Abstract
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. 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 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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Adomian, G.: Solving Frontier Problems of Physics: The Decomposition Method. Kluwer Academic Publishers, The Netherlands (1994).
Basha, H.A.: Multidimensional linearized nonsteady infiltration with prescribed boundary conditions ate the soil surface. Water Resources Research, 35(1), 75–83 (1999).
Basha, H.A.: Burgers equation: A general nonlinear solution of infiltration and redistribution. Water Resources Research, 38(11), 29.1–29.9 (2002).
Brooks, R.H. and Corey, A.T.: Hydraulic Properties of Porous Media. Hydrol. paper 3., Colorado State University (1964).
Celia, M.A., Bouloutas, E.T., and Zarba, R.L.: A general mass conservative numerical solution for the unsaturated flow equation. Water Resources Research, 26(30), 1483–1496 (1990).
Chen, J.M., Tan, Y.C., Chen, C.H., and Parlange, J.Y.: Analytical solutions for linearized Richards equation with arbitrary time-dependent surface fluxes. Water Resources Research, 37(4), 1091–2001 (2001).
Gardner, W.R.: Some steady state solution of unsaturated moisture flow equations with application evaporation from a water table. Soil Science, 85, 228–232 (1958).
Genuchten, M.T.: A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Science Society of America Journal, 44, 892–898 (1980).
O’Neil, P.V.: Advanced engineering mathematics. International Student Edition, University of Alabama at Birmingham, Ed. 7, 82–85 (2011).
Polyanin, A.D. and Zaitsev, V.F.: Handbook of Nonlinear Partial Differential Equations. Chapman and Hall/CRC, (2003).
Wendland, E. and Pizarro, M.L.P.: Modelagem computacional do fluxo unidimensional de Água em meio não saturado do solo. Engenharia Agrícola, Jabotical. 30(3), 424–434 (2010).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Furtado, I.C., Bodmann, B.E.J., Vilhena, M.T.B. (2015). Infiltration in Porous Media: On the Construction of a Functional Solution Method for the Richards Equation. In: Constanda, C., Kirsch, A. (eds) Integral Methods in Science and Engineering. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-16727-5_20
Download citation
DOI: https://doi.org/10.1007/978-3-319-16727-5_20
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-16726-8
Online ISBN: 978-3-319-16727-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)