Simulation of a compressional slow wave in partially saturated poroelastic 1-D column

We simulate wave propagation in a partially saturated porous medium, where the feature is the presence of a slow wave. The pores are filled with a wetting fluid and a nonwetting fluid, and the model, based on a Biot-type three-phase theory. In the present paper, the solution of a finite one dimensional column with Neumann and Dirichlet boundary conditions are presented. The solution is obtained in the Laplace domain and the time-step method is chosen to obtain the time domain solution. The material data of Massillion sandstone are used for calculations. The column response to the dynamic loading is examined in terms of displacement, pore water pressure, pore air pressure. By neglecting the viscosity of the fluid, assuming very large permeabilities, the second compressional wave are identified.