Analytical Solution of Plane-Strain Poroelasticity due to Surface Loading within a Finite Rectangular Domain

Abstract

An analytical solution is presented for plane-strain poroelasticity induced by surface-normal loading within a finite rectangular fluid-saturated domain. In this work, the porous medium is assumed to be isotropic, homogeneous, and composed of compressible constituents. Appropriate Fourier and Laplace transforms and inversions are used to derive the analytical solution. In particular, lateral boundary conditions for the displacement field are specifically prescribed with care to match the Fourier and Laplace transforms. The analytical solution is presented in terms of summations of multiple series. Then, a case study for the consolidation of a water-saturated soft clay layer is carried out. The analytical solution is compared to the finite-element (FE) solution through a nonlinear transient FE analysis software program. The excellent agreement between the FE solution and the analytical solution demonstrates the accuracy and reliability of the analytical solution presented in this paper. Meanwhile, an analysis of coupled hydromechanical behavior is conducted herein. It depicts that the Mandel-Cryer effect occurs, which is a distinctive feature of poroelastic theory. The presented analytical solution can act as a benchmark for the validation of numerical solutions in plane-strain consolidation. It is helpful also for a further understanding of time-dependent hydromechanical behavior of finite two-dimensional fluid-saturated porous media.