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

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6

For each building type (Fig. 8a) and each sector identified in the Municipality of Barberino di Mugello (Fig. 8b, c), the average damage was estimated at varying Macroseismic Intensity. The damage intervals of the new four vulnerability ranges, introduced in Table 1, were also depicted: within Fig. 8 the new high vulnerability range is filled in red, the medium-high vulnerability range in orange, the medium-low in yellow, and the low range in green. (a) (b) (c)

M1 M3 M5 M6 RC1-RC4 RC2-RC5 RC3-RC6

HISTORICAL EXPANSION 1 EXPANSION2 EXPANSION 3

Fig. 8. Vulnerability curves and associated damage ranges, for building typologies (a), building sectors (b) and map representation (c)

As was to be expected older building typologies exhibit a higher degree of vulnerability and this is also confirmed in the historic sectors where their prevalence is higher. On the other hand, the more recent building typologies exhibit a lower degree of vulnerability as well as the more recent expansion sectors in which these typologies are present.

4.2. Damage distribution and usability

For a given macroseismic intensity, it is possible to assess the average damage at the sector level, whose distribution can be defined through the binomial probability density function as reported in Equation 2:

k

k

5

-

(2) where " is the probability of having a degree of damage Dk, i.e.: D0 = no damage, D1 = no structural damage and limited non-structural damage, D2 = limited structural damage, D3 = moderate structural damage, D4 = significant structural damage, and D5 = collapse, and µ d represents the average damage of the discrete distribution, which for low intensities, i.e. I ≤ 7, was derived using the formulation by Menichini et al. (2022), based on data collected after the 2013 Lunigiana and Garfagnana earthquake: (3) For example, for a Macroseismic Intensity of IX (which in the Mugello area occurred several times, including most recently in 1919), the historic sector exhibits high average damage (3.86), while the expansion sector 4 exhibits much lower average damage (0.61) (Fig. 9a). The distribution of damage in the historic sector shows that about 30% of the buildings will suffer collapse while no building will suffer a collapse in the expansion sector 4, where more than half of the buildings suffer no damage (Fig. 9b,c). In addition, in the historic sector, it is estimated that about 95% of the buildings will be unusable, compared with 14% within the expansion sector. ( ) d d k k k p - = ! 5 ! 5 5 5! µ µ ( ) ( ) ( ) ( ) ( ) 5 4 0.15 1 0.7 2 0.9 3 p D p D p D p D p D p y unusabilit + + + + = ÷ ø ö ç è æ ÷ ø ö ç è æ