Boundary element analysis and design in seepage problems using dual integral formulation

Abstract

A dual integral formulation with a hypersingular integral is derived to solve the boundary value problem with singularity arising from a degenerate boundary. A seepage flow under a dam with sheet piles is analyzed to check the validity of the mathematical model. The closed-form integral formulae containing the four kernel functions in the dual integral equations are presented and clearly reveal the properties of the single- and double-layer potentials and their derivatives. The field and boundary quantities of the potential heads and normal fluxes can thus be expressed in terms of both boundary potentials and boundary normal fluxes through the dual boundary integral equations. To facilitate the computation of the seepage flow along and near the boundary, an expression for the flux tangential to the boundary is also derived. The numerical implementations are compared with analytical solutions and the results of a general purpose commercial finite element program. Finally, four design cases of sheet piles are examined, and the best choice among them is suggested.