## 6 Discussion
### Self-Organized Behavior and Critical Phase Transition Mechanism
AE-crack correlated damage progression follows predictable power-law dynamics with quantifiable acceleration rates. Deformation-fracture parameters obey second-order power-law distributions (Figure 19a), characteristic of critical phase transitions. Stage I-II energy accumulation undergoes abrupt release at the first critical point, transitioning through Stage III self-organization to reach the second critical point via power-law accelerated damage propagation. Stage IV meta-instability features crack network percolation, culminating in Stage V macrocrack coalescence (Figure 19a, red trajectory). Progressive loading induces temporary deviations from critical states, yet self-regulation mechanisms restore system criticality prior to rapid terminal failure. Late-stage power-law patterns (III-V, blue) exhibit 89% similarity with complete loading history (I-V, red), compared to 62% for early-stage patterns (I-II, green) in Figure 19b. Stage III self-organization serves as the failure precursor, with power-law exponent escalation providing quantifiable early warning signals. Stage III damage zones enable 92% accurate prediction of ultimate failure geometries. Effective failure prediction requires spatiotemporal characterization of Stage III damage zones--recording their spatial coordinates, temporal emergence, and morphological signatures. The proposed conceptual framework deciphers self-organized critical phase transition mechanics governing deformation-failure processes. Spatiotemporal predictability of sandstone failure is achieved through cross-stage correlation analysis of damage evolution patterns. This study demonstrates significant consistency with prior rock mechanics research in self-organized criticality (SOC), power-law distributions, and nonlinear dynamics. First, SOC characteristics were identified during Stage III of sandstone deformation, where damage evolution followed power-law statistics. This aligns with [PERSON] et al. 's SOC theory [14], confirming system self-organization to critical states. Second, power-law distributions observed in AE energy release and pore volume evolution across loading stages mirror findings from [PERSON] et al. [4] and [PERSON] et al. [32], and similar power-law exponents among samples suggest universality in rock fracturing. Third, nonlinear damage dynamics--manifested as accelerated AE energy, amplitude, and pore morphology growth during Stage III--correspond to [PERSON] et al. [3] and [PERSON] et al. 's studies [1] on nonlinear rock damage acceleration. However, the exponents in this study differ from earthquake-related studies, where exponents typically exceed 1.5 [65]. These variations to the specific heterogeneity of sandstone, such as its pore structure and mineral composition, which influence damage mechanisms and rates. However, this study demonstrates unique innovations in experimental methods, data analysis, and predictive modeling, forming a sharp contrast with previous research. In experimental methods and data acquisition, this study innovatively combines real-time CT scanning and AE monitoring. This enables multi-scale dynamic observation of sandstone's internal structure and damage evolution. Compared to studies relying solely on single techniques (e.g., AE monitoring or mechanical testing alone) [28], this approach comprehensively captures fracture morphology, distribution, and evolution. This provides deeper insights into sandstone's SOC and fracture mechanisms. Additionally, compared to the self-organized critical behavior of experimental materials [58], this study refines the analysis of SOC stages. The self-organized phase during sandstone deformation is divided into two critical thresholds: first critical point (volumetric dilation) and second critical point (peak strength). Damage evolution between these thresholds and its SOC correlation is systematically explored. Such granular phase analysis is rarely seen in prior studies.