System reliability analysis of rock wedge stability considering correlated failure modes using sequential compounding method

Probabilistic analysis of wedge failure has been used as an effective tool to evaluate inherent uncertainty of the variables. In this paper, a system reliability analysis of rock wedge stability is presented. To perform reliability analysis a cut-set system is used for wedge analysis. The reliability indices of the individual components and the correlations between the components are determined by the First-Order Reliability Method (FORM). The Sequential Compounding Method (SCM) is used as an efficient numerical procedure to determine the reliability indices of failure modes and system reliability index, considering correlations between failure modes which are calculated by defining equivalent linear safety margin for each failure mode. The predicted system reliability indices and corresponding probabilities of failure from the proposed method are compared with those of the Monte Carlo simulation (MCs). The results of sensitivity and parametric analyses show that the water pressure parameters are the most effective parameters in rock wedge stability. It is also demonstrated that the relative influences of failure modes on the system reliability differ considerably. Furthermore, the probabilistic rock wedge stability curves are presented to evaluate the system probability of failure as a function of safety factor and its coefficient of variation.