## 1 Introduction  
Widely recognized as a clean and sustainable geological resource, hot dry rocks (HDRs) have garnered global interest as conventional fossil fuels are depleted, and their environmental consequences have become increasingly evident. The primary method for harnessing HDRs is the enhanced geothermal system (EGS) [1; 2]. The EGS concept aims to establish highly permeable fractured zones to facilitate fluid flow and heat extraction through hydraulic stimulation [3; 4; 5]. In recent studies, researchers have demonstrated that conventional hydraulic fracturing is susceptible to inducing reservoir seismicity, an issue that has led to the discontinuation of specific geothermal projects [6; 7]. As an alternative to traditional hydraulic fracturing, cyclic hydraulic fracturing has shown promise in effectively reducing both the crack initiation pressure and fracture toughness of HDRs, mitigating the risk of water injection-induced seismicity [8; 9]. Compared to conventional hydraulic fracturing methods, cyclic hydraulic fracturing techniques offer distinct advantages by promoting gradual and controlled fracture growth. This phenomenon may be attributed to the cyclic loading process, which induces rock softening, hence facilitating easier fracture formation and reducing the initiation pressure, as suggested by [PERSON] et al. [10] and [PERSON] et al. [11]. Alternatively, the cyclic hydraulic fracturing process enables the gradual release of energy stored within the reservoir, effectively lowering the seismic risk. Moreover, within the fatigue process, cracks exhibit increased flexibility in multiple orientations, promoting the formation of interconnected reticulated cracks and expanding the permeable areas, as observed in recent findings by [PERSON] et al. [12]. Nevertheless, the impact of cyclic hydraulic fracturing on fracture toughness in the context of HDR mining remains overlooked. Fracture toughness serves as a critical measure for assessing a rock's resistance to cracking and the expansion of fractures, as noted by [PERSON] et al. [13]. To enhance the efficiency of heat mining in EGS projects, examining the alterations in fracture toughness and the macro/microstructure due to cyclic loading in three-point bending (CTB) tests conducted under high-temperature conditions is a fundamental task. Numerous studies have investigated rocks' physical and mechanical properties following thermal treatment. For instance, [PERSON] et al. [14] observed that the mechanical properties of granite undergo significant alterations at elevated temperatures, often attributed to transformations in rock components and crystalline phases. In a similar context, [PERSON] et al. [15] conducted high-temperature experiments on three distinct varieties of basalts, uncovering intriguing findings. Their results indicated that, at 150 \({}^{\circ}\)C, the fracture toughness of Icelandic basalts surpasses that of the other types examined. Moreover, research has reported a significant decline in the fracture toughness of brittle rocks as temperatures rise, particularly beyond the 400 \({}^{\circ}\)C threshold, as noted by [PERSON] et al. [13]. [PERSON] et al. [16] also analyzed fracture propagation characteristics during the water-cooling shock process and introduced a comprehensive thermal-hydraulic-mechanical coupling model, highlighting the factors contributing to rock fracture reduction. In another study, [PERSON] et al. [17] discussed the impact of heat treatment on the fracture characteristics of mudstone, offering insights into the mechanism behind the observed increase in fracture toughness following heat treatment. Notably, several studies have also reported a rise in fracture toughness for brittle rocks within the temperature range of 25 \({}^{\circ}\)C to 100 \({}^{\circ}\)C, as demonstrated by [PERSON] et al. [18], [PERSON] et al. [19], [PERSON] et al. [20], [PERSON] et al. [21], and [PERSON] et al. [22]. This enhancement of fracture toughness is mainly attributed to the closure of microcracks and pores due to thermal expansion.