Evaluation of a general model for multimodal unsaturated soil hydraulic properties

TL;DR

This study evaluates multimodal hydraulic property models for various soils, demonstrating their practical utility and superior fit to measured data compared to traditional models, through extensive parameter optimization and sensitivity analysis.

Contribution

It introduces and validates multimodal water retention and hydraulic conductivity equations that outperform conventional models across diverse soil types.

Findings

KBC model achieved highest R^2 (0.985) with optimized parameters.

Multimodal models require optimization of two parameters for accuracy.

Proposed equations are simple, consistent, and practically useful.

Abstract

Many soils and other porous media exhibit dual- or multi-porosity type features. In a previous study (Seki et al., 2022) we presented multimodal water retention and closed-form hydraulic conductivity equations for such media. The objective of this study is to show that the proposed equations are practically useful. Specifically, dual-BC (Brooks and Corey)-CH (common head) (DBC), dual-VG (van Genuchten)-CH (DVC), and KO (Kosugi)$_1$BC$_2$-CH (KBC) models were evaluated for a broad range of soil types. The three models showed good agreement with measured water retention and hydraulic conductivity data over a wide range of pressure heads. Results were obtained by first optimizing water retention parameters and then optimizing the saturated hydraulic conductivity (K_s) and two parameters (p, q) or (p, r) in the general hydraulic conductivity equation. Although conventionally the tortuosity factor p is optimized and (q, r) fixed, sensitivity analyses showed that optimization of two parameters (p+r, qr) is required for the multimodal models. For 20 soils from the UNSODA database, the average $R^2$ for log (hydraulic conductivity) was highest (0.985) for the KBC model with r=1 and optimization of (Ks, p, q). This result was almost equivalent (0.973) to the DVC model with q=1 and optimization of (Ks, p, r); both were higher than $R^2$ for the widely used Peters model (0.956) when optimizing (Ks, p, a, $\omega$). The proposed equations are useful for practical applications while mathematically being simple and consistent.