Abstract | This paper examines a risk-based multi-objective optimal design framework for seismic protective devices in buildings, tailored to accommodate recently emerging inerter-based dynamic vibration absorbers (IVAs), while treating the conventional tuned mass damper (TMD) as a limiting case. Following recent research efforts, the formulation utilizes the following as competing design criteria: (1) the seismic losses, representing the IVA vibration suppression capability; and (2) the peak IVA force, associated with the device upfront cost. In view of pressing demands for reducing the life cycle embodied carbon of buildings, the embodied energy associated with repairs is introduced in this paper as a sustainability-driven design criterion for describing seismic losses within the multi-objective design framework. Moreover, modern performance-based earthquake engineering standards are adopted for the problem formulation, using a probabilistic seismic hazard characterization across a range of intensities, utilizing nonlinear response history analysis to estimate structural response and adopting an assembly-based vulnerability assessment to quantify seismic damages and consequences. Reduced order structural modeling is leveraged to alleviate the computational burden while enabling the explicit use of nonlinear time history analysis within the design optimization. An efficient stochastic search approach is adopted to identify Pareto optimal solutions for different design variants and evaluate the IVA benefits across different performance quantifications (distinguishing drift from acceleration-sensitive assemblies), risk metrics (distinguishing risk-neutral from risk-averse attitudes), and device types (distinguishing IVAs from TMDs). Numerical results for an illustrative application to a 9-story steel benchmark demonstrate considerable (i.e., up to 35%) reduction of the embodied energy due to repairs compared to the uncontrolled structure while stressing the usefulness of the developed design optimization framework to support multiple risk quantifications and insights for the IVA behavior and performance.

Abstract | Seismic fragility curves provide the probability of exceedance of a given damage state, should different levels of ground motion intensity be experienced at the site where the structure, or component, is located. Such curves are often derived via multiple nonlinear response history analyses (NLRHA) using sets of “suitable” ground motions that, in line with the best practice, should be consistent with the seismic hazard at the site. Based on the selected sets of records, one can estimate fragility functions that are often assumed to follow a lognormal distribution defined by two parameters, i.e., the logarithmic mean (µ) and the logarithmic standard deviation (β). Our focus is on estimating them using a state-of-the-art approach that involves hazard-consistent record selection via Conditional Spectrum and multiple stripe analysis. However, this approach usually requires many NLRHAs, with high computational costs, especially for the complex structural models typical of the nuclear industry. This study investigates the optimal number of ground motions and intensity levels required to keep the computational burden acceptable without compromising accuracy. To do so, we adopt a Bayesian framework with Markov chain Monte Carlo simulation and Metropolis–Hasting sampling. Our findings show that this approach effectively helps analysts best allocate computational resources while ensuring acceptable accuracy in estimating the probability of reaching or exceeding the considered damage states.