## 3 Results and Discussion
### Mode I Fracture Toughness
In order to characterize the fatigue damage of granite at various temperatures, the damage threshold is defined as the ratio of the fatigue damage load to the peak load of the MTB at the corresponding temperature. Comparing these findings to the work of [PERSON] et al. [57], it becomes apparent that the upper load limit influences the damage threshold. The relationship between the damage threshold and temperature is graphically represented in Figure 10. Granite's damage threshold remains relatively stable within the temperature range of 25 \({}^{\circ}\)C to 200 \({}^{\circ}\)C. This phenomenon has been extensively observed in scholarly experiments [15; 18; 19; 20]. The temperature range (25 \({}^{\circ}\)C to 200 \({}^{\circ}\)C) under consideration exhibits dual effects on the mechanical properties of granite, contributing to an overall tendency of stabilization (i.e., the thermal expansion effect enhances the mechanical properties, while the formation of thermal cracks and the loss of free water weaken the mechanical properties to some extent). However, as the temperature surpasses 200 \({}^{\circ}\)C, there is a notable decline in the damage threshold of granite with increasing temperature [58]. As the temperature escalates to 300 \({}^{\circ}\)C, the vaporization of bound water within the granite occurs. At this stage, the lubrication between internal particles of granite is diminished, causing an increase in friction between mineral particles during cyclic loading. Consequently, fractures occur after multiple cycles at a lower upper load threshold. The decline in granite's critical  
Figure 10: Variation of the damage threshold with increased temperature values. Figure 9: Evolution of mode I fracture toughness with increased temperatures under different upper load limits. damage threshold at this stage can be attributed to an increase in plasticity, leading to the effective accumulation of fatigue damage. Upon reaching 400 \({}^{\circ}\)C, the release of crystal water from the granite leads to the disruption of the internal microstructure of the granite, contributing to a noticeable reduction in the mechanical properties. The granite is weakened by the double effect of increased plasticity and decreased mechanical properties, leading to another decrease in the damage threshold. Moreover, it has been proposed that the deterioration of granite can be attributed to the diminishing mechanical properties of its various components at varying temperatures and a weakening of the cementation between minerals [59; 60]. The experimental results reveal a 30.89% reduction in the fracture toughness of granite at 400 \({}^{\circ}\)C compared to 25 \({}^{\circ}\)C in the MTB tests. Furthermore, in the CTB tests at 400 \({}^{\circ}\)C, the fracture toughness of granite decreases by 49.3% compared to the MTB tests at 25 \({}^{\circ}\)C. This reduction can be attributed to the combined impact of cyclic loading and high temperature, significantly reducing the fracture initiation pressure of HDR formations. Consequently, cyclic hydraulic fracturing of higher-temperature HDR reservoirs can substantially limit the initiation pressure and reservoir stress, ultimately reducing induced seismicity magnitude. Throughout the circulation process, the reservoir fractures undergo extensive development, resulting in the creation of a complex fracture network that enhances the efficiency of EGS when compared to monotonic injection methods, as discussed by [PERSON] et al. [61] and [PERSON] et al. [62].