The hydraulic effect of filter materials around gappy non-ideal field drains

Abstract

The analyses of Widmoser and of Kirkham for flow into gappy non-ideal drain pipes with longitudinal slits and circumferential openings, respectively, were modified to take into account the hydraulic effect of filters when the boundary between filter material and soil is an equipotential surface. Upper and lower bounds were found for the effective drain radii of the drain pipes when surrounded by a cylindrical filter, by calculating the effective drain radii of the drain pipes with filter surrounds whose outer boundaries are the equipotential surfaces just contained within and without the outer cylindrical surface of the filter. The calculated bounds are close to each other for large filter thicknesses, but become further apart as the filter thickness is decreased. These calculated bounds for the effective radius were used to calculate, by the hodograph method, lower and upper bounds for the maximum water-table height for parallel lines of drain pipes installed in an infinitely deep soil. These show that the maximum water-table height in drained land is considerably lowered in the presence of a filter more permeable than the soil surrounding a gappy nonideal drain, and that a thin filter of high hydraulic conductivity relative to the soil is hydraulically more beneficial than a thicker filter of hydraulic conductivity only slightly more than that of the soil. An exact analysis, useful only for large filter thicknesses, is also given for the flow towards pipe drains with circumferential openings when surrounded by permeable material with hydraulic conductivity varying inversely with radial distance.