## 1 Introduction  
As conventional energy sources gradually deplete, hot dry rock (HDR) has attracted widespread attention among various new energy sources due to its abundant reserves, renewability, and clean and efficient characteristics [1]. HDR is primarily stored in high-temperature rock formations located 3-10 km below the surface, which contain little to no fluid, mainly composed of granite, with temperatures ranging from 150 to 650 \({}^{\circ}\)C [2]. During the extraction process of HDR, the deep underground reservoir rocks are typically in a real-time high-temperature state, which can lead to changes in the mineral composition, microstructure, and mechanical properties of granite [3; 4; 5; 6]. Therefore, studying the microscopic damage and failure mechanisms of granite under real-time high temperatures is of great significance for the development of geothermal energy resources from HDR. A considerable number of researchers have conducted studies on the physical and mechanical properties of rocks under high-temperature conditions. [PERSON] et al. [7], [PERSON] al. [8], and [PERSON] et al. [9] analyzed the influence of high temperature on the physical and mechanical properties of granite, such as strength, peak strain, elastic modulus, porosity, and wave velocity. [PERSON] et al. [10] indicated the existence of a threshold temperature for thermal damage in granite and identified 400 \({}^{\circ}\)C as a temperature turning point for changes in its mechanical properties. [PERSON] et al. [11] found that the permeability of granite gradually increased with temperature after high-temperature cooling treatment, followed by a rapid increase, and the brittle-ductile transition temperature range of granite was found to be 500 \({}^{\circ}\)C to 600 \({}^{\circ}\)C. [PERSON] et al. [12], [PERSON] et al. [13], and [PERSON] et al. [14] conducted Type I fracture toughness tests on sandstone at different temperatures using three-point bending, and the experimental results revealed a transition in the fracture mechanism of sandstone from transgranular fractures to a mixture of transgranular and intergranular fractures under high temperatures, ultimately transitioning to thermal cracking. [PERSON] et al. [15] utilized acoustic emission technology to observe the process of granite fracturing and found that thermal cracking was the primary cause of deterioration in the mechanical properties of granite. [PERSON] et al. [16] and [PERSON] et al. [17] analyzed the microstructure and morphology of granite after exposure to high temperatures through CT and scanning electron microscope experiments, indicating that differences in the mineral composition and crack size of samples would affect the strength of granite. [PERSON] et al. [18] and [PERSON] et al. [19] conducted a series of triaxial compression tests on granite under different confining pressures and temperatures, indicating that the mechanical properties of granite weakened with increasing temperature. However, relying solely on laboratory experiments makes it challenging to observe the micromechanical behavior of rock during the failure process, necessitating further analysis using numerical methods [20; 21; 22]. Common numerical methods include the finite element method (FEM), boundary element method (BEM), finite difference method (FDM), and discrete element method (DEM). Among these, the particle flow code (PFC) program, based on the discrete element model framework, is widely used for simulating the microcrack development, thermal cracking process, and damage evolution of rocks under high temperatures. In early studies on granite rock samples, the parallel-bonded model (PBM) was primarily used to simulate the mechanical behavior of intact and fractured rock masses by employing parallel-bonded contacts (PB). However, this model has limitations, such as a low internal friction angle and a low tensile-to-compressive strength ratio [23; 24].