Estimation of Soil Hydraulic Conductivity Function Based on Fractal Geometry and the Capillary Tube Models

In this study, soil hydraulic conductivity function was modeled based on fractal geometry and capillary tube models. The proposed model is expressed as a function of the pore diameter, apparent flow path length, pore fractal dimension and tortuosity fractal dimension. In this study, the relationships concerning calculation of the pore fractal dimension and tortuosity fractal dimension for unsaturated flow was presented as a function of the soil water content. The advantage of this model is lack of empirical constants. Van Genuchten soil water retention curve was used to calculate the pore diameters. In this research, the model was evaluated by using 40 soil samples with 11 different soil textures covering sandy, loam, and clay from the UNSODA database. Results of comparison of unsaturated hydraulic conductivity estimated with fractal model presented in this study and the reported amounts of Van Genuchten model showed that the root mean square error (RMSE) of van Genuchten model was less than the fractal model, while the ratio of geometric mean error (GME) and standard deviation error of fractal geometry model was less than the van Genuchten model. Van Genuchten model had the highest coefficients of variation, with the exception of RMSE parameters. In terms of GMER and GSDER, fractal model was more reliable than the van Genuchten model.