15. Investigation of the Dynamic Response in a One-Dimensional Partially Saturated Poroelastic Medium

In this paper, the dynamic response of a poroelastic material to an impulse load has been analytically investigated. The poroelastic material is represented by a three-phase elastically deformable partially saturated porous medium, one phase is a deformable solid skeleton, and the other two are fluid and gas that fill the pore space. The mathematical formulation is a system of equations including the laws of conservation of mass for fluid phases and a solid frame, an equilibrium equation for a three-phase continuum, a constitutive relation for a three-phase medium, a relation for determining the stress tensor, and Darcy’s law of filtration. The solution of the equations of motion of a one-dimensional poroelastic medium is written in terms of the variables of the displacement of a solid skeleton, and the pore pressure of fluid and gas in the Laplace domain. The time domain solution is calculated using the numerical inversion stepped method of the Laplace transform. The effect of material parameters on the dynamic response is analyzed in a series of numerical experiments. The results of this study may help to gain better insight into one-dimensional wave propagation in unsaturated soils.