Uncertainty Quantification of Failure of Shallow Foundation on Clayey Soils with a Modified Cam-Clay Yield Criterion and Stochastic FEM

Abstract

In this article, a quantitative numerical study of the random distribution of the soil material parameters to the probability density functions of the failure load and failure displacements of a shallow foundation is presented. A modified Cam-Clay yield function is used for this scope into a stochastic finite element numerical formulation. Several hypotheses for the random distribution of the compressibility factor κ, of the material constitutive relation, the critical state line inclination c of the soil, as well as of the permeability k of the continuum, have been tested and assessed with Monte Carlo simulation accelerated with Latin hypercube sampling. It is validated that both failure load and failure displacements follow Gaussian normal distribution despite the non-linear behaviour of the soil. Furthermore, as the soil depth increases, the mean value of failure load decreases and the failure displacement increases. The failure mechanism of clays can be determined with accuracy using this numerical implementation, without the restrictions imposed by analytical solutions, taking into consideration the eccentricity of the load in combination with non-linear constitutive relations.

Keywords

• eccentric loading
• stochastic finite element method
• shallow foundation
• footing settlement
• failure spline