## 3 Analysis of Test Results
### Mechanical Properties of Sandstone Under the Action of a Single Factor  
Based on the method of controlling variables, three samples are selected for each test in the single-factor comparison experiments. These samples are screened using a velocity meter to minimize the influence of sample variability on the experimental results. The most representative stress-strain curve is then selected for analysis. Based on the gradual changes in the stress-strain curve under different factors (see Figure 6), the curve can be divided into four distinct stages: (I) initial compaction stage: the curve is nonlinear and concave; (II) elastic deformation stage: the curve is linear, with the slope representing the elastic modulus; (III) plastic deformation stage: the curve becomes nonlinear and convex; (IV) post-peak failure stage: the rock specimen fails when peak stress is reached. Figure 6a shows the stress-strain curve of sandstone subjected to different freeze-thaw cycles. These cycles significantly weaken the rock's mechanical properties through repeated freezing and thawing. As the number of freeze-thaw cycles increases, the peak stress of the rock specimen decreases, and the peak strain shifts to the right. The maximum shift occurs when the number of freeze-thaw cycles increases from 10 to 20 cycles. Stage I: As the number of freeze-thaw cycles increases, the axial strain increases, the axial stress decreases, and the curve becomes less concave. This is due to the increase in micropores and microcracks within the rock specimen. Stage II: The slope of the curve negatively correlates with the number of freeze-thaw cycles. The elastic modulus of the rock specimen decreases by 76.78% after 40 freeze-thaw cycles, compared to the unfrozen sample. This reduction is due to the frost heave force caused by the phase change of water ice during the freeze-thaw process [26]. Stage III: The convexity of the stress-strain curve decreases as the number of freeze-thaw cycles increases, and the peak strain shifts to the right. Compared to the unfreeze-thaw rock specimen, the peak stress of the rock specimen subjected to 40 freeze-thaw cycles decreases by 55.37%. This indicates that increasing the number of freeze-thaw cycles exacerbates rock damage. Stage IV: As the number of freeze-thaw cycles increases, the axial strain increases. For cycles less than 20, the rock specimen  
Figure 5: Detailed diagram of the acoustic emission installation and auxiliary components. exhibits noticeable brittle failure characteristics. At 40 freeze-thaw cycles, the rock specimen transitions from brittle failure to ductile failure. This transition is primarily attributed to the cumulative damage induced by frost heave forces during the repeated freezing and thawing cycles. As the number of cycles increases, microcracks within the rock specimen propagate, coalesce, and interconnect, leading to the formation of a more fragmented microstructure. This process progressively weakens the rock's internal cohesion and alters its fracture mechanics, resulting in a shift from the characteristic brittle failure, which is sudden and catastrophic, to ductile failure, where the material undergoes more plastic deformation prior to failure. The increased microstructural damage from frost-induced cracking reduces the rock's ability to sustain localized stresses, allowing for more gradual failure under continued loading. This transition is a well-documented phenomenon in brittle materials subjected to freeze-thaw cycles, where repeated cycles progressively degrade the material's integrity and induce a shift in the failure mode. Figure 6b shows the stress-strain curve of sandstone subjected to different grouting materials. Grouting materials improve the rock specimen's bearing capacity by enhancing the bond strength and overall stiffness of the sandstone, which in turn improves its stress-strain behavior. As the strength of the grouting material increases, both the peak stress and peak strain of the rock specimen's stress-strain curve shift upward and to the right, respectively.