Reflection–transmission matrix model for the axisymmetric deformation of a layered transversely isotropic saturated soil

Abstract

The reflection–transmission matrix (RTM) method for the layered transversely isotropic saturated soil (TISS) undergoing axisymmetric consolidation is developed in this study. To this aim, a system of partial differential equations is established based on the governing equations for the TISS first. By means of the Hankel–Laplace integral transform method, the system of partial differential equations is reduced to a system of ordinary differential equations. By using the general solution to the system of ordinary differential equations, the static wave vector corresponding to the state vector of the TISS is introduced, and the transfer matrices for the state and wave vectors are defined. The RTMs for the aforementioned static wave vector of the layered TISS are then established. By means of the RTMs for the layered TISS, solutions for the layered TISS subjected to external sources are derived. Numerical results due to the proposed RTM method are compared with some existing results, validating the proposed RTM method. Parametric analyses are conducted to illustrate the influence of some parameters on the consolidation of the layered TISS.