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New Drain Spacing Formulas Using the Variational Iteration Method
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DOI：10.1002/ird.70107.png)
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Abstract
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In this study, the drain spacing is computed using the variational iteration method (VIM) to the linearized Boussinesq equa tion. 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 lambda, with lambda=m/m(0) ,0<1, (where m is the water table height at the midpoint of the drain spacing at time t and m(0 )is the corresponding height at t=0) 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 lambda 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 lambda 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.
Keywords:
drain spacing
subsurface drainage
unsteady flow
variational iteration method
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