Comparison of Point Estimate and Monte Carlo probabilistic methods in stability analysis of a deep excavation

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.