Calculation of exit gradients at drainage ditches

Seepage gradients play an important role in the detachment of soil particles from the side walls of stream channels and drainage ditches. Most seepage studies have focused on water losses. Relatively few have addressed the determination of these gradients as causes of soil loss and incipient gully development. This paper presents the methodology of calculating these gradients on any point of the soil-water interface of a subsurface flow system, for which a close-form analytical solution was obtained (Römkens 2009). Such a solution was derived using conformal transformations for a situation in which a ponded surface drains by subsurface flow into a ditch with a water table lower than that of the ponded surface. The derived relationships allow a close estimate of the soil detachment forces on the wetted drainage perimeter of the stream system.