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ORIGINAL RESEARCH

An Air–Water Interfacial Area Based Variable Tortuosity Model for Unsaturated Sands

^a Fluor Government Group, P.O. Box 1050, Richland, WA 99352
^b Pacific Northwest National Laboratory, Richland, WA 99354
^* Corresponding author (raziuddin_khaleel{at}rl.gov)

Received 9 November 2005.

A new variable tortuosity definition is introduced that is based on the immiscible fluid (air–water) interfacial area. Unsaturated media tortuosity (_a) is defined as the ratio of a_aw to a_aw,o where a_aw is the estimated air–water interfacial area in a real unsaturated medium (i.e., a soil sample), and a_aw,o is the same variable for the corresponding, idealized capillary bundle. The air–water interfacial area for both real and idealized media is directly proportional to the area under their respective retention curves. With being the saturated tortuosity, we relate the variable tortuosity ratio (/_a) to the S_e term in Mualem's ( = 0.5) and Burdine's ( = 2) pore-size distribution models. Thus, instead of using tortuosity and pore connectivity formulations, which have empirical exponents of either 0.5 or 2, the new model depends on a variable interfacial area for varying saturation and soil texture, as reflected in the measured retention data. We tested the new definition of tortuosity to predict unsaturated hydraulic conductivity, K, as a function of volumetric moisture content, , for 22 repacked Hanford sediments that are comprised of mostly coarse and fine sands but some also contain a sizeable fraction (as high as 27%) of fines (silt and clay). Replacing the S_e term in van Genuchten–Mualem (VGM) model by the tortuosity ratio /_a, and still using saturated hydraulic conductivity and moisture retention parameters as used in the conventional approach, we obtained _a-based K() predictions that are nearly identical to the conventional VGM model predictions. We also compared the _a-based K() predictions with the standard Brooks–Corey–Burdine (BCB) model predictions. In comparison to the VGM model predictions, _a-based BCB K() predictions appear to be less biased relative to the measured K for the coarse-textured samples.

Abbreviations: BC, Brooks–Corey capillary pressure desaturation function • BCB, Brooks–Corey–Burdine model • MRC, moisture retention curve • VG, van Genuchten model • VGM, van Genuchten–Mualem model