Dupuit-Forchheimer Analyses of Steady-State Water-Table Heights due to Accretion in Drained Lands Overlying Undulating Sloping Impermeable Beds

The Dupuit-Forchheimer approximation is used in an investigation of steady-state water-table heights due to accretion in ditch-drained lands resting on an undulating impermeable bed that slopes away from a peak midway between drainage ditches toward a lower level at the drains. Analytical expressions are obtained for the water-table profiles assuming both horizontal flow and flow parallel to the impermeable base. These are compared with numerical results obtained for the Laplace solution of the flow problem that show the equipotentials to be better approximated as being normal to the base than vertical. There is good agreement for large slopes between the water-table heights obtained assuming one-dimensional flow parallel to the sloping base and the two-dimensional numerical results. Poorer agreement is obtained as the slope becomes less with results approaching those given by assuming horizontal flow which always results in underestimates. At small accretion rates agreement is obtained with both Dupuit-Forchheimer analyses and the Laplace solution. The maximum height of the water table above the base decreases and is closer to the drain as the slope increases.