Exact solutions are obtained by the hodograph method for saturated seepage flow over an impermeable base of slope 30° to the horizontal, when the rate of replenishment by distributed infiltration has a ‘critical’ value of 0.0718 times the hydraulic conductivity. Three different problems are considered, (a) Flow over a slope into a horizontal slit drain. The width of drain effective in removing water is equal to about 4.0% of the downslope distance, and the maximum depth of water (measured normal to the impermeable layer) is about 10% and occurs at 72% of the distance downslope. The approximate solution obtained using the extended form of Dupuit-Forchheimer assumption (cf. part 1) is in excellent agreement with the exact result except near the slit drain. (b) Flow with finite depth at the highest point. The Dupuit-Forchheimer assumption is asymptotically correct at large distances downstream but fails as the highest point on the phreatic surface is approached, where the surface is horizontal, (c) Seepage surface parallel to the impermeable layer (the permeable overburden problem). The depth of saturated flow increases with downslope distance, until the phreatic surface intersects the seepage surface at a downslope distance of 7.3 times the overburden depth. Flow across the seepage surface (an inflow) decreases rapidly with further distance downslope. The extended Dupuit-Forchheimer assumption leads to an excellent prediction of the shape of phreatic surface but treats the seepage flow as zero.
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R. A. Wooding (1966) studied this question.