Estimating Effective Hydraulic Parameters of Unsaturated Layered Sediments Using a Cantor Bar Composite Medium Model

Abstract

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.

Hydraulic conductivity of stratified unsaturated soils: Effects of random variability and layering

“…Preuss (2004) further tested the applicability of the harmonic mean as effective K. He applied the van Genuchten (1980) K(h) function to examine 1D (i.e., layering) and 2D heterogeneities and found that the harmonic mean yields reasonable approximations for unsaturated flow in relatively small domains, while the results were less accurate for larger scales. Tang et al (2008) studied the flow characteristics of layered soils with the contour bar model based on the composite medium approximation (COMA) approach introduced by Preuss (2004). Their work was limited to layered soils with two different materials and by some means confirmed the validity of COMA for steady state conditions.…”

Multiscale Soil Investigations: Physical Concepts and Mathematical Techniques

“…Lacunarity proved to be unique among the different parameters studied in its scale‐dependent response to the multiscale image analyses. Tang et al (2008) compute effective hydraulic properties for a monofractal sequence of layers of fine material interbedded within a coarse matrix. Their analytical model, based on the composite medium approximation applied to a Cantor bar, compares favorably with numerical simulations of unsaturated flow, based on Richards' equation, for small hydraulic gradients.…”