## 4 Conclusions  
This paper investigates the sandstone with prefabricated cracks subjected to cyclic loading after freeze-thaw cycles by combining indoor tests and numerical simulation analysis. Taking a high-altitude mine sandstone as the research object, a prefabricated crack with an inclination angle of 45\({}^{\circ}\) at the center of the sandstone specimen was subjected to freeze-thaw cycles and uniaxial cyclic loading and unloading tests. The following conclusions were drawn.  
1. The Wave Velocity Damage Factor (D\({}_{\rm v}\)) increases linearly throughout the cycle period. It provides that the wave propagation velocity within the sandstone is sensitive to changes in the freeze-thaw cycles. In contrast, the Mass Damage Factor (D\({}_{\rm m}\)) shows a significant change only at a higher number of freeze-thaw cycles.
2. The PFC thermal calculation module was used to simulate the freeze-thaw cycle process of sandstone, and the model agreed with the experimental results. Combined with the energy analysis, the model continues accumulating energy due to the freezing and swelling effect. At specific moments, the energy undergoes a drastic and rapid release. Subsequently, the specimen enters the next energy accumulation period, and the frequency of energy release increases as the number of freeze-thaw cycles increases.
3. Cyclic loading leads to the accumulation of internal damage in the specimen, resulting in a gradual weakening of the load-bearing capacity of the specimen. The average value of the Cumulative Strain Difference (\(\varepsilon_{c}\)) is calculated to be 20.57%, which is within a reasonable range. Moreover, the trend of Cumulative Strain Difference (\(\varepsilon_{c}\)) reflects that the difference between simulated and measured plastic strains decreases with the increase in cycle level.
4. The crack extension pattern inside the specimen changes significantly with increased freeze-thaw cycles. When the number of freeze-thaw cycles is higher, the specimen is more likely to form X-shaped conjugate shear damage. When the number of freeze-thaw cycles is less, the specimen is more likely to have monoclinic shear damage. The freezing and swelling forces destroy the mineral particle cementation and reduce its  
Figure 23: Change in percentage of crack types.  
strength. The freeze-thaw destroys the specimen from the outside to the inside, so the cracks are more inclined to expand to the outer surface, leading to block spalling on the outer surface of the specimen. These two factors combine to influence the damage pattern of the rock.
* The emergence of cracks in the cyclic loading process shows a significant correlation with the magnitude of axial stress, and a large number of cracks appear in the late stage of cyclic loading. The number of tensile cracks dominated the whole loading and unloading process. However, after the 50 th freeze-thaw cycle, the proportion of tensile cracks decreased, and the proportion of shear cracks gradually increased. It clarified that the sandstone was more prone to shear damage with increased freeze-thaw cycles.
* Conceptualization, T.L. and H.L.; formal analysis, P.C. and T.L.; writing--original draft, H.L.; writing--review and editing, T.L., L.D. and P.C. All authors have read and agreed to the published version of the manuscript.
* This work was financially supported by the National Natural Science Foundation of China under Grant No. 52374108.
* Not applicable.
* The raw data supporting the conclusions of this article will be made available by the authors on request.
* The authors declare no conflict of interest.