PSI - Issue 44

Carolina Bazzani et al. / Procedia Structural Integrity 44 (2023) 171–178 Carolina Bazzani et al. / Structural Integrity Procedia 00 (2022) 000–000

175

5

3.3. Comparison of methods

To compare and graphically represent the results of the analysed methods, the vulnerability scale was divided into four ranges: high, medium-high, medium-low, and low. Each range was respectively associated with a group of vulnerability indices, I V,average , defined by the Macroseismic Method, one or a group of classes of the EMS98 method (e.g.: medium-low = C-D and low = E-F) while a direct association is given for the S.A.V.E. method (Table 1).

Table 1: New vulnerability ranges vs vulnerability classes covered by EMS98 and S.A.V.E. project.

Vulnerability Class EMS98

Vulnerability ranges

Vulnerability Class S.A.V.E.

I V,average

HIGH

1-0.8

A B

A B C D

MEDIUM-HIGH MEDIUM-LOW

0.8-0.6 0.6-0.4

C - D E – F

LOW

0.4-0

By dividing the built environment of the municipality of Barberino di Mugello into the four vulnerability classes defined in Table 1, it is possible to achieve the results highlighted in Fig. 7:

0%

20%

40%

60%

80% 100%

EMS-98 Lagomarsino et al. (2007) Lagomarsino et al. (2021) Zuccaro e Cacace (2015) Zuccaro et al. (2020)

HIGH MEDIUM HIGH MEDIUM LOW LOW

Fig. 7. Percentages of buildings in high, medium-high, medium-low and low new vulnerability classes. It is worth mentioning that by grouping buildings in the high vulnerability class with those in the medium-high class and those in the medium-low class with those in the low class, the percentages of buildings in the new two groups are very similar for all methods. It can also be noticed that the S.A.V.E. method, in both versions, identifies buildings in the low vulnerability class to a greater extent than the other methodologies. 4. Damage scenarios 4.1. Vulnerability curves The representation of damage scenarios can be carried out through the vulnerability curves according to the formulation proposed by Lagomarsino & Giovinazzi (2006) and Bernardini et al. (2007a,b):

V I

ï î ï í ì

7

-

÷ ø ö

ç è æ

(1)

I

- 3 6.25 12.7 V

+

ç è æ

÷ × ø ö

( ) ,

( ) ,

2

f V I

f V I

2.5 tanh

D µ

= +

=

e

I

7

£

I

1

7

>

where µ D is the average damage value, I is the Macroseismic Intensity on the EMS-98 scale and V is the vulnerability index. For the M1 building typology only, was used the µ D formulation proposed by Menichini et al. (2022), which removes the multiplicative factor f(V,I) from Eq.1 for low intensities ( I ≤ 7).