Analysis of constant head borehole infiltration tests in the vadose zone

摘要

Many environmental studies of water transport through the vadose zone require a field determination of saturated hydraulic conductivity. The purpose of this dissertation is to analyze the reliability of existing methods to determine saturated hydraulic conductivity, K(s), in the vadose zone from constant head borehole infiltration test data. In methods developed by the U. S. Bureau of Reclamation [USBRI, and in lesser known ones, K(s) is computed knowing the height of water in the borehole, length open to the formation, borehole radius, distance above the water table, and steady flow rate. The mathematical formulas on which these methods rest are derived on the basis of numerous simplifying assumptions. The free surface approach is used as the conceptual model of flow from a borehole. Results of numerical simulations are used to compare with the analytical solutions. Simulations with a steady-state finite element computer program, FREESURF, show that the Nasberg-Terletskata solution most closely approximates flow from a borehole with the free surface approach. The influence of capillarity is simulated for saturated-unsaturated porous media in four soils using a finite element computer program, FLUMP, and an integrated finite difference program, TRUST. Contrary to what one finds with the free surface approach, only a small portion of the flow field near the borehole is saturated at steady-state and the cross sectional area normal to the flow path increases with depth below the borehole. For deep water table conditions in fine textured soils, values of K(s) computed using the USBR open-hole equations may be more than 160% greater than the true values; and in coarse sands the USBR solutions may under-estimate the actual value by more than 35%. Mostly because of the influence of unsaturated soil properties there is no unique relationship between K(s), borehole conditions, and steady flow rate, as implied in the analytical solutions. Steady-state simulations demonstrate that existing solutions for borehole infiltration tests in anisotropic or nonuniform soils may also lead to significant errors. Time dependent simulations show that the time to reach a steady flow rate may be more than several days in very dry, low-permeable soils. The time to reach a steady flow rate can be significantly reduced by decreasing the open area between the borehole and formation while increasing the height of water in the borehole. Two methods are proposed to minimize the time, water volume requirements, and cost of conducting constant head borehole infiltration tests. Simulations show that a plot of the inverse of flow rate versus logarithm of time departs from a straight line after about 80% of the steady rate is achieved for various soil and borehole conditions; the steady rate is approximately 0.8 times the rate at the break in slope. In the second method flow rate is plotted versus the inverse of the square root of time and the steady rate is estimated within about 10% by linear extrapolation of early time measurements. USBR field data generally support this linear relationship. Two empirical equations are proposed to compute K(s). The first is applicable for a range of borehole conditions and approximately accounts for capillary effects with a single parameter. The second applies if the height of water in the borehole is I meter, and is based on the time to reach 80% of the steady rate and saturation deficit of the field soil.