## 3 Analysis of Test Results
### Rock Mechanical Properties Under the Interaction of Multiple Factors
#### 3.3.3 Factor Interaction on Elastic Modulus
The slip between cracks is effectively suppressed, and the stress concentration at the crack tips is reduced, leading to a more significant increase in elastic modulus. According to Figure 16, there is an interaction between the number of freeze-thaw cycles and the angle of inclination. As the interactive factor increases, the elastic modulus of the rock specimen decreases and the degree of decrease is greater than the independent  
Figure 15: Visualization of the interaction effect between confining pressure and roughness on the elastic modulus. superposition effect of the two factors (an increase of 42.54%). It can be seen from the density of the contour lines that in the interaction, the number of freeze-thaw cycles has a more prominent effect on the elastic modulus. As the number of freeze-thaw cycles and the inclination of the fissures increase, the trend in the elastic modulus changes. Specifically, under low freeze-thaw cycles, an increase in the fissure inclination raises the elastic modulus of sandstone by 20.51%, consistent with previous trends under single-factor conditions. However, under high freeze-thaw cycles, an increase in fissure inclination reduces the elastic modulus by 2.63%. Under low freeze-thaw cycles, internal damage to the fractured rock has not accumulated. Increasing the fracture inclination optimizes the angle between the fracture surface and the principal stress direction, reducing slippage or expansion, and more effectively transferring stress, which increases the elastic modulus. Under high freeze-thaw cycles, numerous microfractures develop inside the rock, significantly weakening its structural integrity. The increase in fracture inclination not only fails to optimize stress transfer but may also accelerate the structural deterioration of the rock. Moreover, increasing the number of freeze-thaw cycles under low crack dip angles resulted in a 60.02% decrease in elastic modulus, while under high crack dip angles, it led to a 67.70% decrease. High crack inclination may promote the expansion of microcracks near the fracture surface, whose direction of expansion interacts negatively with the principal stress, further exacerbating structural deterioration and resulting in a greater decrease in elastic modulus. In summary, there is a significant interactive enhancement mechanism for the elastic modulus under the combined action of the dip angle of the fissure and confining pressure, the grouting material and roughness, and the confining pressure and roughness. In particular, when both factors are at high levels at the same time, the elastic modulus gain is the greatest, indicating that in rock engineering design, the mechanical properties of the rock mass can be effectively improved by reasonably utilizing the interaction of multiple factors. In addition, under the interactive effect of the number of freeze-thaw cycles and the dip angle of the fissures, the freeze-thaw cycles reverse the trend of the influence of the dip angle of the fissures on the elastic modulus, and there is an interactive reversal mechanism. This indicates that in cold regions, special attention should be paid to the freeze-thaw damage in areas of rock mass with high dip angles of fissures, and targeted protective measures and optimization plans should be formulated. Figure 16: Visualization of the interaction effect between the number of freeze–thaw cycles and fracture dip angle on the elastic modulus.