Revising tortuosity and multi-fractal assumptions of unsaturated hydraulic conductivity from critical path analysis of percolation theory

The relation between soil pore structure and water retention is complex and is often not well determined. We present a novel approach based on critical path analysis from percolation theory to refine hydraulic conductivity estimation from soil water retention curve by introducing a new tortuosity parameter as a function of scaling factor. We generalize this model to account for large shifts in the relation between soil pore structure and water retention, which are indicative of soils with multi-fractal properties, by employing a t-test on scaled saturation and suction data. The proposed model relaxes the constraints that were set on model parameters for multi-fractal soils in the literature by tuning all parameters against observed data using a multiple-start gradient-based optimization algorithm, and is applicable to a wider variety of soil textures. The optimization results are further evaluated against those of a Markov Chain Monte Carlo algorithm to ensure global optimum is found. Goodness-of-fit (GOF) measures, including geometric mean and standard deviation error ratios, and Nash-Sutcliffe efficiency, show that the proposed model presents less bias across the entire range of matric potential compared to its predecessor that under-estimate hydraulic conductivity in all studied cases.