Revisiting of a Three-Parameter One-Dimensional Vertical Infiltration Equation

Abstract

In the present study, the three-parameter one-dimensional vertical infiltration equation recently proposed by Poulovassilis and Argyrokastritis is examined. The equation includes the saturated hydraulic conductivity (Ks), soil sorptivity (S), and an additional parameter c; it is valid for all infiltration times. The c parameter is a fitting parameter that depends on the type of porous medium. The equation is characterized by the incorporation of the exact contribution of the pressure head gradient to flow during the vertical infiltration process. The application of the equation in eight porous media showed that it approaches to the known two-parameter Green–Ampt infiltration equation for parameter c = 0.300, while it approaches to the two-parameter infiltration equation of Talsma–Parlange for c = 0.750, which are the two extreme limits of the cumulative infiltration of soils. The c parameter value of 0.500 can be representative of the infiltration behavior of many soils for non-ponded conditions, and consequently, the equation can be converted into a two-parameter one. The determination of Ks, S, and c using one-dimensional vertical infiltration data from eight soils was also investigated with the help of the Excel Solver application. The results showed that when all three parameters are considered as adjustment parameters, accurate predictions of S and Ks are not achieved, while if the parameter c is fixed at 0.500, the prediction of S and Ks is very satisfactory. Specifically, in the first case, the maximum relative error values were 33.29% and 39.53% for S and Ks, respectively, while for the second case, the corresponding values were 13.25% and 17.42%.

Keywords

• soil sorptivity
• soil hydraulic conductivity
• inverse solution
• Excel Solver