Infiltration in Porous Media: On the Construction of a Functional Solution Method for the Richards Equation

In engineering, knowledge about infiltration and water movement in soil emerges as a preventive measure, both to control the destructive action of water on foundations, dams, and pavements and to predict the behavior of flow and transport of pollutants. Mathematical modeling of these infiltration processes in porous media is substantiated by the equations of Richards, or Fokker–Planck. Fokker–Plank equation Both equations are highly nonlinear, so that analytical solutions to the equations are extremely difficult to find. In order to turn prognostics in applications more efficient, it is essential to consider field observations, because they are necessary for identification of constitutive relations that govern the phenomenon and may be used in theoretical formulations. The best-known models that relate soil parameters are the models found in Brooks and Corey (Hydraulic Properties of Porous Media. Hydrol. Paper 3. Colorado State University, 1964), Genuchten (Soil Science Society of America Journal 44:892–898, 1980) and Gardner (Soil Science 85:228–232, 1958). The Van Genuchten model Van Genuchten model provides more satisfactory results than others when compared with experimental data, but due to its functional form proposed solutions have limited applicability. On the other hand, the other two models result in simplified equations, leading to cases of linearized equations and their associated solutions, as, for instance, in Basha (Water Resources Research 35(1):75–83, 1999; Water Resources Research 38(11):29.1–29.9, 2002) and Chen et al. (Water Resources Research 37(4):1091–2001, 2001). However, most of these solutions are limited to cases with uniform initial conditions and in an infinite domain.