Squeezing a Sponge: A Three-Dimensional Solution in Poroelasticity

A three-dimensional solution is derived for the fluid flow in a deformable porous medium. It is assumed that the deformation of the medium is described by Hooke's law and the flow of the fluid by Darcy's law, i.e. the theory of poroelasticity applies. The governing equations are completed by suitable boundary conditions such that a compressed saturated cubic sponge is modelled. The solution is a three-dimensional generalisation of the one-dimensional solution of Terzaghi. A two-dimensional plane strain solution is derived also. Both solutions give excellent possibilities to test numerical codes.