Boundary element analysis of earthquake induced hydrodynamic pressures in a water reservoir. (Volumes I and II)

The seismic analysis of concrete gravity and arch dams is affected by the hydrodynamic pressures in the water reservoir. Classical solutions for such pressures can be obtained only for a very idealized geometry; in all other cases a numerical solution must be attempted. The boundary element method (BEM) may prove to be an efficient method for a numerical solution of the problem.;In this work, BEM formulations are derived for the hydrodynamic pressures arising in a gravity dam-reservoir-foundation system. Both 2D and 3D cases are treated. The formulations are based on the respective mathematical models which are governed by two-dimensional or three-dimensional Helmholtz equations with appropriate boundary conditions.;In a BEM formulation, only the boundary of the reservoir needs to be discretized. However, for infinite reservoirs, loss of energy due to pressure waves moving away towards infinity strongly influences response. Since it is not possible to discretize an infinite extent, the radiation damping due to outgoing waves must be accounted for incorporating a special boundary condition at the far end. In a similar manner, the loss of the energy due to absorption of waves by a flexible bottom of the reservoir and banks can be accounted for by a special condition along these boundaries. Both of the special boundary conditions are successfully incorporated in 2D and 3D BEM formulations.;Numerical results are obtained and compared with available classical solutions or results obtained by other researchers. Convergence of numerical results with the size and number of boundary elements is studied. Some consideration is given to the size of an element in relation to the excitation frequency. In the 2D formulation, results obtained from a constant boundary element discretization are compared with those obtained from a linear boundary element discretization. Since no special advantage is noticed in the use of the linear elements as compared to constant elements, only constant elements are used in the 3D formulation.;It is concluded that the direct boundary element method is an effective tool for the evaluation of the hydrodynamic pressures in finite and infinite dam-reservoir-foundation systems subjected to harmonic types of motion. The method can be easily extended to the analysis of response to any random type of motion with the use of Fast Fourier Transformation technique.;A summary of the conclusions derived as well as recommendations for future research are presented.