Response of a sloping aquifer to constant replenishment and to stream varying water level

The problem of seepage from a stream into an adjacent unconfined aquifer of semi-infinite extent, underlain by an impermeable sloping bed was considered in this study as a problem of one-dimensional unsteady-state groundwater flow. It was assumed that the water level in the stream gradually rises to a certain height, according to a known exponential function of time, while the aquifer was assumed to be replenished at a constant rate from ground surface. Applying the Laplace transformation method derived an analytical solution to an extended and linearized form of the nonhomogeneous Boussinesq equation used to describe the phreatic surface in sloping aquifers. The comparison of the analytical solution with a numerical solution obtained by applying the finite difference Mac Cormack explicit computational scheme to the nonlinear Boussinesq equation illustrates the validity of the new analytical solution and the effectiveness of the linearization. Some nondimensional diagrams are also presented to show the variation of the water table height and the seepage rate as well as their sensitivity to various sets of parameter values.