DESCRIBING SOIL HYDRAULIC-PROPERTIES WITH SUMS OF SIMPLE FUNCTIONS

Simple functions do not adequately describe the hydraulic properties of many field soils, particularly those with substantial macroporosity. By considering the soil pore-size distribution f(psi) = SIGMA(i=1)N phi(i) F(i)(psi) corresponding to the effective saturation S(psi) = SIGMA(i=1)N phi(i) S(i)(psi), where psi is matric pressure head, the phi(i) are fractions of effective porosity, the S(i)(psi) are simple water retention functions in common use, and f(i)(psi) = S(i)'(psi), we show that the relative hydraulic conductivity according to the Mualem model is K(r)(psi) = S(p)[SIGMA(i=1)N phi(i) g(i)(psi)/SIGMA(i=1)N phi(i) g(i)(0)2, where g(i)(psi) = integral-psi/-x psi-1 f(i)(psi) dpsi and p is a pore interaction index. If the pores of the distributions do not interact, the appropriate relation is K(psi) = SIGMA(i=1)N K(si)K(ri)(psi), where K(si) is the saturated conductivity of distribution i and K(ri) = S(p)[g(i)(psi)/g(i)(0)]2. We note that the van Genuchten function S(psi) = [1 + (-alphapsi)n]-m with the restriction m = 1 - 1/n leads to an infinite slope K'(psi) at psi = 0 unless n greater-than-or-equal-to 2, which is unrealistic for field soils if a wide range of matric pressure heads is considered. Hydraulic conductivity near saturation is often expressed as K(psi) = K(s) exp(apsi). We introduce the function S(psi) = (1 - alphapsi) exp(alphapsi), which gives, according to Mualem's model, a conductivity K(psi) = K(s)(1 - alphapsi)p exp[(p + 2)alphaphi] that approximates K(s) exp(apsi) near saturation if a = 2alpha and is exactly equal if p = 0. As an example, a function using this model for one pore-size distribution and the van Genuchten model for the other was compared with a function using two van Genuchten distributions. The latter gave a slightly improved fit to water content and conductivity data for an aggregated soil.