Drainage of recharge to symmetrically located downstream boundaries with special reference to seepage faces

The seepage face is an important feature of the drainage process when recharge occurs to a permeable region with lateral outlets. Examples of the formation of a seepage face above the downstream water level include agricultural land drained by open ditches and the ballast beneath railway tracks. The first part of the paper considers vertical section two-dimensional analytical and numerical solutions for recharge to permeable regions above horizontal impermeable bases having two symmetrically positioned downstream boundaries with zero or specified external depths of water. For vertical downstream boundaries with seepage faces above the downstream water level, empirical relationships are developed relating the seepage face height on the downstream boundary to the downstream discharge. The same problems are also analysed using the one-dimensional Dupuit–Forchheimer approximation. Improved estimates of the entire water-table profile are achieved when the downstream boundary head is specified as a function of the downstream discharge using relationships derived from the two-dimensional solutions, instead of the customary assumption that the water table is drawn down to the ditch water level. Finally, time-variant simulations, based on the Dupuit–Forchheimer approximation, are introduced for a single layer and for a system of two horizontal layers having different hydraulic conductivities.