Probabilistic analyses of slopes and footings with spatially variable soils considering cross-correlation and conditioned random field

This paper presents probabilistic analyses of slopes and strip footings, with spatially variable soil modeled by the random field theory. Random fields are simulated using Latin hypercube sampling with dependence (LHSD), which is a stratified sampling technique that preserves the spatial autocorrelation characteristics. Latin hypercube sampling with dependence is coupled with polynomial chaos expansion (PCE) to approximate the probability density function of model response. The LHSD-PCE approach is applied to probabilistic slope analyses for soils with cross-correlated shear strength parameters, and is shown to be more robust than raw Monte Carlo simulations, even with much smaller numbers of model simulations. The approach is then applied to strip footing analyses with conditioned random fields of Young's modulus and shear strength parameters, to quantify the reductions in settlement uncertainty when soil samples are available at different depths underneath the footing. The most influential sampling depth is found to vary between 0.25 and 1 times the footing width, depending on the strength mobilization and spatial correlation features. Design charts are established with practical guidelines for quick estimations of uncertainty in footing settlements.