## 3 Results
### Effects of Freezing Temperature and Impact Pressure on the Stress-Strain Curve  
The stress-strain response of rock gives a fundamental understanding of the mechanical behavior of rock. Figure 5 shows the static and dynamic stress-strain curves of the specimen after freeze-thaw cycling treatments.  
Figure 4: Variation of P-wave velocity with freezing temperature.  
Figure 3: Variation of density with freezing temperature.  
Figure 5a shows the effects of freezing temperatures during the freeze-thaw cycling process on the static stress-strain curves. The static stress-strain curves mainly experience  
Figure 5: Stress–strain curves. (**a**) Static stress–strain curves at different freezing temperature. (**b**) Dynamic stress–strain curves at different freezing temperature. (**c**) Dynamic stress–strain curves at different impact pressures.  
four stages: compaction, elastic deformation, yielding deformation, and failure at different freezing temperatures. In the compression stage, the stress increases non-linearly as the strain increases, and the stress-strain shape is approximately concave. The compaction stage during loading may be induced by the closure of pre-existing micro-pores and micro-defects [46]. In the elastic stage, the stress increases almost linearly as the strain increases. In the yield stage, the stress increases non-linearly as the strain increases and reaches a peak, and the stress-strain curve shape is approximately convex. The peak stress is used as the uniaxial compressive strength of the sandstone. The peak stress in these static stress-strain curves decreases as the freezing temperature decreases. In the failure stage, the specimen is quickly destroyed after the peak stress is reached.  
Figure 5b shows the effects of freezing temperatures during freeze-thaw cycling on the dynamic stress-strain curves. The dynamic stress-strain curves mainly experience three stages: elastic deformation, yielding deformation, and failure at different freezing temperatures. The compaction stage in the dynamic stress-strain curve is not obvious compared with the static stress-strain curve, which may be because the pores in the sandstone are too late to close under the dynamic load conditions, and the resistance to deformation is improved [47]. In the elastic stage, the stress increases almost linearly as the strain increases. In the yield yielding stage, the stress increases non-linearly as the strain increases and reaches a peak. The peak stress in the dynamic stress-strain curve is used as the dynamic compressive strength of the sandstone. The peak stress decreases as freezing temperature decreases. In the failure stage, the stress decreases as the strain further increases, and the rock breaks in this stage.  
Figure 5c shows the effects of impact pressures on dynamic stress-strain curves of specimens experiencing 10-times freezing and thawing cycles with freezing temperature of \(-40\)\({}^{\circ}\)C. The stress-strain curves mainly experience three stages: elastic deformation, yielding deformation, and failure at different impact pressures. The compaction stages in the dynamic stress-strain curves are not obvious at the three different impact pressures. In the elastic stage, the stress increases almost linearly as the strain increases, and the slope of the line is used as the dynamic elastic modulus. The dynamic elastic modulus increases as the impact pressure increases. In the yielding stage, the stress increases non-linearly as the strain increases and reaches the peak, and the peak stress increases as the impact pressure increases. In the failure stage, the stress decreases as the strain further increases, and the rock breaks in this stage. The total strain increases as the impact pressure increases.