PSI - Issue 44

Romina Sisti et al. / Procedia Structural Integrity 44 (2023) 1380–1387 Romina Sisti et al. / Structural Integrity Procedia 00 (2022) 000–000

1385

6

Slight

Slight

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Moderate

Moderate

Probability

Probability

Severe

Severe

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

PGA [g]

PGA [g]

a) Façade (2837 churches)

b) Principal nave (2854 churches)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Slight

Slight

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Moderate

Moderate

Probability

Probability

Severe

Severe

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

PGA [g]

PGA [g]

c) Apse (1293 churches)

d) Bell tower (2500 churches)

Fig. 4. Global fragility curves (continuous lines) vs. fragility curves related to macro-elements (dashed lines). Squared and triangular markers indicate the observational damage referring to the global behavior and to the macro-element, respectively.

Fig. 5 compares the fragility curves for the most recurring macro-elements with those obtained for the single mechanisms that contribute to the definition of the related macro-element damage index. This comparison is aimed at evidencing if there are any mechanisms that provide a more significant damage for a given macro-element. For ‘slight damage’ (black lines), the curves related to the single mechanisms (dotted, dashed, dash-dotted black lines) always show a lower vulnerability in comparison with the curves of the corresponding macro-element (continuous lines), especially for the façade (Fig. 5a) and less significantly for the bell tower (Fig. 5d). For ‘moderate damage’ (dark grey lines), the same trend can be observed for the façade (Fig. 5a), the principal nave (Fig. 5b) and the bell tower (Fig. 5d), even if less marked, since in few cases the single mechanisms have a vulnerability comparable to or slightly higher than the macro-element. On the contrary, for the apse (Fig. 5c), the vulnerability of the single mechanisms is always higher than that of the macro-element. For ‘severe damage’ (light grey lines), the trend changes since the single mechanisms show a vulnerability higher than the corresponding macro-elements, with except of the bell tower where only M26 has a vulnerability higher than that of the tower. This trend is due to the intrinsic definition of fragility curves that indicates the exceedance probabilities of the considered damage level. Hence, since containing all the upper damage levels, the ‘slight damage’ curve of a macro-element can be considered as a kind of upper-bound fragility curve for the relevant single mechanisms. With reference to the façade (Fig. 5a), the shear mechanism M3 is the most vulnerable for ‘slight’ and ‘moderate damage’, while for ‘severe damage’, its vulnerability becomes comparable with that of the macro-element and the other two mechanisms, M1 and M2, show a vulnerability comparable or slightly higher than the macro-element. For the principal nave (Fig. 5b), the mechanism of the vaults M8 is always the most critical for all damage levels and its vulnerability becomes higher than that of the macro-element already at ‘moderate damage’. The mechanism of the roof structure M19 is the least problematic for ‘slight’ and ‘moderate damage’, while for ‘severe damage’ it also becomes more vulnerable than the macro-element. For the apse (Fig. 5c), as already commented, the single mechanisms show a vulnerability higher than that of the macro-element already at ‘moderate damage’, with exception of M21, related to damage in the roof, that remains significantly less vulnerable. The damage to the vaults, M18, is the most vulnerable mechanism for ‘slight’ and