Analysis of Seepage from Polygon Channels

Abstract

An exact analytical solution for the quantity of seepage from a trapezoidal channel underlain by a drainage layer at a shallow depth has been obtained using an inverse hodograph and a Schwarz-Christoffel transformation. The symmetry about the vertical axis has been utilized in obtaining the solution for half of the seepage domain only. The solution also includes relations for variation in seepage velocity along the channel perimeter and a set of parametric equations for the location of phreatic line. From this generalized case, particular solutions have also been deduced for rectangular and triangular channels with a drainage layer at finite depth and trapezoidal, rectangular, and triangular channels with a drainage layer and water table at infinite depth. Moreover, the analysis includes solutions for a slit, which is also a special case of polygon channels, for both cases of the drainage layer. These solutions are useful in quantifying seepage loss and/or artificial recharge of groundwater through polygon channels.