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[AGE34-02] Estimation of hydraulic conductivity based on the extended Durner model
Keywords:hydraulic conductivity function, Durner model, Generalized hydraulic conductivity estimation model, extended Durner model
Soil hydraulic characteristics such as Water Retention Function (WRF) and Hydraulic Conductivity Function (HCF), are essential for numerical analysis of unsaturated soil water flow based on Richards equation. WRF (θ(h) or S(h)) describes a relationship between water content θ (or effective saturation S) and soil water pressure head h, while HCF (K(h) or Kr(h)) represents the relationship between hydraulic conductivity K (or relative conductivity Kr) and h. In particular, WRF combined with a hydraulic conductivity estimation model (e.g. Burdine, 1952; Mualem, 1976; Hoffman-Riem et al., 1999) allows us to predict difficult-to-measuring K(h) using only a few parameters, as most of the parameters are shared with WRF.
The classical WRF, represented by the van Genuchten model (van Genuchten, 1980), coupled with the Mualem model for HCF has been widely applied to non-structured or non-aggregated soils. However, it is also well known that it does not work for, for example, aggregated soils in which different types of pore structure exist. To address this issue, Durner (1994) proposed a WRF that linearly combines two van Genuchten models as sub-models (the Durner model). The Durner model is also coupled with the Mualem model to predict HCF. Each sub-model characterizes the WRF values in different soil water pressure regions, thereby expressing the variation in hydraulic properties between these regions.
The Durner-Mualem model (Priesack and Durner, 2006), has only one parameter that is independent from the WRF model. As the value of this parameter affects the entire pressure range, the Durner-Mualem model lacks the necessary parameters to independently adjust the function values in the different soil water pressure regions, making it insufficient for representing changes in hydraulic properties across a wide range of soil water pressure.
As the generalized HCF model proposed by Hoffman-Riem et al., (1999) has three parameters, it is more flexible than the Durner-Mualem model (Seki et al., 2022, 2023). However, there has been little validation of the properties of this HCF (extended Durner model of eDu).
In this study, we proposed to introduce an additional arbitrary shared point (h, Kr) = (hb, Kb) along with the inherent shared point at saturation, where (h, Kr) = (0, 1), in the eDu model. When the HCF shares (0, 1) and (hb, Kb), two of the three parameters satisfy a linear relationship. Under this constraint, while the HCF curves between the two fixed share points (0,1) and (hb, Kb) are relative invariant, curves below hb vary depending upon the choice of the parameter, allowing more flexible modeling of HCF. This demonstrates that the extended Durner model overcomes the limitations of the Durner-Mualem model. This study presents the characteristics of the eDU with a fixed shared point and demonstrates its performance using the experimental WRF and HCF data.
The classical WRF, represented by the van Genuchten model (van Genuchten, 1980), coupled with the Mualem model for HCF has been widely applied to non-structured or non-aggregated soils. However, it is also well known that it does not work for, for example, aggregated soils in which different types of pore structure exist. To address this issue, Durner (1994) proposed a WRF that linearly combines two van Genuchten models as sub-models (the Durner model). The Durner model is also coupled with the Mualem model to predict HCF. Each sub-model characterizes the WRF values in different soil water pressure regions, thereby expressing the variation in hydraulic properties between these regions.
The Durner-Mualem model (Priesack and Durner, 2006), has only one parameter that is independent from the WRF model. As the value of this parameter affects the entire pressure range, the Durner-Mualem model lacks the necessary parameters to independently adjust the function values in the different soil water pressure regions, making it insufficient for representing changes in hydraulic properties across a wide range of soil water pressure.
As the generalized HCF model proposed by Hoffman-Riem et al., (1999) has three parameters, it is more flexible than the Durner-Mualem model (Seki et al., 2022, 2023). However, there has been little validation of the properties of this HCF (extended Durner model of eDu).
In this study, we proposed to introduce an additional arbitrary shared point (h, Kr) = (hb, Kb) along with the inherent shared point at saturation, where (h, Kr) = (0, 1), in the eDu model. When the HCF shares (0, 1) and (hb, Kb), two of the three parameters satisfy a linear relationship. Under this constraint, while the HCF curves between the two fixed share points (0,1) and (hb, Kb) are relative invariant, curves below hb vary depending upon the choice of the parameter, allowing more flexible modeling of HCF. This demonstrates that the extended Durner model overcomes the limitations of the Durner-Mualem model. This study presents the characteristics of the eDU with a fixed shared point and demonstrates its performance using the experimental WRF and HCF data.