Hillside seepage and the steady water table. I: Theory

Abstract

Steady seepage through a hillslope aquifer results in the formation of a water table. In this paper, the boundary conditions governing the steady water table location are analysed, and an analytical series method applied to the problem, using eigenfunction expansions. Eigenfunction expansions, modified for non-orthogonal basis functions, provide a conceptually simple, efficient estimation process, that reduces the steady water table problem to a sequence of curve fitting exercises. A rigorous examination of the hodograph relationships reveals the possibility of more than one water table location, for given recharge rate. An elementary analysis reveals that one of these possibilities can always be eliminated. Also, the boundary conditions governing the steady water table are determined at a non-vertical upstream boundary. Hillslopes subjected to low recharge rates can be very difficult to analyse, and appropriate techniques for this case are detailed. In a companion paper ( Adv. Water Resour., 19(2) (1996) 75–81), the techniques described in this paper are put to the test, and the upstream boundary conditions are investigated, using the series methods.