## 4 Numerical Simulation of Interface Damage of Ballastless Track under Temperature Load
### Interface Damage Analysis under Uniform Temperature Load  
In this case, the initial temperature of each layer was the same and varied synchronously. Under uniform temperature load, the under-rail structural layers exhibited a uniform longitudinal and transverse deformation trend. As the displacements of layers were constrained and thermal expansion coefficients of asphalt concrete and cement concrete were different, there was a relative movement trend between the two layers and shear stress occurred at the interface. When shear stress exceeded the interface bonding strength, shear failure occurred at the interface and the restraint effect of ACWL on the cement base plate failed. The results of previous numerical calculations prove that the bonding performance of the interface between CCBP and ACWL is consistent with each other under the uniform rise and drop in temperature load. Therefore, herein, the evolution process of interfacial bond-slip behavior under uniform rising temperature load is analyzed. The initial temperature was set as 15 \({}^{\circ}\)C, and the temperature rising ranges (\(\Delta t\)) were 1, 5, 10, 15, 20, 30, and 40 \({}^{\circ}\)C, respectively. To investigate the \(\Delta t\) required to achieve complete debonding state, 50 \({}^{\circ}\)C and 60 \({}^{\circ}\)C rising ranges were also employed. The indicators that characterized interface state included shear stress, an index for the interlayer damage initiation (QUADSCRT), and an index for damage degree (SDEG). Figure 7 shows the contour of damage indices (QUADSCRT and SDEG) under different temperature loads. The interface damage evolution process can be divided into four stages. At the first stage (\(\Delta t=1\)-5 \({}^{\circ}\)C), damage accumulated at the interface and interface crack did not yet occur. At the second stage (\(\Delta t=5\)-15 \({}^{\circ}\)C), QUADSCRT reached 1 and interface microcracks generated at the expansion joint, but the maximum value of SDEG was still lower than 1 which meant there were no macrocracks generating at the interface. At the third stage (\(\Delta t=15\)-50 \({}^{\circ}\)C), SDEG at the expansion joint reached the maximum value first, and macrocracks started to generate at the expansion joint and propagated to the other areas of the interface. Finally, when the temperature rising range exceeded 60 \({}^{\circ}\)C, the adjacent layers were totally delaminated and interface contact state turned into sliding friction (see Figure 7f). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Components**} & \multirow{2}{*}{**Width (m)**} & **Thickness** & **Density** & **Young’s** & **Poisson** & **Expansion** \\  & & **(m)** & **(kg/m\({}^{3}\))** & **Modulus** & **Ratio** & **Coefficient** \\  & & & & & & (\({}^{\circ}\)C\({}^{-1}\)) \\ \hline Track slab & 2.55 & 0.2 & 2400 & 36,000 & 0.20 & \(1\times 10^{-5}\) \\ SCC & 3.40 & 0.4 & 2300 & 28,000 & 0.18 & \(1.5\times 10^{-5}\) \\ CCBP & 3.40 & 0.4 & 2300 & 28,000 & 0.18 & \(1.5\times 10^{-5}\) \\ ACWL & 13.4 & 0.1 & 2400 & 4568 & 0.3 & \(2\times 10^{-5}\) \\ Surface layer of road bed & 13.4 & 0.6 & 2200 & 160 & 0.3 & \(1\times 10^{-5}\) \\ Bottom layer of road bed & 13.4 & 2.4 & 1900 & 100 & 0.3 & \(1\times 10^{-5}\) \\ Soil foundation & 21.7 & 5 & 1850 & 60 & 0.3 & - \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Geometries and material parameters of ballastless track system. Figure 6: Sub-rail infrastructure cross-sectional picture. SCC: self-compacting concrete. As shown in the contour of damage indices, the interface under the expansion joint of the base plate was the most vulnerable area under temperature loads. The variation of QUADSCRT and SDEG at the expansion joint with \(\Delta t\) is plotted in Figure 8. The variation of interface damage ratio and detachment area ratio with \(\Delta t\) is presented in Table 4. Interface damage ratio is the percentage of damaged area (QUADSCRT = 1 and SDEG \(>\) 0) in the total area. Detachment area ratio is the percentage of delaminated (SDEG = 1) in the total area.