Abstract

In this study, we developed a general mathematical relationship to determine hydraulic tortuosity. An optimization code was run in MATLAB R2014a software, using Monte Carlo algorithm, to determine tortuosity at different water contents for 69 soil samples of UNSODA. Considering fractal concepts, a linear equation was developed empirically to determine hydraulic tortuosity as a function of effective saturation, pore fractal dimension, porosity, inverse of air entry pressure, and soil water content. Based on the results, estimated values of tortuosity using the proposed relationship were greater than the values proposed by Shepard by about 30%. To evaluate developed equation, statistical parameters of Root Mean Square of Logarithmic Deviation (RMSLD) and Akaike’s Information Criterion (AIC_c) were used for 17 soil samples. According to the calculated statistical parameters, the developed equation to estimate tortuosity has improved the results of Shepard’s method. Though the developed equation has a relatively complicated structure, it displays acceptable performance in terms of the compromise between accuracy and complexity. Furthermore, based on calculated tortuosity values using developed equation, we determined pore continuity according to Burdine’s model (1953). Considering the results, calculated pore continuity is much less than the value proposed by Burdine (1953) and is approximately close to the values proposed by Mualem (1976).

中文翻译：

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非饱和流框架下的曲折分析

摘要

在这项研究中，我们建立了确定水力曲折度的一般数学关系。使用Monte Carlo算法在MATLAB R2014a软件中运行了优化代码，以确定UNSODA的69个土壤样品在不同含水量下的曲折度。考虑分形概念，根据经验开发了线性方程式，以确定水力曲折度与有效饱和度，孔隙分形维数，孔隙度，进气压力的倒数和土壤含水量的关系。根据结果​​，使用建议的关系估算的曲折度要比Shepard建议的估算值大30％。为了评估已开发的方程，对数偏差均方根（RMSLD）和Akaike信息准则（AIC _c）用于17个土壤样品。根据计算的统计参数，开发的估算曲折度的方程改进了Shepard方法的结果。尽管所开发的方程具有相对复杂的结构，但在准确性和复杂性之间的折中方面，它显示出可接受的性能。此外，基于使用发达方程式计算的曲折度值，我们根据Burdine模型（1953）确定了孔隙连续性。考虑到结果，计算出的孔隙连续性远小于Burdine（1953）提出的值，并且近似接近Mualem（1976）提出的值。