An analytical study of groundwater fluctuations in unconfined leaky aquifers induced by multiple localized recharge and withdrawal

Commonly used analytical methods for assessing the effects of recharge and withdrawal on the groundwater flow system are based on an idealistic assumption that the aquifer’s base is fully impervious. In reality, the hydrostratigraphic conditions are often complex and involve leakage induced flow between aquifer and the confining layers. In this study, a simple analytical procedure is presented for determining the spatial and temporal distribution of water head in an unconfined aquifer system due to multiple localized recharge and withdrawal at time-varying rates. A new transient function is introduced that can conveniently approximate the rising and recession limbs of any single recharge hydrograph. Solution of linearized two-dimensional groundwater flow equation under Dirichlet and Neumann boundary conditions is obtained using finite Fourier cosine transform with analytic inversion. The study has at least one clear advantage over the existing solutions that it accounts for the vertical leakage in water table buildup and drawdown analysis. A computational example demonstrates that the leakage induced flow plays an important role in recharge and withdrawal processes of unconfined aquifer system. The model results can be used for estimating aquifer’s hydraulic properties and validation of numerical models.