## 2 Experimental Procedure and Materials
### Experimental Method  
Figure 2 illustrates the experimental setup and procedure, with the specific steps outlined as follows:  
1. The sandstone specimens in this experiment underwent \(N\) freeze-thaw cycles, with the total number of cycles set at 5, 10, 15, and 20 [6; 9; 16], corresponding to the labels A, B, C, and D, respectively. The predetermined freeze-thaw temperatures, \(T\), were set at \(-5\)\({}^{\circ}\)C, \(-10\)\({}^{\circ}\)C, \(-15\)\({}^{\circ}\)C, and \(-20\)\({}^{\circ}\)C, corresponding to the labels 1, 2, 3, and 4. Additionally, a control group, consisting of sandstone specimens that did not undergo freeze-thaw cycles and were maintained at room temperature (20 \({}^{\circ}\)C), was established and labeled as X. In total, there were 20 experimental groups and 1 control group, with each experimental group being repeated 5 times, resulting in a total of 105 specimens. For instance, for 5 freeze-thaw cycles at a temperature of \(-10\)\({}^{\circ}\)C, the specimen would be labeled A2.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Dry Density** & **Crude Density** & **Porosity** & **Natural Moisture** & **Percentage of Saturated** \\
**(kg/m3)** & **(kg/m3)** & **(\%)** & **Content (\%)** & **Water Content (\%)** \\ \hline
2417.1 & 2437.0 & 3.161 & 0.897 & 3.161 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Basic physical parameters of the coal measure sandstone specimens (average).  
Figure 1: Sampling location and sample stratum. The asterisks in the figure are sample stratum.  
2. All specimens were placed in a constant-temperature drying oven at 105 \({}^{\circ}\)C for 24 h. After cooling to room temperature (20 \({}^{\circ}\)C), they were removed and weighed. The dried specimens underwent a wetting treatment, and, after being saturated for 120 h, the surface moisture was absorbed every half hour, with the specimens being weighed until the mass change between the two measurements was less than 0.01 g, indicating that the specimens had reached a saturated state.
3. The saturated specimens were then placed in a freeze-thaw chamber for the freeze-thaw test, with the melting temperature set at 20 \({}^{\circ}\)C. Figure 3 presents the time-allocation scheme for the temperature-fall stage, the freezing stage, the temperature-rise stage, and the thawing stage across the four temperature ranges (\(-\)5 \({}^{\circ}\)C, \(-\)10 \({}^{\circ}\)C, \(-\)15 \({}^{\circ}\)C, and \(-\)20 \({}^{\circ}\)C). To prevent excessive internal temperature gradients that could induce additional stress, the temperature change rates during the temperature-fall and temperature-rise stage should be minimized as much as possible.
4. A WDW-300 electronic universal testing machine was employed to conduct uniaxial compression tests on the sandstone specimens. During the testing process, displacement loading was utilized at a loading rate of 2 mm/min and an Epsilon 3354 circumferential extensometer was used to monitor the circumferential displacement of the specimens. Simultaneously, the testing machine, circumferential strain acquisition system, and high-definition video system were activated to carry out the loading test until the specimens reached their peak strength and subsequently failed.  
Figure 3: Temperature loading and unloading paths in four freeze–thaw cycle tests. **(a)** Four freeze–thaw cycle tests. **(b)** One freeze–thaw cycle. Stage-1: temperature fall; stage-2: freezing; stage-3: temperature rise; stage-4: thawing.  
Figure 2: The experimental equipment and process.