Transient-State Analytical Solution for Groundwater Recharge in Anisotropic Sloping Aquifer

Abstract

The Boussinesq equation has been proved reliable for modeling water table fluctuations in response to external excitations imposed on the aquifer system. This study presents an analytical solution for two-dimensional linearized Boussinesq equation in anisotropic, rectangular-shaped aquifers with sloping impermeable base. Two different configurations of hydrogeological boundary conditions (constant-head and no-flow) are examined. The analytical model is capable of describing the groundwater head distribution due to downward transient recharge from an overlying basin. First, a transformation technique is adopted in order to simplify the mathematical treatment of the problem. Closed form expression for point-recharge is then obtained by applying the method of Green’s function and eigenfunction expansion. This allows treating any arbitrary-shaped recharge basin subject to spatiotemporal varying recharge. It is shown that a number of existing analytical groundwater models may be regarded as special cases of the solution presented herein. Finally, hypothetical examples describing the nature of transient recharge in sloping aquifers are presented. Qualitative examination of the resulting water table maps confirms the validity of the solution, particularly in the vicinity of aquifer borders. Sensitivity analysis is performed to demonstrate how groundwater mounding is affected by variation in various hydrogeological parameters.