## 6 Microscale Fracture Simulation in Shale  
Due to the high difficulty and limited measurement methods of in situ microfracture propagation observation tests, a clear understanding of the microscale fracture propagation behavior cannot be achieved experimentally. However, numerical simulation modeling is flexible and not restricted by experimental conditions, leading to abundant research achievements in related fields. Currently, commonly used fracture propagation simulation methods include discrete element methods and finite element methods [96; 97; 98; 99; 100; 101]. In numerical simulations, widely adopted microscale fracture theories in shale include brittle fracture theory, elastic-plastic theory, damage mechanics theory, and microplane constitutive model theory. However, it should be noted that due to the discontinuous, heterogeneous, and anisotropic nature of rock materials, a single constitutive theory is insufficient to comprehensively reflect the microscale fracture behavior of shale. In order to capture the influence of microstructural features on fracture propagation, various numerical models based on microstructural distributions have been developed. For example, the universal distinct element code (UDEC) particle boundary model [102; 103], three-dimensional distinct element code (3 DEC)-Voronoi model [104; 105], three-dimensional polygon-based discrete element method (DEM) model [106], particle flow code (PFC)-grain based model (GBM) model [107; 108; 109], and Irazu-GBM model [110]. [PERSON] et al. [22; 111] employed the mineral distribution-based finite-discrete element method (FDEM) to investigate the effects of boundary conditions, mineral geometry, and loading rate on the fracture process and the initiation, propagation, and connection of microfractures under uniaxial compression conditions in granite. [PERSON] et al. [15] conducted uniaxial compression experiments based on the UDEC mineral distribution model and found that the nonuniformity of grain size affects the distribution of tensile stress, making rocks with nonuniform grain size more prone to tensile microfractures compared to rocks with uniform grains. [PERSON] et al. [106] studied the influence of grain size on microfracture propagation based  
Figure 7: **(a)** Full-field strain measurement using DIC during fracture propagation [91]. **(b)** Using a misorientation angle in EBSD to represent the magnitude of structural strain [95]. on the 3D polycrystalline discrete element method (3 PDEM) mineral distribution-based finite-discrete element method (FDEM)-Voronoi model and found that when the grain size is larger, fracture propagation along the loading direction is easier, leading to a series of perpendicular tensile failures, while for smaller grain sizes, microfractures are more scattered. [PERSON] et al. [24] established a uniaxial compression experimental model based on the microstructure of coal rock and suggested that mineral interface microfractures are generated due to nonuniform mineral strain, and the formation of tensile microfractures dominates the rock's uniaxial compressive failure behavior. [PERSON] et al. [60] investigated the proportions of shear and tensile microfractures during uniaxial compression using the PFC-GBM model. [PERSON] et al. [63] studied the formation and propagation processes of microfractures in shear bands under different uniaxial compression loads using the cohesive contact model (CCM) in PFC. Based on the methods provided in the aforementioned literature, these models can be conveniently used to model mineral distributions in experiments and conduct mechanical calculations for studying fracture propagation mechanisms and other related aspects (Figure 8). Despite rapid advancements in experimental techniques, there is still a lack of measurement methods at the microscale level. For instance, the measurement of microscale stresses can be inferred through inverse methods [113; 114; 115], but it is difficult to directly measure stress within the microzones of materials.