Theories of Ditch Drainage in Layered Anisotropic Soil

Abstract

Approximate theoretical formulas are derived for predicting the water table position for steady rainfall or steady irrigation recharge into soil bounded by equally spaced ditch drains dug up to an impervious layer in single-, two-, and three-layered anisotropic soils. The ditch drainage problem is first solved for the single-layered case and subsequently, solutions are obtained to the twoand three-layered cases of the problem. All the solutions are based on exact mathematical procedures but utilize a physical assumption that the head loss in the arch-shaped region of the water table is negligible compared with the head loss for the remainder of the region. A correction, however, is provided to account for this head loss for all the solutions and the corrected formulas are found to be on the “safe side” for drainage design since the water table heights predicted by these formulas are higher than the actual ones. The accuracy of the proposed solution to the single-layered problem is tested by comparing it with independent solutions of Kirkham and Youngs to the same problems. A good agreement is obtained among the predicted results and the results obtained from the existing theories.