System reliability analysis of rock slope considering multiple correlated failure modes

It is aimed to propose a systematic quantitative method for system reliability analysis of rock slope with plane failure considering multiple correlated failure modes. A probabilistic fault tree approach is presented to model system reliability of rock slope considering multiple correlated failure modes. The versatile 4-parameter β distribution is used instead of a normal distribution or a lognormal distribution, which is adopted for describing the location of tension crack, the cohesion along the failure surface and the friction angle. The truncated exponential distribution is used for the percentage of tension crack filled with water. The adaptive importance sampling (AIS) method is employed to perform the system reliability analysis of rock slope with plane failure. System reliability sensitivity with respect to distribution parameters of random variables is performed. Results from a numerical example indicate that the system reliability of rock slope considering multiple correlated failure modes can be effectively evaluated using the probabilistic fault tree approach, which will be underestimated without considering the correlation between failure modes. The failure mode of block A failing without interaction force due to block B has the higher probability of failure than that for the failure mode of block A with interaction force due to block B. Both the mean sensitivity coefficient and the standard deviation sensitivity coefficient indicate that the percentage of tension crack filled with water and the location of tension crack are significant random variables with higher sensitivity coefficients. Therefore, to improve the slope stability effectively, a good drainage system of the slope should be designed and a detailed geological investigation of discontinuities in the rock mass should be conducted. The mean sensitivity coefficient and the standard deviation sensitivity coefficient are strongly related and both can be used to identify key contributing random variables.