Time-domain Green’s functions for unsaturated soils. Part II: Three-dimensional solution

The presented paper has been dedicated to complete the closed form three-dimensional fundamental solutions of the governing differential equations for an unsaturated deformable porous media with linear elastic behavior and a symmetric spherical domain in both Laplace transform and time domains. The governing differential equations consist of equilibrium, air and water transfer equations including the suction effect and dissolved air in water. The obtained Green’s functions have been derived exactly, for the first time, using the linear form of the governing differential equations and considering the effects of non-linearity of the governing equations and have been verified in both frequency and time domains.