Solutions to Green-Ampt Infiltration Equation

Abstract

The simple method of solving the Green-Ampt one-dimensional infiltration equations developed from Darcy's law are proposed for practical applications. The explicit solution is an approximation obtained by employing a power series expansion of the logarithmic term. The maximum error resulting from applying this simple explicit solution is 8%. The implicit exact solution is obtained by refining the explicit solution using the second-order Newton method. The maximum error resulting from employing the implicit solution is 0.003%. These new methods have advantages over other existing solutions in that they are derived from the theory of mathematics and the errors due to approximation can be evaluated theoretically. Moreover, the two methods are simple and easy to use either with a desk calculator or in a digital computer, and they are applicable without limitation on ranges.