On the finite element formulation of dynamic two-phase coupled problems

Two finite element approaches are discussed for the analysis of the coupled problems of seepage and deformation of saturated porous media in the presence of an acceleration field varying in time and space (e.g. during an earthquake). The equations governing the two phase problem in dynamic regime are recalled first under assumptions which seem reasonable in the geotechnical context. Then they are cast into a first finite element form without introducing further assumptions with respect to those adopted in deriving them. Subsequently, a simplified formulation is presented which requires a reduced number of nodal variables with respect to the first one. After discussing a time integration scheme, the two approaches are applied to the solution of a benchmark example and some comparative comments are presented on their accuracy and on the required computational effort.