Probabilistic Analysis of Strip Footings Resting on Spatially Varying Soils and Subjected to Vertical or Inclined Loads

A probabilistic analysis of vertically and obliquely loaded strip footings resting on a spatially varying soil is presented. The system responses are the footing vertical and horizontal displacements. The deterministic computation of these system responses is based on numerical simulations using the software FLAC3D. Both cases of isotropic and anisotropic random fields are considered for the soil elastic properties. The uncertainty propagation methodology employed makes use of a nonintrusive approach to build up analytical equations for the two system responses. Thus, a Monte Carlo simulation approach is applied directly on these analytical equations (not on the original deterministic model), which significantly reduces the computation time. In the case of the footing vertical load, a global sensitivity analysis has shown that the soil Young's modulus $E$ mostly contributes to the variability of the footing vertical displacement, the Poisson ratio being of negligible weight. The decrease in the autocorrelation distances of $E$ has led to a smaller variability of the footing displacement. On the other hand, the increase in the coefficient of variation of $E$ was found to increase both the probabilistic mean and the variability of the footing displacement. Finally, in the inclined loading case, the results of the probability of failure against exceedance of a vertical and/or a horizontal footing displacement are presented and discussed.