Seepage shedding by parabolic capillary barriers and cavities

The 1989 analysis of seepage exclusion from underground cavities established the parabolic and paraboloidal geometries as the most efficient. That work is extended here to an analysis of seepage into the cavity. The cavity results carry over to maximal capillary barriers of macroscopically coarse material such as smooth gravel. The analysis is extended further to the conventional submaximal capillary barrier of a coarser soil underlying finer soil. The shedding efficiency of the submaximal barrier is always less than that of the maximal barrier, and in worst case scenarios, poorly designed submaximal barriers actually concentrate seepage into the region they are supposed to protect. The 1989 work, supplemented by the present study, provides a detailed physical basis for the recent proposal that the most efficient geometry for capillary barriers is parabolic. In some (but not all) circumstances barriers are ineffective if their horizontal dimensions exceed a few sorptive lengths.