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A Tensorial Connectivity–Tortuosity Concept to Describe the Unsaturated Hydraulic Properties of Anisotropic Soils

Pacific Northwest National Laboratory, Richland WA

View larger version (122K): [in a new window]   Fig. 1. The contour of log(Ks) of the synthetic heterogeneous anisotropic soils with the 2Y = 2.0. The values of R are (a) 1, (b) 10, (c) 50, and (d) 100. Ks is the saturated hydraulic conductivity, R is the ratio of correlation length at the direction parallel to soil strata and that normal to soil strata, and Y = ln(Ks) and 2Y is the variance of Y.

View larger version (31K): [in a new window]   Fig. 2. Retention curves of anisotropic soils with different levels of heterogeneities and R = 50. Lines: best-fits parallel to soil strata (crosses) and normal to soil strata (circles). R is the ratio of correlation length at the direction parallel to soil strata and that normal to soil strata; is the inverse macroscopic capillary length; n is the pore size distribution parameter; Y = ln(Ks), with Ks being the saturated hydraulic conductivity; and 2Y is the variance of Y.

View larger version (15K): [in a new window]   Fig. 3. The relationship of (a) vs. 2Y and (b) n vs. 2Y. is the inverse macroscopic capillary length; n is the pore size distribution parameter; Y = ln(Ks), with Ks being the saturated hydraulic conductivity; and 2Y is the variance of Y.

View larger version (38K): [in a new window]   Fig. 4. The unsaturated hydraulic conductivity of anisotropic heterogeneous soils with 2Y = 2.0. Lines: best-fits parallel to soil strata (crosses) and normal to soil strata (circles). Lp is the connectivity–tortuosity coefficient at the direction parallel to the strata and Ln at the direction normal to strata; R is the ratio of correlation length at the direction parallel to soil strata and that normal to soil strata; Y = ln(Ks), with Ks being the saturated hydraulic conductivity; and 2Y is the variance of Y.

View larger version (36K): [in a new window]   Fig. 5. The relative error in the unsaturated hydraulic conductivity, K(h), of anisotropic heterogeneous soils with 2Y = 2.0 when the tensorial connectivity–tortuosity (TCT) model is used to describe K(h) at the direction parallel to the soil strata, Kp(h) (crosses), and that at the direction normal to soil strata, Kn(h) (circles). Lp is the connectivity–tortuosity coefficient at the direction parallel to the strata and Ln at the direction normal to strata; R is the ratio of correlation length at the direction parallel to soil strata and that normal to soil strata; Y = ln(Ks), with Ks being the saturated hydraulic conductivity; and 2Y is the variance of Y.

View larger version (30K): [in a new window]   Fig. 6. The relationship between L vs. ln(R*) of the soils with the different levels of heterogeneity. L is the connectivity–tortuosity coefficient; R* is the ratio of correlation length at the direction parallel to flow and that normal to flow; Y = ln(Ks), with Ks being the saturated hydraulic conductivity; and 2Y is the variance of Y.