A Universal Model of Unsaturated Hydraulic Conductivity With Complementary Adsorptive and Diffusive Process Components

Abstract

AbstractAccurate estimation of unsaturated hydraulic conductivity (HC) is one of the most challenging problems in soil science. Here, we propose a novel approach to model HC using percolation theory. Transient behavior of water transport phenomena at low moisture contents requires additional physical process representation, beside capillary conductivity, to ensure accurate prediction of unsaturated HC. We augment the capillary model from percolation theory with two additional components, namely, (1) film flow, which is the product of volumetric flow rate per perimeter by specific perimeter of solid particles, and (2) isothermal vapor HC, derived from the Fick's law of vapor diffusion and relative humidity. The fractal characteristics of last fractal regime are used to model tortuosity and ultimately HC of vapor flow. Since the typical pressure head range of universal scaling from percolation theory is analogous to the range of vapor flow, we demonstrate that the universal scaling presented in previous studies is not sufficient to model HC for water contents below a crossover point. We also, by analyzing the scaled water retention properties, demonstrate that most studied soils exhibit three fractal regimes. Therefore, a piecewise HC function of capillary flow is developed to account for three fractal regimes, providing more flexibility for soils with multimodal characteristics. The proposed joint HC function is more accurate compared to the model of Peters‐Durner‐Iden and predecessor percolation theory models.