Three-dimensional nonlinear hydrodynamic pressures by earthquakes on dam faces with arbitrary reservoir shapes

A complete three-dimensional finite difference scheme has been developed to analyze the earthquake-induced nonlinear hydrodynamic pressures on inclined dam faces with arbitrary reservoir shapes. Both the free surface waves and the nonlinear convective acceleration were included in the analysis. Numerical experiments have been made to determine the desirable mesh arrangements and time increments. The computational accuracy were assured by checking both mass and momentum balance at each time step. The effects of the arbitrary dam-reservoir system on dam hydrodynamics are systematically studied by analyzing the dam-reservoir system with various dam shapes, sloped reservoir banks and uneven reservoir bottoms. For a rectangular reservoir and excited by x-component ground acceleration, the three-dimensional analysis can be simplified by a two-dimensional analysis and the results are independent of the reservoir width. By arbitrary acting direction of ground motion, the fluid near the abutment is excited both by x-component and z-component of ground acceleration, the combination of the two-way action results in the variation of the hydrodynamic pressure distribution on dam face. The dynamic effects on the hydrodynamic pressure increase as the reservoir width does, but this increase becomes negligible when the reservoir width is larger than four times of water depth. The compressibility of water is important in dam-hydrodynamic analysis, but it is truly problem dependent.