Probabilistic failure envelopes of strip foundations on soils with non-stationary characteristics of undrained shear strength

This paper investigates probabilistic failure envelopes of strip foundations on spatially variable soils with profiles of undrained shear strength, s u , linearly increasing with depth using lower-bound random finite-element limit analysis. The spatially variable s u is characterised by a non-stationary random field with linearly increasing mean and constant coefficient of variation (COV) with depth. The deterministic uniaxial capacities and failure envelopes are first derived to validate the numerical models and provide a reference for the subsequent probabilistic analysis. Results indicate that the random field parameters COV su (the COV of s u ) and Δ (dimensionless autocorrelation distance) have a considerable effect on the probabilistic normalised uniaxial capacities, which alters the size of the probabilistic failure envelopes. However, an insignificant effect of COV su and Δ on the shape of probabilistic failure envelopes is observed in the V–H, V–M and H–M loading spaces, such that failure envelopes for different soil variabilities can be simply scaled by the uniaxial capacities. In contrast to COV su and Δ, the soil strength heterogeneity index κ = μ k B/μ su0 has the lowest effect on the probabilistic normalised uniaxial capacity factors, but the highest effect on the shape of the probabilistic failure envelopes. A series of expressions is proposed to describe the shape of deterministic and probabilistic failure envelopes for strip foundations under combined vertical, horizontal and moment (V–H–M) loading.