## 1 Introduction  
Thermal fracturing of reservoir rock under high-temperature conditions occurs ubiquitously in subsurface engineering applications, including deep mining operations, shale gas extraction, and geothermal energy development [1, 2, 3, 4]. Reservoir rock exhibits significant heterogeneity in mineral composition and internal structure due to physico-chemical processes during diagenesis. Two primary mechanisms govern thermal fracturing under high-temperature conditions: (i) fracture initiation driven by sharp temperature gradients during instantaneous thermal shocks, and (ii) crack propagation resulting from heterogeneous thermal expansion of constituent minerals. These mechanisms generate substantial thermal stresses within the rock matrix. When the induced stresses surpass the rock mass's tensile strength, extensive fracture networks develop [5, 6]. Thermal fractures significantly impact engineering integrity. For instance, when assessing the stability of deep rock masses, such fractures compromise structural safety and may induce catastrophic failure. Conversely, thermal stimulation strategically exploits these fractures to enhance reservoir permeability and improve energy recovery efficiency [7; 8; 9]. Consequently, comprehensive investigation of thermal fracture initiation and propagation mechanisms is imperative for developing evidence-based engineering protocols. Although extensive experimental studies on rock thermal fracturing exist, most focus primarily on analyzing how heat treatment or thermal shock affects rock physico-mechanical properties, rather than elucidating underlying fracturing mechanisms. Furthermore, real-time measurement of rock properties at elevated temperatures imposes stringent instrumentation requirements. Given that thermal shock-induced fracturing constitutes a transient phenomenon occurring within millisecond-scale durations, conventional experimental techniques lack sufficient temporal resolution to capture the evolution of fracture networks [10; 11]. Consequently, numerical methods have gained prominence in studying thermal fracturing mechanisms of brittle materials due to their computational efficiency, reproducibility, and cost-effectiveness. [PERSON] et al. [12] employed a non-local model to simulate ceramic thermal fracturing. Adopting a micromechanical perspective, [PERSON] [13] and [PERSON] et al. [14] analyzed granite fracture initiation and propagation under high-temperature conditions via discrete element modeling in PFC2D. [PERSON] et al. [15] implemented Weibull-distributed material properties in RFPA (Rock Failure Process Analysis) to investigate thermal shock-induced fracturing. [PERSON] et al. [16; 17] employed a FDEM for rock thermal fracturing simulations. Using extended finite element methods (XFEM), [PERSON] and [PERSON] [18] simulated large-scale rock salt cooling experiments, establishing fracture mechanics-based failure mechanisms. Furthermore, peridynamics (PD) has emerged as a promising approach for rock thermal fracturing analysis [19; 20]. Recently, the PFM has emerged as a predominant approach for modeling fracture in brittle solids, owing to its robust capability in handling complex crack topologies [21; 22; 23; 24]. Building on [PERSON]'s elastic fracture mechanics theory, the PFM framework was pioneered by [PERSON] et al. [25] and subsequently refined through variational formulations [26; 27; 28]. This method regularizes sharp discontinuities through a diffuse crack representation, introducing an auxiliary phase-field variable to quantify fracture intensity--a concept akin to continuous damage mechanics. Notable applications to thermal fracturing include: [PERSON] et al. [29] who developed a fully TM-PFM, simulating crack propagation in heated circular plates and thermal shock failure in thin glass; [PERSON] et al. [30] who investigated dynamic crack trajectories under thermal shock using PFM; [PERSON] et al. [31] who analyzed temperature-induced fracture effects on thermal energy storage efficiency; [PERSON] et al.