Steady state phreatic surfaces in sloping aquifers

Abstract

[1] Steady state groundwater flow driven by constant recharge in an unconfined aquifer overlying sloping bedrock is shown to be represented, using the Dupuit approximation, by an ordinary differential equation of the Abel type y(x)·y′(x) + a·y(x) + x = 0, whose analytical solution is derived in this work. This article first investigates the case of zero saturated thickness at the upstream boundary, a flow system reminiscent of perched groundwater created by percolation of precipitation or irrigation in a sloping aquifer fully draining at its downstream boundary. A variant of this flow system occurs when the phreatic surface mounds and produces groundwater discharge toward the upstream boundary. This variant is a generalization of the classical groundwater flow problem involving two lakes connected by an aquifer, the latter being on sloping terrain in this instance. Analytical solutions for the phreatic surface's steady state geometry are derived for the case of monotonically declining hydraulic head as well as for the case of a mounded phreatic surface. These solutions are of practical interest in drainage studies, slope stability, and runoff formation investigations. It is shown that the flow factor a = - √K/N tan β (where K, N, and tan β are the hydraulic conductivity, vertical recharge, and aquifer slope, respectively) has a commanding role on the phreatic surface's solutions. Two computational examples illustrate the implementation of this article's results. Copyright 2005 by the American Geophysical Union.