Benchmark for poroelastic and thermoelastic numerical codes

Using the method of complex potentials we present the closed form of analytical solution for the stresses and displacements around an elliptical cavity filled with fluid in the permeable poroelastic medium. The far-field pore pressure is different from the pressure inside cavity. The fluid is allowed to diffuse through the cavity’s wall towards surrounding medium. The two-dimensional plane-strain and plane-stress models are considered with steady-state distribution of diffusive pore-fluid pressure. The diffusion of fluid is coupled to the deformation of a medium using a linear theory of poroelasticity. Since in the static case the diffusion of pore fluid is controlled by an ordinary Laplace equation, the problem is reduced to elastic problem with distribution of volume forces (known as seepage forces) along gradients of pore pressure. Due to similarity between poroelasticity and thermoelasticity, the present solution is applicable both to the poroelastic and thermoelastic problems with a steady-state distribution of pore pressure and temperature, respectively. Since it is getting more common to model the deformation coupled to Darcy-flow in geosciences and no clear criteria has been suggested for verification of numerical codes, we discuss the possible application of the analytical solution as the benchmark for testing of poroelastic and thermoelastic numerical codes. To stimulate a wider use of the solution for stresses, displacements and pore-fluid pressure around an elliptical cavity are implemented in MATLAB and can be downloaded from the web.