Predicting relative permeability from water retention: A direct approach based on fractal geometry

Commonly, a soil's relative permeability curve is predicted from its measured water retention curve by fitting equations that share parameters between the two curves (e. g., Brooks/Corey-Mualem and van Genuchten-Mualem). We present a new approach to predict relative permeability by direct application of measured soil water retention data without any fitting procedures. The new relative permeability model, derived from a probabilistic fractal approach, appears in series form as a function of suction and the incremental change in water content. This discrete approach describes the drained pore space and permeability at different suctions incorporating the effects of both pore size distribution and connectivity among water-filled pores. We compared the new model performance predicting relative permeability to that of the van Genuchten-Mualem (VG-M) model for 35 paired data sets from the Unsaturated Soil hydraulic Database (UNSODA) and five other previously published data sets. At the 5% level of significance, the new method predicts relative permeabilities from the UNSODA database significantly better (mean logarithmic root-mean-square error, LRMSE = 0.813) than the VG-M model (LRMSE = 1.555). Each prediction of relative permeability from the five other previously published data sets was also significantly better.