## 2 Experimental Materials and Methodology
### Analysis Method for Experimental Data and Images  
Engineering-scale rock slope deformation/failure characteristics mirror laboratory-scale sandstone damage fracture behaviors [56]. AE waveform morphologies exhibit strong similarities between field slopes and laboratory sandstone specimens (Figure 2a,b). Leveraging this similarity, real-time crack propagation monitoring in sandstone is achieved through integrated AE monitoring and moment tensor inversion techniques, mirroring faulting mechanisms in engineering rock masses. Surface-mounted AE sensors enable automated source localization and capture critical waveform parameters (onset time, rise time, duration, energy, amplitude, etc.) for each AE event (Figure 2c). AE signals serve as proxies for sandstone damage evolution (e.g., microcracking). AE source localization employed the GCLM-Grid Search Method for precise multi-sensor signal triangulation. Denoising and waveform feature extraction enable quantitative characterization of damage/fracture progression. The progressive evolution of internal cracks in sandstone was non-destructively characterized through time-resolved 4D X-ray CT and synchrotron micro-CT imaging. The crack evolution-encompassing nucleation, initiation, propagation, and coalescence-was digitally reconstructed through Avizo 2020 software. Full CT scans of entire sandstone specimens (100 mm cylindrical samples), and the central region (10 mm cubic subsamples) of sandstone specimens are shown in Figure 3a. The azimuth map of the coordinate axes for scanning sandstone samples is shown in Figure 3a. The naturally collected sandstone specimens of Group 3 showed inherent heterogeneity. It can be seen from the physical and mechanical parameters of the sandstone samples from Group 3 (Table 1), and the two-dimensional CT images of the initial internal structure of the heterogeneous sandstone in Group 3 (Figure 3b). Figure 2: AE signal features derived from: (**a**) engineering-scale rock slope waveforms; (**b**) laboratory-scale sandstone waveforms; and (**c**) sandstone AE signal parameters. The particle-pore interfaces in sandstone were segmented using Interactive Thresholding (Figure 4a), with the grayscale threshold determined by identifying the local minima in the bimodal histogram of CT voxel intensities. Crack morphology was quantified via 3D covariance matrix analysis, yielding three principal eigenvalues (\(\delta_{1}\), \(\delta_{2}\), \(\delta_{3}\)) and two projection angles (\(\theta\), \(\varphi\)) (Figure 4b). Crack morphology parameters were derived from XCT 3D reconstructions through the following steps: (1) Binary masks of cracks were extracted using threshold-based region growing. (2) The spatial coordinates of crack voxels were used to compute covariance matrix, whose eigenvalues (\(\delta_{1}\geq\delta_{2}\geq\delta_{3}\)) represent crack dimensions along principal axes. (3) \(\theta\) (dip angle): Angle between the major principal axis (\(\delta_{1}\) direction) and the vertical axis (\(Z\)-axis of the sample). (4) \(\varphi\) (azimuth angle): Projection of \(\delta_{1}\) onto the horizontal plane (XY-plane), measured counterclockwise from the \(X\)-axis. The Equivalent Pore Network Model (E-PNM) retains interconnected micropores while excluding isolated micropores. Spheres represent pores, and rods between them represent throats. Rod radii and lengths correspond to throat equivalent radii and lengths (Figure 4c). Color-coding by pore size visualizes connectivity in geomaterials. Additionally, the E-PNM categorizes pore space into connected pores and interconnecting throats [57]. The Maximal Ball Algorithm identifies pores and throats. Here, pore equivalent radii are determined by maximum inscribed spheres. Throats are defined as the narrowest connecting sections between pores. At the same time, the pore Coordination Number in topological connectivity analysis is used to judge the connectivity. That is, isolated micropores have a coordination number of 0, and connected micropores show coordination numbers \(\geq\)1.