Steady unsaturated seepage above a sloping impermeable base
J. R. Philip · Water Resources Research · 1988
We establish the nonexistence of steady unsaturated flows in regions infinite in the horizontal and bounded below by a horizontal impermeable base. Asymptotic analyses are given of two‐ and three‐dimensional seepage above a sloping impermeable base, valid far from the water supply source(s). The solutions depend only on total source discharge: details of source configuration are irrelevant. We require only that the total discharge be positive and finite and that the sources be contained in a finite region. Two‐dimensional results are found both for quasi‐linear and for general nonlinear flows. The general results apply also to mixed saturated‐unsaturated flows. The asymptotic three‐dimensional quasi‐linear results involve the same functional forms as analogous two‐dimensional flows in unbounded regions. An upper bound on unsaturated total discharge exists for two‐dimensional systems. Use of the potential Ω, a line integral of the Kirchhoff potential, effectively reduces by one the dimensionality of the problems treated. In one instance the dimensionality is reduced by two after a second integration.