## 3 Results
### Effects of Freezing Temperature and Strain Rate on Dynamic Energy Absorption  
The relationship between the dynamic energy absorption and freezing temperature during the freeze-thaw cycling process is shown in Figure 10. As the freezing temperature decreases, dynamic energy absorption decreases. Compared with the dynamic energy absorption of sandstone specimens at 20 \({}^{\circ}\)C, the dynamic energy absorption of sandstone specimens at the freezing temperature of \(-20\), \(-40\), \(-50\)\({}^{\circ}\)C, and \(-60\)\({}^{\circ}\)C decreases by 12.5%, 24.2%, 26.3%, and 30.7%, respectively. This phenomenon indicates that the energy consumed per unit volume of the sample decreases as the temperature decreases. Figure 8: Variation of dynamic strength with freezing temperature. Figure 9: Variation of dynamic strength with strain rate. Figure 11 shows the effect of strain rate on dynamic energy absorption of specimens experiencing 10-times freeze-thaw cycling treatments with the freezing temperature of \(-40\)\({}^{\circ}\)C. It is seen from Figure 11 that as strain rate increases, dynamic energy absorption of sandstone specimens increases. Compared with the dynamic energy absorption at the strain rate of 38.97 s\({}^{-1}\), the dynamic energy absorption of sandstone specimens at the strain rates of 69.62 and 89.02 s\({}^{-1}\) increases by 76.3% and 126.3%, respectively. The decrease in the density, P-wave velocity, and mechanical strength of sandstone may be closely related to the generation and accumulation of micro-defects. Water weakening effects, inconsistent shrinkage and expansion between mineral grains and frost heave effects may induce the generation and accumulation of micro-defects. For the saturated specimens, the chemical and physical reactions between the water and clay minerals may occur, which may weaken the connection between mineral grains [17]. During freeze-thaw cycling, the decrease and increase in the temperature induce the shrinkage and expansion of mineral grains. The inconsistent shrinkage and expansion between mineral grains induce the generation of stress [48]. The repeated shrinkage and expansion of the mineral grains may induce the generation and accumulation of the micro-defects during freeze-thaw cycling [13]. During freezing, water in pores turns into ice, and the volume expansion due  
Figure 11: Variation of dynamic energy absorption with strain rate. Figure 10: Variation of dynamic energy absorption with freezing temperature. to the water-ice phase transition may induce the generation of the frost heave force. When the frost heave force exceeds the strength of the material, cracking occurs [2]. The generation and accumulation of the micro-defects may induce the shedding of mineral grains due to a decrease in cohesion between the mineral grains, which further induces a decrease in the mass of the specimen [4]. Therefore, the density is calculated by the mass decreases. When ultrasonic waves propagate in rock with micro-defects, the micro-defects can filter the harmonic components of waves with higher frequencies. The dominant frequency of the incident wave decreases, which further decreases the velocity [49; 50; 51]. The existence of the micro-defects decreases the mechanical strength of rock, increases the displacement deformation space during loading, and decreases the static elastic modulus [33; 52]. In addition, the existence of the micro-defects decreases the energy required for fracturing a specimen. The micro-defects induced by the inconsistent deformation between mineral grains may increase as the freezing temperature during freeze-thaw cycling decreases. In addition, the damage induced by the frost heave effect increases as the freezing temperature decreases below a certain critical temperature [19]. Moreover, during thawing, water immersion may increase the deterioration. These factors may induce the decrease in the P-wave velocity, static uniaxial strength, static elastic modulus, dynamic strength, and dynamic energy absorption with the decrease in the freezing temperature.