General Model for Unsaturated Hydraulic Conductivity for Soils with Lognormal Pore‐Size Distribution

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Abstract
Describing water flow in unsaturated soils requires knowledge of the unsaturated hydraulic conductivity. This study was conducted to develop a general conductivity model for soils with lognormal pore‐size distribution based on the Mualem‐Dagan pore‐scale model. The derived model has three parameters other than parameters for a retention model: the parameters α and β, both of which are related to the soil pore tortuosity, and the parameter γ to describe how to evaluate the effective pore radius. The proposed model was applied to observed retention and conductivity data sets for 200 soils. Results showed that both α and β should be treated as fitted parameters for accurate descriptions of conductivity, whereas estimation results were insensitive to γ as long as α and β were optimized. Consequently, a simplified form of the general conductivity model was suggested which uses the constant γ value of unity. Based on the simplified general conductivity model, two predictive methods (AB and FN) were developed. The method AB uses the constant α and β values to minimize the average prediction error. The method FN uses an empirically derived relationship between β and the dimensionless parameter of the retention model, and the constant α value to minimize the average prediction error. Both methods reduced the average prediction error more than 77% compared with the Burdine and Mualem predictive models. The method FN provided slightly better predictions than the method AB, reducing the average prediction error by 28%.

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