A local frequency-dependent absorbing boundary condition for unsaturated porous media based on the theory of mixtures with interfaces

A novel, local and frequency-dependent absorbing boundary condition for unsaturated porous media is presented. It relates the far-field tractions and displacements produced by a wave which travels through an unsaturated porous medium described by the theory of mixtures with interfaces. The absorbing boundary condition is valid for all types of waves that may occur in unsaturated media, namely three types of compression waves (one for each phase) and a single shear wave, propagating through the solid phase. Although it is only exact for absorbing boundaries situated infinitely far from the source of excitation and orthogonal incident waves, an efficiency study, measuring the ratio between the (spurious) reflected energy and the energy of the incident wave, shows that the absorbing boundary condition is highly efficient even when situated at close range and oblique in respect to the incident waves. It is also easy to embed in conventional finite element and finite difference software, as it amounts to a linear Robin boundary condition. A numerical application involving the propagation of a shock wave through a multi-layered semi-unbounded unsaturated media is also presented.