## 4 The Impact of Inhomogeneity on Microfracture Propagation  
The mechanism for the formation of discontinuous fractures is attributed to the combined effect of rocks' internal heterogeneity and complex stress fields. The heterogeneity of rocks is mainly manifested in mineral distribution, pores, joints, cleavages, and fissures. Among them, mineral heterogeneity represents the most fundamental type of heterogeneity in rock materials. Different minerals exhibit distinct mechanical properties at their boundaries, and variations in mineral distribution and geometric morphology also exert diverse influences on the process of microfracture propagation. (1) Intergranular fractures and transgranular fractures  
Some studies have investigated the differences between transgranular fractures and intergranular fractures during the loading process, and some of the major findings are as follows [16; 26; 39; 59]. In tensile loading, over 90% of the tensile fractures exist in the form of intergranular fractures, while the remaining 10% exhibit transgranular fractures. In shear loading, the proportion of transgranular fractures increases but still does not exceed 50% [26; 39]. Regarding the distribution of microfractures, transgranular fractures in shear loading tend to be closer to the shear centerline, with fewer transgranular fractures as the distance from the shear centerline increases [16; 59]. It is evident that the mechanical properties of mineral boundaries are relatively low. Therefore, compared to propagating through mineral grains, fractures are more prone to initiate and propagate along mineral boundaries (Figure 5). However, there are variations in the occurrence of transgranular and intergranular fracture phenomena depending on the loading conditions. (2) Fracture modes of minerals  
The propagation of fractures within different minerals exhibits variations in fracture modes. Microfractures are more prone to propagate in mechanically weaker clay minerals, predominantly through tensile fracture. Conversely, in mechanically stronger minerals such as feldspar and quartz, microfracture formation is less frequent, with shear fracture being the dominant mode [25; 60]. Additionally, there are significant differences in the fractal dimension and morphology of microfractures after fracture among different minerals. These variations arise from the distinct mechanical response characteristics and mechanisms of different minerals [57]. Similarly to macroscopic fracture propagation, the differences in mechanical properties between minerals influence the expansion of microfractures (Figure 5). Figure 4: (**a**) Microscopic discontinuous fractures [7]. (**b**) The hierarchical distribution of microscopic discontinuous fractures [34]. The geometric morphology and distribution of minerals have a significant influence on the generation of microfractures. Scanning electron microscopy observations of microfractures in shale reveal that the distribution of minerals affects the distribution of tensile stress, thereby influencing the location of tensile microfracture initiation [61]. Numerical simulations further confirm that the size of mineral particles also impacts stress distribution, thus influencing the mechanisms underlying microfracture formation [62, 63]. Moreover, the morphology and distribution of minerals also exert an influence on the connectivity patterns of microfractures [64]. Essentially, the geometric morphology and distribution of minerals affect stress distribution, thereby influencing the generation and propagation of microfractures. The influence of natural bedding and fractures within shale on microfractures  
The anisotropy of shale, which is caused by variations in its microscopic structures, has a direct impact on the propagation of microfractures [66, 67, 68, 69]. By integrating fracture  
Figure 5: Microfractures in different minerals. (**a**) Due to the higher mechanical properties of pyrite, fractures are unable to propagate through it. Therefore, fractures tend to extend along the boundaries of pyrite [6].