Risk-informed optimization of the Tuned Mass-Damper-Inerter (TMDI) for seismic protection of buildings in Chile

Abstract

In recent decades, the concept of the passive linear tuned mass-damper (TMD) has been considered as a valid option for vibration suppression of dynamically excited building structures due to its relatively simple design and practical implementation. Conceptually, the TMD comprises a mass attached to the structure whose vibration motion is to be controlled (primary structure) via optimally designed/”tuned” linear spring and viscous damper elements. Aside from the dynamical properties of the primary structure, the effectiveness of the TMD depends heavily on the inertia of the attached mass and on the attributes and nature of the dynamic excitation. For effective control of wind-induced vibrations a TMD mass weighting in between 0.5% to 1% of the total building weight is usually sufficient. However, controlling earthquake induced oscillations in buildings commonly requires a significantly heavier TMD mass. In this respect, recently, a generalization of the passive linear TMD was proposed incorporating an “inerter” device: the tuned mass-damper-inerter (TMDI). The inerter is a two-terminal device developing a resisting force proportional to the relative acceleration of its terminals. The underlying constant of proportionality (inertance) can be up to two orders of magnitude larger than the device physical mass. In this regard, it was shown analytically and numerically that optimally designed TMDI outperforms the classical TMD for a fixed attached mass in terms of relative displacement variance of linear primary structures under stochastic seismic excitations by exploiting the “mass amplification” inerter property.In this work, the optimal risk-informed design of the TMDI for seismic protection of multi-storey buildings in the region of Chile is addressed. Note that the Chilean seismo-tectonic environment is dominated by large magnitude seismic events yielding ground motions of long effective duration whose damage potential can be well reduced by means of TMDs. In this respect, a probabilistic framework is established for design optimization considering seismic risk criteria. Quantification of this risk through response analysis is considered and the seismic hazard is described by a recently developed stochastic ground motion model that offers hazard-compatibility with ground motion prediction equations available for Chile. Multiple criteria are utilized in the design optimization. The main one, representing overall direct benefits, is the life-cycle cost of the system, composed of the upfront TMDI cost and the anticipated seismic losses over the lifetime of the structure. For enhanced decision support, two additional criteria are examined, both represented through some response characteristic with specific probability of exceedance over the lifetime of the structure (therefore corresponding to design events with specific annual rate of exceedance). One such characteristic corresponds to the repair cost, and incorporates risk-averse attitudes into the design process, whereas the other corresponds to the inerter force, which incorporates practical constraints for the force transfer between TMDI and the supporting structure. This ultimately leads to a multi-objective formulation of the design problem. Stochastic simulation is used to estimate all required risk measures, whereas a Kriging metamodel is developed to support an efficient optimization process. The results show that the proposed design framework facilitates a clear demonstration of the benefits of the TMDI (over the TMD) as well as the evaluation of the comparative benefits of increasing the mass of the TMD against increasing the inertance of the TMDI.