Saturated hydraulic conductivity of soil, K_sat, is a critical parameter for mathematical modelling of groundwater and soil water flow. Current empirical K_sat models, such as Kozeny–Carman model, Hazen models, or empirical approaches based on soil pedotranfer functions (PTFs) rely on the specific surface area, certain characteristic particle size(s), for example, d₅, d₁₀, d₁₅, d₅₀, etc., or the fractionation of sand, silt and clay. In this study, we proposed an alternative modelling framework to estimate K_sat from void ratio and arithmetic mean diameter of soil particles. We suggested to describe the particle size distribution (PSD) using a continuous mathematical distribution function, for example, the lognormal distribution function, and to obtain the Sauter mean diameter (d_S) by calculating the moments of the PSD function. The proposed empirical equations were tested against the measured K_sat values for 54 sand samples with available measured PSD and void ratio as reported in Toumpanou et al. and validated using 49 sandy soil samples obtained from the Unsaturated Soil Database (UNSODA). We found that the d_S was more relevant to K_sat than the number mean diameter (d_N) and mass mean diameter (d_M) (the RMSE was 0.486 for K_sat - d_N; 0.187 for K_sat - d_S; and 0.212 for K_sat - d_M, respectively). We also found that the proposed equation with d_S had superior performance over the Hazen equation and PTF-based models. Our results indicated that the K_sat calculated using d_S, which was either estimated from discrete experimental data or calculated from a continuous lognormal PSD function, best matched with the measured values for coarse-textured soils. Future studies should focus on developing empirical relationships for soil water retention curves and other soil properties based on continuous PSD functions.

中文翻译：

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用土壤颗粒Sauter平均直径预测沙土饱和导水率

土壤的饱和导水率K _sat是地下水和土壤水流数学建模的关键参数。当前的经验K _sat模型，例如 Kozeny-Carman 模型、Hazen 模型或基于土壤土壤转移函数 (PTF) 的经验方法依赖于比表面积、某些特征粒径，例如d ₅、d ₁₀ , d ₁₅ , d ₅₀等, 或砂、淤泥和粘土的分馏。在这项研究中，我们提出了一种替代建模框架来估计K _sat土壤颗粒的孔隙比和算术平均直径。我们建议使用连续数学分布函数（例如对数正态分布函数）来描述粒度分布 (PSD)，并通过计算 PSD 函数的矩来获得 Sauter 平均直径 ( d _{S )。}所提出的经验方程针对 54 个砂样的测量K _sat值进行了测试，这些砂样具有可用的测量 PSD 和空隙率，如 Toumpanou 等人报道的。并使用从非饱和土壤数据库 (UNSODA) 获得的 49 个沙土样本进行验证。我们发现d _S与K _sat的相关性高于数字平均直径 ( d_N ) 和质量平均直径 ( d _{M )（} K _sat - d _N的 RMSE 为 0.486 ； K _sat - d _S的 RMSE 为0.187；K _sat - d _M的 RMSE 分别为0.212 ）。我们还发现，提出的具有d _S的方程比 Hazen 方程和基于 PTF 的模型具有更好的性能。我们的结果表明，使用d _S计算的K _sat，它要么根据离散的实验数据估计，要么根据连续对数正态 PSD 函数计算，与粗糙质地土壤的测量值最匹配。未来的研究应侧重于开发基于连续 PSD 函数的土壤保水曲线和其他土壤特性的经验关系。