Analytical Solutions for Poroelasticity Within a Finite Two-Dimensional Domain

This paper presents an analytical solution of two-dimensional poroelasticity in the case of constant point sink and closed boundaries. The studied problem is coupled pore fluid flow and solid deformation due to a point sink within a twodimensional finite rectangular domain. In this study, poroelastic theory takes the form of Biot's consolidation model. Porous media is assumed to be isotropic, linear elastic and saturated by single-phase fluid. On the basis of the author's previous work, the analytical solution is obtained by use of integral transform method, and compared with the existing exact solution in the literature. The results show that they are completely identical, which verifies the accuracy of the presented analytical solution. The presented analytical solution can be used to validate two-dimensional poroelasticity related numerical solutions. Besides, it can provide us further insights into the flow (pore fluid pressure) and deformation (stress) coupling in porous materials.