PSI - Issue 44

Giacomo Lazzerini et al. / Procedia Structural Integrity 44 (2023) 163–170 Giacomo Lazzerini et al. / Structural Integrity Procedia 00 (2022) 000–000

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3.3. Calculation of fragility curves

The calculation of the fragility function starts from the results of the 3Muri software analyses, i.e., the capacity curves are processed to derive the capacity PGAs labelled PGAc. Specifically, each displacement of each curve can be associated with the corresponding capacity PGA by exploiting the parameters of the response spectra. The response spectra were taken at the barycentre of the investigated area, considering type A soil and topographic class T1 according to Italian NTC (2018). What is of interest for constructing the fragility curves are the capacity PGAs corresponding to each considered damage state. The damage states were assumed to be the same as the four limit states defined in NTC (2018), therefore the displacement values corresponding to the damage thresholds are those defined there on the equivalent bilinear curve (see Table 1). Eight pushover analyses were carried out for each model (+X, -X, +Y, -Y direction, with a “uniform” pattern and a “modal” pattern). The limitations provided by the NTC (2018) about the behaviour factor q*, i.e. q*<3 in the case of SLV and q*<4 in the case of SLC, were taken into account in the calculation of PGAc. For each Damage Level considered, it is useful to represent the dispersion of the PGAc obtained in a displacement-PGAc plot (Fig. 6). (a) (b)

0,8

0,8

0,6

0,6

0,4

0,4

0,2 PGAc [g]

0,2 PGAc [g]

0,0

0,0

0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5

0 0,5 1 1,5 2 2,5 3 3,5 4 4,5 5

Displacement [cm] 4 LEVELS 3 LEVELS

Displacement [cm] 4 LEVELS 3 LEVELS

Fig. 6: Dispersion of PGAc related to DL3 (SLV) - Comparison between 4-level and 3-level models: Building A (a), Building B (b) The fragility curves for each damage state are calculated from the mean and standard deviation of the logarithms of the PGAc obtained by combining the results of all the models. It was found that the most impactful parameters are: 1. the building height (meaning the number of floors) 2. the material type at the ground floor 3. the percentage of openings at the ground floor For the building investigated typology, on the other hand, the following parameters are found to have limited influence: the type of material and the percentage of opening at the upper levels, the stiffness of the floors, the thickness of the internal load-bearing walls since the building capacity is largely due to the external wall load-bearing system (perimeter walls are 40 ÷ 50cm thick, while internal walls are 12 or 24cm thick, and the magnitude of the loads on the floors. 4. Database of fragility curves Fig. 7). The considered damage limit states are shown in Table 1. The database can be used for masonry buildings of the 1960s-1970s in the Casentino area with the characteristics reported in section 3.1. The variabilities accounted for the most influential parameters are as follows: • building height: 3 levels or 4 levels • material type at the base level: Disorganized irregular stone or Roughly cut stone with good texture • percentage of openings on the ground floor: High opening percentage (60% - longer building side) or Low opening percentage (30% - longer building side) As a final result of the work, a database of fragility curves for the investigated building typology was built (