On ground water seepage under hydraulic structures

Abstract

This present paper continues paper [1] of the authors and is concerned with the following problems regarding seepage flows with unknown boundaries under hydraulic structures, with use being made of the theory of two-dimensional (2D) steady state seepage of incompressible fluid according to Darcy’s law in a uniform isotropic soil. Below we construct a smooth underground contour of a rectangular subsurface dam of constant seepage rate in the case when a pervious abutment is underlain by a blanket consisting of two curvilinear and one (middle) horizontal elements which are also characterized by constant incident velocity. We are concerned with the fluid flow below Joukowski’s cutoff wall through the watered soil mass underlain by a highly permeable aquifer with confined groundwater; the left semi-infinite part of its roof is simulated by impermeable inclusion. These motions are examined using multiparameter problems of the theory of analytic functions. Their solutions are obtained by the semi-inverse method of the velocity hodograph by P.Ya. Polubarinova-Kochina and I.N. Kochina, by Polubarinova-Kochina’s approach dependent on the analytic theory of linear Fuchsian equations, and using the available conformal mappings of domains of special kinds peculiar for underground hydrodynamics. The results of the numerical calculations are given and the hydrodynamic effect of the physical parameters of models on the flow pattern is ascertained. The limiting cases previously examined in [1] are singled out.