Evaluation of a general model for multimodal unsaturated soil hydraulic properties

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.Comment: To be published in Journal of Hydrology and Hydromechanic

Closed-form hydraulic conductivity equations for multimodal unsaturated soil hydraulic properties

Closed-form expressions of the hydraulic conductivity function for linearly superposed subretention (multimodal) functions were derived for arbitrary sets of the Brooks and Corey (BC), van Genuchten (VG), and Kosugi (KO) water retention models. The generalized Mualem hydraulic conductivity model was evaluated using the mathematical approach of Priesack and Durner. Three types of modification to the multimodel were also proposed. Firstly, the derived conductivity equations can be simplified when the submodel parameters, hbi for the BC model, alpha i-1 for the VG model, and hmi for the KO model have the same (common) value (denoted as CH). Secondly, as in the case of the modified single VG and KO models, a hypothetical air-entry head near saturation can be introduced for the multimodal VG and KO models to prevent unrealistic reductions in the hydraulic conductivity near saturation when the VG n parameter approaches its lower limit of n = 1. Furthermore, the multimodal hydraulic conductivity functions become a simple sum of conductivity subfunctions when the exponent r is unity (such as for Burdine's model), which leads to independent tortuosity effects for each submodel. The models are illustrated for two soils: a highly aggregated Kumamoto Andisol and a relatively unimodal dune sand. The dual-(BC, VG, KO) and the VG(1)BC(2) models equally represented the water retention data of the Andisol, with similar hydraulic conductivity curves. The dual-BC-CH, dual-VG-CH, and VG(1)BC(2)-CH models fitted the water retention data of the dune sand well, with the hydraulic conductivity curves of the dual-porosity model being similar to those of the Fayer and Simmons (FS) model

Evaluation of a general model for multimodal unsaturated soil hydraulic properties

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)1BC2-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 (Ks) 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 R2 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 R2 for the widely used Peters model (0.956) when optimizing (Ks, p, a, ω). The proposed equations are useful for practical applications while mathematically being simple and consistent

Closed-form hydraulic conductivity equations for multimodal unsaturated soil hydraulic properties

Closed-form expressions of the hydraulic conductivity function for linearly superposed subretention (multimodal) functions were derived for arbitrary sets of the Brooks and Corey (BC), van Genuchten (VG), and Kosugi (KO) water retention models. The generalized Mualem hydraulic conductivity model was evaluated using the mathematical approach of Priesack and Durner. Three types of modification to the multimodel were also proposed. Firstly, the derived conductivity equations can be simplified when the submodel parameters, hbi for the BC model, alpha i-1 for the VG model, and hmi for the KO model have the same (common) value (denoted as CH). Secondly, as in the case of the modified single VG and KO models, a hypothetical air-entry head near saturation can be introduced for the multimodal VG and KO models to prevent unrealistic reductions in the hydraulic conductivity near saturation when the VG n parameter approaches its lower limit of n = 1. Furthermore, the multimodal hydraulic conductivity functions become a simple sum of conductivity subfunctions when the exponent r is unity (such as for Burdine's model), which leads to independent tortuosity effects for each submodel. The models are illustrated for two soils: a highly aggregated Kumamoto Andisol and a relatively unimodal dune sand. The dual-(BC, VG, KO) and the VG(1)BC(2) models equally represented the water retention data of the Andisol, with similar hydraulic conductivity curves. The dual-BC-CH, dual-VG-CH, and VG(1)BC(2)-CH models fitted the water retention data of the dune sand well, with the hydraulic conductivity curves of the dual-porosity model being similar to those of the Fayer and Simmons (FS) model