Probabilistic Elastic–Plastic Cam Clay Response of Soils

Abstract

-This study uses Cam Clay model to investigate the influence of uncertainties in soil properties on simulated undrained triaxial constitutive response. To this end, recently developed Fokker-Planck-Kolmogorov (FPK) equation approach to probabilistic elasto-plasticity is employed. The most general form of the three dimensional elastic-plastic constitutive rate equation is written in probability density space, resulting in a multi-dimensional FPK equation. The resultant FPK equation is specialized to undrained stress path. Given the second order statistics of the uncertainties in soil properties and assuming Cam Clay elastic-perfectly plastic constitutive model, the specialized FPK equations are solved to obtain second order accurate evolutionary (with pseudotime/ strain) joint probability density function of the stress response. Marginal statistics -marginal probability density function, marginal mean, and marginal standard deviation -of the stress components are then obtained from the multivariate probability density function using standard integration techniques.