AN ANALYTICAL SOLUTION FOR GROUNDWATER FLOW TO VARIOUS WELLS IN A FINITE UNCONFINED AQUIFER

This paper develops a general mathematical model for describing hydraulic head distributions induced from various wells such as vertical wells or horizontal wells in an unconfined aquifer. The aquifer extends finitely in the horizontal direction and is surrounded by four streams treated as constant-head boundary in the model. A point sink term is embedded in the groundwater flow equation. The simplified free surface equation is used to describe water table change induced from the point sink. The point sink solution is derived by finite Fourier sine transform and Laplace transform. The solution for various wells can then be obtained by integrating the point sink solution along the well axis. Based on Darcy’s law and the solution, the stream depletion rate (SDR) is obtained for describing the infiltration from the stream which is very close to the well. The main advantage of this solution is that it is in terms of series and avoids involving in complicated integral evaluation occurring if the aquifer has an infinite domain. The solution can be used to simulate hydraulic head distributions in an aquifer extending infinitely if the aquifer width is very large. Also, our solution for SDR can be easily evaluated and the results are very close to those predicted by the analytical solution solved form the problems with infinite domain and in terms of an integral form. It is found that the large SDR is produced during the early period of pumping time if the well is located near the corner of the aquifer.