Finite Element Analysis of Reservoir Vibration

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Abstract
The finite element method of analysis is applied to the calculation of hydrodynamic pressures in a reservoir impounded by a gravity dam and subjected to a harmonic ground motion. In the finite element modelling of an infinite reservoir, the fluid region must be truncated at some significant distance from the region of interest. To model the energy loss in outgoing waves in the inifinte reservoir, an appropriate radiation condition must be applied at the truncation boundary. A radiation condition which adequately models the loss over a wide range of excitation frequency is developed and it is shown that this condition gives much better results as compared to the plane wave Sommerfeld condition. Finite element solutions are obtained for several reservoir vibration problems and the result are compared with classical solution where such solutions exist. The method is then applied to the vibration problem of a reservoir with an inclined dam face, for which a classical solution does not exist. It is shown further that the inclination of the dam face significantly reduces the hydrodynamic pressure.

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