Revising Tortuosity and Multi-Fractal Assumptions of Unsaturated Hydraulic Conductivity from Critical Path Analysis of Percolation Theory

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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.