## 4 Conclusions  
This research investigated the effect of cyclic loading on the load-displacement curves, elastic stiffness, the mode I fracture toughness and the crack development of granite at different real-time elevated temperatures (i.e., 25 \({}^{\circ}\)C, 200 \({}^{\circ}\)C, 300 \({}^{\circ}\)C, and 400 \({}^{\circ}\)C) through three-point bending tests. Several vital conclusions are presented as follows:  
1. At a temperature of 25 \({}^{\circ}\)C, the CVD of the granite progressively increased with an increase in the number of cycles, primarily accumulating during the early and damage stages of cyclic loading. In the temperature range of 200 \({}^{\circ}\)C to 400 \({}^{\circ}\)C, the thermal hardening effect led to a trend in the CVD of granite, shifting from a decrease to an increase with an increasing number of cycles.
2. Under cyclic loading, the elastic stiffness of granite exhibited a pattern of increasing-stabilizing-decreasing with a growing number of cycles. After the initial loading cycle, granite stiffness increased substantially by 70% to 80%.
3. When temperatures surpassed 200 \({}^{\circ}\)C, two substantial reductions were observed in the damage threshold. At 300 \({}^{\circ}\)C, the threshold dropped below 80% of the upper load limit, and it further decreased to less than 75% as the temperature reached 400 \({}^{\circ}\)C.
4. The microstructure of granite was significantly influenced by high temperature and cyclic loading. Below 300 \({}^{\circ}\)C, a comparison of SEM images from fracture surfaces in MTB and CTB tests revealed an increase in microfracture zones, cracks, scattered particles, and the size of scattered particles after cyclic loading.
5. Based on the analyses above, this study can serve as a valuable reference for cyclic hydraulic fracturing technology. For instance, a lower upper limit of circulating load can be chosen within a reasonable range to minimize the impact of mining on the geothermal reservoir, thereby reducing the risk of induced earthquakes. Alternatively, hydraulic fracturing can be employed to extract HDRs at the optimal temperature, creating a complex fracture network and thereby enhancing extraction efficiency. In  
Figure 13: SEM images of the SCB fracture surface at varying high temperatures: (**a**,**c**,**e**,**g**) depict MTB samples, whereas (**b**,**d**,**f**,**h**) depict CTB samples (85% upper load limit). In these images, red dashed lines delineate grain boundary cracks, yellow dashed lines represent intergranular cracks, red circles highlight exfoliated mineral particles on the crystal surface, yellow circles indicate microfracture zones, and green rectangles outline shell-like cracks.  
future work, it is recommended to examine the effect of real-time elevated temperatures on the damage threshold, potentially considering even higher temperatures. Given that the maximum number of cycles was limited in the present study, further research will be conducted to explore experiments with an increasing number of cycle loads.  
Conceptualization, F.L. and F.Z.; formal analysis, F.L., S.Z. and K.L.; data curation, F.L. and S.M.; writing--original draft preparation, F.L.; writing--review and editing, F.L. and F.Z.; supervision, F.Z. The results were discussed and conclusions were drafted jointly by all authors. All authors have read and agreed to the published version of the manuscript.  
This work was jointly supported by the National Natural Science Foundation of China (Grant No. 51979100) and Shandong Lunan Geological Engineering Exploration Institute Open Fund (Grant No. LNY2020-Z08).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors are indebted to [PERSON] of Helmholtz Centre Potsdam GFZ German Research Centre for Geosciences for their great help in review.  
The authors declare no conflict of interest.