Fractal modeling of hydraulic conductivity in non-saturated soils

Abstract

From a theoretical point of view we study the hydraulic conductivity that appears at the generalized Darcy law of non-saturated soils. The relation between the hydraulic conductivity and the water's volumetric content is established from the hypothesis that microscopic and macroscopic levels of water movement are described by Poiseuille and Darcy's laws, respectively We made a distinction between pore radius that define areal porosity and volumetric porosity in the emergence of macroscopic law from the microscopic law The relation between radius and porosities has been established from tortuosity concepts of the movement paths of water and The correlation between pores. Concepts Mat are based on the relation between total volumetric porosity and soil's fractal dimension, This distinction has lead into a conceptual hydraulic conductivity model, to which has been introduced the classic hypothesis relative to radius weights in the resistence offered to movement of water by soil. This, in turn, has allowed to obtain different particular models. A simplification of these models has given way to reencounter the classic models proposed in Me literature. The empiric corrections made to classic models of hydraulic conductivity relative to hydraulic conductivity by saturation, are justified in the formalism of fractal geometry The correction depends on the value of the fractal dimension of each soil type.