Passive control of vibrations of seismically activated arch dams with tuned liquid column gas dampers

Abstract

The passive, sealed and modally Tuned Liquid Column Gas Damper (TLCGD) using gas-spring effect increases the damping of lightly damped, vibration prone of large structures effectively within the extended frequency range up to about five Hertz. Upgrading structural damping in civil engineering by Tuned Liquid Column Dampers (TLCD) have been investigated during last decades extensively and control vibrations of some buildings and bridges with dampers have been studied under wind or earthquake loadings as well. The arch dams are extremely large structures with tremendous construction costs. Hence in seismic regions absorbing and dissipating some part of kinetic energy by passive dampers during the strong motion phase of earthquakes is quite important from the viewpoint of both, safety and decreasing the costs of retrofitting. In this dissertation we propose TLCGD to increase the light structural damping of arch dams at low water levels in the reservoir. Adding gas spring effect in TLCD extends the range of its frequency up to 5 Hz. TLCGD increases effectively the damping during the steady-state vibrations of lightly damped structures, within the frequency range of application that limits the maximum fluid speed by about 10 m/s. In this research, we have studied the response of arch dam with TLCGD under harmonic motion and under strong ground motion acceleration. TLCGD is preferably installed in the level of the spillway. The dynamic analysis of the coupled system is implemented by mode super position synthesis. Empty reservoir is considered to omit the hydrostatic pressure and the hydrodynamic effects and in the meanwhile to omit the radiation damping into the water. So it should be the more sensitive case because of the lowest structural damping, also higher natural frequencies are observed when compared to the full or the partially filled reservoir. The structural continuum of concrete dam body should be idealized and discretized as an assemblage of finite elements with finite number of degrees of freedom. It is analysed here by ANSYS. The equation of motion of an incompressible liquid in the rigid and sealed piping system in normal direction to the mid-plane of the dam body, moving with the dam is described regarding to the piston theory of relative flow and of gas compression by a generalized (non-stationary) Bernoulli equation. Conservation of momentum of the fluid mass yields the control forces. The substructure synthesis of the coupled system is (approximately) studied and the equations of motion are given in matrix form. The dynamic analysis of a seismically activated dam with TLCGD is studied and the coupled modal equations considering one isolated structural mode are derived. By transferring into state space and following the optimization procedure, the optimal parameters of TLCGD are defined. The weighted frequency response function of the dam and the time history of the maximum displacement of the main structure under time harmonic motion and under acceleration of a real earthquake with and without TLCGD are derived. The results show some decrease in displacements under the mentioned loadings. The dynamic behavior of a benchmark arch dam is investigated: a real double curvature arch dam named Karun3 that was constructed in Iran is analyzed. The dynamic characteristics of the structure are derived by the finite element method. Low frequency modes are selected within modal analysis even with their state space transformation. The behavior of the modally coupled system arch dam with TLCGD attached is studied under both, time harmonic forcing sweeping frequency in the critical frequency windows and for a recorded seismogram. The optimal frequency and damping ratio of TLCGD in modal tuning are provided on the basis of the classical Den Hartog - optimization for TMD and considering the analogy between TMD and TLCGD. Subsequently performed fine-tuning in state space requires an optimization index to become minimized by calling the function fminsearch of the Matlab optimization toolbar. Both simulation results, presented in time- and frequency domain indicate notable effects of TLCGD by increasing the effective structural damping of the arch dam. The results of the research shows the robustness of this kind of passive damper in absorbing some part of kinetic energy from strong ground motion to the structure. The effectiveness of the proposed method in reducing the vibration amplitudes is shown.