## 3 Results
### Three-Dimensional Progressive Cross-Scale Expansion Characteristics of Cracks
During uniaxial loading, the randomly distributed nano- and micro-scale pores and cracks within the coal sample are compressed along the axial direction. As the surrounding stress field evolves and reaches a critical state, cracks initiate and propagate, with microcrack expansion halting upon uniaxial stress unloading. After two cycles of loading and unloading, no CT-scale cracks were observed, indicating that crack sizes remained below 100 \(\upmu\)m. Increased radial strain in the coal sample cross-section suggested a rise in the quantity and volume of microcracks, with microscopic cracks continuing to develop even during the macroscopic linear elastic stage. Figure 8: SEM images of coal samples. (**a**) Matrix pores; (**b**) Plant cell wall residual pores; (**c,d**) Tensile exogenous microcracks. The CT reconstruction after the third loading-unloading cycle is shown in Figure 9. An O-XYZ coordinate system was defined, with the Z-axis perpendicular to the O-XY plane and the positive direction oriented from the upper to the lower surface of the coal sample. The coal sample was divided into 10 regions along the Z-axis, with approximately 220 CT cross-sectional images per region. Reconstructed volumetric views of all 10 regions were obtained. Figure 9a,b show the top and side views of the region near the upper end of the sample, respectively. Two main crack bands, Crack1 and Crack2, are visible: Crack1 develops approximately along the Y-axis direction, penetrating clay and organic matter bands (yellow strips approximately parallel to the X-Z plane), while Crack2 extends along the interface between clay/organic matter bands and the carbon matrix approximately in the X-axis direction. Figure 9c-k show the XY plane projections (top views) of other nine regions along the Z-axis. In the CT images, sub-CT-scale microcracks expanded, developed, and coalesced under the stress field to form visible small cracks. These cracks expanded in multiple directions under the three-dimensional stress field. In localized regions, small cracks exhibited similar expansion directions, converging to form millimeter-scale large cracks. As the crack scale increased, their quantity rapidly decreased. Crack propagation paths demonstrated nonlinear behavior, with both transgranular and intergranular expansion observed, though transgranular expansion was less prevalent at this stage. The propagation process involved crack convergence and bifurcation. The CT reconstruction of the coal sample after the fourth loading-unloading cycle is presented in Figure 10. At this stage, under the influence of the three-dimensional stress field, more cracks reached their critical state and entered a stable propagation phase, characterized by increased numbers and widths of large cracks. These cracks interconnected, dividing the coal sample into multiple segments, resulting in reduced overall strength. Figure 9: CT reconstruction images after the third loading–unloading cycle. (**a**) The top view of the region near the upper end of the sample; (**b**) The side view of the region near the upper end of the sample; (**c–k**) The top views of other nine regions along the Z-axis. A comparison of Figures 9 and 10 highlights the differences in crack propagation behavior. Figure 9 represents the initial crack propagation stage, where crack expansion stopped after stress unloading. The crack propagation morphology at this stage was influenced by factors such as the spatial distribution of original damage, the heterogeneous body structure, and the three-dimensional stress field. Upon reaching critical conditions and entering stable propagation, the crack morphology evolved into nearly parallel curved patterns shaped primarily by the principal stress field. Cracks propagated at approximately uniform speeds along the principal stress direction.