PSI - Issue 62

6

Author name / Structural Integrity Procedia 00 (2019) 000 – 000

Andrea Nettis et al. / Procedia Structural Integrity 62 (2024) 693–700

698

2.3. Methodology for fragility analysis A cloud-based fragility analysis (Jalayer et al., 2017; Nettis et al., 2021) is performed by using natural scaled ground-motion records. For fragility analysis, the intensity of the seismic record is quantified in terms of an intensity measure (IM). The spectral acceleration associated with a given period value is commonly used for fragility analysis of single structures. However, in this study, the PGA is used as IM, which is convenient to assign a common IM to the fragility curves corresponding to the analysed case studies. After running the NLTHA, the results are recorded in terms of an engineering demand parameter (EDP). In this case, the EDP corresponds to the relative displacements between the top and the bottom plates of the isolators. A single limit state (LS) threshold Δ expressed in terms of the considered EDP is considered for each case study (Table 1). Particularly, the values of Δ are computed by assuming that the LS is achieved for a shear strain equal to 150% (Aghaeidoost and Billah, 2022). Given the distribution of EDP for a given IM, fragility curves expressing the probability of exceeding a given LS can be quantified. It is worth specifying that for a line of elastomeric bearings on the same pier, the LS can be considered exceeded when the first bearing device exceeds the predefined limit. Equation 1 shows the analytical formulation for a given fragility relationship, expressing the probability of reaching the LS, ( | ) . The fragility model is expressed by the normal cumulative distribution function (∙), based on the probabilistic seismic demand model represented by a power-law model ( = ) which is fitted to the “cloud data” in the loga rithmic − plane. The parameters a and b are estimated through regression analysis resorting to the least square method. This logarithmic standard deviation (or dispersion β EDP|IM ) is quantified via Equation 2, where is the number of ground motions. ( | ) = ( − | ) (1) | = √ ∑ ( − ) 2 =1 −2 (2) 3. Results In this section, the influence of the landslide-induced displacement scenarios on bridge fragility is discussed. It is worth noting that the initial landslide-induced strain for the elastomeric bearings is related to the intensity of the settlement (i.e. transverse displacement) related to each substructure component and the stiffness of the superstructure. Preliminary considerations can be derived by observing the landslide-induced strains for the elastomeric bearings of the LDRB-equipped case study shown in Fig. 2. Scenario S1 involves a linear settlement pattern with no deformations (i.e. a rigid displacement) of the superstructure and, therefore, no initial bearing strains is observed. Conversely, the other scenarios involve a more complex settlement profile and consequent initial bearing strains. The scenarios S2 and S3 are based on parabolic settlement profiles involving a parabolic superstructure deformation which opposes the landslide-induced distortions on the original longitudinal profile. In these scenarios, the highest bearing strains are registered at the abutments and on pier P3. Scenario S4 is based on a localised single-pier settlement and leads to the most critical landslide-induced bearing strain. Although these results are related to the case-study bridge having LDRB, similar outcomes can be observed for the other bridges (not reported for brevity). Based on these preliminary observations, the fragility curves shown in Fig. 4 can be discussed. Considering the absence of settlements (scenario S0), the bridge equipped with LRB exhibits lower fragility with respect to the other cases. In this case, the 50% probability of exceeding the considered LS is related to a value of PGA equal to 1.00g. As anticipated, since no initial strain is involved in scenario S1, the influence of S1 on bridge fragility is negligible for all the analysed case-study bridges. The fragility curves for S2 and S3 scenarios coincide, because of equal values of landslide-induced bearing strains. Scenarios S2 and S3 involve a significant increase in fragility with respect to scenario S0. The highest influence is registered for the LRB where the PGA related to the