# Track-Bridge Interaction of CWR on Chinese Large-Span Bridge of High-Speed Railway
## 4 Special Problems of Track-Bridge Interaction
### Complex Temperature Load  
For bridge structures, the temperature field generated by sunlight is a three-dimensional transient problem, but the existing research shows that the temperature distribution along the bridge direction is very similar under the action of sunlight, and the slight change of temperature along the bridge axis can be ignored in engineering. Therefore, the sunshine temperature field problem of the bridge structure can be simplified as a two-dimensional transient nonlinear problem on the section. The temperature effects of solar radiation, convective heat transfer, and radiation heat transfer are transformed into radiation heat flux by using ANSYS. Using the boundary condition function of the ANSYS load table, the heat flux is stored in the table, indexed by time, temperature, and coordinates, and the table is used as the boundary condition for the loading calculation.  
The maximum error between the calculated temperature and the measured temperature is 1.8 \({}^{\circ}\)C, and the average relative error is 3.6%. According to this model, based on the  
Figure 18: Envelope diagram of rail stress response.  
thermodynamic simulation analysis, the vertical temperature load formula of the ballastless track suitable for typical areas in China is fitted:  
\[\begin{split}\text{f}_{\text{positive temperature gradient}}=18e^{-6.5x}+a\end{split} \tag{2}\]  
\[\begin{split}\text{f}_{\text{negative temperature gradient}}=50x^{2}+42x+b\end{split} \tag{3}\]  
where \(t\) is the temperature of the track slab at different depths, \({}^{\circ}\)C; \(x\) is the depth from the track slab surface, m; _a (b)_ is the regional adjustment coefficient of the fitted positive (negative) temperature gradient, as shown in Table 1.  
The surface temperature of the ballastless track changes dramatically with the environment temperature and time, its internal temperature changes have a certain lag in time, and the change amplitude decreases rapidly with the increase of depth. The stronger the sunshine is, the higher the wind speed is, and the greater the vertical temperature gradient is. The maximum positive temperature gradient of the ballastless track in China occurs from 13:30 to 16:00 in May to August, and the average maximum vertical positive temperature difference is 17.0 \({}^{\circ}\)C. The maximum negative temperature gradient occurs from 5:00 to 5:30 in January, and the average maximum negative temperature difference is 8.7 \({}^{\circ}\)C. The surface temperature of the ballastless track in Chengdu, Changsha, and southeast coastal areas exceeds 45 \({}^{\circ}\)C in summer, and the lowest surface temperature of the track slab in Urumqi and Harbin is lower than \(-\)16 \({}^{\circ}\)C in winter. For central China, the vertical temperature gradient of the track slab is \(-\)2\(\sim\)10 \({}^{\circ}\)C [70; 71].  
With the increase of the uneven temperature difference of the bridge, the additional expansion force of the rail decreases, and the longitudinal displacement of the rail also decreases. According to the current code, the expansion force of the rail calculated at 20 \({}^{\circ}\)C is 1.3 times the rail stress under sunlight. However, the increase of the uneven temperature difference of the bridge will affect the ride comfort of CWR on the bridge. It is suggested to consider the influence of the uneven distribution of the bridge temperature to make it closer to the real stress state of the bridge [72; 73].  
Increasing the thickness of the base plate will help to improve the stress of the rail. Under the action of sunlight, the stress of the rail is proportional to the transparency coefficient of the atmosphere. The light color coating on the pavement and keeping the smoothness will help to reduce the stress of the rail [72].