The application of limit analysis to the study of the basal failure of deep excavations in clay considering the spatial distribution of soil strength

Deterministic calculations are a traditional way of determining the limit loads of geotechnical problems. Over the last two decades, probabilistic methods have increasingly been applied to such problems. In this paper, the finite element program mechpy, developed by the authors’ team, is adapted to, firstly, generate samples of the spatial pattern of the undrained shear strength using the log-normal distribution and, secondly, perform upper- and lower-bound limit analysis calculations using those samples. This procedure is applied to determine the mean basal stability number in several cases with different geometries and representative values of the undrained shear strength standard deviation and of the scale of fluctuation. The basal stability numbers obtained are compared with those from the corresponding deterministic calculations.