Multi-dimensional consolidation of layered poroelastic materials with anisotropic permeability and compressible fluid and solid constituents

The Biot's consolidation theory of fluid-infiltrated porous materials is used to formulate the problem of 2D and 3D consolidation of multilayered poroelastic materials with anisotropic permeability and compressible fluid and solid constituents under external force. The Laplace-Fourier transforms technology is adopted to reduce the partial differential equations to ordinary ones in the transformed domain, and an extra Laplace transform is subsequently implemented with respect to the remained variable of depth z to solve the equations. Analytical matrices are then built between the displacements, pore pressure and the stresses, fluid flux for all of the layers. By considering the boundary conditions and continuity between adjacent layers, global stiffness matrix is finally assembled from the analytical matrices in transformed domain. Using the inversion technology of the Laplace-Fourier transforms, actual solutions in the physical domain can be obtained. Finally, a FORTRAN program is made to perform the theory, and a series of numerical examples are carried out to validate and be in-depth insight into 2D and 3D consolidation of multilayered poroelastic materials with anisotropic permeability and compressible fluid and solid constituents. The results exhibit that the characteristic of compressibility of the constituents may have a strong effect on the consolidation process.