Effects of cutoff length in the downstream exit gradients of diversion dams using conformal mapping

The hydraulic gradient at the end of d/s of diversion dams as well as the seepage rate can be controlled by cutoff. In this paper, the hydraulic gradient equations in terms of the d/s distance and seepage discharge have been obtained for an infinite depth of the impervious layer by the use of conformal mapping. Then, they have been used to produce the pertinent graphs that show the variations of seepage discharge as a function of cutoff length and distance from d/s. The results will be useful for the designers of diversion dams. Three scenarios of cutoff walls are discussed: vertical cutoff at d/s, u/s and a couple of cutoffs at d/s and u/s of the impervious floor. The results show that the effect of two cutoffs at the u/s and d/s ends in reducing the seepage discharge is larger than two other cases. Also, for b/S=const., where b is the total length of the impervious floor and S is the cutoff length, the d/s cutoff more effectively reduces the seepage discharge than the u/s one. If b/S=1.5, at x=0.5b from d/s end, the effect of d/s cutoff in reducing seepage discharge is 6% more than the u/s one.