The method of images for leaky boundaries

An analytic solution is presented describing ̄ow to a drain in a semi-in®nite domain bounded by a leaky layer of constant thickness. The solution is developed by applying the method of images to two parallel boundaries: an inhomogeneity boundary and an equipotential boundary. It is then demonstrated that the solution for the problem with the leaky layer approximated by a leaky boundary (a mixed boundary condition) may be obtained by allowing the thickness, h , and the hydraulic conductivity, k , of the leaky layer to vanish while holding the ratio h =k constant. A method of images for leaky boundaries is proposed, in which a drain is imaged with respect to a leaky boundary by an image drain and an image line dipole. The method of images for a leaky boundary is applied to solve the problem of ̄ow to a horizontal drain in a semi-con®ned aquifer. Ó 2000 Elsevier Science Ltd. All rights reserved.