## 3 Experimental Results Analysis
### The Impact of the Number of Freeze-Thaw Cycles and Freezing Temperature on Peak Strength  
Figure 7 illustrates how the relationship curves of the average peak compressive strength (\(\sigma_{c}\)) of the sandstone specimens vary with the freeze-thaw cycle count and freezing temperature. The data set with the highest coefficient of variation in each experimental group is shown in Table 3, with coefficients ranging from 4.998% to 14.443%. Under room temperature conditions (\(T\) = 20 \({}^{\circ}\)C), the average peak compressive strength of the coal-measure sandstone specimens is determined to be 28.67 MPa. As depicted in Figure 7, regardless of the number of freeze-thaw cycles, the peak compressive strength of the sandstone specimens exhibits a rapid decrease, followed by a gradual reduction as the freezing temperature decreases. For example, at \(N\) = 10, when the freezing temperature decreases from \(-\)5 \({}^{\circ}\)C to \(-\)20 \({}^{\circ}\)C, the peak strength decreases by 9.188 MPa (X\(\rightarrow\)B1), 4.313 MPa (B1\(\rightarrow\)B2), 0.671 MPa (B2\(\rightarrow\)B3), and 0.242 MPa (B3\(\rightarrow\)B4), with reduction rates of 32.05%, 22.14%, 4.42%, and 1.67%, respectively. The influence of the freezing temperature on the peak strength of the coal-measure sandstone specimens exhibits a clear interval effect, which is consistent with the influence of freezing temperature on the elastic modulus. However, the peak strength is more sensitive to freezing temperature than the elastic modulus, which is closely related to the impact of freeze-thaw effects on the brittleness and ductility of rocks. Regardless of the freezing temperature, the peak strength of the sandstone specimens shows a rapid decreasing 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 peak strength decreases by 9.099 MPa (X\(\rightarrow\)A3), 5.073 MPa (A3\(\rightarrow\)B3), 0.822 MPa (B3\(\rightarrow\)C3), and 2.888 MPa (C3\(\rightarrow\)D3), with reduction rates of 31.74%, 25.92%, 5.67%, and 21.12%, respectively. The overall impact of the freeze-thaw cycle count on the peak compressive strength of coal-measure sandstone is significant; this maintains consistency with the influence of the freeze-thaw cycle count on the elastic modulus, but the  
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \begin{tabular}{c} **Test** \\ **Scenario** \\ \end{tabular} & **Test Case** & \begin{tabular}{c} **Elastic** \\ **Modulus** \\ **\end{tabular} & \begin{tabular}{c} **Mean** \\ **Value** \\ **(GPa)** \\ \end{tabular} & \begin{tabular}{c} **Absolute** \\ **Deviation** \\ **(GPa)** \\ \end{tabular} & \begin{tabular}{c} **Relative** \\ **Deviation** \\ **(\%)** \\ \end{tabular} & \
\begin{tabular}{c} **Standard** \\ **Deviation** \\ **(GPa)** \\ \end{tabular} &
\begin{tabular}{c} **Coefficient of** \\ **Variation** \\ **(\%)** \\ \end{tabular} \\ \hline \multirow{3}{*}{C3} & Case1 & 1.611 & \multirow{3}{*}{1.381} & 0.230 & 16.655 & \multirow{3}{*}{0.181} & \multirow{3}{*}{13.106} \\  & Case2 & 1.363 & & 0.017 & 1.231 & & \\  & Case3 & 1.168 & & 0.213 & 15.424 & & \\ \hline \multirow{3}{*}{D1} & Case1 & 1.759 & \multirow{3}{*}{1.460} & 0.299 & 20.479 & \multirow{3}{*}{0.213} & \multirow{3}{*}{14.589} \\  & Case3 & 1.346 & & 0.114 & 7.808 & & \\ \cline{1-1}  & Case4 & 1.276 & & 0.185 & 12.671 & & \\ \hline \hline \end{tabular}
\end{table}
Table 2: _Cont._  
Figure 6: Changes in the elastic modulus of the specimen, \(E\), with the number of freeze–thaw cycles, \(N\), and the freeze–thaw temperature, \(T\).  
peak compressive strength is more sensitive to the number of freeze-thaw cycles, similar to the sensitivity of the freezing temperature.