Coupled theory of mixtures for clayey soils

In this work, elasto-plastic coupled equations are formulated in order to describe the time-dependent deformation of saturated cohesive soils (two-phase state). Formulation of these equations is based on the principle of virtual work and the theory of mixtures for inelastic porous media. The theory of mixtures for a linear elastic porous skeleton was first developed by Biot (Theory of elasticity and consolidation for a porous anisotropic solid, Journal of Applied Physics, 1955, 26, 188–185). An extension of Biot's theory into a nonlinear inelastic media was performed by Prevost (Mechanics of continuous porous media, International Journal of Engineering Science, 1980, 18, 787–800). The saturated soil is considered as a mixture of two deformable media, the solid grains and the water. Each medium is regarded as a continuum and follows its own motion. The flow of pore-water through the voids is assumed to follow Darcy's law. The coupled equations are developed for large deformations with finite strains in an updated Lagrangian reference frame. The coupled behavior of the two-phase materials (soil-water state) is implemented in a finite element program. A modified Cam-clay model is adopted and implemented in the finite element program in order to describe the plastic behavior of clayey soils. Penetration of a piezocone penetrometer in soil is numerically simulated and implemented into a finite element program. The piezocone penetrometer is assumed to be infinitely stiff. The continuous penetration of the cone is simulated by applying an incremental vertical movement of the cone tip boundary. Results of the finite element numerical simulation are compared with experimental measurements conducted at Louisiana State University using the calibration chamber. The numerical simulation is carried out for two cases. In the first case, the interface friction between the soil and the piezocone penetrometer is neglected. In the second case, interface friction is assumed between the soil and the piezocone. The results of the numerical simulations are compared with experimental laboratory measurements.