| Abstract: | An approximate analytical solution is presented for earthquake-induced hydrodynamic pressures on rigid gravity dams with a finite reservoir and incompressible fluid. Using the Trefftz-Mikhlin method, the solution is constructed with function expansions of solutions of the problem's governing equation which satisfy boundary conditions at the bottom and free surface. Unknown coefficients of the linear combinations are obtained from a continuous least-squares treatment of the remaining boundary conditions at the upstream dam face and reservoir wall. Numerical results are presented for different geometries of the dam-water and wall-water interfaces. Out-of-phase motion at the end of the reservoir is considered. When the upstream dam face and reservoir wall are vertical, the known solution for in-phase dam and wall movement is recovered. |
