Evaluation of Saturated Hydraulic Conductivity Estimation by Mass and Pore Space Fractal Models

Rezaei, Elnaz; Zeinalzadeh, Kamran

Document Type : Original Article

Authors

Elnaz Rezaei ¹
Kamran Zeinalzadeh ²

¹ Ph.D. Candidate in Irrigation and Drainage, Department of Water Engineering, Urmia University, Urmia, Iran.

² Department of Water Engineering,Urmia Lake Research Institute, Urmia University, Urmia, Iran

Abstract

Over the past few decades, fractal geometry has been extensively used as a powerful tool in characterizing porous media properties and hydraulic soil modeling. In this study, the applicability of fractal dimension values derived from particle size distribution (D_PSD) and soil moisture curve (D_SMC) in estimating saturated hydraulic conductivity (SHC) were compared and evaluated using the new fractal Ghanbarian et al. (2018) model. For this purpose, eight sandy samples were prepared in cylinders with an internal diameter of 4.4 cm and a height of 5 cm. The particle size distribution was determined by the combination of dry and wet sieve methods. Water content was measured in eight tension heads from zero (saturation) to 10 kPa in the sandbox and at 19 higher tension heads, from 18 to 1500 kPa with the pressure plate. For all samples, the bulk and particle density, total porosity, and SHC were also measured. The mass fractal (D_PSD) and pore space fractal (D_SMC) dimensions were determined using the particle size distribution and soil moisture curve (SMC) data, respectively. The root mean square error (RMSE) of fitting SMC by applying the D_SMC and D_PSD were found in the range of 0.004 to 0.022 and 0.009 to 0.069, respectively. The results showed that the D_SMC fits the SMC with higher accuracy than the D_PSD and the D_PSD had no specific correlation with the D_SMC of the samples. The root mean square logarithmic error (RMSLE) for the estimated values of SHC using D_SMC and D_PSD was found to be 0.286 and 0.306, respectively. Although there is no significant difference between the two fractal dimensions, the application of D_SMC values as an image of the microscopic properties of the porous medium and its combination with the percolation theory has improved the accuracy of estimating the SMC and SHC.

Keywords

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Evaluation of Saturated Hydraulic Conductivity Estimation by Mass and Pore Space Fractal Models

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Volume 9, Issue 1June 2021Pages 117-129

Volume 9, Issue 1
June 2021
Pages 117-129