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.

中文翻译：

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基于条件概率的岩土工程系统可靠性分析

摘要 在岩土工程中，存在多种失效模式，任何一种都会导致系统失效。系统可靠性既与每种失效模式的失效概率有关，也与它们之间的相关性有关，这与单一模式的可靠性分析明显不同。本文针对岩土工程应用的系统可靠性分析，提出了一种基于条件概率的高效系统可靠性分析方法，并在无处不在的Excel电子表格平台上实现。通过使用所谓的共源随机变量概念，将系统可靠性问题转化为条件独立失效事件的计算。该过程说明了具有三种破坏模式的圆形岩石隧道，具有四种破坏模式的四面体岩楔，以及具有两种和八种破坏模式的斜坡。此外，将所提出的方法与双峰边界方法和多元正态累积分布函数方法进行了比较。该研究还说明了在极限状态表面不是超平面的情况下，使用二阶可靠性方法 (SORM) 来细化可靠性指标并提高估计系统可靠性的准确性。