## 3 Experimental Results Analysis
### The Impact of the Number of Freeze-Thaw Cycles and Freezing Temperature on Peak Strain  
Figure 8 shows how the average peak strain (\(\epsilon_{c}\)) of the sandstone specimens varies with the freeze-thaw cycle count and freezing temperatures. The data set with the highest coefficient of variation in each experimental group is presented in Table 4, indicating the reliability of the experimental data. From Figure 8 (left), it can be observed that, regardless of the number of freeze-thaw cycles, the peak strain of the sandstone specimens increases in an exponential-like manner as the freezing temperature decreases, although the rate of increase gradually diminishes. For instance, at \(N=10\), when the freezing temperature decreases from \(-5\)\({}^{\circ}\)C to \(-20\)\({}^{\circ}\)C, the average peak strain increases by 14.71% (B1\(\rightarrow\)B2), 3.16% (B2\(\rightarrow\)B3), and 0.13% (B3\(\rightarrow\)B4). From Figure 8 (right), it is evident that, regardless of the freezing temperature, the peak strain of the sandstone specimens shows a gradually increasing trend with an increase in the freeze-thaw cycle count. Taking \(T=-15\)\({}^{\circ}\)C as an example, when the number of freeze-thaw cycles increases from five to twenty, the average peak strain increases by 6.33% (A3\(\rightarrow\)B3), 7.99% (B3\(\rightarrow\)C3), and 7.10% (C3\(\rightarrow\)D3). Additionally, at high freeze-thaw cycle counts, the effect of freezing temperature on the peak strain of the specimens is more pronounced, with the freezing temperature effect more readily exacerbating the transition of coal-measure sandstone from brittleness to ductility. At low freezing temperatures, the freeze-thaw cycle effect more easily intensifies the  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \begin{tabular}{c} **Test** \\ **Scenario** \\ \end{tabular} & \begin{tabular}{c} **Test Case** \\ **Scenario** \\ \end{tabular} & \begin{tabular}{c} **Peak Compressive** \\ **Strength** \\ \end{tabular} & \begin{tabular}{c} **Mean** \\ **Value** \\ **(MPa)** \\ \end{tabular} & \begin{tabular}{c} **Absolute** \\ **Deviation** \\ **(MPa)** \\ \end{tabular} & \begin{tabular}{c} **Relative** \\ **Deviation** \\ **(\%)** \\ \end{tabular} & \
\begin{tabular}{c} **Standard** \\ **Deviation** \\ **(MPa)** \\ \end{tabular} &
\begin{tabular}{c} **Coefficient of** \\ **Variation** \\ **(\%)** \\ \end{tabular} \\ \hline \multirow{3}{*}{A4} & Case1 & 18.451 & 1.860 & 9.632 & \multirow{3}{*}{1.338} & \multirow{3}{*}{6.929} \\  & Case2 & 20.944 & 19.311 & 0.633 & 3.278 & & \\  & Case4 & 21.539 & & 1.228 & 6.359 & & \\ \hline \multirow{3}{*}{B4} & Case3 & 11.352 & \multirow{3}{*}{14.256} & \multirow{3}{*}{1.270} & \multirow{3}{*}{8.909} & \multirow{3}{*}{2.059} & \multirow{3}{*}{14.443} \\  & Case4 & 15.526 & & 1.270 & 8.909 & & \\ \cline{1-1}  & Case5 & 15.890 & & 1.634 & 11.462 & & \\ \hline \multirow{3}{*}{C1} & Case2 & 13.778 & \multirow{3}{*}{14.726} & \multirow{3}{*}{0.846} & \multirow{3}{*}{5.745} & \multirow{3}{*}{0.736} & \multirow{3}{*}{4.998} \\  & Case3 & 15.572 & & 0.102 & 0.693 & & \\ \hline \multirow{3}{*}{D3} & Case1 & 9.346 & \multirow{3}{*}{10.788} & \multirow{3}{*}{1.442} & \multirow{3}{*}{13.367} & \multirow{3}{*}{0.688} & \multirow{3}{*}{6.377} \\  & Case2 & 12.266 & & 1.478 & & & \\ \cline{1-1}  & Case3 & 10.751 & & 0.037 & & & \\ \hline \hline \end{tabular}
\end{table}
Table 3: Peak compressive strength, \(\sigma_{c}\), of the specimens.  
Figure 7: Changes in the peak compressive strength of the specimen, \(\sigma_{c}\), with the number of freeze–thaw cycles, \(N\), and the freeze–thaw temperature, \(T\).  
transition of coal-measure sandstone from brittleness to ductility, which is consistent with the post-peak fluctuation characteristics of the stress-strain curves presented in Section 3.1.