System reliability analysis of rock slope stability involving correlated failure modes

This paper aims to propose a systematic quantitative method for system reliability evaluation of rock slope with plane failure involving multiple correlated failure modes. A probabilistic fault tree approach is presented to model system reliability of rock slope. An n-dimensional equivalent reliability method is employed to perform the system reliability analysis of the slope involving multiple correlated failure modes. Reliability sensitivity analyses at three different levels, namely, the single limit state function level, single failure mode level, and system reliability level, are carried out to study the effect of variables on reliability. An example is presented to demonstrate the validity and capability of the proposed approach. The results indicate that the system reliability of rock slope involving multiple correlated failure modes can be evaluated efficiently using the proposed approach. The system probability of failure is overestimated if the correlations between different failure modes are ignored. The relative importance of different failure modes to the system reliability can differ considerably. The sensitivity coefficients of basic random variables strongly depend on the selected sensitivity analysis level. The system reliability is sensitive to the location of the tension crack and the percentage of the tension crack filled with water.