## 6 Conclusions  
This study investigates the excavation of a deeply buried tunnel associated with a hydropower project situated in the western region. It employs indoor uniaxial and triaxial unloading tests, along with freeze-thaw tests, to explore the degradation patterns of the mechanical properties of unloaded sandstone exposed to freeze-thaw erosion. Furthermore, it examines the associated damage response patterns. This study ultimately presents several conclusions based on the findings.  
1. Unloading damage significantly disrupts the sandstone's structure, resulting in the progressive formation of internal fractures and defects. The interaction between unloading damage and freeze-thaw erosion is not merely additive; rather, it is characterized by a complex interplay. Unloading disturbances facilitate the development of an internal fracture network within the rock mass, thereby creating pathways for moisture migration during freeze-thaw cycles. Concurrently, the expansion forces generated by freeze-thaw cycles further compromise the internal structure of the rock mass, culminating in a cyclical process that contributes to the degradation of the rock's strength.
2. The analysis of sandstone samples indicates that under varying confining pressure conditions, the peak strength diminishes as the number of freeze-thaw cycles increases, with the rate of decrease gradually tapering off. Moreover, polynomial function fitting can effectively characterize the degradation pattern of peak strength in sandstone.
3. The findings from the reloading tests conducted on unloaded sandstone following freeze-thaw cycles demonstrate that a varying degree of deterioration occurred in both strength and deformation characteristics. Notably, the peak strength and elastic modulus are significantly influenced by the confining pressure, whereas the reduction in cohesion resulting from freeze-thaw erosion is particularly pronounced. In contrast, the decline in the internal friction angle is relatively minor.
4. Moisture migration is a critical factor influencing freeze-thaw erosion. The impacts of frost heave are particularly pronounced in areas where pore water migrates and accumulates. As the intensity of freeze-thaw erosion increases, the brittleness of sandstone markedly diminishes, and the strain-softening effect becomes increasingly apparent. Consequently, the residual rock debris on the fracture surface transitions from a hard and sharp texture to a soft and sandy consistency.
5. The elastic modulus serves as a critical parameter for characterizing the evolution of damage variables in sandstone subjected to uniaxial loading conditions. We developed a damage constitutive model that incorporates factors such as unloading damage, initial freeze-thaw erosion, and the effects of freeze-thaw loading. As the intensity of freeze-thaw erosion increases, both the strain at the densification point and the strain at the damage response point exhibit a gradual increase. Specifically, the damage-triggering strain after three, six, and nine freeze-thaw cycles increased by 0.0723%, 0.1156%, and 0.1370%, respectively, compared to those under unfrozen conditions, with the increments gradually stabilizing.  
Conceptualization, X.L., X.C. and Y.W.; Methodology, X.L., X.C., Y.W., L.C. and S.G.; Formal analysis, X.L., L.C. and S.G.; Data curation, X.L., L.C. and S.G.; Writing--original draft, X.L. and X.C.; Writing--review & editing, Y.W., L.C. and S.G.; Supervision, X.C. and Y.W.; Project administration, X.C. and Y.W.; Funding acquisition, X.C. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the National Natural Science Foundation of China (Grant No. 51979218).  
Not applicable.  
The dataset used to support the findings of this study is available from the corresponding author upon request.