## 3 Analysis of Test Results
### Rock Mechanical Properties Under the Interaction of Multiple Factors
#### 3.3.3 Factor Interaction on Elastic Modulus  
According to Figures 13-15, under the interactive effects of fracture dip angle and confining pressure, grouting material and roughness, and confining pressure and roughness, the elastic modulus of the rock specimen increases as the interactive factors rise. The increase is more significant than when the two factors are considered independently (the increase in elastic modulus due to the interaction of fracture dip angle and confining pressure is 39.65%, due to the interaction of grouting material and roughness is 76.82%, and due to the interaction of confining pressure and roughness is 16.57%). From the density of the contour lines, it is evident that confining pressure in the interaction between fracture dip angle and confining pressure, grouting material in the interaction between grouting material and roughness, and confining pressure in the interaction between confining pressure and roughness have a more prominent influence on the elastic modulus, respectively. Figure 14: Visualization of the interaction effect between grouting material and roughness on the elastic modulus. Figure 13: Visualization of the interaction effect between fracture dip angle and confining pressure on the elastic modulus. Interaction between fracture dip angle and confining pressure: During the transition from low to high confining pressure, the elastic modulus gain increases nonlinearly from 2.15 GPa to 8.33 GPa as the dip angle of the fault increases, an increase of 3.87-times. During the transition from low to high dip angle of the fault, the elastic modulus gain increases nonlinearly from 5.97 GPa to 12.15 GPa as the confining pressure increases, an increase of 2.04-times. This can be attributed to the combined effects of high confining pressure and high fracture dip angle, which restructure the fracture network's distribution and contact state. Microfractures are fully compacted, particle contact area increases, the angle between the fracture surface and principal stress direction decreases, and external stress is more effectively transmitted from the particle contact surface into the rock specimen. This results in stronger interaction between fractures, fewer through fractures and shear slips, leading to a significant increase in the rock specimen's elastic modulus. Interaction between grouting material and roughness: During the transition from low to high strength of the grouting material, the elastic modulus gain increases nonlinearly from 1.05 GPa to 5.5 GPa with increasing roughness, an increase of 5.24-times. During the transition from low to high roughness, the elastic modulus gain increases nonlinearly from 3.96 GPa to 8.41 GPa with increasing strength of the grouting material, an increase of 2.12-times. This occurs because high-strength grouting materials effectively reinforce the crack tip region and inhibit crack propagation, while high roughness offers more anchoring points for the grouting material, maximizing its bonding and reinforcing capabilities. This synergistic effect relieves stress accumulation at the crack tip, delaying crack propagation and breakthrough, which significantly increases the overall stiffness of the rock specimen. Interaction between confining pressure and roughness: During the transition from low to high confining pressure, the elastic modulus gain increases from 1.05 GPa to 3.95 GPa nonlinearly with increasing roughness, an increase of 3.76-times. During the transition from low to high roughness, the elastic modulus gain increases from 5.97 GPa to 8.87 GPa nonlinearly with increasing confining pressure, an increase of 1.49-times. This occurs because, under the synergistic effect of high confining pressure and roughness, microcracks are compacted, and the mechanical interlocking and frictional resistance of the high-roughness crack surfaces are fully utilized under the confining pressure.