Unsaturated hydraulic conductivity models based on truncated lognormal pore-size distributions

We develop a closed-form three-parameter model for unsaturated hydraulic conductivity associated with the Kosugi three-parameter lognormal moisture retention model. The model derivation uses a slight modification to Mualem's theory, which is nearly exact for nonclay soils. Kosugi's three-parameter lognormal moisture retention model uses physically meaningful parameters, but a corresponding closed-form relative hydraulic conductivity model has never been developed. The model is further extended to a four-parameter model by truncating the underlying pore-size distribution at physically permissible minimum and maximum pore radii. The proposed closed-form models are fitted to well-known experimental data to illustrate their utility. They have the same physical basis as Kosugi's two-parameter model, but are more general.