## 4 Numerical Simulation of Interface Damage of Ballastless Track under Temperature Load
### Interface Damage Analysis under Gradient Temperature Load  
Because of large annual/daily temperature difference in Northern China and poor thermal conductivity of concrete materials, the seasonal changes in atmospheric temperature can result in a gradient temperature field in the ballastless track. Under the action of gradient temperature, the interface damage caused by the relative displacement trend of the adjacent layers accumulates. Therefore, this section analyzes the evolution process of the interface-bond-slip behavior between ACWL and CCBP under positive and negative gradient temperature loads. According to the recommended value in the \"Code for Design of High Speed Railway\" in China (TB10621-2014), the positive temperature gradient load (the upper layer is hotter than the lower layer) was set as 90 \({}^{\circ}\)C/m, and the negative temperature gradient in track slab (the upper layer is colder than the lower layer) was set as 45 \({}^{\circ}\)C/m, respectively. Although the temperature gradient was negligible in the layers that are over 0.2 m in depth from the track slab surface, 10 \({}^{\circ}\)C/m was set in the cement base plate for design security. The temperature gradient in layers below the base plate was not set. The effect of coupled action of gradient and uniform temperature loads on the interfacial characteristics was also analyzed. The details of the simulation cases are listed in Table 6.  
As shown in Figure 10, in cases 1 and 2, only a few interface microcracks were generated at the expansion joint of the base plate and the damage area was extremely small. The positive/negative gradient temperature load had little effect on the interface between CCBP and ACWL. The transverse and longitudinal shear stress and normal displacement at the interface between CCBP and ACWL in cases 1 and 2 are listed in Table 7. The deformation of the interface was tiny and the stress between the adjacent layers was smaller than the designed strength, which signifies that the ballastless track structure was safe under a 90 \({}^{\circ}\)C/m positive gradient temperature load and a 45 \({}^{\circ}\)C/m negative gradient temperature load. \begin{table}
\begin{tabular}{c c c} \hline
**Case** & **Gradient Temperature Load \({}^{\circ}\)C/m** & **Uniform Temperature Load \({}^{\circ}\)C/m** \\ \hline
1 & Positive, 90 & / \\
2 & Negative, 45 & / \\
3 & Positive, 90 & (+)5, 10, 15, 20, 30, 40, 50, 60 \\
4 & Positive, 90 & (\(-\)5, 10, 15, 20, 30, 40, 50, 60 \\
5 & Negative, 45 & (+)5, 10, 15, 20, 30, 40, 50, 60 \\
6 & Negative, 45 & (\(-\)5, 10, 15, 20, 30, 40, 50, 60 \\ \hline \end{tabular}
\end{table} 
Table 6: Details of temperature loads for different simulated cases. The relationship curves of QUADSCRT/SDEG and temperature rising/dropping range (\(\pm\Delta t\)) in cases 3\(\sim\)6 are plotted in Figure 11. As shown in Figure 11a, when the initial temperature load was 90 \({}^{\circ}\)C/m (positive), the microcracks started to generate when \(+\Delta t\) was 5.5 \({}^{\circ}\)C and macroracks occurred when \(+\Delta t\)= 18.8 \({}^{\circ}\)C. When the temperature was reduced and the initial temperature gradient was 90 \({}^{\circ}\)C/m (positive), the microcracks started to generate when the temperature dropping range was 7.7 \({}^{\circ}\)C. The interface started to debond when the temperature dropping range was 20.8 \({}^{\circ}\)C (Figure 11b). As depicted in Figure 11c, when the negative gradient temperature load and the global warming load worked together, the interface microcracks started to generate when \(-\Delta t\) was 7.4 \({}^{\circ}\)C and the interface started to delaminate when the temperature dropping range was 20.5 \({}^{\circ}\)C. As shown in Figure 11d, when the negative gradient temperature load and the overall cooling load worked together on the structure, the interfacial microcracks started to generate when the temperature dropping range was 5.3 \({}^{\circ}\)C and the macroracks generated when the dropping range was 18.6 \({}^{\circ}\)C.