PSI - Issue 78

Yang Liu et al. / Procedia Structural Integrity 78 (2026) 2030–2037

2033

(

) ( = k 

) ( N IM i s IM i =  =

)

1,2

s ST k IM i = =

k

=

(4)

where α k ( IM=i ) indicates the percentage of the total probability that a near-fault source generates pulse-like (k=1) or non-pulse like (k=2) seismic events conditioned to IM=i. Referring to the PSHD approach presented in Shahi et al. ( 2013), the values of the α k could be determined by statistics to historical seismic records at a specific source. (2) Seismic Fragility Analysis (SFA). In this step, the vulnerability function, here denoted as P V (DS = j | IM = i) , need to be refined accounting for the specific type of ground motion (ST=1,2,3) earthquakes, that is V, = ( = | = ) . To separate the pulse-like and non-pulse-like ground motions, the quantitative identification method for velocity pulse is here adopted, Zhai, et al. (2013). This latter is based on the idea to adopt a simplified numerical model of the real ground motion calibrated through the least-square fitting (LSF) technique. Subsequently, an energy index (Ep) is defined and calculated to identify, among the selected natural earthquake records, the pulse-like ones. Accordingly, the ground motions can be considered pulse-like when the value of Ep is greater than 0.3. (3) Recovery estimation. In this stage, the functionality recovery function for each damage state Q j ( t ) is differentiated by near-fault and far-field earthquakes. Even though the probability distribution of the parameters in Q j ( t ) is generally unknown, the data of real procedure of bridge functionality restoration can be gathered and used to provide empirical values of the recovery parameters, including minimum, moderate and maximum values, Decò, et al. (2013). More details can be found in Liu et al (2024). Basically, the recovery functions are weighted with the number of NF and FF earthquakes associating the most sever recovery conditions to the NF earthquakes. (4) Probabilistic Seismic Resilience Analysis (PSRA). After the three previous stages, the expected functionality level ( ) Q t in Eq. (3) can be rewritten as: Q̄ RE (t)= ∑∑ P S (ST=k | IM=i) n ST k=1 n IM i=1 ∙∑ P V,ST=k (DS=j | IM=i) n DS j=1 Q DS=j || IM=i (t) (5) where S ( ) P ST k IM i = = , V, ( ) ST k P DS j IM i = = = , and ( ) DS j ST k Q t = = are those obtained from the previous stages. Then, the assessment of the bridge resilience in a near-fault region is completed by substituting RE ( ) Q t into Equation (1). In addition, the robustness and rapidity for the refined expected resilience can be calculated following the method presented in section 2.1. Short-medium span steel-concrete composite bridges made of hot-rolled beams and concrete cross beams are very common in non-seismic areas due to the economic benefits related to limit manufacturing and short construction time. In order to extend this favourable structural solution to high seismic-prone areas, and therefore, cover the relevant lack of knowledge on the seismic response of these type of bridges, a wide research activity has been carried out within the European Project SEQBRI, Paolacci, et al. (2012). In this respect, a two-span concrete-steel composite road overpass has been selected as illustrative example for the application of the proposed resilience assessment methodology. Frontal view, a deck section and the pier are illustrated in Fig. 3. The analysed bridge is a typical highway overpass designed according to Eurocodes. The 3D finite element (FE) model has been developed using the collaborative framework OpenSees, McKenna, et al. (2007). In this model, the force-based nonlinear beam elements with fiber cross-sections are used to model the single steel girder and the tributary concrete slab. The Menegotto-Pinto model is adopted to simulate the mechanical behavior of steel girders and slab reinforcement, while the Kent-Park model is used to reproduce the mechanical behavior of concrete. Nonlinear links with elastoplastic behavior are used to model the shear studs that connecting the steel girders to the slab, within the CCB, and along the deck. A component-based model proposed in Paolacci, et al. (2012) has been adopted for representing the behavior of the concrete cross beam (CCB). Fig. 4 shows the details of the 2-D FE model for the CCB. Details of the novel type of pier-to-deck connections can be found in Abbiati, et al. (2018), which is beyond the scope of this study. 4 Illustrative example 4.1 Numerical model