Simplified evaluation of the vibration period and seismic response of gravity dam–water systems

This paper proposes a practical procedure for a simplified evaluation of the fundamental vibration period of dam–water systems, and corresponding added damping, force and mass, all key parameters to assess the seismic behavior. The proposed technique includes the effects of dam geometry and flexibility, dam–reservoir interaction, water compressibility and varying reservoir level. The mathematical derivations of the method are provided considering both incompressible and compressible water assumptions. In the former case, we propose a closed-form expression for the fundamental vibration period of a dam–reservoir system. When water compressibility is included, we show that the fundamental vibration period can be obtained by simply solving a cubic equation. The proposed procedure is validated against classical Westergaard added mass formulation as well as other more advanced analytical and finite element techniques. Gravity dam monoliths with various geometries and rigidities impounding reservoirs with different heights are investigated. The new approach yields results in excellent agreement with those obtained when the reservoir is modeled analytically, or numerically using potential-based finite elements. The analytical expressions developed and the procedure steps are presented in a manner so that calculations can be easily implemented in a spreadsheet or program for simplified and practical seismic analysis of gravity dams.