PSI - Issue 44

A. Sandoli et al. / Procedia Structural Integrity 44 (2023) 1332–1339 A. Sandoli / Structural Integrity Procedia 00 (2022) 000 – 000

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8

Table 1. Building classes percentage of Balvano pre- and post-1980 Pre-1980 Post-1980 Build. Classes Compartment C_01 Compartment C_02 Compartment C_01

90% 10% 0%

100% 0% 0%

5% 15% 80%

URM-1 URM-2 RC-4

In Table 1, the building classes percentages detected for Balvano are summarized, either for the cases pre-and post-1980. Before the Irpinia earthquake, the building stock was mainly composed of URM-1 buildings. Conversely, after the reconstruction process, 80% of the constructions consisted of RC buildings (RC-4), and 15% of buildings were retrofitted with traditional local interventions to prevent out-of-plane of the façade masonry walls (URM-2). The remaining 5% have not been retrofitted (URM-1). 3. Seismic fragility analysis 3.1. Derivation of fragility curves Urban fragility curves describe the probability of exceedance of a Damage State (DS) for an earthquake's given value of the Intensity Measure (IM) in the area understudying. Differently from the typological fragility curves (referred to as a single building class), the urban one is a single curve mean-representative of the expected damage scenario of a certain area, considering building typologies and their population. The hybrid methodology for deriving urban fragility curves herein used is illustrated in Sandoli et al. 2022, and it has been briefly recalled in the following. Fragility curves are obtained assuming a statistical lognormal distribution of the Probability Density Function ( pdf ):

   

   

   

   

2 1

) ln( im







( ) 2 1 im



pdf

e



(1)

 

where im represents the generic value of the chosen IM; while  and  are the lognormal median and standard deviation of the distribution corresponding to a pre-defined DS, calculated as:





n i i

n i i













i

i

(2)

N

N

where n i represents the number of buildings for each typological class and N the total number of buildings in the considered compartment. Instead,  and  are the lognormal mean and standard deviation referred to the i -th building class, whose values can be found in Sandoli et al. 2021 and in Sandoli and Calderoni 2018. Note that the values of  and  are relative to the entire area under consideration and are calculated as weighted values with respect to  and  of the single building classes. Hence, the fragility curve is represented by the Cumulative Density Function ( cdf ) obtained by integrating the eq. (1). Urban fragility curves defined in this paper are relative to a single DS coinciding with the damage level DS4 given by the European Macroseismic scale EMS98, identified with the attainment of the Ultimate Limit States (ULS) in Sandoli et al. 2021. Whereas, as IM the maximum peak-ground acceleration (PGA/g) C bearable by the entire compartment at ULS has been chosen. Figs. 3 and 4 represent the urban fragility curves for the compartments of Balvano related to the cases pre-and post-1980, respectively. In these graphs, three curves – indicated with Minimum, Mean and Maximum – have been plotted, each obtained by considering the minimum, the mean and the maximum value of  and  defined for the building classes (Sandoli et al. 2021). In such a way, a range of variations of the urban seismic fragility,