Conditional probability-based system reliability analysis for geotechnical problems

Abstract

In geotechnical engineering, multiple failure modes exist, and any one can contribute to the failure of a system. System reliability is related to both the probability of failure of each failure mode and the correlations between them, which is obviously different from the reliability analysis of a single mode. This paper focuses on system reliability analysis for geotechnical engineering application, and proposes an efficient system reliability analysis method based on conditional probability, which is implemented in the ubiquitous Excel spreadsheet platform. By using the so-called common source random variables concept, the system reliability problem is converted to the calculation of a conditionally independent failure event. The procedure is illustrated for a circular rock tunnel with three failure modes, a tetrahedral rock wedge with four failure modes, and a slope with two and eight failure modes. In addition, comparisons are made between the proposed method with the bimodal bounds approach and the multivariate normal cumulative distribution function method. The study also illustrates the use of the second-order reliability method (SORM) to refine the reliability indices and improve the accuracy of the estimated system reliability in a case where limit state surfaces are not hyperplanes.