# The Bolt Anchorage Performance of Fractured Rock under a Freeze-Thaw Cycle Load
## 4 Analysis and Discussion
### Effect of Freeze-Thaw Cycles on the Strength of Specimens  
The specimens were subjected to freeze-thaw cycles within a temperature range of \(-20\)\({}^{\circ}\)C to \(20\)\({}^{\circ}\)C, with a cycle duration of 4 h, and their uniaxial compression results are depicted in Figure 7. The relationship between strength and the number of freeze-thaw cycles was modelled using a linear function, as follows:  
\[\sigma_{b}=\hat{a}N+\hat{b} \tag{1}\]  
\(\sigma_{b}\)--strength of the specimen (MPa); \(N\)--number of freeze-thaw cycles; \(\hat{a}\), \(\hat{b}\)--fitting constants. Their specific values are shown in Table 8.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & \(\hat{a}\)/MPa & \(\hat{b}\)/MPa \\ \hline Unbolted specimen with no fracture & \(-0.259\) & \(21.77\) \\ Bolted specimen with no fracture & \(-0.134\) & \(16.33\) \\ Unbolted specimen with \(90^{\circ}\) fracture & \(-0.197\) & \(14.46\) \\ Bolted specimen with \(90^{\circ}\) fracture & \(-0.153\) & \(15.34\) \\ \hline \hline \end{tabular}
\end{table}
Table 8: Values of the fitting constants.  
Figure 6: Comparison of strength and tangential modulus of bolted and unbolted specimens: (\(\mathbf{a}\)–\(\mathbf{c}\)) strength comparison of intact, \(45^{\circ}\) fractured, and \(90^{\circ}\) fractured specimens; (\(\mathbf{d}\)–\(\mathbf{f}\)) elastic modulus comparison of intact, \(45^{\circ}\) fractured, and \(90^{\circ}\) fractured specimens.  
Only the strength of unfractured and 90\({}^{\circ}\) fractured specimens increased with the number of freeze-thaw cycles, whereas the weakening effect on 45\({}^{\circ}\) fractured specimens was less pronounced. This occurrence can be attributed to four categories of specimens: unfractured without anchors, unfractured with anchors, 90\({}^{\circ}\) fractured without anchors, and 90\({}^{\circ}\) fractured with anchors. The freeze-thaw cycles induce an expansion of internal microcracks due to frost action, thereby reducing the specimen's compressive strength. However, for 45\({}^{\circ}\) fractured specimens without and with anchors, the microcracks generated by frost action have minimal impact on the specimen's strength. The absolute value of the fitting constant \(\hat{a}\) is nearly zero, indicating that their strength is primarily governed by the shear strength of their pre-existing structural surface. According to Figure 8, it is evident that the influence of fractures on rock strength is significantly greater than that of freeze-thaw cycles. The red dots in the figure represent the data obtained from the experiments. Different colours in the figure correspond to different strength values. Strength values closer to the blue colour indicate lower strength, whereas values closer to the yellow colour indicate higher strength. Therefore, in engineering applications in permafrost regions, careful consideration should be given to the influence of rock fracture dip angle on rock strength and stability.  
Figure 8: Variation of specimen strength with freeze–thaw cycles and fracture dip angle in the presence and absence of anchors (note: 0\({}^{\circ}\) denotes specimens without fractures): (**a**) strength of unbolted specimens, (**b**) strength of bolted specimens.  
Figure 7: Relationship between compressive strength and freeze–thaw cycles for different types of specimens.