Finite element analysis of non-isothermal multiphase porous media in quasi-statics and dynamics

This chapter presents a mathematical and a numerical model for the analysis of the thermo-hydro-mechanical (THM) behavior of multiphase deformable porous mate rials in both quasi-statics and dynamics. The fully coupled governing equations are developed within the Hybrid Mixture Theory. To analyze the THM behavior of soil structures in the low frequency domain, e.g. under earthquake excitation, the u-p-T formulation is invoked by neglecting the relative acceleration of the fluids and their convective terms. The standard Bubnov-Galerkin method is applied to the governing equations for the spatial discretization, whereas the generalized Newmark scheme is used for the time discretization. The final non-linear and coupled system of algebra ic equations is solved by the Newton method within the monolithic approach. The formulation and the implemented solution procedure are validated through the com parison with other finite element solutions. Moreover, the issue of spurious mesh sensitivity in strain localization analysis is addressed by employing visco-plastic and non-local theories and some numerical results where shear bands develop are presented.