Analytical Study of Water Table Fluctuation in Unconfined Aquifers due to Varying Bed Slopes and Spatial Location of the Recharge Basin

Abstract

This paper presents an analytical solution of linearized Boussinesq equation characterizing transient groundwater flow in a downward sloping unconfined aquifer of semiinfinite extent. The aquifer is in contact with a water body of constant water level at one end and receives localized vertical recharge at a constant rate from a linear recharge basin of finite width. In this idealization, the recharge basin can be located anywhere in the domain, thus its location is treated as an additional parameter. The flow equation is solved using Laplace transform to obtain transient expressions for aquifer piezometric head and flow rate at the interface. The effects of bed slope and the location of recharge basin on the phreatic surface are illustrated by taking a numerical example. The analytical results obtained for horizontal as well as sloping aquifers show that there is considerable increase in the mound height as the recharge basin is shifted away from the interface of aquifer and water body. Moreover, contrary to the results of a horizontal aquifer, the mound growth in a sloping aquifer stabilizes in considerably lesser time period. The computation of mound height for small sloping aquifers is outlined using a numerical method and the sensitivity of the flow rate with respect to the variation of various parameters is analyzed.