Probabilistic models in rock slope kinematic analysis employing the reliability engineering approaches and considering the variability of rock joint orientations

The variability of rock joint orientations significantly influences the type of slope failure, making probability methods crucial in kinematic analysis. This study aims to integrate probability kinematic analysis with reliability engineering methodologies like reliability block diagrams (RBD), event tree analysis (ETA), and fault tree analysis (FTA) to assess slope stability under joint orientation uncertainty. This study also examines the effect of different total friction angles ( Φ ) and lateral limit angles ( γ lim ) using the response surface methodology (RSM). The linear and circular goodness-of-fit tests determine the statistical distribution, allowing 100,000 random joint orientation values to be generated using Latin hypercube sampling (LHS). Results revealed that all three engineering reliability approaches yielded consistent output when integrated with probabilistic kinematic analysis. The probabilistic kinematic analysis and FTA methods analyses failure systems and effectively estimate the probability of occurrence. Whilst RBD evaluates successful systems and reliability. ETA offers both probabilities and is easier to implement, making it suitable for future applications. The RSM shows that the probability of occurrence increases when Φ is lower and γ lim is high, concluding that selecting the appropriate Φ is crucial for determining the probability of occurrence. However, in wedge failure, the regression coefficient ( β₂ ) ranges from 2 × 10 −17 to 0.0043 for γ lim between 80° and 90°, indicating a low effect on the probability of occurrence.