New Drain Spacing Formulas Using the Variational Iteration Method

ABSTRACT In this study, the drain spacing is computed using the variational iteration method (VIM) to the linearized Boussinesq equation. By applying at most two iterations of the VIM method under three different initial condition scenarios, three equations for drain spacing calculation were derived. These equations predict values of drain spacing that are generally closer to those of the van Schilfgaarde equation compared with the Glover–Dumm equation. Specifically, for values of the parameter λ , with (where m is the water table height at the midpoint of the drain spacing at time t and is the corresponding height at ) in the range of 0.42–0.9, the relative error (RE) for one of the three equations compared with the van Schilfgaarde equation is less than 10%, and less than 5% for λ between 0.51 and 0.75. The comparison with the Glover–Dumm equation showed that the same RE values are achieved when the ranges of λ values are considerably narrower. At large m values, the rate of water table recession is lower than that predicted by the van Schilfgaarde equation, whereas at later stages, the trend is reversed.