A Closed‐form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils

TLDR

The paper proposes a new, simple equation for the soil‑water content–pressure head curve, θ(h). The authors derive closed‑form expressions for relative hydraulic conductivity by inserting the new θ(h) equation into N.T. Burdine or Y. Mualem models, yielding a three‑parameter K_r(h) that can be fitted to data.

Abstract

Abstract A new and relatively simple equation for the soil‐water content‐pressure head curve, θ( h ), is described in this paper. The particular form of the equation enables one to derive closed‐form analytical expressions for the relative hydraulic conductivity, K r , when substituted in the predictive conductivity models of N.T. Burdine or Y. Mualem. The resulting expressions for K r ( h ) contain three independent parameters which may be obtained by fitting the proposed soil‐water retention model to experimental data. Results obtained with the closed‐form analytical expressions based on the Mualem theory are compared with observed hydraulic conductivity data for five soils with a wide range of hydraulic properties. The unsaturated hydraulic conductivity is predicted well in four out of five cases. It is found that a reasonable description of the soil‐water retention curve at low water contents is important for an accurated prediction of the unsaturated hydraulic conductivity.