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Describing Soil Hydraulic Properties with Sums of Simple Functions

Division of Soils, CSIRO, PMB, PO Aitkenvale, Townsville, Qld 4814, Australia

*Corresponding author.

ABSTRACT

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() = ^N_{i = 1 i} f_i () corresponding to the effective saturation S() = ^N_{i = 1 i} S_i(), where is matric pressure head, the _i are fractions of effective porosity, the S_i() are simple water retention functions in common use, and f_i() = S^'_i(), we show that the relative hydraulic conductivity according to the Mualem model is K_r() = S^p[^N_{i = 1 i} g_i()/^N_{i = 1 i} g_i(0)]², where g_i() = _-x^–1 f_i() d and p is a pore interaction index. If the pores of the distributions do not interact, the appropriate relation is K() = ^N_{i = 1} K_siK_ri(), where K_si is the saturated conductivity of distribution i and K_ri = S^p[g_i()/g_i(0)]². We note that the van Genuchten function S() = [1 + (–)ⁿ]^–m with the restriction m = 1 – 1/n leads to an infinite slope K'() at = 0 unless n 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() = K_s exp(a). We introduce the function S() = (1 – ) exp(), which gives, according to Mualem's model, a conductivity K() = K_s(1 – )^p exp[(p + 2)] that approximates K_s exp() near saturation if a = 2 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.

Contribution of CSIRO, Australia. This research was supported in part by the CSIRO Coastal Zone Program.

Received for publication March 16, 1992.

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