Shape Optimization in the Design of Concrete Arch Dams - Two Case Studies

The design of arch dams usually involves a prolonged process of successive trial and error redefinitions. The current computer technology however enables to automate this task, in order to achieve the most economic solution overall. In the paper, the implemented optimization method of the geometry of concrete arch dams is presented as well as case studies of its application in the design of two dams under construction in Portugal, namely Baixo Sabor upstream dam, 123 m high, and Fridão dam, 98 m high. The dams have to comply with geometric and performance constraints, besides the requirements intrinsic to the construction process and to good engineering practice. These quantities are functions of the design parameters that determine the geometry of the dams, and most of them are nonlinear. The functions with time consuming evaluations (namely those requiring finite element analyses) were estimated by neural networks trained with the results obtained for a set of instances of dam shapes that satisfied the linear constraints and maximized the minimum distance between them. The implementation of global optimization methods (namely direct search and genetic algorithms) proved to be efficient to obtain the feasible dam design with minimum volume of concrete. The case studies illustrate the versatility of this design process.