A CANTOR BAR MODEL FOR THE EFFECTIVE HYDRAULIC CONDUCTIVITY OF PARTIALLY- SATURATED LAYERED SOIL

Fractal mathematics has been used to characterize and simulate porous media, as well as to model flow and transport phenomena. The objective of this research was to investigate the effective hydraulic conductivity (K_eff) of layered porous media with the thickness and number of horizontal layers being determined by a deterministic Cantor Bar (CB). Simulations of water flow under partially- saturated conditions were performed using the Hydrus 2D software. A layered system of clay loam and silt loam soils was created in Hydrus 2D following the first 4 iterations of a CB with fractal dimension: D = log(2)/log(3) ≈ 0.631 and b = 3. At the zero^th iteration, the vertical water flux was simulated in the column packed with pure clay loam. With increasing iterations, the content of the silt loam increased until it was greater than the material originally constituting the column. Each column was subjected to a 100-hour vertical flow experiment with six different water potential gradients (0 to -1; -1 to -10; -90 to -100; -900 to -1000; -9000 to -10000 and -90000 to -100000 cm), with the gradient always decreasing from the top to the bottom of the column. The results show that after just a few iterations (layers) the K_eff function in the vertical direction tracks the hydraulic conductivity of the finer clay loam material at high water contents, and that of the coarser silt loam material at low water contents. The advantage using the CB model in this context is that the K_eff function can be defined in terms of the fractal parameters (in this case b=3 and D=0.631) used to generate the layering, thereby yielding the possibility of an analytical expression for K_eff. Estimates of the fractal parameters can be obtained from independent measurements of the geometry of layered systems. Therefore, this type of modeling approach can be useful for developing predictive expressions for the effective hydraulic properties of real world systems such as the layered sediments underlying U.S. Department of Energy (DOE) facilities at Hanford, Washington.