Stochastic V-H-M failure envelopes of strip footings on spatially varying clayey slopes with nonstationary characteristics

Shallow foundations are subjected to combined loading under various environmental and operational conditions. Conventional shallow foundation design often neglects the inherent spatial variability of soil properties, leading to either unconservative or overly conservative failure envelopes. This limitation becomes more critical in the presence of non-stationary soil characteristics and sloping ground conditions, which introduce significant uncertainties under different load combinations. To address these issues, this study investigates the probabilistic failure envelopes of strip footings on spatially varying clayey slopes with linearly increasing mean undrained shear strength with depth. Both stationary and non-stationary soil conditions are considered for different loading combinations. The effects of key influencing parameters, including slope angle, footing location, correlation lengths, coefficient of variation, and strength gradient, are systematically examined. The results indicate that the coefficient of variation and correlation lengths significantly influence the size and shape of the failure envelopes, whereas the strength gradient parameter has a comparatively smaller effect. The direction of load components is also found to play a crucial role in altering the failure envelopes. Additionally, a comparative assessment between deterministic factor of safety-based analysis and probability of failure-based stochastic analysis is presented.