## 5 Conclusions  
To investigate the interface damage initiation, propagation, and delamination process between CCBP and ACWL in ballastless track under temperature loads, a 3D finite model of ballastless track which utilizes a bilinear CZM was introduced in this study. By comparing the full-scale transverse shear test results and simulation results, the bilinear CZM was verified as capable of predicting the initiation and propagation of the interface damage. The interface damage evolution process under uniform and gradient temperature loads and the effect of interface material properties on the interface characteristics was investigated. By setting partly and totally delaminated interface state as the initial conditions, the influence of interface damage on the dynamic response was also analyzed. The main findings can be summarized as follows  
1. It is reasonable to obtain the parameters of CZM from the full-scale transverse shear test and apply them in the numerical simulations of interfacial damage evolution under temperature load. 2. For the simulated conditions in this work, the microcracks between CCBP and ACWL were initiated when the temperature rising range was 5.9 \({}^{\circ}\)C, and the adjacent layers started to delaminate when the heating range was 19.2 \({}^{\circ}\)C. When \(\Delta t\) exceeded 60 \({}^{\circ}\)C, the interface totally delaminated and turned into the slipping contacting state. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multirow{2}{*}{**Transverse Tension**} & \multirow{2}{*}{**Longitudinal**} & \multicolumn{3}{c}{**Vertical**} & \multicolumn{2}{c}{**Vertical Stress on**} \\ \cline{3-8}  & & & **Longitudinal** & & **Displacement of** & & **Unbounded** \\ \multirow{-2}{*}{**Bonding State**} & \multirow{2}{*}{**Strain (\(\pm\)\(\pm\))**} & \multirow{2}{*}{**Strain Strain (\(\pm\)\(\pm\))**} & \multirow{2}{*}{**Strain Strain (\(\pm\)\(\pm\))**} & \multirow{2}{*}{**Asphal Layer**} & \multirow{2}{*}{**Aggregate Layer**} \\  & & & & & & **Surface (mm)** & & **(KPA)** \\ \hline \multirow{2}{*}{
\begin{tabular}{c} Perfect bond \\ Microracks’ initiation \\ Partly delaminating \\ Totally delaminating \\ \end{tabular} } & 6 & 5 & 9 & 7 & 0.38 & 0.25 & 7.7 & 4.7 \\  & 87 & 87 & 43 & 41 & 0.33 & 0.24 & 13.3 & 13.3 \\  & 245 & 240 & 75 & 73 & 0.66 & 0.65 & 43.4 & 43.1 \\  & 800 & 800 & 450 & 450 & 1.61 & 1.61 & 181 & 180 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Dynamic characteristics of four interfacial bonding states. 3. The temperature rising range needed for the interfacial damage initiation was mainly affected by the interfacial shear strength and interfacial shear stiffness, while the delamination of the adjacent layers was mainly affected by the critical fracture energy. The interfacial damage evolution process can be effectively controlled by increase in the interfacial shear stress and the critical fracture energy. 4. The research on effects of interface contacting state on the dynamic response of the ballastless track indicates that a great interface bond state is crucial for the safety of ballastless track operation. This interface damage propagation research will help engineers to predict the interface damage propagation process more accurately and optimize the interface safety design of ballastless track structure. To investigate the overall performance of the novel ballastless track, future work will focus on the establishment of a non-linear mechanical model which analyzes the coupling effect of in-layer damage and inter-layer damage. Conceptualization, X.C. and D.C.; methodology, X.C. and T.D. ; software, Y.Z., and T.D. ; validation, T.D. and G.X. ; formal analysis, Y.Z., G.X., and T.D. ; investigation, Y.Z., G.X., and T.D. ; writing--original draft preparation, Y.Z., G.X. ; writing--review and editing, X.C. and D.C. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China (No. 51778136, No.