Stochastic prediction of the failure of an oblique load of a shallow foundation on cohesionless soils with a Drucker Prager constitutive model

Abstract

This study investigates, in a quantitative probabilistic framework, the influence of soil parameter uncertainty on the failure load and displacement of a shallow footing subjected to oblique loading. A stochastic finite element formulation is implemented using the Drucker–Prager constitutive model to represent the nonlinear response of cohesionless soils. Uncertainty is introduced in the unload–reload compressibility parameter \(\kappa \), the critical state line slope c, and the hydraulic conductivity k governing Darcy flow. The spatial variability of the material properties is modeled through both random variables and random fields, while Monte Carlo simulations are accelerated using Latin Hypercube Sampling. The results demonstrate that the failure load and corresponding displacement follow approximately Gaussian probability density functions despite the strongly nonlinear mechanical response. Increasing load obliquity leads to a systematic increase in the mean failure load and displacement, while the dispersion of the stress field at failure remains relatively unaffected. The proposed framework enables reliable estimation of the probabilistic failure envelope of cohesionless soils under oblique loading, accounting simultaneously for nonlinear constitutive behavior, hydraulic coupling, and spatial variability. The methodology is general with respect to geometry and loading configuration and provides a consistent basis for reliability-informed assessment of shallow foundations.