## 3 Analysis of Test Results
### Mechanical Properties of Sandstone Under the Action of a Single Factor
This is because a larger fracture inclination creates a smaller angle with the principal stress direction, facilitating easier transmission of external stress into the rock. It also reduces the likelihood of slippage or cracking at the fracture surface. Stage III: As the crack inclination increases, the peak stress of the rock specimen rises, and the peak strain shifts to the right. Compared to the rock specimen with a 15\({}^{\circ}\) inclination, the peak stress of the sample with a 75\({}^{\circ}\) inclination increases by 118.76%. This is because, at smaller crack inclination angles, the crack direction is more perpendicular to the applied axial stress, leading to stress concentration near the crack. This accelerates crack propagation, resulting in earlier instability and failure of the rock specimen. Stage IV: Regardless of the crack inclination, the stress-strain curve shows a rapid decline, indicating clear characteristics of brittle failure. Figure 6e shows the stress-strain curve of sandstone under various confining pressures. Confining pressure enhances the rock's density, restricts deformation, increases the elastic modulus and peak stress, and promotes the transition from brittle to ductile failure. As confining pressure increases, the peak stress of the rock specimen rises, and the peak strain shifts to the right. The greatest shift occurs when the confining pressure increases from 3 MPa to 6 MPa. This may result from the compaction effect being most significant in this range, causing notable changes in the rock's microcracks and pore structure. Stage I: Compared to the rock specimen at 0 MPa, those at 3-9 MPa did not undergo further densification, suggesting that the initial pressure had already compacted the primary cracks. Stage II: The curve's slope positively correlated with confining pressure. The elastic modulus of the rock specimen at 9 MPa is 70.65% higher than at 0 MPa. This is because confining pressure increases the rock's density, enlarges the contact area between particles, and limits its deformation. Stage III: As confining pressure rises, the rock specimen remains in the plastic-yielding state longer, with increased peak strain and peak deviatoric stress. Compared to the rock specimen at 0 MPa, the peak deviatoric stress at 9 MPa increases by 140.2%, indicating that confining pressure inhibits crack development and propagation. Stage IV: As confining pressure increases, the stress drop rate slows, and the rock specimen transitions from brittle to ductile failure. In summary, the freeze-thaw cycle weakens sandstone, whereas grouting material, fracture dip angle, roughness, and confining pressure all strengthen it. The differences in the influence of various factors on sandstone are shown in Table 5.  
In practical engineering, multiple factors often affect sandstone's mechanical properties, interacting, synergizing, or restricting one another, leading to complex changes. For example, both fracture dip angle and roughness significantly influence stress transfer, while the coupling of grouting material and confining pressure further reinforces the fracture surface. Therefore, studying a single factor cannot fully capture the rock's behavior in practical engineering. In complex environments, interactions between factors can cause nonlinear effects, altering the mechanical properties of the rock. An in-depth exploration of how multiple factors interact to affect sandstone's mechanical properties can provide a more comprehensive basis for rock mass stability analysis and optimal design. Characterization of the Acoustic Emission Evolution of Sandstone Under the Action of a Single Factor  
Acoustic emission is used to monitor elastic waves generated during rock failure, providing real-time insight into the failure status of the rock [27], as shown in Figure 7.  
As shown in Figures 6 and 7, the evolution curves of sandstone ringing counts under various factors can be divided into a steady growth phase and a sudden increase phase.