Abstract
An optimal hydraulic design problem regarding an earth dam cross section is formulated as an inverse problem for the steady model of saturated–unsaturated seepage flows in porous media. In the problem formulation, the choice of soil material to be used in each point of the dam cross sectional domain is considered as the control variable to be identified. The performance index used to evaluate the appropriateness of the design is defined as the sum of two square integral norms, which represent reducing the saturated zone and minimizing material costs. It is also shown that the first norm bounds the total seepage discharge through the earth dam. Since the governing variational boundary value problem as well as the adjoint problem is well-posed, a deterministic approach is taken. A numerical scheme including pseudo-unsteady terms is developed to calculate the optimal solution in an ideal earth dam cross section to be designed utilizing two different types of soil material. The results show that an inclined clay core of less hydraulic conductivity should be located on the upstream side of the cross section. The unsaturated zone turns out to play an important role in the flow field and the optimal design.
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