Analytical solutions of water table variation in a horizontal unconfined aquifer: Constant recharge and bounded by parallel streams

✍ Scribed by Dong-Ju Kim; Myeong-Joon Ann

• Publisher: John Wiley and Sons
• Year: 2001
• Tongue: English
• Weight: 237 KB
• Volume: 15
• Category: Article
• ISSN: 0885-6087
• DOI: 10.1002/hyp.495

✦ Synopsis

Abstract

Analysis of groundwater flow in an unconfined aquifer has received increasing attention by hydrogeologists for the design of drainage systems or the prediction of drawdown patterns of the water table in an aquifer neighbouring a pumping well. In this study, we attempt to analyse mathematically the variation of the water table in a horizontal unconfined aquifer receiving uniform recharge and bounded by parallel streams during a continuous cycle of rising and falling head conditions. The Boussinesq equation was taken to be the governing equation describing the transient changes in the water table. This problem was simplified to a one‐dimensional heat equation based on the assumption that the aquifer thickness is large enough compared to the water table changes and that the Dupuit–Forchheimer approximations are valid. We solved the heat equation using a method of variable separation in which the solution consists of both the steady‐state and nonsteady‐state solutions. With this method, the solutions could be obtained for various initial conditions such as different heads at the left and right boundaries and variable head distribution. In addition, simultaneous analysis of water table changes for both rising and falling head cases could be obtained. Comparison with other analytical solutions obtained for the linearized Boussinesq equation with Laplace transformation gives a nearly identical result, supporting the validity of the assumption and mathematical method used in this study. Advantages of the method over Laplace transformation can be found from the fact that our method renders the initial condition more flexible and simultaneous analysis of water table changes during rising and falling head cases can be done. Copyright © 2001 John Wiley & Sons, Ltd.