SEEPAGE TO DITCHES FROM A PONDED SURFACE

The seepage from an infinite ponded horizontal surface through a unifo rm soil to a ditch is analysed by the method of conformal transformati ons. For a ditch maintained empty, the discharge rate per unit length of ditch for the case of an infinitely deep soil is simply the hydraul ic conductivity multiplied by the depth to the ditch base; for the cas e of an impermeable barrier at the level of the ditch base it is reduc ed to 0.742 of this value. When there is water standing to some height in the ditch, the seepage rate for the latter situation is shown, bot h by the conformal transformation method and by a simpler analysis of the flow problem, initially to decrease slowly with the rise in water level, being reduced to only half of its maximum rate when the ditch i s 0.8 full, and then to decrease rapidly to zero when the ditch is ful l. The results of the analyses show that in all cases the flux through the surface decreases rapidly with the distance from the ditch. The r esults are discussed in the context of the management of areas liable to flooding and also of desalinisation methods used in maintaining lan ds under irrigation.