GNGTS 2023 - Atti del 41° Convegno Nazionale

Session 2.2 GNGTS 2023 of the interconnection semi-blocks and the overloads acting on the interconnection semi-blocks (Casapulla et al., 2021; Cima et al., 2022). Next, at step 4, the seismic input in terms of spectra is determined with reference to the values of the PGA corresponding to eight different return periods. In particular, to adequately take into account the effect of the record-to-record variability in the fragility curves, the spectra are obtained by selecting, through the software REXEL v 3.5, combinations of natural records whose mean spectrum in acceleration is compatible with a target spectrum within the assigned tolerances (Iervolino et al., 2010, NTC, 2018). The compatibility is imposed within a predetermined range of periods, corresponding to the range of the fundamental periods of the buildings, in the case the mechanism occurs at a certain altitude, z, from the ground floor (z>0), or to the range of periods characteristic of mechanisms (Circolare, 2019), in the case the mechanism occurs at z=0. For each combination, the spectra corresponding to the 84 th and 16 th percentile of the selected records are calculated, in addition to the average spectrum. From the spectra obtained in acceleration, the corresponding spectra in terms of ground and floor displacements are obtained, depending on whether the considered mechanisms occur at z=0 or at z>0. The second-last step of the approach consists in defining, for each virtual population, the damage indices, DI DSi , of each building. In particular, such indices are defined as the ratio between the maximum displacement demand (Freeman, 1998), and the damage threshold of the mechanism in correspondence of two prefixed damage states, DS i , (Cima et al., 2023): the damage state "moderate" and the damage state "complete" corresponding respectively to the achievement of the Damage Limit State and the Life Safeguard Limit State (Circolare 2019). The approach ends (step 6) with the derivation of the fragility curves of each building population. For each damage state, assuming the PGA as a measure of the intensity of the seismic input, the corresponding fragility curve is obtained through the formula (CNR-DT, 2014): = 1 − Φ 1−µ | σ | ( ) = Φ µ | σ | ( ) (1) where: - Φ [•] is the lognormal standard distribution function; - μ lnDIiIPGA is the mean value of the average natural logarithm of the variable DI DSi conditioned on the given value of PGA; - σ lnDIiIPGA is the dispersion of the natural logarithm of the variable DI DSi conditioned on the given value of PGA. The mean value μ lnDIiIPGA is assessed through the following expression: µ | = + · ⁡ (2) where A DSi and B DSi are coefficients obtained by a linear regression of the logarithm of the damage indices (evaluated by using the average spectra) versus the logarithm of the PGA (Nielson and DesRoches, 2007). The dispersion σ lnDIiIPGA is determined through the following equation: σ | = σ 2 + σ 2 (3) where: σ mDSi is estimated as: