Basal heave stability analysis of undrained excavations in a limit analysis framework: deterministic and probabilistic approaches

This study introduces a new and efficient methodology for the stability analysis of excavations, accounting for soil variability, by integrating an improved limit analysis (iLA) method with the Polynomial Chaos Kriging (PCK) and Monte Carlo Simulation (MCS) technique. First, the iLA method is proposed for deterministic analysis, incorporating factors such as the soil–wall interface, excavation geometry, and wall embedment depth. This approach allows for the estimation of the basal heave safety factor using the strength reduction method in combination with a bisection optimization technique. The accuracy and versatility of the proposed iLA method are demonstrated through comparisons with numerical simulations and four existing analytical methods. Next, the study introduces an active learning method, PCK–MCS, and integrates it with the iLA method to perform probabilistic analyses of excavation stability. The efficiency and effectiveness of the final integrated methodology, iLA–PCK–MCS, are validated through comparisons with established methods, including direct MCS, Subset Simulation, and Kriging- and Sparse Polynomial Chaos Expansion-based MCS. Finally, leveraging the computational efficiency of the iLA–PCK–MCS framework, a parametric study is conducted to provide insights into the effects of soil uncertainties, the soil–wall interface, and wall embedment depth on excavation stability. The methods presented in this study are expected to advance both deterministic and probabilistic analyses in excavation projects by offering a highly efficient and accurate tool for evaluating basal heave stability.