Effect of Recharge Duration on Water-Table Response

Abstract

The problem of the effect of recharge duration on water-table response in areas with tile drains is studied using Green's function approach to the linearized Boussinesq's equation for one-dimensional, saturated flow with appropriate boundary conditions. Pulse and decaying sinusoidal type recharge excitations with given periods of drainage are fitted by Fourier series and used as forcing functions. The resulting response equation explicitly predicts water-table buildup over time and the oscillations at dynamic equilibrium, providing a method for analyzing the effect of recharge duration on water-table rise and flow toward the drains. The approach presented herein with this feature, is seen as an improvement on the drainage spacing approach of Maasland and McWhorter for annually repeated recharge events. However, it is seen that the duration of recharge, for constant recharge depth has negligible effect on the maximum water-table rise and flow toward drains at dynamic equilibrium in cases similar to those studied by McWhorter. Peak values of water-table height predicted by both the methods were close as parameters of the flow were changed but with different patterns. The method proposed in this paper results in drainage flow pattern different from the result of McWhorter and will be a useful tool for those cases where more realistic water-table heights and flow toward drains are important.