## 3 Experimental Results and Analysis
### Microscopic Fracture Characteristics  
Given the consistent mechanical responses demonstrated by Group 3 sandstone specimens (R-3-1 to R-3-4) in terms of stress-strain behavior, AE patterns, and fracture morphology; and considering journal space constraints, this analysis specifically examines R-3-1 and R-3-3 to elucidate mesostructural fracture mechanisms. Figure 7 graphically reconstructs the complete progressive damage stages through 4D-CT visualization. Figure 7 demonstrates the spatiotemporal transition of AE events and crack propagation, evolving from stochastic distribution to localized failure plane coalescence. During initial loading stages, AE events and pre-existing pores exhibited homogeneous dispersion  
Figure 7: Spatiotemporal evolution of AE events and crack networks during progressive damage evolution in sandstone specimens: (**a**) Specim R-3-1; (**b**) Specim R-3-3. across the sandstone matrix, with quasi-static damage accumulation. Post-dilation phase (Point 3): AE activity transitions to localized clustering, initiating proto-fracture plane formation. This transition arises from stress redistribution mechanisms within damaged microstructures. Stress concentrations migrate towards intact/less-damaged zones, triggering peripheral damage nucleation. Post-peak regime (Point 4): AE sources and voids coalesce along the dominant fracture trajectory. Stress intensification at the crack tip creates mechanical heterogeneity, while stress shadows develop in adjacent regions. Crack network percolation progresses through stress-driven branch connection. AE clusters and void spaces concentrate within the evolving fracture process zone. Catastrophic coalescence occurs via stress-driven crack tip fusion, culminating in global structural failure. The dilation threshold and peak strength thus constitute critical state transitions governing failure progression. These coalescence zones represent kinetic attractors in the self-organized critical system. AE monitoring captured energy-amplitude signatures of microfractures during sandstone failure (Figure 2c). Fracture principal eigenvalues (\(\delta_{1}\), \(\delta_{2}\), \(\delta_{3}\)) and orientation angles (\(\theta\), \(\varphi\)) were derived from CT-based 3D crack covariance matrices. Principal eigenvalues quantify spatial distribution anisotropy along orthogonal axes (X, Y, Z). Principal axis dimensions are defined as: major (\(\delta_{1}\)), intermediate (\(\delta_{2}\)), and minor (\(\delta_{3}\)) axes. Eigenvalue hierarchy follows \(\delta_{1}>\delta_{2}>\delta_{3}\) (as defined in Figure 4b). Parameter crack flatness \(\delta_{3}/\delta_{2}\) quantifies geometric anisotropy through aspect ratio analysis. The three-dimensional (3D) shape factor (VA-3d), quantifying pore-crack morphology complexity, is defined as follows:  
\[VA-3d=\frac{S^{3}}{36\pi V^{2}} \tag{1}\]  
where geometric descriptors are defined as surface area (\(S\)), volume (\(V\)), with \(VA-3d=1\) representing spherical equivalence. In spherical coordinates, polar angle (\(\varphi\)) and azimuthal angle (\(\varphi\)) specify the orientation of principal eigenvector (\(\delta_{1}\)). Axial projection angle (\(\theta\): 0-90\({}^{\circ}\)) quantifies crack alignment relative to specimen axis (\(\sigma\)). Parallel (\(\theta=90^{\circ}\)) and perpendicular (\(\theta=0^{\circ}\)) crack orientations are defined relative to specimen axes (\(\sigma\)). Transverse angular distribution (\(\varphi\): \(-180^{\circ}\) to \(180^{\circ}\)) characterizes lateral crack projection (\(\sigma\)). Integration of AE parametric evolution and crack morphological development (Figure 8) elucidates the micro-to-macro fracture progression. The fracture evolution of sandstone under loading exhibits distinct parameter evolution patterns (Figure 8).