## 3 Results and Discussion
### Mechanical Properties
#### 3.3.4 Shear Strength Parameters  
Investigating shear strength parameters is essential for understanding the mechanical behavior and failure mechanisms of grouting reinforcement bodies. The internal friction angle and cohesion are the two primary parameters that govern shear strength, collectively determining the stability and deformation characteristics of the sample under shear stress. The internal friction angle reflects the resistance to relative motion between rock particles, while cohesion represents the bonding strength between them. Analyzing these parameters allows for a comprehensive discussion of the mechanical properties of the grouting reinforcement body under various engineering conditions, providing a scientific foundation and technical support for geotechnical engineering. Regression analysis is performed using the Coulomb strength criterion to determine the cohesion and internal friction angle of the grouting reinforcement body. The criterion is expressed in terms of maximum principal stress and confining pressure, as represented by the following equation:  
\[\sigma_{1f}=b+a\sigma_{3} \tag{6}\]  
where \(a\) and \(b\) are strength criterion parameters, \(\sigma_{1f}\) is maximum axial stress, and \(\sigma_{3}\) is confining pressure. Meanwhile, it can be observed that the \(\sigma_{1f}\) of a rock sample is linearly related to the \(\sigma_{3}\). The relationship between the values of \(a\) and \(b\) and the cohesion (C) and internal friction angle (\(\varphi\)) is expressed in Equations (7) and (8):  
\[a=\frac{1+\sin\varphi}{1-\sin\varphi} \tag{7}\]  
\[b=\frac{2C\cos\varphi}{1-\sin\varphi} \tag{8}\]  
Using confining pressure as the independent variable (abscissa) and peak strength as the dependent variable (ordinate), a scatter diagram is plotted, and linear fitting is performed to obtain the fitting equation and the correlation coefficient. The cohesion and internal friction angle of the grouting reinforcement body is calculated using Equations (7) and (8). The fitting results and corresponding calculations are presented in Table 5.  
The relationship between the shear strength parameters of the grouting reinforcement body and the number of freeze-thaw cycles is depicted in Figure 23. As illustrated in Figure 23a, the cohesion of the grouting reinforcement body decreases with an increase in freeze-thaw cycles. Initially, during the early stages of the freeze-thaw cycles, the cohesion of the grouting reinforcement bodies with crack dip angles of 0\({}^{\circ}\) and 45\({}^{\circ}\) slightly increases, before undergoing a continuous decline as the cycles progress. After 30 freeze-thaw cycles, the extreme value ratios of cohesion for grouting reinforcement bodies with 0\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\) crack dip angles are 1.80, 1.77, 3.77, and 3.61, respectively. Figure 23b demonstrates that the internal friction angle of the grouting reinforcement body similarly decreases as the number of freeze-thaw cycles increases. After 30 freeze-thaw cycles, the extreme value ratios of the internal friction angle for grouting reinforcement bodies with 0\({}^{\circ}\), 30\({}^{\circ}\), 45\({}^{\circ}\), and 60\({}^{\circ}\) crack dip angles are 1.19, 1.21, 1.09, and 1.66, respectively.