# Probabilistic Modeling of Congested Traffic Scenarios on Long-Span Bridges  
[PERSON]  
1 Department of Bridge Engineering, Tongji University, Shanghai 200092, China; [EMAIL_ADDRESS] (X.W. ); [EMAIL_ADDRESS] (X.R.) [PERSON]  
1 Department of Gridge Engineering, Tongji University, Shanghai 200092, China; [EMAIL_ADDRESS] (X.W. ); [EMAIL_ADDRESS] (X.R.) [PERSON]  
2 Department of Civil and Environmental Engineering, Universitat Politecnica de Catalunya (UPC-BarcelonaTech), [PERSON] 1-3, North Campus, 08034 Barcelona, Spain 22 Department of Civil and Environmental Engineering, Universitat Politecnfor the design and assessment of long-span bridges [11; 21; 22]. Additionally, the increasing volume of traffic often leads to severe congestion on long-span bridges, posing threats to both human safety and structural performance. For short-span bridges, maximum traffic load effects are typically governed by one single heavy vehicle or several heavy vehicles side-by-side. However, for long-span bridges, as the span length increases, the number of vehicles that can be accommodated on the bridge deck also significantly increases, thereby complicating vehicle load management and safety assessments [11; 23; 24]. Numerous studies have indicated that traffic congestion constitutes the most critical scenario for long-span bridges [25; 26; 27]. However, the majority of WIM systems that are utilized globally to gather traffic data are unreliable when congestion appears [28]. In the research of [PERSON] et al. [28], the free-flow traffic of WIM data are used to modeling congested flow traffic by collapsing the inter-vehicle gaps to minimum values. Traditional congested traffic modeling methods can simulate the congestion on bridge decks very well [29; 30; 31]. However, not all congestion scenarios can cause structural effects to reach extreme values. Based on common sense, congested traffic with many stationary vehicles on the span is the critical situation to find the maximum traffic load on the bridge. However, this cannot be the case for maximum traffic effects, as these will depend on the shape of the influence line of the considered load effect. The congested traffic situation also applies traffic load in the areas of the influence line with an effect opposite to the one under analysis. It should be noted that to find the worst loading scenarios for a specific load effect, the term \"long-span bridge\" is not always equivalent to a \"long-loaded length\", where the latter is defined as the part of the bridge that should be loaded to find the worst load effect. As an example, regarding the maximum tensile force in the main cable of a suspension bridge, the worst traffic condition will be congestion over the whole length (in this case \"long-span\" and \"long-loaded length\" are equivalent). However, in looking to the maximum positive bending moment at the mid-span of a cable-stayed bridge and taking into account the shape of the influence line, as shown in Figure 1, scenarios where vehicles are only present near the mid-span may lead to the worst effect. In this case, a long span is not equivalent to a long-loaded length from the point of view of the worst loading effect. The filtering effect of the influence line may convert a long-span bridge into a short-loaded length bridge from the point of view of deriving the maximum load effects. In this sense, it is relevant to cite one of the conclusions from the thesis of [PERSON] [32]: \"The queue of vehicles at a standstill, widely used in previous research, is not always the most critical congested state for long-span bridge loading (Section 2). This is due to the fact that full stop queues involve only one realization of vehicles per congestion event, which may actually reduce the probability of finding an extreme loading scenario\". Therefore, there  
Figure 1: Influence line of bending moment at mid-span of cable-stayed bridge. exists a research gap for the simulation of extreme loading scenarios of congested traffic on long-span bridges.