PSI - Issue 44

Carlo Del Gaudio et al. / Procedia Structural Integrity 44 (2023) 259–266 Carlo Del Gaudio et al. / Structural Integrity Procedia 00 (2022) 000–000

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It can be noted an overall good accordance between fragility curves obtained with the two approaches. As expected, very slight differences can be observed for those typologies characterized by a lower number of buildings and particularly, for DS2-3. These slight differences could be ascribed to the fact that the EC method probably results less binding than EA one, forcing the solution to lay within the range defined by linear inequalities of Eq.5 (where at the most two adjacent parameters could assume the same value), rather than linearly related as a function of two variables (design level/construction age and number of stories). 4. Conclusions This paper aims at fragility curves estimation for RC building typologies representative of the Italian building stock, from empirically processing of observational post-earthquake damage data of the Irpinia (1980) and L’Aquila (2009) seismic events. A correct and unbiased methodological approach represents an essential basis for reliable large scale seismic vulnerability and trustworthy risk applications (e.g. da Porto et al. 2021; Dolce et al. 2021). The adopted taxonomy considers twenty-four building typologies, identified based on the design level (i.e. gravity and seismic loads design), construction age (i.e. 1946-1970; 1971-1980; 1981-1990; >1990) and number of stories (i.e. 1, 2, 3 and ≥4 stories). Fragility curves are derived considering cumulative lognormal distribution as statistical model and PGA to characterize ground shaking, defined at the building locations by using updated INGV ShakeMaps (Michelini et al. 2020). Global damage levels are defined at building level suitably accounting for both structural and non-structural damage observed on preselected building components. To this aim, damage conversion rules consistently with the EMS-98 damage classification (Grünthal et al. 1998) are adopted. An optimization technique via maximum likelihood estimate approach (MLE) and multinomial model for buildings subdivision in the different damage states was adopted to fit empirical data points. A unique constant dispersion value ( β ) on damage state, number of stories, age of construction and design level was used. The general tendency shown by results of this work suggested a reduction in seismic vulnerability with design level and construction age and an increase with the number of storeys. Two alternative empirically-based procedures, taking advantage of different fitting strategies and data processing techniques, are presented to overcome the anomalies shown in the results, in very cases, mainly due to the limited amount of damage data of some building typologies. Thus, the Empirical-Constrained (EC) procedure consists in performing a constrained regression on observational damage data based on the vulnerability hierarchies observed in more populated building typologies. The Empirical-Approximated (EA) procedure consists in fitting linear functions of two variables on empirically-derived median PGA values. Approximating linear functions are defined for individual levels of damage, as a function of design level/construction age and number of storeys. An overall good accordance between fragility curves obtained with the two approaches was observed, except in those typologies characterized by a lower number of buildings and particularly, for DS2-3, where very slight differences are observed. These slight differences could be ascribed to the different fitting strategies, given that the EC method enforce the solution to lay within the range defined by linear inequalities (where at the most two adjacent parameters could assume the same value), whereas the EA method linearly related the unknown parameters of fragility functions by means of two variables (design level/construction age and number of stories). Acknowledgements This work was developed under the financial support of the Italian Department of Civil Protection, within the ReLUIS-DPC 2019-2021 Research Project, which is gratefully acknowledged.

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