Hydrodynamic Modeling of Dam-Reservoir Response during Earthquakes

Abstract

A computational model is developed to analyze the hydrodynamic behavior of dam reservoirs during earthquakes. The mathematical model is based on the solution of two-dimensional (2D) Navier-Stokes equations in a vertical, semi-infinite domain truncated by a far-end boundary condition. A depth integrated continuity equation is used to track the deforming free-surface and ensure global mass conservation. A combination of Sommerfeld nonreflecting boundary and dissipation zone methods is implemented at the far end of the reservoir to prevent any back-reflections of pressure and free-surface waves. Nondimensionalized equations are used to compare contributions of each type of force to the development of the hydrodynamic pressure field and to the maximum run-up of free-surface waves on the dam face. Sinusoidal ground accelerations are applied to an idealized dam-reservoir system to analyze the system response. It is observed that the acoustic wave equation solution gives satisfactory results for the pressure field unless the contributions from the free-surface waves become significant at low reservoir depths. The surface wave run-up on the dam face is found to depend on the ground velocity, oscillation period, and the water depth. On the basis of numerical experiments, an expression for the wave run-up to predict conditions of overtopping from probable earthquake characteristics is proposed.