## 3 Shear Strength Evolution of Structural Plane Infill Specimens
### Effects of Freeze-Thaw Cycles and Burial Depth on Strength Parameters  
Based on the shear strength results under different normal stresses, the internal friction angle and cohesion of the infill material were calculated for each test condition, as shown in Figure 4. The results indicate that with increasing freeze-thaw cycles, the internal friction angle exhibits an initial decrease followed by a slight increase, while the cohesion initially increases and then decreases. This trend reflects the rearrangement of the microstructure and short-term cementation strengthening during the early stages of freeze-thaw cycling, followed by fatigue damage and structural weakening during prolonged cycling. Furthermore, the amplitude of variation in strength parameters decreases with increasing burial depth, indicating that deeper infill materials exhibit a weaker response to freeze-thaw effects compared to shallow layers. Figure 3: Shear stress–displacement curves of infill material under different freeze–thaw cycles: (**a**) 2 freeze–thaw cycles; (**b**) 5 freeze–thaw cycles; (**c**) 10 freeze–thaw cycles; (**d**) 20 freeze–thaw cycles. It is worth noting that after a certain number of freeze-thaw cycles, a slight increase in the internal friction angle was observed in some specimens. This non-monotonic degradation trend may be attributed to the rearrangement and densification of particles under repeated freeze-thaw cycling, leading to a more stable granular skeleton and enhanced inter-particle interlocking and friction. In addition, potential testing uncertainties or local stress disturbances may also contribute to this phenomenon. Further investigation at the microstructural level is planned for future work. To further elucidate the response mechanism of strength parameters to freeze-thaw cycles and burial depth, three-dimensional scatter plots of internal friction angle and cohesion were constructed, and dual-exponential surface fitting was performed (Figure 5). The regression analysis yielded a coefficient of determination (R\({}^{2}\)) of 0.8285 for the internal friction angle and 0.7963 for cohesion, indicating a good level of correlation between the  
Figure 4: Variations in internal friction angle and cohesion of the infill material under different freeze–thaw cycles and burial depths: (**a**) variation in the internal friction angle of infill material under different freeze–thaw cycles; (**b**) variation in the cohesion of infill material under different freeze–thaw cycles; (**c**) variation in the internal friction angle of infill material at different burial depths; (**d**) variation in the cohesion of infill material at different burial depths. experimental data and the fitted models. The fitted equation for the internal friction angle is as follows:  
\[\varphi=29.4063e^{(-0.00148 NY+0.0143N+0.008117)}+5.8519e^{(-0.02947 NY-0.103N-0.50 78Y)}. \tag{2}\]  
The fitted equation for cohesion is as follows:  
\[c=140.6547e^{(0.00615 NY-0.04113N+0.04039Y)}-60.2724e^{(0.02578 NY-0.1307N-0.358Y)}, \tag{3}\]  
where \(Y\) is the depth of the rock mass (m, positive values indicate burial depth) and \(N\) is the number of freeze-thaw cycles. Figure 5 illustrates the three-dimensional variation patterns of the internal friction angle and cohesion of rock masses under different freeze-thaw cycles and burial depths. The results show that the internal friction angle exhibits a nonlinear response characterized by an initial decrease followed by a subsequent increase as the number of freeze-thaw cycles increases. Moreover, it generally increases with depth, indicating that shallow rock masses are more significantly affected by freeze-thaw action, whereas deeper rock masses exhibit greater structural stability.