Estimation of the probability distribution of the random bearing capacity of cohesionless soil using the random finite element method

Soil mathematical modelling is a complex task when considering random soil parameters. To consider soil spatial variability, one can assume that soil properties are random variables or random fields. This study considered the estimation of the probability distribution of the bearing capacity for shallow footings in cohesionless soil using the random finite element method. In the deterministic case, the FEM code was calibrated to receive capacity evaluations similar to the results obtained using Hill's mechanism. Final capacity simulations were conducted under the assumption that the friction angle of the investigated subsoil constitutes a random field characterised by a bounded distribution. The random field was obtained by applying a hyperbolic tangent transformation to a Gaussian random field with an ellipsoidal (anisotropic) correlation function. The final outcome of the numerical analysis was an evaluation of the probability distribution that fits the bearing capacity for various foundation widths and depths. In all the cases considered, the empirical probability distribution of the bearing capacity closely resembled the Weibull distribution. Moreover, the estimated distribution of the bearing capacity was used as the basis for a foundation safety assessment.