Total stress and pressure gradient formulations in coupled poroelasticity problems

The poroelasticity equations may be solved by the finite element method (FEM) with the fluid flow and the porous medium displacement fields coupled togetber through a coupling matrix. It is showed that at the elemental level the coupling matrix is different according to whether a pore pressure gradient or a total stress approach is used. At the global assembled level, however, the two approaehes are fully equivalent as the former cali be obtained from the latter by applying Green's first identity. Both formulations are briefly reviewed and discussed using a bi-dimensional example discretized into triangular finite elements.