Describing Soil Hydraulic Properties with Sums of Simple Functions
1993
Ross, Peter J. | Smettem, Keith R. J.
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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