Liu and Lin developed a numerical model to study 3D nonlinear liquid sloshing with broken free surfaces under 6-degree-of-freedom excitations. They found that time-periodic solutions existed for the system. The free-surface boundary conditions were linearized by potential-flow theory. Cooker used linearized SWEs to model a horizontal rectangular wave tank. Faltinsen studied shaking-wave-tank problems with the boundary-element method, solving the Laplace equation based on potential-flow theory. Įarthquake-excited reservoir systems have been modeled as a shaking-wave tank by many researchers.
Based on the data obtained from numerical simulations for nine selected earthquake ground motions, they presented a relationship between dimensionless run-up height and the Froude number that was defined in terms of maximum ground velocity and water depth.
They used the numerical model to compute the maximum wave run-up height on the dam face during earthquakes. Demirel and Aydin developed a wave-absorption filter for the far-end boundary of semi-infinite large reservoirs and computed the earthquake-excited surface waves and nonlinear hydrodynamic pressures in a dam-reservoir system based on solving the Navier-Stokes equations and a depth-integrated continuity equation. They studied the hydrodynamic pressure on dams during a horizontal earthquake with a computer program.
Zee assumed that water was incompressible and modeled the water flow in reservoirs with a Laplace equation. They concluded that the geometry effects of reservoir shape on hydrodynamic pressures were significant and the effects of surface wave and convective acceleration on hydrodynamic pressure were about the same. Chen et al., solving three-dimensional coupling Euler equations and incompressible continuity equations with a complete three-dimensional (3D) finite-difference scheme, calculated the hydrodynamic pressures and water-level increase for nonlinear conditions, including the nonvertical dam face and the nonhorizontal reservoir bottom. Hung and Chen analyzed the variation of the water surface and the hydrodynamic pressures of dam-reservoir systems during the El Centro Earthquake, solving Euler equations by a finite-element method. They found that the effects of water compressibility for most dams should be considered in their earthquake-response analysis. Chopra and coworkers provided a revised solution to account for the effects of water compressibility on pressure distribution and to investigate dam-water interaction using a finite-element method. Later, Sato modeled a seismic wave as a simple sine wave and proposed a formula for an earthquake-induced water wave using analytical calculations based on linearized shallow-water equations (SWEs). In his study, the hydrodynamic equations were derived in terms of the theory of elasticity of solids, and an analytical solution was obtained. Hydrodynamic pressures in dam reservoirs during earthquakes were first rigorously analyzed by Westergaard in 1933. Strong earthquakes shake the banks of reservoirs and can consequently generate large water waves that may result in a geohazard in mountainous earthquake-prone areas. Finally, an empirical equation for the maximum water elevation of earthquake-induced water waves is developed based on the results obtained using the model, which is an improvement on former models. It is also demonstrated that the proposed model is reliable. The model is verified against the models of Sato and of Demirel and Aydin with three kinds of seismic waves, and the numerical results of earthquake-induced water waves calculated using the proposed model are reasonable. A finite-difference method is used to calculate the SWE. A shallow-water equation (SWE) is used to simulate earthquake-induced water waves in this study.