Representation of radiation damping in a dam–reservoir interaction analysis based on a rational stiffness approximation

In this paper, the dam–reservoir interaction problem is solved directly in the time-domain by modelling a part of the reservoir as a semi-infinite fluid-channel. Radiation damping is taken into account rigorously using an analytical solution with respect to the direction of wave propagation. The key step of the method consists of approximating the resulting modal flux–pressure relationship by a rational function in iΩ, which can be replaced by a system of linear equations in the frequency-domain. Two algorithms for the calculation of the coefficients of the rational function are described and compared. Finally, a system of first-order differential equations in the time-domain is obtained which completely represents the semi-infinite fluid-channel and can be coupled to the equations of motion of a dam and a bounded reservoir. The proposed strategy is verified considering a rigid dam. Moreover, the results of an earthquake analysis of a coupled flexible dam–reservoir system are presented.