Total stress and pressure gradient formulations in coupled poroelasticity problems
M. Ferronato, G. Gambolati, P. Teatini
Dept. Mathematical Methods and Models for Scientific
Applications, University of Padova, Padova, Italy
ABSTRACT
The poroelasticity equations may be solved by the finite element method
(FEM) with the fluid flow and the porous medium displacement fields coupled
together through a coupling matrix. It is shown 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 approaches are fully equivalent as
the former can 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.
