# Probabilistic Modeling of Congested Traffic Scenarios on Long-Span Bridges
## 3 Congested Traffic Simulation Based on CA Method  
For a certain bridge, the site-specific traffic is dynamic, the traffic volume, percentage of heavy vehicles and other characteristics are constantly changing. Disregarding special factors such as lane maintenance, car accidents, etc., it is suggested that congested flow and free flow at the same specific site are interchangeable and somehow intrinsically related as a free-flow situation can automatically result in congestion because of an increment in the traffic volume. In this section, the intrinsic correlation between congested and free flow at the same site is discussed, and the traffic characteristics of congested flow are inferred based on free flow. The congested flow is then modeled based on the CA approach [38]. To simulate the congested traffic flow on long-span bridges, the traffic flow WIM data at the site of a real operational long-span cable-stayed bridge in China, with a span length of 1088 m, was investigated, as shown in Figure 2. From the WIM measurement of 423 days of free-flow traffic, 423 daily extreme response scenarios (i.e., the maximum-per-day event of the effect of the cable force of the investigated bridge) of free flow were obtained from WIM data as the sample for the further simulation of extreme response scenario in free-flow conditions. The point in time at which these 423 samples achieved the maxima (i.e., the response extremes achieved at the points of the day, on a 24 h basis) were further counted, as shown in Figure 3. It can be seen that most of the extreme response scenarios occurred between 20:00 pm and 7:00 am the next day, and only a small number of extreme response scenarios (86 in total) occurred during the daytime hours. Common sense dictates that trucks tend to travel at night. At the same time, almost all large cities in the vicinity of the WIM site are closed to truck traffic during daytime hours, even though there are no restrictions on truck travel times on highways where the WIM station is located. For example, in Shanghai, trucks are banned from the roads in the city area from 07:00 am to 20:00 pm daily. It can be seen that for the daily state free traffic flow, the daily extremes tend to occur more often at night (i.e., with a higher proportion of heavy vehicles and lower traffic volume), when traffic is less likely to be congested. The 86 extreme response scenario samples that achieved extreme response values during the daytime mentioned above were further analyzed. For these samples, the ratio of extreme traffic response to the modeled traffic load in the Chinese D60 code were calculated, and simultaneous hourly traffic volumes were counted, as plotted in Figure 4. The attributes of each extreme response scenario sample are identified with a marked shape. For example, circles indicate that the samples belong to holidays and weekends. The results reveal that extreme response scenarios with high hourly traffic flow typically have low ratios. The highest hourly traffic flow is 4083 veh/h, with a ratio of the response value to the Chinese code D60 of only 0.165. Nonetheless, higher hourly traffic volumes pose a potential risk for congestion in a free traffic flow scenario. To examine the traffic composition in the case of higher hourly traffic volumes, the gross vehicle weight (GVW) information associated with the extreme response scenarios of hourly traffic volumes above 3000 veh/h was obtained. For each high-traffic-volume extreme response scenario, the GVW information within one hour before and after the moment of extreme values was examined, as shown in Figure 5a. For comparison, Figure 5b shows the histogram of the GVW when the extreme response values are high. It can be seen that the GVW tends to concentrate in vehicles weighing less than 4 tonnes for high-traffic-volume extreme response scenarios (Figure 5a). Meanwhile, the number of vehicles weighing between 4 and 66 tonnes are relatively rare for high-traffic-volume extreme response scenarios but very important for high extreme responses (Figure 5b).