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Abstract
A fractal analysis of the soil retention and hydraulic conductivity curves is presented. The retention process is modeled by a two fractal regimes: one pertaining to high water content values, and another accounting for the low water content data. This significantly improves the physical insight of the retention process as compared with the case of one-fractal models. The fractal dimensions characterizing the two regimes are estimated by fitting the retention curve model upon real data, and subsequently they are used to determine the hydraulic conductivity which for the retention curve models of Mualem and Burdine, is obtained in closed form. The reliability of the model is tested against independent conductivity data collected in a field-scale campaign.
Highlights
The hydraulic conductivity is a fundamental prerequisite: 1) to quantify the movement of water, and 2) to predict transport phenomena taking place in soils
The fractal dimensions of the WRCs (3) and (4) were estimated by a nonlinear regression, and the most important results are presented in Figure 1(a), Figure 2(a) and Figure 3(a), whereas the full analysis of the data-set is summarized in the Table 1
A different situation is encountered with the values of the fractal dimension D1 that characterizes the low water content
Summary
The hydraulic conductivity is a fundamental prerequisite: 1) to quantify the movement of water, and 2) to predict transport phenomena taking place in soils. An important boost came from the fractal geometry [6]-[8] which was used to characterize the hydraulic conductivity by means of the fractal properties of pore spaces ([9] [10]). This has permitted relating the fractal dimension at low water content values to the physics of thin water films [11] either by combining Kock’s curve to the flow (Poiseuille) equation [12], or by dealing with the fractal dimension of the porosity and a diffusion-type (Millington and Quirk) equation [13].
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