关键词: 有限二维孔隙弹性介质, Biot固结, 积分变换, 拉普拉斯数值反演, 解析解

Abstract: An analytical solution is presented for Biot’s consolidation induced by surface loading within a finite two-dimensional (2D), isotropic, homogeneous and fluid-saturated poroelastic media. Here, the consolidation is assumed to be governed by the incompressible porous media model. The Dirichlet boundary conditions are adopted for the pore pressure field, and the displacements field on the upper and lower surfaces conforms to physical boundaries. However, the boundary conditions of the displacements field on the lateral sides are specifically given. Finite sine and cosine transforms, Laplace transforms and Laplace numerical inversions are implemented; and the analytical solutions in the closed-form of double summations of series are obtained. Finally, an example of plane strain consolidation is studied. The proposed exact solution is validated against the numerical solution by the finite element analysis software ABAQUS. And based on the presented analytical solution, the spatiotemporal evolution of the pore pressure field and the displacements field is briefly examined. The presented analytical solution can be of great potential to further understand the behavior of flow and deformation coupling in a finite 2D fluid-saturated porous medium.

Key words: finite 2D poroelastic media, Biot’s consolidation, integral transforms, Laplace numerical inversions, analytical solution