Multidimensional linearized nonsteady infiltration with prescribed boundary conditions at the soil surface

The present work explores a class of analytical solutions of moisture movement in unsaturated porous media characterized by an exponential dependence of the hydraulic conductivity and the moisture content on water pressure. The Green's function method is used to derive a general analytical model pertaining to multidimensional nonsteady infiltration in a semi-infinite flow domain with arbitrary initial conditions, boundary conditions, and root-uptake forcing functions and for various simple source geometry. The general solution is expressed in integral form from which particular analytical solutions pertaining to cases of surface and subsurface irrigation, evaporation, root uptake, and moisture redistribution can be easily deduced from the general analytical model. The model offers the analyst significant flexibility in deriving results and analyzing infiltration phenomena of practical interest. New explicit solutions have been obtained for one-dimensional infiltration under various prescribed time-dependent flux boundary conditions and for two- and three-dimensional moisture redistribution. For constant initial or boundary conditions, the multidimensional solution is essentially the product of two or three time-dependent terms with each term being a function of only one space variable.