Estimating the hydraulic conductivity and diffusivity in unsaturated porous media by fractal capillary model

The geometrical distribution of water within the pores of unsaturated soil texture is very complex. Herein, a physical conceptual model for soil texture and pore structure that is based on the concept of fractal geometry is proposed. Traditionally, a capillary model is popular for representing the pores of soil. However, it is not easy to construct the complicated distribution of pores using the simple capillary model, because the water within pore path is affected substantially by anfractuosity. In consideration of the above, this study focuses on the application of fractal geometry to establish the capillary flow path in soil, and to estimate the hydraulic conductivity and diffusivity of unsaturated soil from experimental soil water retention curves. From the results, the fractal dimension of the constructed capillary tube is approximately 1.208 and the optimal value of the tortuosity ratio is 1.27. That is, the tortuosity factor of fractal soil texture is 0.62, in conformity with the experiential value 0.6 similar to 0.66.