ABSTRACT
Transient flow of water in unsaturated soils is a complicated phenomenon. This phenomenon is formulated via a Partial Differential Equation (PDE) known as the Richards Equation. In the last decades, researchers have presented analytical solutions to solve this PDE. The existing analytical solutions can be applied only to problems with simple geometry and boundary conditions and they don’t cover all possible transient flow problems. This paper introduces a new analytical scheme for solving the Richards Equation in homogenous and one-dimensional media. In this scheme, this equation is linearized by applying the exponential form of hydraulic conductivity and SWCC functions and performing the Kirchhoff Transforms. Then by exploiting the Green Function approach, a closed-form relation, which comprises sum of three integral terms, is derived. Moreover, the boundary and initial conditions are defined as arbitrary functions in this solution. Therefore, this new solution is appropriate for modeling all types of unsaturated seepage problems.
