Soil and Tillage Research, ( ISI ), Volume (119), No (1), Year (2012-1) , Pages (60-69)

Title : ( Additional scaled solutions to Richards’ equation for infiltration and drainage )

Authors: Seyyed Morteza Sadeghi , Bijan Ghahraman , Ali Naghi Ziaei , Kamran Davary , K. Reichardt ,

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Warrick and Hussen developed in the nineties of the last century a method to scale Richards’ equation (RE) for similar soils. In this paper, new scaled solutions are added to the method of Warrick and Hussen considering a wider range of soils regardless of their dissimilarity. Gardner–Kozeny hydraulic functions are adopted instead of Brooks–Corey functions used originally by Warrick and Hussen. These functions allow to reduce the dependence of the scaled RE on the soil properties. To evaluate the proposed method (PM), the scaled RE was solved numerically using a finite difference method with a fully implicit scheme. Three cases were considered: constant-head infiltration, constant-flux infiltration, and drainage of an initially uniform wet soil. The results for five texturally different soils ranging from sand to clay (adopted from the literature) showed that the scaled solutions were invariant to a satisfactory degree. However, slight deviations were observed mainly for the sandy soil. Moreover, the scaled solutions deviated when the soil profile was initially wet in the infiltration case or when deeply wet in the drainage condition. Based on the PM, a Philip-type model was also developed to approximate RE solutions for the constanthead infiltration. The model showed a good agreement with the scaled RE for the same range of soils and conditions, however only for Gardner–Kozeny soils. Such a procedure reduces numerical calculations and provides additional opportunities for solving the highly nonlinear RE for unsaturated water flow in soils.


, Richards' equation, invariant solutions, Warrick and Hussen, Dissimilar soils.
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author = {Sadeghi, Seyyed Morteza and Ghahraman, Bijan and Ziaei, Ali Naghi and Davary, Kamran and K. Reichardt},
title = {Additional scaled solutions to Richards’ equation for infiltration and drainage},
journal = {Soil and Tillage Research},
year = {2012},
volume = {119},
number = {1},
month = {January},
issn = {0167-1987},
pages = {60--69},
numpages = {9},
keywords = {Richards' equation; invariant solutions; Warrick and Hussen; Dissimilar soils.},


%0 Journal Article
%T Additional scaled solutions to Richards’ equation for infiltration and drainage
%A Sadeghi, Seyyed Morteza
%A Ghahraman, Bijan
%A Ziaei, Ali Naghi
%A Davary, Kamran
%A K. Reichardt
%J Soil and Tillage Research
%@ 0167-1987
%D 2012