PSI - Issue 62

Fabrizio Paolacci et al. / Procedia Structural Integrity 62 (2024) 732–737 Paolacci F., Quinci G., Marta L., Moretti M. / Structural Integrity Procedia 00 (2019) 000 – 000

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Here, "k" represents the slope of the linear curve that approximates the hazard curve within the PGA range of interest, as illustrated in Fig. 2a. Additionally, "β" corresponds to the standard deviation of the structural response, while "λ(IM,50%)" signifies the frequency of occurrence of a seismic event with an intensity measure (IM) relative to a probability of 50% to exceed the limit state. This value is evaluated from the fragility curve, as depicted in Fig. 2b.

Fig. 2. a) Evaluation of “"λ(IM,50%)" from fragility curve b)Approximation of hazard curve in log-log plane

In this context, the initial step involves evaluating the fragility curve of the structure to determine the value of "λ(IM,50%)". A fragility function is a representation of the probability that a seismic demand imposed on a structure exceeds a specified limit state for a particular intensity measure (IM). Various approaches are available in the literature for assessing fragility curves, and for this purpose, the method proposed by Nielson et al. in 2007 is adopted. This method assumes that both the demand (D) and limit states (LS) follow a log-normal distribution. Consequently, the fragility curve can be computed using Eq. (3): P ሺ ൐ │ IM ሻൌͳǦ Φ( ሺ ሻ − ሺ ሻ √ ʹ ൅ ʹ (3) ȁ In this formulation, Φ(∙) represents the standard normal cumulative distribution function. LSm corresponds to the median estimate of the structural limit state, Dm is the median estimate of the demand, βd|IM is the dispersion of the demand conditioned on the IM, and βLS is the dispersion of the structural limit state. The proposed methodology delves into the seismic structural behavior of bridges, with a specific focus on ductility failure mechanisms. Consequently, the ultimate displacement (Du) of the structure is considered as the structural limit state (LSm), while the maximum displacement (Dmax) anticipated at the site of the bridge is regarded as the demand (Dm). Parameters such as Du, essential for constructing the fragility curve, are evaluated through pushover analysis, where Du corresponds to the ultimate displacement of the structure's capacity curve, as depicted in Fig. 3a. The bridge is modeled using a simplified Finite Element Model, with piers represented as beam elements and the deck as a concentrated mass. The obtained pushover capacity curve can be approximated to a bilinear capacity curve, following the methodology described by Günay in 2008, as illustrated in Fig. 3a. Upon establishing the linear pushover capacity curve, Du is swiftly determined. The demand parameter Dmax can be assessed from the spectra related to the considered PGA and the pushover capacity curve. The maximum elastic displacement of the structure, De,max, is derived by plotting the acceleration-displacement seismic response spectra (ADSR) and the bilinear pushover curve on the same plane. The intersection point between the extension of the slope line of the capacity curve and the spectra denotes the elastic maximum displacement of the structure, as shown in Fig. 3b.