## 4 Macroscopic Failure Characteristics and Intrinsic Mechanisms of the Specimens  
### Macroscopic Failure Characteristics of the Specimens  
The typical macroscopic fracture morphologies of coal-measure sandstone under different freeze-thaw cycle counts and temperatures are illustrated in Figure 9. The fundamental failure modes of the cylindrical specimens are tensile failure and shear failure [18]. As shown in Figure 9, when the freeze-thaw cycle count is five or ten, the failure of the specimens primarily manifests as single diagonal shear or \"X\"-shaped conjugate diagonal shear failure modes, with some specimens exhibiting a few localized splitting cracks. When the freeze-thaw cycle count reaches 15 or 20, the failure modes of the specimens predominantly display single diagonal shear or \"X\"-like conjugate diagonal shear failure patterns, with localized splitting fissures on the specimen surfaces that progressively develop. The experimental results indicate that the number of freeze-thaw cycles significantly affects the macroscopic fracture characteristics of coal-measure sandstone. As the number of freeze-thaw cycles increases, the degree of damage intensifies, and the failure modes transition from shear failure to a composite mode of shear and tensile failure. Additionally, the angle between the fracture surface and the load axis tends to increase, primarily due to the frost-heave effect of water freezing, which exacerbates the void structure of 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** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Peak Strain \(\varepsilon_{c}\)** \\ **Value (\%)** \\ \end{tabular} & \begin{tabular}{c} **Mean** \\ **Deviation** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Absolute** \\ **Deviation** \\ **(\%)** \\ \end{tabular} & \begin{tabular}{c} **Relative** \\ **Deviation** \\ **(\%)** \\ \end{tabular} & \
\begin{tabular}{c} **Standard** \\ **Deviation** \\ **(\%)** \\ \end{tabular} &
\begin{tabular}{c} **Coefficient of** \\ **Variation** \\ **(\%)** \\ \end{tabular} \\ \hline \multirow{3}{*}{A4} & Case1 & 1.583 & \multirow{3}{*}{1.689} & 0.106 & 6.276 & \multirow{3}{*}{0.082} & \multirow{3}{*}{4.855} \\  & Case2 & 1.701 & & 0.012 & 0.710 & & \\  & Case4 & 1.783 & & 0.094 & 5.565 & & \\ \hline \multirow{3}{*}{B3} & Case2 & 1.777 & \multirow{3}{*}{1.723} & 0.054 & 3.134 & \multirow{3}{*}{0.069} & \multirow{3}{*}{4.005} \\  & Case3 & 1.626 & & 0.097 & 5.630 & & \\  & Case4 & 1.766 & & 0.043 & 2.496 & & \\ \hline \multirow{3}{*}{C1} & Case2 & 1.392 & \multirow{3}{*}{1.574} & 0.182 & 11.563 & \multirow{3}{*}{0.129} & \multirow{3}{*}{8.196} \\  & Case3 & 1.651 & & 0.077 & 4.892 & & \\ \cline{1-1}  & Case5 & 1.680 & & 0.106 & 6.734 & & \\ \hline \multirow{3}{*}{D4} & Case2 & 2.001 & \multirow{3}{*}{2.089} & 0.088 & 4.213 & \multirow{3}{*}{0.076} & \multirow{3}{*}{3.638} \\  & Case4 & 2.187 & & 0.098 & 4.691 & & \\ \cline{1-1}  & Case5 & 2.079 & & 0.010 & 0.479 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Peak strain, \(\varepsilon_{c}\), of the specimens. Figure 8: Changes in the peak strain, \(\varepsilon_{c}\), of the specimen with the number of freeze–thaw cycles, \(N\), and the freeze–thaw temperature, \(T\). coal-measure sandstone matrix. After multiple freeze-thaw cycles, not only do the internal pores of the specimens enlarge, but the matrix itself also undergoes morphological and positional changes, aggravating the damage to the specimens and leading to a gradual decline in their mechanical properties, which is reflected in the alteration of failure modes at the macroscopic level. Under any number of freeze-thaw cycles, as the freeze-thaw temperature decreases, the number of surface cracks on the specimens gradually increases, and the degree of damage escalates.