Numerical modeling has been largely developed in soil mechanics behavior by different methods. Among them, the development of the boundary element method, which is the most suitable one for domains with infinite boundary conditions like soils media, has been restricted by the necessity of deriving the Green’s functions of the governing differential equations. Indeed, attempting to solve the three-dimensional boundary value problems for unsaturated soils leads one to search for the associated Green’s functions of the governing differential equations.
In this paper the governing differential equations of the phenomena are presented which consist of three main groups of equations: 1- equilibrium and constitutive equations of soil’s solid skeleton, 2- conservation and transfer equations for air phase and 3- conservation and transfer equations for moisture phase.
The associated Green’s functions have been manipulated with a few assumptions to first linearize the completely non-linear governing differential equations and next to make possible deriving the results, mathematically. After applying the Laplace transform to eliminate the time variable, Green’s functions of the governing differential equations have been derived using the straightforward Kupeadze’ s method. Then using the inverse Laplace transforms, the completely closed-form Green’s functions have been derived in the time domain.
Finally, for verification of the results it has been demonstrated that when the conditions approach to the poroelastostatic case, the Green’s functions approach to the corresponding poroelastostatic Green’s functions as well. As no analytical solutions are available in the literature for the mentioned Green’s functions, it seems to be a new experience to introduce a set of fundamental solutions for the unsaturated case for the first time.
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