PSI - Issue 44

Carlo Del Gaudio et al. / Procedia Structural Integrity 44 (2023) 259–266 Carlo Del Gaudio et al. / Structural Integrity Procedia 00 (2022) 000–000

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3.2. Empirical-Approximated (EA) procedure The empirical-approximated (EA) approach fits linear functions of two variables (i.e. design level/construction age and number of stories) on empirically-derived median PGA values. Approximating linear models are defined for individual damage levels. As a result, median PGA value of the i th damage level ( DS i ), PGA 50th,DSi , can be expressed as: !"#$,&' ! ( / , ) = + B × / + C × (6) where A , B and C are the regression coefficients of the linear model, whilst Design/Age and Storeys are the explanatory variables. The variable Design/Age takes the following values: 1: Gravitational (G): 1946-70; 2: Gravitational (G): 1971-80; 3: Seismic (S): 1946-70; 4: Seismic (S): 1971-80; 5: Seismic (S): 1981-90 and 6: Seismic (S): > 1990. The variable Storeys is instead defined as: 1: 1 Storey; 2: 2 Storeys; 3: 3 Storeys and 4: ≥4 Storeys. Fig. 1 shows the outcome of the empirically based EA approach. In the figure, round markers denote empirically derived PGA median values, whilst non-intersecting planes, resulting from fitting linear models as a function of design/age and number of stories, ensure the ordinal nature of damage. Thanks to the intrinsically hierarchical nature of the proposed EA model, possible unexpected trends in the observed vulnerability of less populated building types are counteracted.

DS1 DS2 DS3 DS4 DS5

Design/Age

Fig. 1. Linear models fitting empirically-derived PGA median values (round markers) and resulting from the EA approach.

3.3. Comparison of fragility functions resulting from the proposed approaches The feasibility of the proposed approaches is demonstrated by Fig. 2, comparing fragility functions of some RC building typologies, resulting from the EC (continuous lines) and EA (dashed lines) procedures, respectively, for seismic designed (SD) buildings, thus arising from L’Aquila 2009 database. In the same figure are also reported the observational points reproducing the percentage of exceedance ∑ / ! !# # V for the j th PGA bin and damage level DS i , which dimension is proportional to the !# term.