PSI - Issue 78

Abed Soleymani et al. / Procedia Structural Integrity 78 (2026) 815–822 817 The steel rebar used in the examined bridge, which was characterized as TOR60, had an average yielding stress ≈600MPa . Without considering the ageing effects on initial mechanical properties, the average concrete compressive strength was assumed to be ′ =28MPa . 3.Methodology for evaluating the post-earthquake traffic capacity of the bridge Structural robustness can be defined as the ability of the structure to resist abnormal and extreme events such as fire, explosion, vehicle impacts, and earthquake. In order to quantify structural robustness, specific indicators and events are required. Some researchers proposed different types of robustness indicators according to either deterministic or probabilistic approaches (see, e.g. Dhir et al., 2025). In this study, residual redundancy factor was defined as a robustness indicator according to Eq. (1) (Frangopol and Curley, 1987): = (1) where: is a residual redundancy factor, is the load-bearing capacity of the damaged structure, and is the load-bearing capacity of the intact structure. It should be noted that, in this work, post-earthquake vertical load-carrying capacity and pre-earthquake vertical load-carrying capacity were respectively considered as and , respectively. Traffic loading was modeled in accordance with Load Model 1 (LM1) provided by Eurocode 1 – Part 2 (herein abbreviated as EC1–2; see EN1991-2, 2003). The performance levels of the bridge after an earthquake can be categorized based on loss in vertical and lateral load-carrying capacity (Mackie and Stojadinovic, 2004). For this purpose, the robustness indicator presented in Eq. (1) was considered to calculate the performance levels of the bridge. Based on the criteria of defining performance levels proposed by Mackie and Stojadinovic (2004) and the robustness indicator presented in Eq. (1), the performance levels of the bridge are categorized according to Table 1. Table 1. Decision criteria for allowable traffic flow in different post-earthquake performance levels proposed by Mackie and Stojadinovic (2004) Post-earthquake performance level Remaining traffic capacity (volume%) Loss of lateral load carrying capacity Robustness indicator ( R ) Immediate access 100 <2% >95% Weight restriction 75 <2% >90% One lane open only 50 <5% >75% Emergency access only 25 <20% >50% Closed 0 >20% <50% The methodology used in assessing post-earthquake bridge traffic capacity loss is described according to the following stages: (a) Creation of a nonlinear FE model of RC deck-stiffened arch bridge in the software SAP2000 (CSI, 2022). (b) Pushdown analysis of the examined bridge to evaluate pre-earthquake vertical load-carrying capacity ( ) through Nonlinear Static Analysis (NSA). (c) NTHA of the examined bridge under spectrum-compatible natural accelerograms to assess seismic resistance of the bridge and induced damage by earthquake, subsequently performing pushdown analysis to calculate post earthquake vertical load-carrying capacity ( ). (d) Determination of robustness indicator by means of residual redundancy factor presented in Eq. (1). (e) Assessment of allowable remaining traffic capacity in order to operate the bridge under full or some portion of the traffic flow.