Capacity curves for monitored existing buildings and within- and between-building variability of secant stiffness

Bulletin of Earthquake Engineering (2024) 22:4003–4021 https://doi.org/10.1007/s10518-024-01902-3 ORIGINAL ARTICLE Capacity curves for monitored existing buildings and within‑ and between‑building variability of secant stiffness Subash Ghimire1 · Philippe Guéguen1 Received: 6 July 2023 / Accepted: 19 March 2024 / Published online: 22 April 2024 © The Author(s) 2024 Abstract In this study, accelerometric data from seven Japanese buildings under long-term monitoring were analysed to explore the variability of the buildings’ co-seismic response over time and its within- and between-building components, using co-seismic capacity curves developed in acceleration-displacement-response-spectrum format. The data include the 2011 Tohoku Mw9.1 earthquake, which caused building damage of different levels of severity, and the time-varying actual capacity curves were analysed considering earthquakes before and after 2011. Result showed that the initial slope of the capacity curves reflects the amount of damage. The between-building and within-building components of the variability are discussed by comparing a single building and several buildings in the same class for several earthquakes. Finally, the epistemic uncertainty of seismic risk assessment studies is discussed in relation to the selection of a generic capacity model for all buildings in a single class. Keywords Experimental capacity curves · Building damage · In-situ monitoring · Earthquake data recordings from buildings · Building’s co-seismic capacity variation after damage · Operational earthquake loss forecasting · Structural health monitoring 1 Introduction Earthquake engineering is currently focused on improving the seismic resistance of structures through earthquake capacity design. Capacity design refers to the design of a building to ensure controlled ductile behaviour to avoid collapse in a design-level earthquake specified by stakeholders. The main objective is to minimise the direct and indirect losses generally correlated with any level of structural damage that affects the assets and people exposed and, indirectly, to limit the downtime of vital functions and essential facilities in urban areas following an earthquake. Herein, damage refers to any undesirable change in structural properties that significantly affects the intended functions of a structure over its expected lifespan (Farrar and Worden 2007). Anticipating seismic * Subash Ghimire 1 ISTerre, Université Grenoble Alpes, Université Savoie Mont-Blanc, CNRS, IRD, Université Gustave Eifel, CS40700 38058 Grenoble cedex 9, 1381 Rue de la Piscine, 38610 Gières, France 13 Vol.:(0123456789) 4004 Bulletin of Earthquake Engineering (2024) 22:4003–4021 consequences requires prior information on the damage that structures might be expected to suffer in a given earthquake, i.e., capacity models for the structures exposed. In the recent European Seismic Risk Model (Crowley et al. 2021), three main approaches are considered to assess seismic risk: scenario-based, intensity-based and frequencybased. The main difference lies in the definition of seismic hazard, but once the latter has been defined, risk is calculated as the convolution of the hazard with the vulnerability or fragility functions. This results in a loss estimate for a given class of building, which is then aggregated to the geographical area under consideration for regional scale risk assessment. The fragility functions are developed based on the capacity model of the building or building class, which describes the lateral strength and deformation capacity in acceleration-displacement-response-spectrum format (ADRS). Capacity curves are then developed, considering various structural attributes (e.g., materials, lateral load resistance system, number of storeys, etc.) to cover a wide range of building classes in the exposed area. In urban-specific seismic risk studies, it is common practice to start by assessing the exposure model at the site concerned and then to attribute class-capacity curves to each building (Crowley et al. 2021). This approach offers the potential advantage of taking into account a large set of buildings, but specific attributes within a class can cause significant deviations from the generic model. For example, Martins and Silva (2021) released a databank of capacity curves that has been used to represent the vulnerability classes of current European buildings (Crowley et al. 2021). For each class, the backbone capacity curves were compiled from simulated design-based research studies, i.e., push-over analysis (Fajfar 2000) or incremental dynamic analysis (Vamvatsikos and Cornell 2002). The method returned an average capacity curve for a generic building model without considering the effects of any specific building features. The application of generic backbone models to large sets of buildings in a single class introduces epistemic uncertainties into damage assessment (Ghimire et al. 2021; Perrault and Guéguen 2015; Spence et al. 2003). Among other attributes, specific features may control the nonlinear seismic response of a building (Lagomarsino and Giovinazzi 2006; Martins and Silva 2021), thus bringing significant epistemic uncertainty to the damage estimation (Lestuzzi et al. 2016). The most advanced numerical models (e.g., finite element-based models, Mazzoni et al. 2006) explicitly take into account all the specific attributes of the design and geometry of an individual building. However, these more complex models may also have to cope with additional sources of uncertainties: (i) the description of the design and materials, including foundation systems, and (ii) the assessment of the actual condition of the structures. These uncertainties are all the more critical in seismic prone regions because of the possible effects of cumulative seismic damage (e.g., Perrault et al. 2020). To resolve the afore-mentioned issues, other approaches can be used to implement a so-called “host-to-target” adjustment to eliminate the adverse effects of considering average “generic” building class models. This adjustment can be based on a modal analysis of existing buildings to define their elastic properties related to design and actual condition, or the processing of earthquake data recorded in buildings (e.g., Mucciarelli et al. 2004; Dunand et al. 2004; Clinton et al. 2006; Masi and Vona 2010; Michel et al. 2012; Vidal et al. 2014; Perrault et al. 2013; Astorga et al. 2018, 2019; Astorga and Guéguen 2020) to take into account the nonlinear processes activated in the buildings during earthquakes and estimate their residual load-resisting capacity by measuring the amplitude of roof displacement and structural period (Dowgala and Irfanoglu 2016; Freeman et al. 1999; Pan et al. 2019). Using these data, within-building variability ϕ (i.e., the misfit between a single structure response for a given earthquake and the structure-specific mean response model, 13 Bulletin of Earthq (...truncated)