## 2 Materials and Methods
### Strain Monitoring Method  
Most natural rock masses contain initial cracks, and under external loading, the localized area near the crack tip is highly prone to damage or failure. The stress-weak plane of a cracked rock mass is directly related to the orientation of the crack. Therefore, monitoring strain changes around the crack allows for investigating its deformation behavior, which in turn can help assess the freeze-thaw damage in cracked rock masses. To monitor the strain changes around the crack, measurement points were selected on the rock specimen surface at the edges of the crack, in a direction perpendicular to the short edge and parallel to the long edge of the crack. Additionally, two symmetric points were selected as reference measurement points, as shown in Figure 2. Strain gauges were attached at all four measurement points to measure the strain values and monitor the variation patterns. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Category**} & **Crack** & **Crack** & **Crack** & **Dry** & **Saturated** & **Water Ab-** & **Porosity** \\  & **Length** & **Width** & **Depth** & **Volume * [mm]** & **[mm3]** & **[g/cm3]** & **[g/cm3]** & **[g/cm3]** & **[\%]** & **[\%]** \\ \hline D1 & 30 & 3 & 20 & 1943 & 2.085 & 2.215 & 6.222 & 13.972 \\ D2 & 30 & 3 & 30 & 2843 & 2.079 & 2.208 & 6.193 & 14.338 \\ D3 & 30 & 3 & 40 & 3743 & 2.073 & 2.201 & 6.142 & 14.660 \\ \hline \hline \end{tabular}  
* The crack volume is considered as a part of the total volume of the rock specimen.  
\end{table} 
Table 1: Basic physical property parameters of the rock specimen. Figure 1: Rock specimen: (**a**) rock specimen dimensions; (**b**) actual rock specimen; (**c**) the XRD diffraction pattern of the rock specimen; (**d**) the mineral composition proportions of the rock specimen. The signal transmitted by the strain gauge was collected using a static resistance strain gauge instrument. Due to the significant influence of environmental temperature on the resistance of strain gauges, the resistance of the strain gauge changes with fluctuations in external temperature. The resistance change caused by temperature variations is of the same order of magnitude as that caused by the strain in the specimen, leading to considerable measurement errors, referred to as temperature errors of the strain gauge. This occurs for two reasons: first, the resistance wire of the strain gauge has a certain temperature coefficient, and second, the thermal expansion coefficients of the resistance wire and the test material are different. Therefore, it is necessary to eliminate the temperature error of the strain gauge to obtain accurate strain values, and the bridge compensation method is a commonly used approach for this purpose. Quartz glass is typically selected as the material for the temperature compensation strain gauge due to its extremely low and stable thermal expansion coefficient, which is an order of magnitude lower than that of typical rock materials, with a thermal expansion coefficient of 5.3 \(\times\) 10\({}^{-7}\)\({}^{\circ}\)C\({}^{-1}\). The specific procedure is as follows: On the static resistance strain gauge instrument, select the half-bridge circuit configuration. Attach the working strain gauge to the measurement point on the rock specimen and attach the temperature compensation strain gauge to the quartz glass. During testing, place both the temperature compensation strain gauge and the working strain gauge in the same temperature environment, as shown in Figure 3a. Since strain gauges malfunction when exposed to water, waterproofing measures must be applied when attaching the strain gauges, as shown in Figure 3b. The actual working strain gauge and its waterproof treatment are shown in Figure 3c,d, respectively. The actual temperature compensation strain gauge and its waterproof treatment are shown in Figure 3e,f, respectively. The strain gauge model is \"BFH120-5 AA-D300\", with a sensitivity coefficient of 2.0 \(\pm\) 1% and an accuracy grade of Class A.