Shape optimization for a seepage problem with low contrast core

Abstract

In this work we propose a numerical method to minimize the steady flow in the outlet of an embankment dam by optimizing the location of a less permeable material, which is available in a limited amount, inside a matrix of a more permeable material. This is performed by considering the Darcy equation with the permeability taking two different values and a fully saturated media below the phreatic surface. The optimization method is based on an asymptotic relaxation under the assumption of a small contrast between the permeabilities of both materials.Numerical results show the gains obtained when compared to simple layouts for two different volumes of core material and for different contrasts in permeability. Compared to simple layouts and with a core permeability equal to 30%of the permeability of the matrix, the optimized layout reduces the outflow by 15% when compared to putting all the core on the exit side of the dam and by 45% when compared to putting the core as a column in the center of the dam.