## 3 Experimental Results and Analysis
### Dynamic Impact Test Results  
#### 3.2.1 Dynamic Stress-Strain Behavior  
In this study, four impact velocities were determined by adjusting N\({}_{2}\) pressure and the position of the striker [15]. The dynamic stress-strain curves of the sample with different saturations are shown in Figure 8a-e, while Figure 8f presents a typical stress-strain curve of the sample. The stress-strain behavior of frozen sandstone at low temperature has four stages, as shown in Figure 8f: (I) the initial compression stage, in which defects such as pores or microcracks in the sandstone gradually close under the action of compressive stress waves; (II) the linear elastic stage, in which elastic energy is rapidly accumulated; (III) the plastic deformation stage, in which defects such as microcracks in the sandstone begin to develop rapidly, characterized by a rapid increase in strain and a slow increase in stress; the initial and final points of the plastic stage are the yield point and the peak point of the sample with coordinates (\(\sigma_{\rm e}\), \(\epsilon_{\rm e}\)) and (\(\sigma_{\rm p}\), \(\epsilon_{\rm p}\)); and (IV) the post-peak stage, which is rarely mentioned because the samples are detached from the compression bars during this stage [5]. As can be seen in Figure 8, the stress-strain curves of the dried specimen show a distinct compression stage and decrease with the increasing impact velocity. Since the pore water freezes into ice with some bearing capacity at low temperatures, stage I gradually decreases with increasing saturation. For example, the curves show no compaction process when the saturation reaches 50%. On the other hand, thermal shrinkage of some mineral particles reduces the defect volume, thus reducing the initial damage. Moreover, the plastic stage III is closely related to saturation and impact velocity, which first decreases and then increases with increasing saturation. According to Equation (1), the dynamic stress versus time is shown in Figure 9. As the impact velocity increases, the plastic deformation occurs earlier, which is consistent with the results of [PERSON] et al. [29]. In addition, the time of plastic  
Figure 7: Distribution of the \(T_{2}\) spectrum of the samples with different saturations. deformation first increases and then decreases with increasing saturation. Moreover, the time to reach the dynamic stress peak is negatively correlated with the impact velocity, while it is positively correlated with the impact strength. To clearly describe the changes in dynamic behavior, several parameters, namely peak strength, elastic modulus, and brittleness index (_BI_), were used to assess the effects of saturation and impact loading on the dynamic mechanical properties of the frozen sample. The results are listed in Table 2.  
Figure 8: Dynamic stress–strain curves of the sample at low temperatures: (**a–e**) denote samples with saturation of 0%, 30%, 50%, 80%, and 100%, respectively; (**f**) shows the deformation phase divisions of typical stress–strain curves. According to the data obtained from Table 2, the relationship between dynamic strength as a function of impact velocity and saturation of the frozen sandstone is shown in Figure 10. The dynamic strength of the sample at low temperatures increases linearly with increasing impact velocity. For example, when the impact velocity increased from 4 m/s to 7 m/s, the dynamic strengths of the sample with different saturations increased by 1.53 (0%), 1.77 (30%), 1.74 (50%), 1.89 (80%), and 1.48 (100%) times, respectively. However, it can be seen in Figure 10 that the dynamic strength of the sample does not increase uniformly with saturation. The dynamic strength (v = 5 m/s) increased by 24.9%, 32.7%, 2.86%, and \(-\)7.31% when the saturation increased from 0 to 100%. This indicates that the enhancement effect of pore ice is gradually suppressed by frost damage when the saturation of red sandstone exceeds 80%.