Axisymmetric Biot's Consolidation of Multi-Layered Soils with Compressible Constituents

Abstract

Transfer matrix method has an obvious advantage that the size of the final equation system is independent of the number of the layered systems. Hence, this method is more efficient and accurate. For example, a two-dimensional consolidation of plane strain problem can be solved just using 3×3 linear equations. In this study, transfer matrix method is extended and used to axisymmetric Biot's consolidation of multi-layered soils with compressible constituents. From the governing differential equations of a porous medium filled with an compressilble pore fluid, and combined with Laplace-Hankel transforms and McNamee-Gibson displacement functions, the relationship of displacements, stresses, excess pore water pressure, and flux for arbitrary two horizontal planes is established in the Laplace-Hankel transforms domain. Based on the continuity conditions between adjacent layers and the boundary conditions of the layered soil system, the transfer matrix method is utilized to derive the solution for axisymmetric Biot's consolidation problem of multi-layered soils in the transformed domain. The solutions in the physical domain can be acquired by inverting the Laplace-Hankel transforms. Numerical analysis has been performed, and the feasibility and accuracy of the proposed method in this study are validated against existing results.