## 3 Analysis of Experimental Results
### Deterioration of Strength and Deformation Characteristics  
The fitted curve illustrating the relationship between confining pressure and peak strength under freeze-thaw conditions is presented in Figure 11. After undergoing freeze-thaw cycles, the peak strength of unloaded sandstone during single and triaxial reloading decreases, with the pattern of attenuation remaining consistent. As the frequency of freeze-thaw cycles escalates within various confining pressure conditions, there is a progressive decline in the peak strength of the sample. The relationship established through a decreasing exponential function demonstrates a strong correlation, which is consistent with the underlying physical principles, effectively representing the diminishing trend of the sample's peak strength.  
The relationship between the elastic modulus and the number of freeze-thaw cycles is illustrated in Figure 12. The process of freeze-thaw erosion leads to a substantial reduction in the elastic modulus of unloaded sandstone, which is significantly influenced by the value of confining pressure. For a given number of freeze-th  
Figure 11: Peak strength is influenced by the number of freeze–thaw cycles.  
negative correlation between confining pressure and the decay rate of the elastic modulus; specifically, as confining pressure increases, the decay rate of the elastic modulus decreases. Furthermore, as the frequency of freeze-thaw cycles escalates, the rate at which the elastic modulus diminishes progressively lessens, a trend that remains unaffected by variations in confining pressure conditions.  
By examining the relationship between peak strength and confining pressure from uniaxial and triaxial reloading tests, the Mohr-Coulomb circle and the fitting of envelope lines were constructed. By calculating the slope and intercept of the envelope lines in relation to the coordinate axes, the shear strength parameters of unloading-damaged sandstone under varying confining pressure conditions were determined, as illustrated in Figure 13.  
Table 3 provides the quantitative data regarding the unloading strength and deformation characteristics of sandstone that has undergone freeze-thaw cycles followed by reloading. Additionally, the decay rates calculated for each indicator are depicted in Figure 14. In summary, freeze-thaw erosion has a significant influence on both the elastic modulus and peak strength of unloaded sandstone. The calculated attenuation rate indicates that the degree of deterioration caused by freeze-thaw erosion on the elastic modulus and peak strength is closely associated with the value of confining pressure.  
Figure 12: Relationship between the elastic modulus and the number of freeze–thaw cycles.  
Figure 13: Relationship between shear strength parameters and the number of freeze–thaw cycles.  
Notably, when the confining pressure is doubled, the degree of attenuation of the indices is approximately halved.  
The analysis of the variation in shear strength parameters with the number of freeze-thaw cycles indicates that the damage inflicted by freeze-thaw erosion on the cohesion of unloaded sandstone is significantly more pronounced than its impact on the internal friction angle. This phenomenon can be attributed to the fact that freeze-thaw erosion primarily facilitates the expansion and development of micro-cracks and pores within the rock structure. In contrast, it exerts minimal influence on the frictional resistance between the particles constituting the rock. Consequently, there is a substantial reduction in cohesion, while the internal friction angle remains largely unaffected.