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Abstract
For rectangularly abrupt water-content transients (water content (theta) versus time t at fixed positions), the familiar Green and Ampt equation was rigorously derived for both downward infiltration and upward rise of water into porous media. This provided an unambiguous interpretation for the water-front suction head P, including its dependence on both the unsaturated conductivity function and the initial water content (theta)(,0). For more gradually changing water-content transients, a solution to the minimally nonlinear Burgers equation yielded the Swartzendruber equation for upward water rise, as the counterpart to the similarly derived Knight equation for downward infiltration.
Experimentally, downward infiltration and upward rise of water were measured on uniformly packed laboratory columns of narrow-sized (0.149-0.210 mm) quartz sand, both initially moist and initially air-dry. Intra-column water contents at various times and fixed positions were measured with a thin beam (1 mm) of gamma rays from a ('137)Cs source. The equation of the cumulative normal distribution served very well as an empirical description of these experimental transients, especially for a quantitative measure of abruptness. Cumulative quantities of water entering the columns, along with visual wet-front penetration, were also measured with time.
For downward infiltration, the Green and Ampt equation fitted the sand data better than the Knight equation, and gave a hydraulic conductivity K(,1) essentially equal to the hydraulic conductivity K(,d) for water dripping steadily from the bottom end of the sand column. Two methods of determining the Green-and Ampt- suction head P gave the unexpected result of a larger P for sand when initially moist than when initially air dry. For upward water rise, the Green and Ampt approach failed in practically every respect.
