Numerical integration and analysis of equilibrium in unsaturated multiphase media

Unsaturated soil mechanics has been largely focused on the phenomena of collapse upon wetting. Since the early studies this mechanical feature has influenced the way of representing experimental data and the constitutive modelling. Collapse has been generally modelled with a plastic amount of strains coupled with the suction rate. This constitutive approach is discussed. In the paper, the equilibrium and stability of the granular matrix is studied applying the criteria of thermodynamics. The system is considered as an open continua and the filtration of the wetting phase during collapse is taken into account. The paper provides some remarks about the hardening in partially saturated conditions. The incremental constitutive system of equations is implicitly integrated adopting the Laplace transform and the Newton Raphson technique. This allows defining the problem in the domain of a physical quantity that can be measured in laboratory tests (namely the degree of saturation). Time evolution of the capillary stress is obtained with the inverse transformation. The proposed integration is a part of the research program on lime stabilized material in partially saturated condition. The integration for the partially saturated model is described in the present paper.