Earth dam with toe drain on an impervious base

The required height of a toe drain for a homogeneous earth dam on an impervious base has been determined considering reservoir water level, capillary rise for the embankment soil, free board, top width of the earth dam, embankment slopes, and tail-water position, such that the surface of seepage does not develop on the downstream sloping face of the earth dam and capillary saturation above phreatic line is contained well within the downstream sloping face. Using Kozeny's analytic function, exact solution to the unconfined flow through an earth dam having parabolic equipotential boundaries on either side has been obtained. For straight toe drain face, and for various positions of tailwater, approximate toe drain heights and heights of surface of seepage have been determined using the Kozeny's function and the method of fragments. It has been found that for an earth dam with 1/2 upstream slope, -1/3 downstream slope, no tailwater, and 2m capillary rise, capillary saturation is contained within the earth dam and the phreatic line is prevented from emerging on the downstream sloping face by providing a toe drain of height equal to 1/3 of the height of water level in the reservoir.