Application of matrix-based system reliability method in complex slopes

Complex slopes are characterized by large numbers of failure modes, cut sets or link sets, or by statistical dependence between the failure modes. For such slopes, a systematic quantitative method, or matrix-based system reliability method, was described and improved for their reliability analysis. A construction formula of event vector c (E) was suggested to solve the difficulty of identifying any component E in sample space, and event vector c of system events can be calculated based on it, then the bounds of system failure probability can be obtained with the given probability information. The improved method was illustrated for four copper mine slopes with multiple failure modes, and the bounds of system failure probabilities were calculated by self-compiling program on the platform of the software MATLAB. Comparison in results from matrix-based system reliability method and two generic system methods suggests that identical accuracy could be obtained by all methods if there are only a few failure modes in slope system. Otherwise, the bounds by the Ditlevsen method or Cornell method are expanded obviously with the increase of failure modes and their precision can hardly satisfy the requirement of practical engineering while the results from the proposed method are still accurate enough.