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 GreenÕs 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.
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 GreenÕs 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 GreenÕs functions have been derived exactly and verified in both Laplace transform and time domains.
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