The Green-Ampt Approximation. Xxxxx’x Law is often used to describe infiltration in unsaturated systems through an approximation that is termed the Green-Ampt equation (e.g., Chin, 2000). The Green- Ampt equation was developed by using Xxxxx’x Law in conjunction with a set of assumptions regarding flow field geometry and material properties. This approach assumes ponded water at the ground surface and a wetting front that extends to a depth, L, as shown in Figure 1.1. The wetting front is assumed to move downward as a sharp interface. The soil is assumed to be saturated above the wetting front (the water content is assumed equal to the porosity). The water content below the wetting front is assumed to be equal to some lower initial value. The rate of infiltration is approximated by the following expression: f (t) = K ⎡ Ho + L + hwf ⎤
The Green-Ampt Approximation. Xxxxx’x Law is often used to describe infiltration in unsaturated systems through an approximation that is termed the Green-Ampt equation (e.g., Chin, 2000). The Green- Ampt equation was developed by using Xxxxx’x Law in conjunction with a set of assumptions regarding flow field geometry and material properties. This approach assumes ponded water at the ground surface and a wetting front that extends to a depth, L, as shown in Figure 1.1. The wetting front is assumed to move downward as a sharp interface. The soil is assumed to be saturated above the wetting front (the water content is assumed equal to the porosity). The water content below the wetting front is assumed to be equal to some lower initial value. The rate of infiltration is approximated by the following expression: f (t) = K ⎡ Ho + L + hwf ⎤ (1.5) sat ⎢ ⎥ ⎣ L ⎦ where f(t) = the infiltration rate at time t (L/t), Ksat = saturated hydraulic conductivity (L/t), Ho = depth of water in the pond or infiltration facility (L), L = depth of the wetting front below the bottom of the pond (L), and hwf = average capillary head at the wetting front (L). Approximately equal to the air entry pressure or bubbling pressure. Equation (1.5) can be solved to estimate infiltration rate as a function of time (e.g., Xxxxxxxx and Xxxxxxxxx, 1994). Table 1.2 summarizes the values for input variables that were used to compare infiltration rates for different soil types. These values were chosen on the basis of averages reported by Xxxxxx and Xxxxxxx (1988) for these soil types. The depth of water in the infiltration facility, Ho, is assumed to be small in these calculations. The general shape of the infiltration curve that derived from Equation 1.5 is shown in Figure 1.2 for a “loamy sand” soil type. Curves for other soil types will have similar shapes, but with different infiltration rates at steady-state and different time periods required to achieve these steady-state rates. The initial infiltration rates are higher than the saturated hydraulic conductivity because of the relatively high gradients when the wetting front is shallow (L in equation (1.5) is small). As the depth of the wetting front increases, the gradient decreases and the infiltration rate approaches the saturated hydraulic conductivity, Ksat. Table 1.2 summarizes the results for three different soil types that are often associated with infiltration facilities. The results presented in Figure 1.2 and Table 1.3 have important implications for the desig...
