## 5 Conclusions  
1. Prefabricated cracks increase stress concentration in granite during freeze-thaw cycles, promoting freeze-thaw damage accumulation. After these cycles, the saturated mass and longitudinal wave velocity of cracked granite gradually decrease. Network microcracks and block-like spalling develop around the prefabricated cracks. The NMR T2 spectrum of the sample showed a three-peak distribution, with the second peak area accounting for more than 85%. After freezing and thawing, the peaks of the second wave of T2 spectral curves increased by 11.11% and 22.61%, respectively. The T2 spectrum of the fractured granite shifts significantly to the right after fatigue load failure, and the amplitude of the third peak increases notably.
2. Under fatigue load, the damage to the granite samples without freeze-thaw cycles is sudden and explosive. After freeze-thaw cycles, the failure of the granite specimens becomes more gradual. With an increasing number of freeze-thaw cycles, the granite samples endured 498, 21, and 5 loading cycles, respectively, demonstrating an exponential decrease in fatigue resistance. Freeze-thaw cycles weaken the internal structure of granite, reducing its bearing and energy storage capacities, but making the failure patterns more complex.
3. By integrating the irreversible strain evolution model, a fatigue damage constitutive model for fractured granite, encompassing initial fracture damage, freeze-thaw damage, and load damage, is established. This model effectively accounts for the combined effects of freeze-thaw cycles and fatigue load on fractured granite. The theoretical curves align well with experimental data, demonstrating good applicability.  
This study performed freeze-thaw cycle tests, SEM scanning, nuclear magnetic resonance tests, and cyclic load fatigue tests on fissured granite. The evolution of the multi-scale structure of fractured granite under the combined effects of freeze-thaw cycles (0, 40, and 80 cycles) and cyclic loading was investigated. This study's findings highlight the critical impact of combined F-T cycles and fatigue loading on granite's structural integrity, providing a basis for improved predictive models in engineering. However, this study has certain limitations. For example, the fracture angle, length, and periodic loading parameters of the samples lack diversity. In addition to laboratory experiments, numerical simulation is also an effective method to reproduce the fracture mechanism of rocks [61; 62]. Therefore, future research should integrate various influencing factors, test methods, and analysis techniques to further study the mechanics of frozen and thawed rocks in cold regions.  
Conceptualization, M.Y. and J.R.; methodology, L.Z. and C.S.; validation, J.R. and Y.S.; formal analysis, M.Y., C.S. and P.C.; investigation, M.Y. and L.Z.; resources, C.S. and X.C.; data curation, J.R. and Y.S.; writing--original draft preparation, M.Y., P.C. and X.C.; writing--review and editing, M.Y. and J.R.; visualization, L.Z. and C.S.; funding acquisition, J.R. All authors have read and agreed to the published version of the manuscript. This research was funded by the National Natural Science Foundation of China, grant number 12072259, 42377187, the China Postdoctoral Science Foundation, grant number 2022 MD/23831, and the Shaarxi Provincial Natural Science Basic Research Program, grant number 2024 JC-YBQN-0029. Not applicable. Not applicable. Not applicable. Data Availability Statement: The data presented in this study are available on request from the corresponding author. The authors declare no conflicts of interest.