American Society of Civil Engineers

Engelund’s Two-Dimensional Drainage Equation for a Toe-Drain and the Dupuit-Forchheimer Drainage Equation for a Ditch: A Coincidental Match

by E. G. Youngs, (corresponding author), (Visiting Research Professor, Dept. of Life Sciences, Open Univ., Milton Keynes MK7 6AA, UK. E-mail:;

Journal of Irrigation and Drainage Engineering, Vol. 138, No. 3, March 2012, pp. 282-284, (doi:

     Access full text
     Purchase Subscription
     Permissions for Reuse  

Document type: Technical Note
Abstract: Water-table heights attributable to steady uniform surface accretion rates in drained lands overlying a horizontal impermeable bed are given analytically by Engelund’s solution for toe-drains and by the approximate Dupuit-Forchheimer analysis for ditch drains. Both give the same water tables, although for different types of drain, when the spacing of the ditches in the latter is taken to be that in which the water table is drawn down to the level of the toe-drain in Engelund’s derivation. This fortuitous match also occurs in anisotropic soils when the horizontal hydraulic conductivity component is used in the formulae with the drain spacing dependent on the anisotropy factor. For soils with an infinite anisotropy factor, the Dupuit-Forchheimer analysis is exact so that the match is no longer fortuitous.

ASCE Subject Headings:
Water table

Author Keywords:
Engelund’s drainage equation
Ditch drainage
Dupuit-forchheimer analysis
Colding’s formula