Non-linear dynamic analysis of Arch Dams: Eulerian and Lagrangian solutions

Abstract

In this study, Eulerian and Lagrangian finite element formulations are given for the dynamic interaction problem of a fluid-structure system. Non-linear dynamic analyses of Karakaya arch dam were performed to obtain the effectiveness of the Eulerian and Lagrangian approaches. The Drucker-Prager yield criterion was used for the non-linear model of dam concrete. The fluid and foundation domains were considered to be linearly elastic. The Karakaya Dam is located in the first zone of Turkey's seismic zone map. The expected effective peak acceleration value at the dam site is about 0.55g over its structural life. For the dynamic input used in the solutions of the presented study, the S69E component of the 21 July, 1952 Taft earthquake was selected as the horizontal component, acting in the downstream-upstream direction of the dam-reservoir-foundation system. The Eulerian and Lagrangian solutions were compared with each other. The results obtained from both methods were similar in terms of frequency. However, acceptable differences in amplitudes occured. The programming of the dynamic interaction problems of fluid-structure systems using the Lagrangian approach and incorporating this programme into existing computer programs are simpler with respect to that of the Eulerian approach. Nevertheless, the requirement for computing memory and time are increased because the Lagrangian approach requires the use of significantly more degrees of freedom.