Finite element methods for unsaturated porous solids and their application to dam engineering problems

This work presents a finite element formulation of equations proposed in a companion paper to describe the hyperelastic response of three-phase porous media. Attention is paid to the development of consistent tangents required by the Newton-Raphson procedure used to solve the highly non-linear finite element equations. Among several sources of non-linearity, we also model the permeability dependence on strain as typically observed in intensely jointed rock masses, thus introducing a further reason of hydro-mechanical coupling. Several numerical examples are presented to validate the considered poro-elastic laws and to assess the performance of the numerical formulation. These tests include comparisons with available experimental data relative to a sand column desaturation and with the Philip's analytical solution for the propagation of a saturation front in an initially dry porous solid. Finally, the formulation is applied to problems of interest for dam engineering, namely the simulation of reservoir bank response to rapid drawdown and a three-dimensional study of concrete gravity dam interaction with foundation and abutment rock masses during reservoir operation.