PSI - Issue 44

Laura Gioiella et al. / Procedia Structural Integrity 44 (2023) 1808–1815 Laura Gioiella et al. / Structural Integrity Procedia 00 (2022) 000–000

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damage obtained at the upper bound of the range is 0.38. With reference to Fig. 5b), instead, the amplitude of the bells is similar at the lowest and highest intensity levels, while it becomes notably higher for i =0.3 g that is nearly the maximum value of the intensity experienced by the schools under investigation during the Central Italy seismic sequence.

a

b

i =0.1g i =0.2g i =0.3g i =0.4g i =0.5g

1

d

0.8

0.6

0.4

0.2

2 0 | 2 0 | 2 0 | 2 0 | 2 0 |

0

0

0.1

0.2

0.3

0.4

0.5

0.6

i [g]

mean damage

extrapolated behaviour

Fig. 5. (a) Mean damage trend; (b) | ( | ) distributions for discrete values of the intensity.

3.4. Fragility functions The seismic vulnerability evaluation of public and strategic buildings is often treated in literature, e.g. da Porto et al. (2021), by developing fragility curves, which provide the probability to exceed a consequence class for different values of the seismic intensity. This description of the earthquake consequences starts from a discrete evaluation of the effects (the overall damage in the considered case), and involves a finite number of ordered classes, e.g. Almufti et al. (2013). A fragility curve provides the probability to exceed a consequence class for different values of the seismic intensity. This type of result is included in the proposed model, based on a continuous description of the earthquake effect, and can be recovered by integrating previous conditional distribution functions. With the aim of deriving fragility curves, it is sufficient to introduce a set of damage levels, which in this case are chosen in accordance to De Martino et al. (2017) and are ( = 0 , 1, … , 6) associated to a finite number = − 1 of ordered damage states ( = 1, … , 5) , each of which includes damage values belonging to the interval −1 ≤ < . Fig. 6 shows the fragility curves of damage for the subset of schools located into the seismic crater. Such functions, provide the probability of observing a damage level higher or equal to ∗ , given intensity . As already done for the and the , the grey window highlights the extrapolated curves evaluated out of the range of observed intensities. It is worth to observe that for an intensity equal to 0.5 g the curves related to the damage levels 1 − 3 provide a unitary probability of observing a certain damage, while the damage level 4 approaches a unitary probability at nearly 0.6 g and 5 only for an intensity higher than 0.9 g. 1

0.8

extrapolated behaviour

0.6

d 0 : d ≤0.16 d 1 : 0.16< d ≤0.36 d 2 : 0.36< d ≤0.53 d 3 : 0.53< d ≤0.71 d 4 : 0.71< d ≤0.89 d 5 : d ≥0.89

0.4

0.2

0

0

0.5

1

i [g]

Fig. 6. Fragility functions derived from the probabilistic damage model for the schools of the seismic crater.