PSI - Issue 78

Abed Soleymani et al. / Procedia Structural Integrity 78 (2026) 815–822

820

structural elements. For instance, shear failures experienced by deck beams and arch elements under seismic analysis using accelerogram A1 are presented in Fig. 4. Shear failures of structural elements are shown by red line labels in Fig. 4.

Fig. 4. Shear failures identified after seismic analysis based on A1 accelerograms: (a) beams of deck; (b) arch elements.

6.Pushdown analysis of earthquake-damaged bridge In order to assess both pre- and post-earthquake vertical load-carrying capacities of the bridge, a type of NSA typically called ‘ pushdown analysis ’ in robustness -related studies (see, e.g., De Biagi et al., 2017; Mucedero et al., 2021; Scalvenzi and Parisi, 2021; Dhir et al., 2025) was carried out. For this purpose, the NSA of the FE model was applied in SAP2000 (CSI, 2022). In NSA, all intersection points of the primary (longitudinal) and secondary (transversal) beams in the bridge deck were subjected to increasing vertical loading until failure. It is important to underline that pushdown analysis for determining post-earthquake vertical load-carrying capacity of the bridge was performed after seismic analysis of the bridge. This delineated a sequential analysis procedure that is able to account for cumulative damage due to different loading conditions, i.e., in this case NLTHA under horizontal seismic ground motions followed by NSA under gravity loads (including traffic loads). For instance, the collapse configuration under pushdown analysis of the bridge damaged by A5 accelerograms is shown in Fig. 5.

Fig. 5. Collapse configuration under pushdown analysis of the bridge damaged by A5 accelerograms.

Based on pushdown analysis of the intact (undamaged) bridge, the initial (pre-earthquake) vertical load-carrying capacity was equal to 315,349 kN. Moreover, after applying seismic loads and inducing seismic damage to the bridge, the residual (post-earthquake) load-carrying capacity was determined through pushdown analysis, as shown in Table 3. Then, the robustness indicator presented in Eq. (1) was calculated based on both pre- and post-earthquake vertical load-carrying capacities, see Table 3. The decision-making process for allowable traffic flow was carried out based on the criteria presented in Table 1. With reference to the value of the robustness indicator for each seismic loading scenario, the remaining traffic capacity (permissible traffic flow) after the earthquake is also presented in Table 3.