two-dimensional time domain fundamental solution to dynamic unsaturated poroelasticity

this paper presents time domain fundamental solutions for the extended biot's dynamic formulations of two-dimensional (2d) unsaturated poroelasticity. unsaturated porous media is considered as a porous media in which the voids are saturated with two immiscible fluids, i.e. liquid and gas. at first, the corresponding explicit laplace transform domain fundamental solution is obtained in terms of skeleton displacements, as well as liquid and gas pressures. subsequently, the closed-form time domain fundamental solutions are derived by analytical inversion of the laplace transform domain solutions. finally, a set of numerical results are presented which verifies the accuracy of the analytically inversed transient fundamental solution and demonstrates some salient features of the elastic waves in unsaturated media..