## 4 Conclusions  
Based on DIC and AE technology, in this study, the process of frost-heave crack propagation in concrete specimens was studied, respectively. An evolution law of generalized strain (\(\varepsilon\)) and AE events location on the surface of the specimens during frost-heave crack propagation is revealed. Using experiment-based analysis, a double-strain criterion for frost-heave crack propagation and factors affecting frost-heave crack propagation were investigated. The main conclusions can be summarized as follows:  
(1) Based on DIC and AE technology, in this study, the process of frost-heave crack propagation in concrete specimens was studied respectively. This verified the correctness of using the surface strain at the crack tip to study the frost-heave crack propagation process. Additionally, methods for determining double-strain fracture parameters (micro-crack initiation strain and unstable strain) using the DIC technique were suggested. (2) By studying the frost-heave crack propagation process, it was found that the frost-heave crack propagation was caused by an ice plug which formed at the crack opening. The process of crack propagation was divided into five different stages. For more detail sees Section 3.1. (3) It was found that a computer-based DIC technique which captures continuous full-field strains can be used to adequately investigate the crack-initiation and crack-propagation processes of concrete specimens under frost-heave. The average values of micro-crack initiation strain and unstable propagation strain were found to be 224 \(\mu\varepsilon\) and 243 \(\mu\varepsilon\), respectively. Moreover, frost-heave crack propagation was found to belong to mode I crack. (4) The double-strain model set out in this paper can be used to evaluate the whole process of crack propagation, which avoids the need to determine the stress intensity factor at the crack tip and the fracture toughness of materials under complex frost-heave force. (5) When the crack width is larger than 0.27 mm and the external temperature is lower than \(-6.6\,^{\circ}\mathrm{C}\), cracks propagate easily under the frost-heave force. Therefore, it is suggested that corresponding maintenance measures should be taken for cracks with a width larger than 0.27 mm to avoid the further propagation of cracks under frost-heave force and ensure the durability of slab-tracks. (6) Frost-heave crack propagation is highly sensitive to the moisture content in the cracks. Crack-sealing measures are usually adopted to prevent fracture damage to slab-tracks. Therefore, \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Damage Site**} & **Grade/Crack Width (mm)** & **Maintenance Regulations** & **Maintenance Recommendations** & **Note** \\ \hline \multirow{4}{*}{Track slab} & \multirow{2}{*}{I/0.1} & II: pressure-free & Areas with temperatures above \(6.6\,^{\circ}\mathrm{C}\): & \\  & & & II: pressure-free grouting; III: & & \\  & & & low-pressure grouting. & & \\ \cline{2-5}  & II/0.2 & low-pressure & Areas with temperatures below \(6.6\,^{\circ}\mathrm{C}\): & \\  & & & & I: surface closure; II: pressure-free & \\  & III/0.3 & & & grouting; III: low-pressure grouting & \\ \hline \multirow{4}{*}{Bearing layer} & \multirow{2}{*}{I/0.2} & II: surface closure; & & \\  & II/0.5 & III: pressure-free & Areas with temperatures above \(6.6\,^{\circ}\mathrm{C}\): & temperatures above \\  & III/1.0 & grouting & & 6.6\,^{\circ}\mathrm{C}\): II: surface & \\ \hline \multirow{4}{*}{Base plate} & \multirow{2}{*}{I/0.2} & II: surface closure; & Areas with temperatures below \(6.6\,^{\circ}\mathrm{C}\): & \\  & II/0.3 & III: pressure-free & I and II: surface closure; III: & \\ \cline{1-1} \cline{2-5}  & III/0.5 & grouting & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Slab-track bed damage grade and maintenance recommendations. before crack sealing in slab-tracks, the crack moisture content should be strictly controlled to avoid frost-heave damage to slab-track caused by residual water in cracks. Data curation, X.C. and W.Z.