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Contaminates behave differently in the vadose zone than they do in the saturated zone and the governing equations for them are more involved. The hydraulic conductivity and porosity are the most important parameters affecting water and contaminates movements in the vadose and the saturated zones. To estimate these parameters certain methods are examined for measuring the hydraulic properties where the soil permeability is low and, where possible, the results are compared with measured data. Unsaturated hydraulic conductivity (UHC), unlike saturated hydraulic conductivity (SHC), is difficult to obtain especially for clayey soils and fractured rocks. Most available studies either overestimate or underestimate the UHC, especially for values close to the surface where the UHC values are several orders less than their corresponding values for SHC. The goal of this paper is to adjust and modify some empirical equations for obtaining UHC and compare the results with those already available in the literature. This is achieved through the use of non-linear least squares. Values that represent parameter b, in the Campbell's power function is allowed to vary in a given range instead of having a single value. For every value in this range the non-linear least squares equations is calculated and the b value with the smallest error term is picked to represent the empirical parameter for the Campbell's power function. Results indicate adjustment to the reported empirical parameter b is needed to minimize the sums of squares and to obtain a closer match between the measured and the experimental data. That is the sum of errors for the non-linear least squares between measured and empirical data is minimum somewhere near the values that they suggested. Therefore, for the clayey soil and fractured rocks the empirical parameters for the power function are modified to reflect the minimum sums of squares for non-linear least squares equation. To fine tune b further, non-linear least squares are used to find the best fitted value of b using the empirical equation that relates depth (h) to water content. We are in the process of classifying fractured rocks and are testing them to see how their hydraulic conductivity compares with clayey, sandy and silty soils. This is done through the application of fractal geometry and use of Sierpinski carpet. The empirical and the theoretical relationships used here are simple and practical and may directly be applied to obtain corresponding UHC. The equations that are utilized here are based on the theory or have their roots in statistical modeling. Results obtained from this investigation should be compared with the field data before they are applied toward solving Richards' equation.
vadose zone, saturated zone, permeability, hydraulic conductivity, least squares
Statistical Consultant & Assistant Professor, University of Mississippi, University, MS
Graduate Student, University of Mississippi, University, MS