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This article in SSSAJ

  1. Vol. 57 No. 1, p. 26-29
    Received: Mar 16, 1992

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Describing Soil Hydraulic Properties with Sums of Simple Functions

  1. Peter J. Ross  and
  2. Keith R. J. Smettem
  1. Division of Soils, CSIRO, PMB, PO Aitkenvale, Townsville, Qld 4814, Australia



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(ψ) = ΣNi = 1 ψi fi (ψ) corresponding to the effective saturation S(ψ) = ΣNi = 1 ψi Si(ψ), where ψ is matric pressure head, the ψi are fractions of effective porosity, the Si(ψ) are simple water retention functions in common use, and fi(ψ) = S'i(ψ), we show that the relative hydraulic conductivity according to the Mualem model is Kr(ψ) = Sp[ΣΣNi = 1 ψi gi(ψ)/ΣNi = 1 ψi gi(0)]2, where gi(ψ) = εψ-xψ−1 fi(ψ) dψ and p is a pore interaction index. If the pores of the distributions do not interact, the appropriate relation is K(ψ) = ΣNi = 1 KsiKri(ψ), where Ksi is the saturated conductivity of distribution i and Kri = Sp[gi(ψ)/gi(0)]2. We note that the van Genuchten function S(ψ) = [1 + (−αψ)n]m with the restriction m = 1 − 1/n leads to an infinite slope K'(ψ) at ψ = 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(ψ) = Ks exp(aψ). We introduce the function S(ψ) = (1 − αψ) exp(αψ), which gives, according to Mualem's model, a conductivity K(ψ) = Ks(1 − αψ)p exp[(p + 2)αψ] that approximates Ks exp(αψ) near saturation if a = 2α 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.

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