Estimating soil mass fractal dimensions from water retention curves

The drying branch of the water retention curve is widely used for modeling hydrologic processes and contaminant transport in porous media. A prefracta l model is presented for this function based on the capillary equation and a randomized Menger sponge algorithm with upper and lower scaling limits. T he upper limit is the air entry value (Psi(0)) and the lower limit is the t ension at dryness (Psi(j)). Between these two limits the theoretical curve is concave when plotted as relative saturation (S) vs, the log of tension ( Psi). The mass fractal dimension (D) controls the degree of curvature, with decreasing concavity as D --> 3. The theoretical equation was fitted to wa ter retention data for six soils from Campbell and Shiozawa [Campbell, G.S. , Shiozawa, S., 1992. Prediction of hydraulic properties of soils using par ticle size distribution and bulk density data. International Workshop on In direct Methods for Estimating the Hydraulic properties of Unsaturated Soils . University of California Press, Berkeley, CA, pp. 317-328]. These data co nsisted of between 31 and 39 paired measurements of S and Psi for each soil , with Psi ranging from 3.1 x 10(0) to 3.3 x 10(5) kPa. All of the fits wer e excellent with adjusted R-2 values greater than or equal to 0.96. The res ulting estimates of D were all significantly less than three at P < 0.05. T he lowest value of D was 2.60 for a sandy loam soil, and the highest was 2. 90 for a silty clay soil. Refitting the same data, but over a restricted su bset of Psi's less than or equal to 1.5 x 10(3) kPa, produced errors in the estimation of D. Two of the estimates of D were significantly greater than three at P < 0.05. To estimate D accurately, water retention data covering the entire tension range from saturation to zero water content are require d. In the absence of such data, it is possible to obtain physically reasona ble estimates of D by setting Psi(j) = 10(6) kPa, the approximate tension a t oven dryness, and fitting the proposed equation as a two parameter model. (C) 1999 Elsevier Science B.V. All rights reserved.