Automated Identification and Quantification of 3D Failure Domains in Spatially Variable Soil Slopes Under Rectangular Footings

Accurate identification of slope failure mechanisms under shallow foundations is essential for reliable risk assessment and reinforcement design. However, existing studies often neglect the spatial variability of soil properties and the influence of footing shape. This study develops a non-intrusive stochastic finite difference framework integrating random field theory, Monte Carlo simulation, and a Gaussian mixture model to automatically characterize three-dimensional slope failure domains under rectangular footing loads. Results show that slope failure mechanisms are primarily governed by the footing aspect ratio and the scale of fluctuation in soil strength. Square footings mainly induce shallow slope face failure, whereas rectangular footings significantly increase the probability of deep toe failure as the scale of fluctuation increases. Stochastic analyses generally yield larger mean failure volumes than deterministic analyses. Risk assessment further indicates that risk levels are primarily controlled by the absolute failure volume at low safety factors, whereas failure variability becomes increasingly influential at higher safety factors.