# Probabilistic Modeling of Congested Traffic Scenarios on Long-Span Bridges
## 4 Extreme Response Scenario of Congested Traffic Loading  
The extreme response scenarios of congested flow are calculated for five representative load effects of the investigated bridge: the axial force of the longest cable (AFC, effect 1); the vertical deflection at the mid-span of the main span (VDMS, effect 2); the longitudinal displacement at the top of the pylon (LDTP, effect 3); the bending moment at the mid-span of the main span (BMMS, effect 4); and the bending moment at the bottom of the pylon (BMBP, effect 5). For each effect, the extreme response scenario is obtained every second, and the top 100 extreme response scenarios with the largest response are selected as simulation samples for further validation of the probabilistic model proposed by the authors [33] under congested flow traffic. For the extreme response scenarios of the congestion flow, the probability of occurrence of vehicles in each cell on the outer lanes was counted, as shown in Figure 7. It can be seen that in the extreme response scenarios of congestion, the distribution of vehicles along the longitudinal direction of the bridge, which varies according to the load effect, is not uniform, and the vehicles tend to concentrate in the zones of the influence lines where the maximum appears depending on the load effect. Therefore, the simulation of the location of vehicles on the bridge deck can still be performed using a non-stationary Poisson distribution as in the free-flow case [33]. Subsequently, the probabilistic model of extreme response scenario was applied to simulate the extreme response scenarios of congestion, taking effect 1 as an example. Figure 8 depicts the probabilities of a cell being occupied by a vehicle in an extreme response scenario for the congested situation. The non-stationary characteristic of the outer lane is more pronounced than that of the inner lane. For congested traffic, the proportion of heavier vehicles is not high. Their tendency to drive in the outer lane is more pronounced. Figure 7: The probability of occurrence of vehicles in each cell on the outer lanes. Also, the data and the GMM fitting of GVWs for the extreme congestion response scenarios are given in Figure 9, which is the basic information for simulating GVW. Figure 10 depicts several extreme response scenarios of effect 1 for congested traffic. As mentioned before, in the case of free-flow conditions, the dimension of the cell occupied or not by a vehicle was set to 20 m based on the normal dimensions and inter-gaps of heavy vehicles. Also, as shown in [33], the effect of light vehicles (less than 10 tonnes) could be neglected. In the simulation of the extreme response scenario under congestion, it had to be verified if these two conditions still applied. A comparison of ignoring or considering light vehicles in the congestion scenario is presented in Figure 11. If the lighter vehicles are ignored, the effect loss is in the range of 8% to 24% with a median of 15%. As shown before, during congestion, the proportion of light vehicles is higher, and the GVW of heavy vehicles is lower compared to the level of normal traffic scenarios in the free-flow situation. Therefore, the effect of light vehicles should not be ignored when performing simulations of extreme congestion response scenarios. Figure 8: Probabilities of a cell to be occupied by a vehicle in an extreme response scenario and congested flow for load effect 1. (**a**) Inner lane, (**b**) outer lane. Figure 9: Data and fitting of GVW in (**a**) inner lanes and (**b**) outer lanes. Figure 10: Samples of extreme response scenarios of congestion flow (effect 1). Based on the fact that light vehicles should be considered in the simulation, then the length of the cell should be adjusted. The length of small vehicles for domestic use is generally greater than 4.5 m, and the relevant Chinese regulations recommend a safe following distance of 10 m when the speed is below 20 km/h. Therefore, the cell length is chosen as 10 m when simulating extreme congestion response scenarios.