Two and Three-Phases Fractal Models Application in Soil Saturated Hydraulic Conductivity Estimation

Soil Hydraulic conductivity is considered as one of the most important hydraulic properties in water and solutionmovement in porous media. In recent years, variousmodels as pedo-transfer functions, fractal models and scaling technique are used to estimate the soil saturated hydraulic conductivity (Ks). Fractal models with two subset of two (solid and pore) and three phases (solid, pore and soil fractal) (PSF) are used to estimate the fractal dimension of soil particles. The PSF represents a generalization of the solid and pore mass fractal models. The PSF characterizes both the solid and pore phases of the porous material. It also exhibits self-similarity to some degree, in the sense that where local structure seems to be similar to the whole structure.PSF models can estimate interface fractal dimension using soil pore size distribution data (PSD) and soil moisture retention curve (SWRC). The main objective of this study was to evaluate different fractal models to estimate the Ksparameter.
The Schaapetal data was used in this study. The complex consists of sixty soil samples. Soil texture, soil bulk density, soil saturated hydraulic conductivity and soil particle size distribution curve were measured by hydrometer method, undistributed soil sample, constant head method and wet sieve method, respectively for all soil samples.Soil water retention curve were determined by using pressure plates apparatus.The Ks parameter could be estimated by Ralws model as a function of fractal dimension by seven fractal models. Fractal models included Fuentes at al. (1996), Hunt and Gee (2002), Bird et al. (2000), Huang and Zhang (2005), Tyler and Wheatcraft (1990), Kutlu et al. (2008), Sepaskhah and Tafteh (2013).Therefore The Ks parameter can be estimated as a function of the DS (fractal dimension) by seven fractal models (Table 2).Sensitivity analysis of Rawls model was assessed by making changes)±10%, ±20% and±30%(in input parameters (porosity, fractal dimension and the intake air suction head).Some indices like RMSE, AIC and R2 were used to evaluate different fractal models.
The results of the sensitivity analysis of Rawls - Huang model, showed the least sensitivity to changes in porosity and suction entry air and the most sensitivity to changes in fractal dimension. The saturated hydraulic conductivity is underestimated by increasing the fractal dimension in Rawls - Huang model. The high sensitivity of the combined model to changes in fractal dimension, is considered as one of the model limitations.In other words, fractal dimension underestimation increased the error related to the hydraulic conductivity estimation. Sensitivity analysis of Ks regression model was done among parameters like bulk density, dry density, silt, sand, fractal dimension of particle size and porosity. Results showed less sensitivity to fractal dimension and porosity. The highest RMSE was 0.018 for fractal dimension and porosity (in the range of ±30% changes). The results showed that the amount of clay in the estimation of fractal dimension is of crucial importance. Statistical analyzes indicated the high accuracy of the PSF models based on soil texture data.Error indices showed the high accuracy of Rawls and three-phase fractal (pore- solid- fractal) models combination in estimating the Ks value. The results suggest that Huang and Zhang model, with the highest correlation, the least Root Mean Square Error and the least Akaike criteria among the studied fractal models for estimation of the Ks values. Fuentesand Hunt models, overestimated soil saturated hydraulic conductivity. Fuentes et al. (1996) as an experimental fractal model to estimate the saturated hydraulic conductivity indicatedvery poor results. Bird model had higher error values compared with the best model, (RMSE =0.73). This model fit well with the measured values compared to Sepaskhah and Taylor models particularly at low Ksvalues. Taylor's two-parameter model, which is similar to the Brooks - Corey and the Campbell model, was inserted in the fourth priority. The RMSE values of Sepaskhah and Taylor models were 0.62 (cm/h) and 0.55(cm/h) respectively. The fractal dimension is a function of soil texture. Heavy soils resulted in a larger fractal dimension and less hydraulic conductivity. Therefore, the Huang-Zhang model as a result of clay value using model (lower values for Ks), had a close fit with the measured data in probability distribution.
The results showed that the soil clay percent had a significant role in fractal dimension calculation.