A Boundary Element Formulation for the Wave Propagation in the Unsaturated Soils

Abstract

This paper aims at obtaining an advanced formulation of the time-domain Boundary Element Method (BEM) for two-dimensional dynamic analysis of unsaturated soil. Unlike the usual time-domain BEM the present formulation applies a Convolution Quadrature which requires only the Laplace-domain instead of the time-domain fundamental solutions. The coupled equations governing the dynamic behavior of unsaturated soils ignoring contributions of the inertia effects of the fluids (water and air) are derived based on the poromechanics theory within the framework of the suction-based mathematical model. In this formulation, the solid skeleton displacements, water pressure and air pressure are presumed to be independent variables. As there is no analytical solution for the 2D wave propagation in unsaturated soils in the literature, to verify the accuracy of this implementation, the displacement response obtained by the boundary element formulation is partially verified by comparison with the elastodynamics problem.

Modeling of Wave Propagation in the Unsaturated Soils Using Boundary Element Method

“…The method is very attractive for wave propagation problems, because the discretization is done only on the boundary, yielding smaller meshes and systems of equations. Another advantage is that this method represents efficiently the outgoing waves through infinite domains, which is very useful when dealing with scattered waves by topographical structures [2].…”