Unsaturated Hydraulic Conductivity Models Based on Truncated Lognormal Pore-size Distributions

TL;DR

This paper introduces new closed-form models for unsaturated hydraulic conductivity based on truncated lognormal pore-size distributions, extending Kosugi's moisture retention model with improved physical realism and applicability.

Contribution

It develops a three-parameter and a four-parameter model for hydraulic conductivity, incorporating pore size truncation to better match physical constraints.

Findings

Models fit well to experimental data

Extended models are more general than previous ones

Physically meaningful parameters enhance model interpretability

Abstract

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 non-clay 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.