientific value of the slope failure angle. A computer program called KINEMATIC was written to perform probabilistic kinematic analysis. Stereographic projection was used to verify the values obtained from the methods. Through the methodology proposed in the study, the failure angle of each excavation slope could be well calculated.