Estimating effective hydraulic parameters of unsaturated layered sediments using a cantor bar composite medium model

The estimation of effective hydraulic parameters of variably saturated layered sediments has been extensively studied using deterministic, stochastic, and combined modeling approaches. Heterogeneity and scale dependence remain as major obstacles, however, for the prediction of water flow and contaminant transport at many U.S. Department of Energy sites. We used a physically based Cantor bar model to describe scale dependence of the fractions of coarse and fine materials in layered sediments. The Cantor bar is determined by three fractal parameters: the subdivision factor, b, the fractal dimension, D, and the iteration level, i, which can be estimated from observation (e.g., borehole logs). Because b and D are scale invariant, the model can be used to predict layering at scales other than the observation scale. Together with a composite medium approximation (COMA), the Cantor bar model can be used to predict effective hydraulic properties as a function of scale. Numerical simulation results showed that COMA works well for steady-state unsaturated flow through a stratigraphic sequence comprised of thin layers of fine material interbedded within a coarse material. Further work is necessary to validate the model predictions by performing measurements at different scales, and to assess the applicability of this approach for transient flow.