PSI - Issue 78

Enrico Bernardi et al. / Procedia Structural Integrity 78 (2026) 599–606

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1. Introduction Inter-story isolation (IIS) is an innovative construction technique and consists in inserting one or more levels of seismic isolation along the height of the structure. Its primary application is in high-rise buildings, where the IIS system allows for a reduction of seismic forces at the base (Liu et al. 2018; Donà et al. 2021). IIS can also be used for seismic retrofitting; indeed when the existing structure allows the addition of new stories, a properly designed isolated level can improve the seismic response of the existing building (Bernardi et al. 2021, 2023a). Several studies focus on the IIS technique for retrofitting existing structures through case study analysis (Faiella 2020; Donà 2022; Bernardi et al. 2023b, 2023c). The dynamic behavior of structures with inter-story seismic isolation is strongly influenced by the mass ratio ( μ ), i.e., the ratio between the isolated modal mass and the modal mass of the substructure. Studies in the literature (e.g., Tan et al. 2008; Zhou et al. 2016; Faiella et al. 2019) show that the structural behavior is influenced by the mass ratio. These studies indicate that, as the mass ratio increases (that is, as the isolated modal mass becomes larger relative to the substructure), the structural response shifts from "Mass Damping" behavior (where the substructure dominates the response), to an “Inter - story Isolation System” (where higher modes of the isolated superstructure may become significant), and eventually to a “Base Seismic Isolation” behavior (in which the isolated superstructure essentially becomes the primary structural system). Depending on the type of behavior observed, different dynamic models should be considered. Specifically, 3DOF (or MDOF) systems, which account for all three structural components (substructure, isolation, and superstructure), are appropriate when the structure exhibits an “Inter - story Isolation System” behavior. Conversely, in cases of low mass ratios, a simpler 2DOF model is sufficient to represent the structural dynamics. This is often the situation when the IIS is used for retrofitting, as the additional mass that the existing structure can support is limited. In these cases, the optimization of the IIS can be conducted using well-established methods (Warburton 1982; Villaverde 1985; Sadek et al. 1997; Miranda 2005; Moutinho 2012; Reggio and De Angelis 2015; Zhou et al. 2016; Pietrosanti et al. 2017), which employ simplified 2DOF models. These studies provide solutions to define optimal TMD parameters that improve the performance of the main structure (or substructure). In Bernardi (2021, 2023a), a multi-objective optimization approach is proposed, which takes into account the performance of all structural components: substructure, isolation system, and superstructure. Indeed, limiting the displacement of the isolation system and reducing its drift can help mitigate P- ∆ effects on the substructure, lower the risk of hammering, and potentially reduce device costs. On the other hand, controlling the superstructure’s accele ration response is particularly important when sensitive equipment is present. In fact, solutions based on the traditional TMD approach typically result in higher acceleration levels compared to those observed in classical base-isolated structures. On the basis of the results of this approach, Bernardi (2023a) introduces a model for determining optimal design parameters. This study presents an extension of the model developed by Bernardi et al. (2023a), aimed at including cases with mass ratios greater than one. Although the addition of mass to existing structures is generally limited by their static capacity, scenarios with slightly higher mass ratios can still occur. This is because, unlike the isolated superstructure (where the modal mass of the first mode is approximately equal to the physical mass) in the substructure the modal mass represents only a portion of the total physical mass. Two separate multi-objective optimizations were performed. The first ( OPT1 ) targets the reduction of both the seismic response of the substructure and the drift of the isolation system. The second ( OPT2 ) focuses on limiting the drift of the substructure while also controlling the acceleration of the isolated superstructure. Based on the optimization results, models have been calibrated for calculating the optimal parameters of the IIS system and the effectiveness of the technique, as well as the reliability of the design model, has been assessed through time-history analyses. 2. Dynamic model The dynamic behavior of structures with Inter-story Isolation System (IIS) depends on the parameter μ , which is defined as the mass ratio, i.e., the ratio between the isolated modal mass and the modal mass of the substructure.