PSI - Issue 78

1180 Caterina Carbone et al. / Procedia Structural Integrity 78 (2026) 1175–1182 exceeding a given damage state, as a function of the ground motion severity, ( ≥ | ) , was described by the cumulative lognormal distribution: ( ≥ | ) = [log ( ) ] (1) where Φ[∙] is the cumulative standard normal distribution, is the median PGA value associated with damage level and is the logarithmic standard deviation. To avoid crossing fragility functions and to guarantee the ordinal nature of damage, a constant value of dispersion ( ) was adopted for each set of fragility functions. The multinomial distribution was adopted to describe the repartition of buildings in different damage levels: ~∏ ! ! ( = | ) =0 (2) where is the number of damage levels, id the total number if buildings in the ℎ PGA bin, is the number of buildings experienced damage level at the ℎ PGA bin and ( = | ) is the conditional probability of occurrence of damage level , given by: ( = | )= { 1 − ( ≥ +1 | ) ( ≥ | ) − ( ≥ +1 | ) ( ≥ | ) 0 =< 0 < (3) = To obtain the optimal parameters and of the fragility curves for every building class, fragility functions were simultaneously imposed to empirical data points via the maximum likelihood estimate (MLE) approach: ( , ) = arg max [log( ( , )] = arg max [log ( ∏ ∏ ! ! ( = | ) =0 =1 )] (4) Obtained fragility curves (Fig. 5) resulted well constrained in the low ground motion range, because of the consideration of the negative evidence of damage. The incompleteness of surveys in areas of intense and moderate seismic shaking, for the 2012 Emilia and the 2016-2017 Central Italy seismic sequences, does not allow for the derivation of robust and quantitatively reliable fragility curves. However, the obtained fragility curves provide results consistent with other studies (e.g., Dolce and Goretti, 2015; Rosti et al. 2021). Comparison among fragility curves suggest that height and age of construction are influent parameters impacting the seismic vulnerability; globally, the class of high-rise buildings realized before 1982 and the class of low-rise buildings realized after 2001 resulted as the most and the less vulnerable categories, respectively. At lower damage levels, building height has a larger influence on seismic vulnerability than age of construction, while at moderate and severe damage levels, age of construction becomes a major factor for seismic vulnerability; in case of DS4, when the seismic performance is dominated by behaviour of vertical structures, age of construction is the predominant parameter influencing seismic performance. Note that, for low and moderate damage levels, fragility curves of buildings constructed between 1982 and 2001 and those of buildings constructed after 2001 exhibit comparable probabilities of exceedance regardless their height.