PSI - Issue 44

Fabrizio Paolacci et al. / Procedia Structural Integrity 44 (2023) 697–704 Fabrizio Paolacci et al. / Structural Integrity Procedia 00 (2022) 000–000

701

5

4. Level 3: a simplified PBEE methodology for quantitative seismic risk assessment of bridges 4.1. Description of the methodology A new simplified methodology, based on the PBEE approach, for a quickly quantitative seismic risk assessment of the bridges is herein proposed in order to provide a powerful tool to individuate the most critical bridges in the region and draw up a ranking of attention. The mean annual frequency to exceed a specific limit state (λ[LS]) is herein assumed as seismic risk index. It can be evaluated, as well known in literature (Cornel et al. 1996), with Eq. (1): λ ( LS )= ∫ P ( D>LS │ IM ) | d λ ( IM ) | (1) where P ( D>LS │ IM ) is the probability of exceeding a specific limit state given a seismic event of intensity IM, better known as fragility curve (de Felice et al. 2014), while λ ( IM ) is the mean annual frequency with which a seismic event with intensity IM occurs, given by hazard curve. The previous integral can be simplified and written in a closed form, using significant parameters to represent both hazard and fragility curve, as demonstrated in Cornel et al. 2003. Along this vein, λ[LS] can be more easily evaluated with Eq. (2): λ ( LS )= λ ( IM,50%) ∙ 1 2 ( ) 2 (2) where is the slope of the linear curve that approximate the hazard curve in the logarithmic plane in the PGA range of interest, as shown in Fig, 3a; is the standard deviation of the structural response and λ ( IM,50%) is the frequency of occurrence of a seism with an IM relative to a probability of 50% to exceed the limit state, evaluated from fragility curve as shown in Fig. 3b.

(a)

(b)

Fig. 3 a) Evaluation of λ( IM,50%) from fragility curve b) Approximation of hazard curve in log-log plane Along this vein, the first step is to evaluate the fragility curve of the structure in order to carry out the value of λ ( IM,50%) . A fragility function represents the probability that a seismic demand placed on a structure exceeds a structural limit state for a specific intensity measure (IM). Many approaches are proposed in literature to evaluate the fragility curve, the method proposed by Nielson et al. 2007 is herein taken in account that assumes that both demand (D) and limit states (LS) follow a log-normal distribution. Consequently, the fragility curve can be evaluated with Eq. (3): P ( D>LS │ IM )=1- Φ( ( ) − ( ) � | 2 + 2 (3)