Multiaxial probabilistic elastic-plastic constitutive simulations of soils

In this study, recently developed Fokker-Planck-Kolmogorov (FPK) approach to probabilistic elasto-plasticity is extended to numerically simulate conventional triaxial undrained and drained constitutive behaviors of uncertain soils. To this end, the most general form of the elastic-plastic constitutive rate equation is written in the probability density space to obtain a generalized, multi-dimensional FPK partial differential equation (PDE)which describes the evolution of the joint probability density function (PDF) of stress components with pseudo time/strain. The generalized FPK PDE is then specialized to triaxial space with undrained and drained stress paths. Assuming a suitable constitutive model and appropriate (probabilistic) soil parameters, each specialized FPK PDE is numerically solved - with relevant initial and boundary conditions - to obtain the respective evolutionary joint PDF of stress components with pseudo time/strain. Marginal PDFs of the stress components are then computed from the joint PDFs and the simulation results are presented in terms of evolutionary mean and standard deviation of deviatoric stress with axial strain/triaxial shear strain. Probabilistic evolutions of pore water pressure (for undrained simulation) and volumetric strain (for drained simulation) with triaxial shear strain are also computed and presented as well.