Finite Element Modeling of Infinite Reservoirs

Abstract

A technique is developed to model the effects of radiation damping in the finite element analysis of hydrodynamic pressures on dams subjected to a harmonic horizontal ground motion. The water in the reservoir is treated as being compressible; however, its vibration is assumed to be two‐dimensional and of small amplitude. In the finite element modeling, an infinite reservoir must be truncated at a finite distance from the dam, and a suitable boundary condition must be imposed at the truncation surface. Sommerfeld or similar existing boundary conditions are found to be satisfactory for excitation frequencies greater than the fundamental frequency of the reservoir. However, for lower frequencies, which are of greater importance in the seismic response analysis of dams, such boundary conditions require a very large extent of the reservoir to be considered in the analysis. The principal merit of the proposed boundary condition is that the reservoir may be truncated at a very short distance from the dam, resulting in great computational advantages. The effectiveness of the proposed method is demonstrated by analyzing several cases.