Recharge from an Array of Polygonal Channels

Abstract

An exact analytical solution for the quantity of recharge from an array of trapezoidal channels underlain by a drainage layer at a shallow depth has been obtained using an inverse hodograph and 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 considers the drainage layer at shallow depth with or without pressure. 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 an array of triangular and rectangular channels. Also particular solutions for different conditions of the drainage layer for all three shapes of channels are possible like the drainage layer at shallow depth without pressure or absence of drainage layer. The solutions can further be reduced to an isolated channel with drainage layer at shallow depth or at large depth and water table below the drainage layer. The solution is useful in quantifying artificial recharge and/or seepage loss from an array of polygonal channels.