Probabilistic bearing capacity analysis of square and rectangular footings on cohesive soil slopes considering three-dimensional rotational anisotropy

Abstract

The influence of soil variability on the probabilistic bearing capacity of strip footings near slopes has been extensively studied, particularly under short-term undrained conditions. However, these investigations, predominantly based on the plane-strain assumption, fall short in accurately estimating the bearing capacity of square and rectangular footings and in capturing the spatial variability of soils. This study focuses on short-term undrained conditions and employs the random finite element method (RFEM) and Monte Carlo simulation (MCS) techniques to explore the effect of rotational anisotropy on the bearing capacity response and failure probability of a square and rectangular footing-cohesive slope system under a three-dimensional (3D) framework. The findings reveal that the rotation angles of soil strata significantly impact both the mean and coefficient of variation of the bearing capacity, with distinct variation patterns emerging for different footing orientations and aspect ratios. Typical failure patterns are identified, illustrating the correlation between the bearing capacity response, the footing orientations and aspect ratios, and the extension direction of plasticity. The probabilistic results are presented as probability density functions (PDF) and cumulative distribution functions (CDF) for various rotation angles around the x-axis and y-axis and for different L/B ratios of the footings. Additionally, detailed design tables, including failure probability results and corresponding safety factors for specific target failure probabilities, are provided to guide engineering applications.