## 3 Experimental Results and Analysis
### Energy Evolution  
The failure of rock under impact loading can be considered as the result of the mutual transformation of the different forms of energy. During impact testing, the main forms of energy include the incident energy \(E_{\text{in}}\), reflected energy \(E_{\text{re}}\), transmitted energy \(E_{\text{ii}}\), dissipated energy \(E_{\text{di}}\), and other magnetic heat energy, with dissipated energy reflecting impact energy converted into fracture energy and other energy. From a microscopic point of view, energy dissipation reflects the continuous development of microdefects in the rock, while macroscopically it is represented as the gradual loss of rock strength. The energy evolution of the frozen sample under the impact load is calculated by Equation (6) [2], where \(A_{\text{s}}\) is the cross-sectional area of the incident bar.  
\[\left\{\begin{array}{l}E_{\text{in}}=E_{0}C_{\text{s}}A_{\text{s}}\int_{0}^ {t}{{\epsilon_{\text{i}}}^{2}(t)dt}\\ E_{\text{re}}=E_{0}C_{\text{s}}A_{\text{s}}\int_{0}^{t}{{\epsilon_{\text{r}}}^ {2}(t)dt}\\ E_{\text{tr}}=E_{0}C_{\text{s}}A_{\text{s}}\int_{0}^{t}{{\epsilon_{\text{t}}}^ {2}(t)dt}\\ E_{\text{di}}=E_{\text{in}}-(E_{\text{re}}+E_{\text{tr}})\end{array}\right. \tag{6}\]  
The energy conversion for frozen samples with different saturations is shown in Figure 15. As the impact velocity increases, all forms of energy show an increasing trend, with a quadratic polynomial accurately reflecting the changes. Moreover, the dissipated energy gradually overtakes the reflected energy as the saturation increases (Figure 15a). However, when the saturation increases above 50%, the reflected energy gradually increases faster than the dissipated energy (Figure 15b). This is due to the continuous increase in pore ice, which leads to a decrease in the wave impedance of the samples. To better assess the effect of saturation on the dissipated energy of the frozen sample, Equation (7) was used to calculate the dissipated energy per unit volume, \(\eta_{\text{d}}\). The evolution of \(\eta_{\text{d}}\) with saturation for different impact velocities is shown in Figure 16. Taking 5 m/s as an example, \(\eta_{\text{d}}\) of the dried sample is 0.67 J/cm\({}^{3}\) at low temperatures. As saturation increases, \(\eta_{\text{d}}\) begins to increase and reaches 0.76 J/cm\({}^{3}\) and 0.82 J/cm\({}^{3}\) at 30% and 50% saturation, corresponding  
Figure 14: _BI_ values versus impact velocity and saturation of the sample.  
to an increase of 13.4 % and 22.4 %, respectively, over the dried sample. However, at 80 % and 100 % saturation, there is a significant decrease in \(\eta_{\text{d}}\) to 0.56 J/cm\({}^{3}\) and 0.52 J/cm\({}^{3}\), respectively. Therefore, it can be inferred that saturation has a considerable effect on the energy dissipation capacity of the frozen sample, where the range of 0-50% increases the energy dissipation capacity, while 50-100 % shows the effect of weakening. The effect of increasing the dissipated energy is less than the effect of weakening, indicating that the rock sample is sensitive to the work caused by the internal frost heave forces. In other words, when the saturation increases above 50 %, the frost heave forces promote the formation of more microcracks in the sample, which decreases the dissipated energy demand.  
\[\eta_{\text{d}}=\frac{E_{\text{di}}}{V_{\text{s}}} \tag{7}\]