## 3 Shear Strength Evolution of Structural Plane Infill Specimens
### Evolution of Mechanical Parameters of Infilled Fractured Rock Masses Under Freeze-Thaw Action
#### 4.1.3 Evolution of Rock Mass Mechanical Parameters Under Freeze-Thaw Cycles  
Based on the previously determined representative elementary volume (REV) model, triaxial compression simulations were conducted under different freeze-thaw cycles and burial depths. The internal friction angle and cohesion of the fractured granite were calculated, and the results are shown in Figure 8. It can be observed that both parameters decrease significantly with an increasing number of freeze-thaw cycles and decreasing burial depth. In general, the trends for internal friction angle and cohesion are similar, although the decline in internal friction angle is more pronounced.  
Figure 7: Peak compressive strength of models with different sizes under 1 MPa confining pressure.  
Specifically, before undergoing any freeze-thaw cycles, the internal friction angle and cohesion of the rock mass were 36.167\({}^{\circ}\) and 207.485 kPa, respectively. After 20 freeze-thaw cycles at a burial depth of 5.27 m, the values decreased to 23.788\({}^{\circ}\) and 171.410 kPa, corresponding to reductions of 34.23% and 17.39%, respectively. At a shallower depth of 0.10 m, the degradation was more severe, with reductions of 51.10% and 41.44%, respectively, under the same freeze-thaw conditions.  
To characterize these trends, a double-exponential function model was established using the Levenberg-Marquardt algorithm to fit the relationship between strength parameters, freeze-thaw cycles, and burial depth. The resulting fitting models (Equations (4) and (5)) achieved coefficients of determination of 0.67 and 0.75, respectively, indicating good applicability for capturing the evolutionary patterns of mechanical parameters.  
\[\varphi=36.166e^{(0.00316 NY-0.0351N+0.0024Y-0.15)}. \tag{4}\]  
\[c=207.485e^{(0.00223 NY-0.0183N+0.0106Y-0.0916)}. \tag{5}\]  
The double-exponential model established in this study for strength parameters versus the number of freeze-thaw (F-T) cycles is fitted based on experimental data from 0 to 25 cycles, with R\({}^{2}\) values ranging from 0.67 to 0.75, indicating an acceptable level of fit. The model predicts a critical instability state at \(N=42\) cycles, which serves primarily as a theoretical upper-bound estimate for failure trends. However, this prediction has not yet been validated by long-term experimental or field data and should not be interpreted as a definitive failure threshold. Future research should refine and verify this estimate through extended F-T testing and in situ monitoring.  
The results indicate that under freeze-thaw cycling, both the internal friction angle and cohesion of fractured rock masses exhibit significant variation with the number of cycles and burial depth, and both parameters are closely associated with shear strength. Based on the Mohr-Coulomb strength criterion in the form \(\tau=c+\sigma\tan\varphi\), and in conjunction with the fitted results, the parameters were extended to develop a modified  
Figure 8: Variations in internal friction angle and cohesion of the rock mass with burial depth and number of freeze–thaw cycles: (**a**) variation in internal friction angle with burial depth and freeze–thaw cycles; (**b**) variation in cohesion with burial depth and freeze–thaw cycles (different colored spheres represent the magnitude of internal friction angle and cohesion under different burial depths and numbers of freeze-thaw cycles).  
Mohr-Coulomb criterion (Equation (6)), which is applicable under coupled freeze-thaw and depth conditions for fractured rock masses.  
\[\tau=207.485e^{(0.00223 NY-0.0183N+0.0106Y-0.0916)}+\sigma tan\left(36.166e^{(0.003 16 NY-0.0351N+0.0024Y-0.15)}\right). \tag{6}\]