## 6 Discussion  
### Self-Organized Behavior and Critical Phase Transition Mechanism  
This investigation analyzes natural rock mass weakness planes through integrated methodologies including SEM imaging, AE signal propagation analysis, and crack path mapping. These techniques collectively characterize self-organized criticality and phase transition dynamics during progressive fracture evolution. SEM results and conceptual diagram of sandstone's (Specimen R-3-2) internal structure at four critical loading stages are presented in Figure 18. The derived conceptual framework integrating micro-macro fracture mechanics is presented in Figures 18 and 19. Figure 17: Spatial evolution of pores intervals in sandstone specimens: (**a**) R-3-1, (**b**) R-3-2, (**c**) R-3-3, (**d**) R-3-4 through Stage III (self-organization) and complete loading history (I–V). Combined with the SEM results and conceptual diagram of sandstone's (R-3-2) internal structure in Figure 18, three distinct evolutionary stages in sandstone fracturing--nucleation, propagation, and coalescence. The mechanical thresholds govern this progression. The first critical point under low-stress conditions initiates crack nucleation, while the second critical point at elevated stresses drives crack propagation. Ultimate failure enables crack coalescence. Stage III initiates at the first critical point under low-stress conditions, exhibiting minimal volumetric strain. Spontaneous structural defect reorganization induces grain boundary-aligned cracking, resulting in volumetric dilatancy. AE signals exhibit gradual intensification during nucleation, expanding crack density while reducing inter-crack spacing. Propagation phases demonstrate accelerated  
Figure 19: (**a**) Progressive sandstone damage–failure continuum follows second-order power–law behavior. (**b**) Late-stage fracture evolution (III–V) exhibits closer alignment with complete loading history (I–V) than early-stage patterns (I–II). AE activity, amplifying both crack volume and length. Stage III culminates at the second critical point under high-stress conditions. This regime triggers crystalline particle reorientation, amorphous matrix disintegration, and micro-to-macro crack transition through coalescence. Coalescence-driven instability predominantly manifests through intergranular (IG) fracture modes. Transgranular (TG) fracture mechanisms accelerate system-wide instability via rapid crack network formation. Specifically, the sandstone initially undergoes compaction, where existing pores and microcracks begin to close and merge, increasing the contact and density of mineral particles. With increasing stress, the rock enters the elastic deformation stage, characterized by the closure of pores and the reduction in crack size, with minerals becoming more tightly packed. In Stage III, new microcracks form perpendicular to the maximum principal stress direction, expanding and linking up to increase crack density. With further loading (Stage IV), the rock enters the failure stage, where cracks rapidly interconnect and expand, forming macroracks that propagate and eventually cause fracture. The particles within the rock undergo reorientation, and the amorphous matrix disintegrates, weakening the bonding between particles and facilitating crack propagation. Preexisting microdamage configurations dictate deformation pathways, as demonstrated by [PERSON] et al. [64]. Rock mass weakness planes nucleate deformation, governing fault geometry and spatial distribution during failure. The temporal convergence of macrofracture propagation provides reliable precursor timing for failure. SEM images mesoscopically document damage evolution. Combined macro-meso analysis reveals self-organized criticality of sandstone damage progression. These self-organization criticality principles enable predictive analysis of engineering rock mass behavior under complex loading scenarios. Heterogeneous sandstone exhibits self-organized criticality during damage evolution.