## 4 Stochastic Traffic Model
### Data Source and Instantiation  
After the framework is established, the parameters could be determined after two primary sources: (1) the existing traffic data in the publications such as design codes and guidelines; (2) the direct measurement by the monitoring systems installed on bridges, e.g., the weigh-in-motion system. Due to the lack of traffic data in the bridge site, the traffic model is first instantiated based on the fatigue truck models in the Chinese code JTG [20], European code Eurocode 1 (EC1) [21] and American code AASHTO [22]. Figure 5 shows the standard truck models proposed in the three codes. It is worth noting that no considerable difference could be found between the truck models in the JTG and EC1 except for the footprint. Also, the dynamic impactor factor is already considered in these two models. On the contrary, an additional impact factor of 1.15 should be applied when using the AASHTO truck since it is not included [22]. Furthermore, according to the measurements on the Williamsburg bridge and Bronx-Whitestone bridge [34; 35], an extra amplification factor of 1.5 is suggested by the AASHTO in the fatigue evaluation of RD joints. Thus, when employing the AASHTO truck model, an overall amplification factor has been applied as \(1.15\times 1.5=1.725\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Type** & **Parameters** & **Description** \\ \hline \multirow{4}{*}{Vehicle properties} & Axle number & The number of axles in a vehicle \\  & Axle spacing & The distance between the centre of axles \\  & Axle weight & The weight of each axle in a vehicle \\  & Axle track & The distance between wheels in the same axle \\  & Footprint & The contact area of wheels on the deck \\ \hline \multirow{2}{*}{Lateral distribution} & Occupancy rate & The distribution of the vehicle in different lanes \\  & In-lane position & The lateral position of the vehicle within a lane \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters in the framework of the stochastic traffic model. According to the EC1 [21], 10% of the truck number in the slow lane can be used for the lane mainly occupied by light-weight cars, e.g., the fast lane in Figure 4. Under this assumption, the occupancy rate could be determined. In the AASHTO [22], the occupancy rate is related to the number of lanes available to trucks. Due to the traffic regulations and physic limitation, trucks seldom choose the fast lane when running on the three-lane highway, especially when heavily loaded. Thus, two lanes are assumed to be available to trucks for the prototype bridge, i.e., the middle lane and slow lane. As suggested by the AASHTO [22], the occupancy rate is determined as 85% for the slow lane and 15% for the middle lane. In the JTG [20], no specific provision could be found on the occupancy rate. As proposed by a supplementary document about the design of OSDs in China [36], the occupancy rate is kept the same as the value in the AASHTO. The occupancy rate in different traffic models is also listed in Figure 5.  
Apart from the occupancy rate, the in-lane position is another essential factor in determining the lateral distribution of vehicles. In this aspect, no suggestion could be found in the AASHTO [22] while a distribution model is proposed in the EC1 [21] and adopted in the JTG [20]. Thus, the distribution has been employed for all three traffic models. As per the EC1 [21], the vehicle centre is considered as a random variable, discretely distributed over the width of lanes with the highest density in the lane centre, as shown in Figure 5. However, the lateral position is more likely a continuous variable that the vehicle can occur at every possible. Thus, the distribution has been fitted to the normal distribution using the maximum likelihood estimation [37], as shown in Figure 6. As a result, a zero mean and a standard deviation of 100 have been obtained. Figure 5: Fatigue truck models in the codes.