Transfer matrix solutions to plane-strain and three-dimensional Biot’s consolidation of multi-layered soils

Starting from the governing equations of a saturated poro-elastic soil in the Cartesian system, and introducing the displacement functions, the transfer matrix relationship of displacements, stresses, excess pore water pressure, and flux between the ground surface (z = 0) and an arbitrary depth z of a finite soil layer is established in the Laplace-Fourier transforms domain. Based on this relationship and transfer matrix concept and by considering the continuity conditions between adjacent layers and the boundary conditions of the layered soil system, the solutions for plane-strain and three-dimensional Biot’s consolidation problems of a multi-layered soil system in the transformed domain are derived, respectively. The actual solutions in the physical domain can be acquired by the inversion of the Laplace-Fourier transforms. The numerical results for plane-strain and three-dimensional Biot’s consolidation problems of a single layer and multi-layered soil system are performed, and the feasibility and accuracy of the proposed solutions in this study are proved by comparing with some existing results.