## 6 Results and Discussion  
### Stress Spectra  
As aforementioned, the joint U12L is exposed to a critical situation since it is located at the slow lane and close to the frequent loading position of wheels. Thus, the joint U12L is selected to investigate the difference in the stress spectra solved with the different traffic models. Since the spectra are highly similar in the nominal stress approach and hot spot stress approach, except for the amplitude, only the results in terms of the hot spot stress are listed, as shown in Figure 15. For clarity, the stress ranges with a small probability are truncated in Figure 15.  
The result suggests that the stress ranges are highly scattered in the spectra, further illustrating that it is too concise to reflect the fatigue action in OSDs by the equivalent stress range solved with the deterministic truck model. At the same time, notable similarities could be found in the spectra solved under the three standard truck models. Although the critical joint U12L is selected, the low-level  
Figure 14: Modified stress-life curves for rib-to-deck joints: (**a**) OSDs with CUs; (**b**) OSDs with TEUs. stress ranges (less than 15 MPa) still account for a considerable proportion in the spectra due to the randomness in the lateral position. As a result, it can lead to over-conservative results when only considering one or several critical lateral positions, as is the case in deterministic evaluation. It is also worth noting that the spectra solved by the JTG are more concentrated at the high-level ranges when compared with the one solved by the EC1, as shown in Figure 14a,b. The result could be explained by the only difference in footprints between the two models. Unlike the above two models, a local peak could be observed at the middle-level ranges (from 15 to 30 MPa) in the spectra solved by the AASHTO model. The front axle should be accounted for that, which further demonstrates its importance in the fatigue evaluation. Meanwhile, compared with the results solved with the standard truck models, unique features could be observed in the spectra solve with the observation model: (1) the probability density of low-level ranges is relatively high; (2) the distribution is more even and continuous. The following factors could be accounted for: (1) six different groups of vehicles are considered in the observation model instead of a single truck; (2) the randomness in axle weight is considered in the model. As a result, the observation model could lead to a significant insight into the randomness in traffic, and it is applied in the following comparison. Also, the joints U7\({}_{\rm L}\) in the middle lane and U2\({}_{\rm L}\) in the fast lane are selected to investigate the effect of occupancy rate on the spectra since the two joints are located at the same in-lane position as the joint U12\({}_{\rm L}\). The hot spot stress spectra are listed in Figure 16a,b, respectively. Figure 15: Hot spot stress spectra of the joint U12\({}_{\rm L}\) solved by different traffic models: (**a**) JTG; (**b**) EC1; (**c**) AASHTO; (**d**) Observation model. The result indicates that the spectra of the joint U7\({}_{\rm L}\) are similar to the spectra of the joint U12\({}_{\rm L}\), as shown in Figure 16a. According to Table 3, the difference in occupancy rate is small between the middle lane and slow lane for all the vehicles except the two-axles lightweight cars. Especially in terms of the five-axles and six-axles trucks, the differences in occupancy rate are only 10.6% and 5.8%, respectively. Meanwhile, the level of stress ranges in the joint U2\({}_{\rm L}\) is generally lower than in the above two joints, as shown in Figure 16b. This result could be attributed to the following reason: although the total occupancy rate of the fast lane is the highest (i.e., around 42%), the proportion of heavier trucks in the fast lane is notably lower than in the other two lanes.