Geotechnical engineers have long used the lumped factor of safety approach in design of retaining walls. In recent years, uncertainty inherent in soil properties has caught more attentions from researchers, thus reliability analyses are used widely. In short, combining the probabilistic and deterministic analysis is common practice nowadays and failure probability calculated by risk analysis is a kind of complement of safety factor. In this paper, reliability analysis of a deep excavation is presented using two probabilistic methods called Point Estimate Method (PEM) and Monte Carlo Simulation (MCS) method. Horizontal displacement of the excavated wall, as well as safety of factor, are adopted as a basis for assessing the performance stability of the system. The paper explains why probabilistic analysis with numerical methods is challenging, and how PEM and MCS can be used to calculate the statistical moments of output variables and to estimate probability of failure. The results are presented and compared in terms of statistical moments, probability of occurrence and most likely values at every stage of construction.

中文翻译：

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点估计与蒙特卡罗概率方法在深基坑稳定性分析中的比较

岩土工程师长期以来在挡土墙设计中一直使用集总安全方法。近年来，土壤属性固有的不确定性引起了研究者的更多关注，因此可靠性分析得到了广泛的应用。简而言之，将概率分析和确定性分析相结合是当今的普遍做法，通过风险分析计算出的故障概率是安全系数的一种补充。在本文中，使用点估计法（PEM）和蒙特卡洛模拟（MCS）方法两种概率方法对深基坑进行可靠性分析。开挖墙的水平位移以及安全系数作为评估系统性能稳定性的基础。本文解释了为什么用数值方法进行概率分析具有挑战性，以及如何使用PEM和MCS来计算输出变量的统计矩并估计故障概率。呈现并比较结果，包括统计矩，发生概率和施工各个阶段的最可能值。