A semi-analytical solution to the dynamic response of saturated multi-layer porous media under progressive waves

A two-dimensional semi-analytical solution to the dynamic response of saturated porous media is presented considering a number of heterogeneous layers. The governing equations proposed by Biot are written in their fully dynamic form and possible simplifications of quasi-static and partially dynamic formulations developed in terms of the presence of inertial terms are also introduced. The analytical solutions for a plane strain saturated porous layer developed before by the author are extended to multi-layers for all formulations in terms of non-dimensional parameters. Dynamic response of the system is evaluated in terms of displacements, pore pressure as well as effective and shear stress variations in the medium. Since inertial terms in the equations associated with both the solid and the fluid part play a significant role in the dynamic response, applicability of these terms for a variety of problems is investigated. It is found that accelerations due to relative motion of pore fluid to that of solid skeleton becomes more important as higher frequencies are present in the medium. The applicability of formulations for the problems involving multi-layer porous media is determined in terms of maximum discrepancy in magnitude between the responses. As it is found quite useful by both researchers and engineers, the response is studied for different conditions and the regions of validity of the formulations are identified in a non-dimensional parametric space indicating the effect of multi-layering.