Accurate estimation of unsaturated hydraulic conductivity, (), is crucial for modeling water and solute transport in variably-saturated soils. In this study, a new model for the estimation of () based on percolation theory and critical path analysis is presented, in which the pore-throat size distribution is described by the three-parameter Weibull probability density function. To evaluate the performance of the proposed () model, two datasets including more than three hundred samples are analyzed. The first dataset includes 240 pore-network simulations, while the second dataset consists of 101 soil samples from the UNSODA database. For the pore-network simulations, for which both pore-throat size distributions and capillary pressure curves are available, we estimate () from the capillary pressure curve with RMSLE = 0.54 slightly better than the estimations obtained from the pore-throat size distribution with RMSLE = 0.6. For the soil samples, since only the capillary pressure curve is measured, we estimate () from the capillary pressure curve and evaluate three previously proposed approaches for determining the exponent, α, in Poiseuille's law. We find that RMSLE = 0.98 for α = 3, RMSLE = 0.87 for α = 2(4 − ) − (3 − )/(2 − 3), and RMSLE = 1.06 for α = 4 − 0.74, in which is the fractal dimension characterizing the pore space. Comparing the results with previous studies in which the power-law probability density function was used to characterize capillary pressure curve and pore sizes shows that the proposed three-parameter Weibull distribution, in conjunction with the CPA analysis, may more accurately estimate () for a wide variety of soils ranging from very fine to very coarse textures.

中文翻译：

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使用三参数威布尔分布的非饱和导水率渗流模型


准确估计非饱和导水率 () 对于模拟饱和土壤中的水和溶质迁移至关重要。本研究提出了一种基于逾渗理论和关键路径分析的()估计新模型，其中孔喉尺寸分布由三参数威布尔概率密度函数描述。为了评估所提出的（）模型的性能，对包含三百多个样本的两个数据集进行了分析。第一个数据集包含 240 个孔隙网络模拟，第二个数据集包含来自 UNSODA 数据库的 101 个土壤样本。对于孔隙网络模拟，孔喉尺寸分布和毛细管压力曲线均可用，我们根据 RMSLE = 0.54 的毛细管压力曲线估计 () 略好于根据 RMSLE 孔喉尺寸分布获得的估计值= 0.6。对于土壤样品，由于仅测量毛细管压力曲线，因此我们根据毛细管压力曲线估计 () 并评估先前提出的三种确定泊肃叶定律中指数 α 的方法。我们发现，对于 α = 3，RMSLE = 0.98；对于 α = 2(4 − ) − (3 − )/(2 − 3)，RMSLE = 0.87；对于 α = 4 − 0.74，RMSLE = 1.06，其中 是分形表征孔隙空间的尺寸。将结果与以前使用幂律概率密度函数来表征毛细管压力曲线和孔径的研究结果进行比较表明，所提出的三参数威布尔分布与 CPA 分析相结合，可以更准确地估计 ()土壤种类繁多，从非常细的土壤到非常粗的质地。