Time-domain Green’s functions for unsaturated soils. Part I: Two-dimensional solution

In this article, primarily a brief discussion about the formulation of unsaturated soils including the equilibrium, air and moisture transfer equations is presented. Then the closed form two-dimensional Green’s functions of the governing differential equations for an unsaturated deformable porous medium with linear elastic behavior for a symmetric polar domain in both Laplace transform and time domains have been introduced, for the first time. Using the linear form of the governing differential equations and considering the effects of non-linearity of the governing equations, the Green’s functions have been derived exactly and verified in both Laplace transform and time domains.