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The drying branch of the water retention curve is widely used for modeling hydrologic processes and contaminant transport in porous media. A prefractal model is presented for this function based on the capillary equation and a randomized Menger sponge algorithm with upper and lower scaling limits. The upper limit is the air entry value (Ψ0) and the lower limit is the tension at dryness (Ψj). Between these two limits the theoretical curve is concave when plotted as relative saturation (S) vs. the log of tension (Ψ). The mass fractal dimension (D) controls the degree of curvature, with decreasing concavity as D→3. The theoretical equation was fitted to water retention data for six soils from Campbell and Shiozawa [Campbell, G.S., Shiozawa, S., 1992. Prediction of hydraulic properties of soils using particle size distribution and bulk density data. International Workshop on Indirect Methods for Estimating the Hydraulic properties of Unsaturated Soils. University of California Press, Berkeley, CA, pp. 317–328]. These data consisted of between 31 and 39 paired measurements of S and Ψ for each soil, with Ψ ranging from 3.1×100 to 3.3×105 kPa. All of the fits were excellent with adjusted R2 values ≥0.96. The resulting estimates of D were all significantly less than three at P |
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